Write the equation −2x−4y=−8 in slope-intercept form. Then graph the line described by the equation.

Answers

Answer 1

Answer:

y=-1/2x+2 start at y-intercept 2 and go down by 1 and right by 2

Step-by-step explanation:

Answer 2
Final answer:

The slope-intercept form of the equation −2x−4y=−8 is y = 0.5x + 2. Starting from the y-intercept (0,2), the graph of this line is drawn by moving a half unit up and one unit to the right from the intercept.

Explanation:

The given mathematical equation is −2x−4y=−8. To convert this equation into slope-intercept form (y=mx+b), we want to isolate y. Start by dividing every term by -4, which simplifies the equation to 0.5x + y = 2. In this equation, the slope (m) is 0.5, and the y-intercept (b) is 2.

To graph this line, start by plotting the y-intercept (b) at the point (0, 2) on the y-axis. The slope (m) is 0.5, which we can interpret as a rise of 0.5 units for every run of 1 unit. So, from the y-intercept, move up half a unit and right one unit to plot your second point. Drawing a straight line through these points will give you the graph of your equation.

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Related Questions

The value of a used car can be modeled by the formula V=Vo(1-r)^t where Vo is the car's purchase price, in dollars; r is the car's constant annual rate of decrease in value, expressed as a decimal; and V is the car's dollar value at the end of t years. A used car has a constant annual rate of decrease in value of 0.075. According to the model, what expression would give the number of years after purchase for the car to reach a value that is 50% of its purchase price?

Answers

Following the equation

[tex]V(t) = V_0(1-r)^t[/tex]

We start with an initial price of

[tex]V(0)=V_0[/tex]

and we're looking for a number of years t such that

[tex]V(t)=\dfrac{V_0}{2}[/tex]

If we substitute V(t) with its equation, recalling that

[tex]r = 0.075 \implies 1-r = 0.925[/tex]

we have

[tex]V_0\cdot (0.925)^t=\dfrac{V_0}{2} \iff 0.925^t = \dfrac{1}{2} \iff t = \log_{0.925}\left(\dfrac{1}{2}\right)\approx 8.89[/tex]

So, you have to wait about 9 years.

Final answer:

The expression to determine the number of years it takes for the car to reach a value that is 50% of its purchase price is t = ln(0.5) / ln(1 - 0.075), using the given formula V = Vo(1 - r)^t.

Explanation:

To determine the number of years t after purchase for the car to reach a value that is 50% of its purchase price, we can use the model V = Vo(1 - r)^t where V is the car's value after t years, Vo is the original purchase price, r is the constant annual rate of decrease, and t is the number of years.

V is set to be 50% of Vo, which can be written as V = 0.5Vo, and we know the constant annual rate of decrease r is 0.075. Plugging these values into the formula gives us:

0.5Vo = Vo(1 - 0.075)^t

Dividing both sides by Vo and taking the natural logarithm of both sides, we obtain:

ln(0.5) = ln((1 - 0.075)^t)

Using the properties of logarithms, we can rewrite this as:

ln(0.5) = t * ln(1 - 0.075)

Solving for t yields:

t = ln(0.5) / ln(1 - 0.075)

This expression can be used to find the number of years it takes for the car to be worth half of its purchase price.

The area of a rectangle is 99 in?. The length of the rectangle is 2 in. Longer than the width. What is the width of the rectangle? What is the area of a 99. By 9 rectangle

Answers

Answer: so bc. a length not can being minus so this mean that the width of the rectangle is equal 9 in

Andre makes a trip to Mexico. He exchanges some dollars for pesos at a rate of 20 pesos per dollar. While in Mexico, he spends 9000 pesos. When he returns, he exchanges his pesos for dollars (still at 20 pesos per dollar). He gets back 1/10 the amount he started with. Find how many dollars Andre exchanged for pesos and explain your reasoning. If you get stuck, try writing an equation representing Andre’s trip using a variable for the number of dollars he exchanged.

Answers

Hello!

The answer is:

Andre exchanged 450 dollars for pesos.

Why?

To solve the problem, we need to write two principal equations in order to establish a relation between the number of dollars before and after the trip.

So,

Before the trip, we have:

[tex]Dollars_{beforetrip}*rate=9000pesos\\\\Dollars_{beforetrip}*\frac{20pesos}{1dollar} =9000pesos\\\\Dollars_{beforetrip}=9000pesos\frac{1dollar}{20pesos}=450dollars[/tex]

We have that he exchanged 450 dollars for pesos.

Also, we can calculate how many pesos he had before he exchanged it back to dollars, so:

After the trip, we have:

[tex]Pesos{AfterTrip}*rate=\frac{1}{10}Dollars_{BeforeTrip}\\\\Pesos{AfterTrip}*\frac{1dollar}{20pesos}= \frac{1}{10}Dollars_{BeforeTrip}\\\\Pesos{AfterTrip}= \frac{1}{10}Dollars_{BeforeTrip}*\frac{20pesos}{1dollar}\\\\Pesos{AfterTrip}= \frac{1}{10}*450dollars*\frac{20pesos}{1dollar}=900pesos\\[/tex]

We have that he had 900 pesos before he exchanged it back to dollars.

Hence, we know that:

Andre exchanged 450 dollars for pesos.

Have a nice day!

Andre exchanged $500 for pesos at the beginning of his trip.

Let's denote the number of dollars Andre exchanged for pesos at the beginning of his trip as ( D ). According to the exchange rate, he would receive ( 20D ) pesos for ( D ) dollars.

 Andre then spends 9000 pesos while in Mexico. After spending, he has 20D - 9000 pesos left.

Upon returning, Andre exchanges the remaining pesos back to dollars at the same rate of 20 pesos per dollar. The number of dollars he gets back is [tex]\( \frac{20D - 9000}{20} \)[/tex].

 According to the problem, the amount of dollars he gets back is [tex]\( \frac{1}{10} \)[/tex] of the amount he started with, which is [tex]\( \frac{D}{10} \)[/tex].

We can now set up the equation:

[tex]\[ \frac{20D - 9000}{20} = \frac{D}{10} \][/tex]

To solve for ( D ), we multiply both sides of the equation by 20 to get rid of the denominator:

[tex]\[ 20D - 9000 = 2D \][/tex]

Subtract ( 2D ) from both sides to isolate the term with ( D ) on one side:

[tex]\[ 18D - 9000 = 0 \][/tex]

Add 9000 to both sides to solve for ( D ):

[tex]\[ 18D = 9000 \][/tex]

Divide both sides by 18 to find the value of ( D ):

[tex]\[ D = \frac{9000}{18} \] \[ D = 500 \][/tex]

Therefore, Andre exchanged $500 for pesos at the beginning of his trip.

Help asap!!!!

What is the length of the arc intercepted by a central angle of 62° on a circle with radius 8? Use 3.14 for π and round your answer to the nearest hundredth, if necessary.

7.25


9.11


8.65


7.82


Answers

8.65 is the answer to this question.

Answer:

Option 3 - 8.65  

Step-by-step explanation:

Given : The arc intercepted by a central angle of 62° on a circle with radius 8.

To find : What is the length of the arc?

Solution :

The formula to find arc length is

[tex]l=2\pi r\times (\frac{\theta}{360^\circ})[/tex]

Where, l is the length of the arc

r is the radius of the circle r=8

[tex]\theta=62^\circ[/tex] is the angle subtended

Substitute the values in the formula,

[tex]l=2\times 3.14\times 8\times (\frac{62^\circ}{360^\circ})[/tex]

[tex]l=50.24\times 0.1722[/tex]

[tex]l=8.65[/tex]

Therefore, option 3 is correct.

The length of the arc is 8.65 unit.

Simon bought a new shop and wants to order a new sign for the roof of the building. From point P, he finds the angle of elevation of the roof, from ground level, to be 31º and the angle of elevation of the top of the sign to be 42º. If point P is 24 feet from the building, how tall is the sign to the nearest tenth of a foot?

Answers

Let y - x = height of sign

tan 31 = x/24

tan 31 • 24 = x

14.4206548567 = x

tan 42 = y/24

tan 42 • 24 = y

21.6096970631 = y

Now subtract x from y.

y - x = 21.6096970631 14.4206548567

y - x = 7.1890422064

Rounding off to the nearest tenth of a foot, we get 7.2 feet.

The sign for the roof is 7.2 feet.

The height of the sign is approximately 7.2 feet, calculated from the differences in elevation angles and distance.

To determine the height of the sign, we'll start by calculating the height of the roof and the height of the top of the sign from point P.

First, let's define the variables:

[tex]- \( h_1 \):[/tex]  height of the roof

[tex]- \( h_2 \)[/tex]: height of the top of the sign

[tex]- \( h_s \):[/tex] height of the sign itself

From point P, the angle of elevation to the roof is [tex]\( 31^\circ \)[/tex] and the angle of elevation to the top of the sign is [tex]\( 42^\circ \).[/tex]  The horizontal distance from point P to the base of the building is 24 feet.

Using the tangent of the angles of elevation, we have the following relationships:

[tex]\[\tan 31^\circ = \frac{h_1}{24}\]\[\tan 42^\circ = \frac{h_2}{24}\][/tex]

First, let's calculate [tex]\( h_1 \):[/tex]

[tex]\[h_1 = 24 \times \tan 31^\circ\]Using a calculator to find \( \tan 31^\circ \):\[\tan 31^\circ \approx 0.6009\]\[h_1 = 24 \times 0.6009 \approx 14.422\][/tex]

Next, let's calculate  [tex]\( h_2 \):[/tex]

[tex]\[h_2 = 24 \times \tan 42^\circ\][/tex]

Using a calculator to find [tex]\( \tan 42^\circ \):[/tex]

[tex]\[\tan 42^\circ \approx 0.9004\]\[h_2 = 24 \times 0.9004 \approx 21.610\][/tex]

The height of the sign [tex]\( h_s \)[/tex] is the difference between  [tex]\( h_2 \) a[/tex]nd [tex]\( h_1 \):[/tex]

[tex]\[h_s = h_2 - h_1\]\[h_s = 21.610 - 14.422 \approx 7.188\][/tex]

To the nearest tenth of a foot, the height of the sign is:

[tex]\[h_s \approx 7.2 \text{ feet}\][/tex]

Thus, the height of the sign is ( 7.2 ) feet.

If y varies inversely with x, and y = 8 when x = 3, find y when x = 10.

SHOW ALL WORK!!!

Answers

Answer:

y = 2.4

Step-by-step explanation:

Given y varies inversely with x then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

To find k use the condition y = 8 when x = 3

k = yx = 8 × 3 = 24

y = [tex]\frac{24}{x}[/tex] ← equation of variation

When x = 10, then

y = [tex]\frac{24}{10}[/tex] = 2.4

The variation is an illustration of inverse variation, and the value of y when x = 10 is 2.4

How to determine the value of y?

The variation is an inverse variation.

An inverse variation is represented as:

k = xy

Rewrite as:

x₁y₁ = x₂y₂

When y = 8, x = 3; we have:

3 * 8 = x₂y₂

This gives

24 = x₂y₂

When x = 10; we have:

24 = 10 * y

Divide both sides by 10

y = 2.4

Hence, the value of y when x = 10 is 2.4

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What is the solution to the equation below?

Answers

Answer:

C  x=6

Step-by-step explanation:

sqrt(x+3) = x-3

Square each side

(sqrt(x+3))^2 = (x-3)^2

x+3 = (x-3)^2

x+3 = (x-3)(x-3)

FOIL

x+3 = x^2 -3x-3x+9

Combine like terms

x+3 = x^2 -6x+9

Subtract x from each side

x-x+3 = x^2 -6x-x +9

3 =  x^2 -7x +9

Subtract 3 from each side

3-3 =  x^2 -7x +9-3

0 = x^2 -7x+6

Factor

0 = (x-6)(x-1)

Using the zero product property

x-6=0   x-1 =0

x=6  x=1

Since we squared we need to check for extraneous solutions

x=1

sqrt(1+3) = 1-3

sqrt(4) = -2

2=-2

False

Extraneous

x=6

sqrt(6+3) = 6-3

sqrt(9) = 3

3=3

True   solutions

Answer: Option C.

Step-by-step explanation:

First, we need to square both sides of the equation:

[tex]\sqrt{x+3}=x-3\\\\(\sqrt{x+3})^2=(x-3)^2[/tex]

We know that:

[tex](a-b)^2=a^2-2ab+b^2[/tex]

Then, applying this, we get:

[tex]x+3=x^2-2(x)(3)+3^2\\\\x+3=x^2-6x+9[/tex]

Now we need to subtract "x" and 3 from both sides of the equation:

[tex]x+3-(x)-(3)=x^2-6x+9-(x)-(3)\\\\0=x^2-6x+9-x-3[/tex]

Adding like terms:

[tex]0=x^2-7x+6[/tex]

Factor the quadratic equation.  Find two numbers whose sum be -7 and whose product be 6. These numbers are: -1 and -6. Then:

[tex](x-1)(x-6)=0[/tex]

Then:

[tex]x_1=1\\x_2=6[/tex]

Checking the first solution is correct:

[tex]\sqrt{1+3}=1-3\\ 2=-2 \ (False)[/tex]

Checking the second solution is correct:

[tex]\sqrt{6+3}=6-3\\ 3=3 \ (True)[/tex]

Jackson works as a veterinarian technician and earns $12.20 per hour Jackson normally works 40 hours a week in a normal week what is his total pay before taxes and other deductions

Answers

Answer:488

Multiply 12.20 and 40

HELP ASAP PLEASE!!!

Use the Remainder Theorem to determine if (x + 6) is a factor of x3 + 7x2+ 4x - 12. Explain your response.

Answers

The remainder theorem says [tex]x-c[/tex] is a factor of a polynomial [tex]p(x)[/tex] if [tex]p(c)=0[/tex]. So all you need to do is check the value of [tex]x^3+7x^2+4x-12[/tex] when [tex]x=-6[/tex]. We have

[tex](-6)^3+7(-6)^2+4(-6)-12=0[/tex]

so [tex]x+6[/tex] is indeed a factor.

What is the volume of the cylinder shown below?

Answers

Answer:

B) 1452π units³

Step-by-step explanation:

To find the Volume of a cylinder, use this formula:

V (cylinder) = πr²h

Note that:

r = radius of the circle (base) = 11

h = height of the cylinder = 12

π = 3.14

Plug in the corresponding numbers to the corresponding variables.

V = (3.14)(11)²(12)

Remember to follow PEMDAS. First, solve for the power, then solve left -> right.

V = (3.14)(121)(12)

V = (379.94)(12)

V = 4559.28 units³

Note that the answer choices have π  in them, divide π from the answer, and add to the answer.

V = (4559.28)/3.14 = 1452π units³

B) 1452π units³ is your answer.

~

What is the simplest form of 3sqrt x^2

Answers

Answer:

  3|x|

Step-by-step explanation:

√(x^2) = |x|, the positive root. Multiplying this by 3, you get ...

  3√(x²) = 3|x|

please help thank you

Answers

Answer:

1

Step-by-step explanation:

Count the amount of dots given. There are 20 dots in all. To find the middle value, set the numbers in a line first.

0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 4, 4, 4, 5

Find the middle value. Note that the two middle values are both 1. Find the mean of the two values.

1 + 1 = 2

2/2 = 1

1 is your median .

~

Answer:

1

Step-by-step explanation:

If you go in from left to right starting on the left side on the top of the dots (0) and start from the right side on the bottum and go up (5) and you slowly work your way up to the top, you get the answer 1.

The limit of sqrt(9x^4 + 1)/(x^2 - 3x + 5) as x approaches infinity is


[tex]\displaystyle\lim_{x \to \infty} \frac{\sqrt{9x^4+1}}{x^2 -3x + 5}[/tex]


(A) 1

(B) 3

(C) 9

(D) nonexistent

Answers

Answer:

B. 3.

Step-by-step explanation:

At the limit we can take the numerator  to be √(9x^4) = 3x^2

The function is of the form ∞/ ∞ as x approaches ∞ so we can apply l'hopitals rule:

Differentiating top and bottom we have   6x / 2x - 3. Differentiating again we get 6 / 2 = 3.

Our limit as x  approaches infinity  is 3.

Final answer:

The limit of [tex]\(\sqrt{9x^4 + 1}/(x^2 - 3x + 5)\)[/tex] as x approaches infinity is 3, after comparing the highest powers of x in both the numerator and the denominator and simplifying.

Explanation:

To find the limit of the given function [tex]\(\displaystyle\lim_{x \to \infty} \frac{\sqrt{9x^4+1}}{x^2 -3x + 5}\)[/tex] as x approaches infinity, we can use the property of limits involving infinity. We need to compare the highest powers of x in both the numerator and the denominator. The highest power of x in the numerator under the square root is x⁴, and outside the square root, it will be . In the denominator, the highest power is . If we divide the numerator and the denominator by , we get:

[tex]\[ \frac{\sqrt{9x^4+1}}{x^2 -3x + 5} = \frac{\sqrt{\frac{9x^4}{x^4}+\frac{1}{x^4}}}{\frac{x^2}{x^2} -\frac{3x}{x^2} + \frac{5}{x^2}} = \frac{\sqrt{9+\frac{1}{x^4}}}{1 -\frac{3}{x} + \frac{5}{x^2}} \][/tex]

As x approaches infinity, the terms [tex]\(\frac{1}{x^4}\), \(\frac{3}{x}\), and \(\frac{5}{x^2}\)[/tex] approach zero, and we are left with:

[tex]\[ \frac{\sqrt{9}}{1} = 3 \][/tex]

Therefore, the limit of the given function as x approaches infinity is 3, which corresponds to option (B).

A factory makes 12 bottles every 2 minutes. The factory makes bottles for 8 hours each work day. Enter a whole number to represent the fewest number of work days the factory will need to make 28,000 bottles

Answers

8 hours is 480 minutes

480 minutes is 2800 bottles

2800 bottles per day

28000 devided by 2800 is 100

100 days

Answer:

100 days

Step-by-step explanation:

Which classification describes the system of linear equations?

{x−2y=1 y=1/2x+3


a) consistent independent

b) inconsistent

c) consistent dependent

Answers

Answer:

Inconsistent

Step-by-step explanation:

Consistent independent means that there is only one solution; ie one place where the 2 lines intersect.

Inconsistent means that the lines will NEVER cross because they are parallel

Consistent dependent means that the 2 lines, when solved for y, are the exact same line (same slope, same y-intercept)

In our system, one of the equations is already solved for y, so let's solve the other one for y:

[tex]x-2y=1[/tex] so

[tex]-2y=-x+1[/tex] and

[tex]y=\frac{1}{2}x-\frac{1}{2}[/tex]

The slopes of the 2 lines are the same; therefore, they are parallel and will never intersect.  Inconsistent system.

Answer:

inconsistent

Step-by-step explanation:

1.42 x 107 x 2.81 x 101 = ??
Select one:
a. 3.99 e8.00
b. 0.51 e6.0
c. 3.99 e6.00
d. 0.51 e8.0

Answers

ANSWER

Option A

EXPLANATION

The given product is

[tex]1.42 \times {10}^{7} \times 2.81 \times {10}^{1} [/tex]

[tex]1.42 \times 2.81 \times {10}^{7} \times {10}^{1} [/tex]

We multiply to get;

[tex]3.9902 \times {10}^{7} \times {10}^{1} [/tex]

Recall the product rule

[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]

We apply the product rule to get,

[tex]3.9902 \times {10}^{7 + 1} [/tex]

[tex]3.9902 \times {10}^{8} [/tex]

Correct to the nearest tenth, we have

[tex]3.99 \times {10}^{8} [/tex]

This can also be written as;

[tex]3.99 {e}^{8.00} [/tex]

The correct choice is A.

PLEASE HELP ME THANK YOU

Answers

Answer:

Midpoint Formula is (x1+x2/2, y1+y2/2)

(-3+4/2, -5+4/2)

Midpoint is (1/2, -1/2)

Step-by-step explanation:

Solve 2x2 + x − 4 = 0. x2 + x + = 0

Answers

Answer:

2x^2+x-4=0

x^2+\dfrac12x-2=0

x^2+\dfrac12x+\dfrac1{16}-\dfrac{33}{16}=0

\left(x+\dfrac14\right)^2=\dfrac{33}{16}

x+\dfrac14=\pm\dfrac{\sqrt{33}}4

x=\dfrac{-1\pm\sqrt{33}}4

Step-by-step explanation: lol tooooo much ∅∞

Answer:

1/2 and -2 are the first answers to the question

1/16 and 1/16 are the next answers  

1/4 and 33/16 are the last ones

and for the multiple choice answer which is last is A

Step-by-step explanation:

Find the length of a picture frame who’s width is 3 inches and whose proportions are the same 9 inch wide by 15 inch long

Answers

Answer:

5 inch

Step-by-step explanation:

The frames are proportional, so we can set the ratios equal:

width / height = width / height

3 / h = 9 / 15

9h = 45

h = 5

Final answer:

Given the proportionality between two pictures one with width 3 inches and another with dimensions 9 inches by 15 inches, we can set up a ratio and solve for the unknown length, yielding the length of the picture frame as 5 inches.

Explanation:

The question is asking to find the length of a picture frame, given that its width is 3 inches and that it has the same proportions as a picture that is 9 inches wide and 15 inches long. The proportions can be used to set up a ratio, as follows:

3 inches (width of the new picture frame) divided by 9 inches (width of the existing picture) = x (unknown length of the new picture frame) divided by 15 inches (length of the existing picture).

To solve for x, cross-multiply: 3 inches * 15 inches = 9 inches * x.

Then, divide by 9 to solve for x: 45 inches/9 = 5 inches.

So, the length of the picture frame whose width is 3 inches would be 5 inches, if it shares the same proportions as the 9 inch wide by 15 inch long picture.

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Assume that the wooden triangle shown is a right triangle.
​​ a. Write an equation using the Pythagorean Theorem and the measurements provided in the diagram. Hint: (leg 1)2 + (leg 2)2 = (hypotenuse)2
b. Transform each side of the equation to determine if it is an identity.

Answers

Answer:

Part 1) [tex](10x+15y)^{2}=(6x+9y)^{2}+(8x+12y)^{2}[/tex]

Part 2) The answer in the procedure

Step-by-step explanation:

Part 1)

we know that

Applying the Pythagoras Theorem

[tex]c^{2}=a^{2}+b^{2}[/tex]

we have

[tex]c=(10x+15y)[/tex]

[tex]a=(6x+9y)[/tex]

[tex]b=(8x+12y)[/tex]

substitute the values

[tex](10x+15y)^{2}=(6x+9y)^{2}+(8x+12y)^{2}[/tex]

Part 2) Transform each side of the equation to determine if it is an identity

[tex](10x+15y)^{2}=(6x+9y)^{2}+(8x+12y)^{2}\\ \\100x^{2}+150xy+225y^{2}=36x^{2}+54xy+81y^{2}+64x^{2}+96xy+144y^{2}\\ \\100x^{2}+150xy+225y^{2}=100x^{2}+150xy+225y^{2}[/tex]

The left side is equal to the right side

therefore

Is an identity

Answer:

b. [tex]\displaystyle 225y^2 + 150xy + 100x^2 = 225y^2 + 150xy + 100x^2[/tex]

a. [tex]\displaystyle [8x + 12y]^2 + [6x + 9y]^2 = [10x + 15y]^2[/tex]

Step-by-step explanation:

b. [tex]\displaystyle 225y^2 + 150xy + 100x^2 = 225y^2 + 150xy + 100x^2[/tex]

a. [tex]\displaystyle [8x + 12y]^2 + [6x + 9y]^2 = [10x + 15y]^2[/tex]

The two expressions are identical on each side of the equivalence symbol, therefore they are an identity.

I am joyous to assist you anytime.

I need the work to this please

Answers

Answer:

  ? = 14

Step-by-step explanation:

If ∆EFG ~ ∆CBA, we have the proportion

  FG/FE = BA/BC . . . . . any pairs of corresponding sides will have the same ratio for similar triangles. (It is convenient to put the unknown in the numerator.)

  ?/18 = 21/27 . . . . . . filling in the given numbers

Multiplying by 18, we have ...

  ? = 18·21/27

  ? = 14

_____

If the triangles are not designated as being similar, the problem is unworkable.

Write the formula of the function y whose graph is show.

Answers

Answer:

im on the same question

Now, consider a right triangle with legs of lengths 5 cm and 12 cm. what is the length c of the hypotenuse of this triangle? express your answer to t

Answers

Final answer:

The length of the hypotenuse of a right triangle with legs of 5 cm and 12 cm is 13 cm.

Explanation:

The length of the hypotenuse of a right triangle can be found by using the Pythagorean theorem. The theorem states that the square of the hypotenuse is equal to the sum of the squares of the two legs.

In this case, we have a right triangle with legs of 5 cm and 12 cm. To find the length of the hypotenuse, we can use the formula c = √(a² + b²).

Substituting the given values, we get c = √(5² + 12²) = √(25 + 144) = √169 = 13 cm.

Which relationships would most likely be causal? Check all that apply.

a positive correlation between depth under water and pressure

a negative correlation between total distance run and the runner’s height

a positive correlation between a puppy’s age and weight

a negative correlation between temperature and snowboards sold

a positive correlation between the price of milk and the price of socks

Answers

The correlation of two pairs of data values tells about the degree of movement(along or opposite) that can occur. The correct option is A, C, and D.

What is correlation?

The correlation of two pairs of data values tells about the degree of movement(along or opposite) that can occur in one of the data values when another data value is increased or decreased respectively.

The relationships that would most likely be causal are:

A.) A positive correlation between depth under water and pressure.

This is a casual relationship since the water pressure increases with depth, and can be observed while swimming in a deep swimming pool.

C.) A positive correlation between a puppy’s age and weight.

This is a casual relationship because as the puppy grows, its weight as well as its size both increase.

E.) A negative correlation between temperature and snowboards sold

This is a casual relationship because as the temperature increases fewer people prefer going out snowboarding.

Hence, the correct option is A, C, and D.

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In the triangle RST, RS = 65 and ST = 60. Which equation could be used to find the value of angle S?

A) tan(S) = 65/60



B) sin(S) = 65/60



C) sin(S) = 60/65



D) cos(S) = 60/65

Answers

Answer:cos(S) =  

60

65

Step-by-step explanation:

Answer:

D.[tex]Cos S=\frac{60}{65}[/tex]

Step-by-step explanation:

We are given that in triangle RST, RS=65 and ST=60

We have to find the equation that could be used to find the value of angle S.

We know that

[tex]cos\theta=\frac{Base}{Hypotenuse}[/tex]

Base=ST=60 units

Hypotenuse=RS=65 units

[tex]\theta=S[/tex]

Substitute the values in the given formula

Then, we get

[tex]Cos S=\frac{60}{65}[/tex]

Hence, option D is true.

Determine the axis of symmetry for the function f(x) = −4(x + 7)2 − 3.

Answers

Answer:

  x = -7

Step-by-step explanation:

The vertex form of this equation tells us it is a downward-opening parabola with its vertex at (-7, -3). The line of symmetry is the vertical line through the vertex: x = -7.

___

Vertex form is ...

  y = a(x -h) +k

where a is the vertical expansion factor, and (h, k) is the vertex. When a < 0, the parabola opens downward. When a > 0, it opens upward. (When a=0, the "parabola" is a horizontal line at y=k.)

The equation of the axis of symmetry for [tex]f(x) = -4\cdot (x+7)^{2}-3[/tex] is [tex]x = -7[/tex].

The function given in statement represents a parabola whose axis of symmetry is parallel to the y-axis. The standard form of the function is described below:

[tex]f(x) -k = C\cdot (x-h)^{2}[/tex] (1)

Where:

[tex]C[/tex] - Vertex constant.[tex]x[/tex] - Independent variable.[tex]f(x)[/tex] - Dependent variable.[tex]h, k[/tex] - Vertex coordinates.

The equation for the axis of symmetry is of the form [tex]x = h[/tex]. By direct comparison, we determine that the equation of the axis of symmetry for [tex]f(x) = -4\cdot (x+7)^{2}-3[/tex] is [tex]x = -7[/tex].

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Colin and Brian were playing darts. Colin scored 171. Brian scored 17 more than Colin. What was their combined score?

Answers

1) first find brian’s score

a.) 171+17=188

2) Add brian and colin’s score.

a.) 171+188= 359

Final answer:

Colin scored 171. Brian scored 17 more than Colin, which is 188. Adding both scores together, their combined score is 359.

Explanation:

This is a straightforward arithmetic problem. Colin scored 171 points and Brian scored 17 more than Colin. So first, you need to determine Brian's score by adding 17 to 171, which equals 188. Then, to find their combined score you need add Colin's and Brian's scores together. Therefore, 171 (Colin's score) + 188 (Brian's score) = 359. So, their combined score is 359.

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Help a girl a out please and thank you!

Answers

Answer:

Step-by-step explanation:

Add 29 to both sides of this equation, obtaining:  x² - 10x + 25.  At this point it becomes obvious that this is a perfect square, the square of x - 5.

Thus, in the first two blanks, write x - 5.

In the second two blanks, write 5 (since 5 is the root corresponding to the factor x - 5).

The first figure of the Sierpinski
triangle has one shaded triangle. The
second figure of the Sierpinski triangle
has three shaded triangles. The third
figure of the Sierpinski triangle has
nine shaded triangles. Write the
summation notation that represents
the total number of shaded triangles
in the first 9 figures?

Answers

Answer:

9841

Step-by-step explanation:

Each time the number of shaded triangles is multiplied by 3.  So this is a geometric series:

an = 1 (3)ⁿ⁻¹

The sum of the first n terms of a geometric series is:

S = a₁ (1 - rⁿ) / (1 - r)

Here, a₁ = 1, r = 3, and n = 9.

S = 1 (1 - 3⁹) / (1 - 3)

S = 9841

Answer:

on e2020 its 1 option

Step-by-step explanation:

what is slope and y-intercept of the two points (0,4) and (7,18)

Answers

Answer:

Answer: The slope is 2. The y-intercept is 4 which means point (0, 4).

Step-by-step explanation:

First, find the slope of the line that passes through those two points using the slope formula.

[tex] slope = m = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]

where the points are [tex] (x_1, y_1) [/tex] and [tex] (x_2, y_2) [/tex]

[tex] slope = m = \dfrac{18 - 4}{7 - 0} = \dfrac{14}{7} = 2 [/tex]

The slope is 2.

One of the given points is (0, 4). Since the y-intercept lies on the y-axis, the x-coordinate of the y-intercept is 0. Point (0, 4) is the actual y-intercept.

Answer: The slope is 2. The y-intercept is 4, or point (0, 4).

To find the slope, use the S=(y2 - y1)/(x2 - x1) formula

S=(18-4)/(7-0)

S=14/7

S=2

After finding the slope, us the intercept formula to find the intercept

m is the slope

y-y1=m(x-x1)

y-4=2(x-0)

y=2x+4

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