Which statements about the system are true? Select two options.
y= 2 x - 4
3y - x = -7

Answer: w = 15

Original Question: 40w + (1.5)(8)(w) =780

Step-by-step explanation:

1) 40w + 1.5 x 8w = 780

2) 40w + 12w = 780

3) 52w = 780

4) 52w/52 = 780/52

w = 15

Answer:

Step-by-step explanation:

[tex](\sqrt[3]{2} )^{5}=(2^{\frac{1}{3}})^{5}=2^{\frac{1}{3}*5}=2^{\frac{5}{3}}[/tex]

Answer:

4.4 cubic inches

Step-by-step explanation:

From the question;

We are required to determine the volume of a cone;

Volume of a cone is given by the formula;

V=1/3πr²h

Therefore; taking π to be 3.142

Volume =1/3 × 3.142 × 1.2² × 2.9

             = 4.373664

             = 4.4 cubic inches (to the nearest tenth)

Thus, the volume of a cone is 4.4 cubic inches

Answer:

B, D

Step-by-step explanation:

Solve all equations:

A.

[tex]x-3x=-2x+4\\ \\-2x=-2x+4\\ \\0=4[/tex]

This is false equality, so this equation has no solutions.

B.

[tex]x-\dfrac{1}{3}(3x)=0\\ \\x-x=0\\ \\0=0[/tex]

This equality is true for all values of x, so this equation has infinitely many solutions.

C.

[tex]\dfrac{1}{3}x-3=4+2x\\ \\x-9=12+6x\\ \\x-6x=12+9\\ \\-5x=21\\ \\x=-\dfrac{21}{5}[/tex]

This equation has the unique solution.

D.

[tex]3x+2-\dfrac{1}{3}(3x)=2+2x\\ \\9x+6-3x=6+6x\\ \\6x+6=6+6x\\ \\0=0[/tex]

This equality is true for all values of x, so this equation has infinitely many solutions.

E.

[tex]x-\dfrac{1}{3}x+2=0\\ \\3x-x+6=0\\ \\2x=-6\\ \\x=-3[/tex]

This equation has the unique solution.

Answer:

Amount in 4% account: $550

Step-by-step explanation:

Use simple interest formula [tex]I=P\cdot r\cdot t,[/tex] where

I = interest

P = principal

r = rate (as decimal)

t = time.

4% account:

[tex]P_1=x\\ \\r_1=0.04\\ \\t_1=1,[/tex]

then

[tex]I_1=x\cdot 0.04\cdot 1=0.04x[/tex]

5% account:

[tex]P_2=1,500-x\\ \\r_2=0.05\\ \\t_2=1,[/tex]

then

[tex]I_2=(1,500-x)\cdot 0.05\cdot 1=0.05(1,500-x)[/tex]

You have earned $69.50 in total, so

[tex]I_1+I_2=69.50\\ \\0.04x+0.05(1,500-x)=69.50\\ \\4x+5(1,500-x)=6,950\\ \\4x+7,500-5x=6,950\\ \\4x-5x=6,950-7,500\\ \\-x=-550\\ \\x=550\\ \\1,500-x=1,500-550=950[/tex]

Amount in 4% account: $550

Amount in 5% account: $950

The solutions of the polynomial are  [tex]x=-\frac{1}{2}+\frac{3}{2}i[/tex]  ,  [tex]x=-\frac{1}{2}-\frac{3}{2}i[/tex]

Step-by-step explanation:

The solutions of a polynomial is the value of x when the polynomial equal to zero

The formula of quadratic polynomial is [tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}}{2a}[/tex] , where

∵ The polynomial is 4x² - 4x + 10

- Equate it by zero to find its solutions

∴ 4x² - 4x + 10 = 0

∵ The coefficient of x² is 4

∴ a = 4

∵ The coefficient of x is -4

∴ b = -4

∵ The numerical term is 10

∴ c = 10

- Use the formula to find the values of x

∵ [tex]x=\frac{(-4)(+/-)\sqrt{(-4)^{2}-4(4)(10)}}{2(4)}[/tex]

∴ [tex]x=\frac{-4(+/-)\sqrt{16-160}}{8}[/tex]

∴ [tex]x=\frac{-4(+/-)\sqrt{-144}}{8}[/tex]

∵ [tex]\sqrt{-144}=12\sqrt{-1}[/tex]

- Substitute  [tex]\sqrt{-1}[/tex]  by i

∴ [tex]12\sqrt{-1}=12i[/tex]

∴ [tex]x=\frac{-4(+/-)12i}{8}[/tex]

- Divide up and down by 4 to simplify the fraction

∴ [tex]x=-\frac{1}{2}+\frac{3}{2}i[/tex]   ,   [tex]x=-\frac{1}{2}-\frac{3}{2}i[/tex]

The solutions of the polynomial are  [tex]x=-\frac{1}{2}+\frac{3}{2}i[/tex]  ,  [tex]x=-\frac{1}{2}-\frac{3}{2}i[/tex]

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Answer:

A. x=13

Step-by-step explanation:

[tex]x + 11 = 24 \\ x = 24 - 11 \\ x = 13[/tex]

Answer:

The straight-line distance (in paces) from the tree to the treasure is 80.62 paces

Step-by-step explanation:

Given:

Distance walked towards the north = 70 Paces

Distance walked towards the East = 40 Paces

To Find:

The straight line distance  from the tree to the treasure =?

Solution:

We we track the trail we can find a right triangle formed where the two sides are 70 pace and 40 pace each. The straight line distance is the hypotenuse of the triangle(Refer the figure below

Now we can find the length of the hypotenuse by Pythagorean theorem

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

where b and c are the sides of the triangle

and a is the hypotenuse

[tex]a^2 = 70^2 +40^2[/tex]

[tex]a^2 =4900 + 1600[/tex]

[tex]a = \sqrt{4900 + 1600}[/tex]

[tex]a =\sqrt{6500}[/tex]

a =  80.62

Answer:

The complete answer is explained below.

Step-by-step explanation:

The problem is demanding to simply determine the number of years each color light would last.

We know the following information from the question:

Also the bulbs for each color are LED and are designed to last 100,000 hours. So, each light does last 100,000 hours.

lets make conversions

As

[tex]1\:day\:=\:24\:hours[/tex]  

[tex]1\:year\:=\:365\:days[/tex]

Dividing [tex]100,000[/tex] hours by [tex]24[/tex] hours would bring [tex]4166.67[/tex] days

Dividing [tex]4166.67[/tex] days by [tex]365[/tex] days would bring [tex]11.4[/tex] years, meaning 11 years and 4 months.

Keywords: light, conversion, day, hours

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Answer:

11 x^2 + 4x -6

Step-by-step explanation:

combine like terms but be careful with the minus sign in front of the second set of parentheses.

4x^2 + 9x -7 + 7x^2 -5x +1

Answer: [tex]-3x^2+4x-6\\[/tex]

Step-by-step explanation:

4x^2 +9x-7 does not need distributive propery

-(7x^2+5x-1) does with that negitive in front of parentheses

It then becomes -7x^2-5x+1

Add it all together

[tex]-3x^2+4x-6[/tex]

Answer:

290 miles.

Step-by-step explanation:

To answer this, first multiply the hours by miles. 2 hours at 55 miles per hour means a total of 110 miles. 3 hours at 60 miles per hour means a total of 180 miles. Therefore, 110 + 180 = 290, so you drive 290 miles.

Answer:

Step-by-step explanation:

Answer:

34

Step-by-step explanation:

when n=4.

n^2+6n-6 = (4)^2+6(4)-6 = 16 + 24 - 6 = 10 + 24 = 34

The algebraic expression for given statement is: 10x + 25 or 3(x + 4) + (7x + 13)

Solution:

Given the statement:

Three sets of a sum of a number and four are added to the sum of seven times the same number and thirteen

Let us first understand the given statement,

Let the number be "x"

" sum of a number and four" means x + 4

"Three sets of a sum of a number and four" translated to 3(x + 4)

"sum of seven times the same number and thirteen" means 7x + 13

Thus the algebraic expression for given statement is:

[tex]3(x+4)+(7x + 13)[/tex]

Using distributive property in above expression

[tex]a(b+c) = ab + bc[/tex]

Therefore,

[tex]3(x+4)+(7x + 13) = 3x + 12 + 7x + 13[/tex]

Combine the like terms

[tex]3(x+4)+(7x + 13) = 10x+25[/tex]

Thus the required expression for given statement is: 10x + 25 or 3(x + 4) + (7x + 13)

Answer:

100

Step-by-step explanation:

We know that if we convert 1/4 into a decimal it becomes 0.25 so,

0.25

x

400

____________________

100

Hope this helps!

Answer:

{(3, 4), (4, 8), (6, 6), (7, 10)}

Step-by-step explanation:

Only the first one is a function because the others have repeated x values in some of the ordered pairs.

For example,  {-1, 4), (0, 3), (0, -2)}   has a repeated x = 0.

Answer:

84 cases

Step-by-step explanation:

The amount of money need to be raised = $ 500

Selling price of each ball = $2

1 Tennis case = 3 balls.

Earnings = Selling Price of each ball x Number of balls sold

Quantity sold = Earnings / Selling Price of each ball

Quantity sold = $ 500 / $ 2 = 250 balls

Using direct proportions

1 case = 3 balls

? cases = 250 balls

No.cases = 250 balls / 3 balls = 83.333

Note: Minimum number of cases required are 83.3333 to earn $ 500; however, we can not sell 0.3333 number of cases, hence, we will sell atleast 84 cases.

[tex]\text{The sum of given polynomials is } 8x^2+x+14[/tex]

Solution:

Given given expression to calculate is:

[tex](x^2+x+9) + (7x^2+5)[/tex]

We have to add both the polynomials

Addition of two polynomials involves combining like terms present in the two polynomials

We have to add like terms

Like terms means "the terms having same variable and same exponent"

And we have to add the constants

[tex]\rightarrow (x^2+x+9) + (7x^2+5)\\\\\text{Remove the parenthesis and simplify }\\\\\rightarrow x^2 + x + 9 + 7x^2 + 5\\\\\text{Combine the like terms }\\\\\rightarrow x^2 + 7x^2 + x + 9 + 5\\\\\text{Add the coefficients of like terms }\\\\\rightarrow 8x^2 + x + 9 + 5\\\\\text{Add the constants 9 and 5 }\\\\\rightarrow 8x^2 + x + 14[/tex]

Thus the polynomials are added

Answer:

1.5

Step-by-step explanation:

y2 - y1 ÷ x2 - x1

(3,4) (8, -3)

(x1,y1) (x2,y2)

The resulting graph is valid as it uses the concept of area scaling, where the area of each square accurately represents the relative land sizes of the different countries.

Yes, the resulting graph is valid. This is because a proportional representation by different-sized squares aligns with the principle of area scaling. Area scaling is a mathematical concept where each length is scaled by a particular factor and the area will scale by the square of that factor. If the areas of the countries are correctly scaled to the squares, then the graph accurately represents the relative sizes of the land areas of the five largest countries.

For example, if country A is twice as big as country B, the square representing country A should have an area that is four times (2^2) the area of the square representing country B. Vice versa, if country C is half the size of country D, the square for country C should have an area that is a quarter of the square for country D. Therefore, through area scaling, each country will be proportionately represented on the graph.

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Answer:

Step-by-step explanation:

d = rt....and just so you know, speed is the same as rate

since we are looking for r, I am gonna change the equation

d = rt......r = d / t

d = 400

t = 10

now sub

r = d / t

r = 400/10

r = 40 ft per minute <=====

Answer: 40 per minute

Step-by-step explanation:

Answer:

Option a=$6.37 is correct

The value of the variable is the solution of the given equation is a=$6.37

Step-by-step explanation:

Given equation is a+$5.92=$12.29

To find the value of the variable is the solution of the given equation :

a+$5.92=$12.29

Subracting the above equation by $12.29 on both sides we get

a+$5.92-$12.29=$12.29-$12.29 ( Subtraction property of equality)

a-$6.37=0

Now add $6.37 on both sides we get

a-$6.37+$6.37=0+$6.37 ( Addition property of equality)

a-0=$6.37

Therefore a=$6.37

Therefore option a=$6.37 is correct

Answer:

3rd answer is correct, $6.37

Step-by-step explanation:

Answer:

The answer is A 160% and E [tex]\frac{160}{100}[/tex].

Step-by-step explanation:

To find what percentage 40 is of 25, you first need to find what 1% of 25 is. To solve you do 25 ÷ 100 which is equal to 0.25. You then need to divide 40 by 0.25, which would be the same as multiplying 40 by 4. 40 ÷ 0.25 = 160. Therefore, 40 is 160% of 25. 160% is the same as saying [tex]\frac{160}{100}[/tex] or 160 out of 100 or you could say 160 ÷ 100 = 1.6, which would mean 25 × 1.6 = 40.

40 as a percentage of 25 can be applied such that the percentage would be:

To find what percent 40 is of 25, you would use the formula:

= (Part / Whole) * 100%

So here, 40 is the part and 25 is the whole:

= (40 / 25) * 100%

= 160%

40 is 160 % of 25.

160 / 100 is also 160 %. The rest of the options are incorrect leaving options A and E.

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Answer:

[tex]y+2=(x+2)[/tex]

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Find the slope

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

(-2,-2) and (2,2)

substitute the values

[tex]m=\frac{2+2}{2+2}=1[/tex]

step 2

Find the equation of the line in point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=1\\(x1,y1)=(-2,-2)[/tex]

substitute

[tex]y-(-2)=(1)(x-(-2))[/tex]

[tex]y+2=(x+2)[/tex]

The height of the house, given the angle of elevation and the distance of the point is 25. 98 meters.

How to find the height ?

You can use the tangent function because it relates the angle of elevation to the opposite side and the adjacent side (the horizontal distance).

The tangent of the angle of elevation is equal to the ratio of the height to the horizontal distance:

tan(30 degrees) = h / 45 meters

Solve for "h" by multiplying both sides by 45 meters:

h = 45 meters x tan(30 degrees)

You can calculate the value of tan(30 degrees):

tan(30 degrees) = 0.5774

Multiply:

h = 45 meters x 0.5774

= 25.98 meters

Answer:

Karen had 45 m and m's candy.

Step-by-step explanation:

Let the number of m and m's candy be 'x'.

Now given:

Karen gave an equal amount of m and m's to herself and four friends.

So we can say that;

Number of people m and m's candy distributed equally = 5

Also Given:

Each person receives m and m's equivalent to the largest one digit number.

Now we know that;

Largest one digit number is 9.

So we can say that;

Each person receives m and m's = 9

We need to find number of m and m's Karen have.

Solution:

So we can say that;

Total number of m and m's Karen have is equal to Number of people m and m's candy distributed equally multiplied by number of m and m's can each person receives.

framing in equation form we get;

Total number of m and m's Karen had = [tex]9\times5 = 45[/tex]

Hence Karen had 45 m and m's candy.

Probability is the calculation of = (desired outcomes/total outcomes)

therefore,10/107).

Answer: Interest rate = 0.065

Step-by-step explanation:

I=PRT

3250=5000r*10

Divide by 10 on both sides

325=5000r

r=0.065