which is the best name for the quadrilateral with vertices at (2,2) (5,-2) (1,-5) (-2,-1)

Answer:

Step-by-step explanation:

Instead of x substitute (x + 4) to f(x) = x² - 12

f(x + 4) = (x + 4)² - 12        use (a + b)² = a² + 2ab + b²

f(x + 4) = x² + 2(x)(4) + 4² - 12

f(x + 4) = x² + 8x + 16 - 12

f(x + 4) = x² + 8x + 4

Answer:

Step-by-step explanation:

[tex]x,y-\text{positive integers}\\\\\text{The system of equations:}\\\\\left\{\begin{array}{ccc}x+y=10&\text{subtract}\ y\ \text{from both sides}\\xy=21\end{array}\right\\\\\left\{\begin{array}{ccc}x=10-y&(1)\\xy=21&(2)\end{array}\right\\\\\text{substitute (1) to (2):}\\\\(10-y)(y)=21\qquad\text{use the distributive property}\ a(b-c)=ab-ac\\\\10y-y^2=21\qquad\text{subtract 21 from both sides}\\\\-y^2+10y-21=0\qquad\text{change the signs}\\\\y^2-10y+21=0\\\\y^2-3y-7y+21=0\\\\y(y-3)-7(y-3)=0[/tex]

[tex](y-3)(y-7)=0\iff y-3=0\ \vee\ y-7=0\\\\y-3=0\qquad\text{add 3 to both sides}\\\\y=3\\\\y-7=0\qquad\text{add 7 to both sides}\\\\y=7\\\\\text{Put the value of}\ y\ \text{to (1):}\\\\x=10-3=7\ or\ x=10-7=3[/tex]

Answer:

Problem:

Solve x+y=7;x+2y=11

Steps:

I will try to solve your system of equations.

x+y=7;x+2y=11

Step: Solvex+y=7for x:

x+y+−y=7+−y(Add -y to both sides)

x=−y+7

Step: Substitute−y+7forxinx+2y=11:

x+2y=11

−y+7+2y=11

y+7=11(Simplify both sides of the equation)

y+7+−7=11+−7(Add -7 to both sides)

y=4

Step: Substitute4foryinx=−y+7:

x=−y+7

x=−4+7

x=3(Simplify both sides of the equation)

Answer:

x=3 and y=4

Answer:

They paid $2.85 for each burger and $1.8 for each order of fries

Step-by-step explanation:

It will be solved simultaneously,

let x represent burger and y represent fries

John's order gives the first equation

3x + 2y = 12.15   ........(1)

Emily's order gives the second equation

4x + 3y = 16.80 ..........(2)

multiply equation (1) by 3 and equation (2) by 2 so as to eliminate y

9x + 6y = 36.45 ....... (3)

8x + 6y = 33.6 ........... (4)

subtract equation (4) from (3)

9x - 8x + 6y -6y = 36.45 - 33.6

x = 2.85

substitute x= 2.85 in equation (1)

3(2.85) + 2y = 12. 15

8.55 + 2y = 12.15

2y = 12.15 -8.55

2y = 3.6

y = 1.8

Answer:

Cost of burger = $2.85 and Cost of fries =   $ 1.80.

Step-by-step explanation:

Given  : john order 3 burgers and 2 fries for $12.15. Emily bought 4 burgers and 3 fries for $16.80.

To find : How much did the pay for each burger and order of fries.

Solution : We have given 3 burgers and 2 fries for $12.15.

Let the cost of 1 burger = x .

Let the cost of 1 Fries = y .

3 x + 2 y = $12.15 ------(1)

4 x + 3 y =  $16.80-----(2)

On multiplying (i) by 4 and (ii) by 3 and subtracting the equation .

12x + 8y = $48 .60

(-)12x +(-) 9y = (-)$50 .40

_____________

0 -y = -$ 1.80

y =  $ 1.80.

3x + 2(1.80) = $12.15 .

3x + 3.60 = 12.15

3x = 12.15 -  3.60

3x = 8.55

On dividing both sides by 3.

x = $2 .85

Therefore, Cost of burger = $2.85 and Cost of fries =   $ 1.80.

6 adults and 11 children.

In order to solve this problem we going to use linear equations.

A group of 17 people went to the concert. There are adults and children in that group x + y = 17 where x are adults and y are children. That group pay $57.50 for tickets, if tickets cost $5.00 for adults and $2.50 for children, then 5.00x + 2.50y = 57.50.

x + y = 17 ---------->  y = 17 - x

Substituting the value of y in the equation 5.00x + 2.50y = 57.50:

5.00x + 2.50(17 - x) = 57.50 solving

x = 6

Substituting x = 6 in the equation x + y = 17

6 + y = 17 solving

y = 11

From a group of 17 people who went to the concert 6 are adults and 11 are children.

Sorry this took awhile.

So for Friday, it would be $550

Saturday, $895

Sunday, 1,095

So the total is $2540 if you add the numbers up. Hope this helps!

Answer:

Step-by-step explanation:

y=kx

4=k(-2)

k=-2

y=-2x

when x=30

y=-2*30=-60

Answer:

66

Step-by-step explanation:

cos 0=20/50

The approximate measure of the angle formed by the top of the slide and the vertical support is approximately 21.8 degrees.

In trigonometry, the tangent function can help us find the angle in a right-angled triangle. The tangent of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side. In this case, the side opposite the angle is the height of the slide (20 feet), and the adjacent side is the length of the slide (50 feet).

Now, we can use the tangent function to find the angle (θ):

tan(θ) = Opposite / Adjacent

tan(θ) = 20 feet / 50 feet

tan(θ) = 0.4

To find the value of θ, we can take the inverse tangent (also known as arctan or tan⁻¹) of 0.4:

θ ≈ arctan(0.4) ≈ 21.8 degrees

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Answer:

The equation is equal to 78°-x=56°

The decrease in temperature is 22°

Step-by-step explanation:

Let

x-----> the decrease in temperature

we know that

The equation that represent this situation is equal to

78°-x=56°

Solve for x

x=78°-56°

x=22°

Answer:

The required equation is [tex]78^\circ F-t=56^\circ F[/tex]

The decrease in temperature is 22°F.

Step-by-step explanation:

Given : The temperature in Springfield at 10:00 a.m. was 78°F. During the day, it dropped to 56°F.

To find : Write and solve an equation to  find the decrease in temperature ?

Solution :

We have given that temperature is dropped i.e. there is decrease in teh temperature.

Let the decrease in the temperature be 't'.

According to question,

The temperature in Springfield at 10:00 a.m. was 78°F. During the day, it dropped to 56°F.

i.e. the required equation is [tex]78^\circ F-t=56^\circ F[/tex]

Solve,

[tex]t=78^\circ F-56^\circ F[/tex]

[tex]t=22^\circ F[/tex]

The decrease in temperature is 22°F.

It’s c which is 28 degree Celsius

The value of x will be equal to 28. The correct option is C.

'The intersecting chords theorem is a statement that describes a relation of the four-line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal.'

According to the given problem,

Given,

We know, according to intersecting chords theorem,

⇒ x = [tex]\dfrac{CD + AB}{2}[/tex]

⇒ x = [tex]\dfrac{56}{2}[/tex]

⇒ x = 28

Hence, we can conclude, that the value of x is 28.

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Answer:

i was a little unclear about your sugar amount..

Step-by-step explanation:

if the amount was 1 1/4 ( 1 cup and 1/4 cup) them the answer would be 12

12 x 1.25 = 15

if the sugar amount was just 1/4 cup of sugar the answer would be 60

.25 x 15 = 60

Answer: 8/9

Hope it helped!

Answer:

8/9

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator

GCD of 72 and 81 is 9

72 ÷ 9

81 ÷ 9

= 8/9

The answer is:

The value of the given expression evaluated with x equals to -2 and y equals to 4, is equal to 56 units.

To solve the problem, we need to evaluate both variables for the given values:

[tex]x=-2[/tex]

and

[tex]y=4[/tex]

So, we are given the expression:

[tex]-6x^{3}-y^{2}-3xy[/tex]

Then, evaluating the given values for both variables, we have:

[tex]-6*(-2)^{3}-(4)^{2}-3*(-2)*(4)=(-6*-8)-(16)+24=48-16+24=56[/tex]

Hence, we have that the answer is:

The value of the given expression evaluated with x equals to -2 and y equals to 4, is equal to 56 units.

Have a nice day!

Answer:

The value of given expression = 56

Step-by-step explanation:

It is given an expression in variable x and y

-6x³ - y² - 3xy

To find the value of given expression

Let expression be,

-6x³ - y² - 3xy

When x = -2 and y =4

-6x³ - y² - 3xy = -6(-2)³ - 4² - (3 * -2 * 4)

 = -6*-8 - 16 + 24

 = 48 - 16 + 24

 = 56

Therefore the value of given expression is 56

Answer:

Step-by-step explanation:

We have given:

√2x+3 - √x+1  = 1

First of all isolate the square root of the left hand side:

√2x+3 = √x+1 +1

Now take square on both sides.

(√2x+3)^2 = (√x+1 +1)^2

Open the R.H.S by squaring formula.

∴(a+b)^2 = a^2+2ab+b^2

2x+3 = (√x+1)^2 + 2(√x+1)(1)+(1)^2

2x+3 = x+1 +2√x+1 +1

2x+3 = x+2 +2√x+1

Combine the like terms:

2x-x+3-2 = 2√x+1

x+1 = 2√x+1

Take square on both sides

(x+1)^2 = (2√x+1)^2

x²+2x+1 = 4x+4

x²+2x-4x+1-4 = 0

x²-2x-3 = 0

Now solve the quadratic equation:

a = 1 , b= -2 , c = -3

x = -b+/-√b²-4ac/2a

x = -(-2)+/-√(-2)² - 4(1)(-3) / 2(1)

x = 2 +/- √4+12 / 2

x = 2+/- √16/2

x = 2+/- 4 /2

x = 2+4/2     , x = 2-4/2

x = 6/2      , x = -2/2

x = 3      , x = -1

The solutions we get is (3, -1).

Answer:

Quadratic Equation:  x²-2x-3 = 0

Solutions (Next Question): (3, -1)

Step-by-step explanation:

Absor201 is correct! (look at the BOLDED text in their answer)

Answer:

Option B. [tex]11.78\ in^{3}[/tex]

Step-by-step explanation:

we know that

The volume of a cone is equal to

[tex]V=\frac{1}{3} \pi r^{2}h[/tex]

we have

[tex]r=1.5\ in[/tex]

[tex]h=5\ in[/tex]

substitute

[tex]V=\frac{1}{3} \pi (1.5)^{2}(5)[/tex]

[tex]V=3.75\pi\ in^{3}[/tex]

assume

[tex]\pi =3.14[/tex]

[tex]V=3.75(3.14)=11.78\ in^{3}[/tex]

Answer:

Base of each triangular face = 4 inches

Height of each triangular face = 6 inches

Step-by-step explanation:

The length of each side of the square base is the base of each isosceles triangle forming the pyramid.

We know from our problem that the ratio of the height of each triangle to its base is 3:2, so [tex]\frac{height}{base} =\frac{3}{2}[/tex]. We also know that the base is a square with sides 4 inches long, since the bade of the square is the base of the isosceles triangle, [tex]base=4[/tex].

Replacing the value of the base in our proportion:

[tex]\frac{height}{base} =\frac{3}{2}[/tex]

[tex]\frac{height}{4} =\frac{3}{2}[/tex]

Multiply both sides by 4

[tex]\frac{height}{4}*4 =\frac{3}{2}*4[/tex]

[tex]height=\frac{3*4}{2}[/tex]

[tex]height=\frac{12}{2}[/tex]

[tex]height=6[/tex]

We can conclude that he base of each isosceles triangle is 4 inches and its height is 6 inches.

Answer:

Step-by-step explanation:

The square of the sum of the first five positive integers:

(1 + 2 + 3 + 4 + 5)² = 15² = 225

The sum of the first positive perfect square:

1² + 2² + 3² + 4² + 5² = 1 + 4 + 9 + 16 + 25 = 55

225 - 55 = 200

The positive difference between the square of the sum of the first five positive integers and the sum of the first five positive perfect squares is 170. This is obtained by taking the sum of first five numbers, squaring the sum and subtracting the sum of first five perfect squares.

The sum of first five positive integers = 1+2+3+4+5 = 15

Square of the sum of the first five positive integers = 15² = 225

The sum of the first five positive perfect squares =1²+2²+3²+4²+5²

                                                                                 =1+4+9+16+25

                                                                                 =55

The positive differenece = 225-55=170

Hence the positive difference between the square of the sum of the first five positive integers and the sum of the first five positive perfect squares is 170.

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Answer:

Step-by-step explanation:

cross multiply

4*4x=1*3+6

16x=9

x=9/16

Subtract the monthly fee from the total, then divide by the price of each session.

125 - 15 = 110

110 / 13.75 = 8

She got 8 sessions.

Final answer:

To determine the number of one-point and two-point shots made by a basketball team that scored 92 points from 55 shots, set up a system of equations. Solve the system to find that the team made 18 one-point shots and 37 two-point shots.

Explanation:

Finding the Number of One-Point and Two-Point Shots

Let's define x as the number of one-point shots and y as the number of two-point shots. We then have the following system of equations based on the information provided:

x + y = 55 (Total number of successful shots)

1x + 2y = 92 (Total points scored)

To solve for x and y, we can use either substitution or elimination methods.

Using substitution:

Solve the first equation for x: x = 55 - y.

The team made 18 one-point shots and 37 two-point shots.

Answer:

Option B) y=4/5x

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

we have that

case A) y=x+4/5

The line does not passes through the origin, is not a proportional relationship

case B) y=(4/5)x

The line passes through the origin ---->represents a proportional relationship

The slope m is equal to the constant of proportionality k

The slope m=4/5

therefore

The line  y=4/5x

Represents a proportional relationship that has a constant of proportionality equal to 4/5

case C) xy=4/5

Represent an inverse variation is not a proportional relationship

case D) x+y=(4/5)

The line does not passes through the origin, is not a proportional relationship

Answer:

The Answer is B.

Step-by-step explanation:

Trust me .

Answer:

49

Step-by-step explanation:

y = -x² - 10x + 24

For a parabola ax² + bx + c, the vertex is at x = -b/(2a).

In this case, a = -1 and b = -10.  So:

x = -(-10) / (2 * -1)

x = -5

The y coordinate is:

y = -(-5)² - 10(-5) + 24

y = -25 + 50 + 24

y = 49

Answer:

s = 4

Step-by-step explanation:

Solve for s:

8 s - 10 = 34 - 3 s

Add 3 s to both sides:

8 s + 3 s - 10 = (3 s - 3 s) + 34

3 s - 3 s = 0:

8 s + 3 s - 10 = 34

8 s + 3 s = 11 s:

11 s - 10 = 34

Add 10 to both sides:

11 s + (10 - 10) = 10 + 34

10 - 10 = 0:

11 s = 34 + 10

34 + 10 = 44:

11 s = 44

Divide both sides of 11 s = 44 by 11:

(11 s)/11 = 44/11

11/11 = 1:

s = 44/11

The gcd of 44 and 11 is 11, so 44/11 = (11×4)/(11×1) = 11/11×4 = 4:

Answer:  s = 4

The gross pay will be $1496.78

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Brett is paid $18.95 per hour.

For 0 to 40 hours a week,

For any hours over 40, Brett makes

= 1.5 ($18.95)

= $28.425/hour

In Week 1:  40 hours x $18.95/hour = $758

2 hours x $28.425/hour = 56.85

Week 2:  36 hours x $18.95/hour = 682.2

So, total pay= 758 + 56.58+ 682.2 = $1496.78

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Final answer:

Brett's gross pay for working 42 hours one week and 36 hours the next, for a total of 78 hours, is $1495.05, which includes 2 hours of overtime pay.

Explanation:

Brett is paid an hourly wage of $18.95, with overtime paid at 1.5 times his regular rate. To calculate Brett's gross pay for the two-week pay period where he worked 42 hours one week and 36 hours the next week, we have to account for the fact that he worked 2 hours of overtime in the first week (since he worked more than 40 hours).

Step-by-Step Calculation

Brett's gross pay for the 78 hours worked would be $1495.05.

Answer: Inconsistent.

Step-by-step explanation:

The equation of the line in Slope-intercept form is:

[tex]y=mx+b[/tex]

Where m is the slope and b is the y-intercept.

Solve for y from each equation:

Equation 1:

[tex]-\frac{1}{2} x = -6 - y\\\\y-\frac{1}{2} x = -6\\\\y=\frac{1}{2} x-6[/tex]

Equation 2:

[tex]3+y= \frac{1}{2} x + 4\\\\y= \frac{1}{2} x + 4-3\\\\y= \frac{1}{2} x+1[/tex]

A system of equations can be classified by its number of solutions.

You can observe that the slopes of both equations are the same but the y-intercepts are different, then these lines are parallel, which means that they do not intersect.

By definition, when to lines are parallel there is NO SOLUTION and the system is classified as "Inconsistent".

Answer:

The correct option is 4.

Step-by-step explanation:

If a figure it dilated by scale factor k, then the image and preimage are similar figures and their corresponding sides are proportional.

In triangle I, the base of the triangle is 1 unit and length of the perpendicular is 1 units.

In triangle II, the base of the triangle is 1 unit and length of the perpendicular is 2 units.

[tex]\frac{1}{1}\neq \frac{1}{2}[/tex]

The corresponding sides are not proportional. It means both triangles are not similar. So, there is no dilation transforming triangle I into triangle II.

Therefore the correct option is 4.

Answer:

There is no dilation transforming triangle I into triangle II.

Step-by-step explanation:

Answer:

The employers pay their employees based on hourly rates, commission and salary.

Step-by-step explanation:

The employees get their pay based on hourly rates that can range from a minimum hourly rate of say $12 per hour to any maximum figure like $40 per hour.

The final salary is based on the numbers of hours worked multiplied by the hourly rate.

Secondly, the pays are also commission based. That is your base salary plus the commission.

The salary is typical in management positions. These are not hourly based but a lump sum pay.

So, the correct answers are : commission, hourly pay and salary.

Answer:

commission

hourly pay

salary

Step-by-step explanation:

PLATO USERS

Answer:

(C) 19x+6^2+2

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

edge 2021

The flow rate is 2 quarts per minute. There are 4 quarts in a US gallon, so 2 quarts divide 4 quarts per US gallon = 0.5 gallons per minute There are 60 seconds in a minute, so the flow rate is 0.5 gallons per minute divide 60 seconds per minute = 0.0083 gallons per second

Converting 2 quarts per minute to gallons per second requires the use of two conversion factors. First, quarts are converted to gallons by dividing by 4. Then, minutes are converted to seconds by dividing by 60. After performing these steps, it is found that 2 quarts per minute is approximately equal to 0.00833 gallons per second.

The student is asking to convert a flow rate from quarts per minute to gallons per second. There are a few fundamental conversions you need to use to find the answer. Firstly, remember that 1 gallon (gal) is equivalent to 4 quarts (qt). So, to convert the quarts to gallons, divide the quarts by 4. Secondly, there are 60 seconds in a minute; thus, you have to convert the minutes to seconds by dividing by 60.

Let's go step-by-step:

Therefore, 2 quarts per minute is approximately equal to 0.00833 gallons per second.

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Answer:

[tex]f(n)=f(n-1)-6[/tex], where [tex]f(1)=5[/tex] and [tex]n\:>\:1[/tex]

Step-by-step explanation:

The terms of the sequence are:

[tex]5,-1,-7,-13,-19[/tex]

The first term of this sequence is [tex]f(1)=5[/tex].

There is a constant difference among the terms.

This constant difference can determined by subtracting a previous term from a subsequent term.

[tex]d=-1-5=-6[/tex]

The general term of this arithmetic sequence is given  recursively by [tex]f(n)=f(n-1)+d[/tex]

We substitute the necessary values to obtain:

[tex]f(n)=f(n-1)+-6[/tex]

Or

[tex]f(n)=f(n-1)-6[/tex], where [tex]f(1)=5[/tex] and [tex]n\:>\:1[/tex]

Answer:

C

Step-by-step explanation: