Byran is pushing his niece, Callie, on a park swing. Her displacement over time can be modeled by the following graph.




How long does it take Callie to complete one full swing?

A.

20 seconds

B.

5 seconds

C.

10 seconds

D.

60 seconds

The first Graph is correct.

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We know that a ray is a line that has one end point and extends infinitely from the other end.

i.e. it is a line that originates at a point and goes to infinity.

Now, it is given that:

A ray has one point at a given distance from the endpoint of the ray.

The graph that describes this statement is attached to the answer.

( while the other graph describes that there is a line that passes through the line segment AB.

Since it extends to infinity in both the direction )

Answer: The area of the mobile is 140.4 m².

Step-by-step explanation:

Hi to solve this problem we have to analyze the information given:

Width : 7.2 meters (a)

Length : 19.5 meters (b)

The mobile is rectangular. So, we have to apply the area of a rectangle formula.

The area of the mobile is 140.4 m².

Feel free to ask for more if it´s necessary or if you did not understand something.

Answer:

b.14.2 mph

Step-by-step explanation:

Answer:

The cart’s speed in miles per hour is 14.2 miles per hour .

Option (B) is correct .

Step-by-step explanation:

As given

Rob measures his go-cart’s speed to be 250 inches per second.

As

[tex]1\ inch = \frac{1}{63360}\ miles[/tex]

[tex]1\ second = \frac{1}{3600}\ hours[/tex]

Now convert 250 inches per second into miles per hour .

[tex]250 inches\ per\ second = \frac{250\times \frac{1}{63360}}{\frac{1}{3600}}\ miles\ per\ hour[/tex]

[tex]250 inches\ per\ second = \frac{\frac{250}{63360}}{\frac{1}{3600}}\ miles\ per\ hour[/tex]

[tex]250 inches\ per\ second = \frac{250\times 3600}{63360}\ miles\ per\ hour[/tex]

[tex]250 inches\ per\ second = \frac{900000}{63360}\ miles\ per\ hour[/tex]

250 inches per second = 14.2(Approx) miles per hour.

Therefore the cart’s speed in miles per hour is 14.2 miles per hour .

Option (B) is correct .

12x^2-44x+7 = (6x - 1)(2x - 7)

35x^2-27x-18 = (7x - 9)(5x +2)

Answer:

iit =

Step-by-step explanation:

toby will reach more people in 40 phone calls

The way to solve this problem is to turn both denominators into 40

4 * 4        16

_          =  ---       so Clara will reach 16 people in 40 phone calls

10 * 4       40

3  * 5       15

_           = ----        so Toby will reach 15 people in 40 phone calls

8 * 5         40

Therefore Clara will reach more people in 40 phone calls than Toby.

Answer:

Option C

Step-by-step explanation:

given two equations

6m-5n= 14   ... i

2m+2n= -10  ...ii

We can solve this by elimination.

For elimination consider the coefficients of m.

They are 6 and 2, with LCD 6

You multiply 2nd equation by 3 to have

6m+6n =-30 ... iii and

6m-5n  = 14  ... i

Subtract i from iii

11n = -44

Divide by 11 to get n

n = -4

Substitute in I equation

6m-5(-4) =14

6m +20 = 14

subtract 20

6m =14-20 =-6

divide by 6

m =-1

Hence answer is m=-1 and n=-4

(-1,-4)

Option C is the answer.

Erika will spend $60 on cupcakes for the 20 guests at her party by purchasing one $3 cupcake for each guest.

To calculate how much Erika will spend on cupcakes for the party, we need to multiply the number of guests by the cost of each cupcake. Each guest will get one cupcake, and since there are 20 guests, we need 20 cupcakes. The cost of one cupcake is $3.

To find the total cost, we perform the following calculation:

Therefore, Erika will spend $60 on cupcakes for the party.

ANSWER

[tex]x=-2\pm 2\sqrt{2}[/tex]

EXPLANATION

Given:

[tex]x^2+4x-4=0[/tex]

We complete the square as follows;

Add 4 to both sides of the equation:

[tex]x^2+4x=4[/tex]

Add half the coefficient of [tex]x[/tex] to both sides of the equation.

[tex]x^2+4x+(2)^2=4+(2)^2[/tex]

The Left Hand Side of the equation is now a perfect square.

[tex](x+2)^2=4+4[/tex]

[tex](x+2)^2=8[/tex]

Take the square root of both sides

[tex]x+2=\pm \sqrt{8}[/tex]

[tex]x=-2\pm 2\sqrt{2}[/tex]

Hence the correct answer is option C

Given equation is [tex]x^2+4x-4=0[/tex]

compare with [tex]ax^2+bx+c=0[/tex]

we get: a=1, b=4, c=-4

plug these values into quadratic formula:

[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\frac{-4 \pm \sqrt{4^2-4(1)(-4)}}{2(1)}[/tex]

[tex]x=\frac{-4 \pm \sqrt{16-4(-4)}}{2}[/tex]

[tex]x=\frac{-4 \pm \sqrt{16+16}}{2}[/tex]

[tex]x=\frac{-4 \pm \sqrt{32}}{2}[/tex]

[tex]x=\frac{-4 \pm 4\sqrt{2}}{2}[/tex]

[tex]x=-2 \pm 2\sqrt{2}[/tex]

Hence finall answer is:

[tex]x=-2+2\sqrt{2}[/tex] and [tex]x=-2-2\sqrt{2}[/tex]

Answer:

Zoe counted 20 more black kittens than white kittens.

Step-by-step explanation:

Let the white kittens be = x

Then the black kittens be = 4x

Zoe counts a total of 25 kittens.

So, we get;

[tex]x+2x=25[/tex]

=> [tex]5x=25[/tex]

Dividing both sides by 5, we get;

x = 5

White kittens are = 5

Black kittens are = [tex]4\times5=20[/tex]

So, the black kittens are [tex]25-5=20[/tex] more than white ones.

Therefore, Zoe counted 20 more black kittens than white kittens.

A. hope this helps. Mark as Brainliest.

Answer:

Value of house before Increase = $700000.

Step-by-step explanation:

Let the value of house before increase be $x.

Increase in value = 7%of x= .07x

Value of house before increase+ Increase in value = Total value.

x+.07x=749000

Adding like terms,

1.07x=749000

Dividing both sides by 1.07.

x=700000.

Value of house before Increase = $700000.

Answer:

[tex]r(x)=(4x)^7[/tex]

Step-by-step explanation:

For example,

If we wanted to horizontally compress [tex]y=x^2[/tex], we would multiply by 4 to get [tex]y=(4x)^2[/tex], and

if we wante to horizontally expand [tex]y=x^2[/tex], we would multiply by [tex]\frac{1}{4}[/tex] to get [tex]y=(\frac{1}{4}x)^2[/tex]

Since this question asks for horizontal compression, we multiply the [tex]x[/tex] of the function by 4. So the function we need is [tex]f(x)=(4x)^7[/tex]. The second choice is correct.

F(x) = 1/2x^2 is a variation of the basic graph y = x^2 (the squaring function).

The graph of the squaring function has the shape of a parabola that opens up.  Its vertex is at (0,0).

The graph of F(x) = (1/2)x^2 has the same shape, but is compressed vertically by a factor of (1/2).   The vertex of F(x) = (1/2)x^2 is still (0,0).  That eliminates the first 2 possible answers.  Note that F(1) = (1/2)(1)^2 = 1/2.  The point (1, 1/2) is on the third graph, but not on the fourth.  Thus, the third graph is correct.

Only the third graph (option C) represents the graph of [tex]F(x) = \frac{1}{2} x^2[/tex]

The given function is:

[tex]F(x) = \frac{1}{2} x^2[/tex]

This graph is of the form [tex]y = ax^2[/tex] and it takes the shape of a parabola with center at (0, 0)

Only two of the graphs shown among the options have the center at the origin (0, 0), but only one is scaled by 0.5

Therefore, the graph of the function [tex]F(x) = \frac{1}{2} x^2[/tex] is plotted below

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[tex]y=\dfrac{8x+3}{4}=\dfrac{8x}{4}+\dfrac{3}{4}=2x+\dfrac{3}{4}[/tex]

It's a linear function y = mx + b. The domain of linear function is the set of all real numbers.

We have no objections to the value of x. x can be any number.

Therefore your answer is:

a) All real numbers.

Answer:

a is the middle point on x-axis = 3

Step-by-step explanation:

On probability distribution graph, P(x≥a) means area under the curve from x=a to x=6.

On a probability distribution graph, the entire area under curve =1

But we are given that P(X≥a) is 0.5 which is half of 1.

And we are given with a normal distribution graph which has center at x=3.

Hence half of the area means area from x=3 to x=6 which is nothing but P(X≥3).

Therefore a is 3.

We can also check it by finding area under curve from x=3 to x=6.

Area under curve from x=3 to x=6 can spitted into a rectangle and a triangle.

Rectangle area = (5-3)X0.2=0.4

Triangle area=[tex]\frac{1}{2}X0.2X1=0.1[/tex]

Hence total area from x=3 to x=6 is 0.4+0.1=0.5

No. A parallelogram has 2 sets of parallel lines, each the same length. This doesn't mean that the angles are perpendicular.

The solution to the inequality 8(1/2x - 1/4) > 12 - 2x is x > 7/3.

To solve the given inequality 8(1/2x - 1/4) > 12 - 2x, first you should distribute the 8 to both terms in the parentheses. This gives you 4x - 2 > 12 - 2x. Next, we need to group like terms, so let's add 2x to both sides of the inequality to obtain 6x - 2 > 12. Afterwards, add 2 to both sides, resulting in 6x > 14. Finally, divide each side by 6 to isolate x, which gives x > 7/3. So, the solution is x > 7/3.

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[tex]\sqrt{63} = \sqrt{9*7} = \sqrt{3*3*7}  = 3\sqrt{7}[/tex]

The simplified form of √(63) after removing all perfect squares from inside the square root is 3√(7).

To simplify the square root of 63 and remove perfect squares, we start by finding the prime factorization of 63. The prime factorization of 63 can be obtained by dividing the number by its smallest prime factor, which is 3, and then continuing the process for each quotient until we get a prime number. The prime factorization of 63 is:

63 = 3 * 3 * 7.

Now, we look for any perfect square factors within the square root of 63. In this case, the perfect square factor is 3 * 3 (3 squared). We can remove this perfect square from the square root, leaving us with:

√(63) = √(3 * 3 * 7).

Since we removed one pair of 3's (3 * 3), the simplified square root of 63 becomes:

√(63) = 3√(7).

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1. D

2. D

I don't know the answer to number 3 sorry.

Answer with explanation:

1. x+0=x

0 is the identity element.When number is added to identity the resultant is number.

Option D : Identity

2.

3x-2=60

Adding 2 on both sides

→3x-2+2=60+2

→3x=62

Dividing by 3, on both sides

[tex]x=\frac{62}{3}[/tex]

Option (B.)→ Add 2 . Divide by 3

3.

y> -2,

y=(-2, Infinity)

So, -3 is not the solution of ,y>-2.

Option A: False

4.

The equation in slope-intercept form, is, y = mx + b.

4x-2y=10

4x=2y+10

2y=4x-10

Dividing by 2, on both sides

y=2x-5

Option A:→y=2x-5

5.

The equation of line is

 y=2x-11

We have to check whether point (3,0) lies on the line or not.

LHS=y=0

RHS=2x-11

       =2 ×3-11

       =6-11

       = -5

So, point (3,0) does not lie on the line,→y=2x-11.

Option B : False

6.

Slope of line joining the points (-2,-1) and (3,4) is

 [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m=\frac{4+1}{3-(-2)}\\\\m=\frac{5}{5}\\\\m=1[/tex]

Slope=1

Option A

7.

When solving a system of equations, you are finding the

Option C: Intersection point

8.

[tex]3x + 2y = 10------(1) \\\\2x + 3y = \frac{15}{12}-----------(2)\\\\1+2\\\\5x+5y=\frac{135}{12}\\\\x+y=\frac{27}{12}-----(3)\\\\1-2\\\\x-y=\frac{105}{12}-----(4)\\\\ 3+4\\\\2x=\frac{132}{12}\\\\2x=11\\\\x=\frac{11}{2}\\\\y+\frac{11}{2}=\frac{27}{12}\\\\y=-\frac{11}{2}+\frac{27}{12}\\\\y=\frac{-39}{12}[/tex]

Total cost of the purchase by Barry is given by the equation A = $ 36 and the amount saved by Barry is $ 14

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the cost of all the purchase by Barry be A

Now , the equation will be

The cost of the sweater = $ 50

The marked down percentage of sweater = 20 %

So , the new cost of the sweater = cost of the sweater - ( marked down percentage x cost of the sweater )

Substituting the values in the equation , we get

The new cost of the sweater = 50 - ( 20/100 ) x 50

The new cost of the sweater = 50 - 10

The new cost of the sweater = $ 40

Now , the coupon discount percentage = 10 %

So , the final cost of the purchase A = new cost of the sweater - ( coupon discount percentage x new cost of the sweater )

Substituting the values in the equation , we get

The final cost of the purchase A = 40 - ( 10/100 ) x 40

The final cost of the purchase A = 40 - 4

The final cost of the purchase A = $ 36

So , the amount saved by Barry = cost of the sweater - final cost of the purchase

The amount saved by Barry = 50 - 36 = $ 14

Hence , the cost of the sweater is $ 36

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Answer:

You need annual gross pay of 20000.

Step-by-step explanation:

Suppose, your annual gross pay is  [tex]x[/tex]

You estimate that the net pay will be 65% of your gross pay. So, the annual net pay will be:  [tex]x*65\% = 0.65x[/tex]

As there are 52 weeks in 1 year, so your weekly net pay will be:  [tex]\frac{0.65x}{52}[/tex]

Given that, you will need 250 per week after taxes to get by. So, the equation will be......

[tex]\frac{0.65x}{52}=250\\ \\ 0.65x= 52*250=13000\\ \\ x=\frac{13000}{0.65}=20000[/tex]

So, you need annual gross pay of 20000.

[tex]f(x)=3x+5,\ g(x)=-2x^2-5x+3\\\\(f+g)(x)=f(x)+g(x)=(3x+5)+(-2x^2-5x+3)\\\\=3x+5-2x^2-5x+3=-2x^2+(3x-5x)+(5+3)=-2x^2-2x+8\to\boxed{C.}[/tex]

Answer:

(-6, 36)

Step-by-step explanation:

The standard form: ax^2 + bx + c

In this case:

a is 1

b is 12

c is 0

Calculate -b / 2a. This is the x-coordinate of the vertex.

To find the y-coordinate of the vertex, simply plug the value of -b / 2a into the equation for x and solve for y. This is the y-coordinate of the vertex.

-12 / ( 2 x 1 )

-12 / 2

-6

You log -6 in the function

f(x) = x^2 + 12x

f(-6) = (-6)^2 + 12(-6)

      = 36 +  (-72)

      = 36 - 72

      = 36

I hope this

Answer: A (-6, -36)

Step-by-step explanation:

Answer 5/14

Step-by-step explanation:

The simplest form of the given expression [tex]\frac{5}{8} \times \frac{4}{7}[/tex] is [tex]\frac{5}{14}[/tex].

An expression is a combination of numbers, variables, operations, functions, and often symbols that are combined according to particular rules to represent a mathematical computation or relation.

Expressions can be both simple as a single number or variable and complex by involving multiple variables and operations.

Some examples of Expressions are x, 4, x² + 6y + 2xy +6, [tex]\frac{x}{y}[/tex], [tex]\frac{x}{y} \times \frac{p}{q} \div e^7[/tex] etcectra.

The given expression is

[tex]\frac{5}{8} \times \frac{4}{7}[/tex] [tex]= \frac{5}{2}\times \frac{1}{7}[/tex]

        [tex]= \frac{5\times1}{2\times7}\\ = \frac{5}{14}[/tex].

Hence the given expression [tex]\frac{5}{8} \times \frac{4}{7}[/tex] can be simplified as [tex]\frac{5}{14}[/tex].

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X=11 because

5x+9x+26=180

14x+26=180

14x=154

x=11

Answer:  The required value of x is 11.

Step-by-step explanation:  Given that the lines f and g are parallel to each other.

We are to find the value of x.

From the figure, we note that the parallel lines f and g are cut by a transversal,  and

angles with measures 5x° and (9x+26)° are interior angles on the same side of the transversal.

We know that, if two lines are parallel, then the measures of the angles on the same side of the transversal is 180°.

Therefore, we get

[tex]5x^\circ+(9x+26)^\circ=180^\circ\\\\\Rightarrow 5x+9x+26=18\\\\\Rightarrow 14x=180-26\\\\\Rightarrow 14x=154\\\\\Rightarrow x=\dfrac{154}{14}\\\\\Rightarrow x=11.[/tex]

Thus, the required value of x is 11.