Consider the graph of f(x) given below.

Answer:

Here you go with your correct answer

Answer:

5 weeks

Step-by-step explanation:

We know that she works at a rate of $12 an hour, she also works 20 hours a week.

The total amount she makes per week is $240 (12 x 20). However, that is without deductions. We have to subtract $34 from the $240.

$240 - $34 = $206.

$206 is the amount she makes in a week and she wants to save $950. How many weeks does she have to save? Well, let's divide.

$950 / $206 = 4.6 weeks. However, if we have to round up to 5 weeks.

I think factorizing everything you can first will make the simplification ... well, simpler.

[tex]\dfrac{x^2 - 3x}{x^2 + 13x + 36} \div \dfrac{x^2+7x}{x^2+16x+63} = \dfrac{x(x-3)}{(x+4)(x+9)} \div \dfrac{x(x+7)}{(x+7)(x+9)}[/tex]

The factors of [tex]x+7[/tex] in the second rational expression cancel:

[tex]\dfrac{x^2 - 3x}{x^2 + 13x + 36} \div \dfrac{x^2+7x}{x^2+16x+63} = \dfrac{x(x-3)}{(x+4)(x+9)} \div \dfrac{x}{x+9}[/tex]

Now, use the property

[tex]\dfrac ab \div \dfrac cd = \dfrac ab \times \dfrac dc[/tex]

(this is the property of multiplication having to do with multiplicative inverse, or "inverting the divisor" as the question calls it) to write

[tex]\dfrac{x^2 - 3x}{x^2 + 13x + 36} \div \dfrac{x^2+7x}{x^2+16x+63} = \dfrac{x(x-3)}{(x+4)(x+9)} \times \dfrac{x+9}x[/tex]

and we see some more cancellation, namely of the factors of [tex]x[/tex] and [tex]x+9[/tex].

[tex]\dfrac{x^2 - 3x}{x^2 + 13x + 36} \div \dfrac{x^2+7x}{x^2+16x+63} = \boxed{\dfrac{x-3}{x+4}}[/tex]

Answer:

x=-5, y=-2

Step-by-step explanation:

10x-9y=-32

2x-10y=10

(2x-10y)*5=10*5

10x-50y=50

(10x-9y)-(10x-50y)=-32-50

41y=-82

y=-82/2

y=-2

10x-9(-2)=-32

10x+18=-32

10x=-50

x=-5

Answer:

38

Step-by-step explanation:

hope it helps good day.

Answer:

38 pencils and pens

Step-by-step explanation:

Given

Cost of pencil= $1.20

Cost of pen= $2.90

Difference in cost

= $2.90 -$1.20

= $1.70

Since she bought an equal number of pens and pencils, the additional amount of money spent on pens is due to the difference in price of a pen as compared to a pencil. Let one pen and one pencil be a set.

Number of sets

= $32.30 ÷$1.70

= 19

Since there are 19 sets,

total number of pencils and pen

= 19(2)

= 38

The congruence property that shows that  if ΔABC ≅ ΔDEF, then  ΔDEF ≅ ΔABC is; A: Reflexive Property

In geometry, the reflexive property of congruence states that an angle, line segment, or shape is always congruent to itself.

Now, since we are told that ΔABC is congruent to ΔDEF, then it means that by the reflexive property of congruence we can equally say that ΔDEF are congruent to angles of ΔABC

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The different statements and reasons to prove that −3(x + 8) = −21 are as detailed below.

Statement 1; −3(x + 8) = −21

Reason 1; Given

Statement 2; −3(x + 8)/-3 = −21/-3

Reason 2; Division property of Equality

Statement 3; x + 8 - 8 = 7 - 8

Reason 3; Subtraction Property of Equality

Statement 4; x = -1

Reason 4; Given

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The equations that are true for x = -2 and x = 2 are (a) x^2 - 4 = 0 and (d) 4x^2 = 16

We have:

x = -2 and x = 2

Rewrite as:

x + 2 = 0 and x - 2 = 0

Multiply both equations

(x + 2)(x - 2) = 0

This gives

x^2 - 4 = 0 --- option (a)

Add 4 to both sides

x^2 = 4

Multiply by 4

4x^2 = 16 --- option (d)

Hence, the equations that are true for x = -2 and x = 2 are (a) x^2 - 4 = 0 and (d) 4x^2 = 16

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The coordinates of the function will be T (x , y ) = (2 x, y + 5) ; Option B is the answer.

A function is a mathematical statement that relates an independent and a dependent variable .

An inverse of a function is given

T⁻¹ (x, y) :  (½x, y - 5)

 T(x, y)  : ?

As the inverse in given , to find the function , the reverse of all the transformation has to be done .

The x coordinate has been halved , so the original function will be double.

The y coordinate has  5 subtracted to it , so it will be added to the coordinate.

So the coordinates of the function will be

T (x , y ) = (2 x, y + 5)

Therefore Option B is the answer.

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Answer:

B. y = x + 2; y = 5

Step-by-step explanation:

100% on edge 2022!

Answer: Its A and A

Step-by-step explanation: I did the question

The number of sides the regular polygon has is: B. 8.

A polygon with an n-side have a sum of interior angles which can be determined using the formula: (n - 2)180, where n is the number of sides of the regular polygon.

Thus, to find the measure of each interior angle of the polygon, we have: interior angle of a polygon = sum of interior angles ÷ number of sides.

Given the following information about the regular polygon:

Interior angle of the regular polygon = 135 degrees.

Plug this into the given formula for finding the interior angle of a polygon:

135 = (n - 2)180/n

Multiply n by both sides of the equation

135 × n = (n - 2)180/n × n

135n = (n - 2)180

Open the bracket

135n = 180n - 360

Subtract both sides by 180n

135n - 180n = 180n - 360 - 180n

-45n = -360

Divide both sides by -45

-45n/-45 = -360/-45

n = 8

Thus, the number of sides that the regular polygon has is: B. 8 sides.

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24.85

Step-by-step explanation:

First find the square root of 8.2 and subtract from the square root of 7.5. Multiply 3.5 by 0.71, the answer you get divide it by the answer you get after finding the square root.

The time taken to burn off the entire pizza by walking is 568.32 minutes.

2,368 = 125 × w

2,368 = 125w

w = 2,368 / 125

w = 18.944

Total time needed to burn all calories = 30 minutes × 18.944

= 568.32 minutes

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The least distance from point P to line l is approximately equal to 3.536 units.

There are several ways to calculate the least distance, in this case we decided to use the approach based on vectors and projections. First, we generate two auxiliary vectors:

Vector parallel to the line l

[tex]\overrightarrow {AB} = (5, 1) - (2, 4)[/tex]

[tex]\overrightarrow{AB} = (3, - 3)[/tex]

A vector from one point on the line l to the point P

[tex]\overrightarrow{AP} = (1, 1) - (2, 4)[/tex]

[tex]\overrightarrow {AP} = (- 1, - 3)[/tex]

Now we proceed to find the vector distance by using the following vectorial formula:

[tex]\vec d = \frac{\overrightarrow{AP} \,\bullet\, \overrightarrow {AB}}{\overrightarrow {AB} \,\bullet \,\overrightarrow {AB}} \cdot \overrightarrow{AB} - \overrightarrow {AP}[/tex]

[tex]\vec d = \frac{(-1)\cdot (3) + (- 3) \cdot (- 3)}{3^{2}+ (-3)^{2}} \cdot (3, - 3) - (-1, - 3)[/tex]

[tex]\vec d = - \frac{1}{6}\cdot (3, - 3) - (- 1, - 3)[/tex]

[tex]\vec d = \left(-\frac{1}{2}, \frac{1}{2} \right) + (1, 3)[/tex]

[tex]\vec d = \left(\frac{1}{2}, \frac{7}{2} \right)[/tex]

The magnitude of the vector distance is determined by Pythagorean theorem:

[tex]d = \sqrt{\left(\frac{1}{2} \right)^{2}+\left(\frac{7}{2} \right)^{2}}[/tex]

d ≈ 3.536

The least distance from point P to line l is approximately equal to 3.536 units.

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Answer:

b = 24 meter

Step-by-step explanation:

Using Pythagoras theorem:

a² + b² = c²

Here given: a = 10 m, b = ?, c = 26 m

Insert values

10² + b² = 26²

b² = 26² - 10²

b² = 676 - 100

b² = 576

b = √576

b = 24

Answer:24

Step-by-step explanation: i found the answer using the pythogaras theorem,the formula used is, h squared=b squared +p squared,formula used to find missing legnths of triangles such as hypotaneous and height.in this question you have to find the height,as you can see to the opposite of hypotaneous its height/perpendicular.

so according to formula,h squared=b squared+p squared

so,26 squared=10 squared+p squared.

in order to find p

p squared=26 squared -10 squared

which gives us 576

and p squared =576

the square on the p will go on the other side and become an underroot.

take the underoot of 576

which gives us p=24.

so the legnth is 24, found using pythogares theorem.by rearranging the formula and making p the subject in the formula

The first machine has added maximum 25 scoops of candies.

Given Machine 1 can add 46899 pieces of candies in the giant vat and machine 2 can add 13576 pieces of candies in the giant vat to form total supply of 600000.

let the number of scoops added by first machine be x and number of scoops added by second machine is y.

The equation will be as under:

46899x-13576y=600000

It can be solved logically. Because other machine is removing the candies from the giant vat so the value of 13576y is minimum 600000-13576=586424. Because it atleast withdrawn 1 scoop.

So the value of 46899x is maximum 1186424 which can bewhen the number of scoops is =1186424/46899=25 approximately.

Hence the number of scoops added by first machine is maximum  25.

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Question contains an error as the line related to left over 1 candy should be deleted.

Answer:

The product is the difference of squares is [tex]$$\left(11-b\right)\left(11+b\right)=121-{{b}^2}$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\begin{aligned}&(11-b)(11+b)=(11)^{2}-(b)^{2} \\&(11-b)(11+b)=121-b^{2}\end{aligned}$$[/tex]

Answer:

not a function because it doesn't pass the vertical line test

Step-by-step explanation:

even though they have different y coordinates they still don't pass the test

Answer: 2.96% rounded

Step-by-step explanation: 10/30) x (9/29) x (8/28)  =  720 / 24,360 = 6/203 = 2.96%

The tens digit is 3; the units digit is 3-1 = 2; and the number itself is 32.

Lets simplify the problem,

Let assume  the "tens" digit be x

Then the "units" difference =  (x-1), according to the condition.

Hence, the number itself is N = 10x + (x-1).

Then the number N+8 is 10x + (x-1) + 8 = 10x + x + 7 = 11x + 7.

From the last statement of the problem, we have this equation

[tex]N+8 = 8*(x+y),or11x + 7 = 8*(x+(x-1)).[/tex]

Simplify and find "x"

[tex]11x + 7 = 8*(2x-1)11x + 7 = 16x - 87 + 8 = 16x - 11x15 = 5xx = 15/5 = 3[/tex].

Thus the tens digit is 3; the units digit is 3-1 = 2; and the number itself is 32.

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Option 3 and 4. The two options that shows the correct representation of the inequality are:

–3(2x – 5) < 5(2 – x)

We have to open up the brackets by multiplying the sides

= -6x + 15 < 10 - 5x

Hence the  third option is certified to be correct.

Next this inequality has to be shown on a number line.

To do this we have to solve the inequality completely

From -6x + 15 < 10 - 5x

we have to take like terms

-6x+5x < 10 - 15

-x < -5

x<5

The sign of inequality has to be reversed given that the coefficient of x was negative.

Hence x>5. The number line would start from the right and it would move towards the right

From the solution here, we can see that the two correct options are

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The system of equation have one solution.

x² + y² = 25

x² - 6 = 0

x² = 6

x = √6

Therefore, let's substitute the value of x in equation (i)

x² + y² = 25

(√6)² + y² = 25

y² = 25 - 6

y² = 19

hence,

y = √19

Therefore, the system of equation have one solution.

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1 gallon (gal) = 128 fluid ounce (fl oz)

1 hour (hr) = 60 minutes (min)

Convert 1 fl oz/min to gal/hr.

[tex]\dfrac{1\,\rm fl.oz}{1\,\rm min} \times \dfrac{1\,\rm gal}{128\,\rm fl.oz} \times \dfrac{60\,\rm min}{1\,\rm hr} = \dfrac{60}{128} \dfrac{\rm gal}{\rm hr} \approx \boxed{0.47 \dfrac{\rm gal}{\rm hr}}[/tex]

Answer:

Slope=14.000/2.000=7.000

x-intercept = 300/-7 = -42.85714

 y-intercept = 300/1 = 300.00000

Step-by-step explanation:

A scenario that would best model the graph on Holly, her home, and school is:

As Holly was heading to school, she felt uneasy and had to wait for 10 mins to catch her breath.

After doing so, she then continued to school which was 6 miles from her home. When she got there, she went to the nurse's office.

She waited in school for 15 minutes and was then told to go home to rest and recuperate. She then made the journey back home in a car and arrived in 10 minutes.

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The true statement about this information is that: A. It is both a relation and a function.

A function can be defined as a mathematical expression which can be used to define and represent the relationship that exist between two or more variables in a population.

In this context, we can infer and logically deduce that the true statement about this information collected by Jen is that it's both a relation and a function because it indicates a relationship between two variables.

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Answer:

It is both a relation and a function.

Step-by-step explanation:

Answer:

The answer is C. U=3x and V=2y^3

Step-by-step explanation:

3x*3x=9x^2

2y^3*-2y^3=-4y^6

Other variables cancel each other out