How does f(x) = 9x change over the interval from x = 4 to x = 5?

Answer:

x = 10

Step-by-step explanation:

We are given a diagram with lines AB and CD intersected by a line EH.

Given that the lines AB and CD are parallel, we are to find the value of x.

Since the lines are parallel so the angles are interior alternate angles and are equal to each other.

Therefore, we can write it as:

[tex] ( 3 x + 15 ) = ( 5 x - 5 )  [/tex]

[tex] 5 x - 3 x = 15 + 5 [/tex]

[tex] 2 x = 20 [/tex]

[tex] x = \frac { 20 } { 2 } [/tex]

x = 10

Answer:

The value of x = 10

Step-by-step explanation:

From the figure we can see that, AB║CD

And HE is a traversal. Two angles are given. These angles area alternate interior angles which are equal

To find the value of x

Two alternate interior angles are

(3x + 15)° and (5x - 5)°

(3x + 15) = (5x - 5)

5x - 3x 15 + 5

2x = 20

x = 20/2 = 10

Therefore the value of x = 10

Answer:

D

Step-by-step explanation:

She will have 0.09 lbs of GORP left over.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

Total of 19.5 lbs of GORP

She needs to divide them into 2.75 lb

So,

=19.5/2.75

=7.09

Here, 0.09 means She will have 0.09 lbs of GORP left over.

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Answer:

When x=20, y =9.

Step-by-step explanation:

Rewrite the equation into slope-intercept form.

4y=-4+2x

Divide by 4 to isolate y

y=-1+(2/4)x

y=(1/2)x -1

Then plug in 20 for x.

y=(1/2)(20)-1

y=10-1

y=9

Answer:

Step-by-step explanation:

There are several words that might well fit this sentence:

"supplemental"

"entrepreneural"

"earned"

Answer:

1/3 0r 33%

Step-by-step explanation:

P(roll greater than 4) is 1/3.

If we take the ratio of number of favourable outcomes to the number of all possible outcomes of an event, then this ratio is called probability.

We roll a fair 6 sided die.

All the possible outcomes are (S) = {1, 2, 3, 4, 5, 6}

Number of all possible outcomes = n(S) = 6

Numbers greater than 4 are {5, 6}

So, n(roll greater than 4) = 2

∴ P(roll greater than 4) = n(roll greater than 4)/n(S)

                                        = 2/6 = 1/3

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Answer:

The rule or the sequence is : an = -3n - 1

Step-by-step explanation:

* Lets look to the terms of the sequence

 -4 , -7 , -10 , -13

- The difference between each two consecutive terms is:

 -7 - -4 = -3 , -10 - -7 = -3 . -13 - -10 = -3

∴ It is an arithmetic sequence

* because we add a constant value to each term to find the second term

- That means a1 = a , a2 = a + d , a3 = a + 2d , ............

* The rule of any term of the arithmetic sequence is;

- an = a + (n - 1) d , where a is the first term , d is the constant

 difference and n is the position of the number in the sequence

∵ a = -4 and d = -3

∴ The rule of any term in this sequence is:

* an = -4 + (n - 1)(-3)

* Lets simplify the formula

∴ an = -4 + -3n + 3

∴ an = -3n - 1

* The rule or the sequence is : an = -3n - 1

Answer:

its B on edge 2020

Step-by-step explanation:

Answer:

Part 7) Option C. The approximate perimeter of the patio is [tex]54\ ft[/tex]

Part 8) Option G. [tex]3\ floats[/tex]

Part 9) [tex]150.72\ minutes[/tex]

Step-by-step explanation:

Part 7) we know that

The perimeter of the figure is equal to the circumference of the larger half circle plus the circumference of the smaller half circle plus two times the length of 8 ft

step 1

Find the circumference of the larger half circle

The circumference of the larger half circle is

[tex]C=\pi r[/tex]

we have

[tex]r=8+2=10\ ft[/tex]

substitute

[tex]C=\pi(10)[/tex]

[tex]C=10\pi\ ft[/tex]

step 2

Find the circumference of the smaller half circle

The circumference of the smaller half circle is

[tex]C=\pi r[/tex]

we have

[tex]r=2\ ft[/tex]

substitute

[tex]C=\pi(2)[/tex]

[tex]C=2\pi\ ft[/tex]

step 3

Find the perimeter of the figure

[tex]10\pi\ ft+2\pi\ ft+2(8)\ ft=(12\pi+16)\ ft[/tex]

assume [tex]\pi=3.14[/tex]

so

[tex](12(3.14)+16)=53.68=54\ ft[/tex]

Part 8) we know tat

The area of a circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]A=28.26\ ft^{2}[/tex]

assume [tex]\pi=3.14[/tex]

substitute the values and solve for r

[tex]28.26=(3.14)r^{2}[/tex]

[tex]r^{2}=28.26/(3.14)[/tex]

[tex]r^{2}=9[/tex]

[tex]r=3\ ft[/tex]

Find the diameter D

[tex]D=2r=2(3)=6\ ft[/tex]

Divide the width of the pool by the diameter of the floats

so

[tex]\frac{18}{6}=3\ floats[/tex]

Part 9)

step 1

Find the circumference of one coaster

The circumference of circle is

[tex]C=2\pi r[/tex]

we have

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

assume [tex]\pi=3.14[/tex]

substitute

[tex]C=2(3.14)(1.5)=9.42\ in[/tex]

step 2

Find the circumference of 48 coasters

so

[tex]48(9.42)=452.16\ in[/tex]

step 3

we know that

The laser cut woods at the rate of 3 inches per minute

By proportion find how many minutes will it take to cut out 48 coasters

[tex]\frac{3}{1}\frac{inches}{minute} =\frac{452.16}{x}\frac{inches}{minutes}\\ \\x=452.16/3\\ \\x=150.72\ minutes[/tex]

Answer:

Part A) For the number of hours less than 5 hours it make more sense to rent a scooter from Rosie's

Part B) For the number of hours greater than 5 hours it make more sense to rent a scooter from Sam's

Part C) Yes, for the number of hours equal to 5 the cost of Sam'scooters is equal to the cost of Rosie's scooters

Part D) The cost is $90

Step-by-step explanation:

Let

x-------> the number of hours (independent variable)

y-----> the total cost of rent scooters (dependent variable)

we know that

Sam's scooters

[tex]y=8x+30[/tex]    

Rosie's scooters

[tex]y=10x+20[/tex]

using a graphing tool

see the attached figure

A. when does it make more sense to rent a scooter from Rosie's? How do you know?

For the number of hours less than 5 hours it make more sense to rent a scooter from Rosie's  (see the attached figure) because the cost in less than Sam' scooters

B. when does it make more sense to rent a scooter from Sam's? How do you know?

For the number of hours greater than 5 hours it make more sense to rent a scooter from Sam's  (see the attached figure) because the cost in less than Rosie' scooters

C. Is there ever a time where it wouldn't matter which store to choose?

Yes, for the number of hours equal to 5 the cost of Sam'scooters is equal to the cost of Rosie's scooters. The cost is $70 (see the graph)

D. If you were renting a scooter from Rosie's, how much would you pay if you were planning on renting for 7 hours?

Rosie's scooters

[tex]y=10x+20[/tex]

For x=7 hours

substitute

[tex]y=10(7)+20=90[/tex]

The cost is $90

When renting a scooter, the independent variable is the number of hours rented, and the dependent variable is the total cost. Renting from Rosie's is cheaper after 10 hours, while renting from Sam's is cheaper for fewer than 10 hours. There is no cost difference at exactly 10 hours, and renting from Rosie's for 7 hours would cost $90.

To solve systems of equations word problems involving rental costs for scooters from two different companies, we must first establish a system of equations to represent each company's pricing structure. For Sam's Scooters, the equation is y = 30 + 8x, where y is the total cost to rent a scooter and x is the number of hours the scooter is rented. For Rosie's, the equation is y = 20 + 10x.

The independent variable (x) is the number of hours the scooter is rented, and the dependent variable (y) is the total cost of the rental.

Questions:

Answer:

56°

Step-by-step explanation:

Because the two lines are parallel, the corresponding angles are equal. The two corresponding ∠s are ∠A and ∠B. ∠A=∠B

∠A=4x

∠B=2(x+14)

4x = 2 (x+14)

the right side requires the distributive property

a) 4x = 2x+28

2x = 28

x = 14

b) now plug in x for both ∠s to find ∠A and ∠B

∠A = 4x = 4(14) = 56°

∠B = 2(x+14) = 2(14+14) = 2(28) = 56°

I just did both angles to show that they are equal and it is a way to check your work

Answer:

the answer is a

Step-by-step explanation:

Answer:

Many expressions would satisfy this set. One example would be y = 7x + 2

Step-by-step explanation:

To find this, give x a random coefficient, for this purpose, we'll use 7.

y = 7x + c

Now plug in and solve to get the constant.

-33 = 7(-5) + c

-33 = -35 + c

2 = c

Now model the equation.

y = 7x + 2

Answer:

Option A. [tex]192\ m^{2}[/tex]

Step-by-step explanation:

we know that

The lateral area of the square pyramid is equal to the area of its four triangular faces

so

[tex]LA=4[\frac{1}{2}(12)(8)]=192\ m^{2}[/tex]

Answer:

Step-by-step explanation:

4

Answer:

Answer is B on e2020. (4)

Step-by-step explanation:

Divide the cost to get into the park by the amount you make per day:

46.75 / 4.75 = 9.84

Round up to 10 days.

The answer is B. 10

Answer:

x = 40

Step-by-step explanation:

Solve the equation using inverse operations.

5 = 1/5x - 3          Add 3 to both sides

8 = 1/5x               Multiply by 5 on both sides

40 = x

Answer:

(5,7)

Step-by-step explanation:

x + 2 = 2x - 3

2x - x = 5

x = 5

When X = 5, Y= 7

Best regards

Answer: The answer is (3,0).

Step-by-step explanation: We know this because we have to move the positive 5, 2 to the left. Then we have to do the -5 up 5. After you do that you get (3,0). Hope this helps!

Point P is translated by 2 units to the left and 5 units to the upward direction. Then the coordinate of the point P' is (3, 0).

It simply means that the point is being shifted from [tex]\rm (x_1, y_1)[/tex] to [tex]\rm (x_2, y_2)[/tex] in a cartesian coordinate.

Given

The point P' is the image of point P (5,-5) under a translation by 2 units to the left and 5 units up.

Then the position of the point P' will be.

Point P is translated by 2  to the left is the negative x-axis. Then coordinate of point P will be

[tex](5 - 2, -5)\\\\(3, -5)[/tex]

Point P is translated by 5  to the upward is the positive y-axis. Then coordinate of point P will be

[tex](3, -5 + 5)\\\\(3, 0)[/tex]

Then, the coordinate of the point P' is (3, 0).

More about the translation of the point link is given below.

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Answer: OPTION C

Step-by-step explanation:

To solve the exercise you must descompose the number 648 into its prime factors, as you can see below:

[tex]648=2*2*2*3*3*3*3[/tex]

You can rewrite the above as following:

[tex]648=2^3*3^4[/tex]

Then:

[tex]\sqrt{648}=\sqrt{2^3*3^4}[/tex]

Therefore, as you can see, the value of  a and b are the following:

[tex]a=3,b=4[/tex]

Answer:

The correct answer option is C. a=3, b=4.

Step-by-step explanation:

We are given the following expression and we need to determine whether which of the values of [tex]a[/tex] and [tex]b[/tex] should be used to make the equation true:

[tex] \sqrt { 648 } = \sqrt { 2 ^ a \times 3 ^ b } [/tex]

A. a=3, b=2:

[tex] \sqrt { 2 ^ 3 \times 3 ^ 2 } = \sqrt { 72 } [/tex]

B.  a=2, b=3:

[tex] \sqrt { 2 ^ 2 \times 3 ^ 3 } = \sqrt { 108 } [/tex]

C. a=3, b=4 :

[tex] \sqrt { 2 ^ 3 \times 3 ^ 4 } = \sqrt { 648 } [/tex]

D. a=4, b=3:

[tex] \sqrt { 2 ^ 4 \times 3 ^ 3 } = \sqrt { 432 } [/tex]

Therefore, the correct answer option is C. a=3, b=4.

The cost of purchasing team shirts from Reggie's Tees and City Printing is the same for 5 shirts. This is determined by setting up an algebraic equation and solving for the number of shirts where both costs are equal.

The student has posed a problem involving algebra where they are comparing the costs of two options for purchasing team shirts.

To find out at which point the cost of buying team shirts from Reggie's Tees with a $40 setup fee and $4 per shirt is equal to the cost of buying from City Printing with a $20 setup fee and $8 per shirt, we can set up the following algebraic equation:

Let x represent the number of shirts.

Equation for Reggie's Tees: 40 (setup fee) + 4x (price per shirt)

Equation for City Printing: 20 (setup fee) + 8x (price per shirt)

To find the number of shirts for which the costs are the same, we set the two equations equal to each other:

40 + 4x = 20 + 8x

Solving further:

4x - 8x = 20 - 40

-4x = -20

x = (-20)/(-4)

x = 5

So, the cost for both options is the same when the team orders 5 shirts.

Answer:

[tex]\large\boxed{-2x(6x^4-7x^2+x-5)=-12x^5+14x^3-2x^2+10x}[/tex]

Step-by-step explanation:

[tex]-2x(6x^4-7x^2+x-5)\qquad\text{use the distributive property}\\\\=(-2x)(6x^4)+(-2x)(-7x^2)+(-2x)(x)+(-2x)(-5)\\\\=-12x^5+14x^3-2x^2+10x[/tex]

QUESTION 1

Recall the mnemonics; SOH

[tex]\sin L =\frac{Opposite}{Hypotenuse}[/tex]

[tex]\sin L =\frac{12}{13}[/tex]

QUESTION 2

Recall the mnemonics; CAH

[tex]\cos L =\frac{Adjacent}{Hypotenuse}[/tex]

[tex]\sin L =\frac{5}{13}[/tex]

QUESTION 3

Recall the mnemonics; TOA

[tex]\tan M =\frac{Opposite}{Adjacent}[/tex]

[tex]\tan M =\frac{5}{12}[/tex]

QUESTION 4

[tex]\sin M =\frac{Opposite}{Hypotenuse}[/tex]

[tex]\sin M =\frac{5}{13}[/tex]

QUESTION 5

a) From the Pythagoras Theorem,

[tex]AC^2+AB^2=BC^2[/tex]

[tex]AC^2+4^2=5^2[/tex]

[tex]AC^2+16=25[/tex]

[tex]AC^2=25-16[/tex]

[tex]AC^2=9[/tex]

[tex]AC=\sqrt{9}[/tex]

[tex]AC=3yd[/tex]

b) Using the cosine ratio,

[tex]\cos (m\angle B)=\frac{4}{5}[/tex]

Take the inverse cosine of both sides;

[tex] m\angle B=\cos ^{-1}(\frac{4}{5})[/tex]

[tex] m\angle B=36.86[/tex]

[tex]\therefore m\angle B=36.9\degree[/tex] to the nearest tenth.

c) [tex]m\angle B +m\angle C=90\degree[/tex]

[tex]\Rightarrow 36.9\degree +m\angle C=90\degree[/tex]

[tex]\Rightarrow m\angle C=90\degree-36.9\degree[/tex]

[tex]\Rightarrow m\angle C=53.1\degree[/tex]

QUESTION 6

a)  using the sine ratio,

[tex]\sin(51\degree)=\frac{DE}{18}[/tex]

[tex]DE=18\sin(51\degree)[/tex]

[tex]DE=13.99[/tex]

[tex]\therefore DE=14.0yd[/tex] to the nearest tenth.

b) Using the cosine ratio,

[tex]\cos (51\degree)=\frac{EF}{18}[/tex]

[tex]EF=18\cos (51\degree)[/tex]

[tex]EF=11.3yd[/tex] to the nearest tenth.

c) [tex]m\angle D+ m\angle F=90\degree[/tex]

[tex]\Rightarrow m\angle D + 51\degree=90\degree[/tex]

[tex]\Rightarrow m\angle D=90\degree-51\degree[/tex]

[tex]\Rightarrow m\angle D=39\degree[/tex]

QUESTION 7

a) Using the Pythagoras Theorem;

[tex]lG^2+GH^2=lH^2[/tex]

[tex]l15^2+GH^2=17^2[/tex]

[tex]225+GH^2=289[/tex]

[tex]GH^2=289-225[/tex]

[tex]GH^2=64[/tex]

[tex]GH=\sqrt{64}[/tex]

[tex]GH=8km[/tex]

b) Using the sine ratio,

[tex]\sin(m\angle H)=\frac{15}{17}[/tex]

[tex]m\angle H=\sin^{-1}(\frac{15}{17})[/tex]

[tex]m\angle H=61.9\degree[/tex]

c) [tex]m\angle l + m\angle H=90\degree[/tex]

[tex]m\angle l +61.9\degree=90\degree[/tex]

[tex]m\angle l =90\degree-61.9\degree [/tex]

[tex]m\angle l =28.1\degree [/tex]

QUESTION 8

We plot the points as shown in the diagram.

QUESTION 9

From the diagram, the side lengths XY and YZ can be obtained by counting the boxes. Each box is 1 unit.

This implies that;

XY =3 units

YZ=5 units.

We use Pythagoras Theorem, to obtain XZ.

This implies that;

[tex]XZ^2=XY^2+YZ^2[/tex]

[tex]XZ^2=3^2+5^2[/tex]

[tex]XZ^2=9+25[/tex]

[tex]XZ^2=34[/tex]

[tex]XZ=\sqrt{34}[/tex] units

QUESTION 10.

a) Using the tangent ratio;

[tex]\tan(m\angle X)=\frac{5}{3}[/tex]

[tex]m\angle X=\tan^[-1}(\frac{5}{3})[/tex]

[tex]m\angle X=59.0\degree[/tex]

b) [tex]m\angle Z+m\angle X=90\degree[/tex]

[tex]m\angle Z+59.0\degree=90\degree[/tex]

[tex]m\angle Z=90\degree-59.0\degree[/tex]

[tex]m\angle Z=31.0\degree[/tex]

QUESTION 11

a) Triangle BCD is shown in the attachment.

The length of side DC=|3-2|=1 unit

The length of side DB=|4-3|=1 unit

Using Pythagoras Theorem;

[tex]BC^2=DC^2+DB^2[/tex]

[tex]BC^2=1^2+1^2[/tex]

[tex]BC^2=1+1[/tex]

[tex]BC^2=2[/tex]

[tex]BC=\sqrt{2}[/tex]

b) DB is perpendicular to DC, therefore m<D=90 degrees.

The length of DB is equal the length of DC.

This implies that;

m<C=m<B=45 degrees.

QUESTION 12

[tex]\sin 30\degree=\frac{1}{2}[/tex]

QUESTION 13

[tex]\cos 30\degree=\frac{\sqrt{3} }{2}[/tex]

QUESTION 14

[tex]\tan 30\degree =\frac{\sqrt{3} }{3}[/tex]

QUESTION 15

[tex]\tan 45\degree =1[/tex]

QUESTION 16

[tex]\cos 45\degree =\frac{\sqrt{2} }{2}[/tex]

QUESTION 17

[tex]\tan 45\degree =1[/tex]

Answer:

Step-by-step explanation:

Given :  -(3x+y)+2(x-4y).

To find : which expression is the simplest form .

Solution : We have given

 -(3x+y)+2(x-4y).

Remove parenthesis

-3x -y + 2x -8y .

Combine like terms

-3x + 2x -y - 8y .

-x -9y.

x=2

sorry for the bad handwriting btw.

Answer:

The solution for the absolute value equation is  [tex]x=-1\quad \mathrm{or}\quad \:x=2[/tex].

Step-by-step explanation:

Consider the provided absolute value equation.  

[tex]|2x-1|=3[/tex]

[tex]\mathrm{If}\:|u|\:=\:a,\:a>0\:\mathrm{then}\:u\:=\:a\:\quad \mathrm{or}\quad \:u\:=\:-a[/tex]

By using the above rule.

[tex]2x-1=-3\quad \mathrm{or}\quad \:2x-1=3[/tex]

[tex]2x=-3+1\quad \mathrm{or}\quad \:2x=3+1[/tex]

[tex]2x=-2\quad \mathrm{or}\quad \:2x=4[/tex]

[tex]x=-1\quad \mathrm{or}\quad \:x=2[/tex]

Hence the combine solution is [tex]x=-1\quad \mathrm{or}\quad \:x=2[/tex]

Answer:

[tex]m\angle BAD=73^o[/tex]

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Find the value of x

Let

O ----> the center of the circle

we know that

Triangle BOC≅Triangle COD

[tex]m\angle BOC=arc\ BC[/tex] ----> by central angle

[tex]m\angle COD=arc\ CD[/tex] ----> by central angle

[tex]m\angle BOC=m\angle COD[/tex]

therefore

[tex]arc\ BC=arc\ CD[/tex]

substitute the given values

[tex](9x-53)^o=(2x+45)^o[/tex]

solve for x

[tex]9x-2x=45+53\\7x=98\\x=14[/tex]

step 2

Find the measure of angle BAD

we know that

The inscribed angle is half that of the arc it comprises.

so

[tex]m\angle BAD=\frac{1}{2} [arc\ BC+arc\ CD][/tex]

[tex]arc\ BC=9(14)-53=73^o[/tex]

[tex]arc\ CD=2(14)+45=73^o[/tex]

substitute

[tex]m\angle BAD=\frac{1}{2} [73^o+73^o]=73^o[/tex]

The measure of mBAD is 73⁰

Given the following expression

mBC = (9x-53) and mCD = (2x + 45)

From the given diagram, both arcs are equal, hence

9x - 53 = 2x +45

7x = 98

x = 14

Get the measure of arc BC

arcBC = 9x - 53

arcBC = 9(14)-53

arcBC = 73 degrees

The measure of mBAD = 1/2(73+73) = 73 degrees

Hence the measure of mBAD is 73⁰

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Answer: The required value of x is 12 units.

Step-by-step explanation:  Given that the figure A is a scale image of figure B.

We are to find the value of x.

Since figure A is the scale image of figure B, so both the figures are similar to each other.

Also, the corresponding sides of the similar figures are proportional, so we get

[tex]\dfrac{30}{25}=\dfrac{x}{10}\\\\\\\Rightarrow\dfrac{6}{5}=\dfrac{x}{10}\\\\\\\Rightarrow x=5x=60\\\\\Rightarrow x=\dfrac{60}{5}\\\\\Rightarrow x=12.[/tex]

Thus, the required value of x is 12 units.

Answer:

x=12 units

Step-by-step explanation:

Answer:

(-1, 5)

Step-by-step explanation:

First, you move it to the right of y-axis from -4 to -1

Then, you move it to the down of x-axis from 8 to 5

so the answer was (-1, 5).

Answer: -9,-1

Step-by-step explanation:

Subtract 5 from x coordinate

Subtract 3 from y coordinate

Cross out out comes that should happen. The others are evidence based, the one you cross out was theory based

Answer:

B and D

Step-by-step explanation:

A difference of squares has the form a² - b²

4p² - 9 = (2p)² - 3² ← is a difference of squares

q² - 36 = q² - 6² ← is a difference of squares

Answer:

answer:

4p²-9 and q²-36 as it is in the form of x²-y²