Self-Check
Practice Exercise 4

Answer:

First car:  35 gallons

Second car: 15 gallons

Step-by-step explanation:

Assuming [tex] x [/tex] to be the gas consumed by 1st car and [tex] 50 - x [/tex] to be the gas consumed by 2nd car.

We know that:

Distance traveled = fuel efficiency × gas consumed

[tex]20x+35(50-x)=1225[/tex]

[tex]20x+1750-35x=1225[/tex]

[tex]35x-20x=1750-1225[/tex]

[tex]15x=525[/tex]

[tex]x=35[/tex]

So [tex]50 - x = 50-35=15 [/tex]

Therefore, first car consumed 35 gallons while second car consumed 15 gallons.

Answer:

First car: 35 gallons

Second car: 15 gallons

Step-by-step explanation:

Set up a system of equations.Let be "x" the number of gallons consumed by the first car and "y" the number of gallons consumed by the second car.

Then:

[tex]\left \{ {{x+y=50} \atop {20x+35y=1,225}} \right.[/tex]

Applying the Elimination method, multiply the first equation by -20, then  add both equations and solve for "y":

[tex]\left \{ {{-20x-20y=1,000} \atop {20x+35y=1,225}} \right. \\.......................\\15y=225\\y=15[/tex]

Substitute this value into the first equation and solve for "x":

[tex]x+15=50\\x=35[/tex]

Answer:

25%

1/3

100%

5/4

2.5

Step-by-step explanation:

Convert all the values into decimals and order them from least to greatest.

Answer:

f(5) = 17

Step-by-step explanation:

f(x) = 3x+2

Let x =5

f(5) = 3(5) +2

f(5) = 15+2

f(5) = 17

By applying the principle of inclusion-exclusion and considering students in History, we find that 3 students are in neither Math Competition classes nor Geometry.

To determine how many students are in neither Math Competition classes nor Geometry, we can use the principle of inclusion-exclusion. We have 50 students in total, with 25 in Math Competition classes and 29 in Geometry. However, since 19 students are in both classes, they were counted twice when we added the students in Math Competition classes and Geometry together. Thus, we subtract the number of students in both to avoid double-counting:
(25 + 29 - 19) = 35 students are in at least one of the math classes. Additionally, 12 students are in a History class and no math classes. Therefore, the number of students in at least one class (math or history) is 35 + 12 = 47.

Finally, to find the number of students in neither class, we subtract the number of students in at least one class from the total number of students:
50 - 47 = 3 students are in neither Math Competition classes nor Geometry.

Answer:

Option A)724 square centimeters

Step-by-step explanation:

we know that

The surface of the prism is equal to the area of its six rectangular faces

The surface area is equal to

[tex]SA=2B+PH[/tex]

where

B is the area of the base

P is the perimeter of the base

H is the height of the prism

we have

[tex]L=12\ cm[/tex]

[tex]W=11\ cm[/tex]

[tex]H=10\ cm[/tex]

Find the area of the base B

[tex]B=LW[/tex]

[tex]B=(12)(11)=132\ cm^{2}[/tex]

Find the perimeter of the base P

[tex]P=2(L+W)[/tex]

[tex]P=2(12+11)=46\ cm[/tex]

Find the surface area SA

[tex]SA=2(132)+(46)(10)=724\ cm^{2}[/tex]

Answer:

[tex]n=5[/tex]

Step-by-step explanation:

We have the following expression [tex]\frac{2}{8} = \frac{n}{20}[/tex] and we must solve for variable n.

To solve the equation multiply by 20 on both sides of the equality and you will get the following

[tex]20*\frac{2}{8} = 20*\frac{n}{20}[/tex]

[tex]\frac{20*2}{8} = \frac{20n}{20}[/tex]

[tex]\frac{40}{8} = n[/tex]

[tex]n= \frac{40}{8}[/tex]

Finally we have that:

[tex]n=5[/tex]

Answer:

n=5

Step-by-step explanation:

2/8 = n/20

Using cross products

2 * 20 = 8*n

40 = 8n

Divide each side by 8

40/8 = 8n/8

5 =n

Answer:

-1,3,5,9,13

Step-by-step explanation:

2(-3)+5=-6+5=-1

2(-1)+5=-2+5=3

2(0)+5=0+5=5

2(2)+5=4+5=9

2(4)+5=8+5=13

Answer:

$20(.85)(1.06) = $18.02

Answer:

D) (the fourth one)

Step-by-step explanation:

The function will never go below 0 since the absolute of a negative number is a positive number, so C is out of the question.

The equation of an absolute function is f(x) = a|x-h|+k

h is the offset on the x axis, and the equation of this function is |x-(1)|, so that means the function is shifted one to the right, making it D.

Answer:

15 inches

Step-by-step explanation:

The formula for the circumference of a circle of radius R is 2*Pi*R.  Similarly, the volume of a ball enclosed by a sphere of radius R is (4/3)*Pi*R3. And the formula for the surface area of a sphere of radius R is 4*Pi*R2. And, you can check that the latter is the derivative of the former with respect to R.

Answer:

15 inches

Step-by-step explanation:

SA=4PIR^

900PI=4PIR^2

R^2=900PI/4PI

R^2=225

R=SQRT225

R=15 IN.

PROOF:

900PI=4PI^15^2

900PI=4PI*225

900PI=900PI

Answer:

Step-by-step explanation:

Angles (2x + 14)° and (x + 7)° are complementary angles.

If two angles are complementary, then they add up to 90°.

Therefore we have the equation:

(2x + 14) + (x + 7) = 90      combine like terms

(2x + x) + (14 + 7) = 90

3x + 21 = 90          subtract 21 from both sides

3x = 69          divide both sides by 3

x = 23

Answer:

xy(x+8)(x^2-6y)

Step-by-step explanation:

To long to explain, but you can just google it if you just need the answer

Answer:

xy(x^2 - 6y)(x + 8 ) .

Step-by-step explanation:

The Greatest Common Factor of this expression is:

 xy so dividing by this:

= xy(x^3 + 8x^2  - 6xy - 48y).

Factoring the expression in the parentheses by grouping:

= xy [ x^2( x + 8) - 6y (x + 8)]

= xy(x^2 - 6y)(x + 8 )  (answer).

Answer: 4/5

Step-by-step explanation:

1. you need to know the formula which is m = y2-y1/x2-x1

2. you plug in the numbers which would be 9-5/3-(-2)

3. you get your answer as 4/5

4. the answer is 4/5

Answer:

○ b ⅘

Step-by-step explanation:

-y₁ + y₂\-x₁ + x₂ = m

[tex] \frac{4}{5} = \frac{ -5 + 9}{2 + 3}[/tex]

I am joyous to assist you anytime.

Answer:

9

Step-by-step explanation:

(5)+4=9

The missing output value is:

                             9

The function in terms of the variable x, where x represents  the input value is given by the formula:

                [tex]F(x)=x+4[/tex]

where F(x) is the output value corresponding to the input value x.

We are asked to find the missing output value i.e. we are asked to find the value of F(x) at x=5.

i.e. we have:

[tex]F(5)=5+4\\\\i.e.\\\\F(5)=9[/tex]

          Hence, the missing output value is: 9

Answer:

40 deg

Step-by-step explanation:

This is just m anglex=.5(58+22)=.5(80)=40

Answer:

x = 40

Step-by-step explanation:

When 2 chords intersect inside a circle then the measure of the angle formed is half the sum of the arcs intercepted by the angle and it's vertical angle, so

x = 0.5(58 + 22)° = 0.5 × 80° = 40°

Final answer:

Jonathan's weekly income is determined by a linear function M(h) = 9.5h + 25, with the domain being 0 ≤ h ≤ 20 to reflect his work hour limitations. A sketch of this function would show a linear increase from an initial allowance of $25, rising by $9.50 for each hour worked up to 20 hours.

Explanation:

Jonathan makes a weekly allowance of $25 and earns $9.50 per hour at his job, with a maximum work limit of 20 hours per week.

a) Function for Jonathan's weekly earnings:

The function M(h) = 9.5h + 25 represents the amount of money Jonathan makes each week, where h is the number of hours he works.  

b) Domain of the function:

The domain of this function, considering Jonathan's work hour limitation, is 0 ≤ h ≤ 20. This range is because Jonathan cannot work more than 20 hours a week due to his age restrictions.

c) Sketch of the graph:

The graph would start at the point (0, 25), which represents Jonathan's weekly allowance without any worked hours. Then, it would rise linearly at a slope of $9.50 for each additional hour worked, up to the point (20, 215), which represents the maximum amount Jonathan can earn by working 20 hours plus his weekly allowance. Note: The actual graph is not displayed here but can easily be sketched using the described points and slope.

Answer:

B. [tex]x=3,\ y=20,\ z=-14[/tex]

Step-by-step explanation:

Consider the system of three equations:

[tex]\left\{\begin{array}{l}2x+2y+3z=4\\5x+3y+5z=5\\3x+4y+6z=5\end{array}\right.[/tex]

Multiply the first equation by 5, the second equation by 2 and subtract them:

[tex]\left\{\begin{array}{r}2x+2y+3z=4\\4y+5z=10\\3x+4y+6z=5\end{array}\right.[/tex]

Multiply the first equation by 3, the second equation by 2 and subtract them:

[tex]\left\{\begin{array}{r}2x+2y+3z=4\\4y+5z=10\\-2y-3z=2\end{array}\right.[/tex]

Multiply the third equation by 2 and add the second and the third equations:

[tex]\left\{\begin{array}{r}2x+2y+3z=4\\4y+5z=10\\-z=14\end{array}\right.[/tex]

Fro mthe third equation

[tex]z=-14[/tex]

Substitute it into the second equation:

[tex]4y+5\cdot (-14)=10\\ \\4y=10+70\\ \\ 4y=80\\ \\y=20[/tex]

Substitute y=20 and z=-14 into the first equation:

[tex]2x+2\cdot 20+3\cdot (-14)=4\\ \\2x+40-42=4\\ \\2x-2=4\\ \\2x=6\\ \\x=3[/tex]

The solution is

[tex]x=3,\ y=20,\ z=-14[/tex]

Answer:

Pie: Pie is a dessert that has pastry from top to bottom and has filling in the middle.

Best type of pie: In my opinion: Key Lime Pie

Pie Emoji: No clue, you'll have to email Apple or Samsung (or whatever your phone provider is) and ask them to update or change the emoji.

Step-by-step explanation:

These are very important questions

Answer:

x= 2.2​

Step-by-step explanation:

-0.45х + 0.33 = -0.66

Subtract .33 from each side

-0.45х + 0.33-.33 = -0.66-.33

-.45x = -.99

Divide each side by -.45

-.45x/.-45 = -.99/.-45

x =2.2

Answer:

296 inches

Step-by-step explanation:

The perimeter is the sum of sides of a rectangle

As the length is in feet while the width is in inches, a unit conversion must take place

As 1  feet  equals to 12 inches

9 feet would be equal to 12*9=108 inches

The perimeter of a rectangle= 2(width)(length)

= 2(108)(40)

=296 inches

Answer:

The difference in volume is that the prism's volume is 3 times greater than the pyramid's volume.

Without seeing the graph, I can't tell what the slope is, but depending on the way the graph is drawn, the slope should be 1/3 or 3.

Answer:

The answer is 1/3

The ratio of time on vacation to time working as a fraction in lowest terms when working 24 weeks and rewarded with 3 days of vacation is 1/56.

If you spent 24 weeks working on a project for your job and were rewarded with 3 days of vacation, the ratio of time on vacation to time working as a fraction in lowest terms can be calculated as follows:

Answer:

Their point of intersection will always be on the line y = x.

Step-by-step explanation:

We have a function f(x) and its inverse is the function f⁻¹(x).

The domain and range of a function replaces each other for the inverse of that function.

So if f(x) and f⁻¹(x) are inverse of each other

and f(a) = b

then a = f⁻¹(b)

Another example to make it clear is that

f(5) = 25

f⁻¹(25) = 5

The function and its inverse will intersect each other at the point where f(x) = f⁻¹(x) which is only possible when a = b.

Hence, a function and its inverse will always intersect at a point on the line x=y.

Answer: [tex]\triangle{ZXY}\sim\triangle{QRS}[/tex]

Step-by-step explanation:

in the given picture , we have two triangles ΔXYZ and ΔRSQ, in which

[tex]\overline{XY}=14=4\times3.5=4\times\overline{RS}[/tex]

[tex]\overline{YZ}=16=4\times4=4\times\overline{SQ}[/tex]

[tex]\overline{ZX}=12=4\times3=4\times\overline{SR}[/tex]

i.e. [tex]\dfrac{XY}{RS}=\dfrac{YZ}{SQ}=\dfrac{ZX}{QR}=\dfrac{4}{1}[/tex]

By SSS-similarity postulate, we get

[tex]\triangle{ZXY}\sim\triangle{QRS}[/tex]

SSS-similarity postulate says that if the lengths of the corresponding sides of two triangles are proportional, then the triangles must be similar

Answer:

9 rows, each having 3 tomato plants, 5 bean plants, and 6 carrot plants.

Step-by-step explanation:

This requires the GCF, or the greatest common factor. This means that you need the largest whole number that divides evenly into each of the numbers (27, 45, and 54).

27, 45, and 54 can all be divided by 9 to get a whole number.

27/9=3

45/9=5

54/9=6

This means that in each row, there will be 3 tomato plants, 5 bean plants, and 6 carrot plants.

Answer:

53

Step-by-step explanation:

Let's make some equations.

The number is two-digit, so let's make it [tex]xy[/tex]

Also, the two digits add up to 8, so [tex]x+y=8[/tex]

Now the value of [tex]xy=10x+y[/tex]

and the value of [tex]yx=10y+x[/tex]

Since we know that when we reverse the digits the number is less than the resulting number by 18, we can formulate an equation.

[tex]10y+x=10x+y+18[/tex]

Solve this equation.

[tex]9y-9x=18[/tex]

[tex]9(y-x)=18[/tex]

[tex]y-x=2[/tex]

Now let's use the equation we made earlier.

Change [tex]x+y=8[/tex] into [tex]y=8-x[/tex]

Solve the system of equations.

[tex]y-x=2[/tex]

[tex]y=8-x[/tex]

[tex]8-x-x=2[/tex]

[tex]8-2x=2[/tex]

[tex]-2x=-6[/tex]

[tex]x=3[/tex]

[tex]y-3=2[/tex]

[tex]y=5[/tex]

So the original number is 53.

Answer:

C

Step-by-step explanation:

Answer:

Simplified to -281250

Step-by-step explanation:

Answer:

A = 10.9 cm^2

Step-by-step explanation:

If a circle has a radius of 13 and a sector defined by a 7.4 degree arc, the area, in cms, of the sector is 10.9 cm^2 or 10 cm^2 to the nearest tenth.

The other endpoint V of the line segment is found by doubling the coordinates of the midpoint M and subtracting the coordinates of the known endpoint W. Applying this method, the coordinates of V are (10, 10).

In Mathematics, the midpoint formula allows us to find the midpoint coordinates of a line segment. Given that M(9, 8) is the midpoint and W(8, 6) is one endpoint, you can find the coordinates of the other endpoint V using the formula:
V = (2M - W).

So, simply double the coordinates of the midpoint and subtract the coordinates of the known endpoint. This determines the coordinates of the other endpoint. For the given question, we apply this to get:

Vx = 2*9 - 8 = 10,
Vy = 2*8 - 6 = 10.

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