Benchmark 1 - Big Ideas Math - Grade 7
24. Jack's mother is 44 years old. She is 4 years older than 8 times Jack's age. The
equation 8a + 4 = 44 represents this situation.
How old is Jack?
A. 5
B. 6
c. 9
d.13​

Answer:

3.45

Step-by-step explanation:

if you look at the picture all the steps are provided

GOOD LUCK!!

Answer:

C. Rose oil

Step-by-step explanation:

Which medicinal product is made using animal products?

A. Flu vaccine

O

B. Aspirin

C. Rose oil

O

D. Morphine

SUBM

Answer:A. Flu vaccine

Step-by-step explanation:

Answer:

y = 2

Step-by-step explanation:

Given that y varies inversely as the square of x then the equation relating them is

y = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation

To find k use the condition y = 2 when x = 4

k = yx² = 2 × 4² = 2 × 16 = 32, thus

y = [tex]\frac{32}{x^2}[/tex] ← equation of variation

When x = 4, then

y = [tex]\frac{32}{4^2}[/tex] = [tex]\frac{32}{16}[/tex] = 2

Two expressions connected with equal sign is called equation. a=1/3b is the value for equation 12ab=4.

Two expressions connected with equal sign is called equation.

Given 12ab=4

We need to solve for a

12ab=4

Divide both sides by 12b

a=4/12b

a=1/3b

So  a=1/3b is the value of a for equation 12ab=4

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Answer: 13.92

Step-by-step explanation: 8x4 then 8x2

zero the hero

5x4 then 5x2

lastly add

Answer:

13.92

Step-by-step explanation:

So the explanation is on the picture lol

Answer:

Let 'x' represent the width.

2*48 + 2x = 126

x = 15 in

The maximum width could be 15 inches.

Final answer:

To find the maximum width of the rectangular banner, calculate the total length of bias tape used, subtract it from the available bias tape, and divide the remaining inches by 2. The maximum width of the banner is 15 inches.

Explanation:

Maximum Width Calculation:

Calculate the total length of bias tape used: 48 inches x 2 sides = 96 inches.

Subtract the total length from the available bias tape: 126 - 96 = 30 inches.

Divide the remaining inches by 2 (since there are 2 widths): 30 / 2 = 15 inches.

Answer:

A=lw is a formula for the area. L is length, W is width.

Answer:

B.[tex]x=\frac{4}{15}[/tex]

Step-by-step explanation:

Answer:4/15

Step-by-step explanation:

Answer:

The answer is A

Step-by-step explanation:

y = mx + c

m = 1/2

(2,-3)

y = (1/2)x + c

-3 = (1/2)(2) + c

c = -4

y = (1/2)x - 4

Answer:

Part a) [tex]V(h)=6.25\pi h\ in^3[/tex]

Part b) [tex]V(3)=18.75\pi\ in^3[/tex]  (see the explanation)

Step-by-step explanation:

we know that

The volume of a cylinder is equal to

[tex]V=Bh[/tex]

where

B is the area of the base of cylinder

h is the height of the cylinder

we have that

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

Part a) Write the function, V(h), that represents the volume of the cylinder

we have

[tex]r=5/2=2.5\ in[/tex] ----> the radius is half the diameter

substitute

[tex]B=\pi (2.5)^{2}[/tex]

[tex]B=6.25\pi\ in^2[/tex]

The volume is

[tex]V(h)=6.25\pi h\ in^3[/tex]

Part b) Find V(3) and tell what it represents

V(3) represent the volume of the cylinder with a height of 3 inches

so

For h=3 in

substitute

[tex]V(3)=6.25\pi(3)\ in^3[/tex]

[tex]V(3)=18.75\pi\ in^3[/tex]

Final answer:

The function for the volume of the cylinder with diameter 5 inches is V(h) = π * (2.5 inches)² * h. To find V(3), we calculate the volume with height 3 inches, which represents the physical volume of the cylinder at that height.

Explanation:

To find the volume of the cylinder, V(h), we must use the formula V = πr²h, where r is the radius of the base, and h is the height of the cylinder.

Part A: Given that the diameter is 5 inches, the radius is half of the diameter, so r = 5 / 2 = 2.5 inches. Thus, the function representing the volume is V(h) = π * (2.5 inches)² * h.

Part B: To find V(3), we substitute h with 3 inches into the function: V(3) = π * (2.5 inches)² * 3 inches. This gives us the volume of the cylinder when the height is 3 inches.

Answer:

6 inches

Step-by-step explanation:

the map is equal to

1/2.5 inch / miles

by proportion :

1/2.5 inch/miles  = x inches / 15 miles

x = 15/2.5

x=6 inches!!

I hope this helped you!! :)

Answer:

The order pair is (2,0)

Step-by-step explanation:

On the picture

Answer:

(2,6)

Step-by-step explanation:

The equation of line in point-slope form with slope 5/3 passing through the point (10-5) is:

[tex]y+5 = \frac{5}{3}(x-10)[/tex]

Step-by-step explanation:

Given

Slope = m = 5/3

Point = (x1,y1) = (10, -5)

Point-slope form is:

[tex]y-y_1 = m(x-x_1)[/tex]

As the slope and point is already given, we only have to put the values in the equation to get the equation of required line:

[tex]y-(-5) = \frac{5}{3}(x-10)\\y+5 = \frac{5}{3}(x-10)[/tex]

Hence,

The equation of line in point-slope form with slope 5/3 passing through the point (10-5) is:

[tex]y+5 = \frac{5}{3}(x-10)[/tex]

Keywords: equation of line, point-slope form

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Answer:

Step-by-step explanation:

Let's angle be x and y

Then......

⅓x+12=y......eqn(I)

Since are linear

x+y=180

y=180-x.....eqn(ii)

Substitute the eqns

You get x=126°

From eqn (iii)

You get y=54°

Those are angles

The measures of both angles are 126° and 54°.

Linear pair of angles are the pair of angles formed when two lines are intersected at a point forming on a line.

Sum of the measures of angles of linear pair is supplementary.

Given that,

Two angles are a linear pair.

Let x and y be the measures of two angles.

We have,

y = 1/3 x + 12

Sum of the angles is supplementary.

x + y = 180

x + 1/3 x + 12 = 180

4/3 x = 168

x = 126°

y = 180 - 126 = 54°

Hence the angles are 126° and 54°.

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They sold 25 packets, containing 7 pencils each. So, they sold a total of

[tex]25\cdot 7=175[/tex]

pencils. This means that

[tex]319-175=144[/tex]

pencils were not sold.

Answer:

Graphic A. (Upper left graphic)

Step-by-step explanation:

The roots of the fourth-order polynomial are, that is the values of x which make polynomial equal to zero:

[tex]x = 1[/tex] and [tex]x = -5[/tex]

By comparing the results with each graphic, it is evident that option A corresponds with the function. (Upper left graphic)

To graph the function f(x)=x4+8x3+6x2−40x+25, choose values of x, find corresponding y-values, and plot the points to form a curve.

To graph the function f(x) = x4 + 8x3 + 6x2 - 40x + 25, we need to plot points on a coordinate plane and connect them to form a graph. Here are the steps:

The resulting graph should be a curve that goes through the plotted points.

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Answer:

500

Step-by-step explanation:

100 X 5 = 5 + 5 + 5 + 5...100 times = 100 + 100 + 100 + 100 + 100 = 500

Answer:

500

Step-by-step explanation:

yes

Answer:

Both fireworks  will explode after 1 seconds after firework b launches.

Step-by-step explanation:

Given:

Speed of fire work A= 300 ft/s

Speed of Firework B=240 ft/s

Time before which fire work b is launched =0.25s

To Find:

How many seconds after firework b launches will both fireworks explode=?

Solution:

Let t be the time(seconds) after which both the fireworks explode.

By the time the firework a has been launched, Firework B has been launch 0.25 s, So we can treat them as two separate equation

Firework A= 330(t)

Firework B=240(t)+240(0.25)

Since we need to know the same time after which they explode, we can equate both the equations

330(t) = 240(t)+240(0.25)

300(t)= 240(t)+60

300(t)-240(t)= 60

60(t)=60

[tex]t=\frac{60}{60}[/tex]

t=1

Final answer:

By setting the distance traveled by both fireworks equal, we find that both Firework A and B will explode 1.25 seconds after Firework B is launched.

Explanation:

To solve the problem of when both fireworks will explode, we can use the constant speed equation distance = speed × time. Firework A travels at 300 ft/s, and Firework B travels at 240 ft/s. Firework B is given a 0.25s head start. We need to find the time when they have traveled the same distance.

Let's call the time after Firework B launches when both explode as t. Since Firework A launches 0.25s after B, it will have traveled for t - 0.25s when they explode together. The equations for the distances traveled by both fireworks until that point will be:

Setting these distances equal to each other:

300 (t - 0.25) = 240 t

Solving for t:

300t - 75 = 240t

60t = 75

t = 1.25s

Therefore, both fireworks will explode 1.25 seconds after Firework B launches.

Answer:

The top cable is 115.52 feet long

The bottom cable is 110.86 feet long

Step-by-step explanation:

The ground anchor #2, the tower, ground level, and both cables form a figure made of two right triangles as shown in the figure below

We are required to compute L1 and L2 which are the hypotenuses of both triangles from which we have both legs

We'll apply the Pythagoras's theorem. If a and b are the legs of a right triangle and c its hypotenuse, then

[tex]c^2=a^2+b^2[/tex]

For the bottom ground support cable, a=41, b=103

[tex]L2^2=41^2+103^2[/tex]=110.86\ feet

For the top ground support cable, a=41, b=108

[tex]L1^2=41^2+108^2[/tex]=115.52\ feet

The top cable is 115.52 feet long

The bottom cable is 110.86 feet long

Answer:

B 35%

Step-by-step explanation:

35/100 reduces to .35. To turn this into a percent, multiply it by 100 and add a percent sign. .35 * 100 = 35. 35%

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

Total number of squares = 100

Number of shaded squares = 35

The percentage of shaded squares is 35%

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Total number of squares = 100

Number of shaded squares = 35

The percentage of shaded squares.

= 35/100 x 100

= 35%

Thus,

The percentage of shaded squares is 35%

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The number of bags he can make without having any cookies left over is 4 bags.

48 = 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.

64 = 1, 2, 4, 8, 16, 32 and 64

100 = 1, 2, 4, 5, 10, 20, 25, 50, and 100.

The highest common factor of 48, 64 and 100 is 4

Therefore, the number of bags he can make without having any cookies left over is 4 bags

Each bag has:

chocolates cookies = 48/4

= 12 each

Vanilla cookies = 64/4

= 16 each

Raisin cookies = 100/4

= 25 each

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Diego can make 12 bags without having any cookies left over, ensuring each bag contains an equal number of each flavor.

To determine how many bags Diego can make without having any cookies left over, we need to find the greatest common divisor (GCD) of the quantities of each type of cookie.

Step 1:

Find the GCD of the quantities of each type of cookie:

GCD(48, 64, 100) = 4

Step 2:

Calculate the number of bags Diego can make:

Each bag will contain 4 cookies of each flavor, as determined by the GCD.

For chocolate chip cookies: 48 cookies ÷ 4 cookies/bag = 12 bags

For vanilla cookies: 64 cookies ÷ 4 cookies/bag = 16 bags

For raisin cookies: 100 cookies ÷ 4 cookies/bag = 25 bags

Step 3:

Determine the minimum number of bags Diego can make without any cookies left over:

The minimum number of bags is determined by the smallest number of bags he can make for any type of cookie, which is 12 bags for chocolate chip cookies.

Therefore, Diego can make 12 bags without having any cookies left over.

For this case we must solve the following sum:

    23,234

 +  12,346

---------------

    35,580

We place the addends one below the other so that the units coincide in the same column. We add each digit, we get the expression:

[tex]35,580[/tex]

ANswer:

[tex]35,580[/tex]

First we're going to change the 3 1/4 into an improper fraction.

3 1/4 is the same as 13/4

When dividing fractions, it's the same thing as multiplying by the reciprocal.

What this means is we're going to flip the second fraction.

So the original problem is this:

13/4 divided by 3/1

It now looks like this:

13/4 multiplied by 1/3

Then, simply multiply the top numbers together and then multiply the bottom numbers together.

13*1=13

4*3=12

your answer is 13/12

Answer: Radius

Step-by-step explanation: The radius of a circle is a segment that joins the center of the circle to a point on the circle.

The minute hand on a clock would start in the center and go outwards towards a certain number. However, the minute hand would not go the full length across the clock so it's not the diameter.

The circumference of a circle which is another way of saying the perimeter of the circle is the distance around the circle so it would not be the circumference.

This means that the minute hand would represent the radius of a clock.

The 5 inch length of the minute hand on the clock is actually a radius, not a diameter or circumference. This radius is the distance from the center of the clock face to the tip of the minute hand. The diameter, which would be twice the length of the radius, would be 10 inches, and the circumference of the circle formed by the minute hand's movement would be approximately 31.4 inches.

In this case, the 5 inches refers to the radius of the circle that is created by the minute hand of the clock as it moves around the clock face. This radius is the distance from the center of the clock face to the tip of the minute hand. In general, in any circular motion, the length of the revolving component, like a clock hand, from the center to its tip is called the radius of the circle.

The diameter is simply twice the radius, and in this case if the radius is 5 inches, the diameter would be 10 inches. The circumference of a circle is calculated by the formula 2πr (2 times the value of pi times the radius), hence, in this instance, it would be 10π inches or approximately 31.4 inches.

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Answer:     edmentum 100%

f(x) − g(x)  = 2.5e-0.04x − (1.2 + 0.2x)

= 2.5e-0.04x − 1.2 − 0.2x

Step-by-step explanation:

The algebraic expression resulting from subtracting g(x) from f(x), required to subtract g(x) from f(x) term by term is [tex]2.5e^{(-0.04x)} - 1.2 - 0.2x.[/tex]

Given that the functions from part A are :

[tex]f(x) = 2.5e^{(-0.04x)}\\g(x) = 1.2 + 0.2x[/tex]

To find the expression resulting from subtracting g(x) from f(x), required to subtract g(x) from f(x) term by term.

Step 1: Given two functions

[tex]f(x) = 2.5e^{(-0.04x)}\\g(x) = 1.2 + 0.2x[/tex]

Step 2: find f(x) - g(x),  subtract each term:

[tex]f(x) - g(x) = (2.5e^{(-0.04x)}) - (1.2 + 0.2x)[/tex]

Simplifying further, combine like terms:

[tex]f(x) - g(x) = 2.5e^{(-0.04x) }- 1.2 - 0.2x[/tex]

Therefore, the algebraic expression resulting from f(x) - g(x) is [tex]2.5e^{(-0.04x)} - 1.2 - 0.2x.[/tex]

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Answer:

Your answer is C. ( - infinity , 2]

Step-by-step explanation:

Because it is, and I found the answer right next to an image I was searching up. Coincidences, am I right?

Answer:

38 Weeks

Step-by-step explanation:

1999$ x .05% = 99.95 Down Payment

Remaining Balance = 1899.05

1899.05$ / 50$ = 37.98100

It would approximately take a total of 38 weeks to pay it off!

Answer: 38 weeks

Step-by-step explanation:

$1999 * 0.05 = $99.95

1999 - 99.95 = 1899.05

1899.05/50 = 37.981

38 weeks

Answer:

The result is 10.42 kilometers, or 10,420 meters or 1'042,000 centimeters.

Step-by-step explanation:

1. Let's review the information given to us for solving the question:

8 kilometers plus 2,300 meters plus 12,000 centimeters

2. Let's do the conversions to find the result either in kilometers, meters or even centimeters.

A. In kilometers:

8 kilometers

2,300 meters = 2.3 kilometers

12,000 centimeters = 120 meters = 0.12 kilometers

10.42 kilometers

B. In meters

8 kilometers = 8,000 meters

2,300 meters

12,000 centimeters = 120 meters

10,420 meters

C. In centimeters

8 kilometers = 8,000 meters = 800,000 centimeters

2,300 meters = 230,000 centimeters

12,000 centimeters

1'042,000 centimeters

The final sum is 10,420 meters.

To solve the mathematical problem of adding different units of measurement, we first need to convert everything to the same unit. In this case, let's convert all measurements to meters (m).

Now, add these values together:

8000 m + 2300 m + 120 m = 10,420 meters

Answer:

Part 1) [tex]PQ=10\ units[/tex]

Part 2) [tex]PR=7\ units[/tex]

Step-by-step explanation:

The correct question is

The triangles MNO and PQR are congruent. (MNO≅PQR)

Find the lengths of PQ and PR.

we know that

If two figures are congruent, then its corresponding sides are congruent

In this problem

MN and PQ are corresponding sides

MO and PR are corresponding sides

NO and QR are corresponding sides

therefore

MN≅PQ

MO≅PR

NO≅QR

step 1

Find the value  of y

we have

[tex]MN = 6 +2y\\ PQ = 3y + 4[/tex]

equate the equations

[tex]3y + 4=6 +2y[/tex]

solve for y

[tex]3y-2y=6-4[/tex]

[tex]y=2[/tex]

step 2

Find the length of PQ

[tex]PQ = 3y + 4[/tex]

substitute the value of y

[tex]PQ = 3(2) + 4=10\ units[/tex]

step 3

Find the value  of x

we have

[tex]MO = 2x + 1\\PR = 10 - x[/tex]

equate the equations

[tex]2x+1=10-x[/tex]

solve for x

[tex]2x+x=10-1[/tex]

[tex]3x=9[/tex]

[tex]x=3[/tex]

step 4

Find the length of PR

[tex]PR = 10 - x[/tex]

substitute the value of x

[tex]PR = 10-3=7\ units[/tex]