What is the slant height of the pyramid to the nearest tenth?

A.) 13.9 mm

B.) 15.5 mm

C.) 12.5 mm

D.) 19.0 mm

[tex]2(a+b)=p\qquad\text{divide both sides by 2}\\\\a+b=\dfrac{p}{2}\qquad\text{subtract a from both sides}\\\\\boxed{b=\dfrac{p}{2}-a}\\\\or\\\\2(a+b)=p\qquad\text{use distributive property}\\\\2a+2b=p\qquad\text{subtract 2a from both sides}\\\\2b=p-2a\qquad\text{divide both sides by 2}\\\\\boxed{b=\dfrac{p-2a}{2}}[/tex]

[tex]3rs-5cr-15cs+25c^2=r(3s-5c)-5c(3s-5c)\\\\=(3s-5c)(r-5c)\\\\Answer:\ \boxed{3rs-5cr-15cs+25c^2=(3s-5c)(r-5c)}[/tex]

Answer:

55 + 14 sqrt(6)

Step-by-step explanation:

(7+√6)(7+√6)

We can figure out this problem by FOILing

First : 7*7 = 49

Outer: 7* sqrt(6) = 7 sqrt(6)

Inner:  7* sqrt(6) = 7 sqrt(6)

Last: sqrt(6) * sqrt(6) = 6

Add these together

49+ 7 sqrt(6)+ 7 sqrt(6)+6

55 + 14 sqrt(6)

Answer:

97/100

Step-by-step explanation:

9/10 = 90/100

90/100 + 7/100 = 97/100

M and O are congruent

N, M and O are similar

M and N are similar because the sides of M are proportional to sides of N:

[tex]\dfrac{2}{4}=\dfrac{1}{2}[/tex]

Two figures are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

20/50 = 2/5 = 0.40 which is found in the dot plot given. Since this value is in the dot plot, this means that it is possible to obtain this value with a random simulation.

Answer: Yes, the sample proportion 20/50 falls within the margin of error.

Answer

20/50 = 2/5 = 0.40

Ok.

Answer:

Nancy is 6 years old and Stan is 11 years old now.

Step-by-step explanation:

Let the present age of Stan be x.

Then age of Nancy = y

x - y = 5

Last year she was twice as young as he was

Age of Nancy last year = y-1

Age of Stan last year = x-1

2 × (y-1)= x-1

2y -2 = 5 + y -1

y = 6

x = y + 5 = 6 + 5 = 11

Nancy is 6 years old and Stan is 11 years old now.

Answer:

D

Step-by-step explanation: 1/3 x 3 = 1/9 same with 2/3

Answer:

B is the one here as well

Answer:

-6, -6, & -6

Step-by-step explanation:

-6(-6)(-6) = -216

-6 + (-6) + (-6) = -18

Answer:

x=12

Step-by-step explanation:

Solve for x:

(3 (x/6 + 16))/4 = (3 ((4 + 3/8) x - 21))/7

Put 4 + 3/8 over the common denominator 8. 4 + 3/8 = (8×4)/8 + 3/8:

(3 (x/6 + 16))/4 = (3 ((8×4)/8 + 3/8 x - 21))/7

8×4 = 32:

(3 (x/6 + 16))/4 = (3 ((32/8 + 3/8) x - 21))/7

32/8 + 3/8 = (32 + 3)/8:

(3 (x/6 + 16))/4 = (3 ((32 + 3)/8 x - 21))/7

32 + 3 = 35:

(3 (x/6 + 16))/4 = (3 ((35 x)/8 - 21))/7

Put each term in x/6 + 16 over the common denominator 6: x/6 + 16 = x/6 + 96/6:

3/4 x/6 + 96/6 = (3 ((35 x)/8 - 21))/7

x/6 + 96/6 = (x + 96)/6:

3/4 (x + 96)/6 = (3 ((35 x)/8 - 21))/7

3/6 = 3/(3×2) = 1/2:

(x + 96)/(2×4) = (3 ((35 x)/8 - 21))/7

Put each term in (35 x)/8 - 21 over the common denominator 8: (35 x)/8 - 21 = (35 x)/8 - 168/8:

(x + 96)/(2×4) = 3/7 (35 x)/8 - 168/8

(35 x)/8 - 168/8 = (35 x - 168)/8:

(x + 96)/(2×4) = 3/7 (35 x - 168)/8

2×4 = 8:

(x + 96)/8 = (3 (35 x - 168))/(8×7)

8×7 = 56:

(x + 96)/8 = (3 (35 x - 168))/56

Multiply both sides by 56:

(56 (x + 96))/8 = (56×3 (35 x - 168))/56

56/8 = (8×7)/8 = 7:

7 (x + 96) = (56×3 (35 x - 168))/56

(56×3 (35 x - 168))/56 = 56/56×3 (35 x - 168) = 3 (35 x - 168):

7 (x + 96) = 3 (35 x - 168)

Expand out terms of the left hand side:

7 x + 672 = 3 (35 x - 168)

Expand out terms of the right hand side:

7 x + 672 = 105 x - 504

Subtract 105 x from both sides:

(7 x - 105 x) + 672 = (105 x - 105 x) - 504

7 x - 105 x = -98 x:

-98 x + 672 = (105 x - 105 x) - 504

105 x - 105 x = 0:

672 - 98 x = -504

Subtract 672 from both sides:

(672 - 672) - 98 x = -672 - 504

672 - 672 = 0:

-98 x = -672 - 504

-672 - 504 = -1176:

-98 x = -1176

Divide both sides of -98 x = -1176 by -98:

(-98 x)/(-98) = (-1176)/(-98)

(-98)/(-98) = 1:

x = (-1176)/(-98)

The gcd of -1176 and -98 is -98, so (-1176)/(-98) = (-98×12)/(-98×1) = (-98)/(-98)×12 = 12:

Answer:  x = 12

Answer:

40

Step-by-step explanation:

5+1 3/8n=60

Subtract 5

1 3/8n=55

11/8n=55

8/11(55/1)  

n=40

Answer:

2/25 chance for both.

Step-by-step explanation:

There is a total of 25 students = 25 as my denominator.

11 + 12 = 23.

25 -23 = 2

Therefore my numerator is 2.

----> 2/25

Answer:

42 miles

Step-by-step explanation:

She drove 35% of 120 miles.

To find a percent of a number, multiply the percent by  the number.

35% of 120 miles =

= 35% * 120 miles

= 0.35 * 120

= 42

Answer:

y=8x+4 has a steeper slope. itś slope is 8 while y=6x-4 has a slope of 6.

Step-by-step explanation:

The graph of the equation  y=8x+4 is steeper because it has a higher slope.

The equation of a line is given as

y = mx + c

Where m is the slope and c is the y-intercept.

The given equations are y=8x+4 and  y=6x-4. Compare the equations with the standard form to find the slope.

y = mx + c

y=8x+4

y=6x-4.

The slope of the first equation is 8 and the other equation is 6.

Therefore, the graph of the equation  y=8x+4 is steeper because it has a higher slope.

More about the equation of line link is given below.

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Answer: B - 3/40

Step-by-step explanation: in order to find their difference, set up their common denominators equally, resulting in them having 5/40 and 8/40. subtract and you will get 3/40 as your final answer.

Answer:

Consider the following cases

Case 1: In n first gear,  an automobile's engine runs about three times as fast as the drive shaft.

So, if Speed of Engine = 1,850 r.p.m

Then Speed of Drive Shaft  [tex]=\frac{1850}{3}=616.67[/tex] r.p.m

Case 2 : In second gear, the engine does not have to run as fast; usually it runs about 1.6 times faster than the drive shaft.

 So, if Speed of Engine = 1,850 r.p.m

Then Speed of Drive Shaft  [tex]=\frac{1850}{1.6}=1156.25[/tex] r.p.m

Case 3:  Finally, in third, or high gear, the engine runs at the same speed as the drive shaft.

So, if Speed of Engine = 1,850 r.p.m

Then Speed of Drive Shaft is also equal to 1,850 r.p.m

[tex]\mathbb{ANSWER:}[/tex]

Refer to the attachment to view the answer.

Answer:

(1,3)

Step-by-step explanation:

From the graph, determine the coordinates of the point of intersection of the two.  They are x=1 and y=3:  (1,3)

This is the last of the four given possible answers.

Answer:

(1,3)

Step-by-step explanation:

The solution to a system of equations that is graphed is where the two graphs intersect.  The two lines intersection at 1, 3.  We can check this by putting them into the equation

y = 3x

3 = 3*1

True

y =x+2

3 = 1+2

3=3

True

This is the solution to the system of equations

Answer:

15a=b

Step-by-step explanation:

so you have a=b/15.. we want b to be on its own.. you have to use inverse operations to get by by itself.  so, we need to get rid of the 15.. it is being divided, so therefore multiply both sides by 15..

15a=b

Answer:

0.707 to nearest thousandth

Step-by-step explanation:

People who go at least 2 times a month = 219 + 180 + 96

= 495

So the required probability = 495 / 700

= 0.707 14

Answer:

y-2 = 2/3(x-8)

Step-by-step explanation:

We have the line 6x-9y = -7

Let's rewrite it in the form y=mx+b

6x-9y = -7

Subtract 6x from each side

6x-6x-9y = -7 -6x

-9y = -6x-7

Divide by -9

-9y/-9 = -6x/-9 -7/-9

y = 2/3 x + 7/9

The slope is 2/3

If the line is parallel, the slope will be the same so the slope will be 2/3

We have the slope and a point (8,2) on the new line, so we can use the point slope form of a line

y-y1 = m(x-x1)

y-2 = 2/3(x-8)

Yes, the equation 7x-4y=0 represents a direct variation with the constant of variation being 7/4.

The equation 7x-4y=0 does represent a direct variation. To see this, we can rearrange the equation into the form y = kx, which is the general form for direct variation. Solving for y, we divide both sides by -4 to get:

y = (7/4)x

Here, the coefficient of x, which is 7/4, is the constant of variation. Thus, in the given equation, the constant of variation is 7/4, meaning for every unit increase in x, y increases by 7/4 units. This proportional relationship where y varies directly as x, with a constant ratio of 7/4, confirms it's a direct variation.

The maximum number of trees the student can plant per row is 10. This is found by identifying the greatest common divisor of the total number of apple trees and peach trees he has which is 10.

To solve this problem, you need to find the greatest common divisor of 50 (the number of apple trees) and 30 (the number of peach trees). The greatest common divisor is the highest number that can divide both numbers without a remainder.

Both 50 and 30 can be divided by 10 without any remainder, but they can't be divided evenly by any number higher than 10. Therefore, 10 is the greatest common divisor of 50 and 30.

In this context, being able to divide the number of trees evenly means that you can plant the same number of each type of tree in each row. So, given the total numbers of apple and peach trees, the maximum number of trees you can plant per row is 10.

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To determine the maximum number of trees that can be planted per row when planting 50 apple trees and 30 peach trees with uniformity, calculate the greatest common divisor (GCD) of the two quantities, which is 10. This means the maximum number of trees per row that can evenly divide both 50 and 30 is 10 trees per row.

The question involves finding the maximum number of trees that can be planted per row when planting 50 apple trees and 30 peach trees with the same number and type of trees per row. To find this number, we need to determine the greatest common divisor (GCD) of the two quantities, which will tell us the largest number of trees that can uniformly fit into each row for both types of trees.

First, list the factors of 50 (1, 2, 5, 10, 25, 50) and the factors of 30 (1, 2, 3, 5, 6, 10, 15, 30).

Find the largest factor that appears in both lists. In this case, it is 10.

The maximum number of trees per row that can evenly divide both 50 and 30 is 10 trees per row.

Therefore, you can plant up to 10 trees per row for a neat and organized orchard layout.

Answer:

y = 5x + 25

Explaination:

To get the equation of a line, first get the slope of the line.

Slope = (change in y)/(change in x)

          = (60-30)/(7-1)

          = 30/6

            = 5

Now use one point in the line (4,45) and a general point (x,y).

Slope = (change in y)/(change in x)

    5 = (y - 45)/(x - 4)

    5(x - 4) = (y - 45)

  5x - 20 = y - 45

y = 5x -20 + 45

Answer:

y = [tex]\frac{1}{2}[/tex] x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y-intercept )

here m = [tex]\frac{1}{2}[/tex] and b = 4, hence

y = [tex]\frac{1}{2}[/tex] x + 4 ← equation of line

Answer:

where is the question?

Answer:

X=28

Step-by-step explanation:

3x-8=2x+20. So x=28

Answer:

4/113

Step-by-step explanation:

1/28 for non leap years and 1/29 for leap years

However if u put those together it would be 4/113 overall

This is because every 4 years there are 113 days in February and 4 of those days will be the 28th.

Final answer:

The probability of someone being born on February 28th given that they were born in February is 1/28, assuming a non-leap year scenario.

Explanation:

The student is asking about the probability of being born on February 28th, given that they were born in February. Given that February usually has 28 days, except for leap years when it has 29 days, to find this probability, we consider a non-leap year scenario.

The total number of possible birth dates in February, in a non-leap year, is 28. Since being born on any given day in February is equally likely, the probability of being born on February 28th is simply 1 divided by the number of days in February.

Therefore, the probability is:
P(born on Feb. 28) = 1/28

Answer:

4/5x + y = -2

Step-by-step explanation:

Answer:

4x+5y=-10

Step-by-step explanation:

We have to arrange [tex]y=\frac{-4}{5}x-2[/tex] in the standard form using integers.

The standard form of the equation of a line is represented as Ax+By=C, where A,B,C are integers and A≥0.

Therefore, multiplying the given equation by 5 on the both sides, we have,

[tex]5y=-4x-10[/tex]

On rearranging,we get,

[tex]4x+5y=-10[/tex]

Which is the required standard form using integers.

Answer:

x=2  and x=3

Step-by-step explanation:

(3x-6)(-x+3)=0

We can use the zero product property to solve for x

3x-6 = 0 and -x+3 =0

3x-6 = 0

Add 6 to each side

3x-6+6 = 6

3x=6

Divide by 3

3x/3 =6/3

x =2

-x+3 =0

Add x to each side

-x+x+3 = +x

3 =x