is it always true that trapezoids height is the distance between the 2 bases?

Answers

Answer 1

No. One side can be higher than the other side, therefore, a trapezoids height isn't always the distance between the 2 bases.

Related Questions

Express 0.0037 as a power of 10.

Answers

it is 3.7 x [tex] 10^{-3} [/tex]

Final answer:

To express 0.0037 as a power of 10, we move the decimal point 3 places to the right, resulting in 3.7 × 10⁻³.

Explanation:

To express 0.0037 as a power of 10, we need to count the number of places we have to move the decimal point to get a number between 1 and 10. In this case, we have to move the decimal point 3 places to the right, so the power of 10 is -3.

0.0037 = 3.7 × 10-3

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Express answer in exact form.

A regular hexagon with sides of 3" is inscribed in a circle. Find the area of a segment formed by a side of the hexagon and the circle.

(Hint: remember Corollary 1--the area of an equilateral triangle is 1/4 s2 √3.)

Answers

we know that
the regular hexagon can be divided into 6 equilateral triangles

area of one equilateral triangle=s²*√3/4
for s=3 in
area of one equilateral triangle=9*√3/4 in²

area of a circle=pi*r²

in this problem the radius is equal to the side of a regular hexagon
r=3 in
area of the circle=pi*3²-----> 9*pi in²
we divide that area into 6 equal parts------> 9*pi/6----> 3*pi/2 in²

the area of a segment formed by a side of the hexagon and the circle is equal to 1/6 of the area of the circle minus the area of 1 equilateral triangle
so
[ (3/2)*pi in²-(9/4)*√3 in²]

the answer is
[ (3/2)*pi in²-(9/4)*√3 in²]

1. What is the median of the following set of numbers?
48.4, 47, 43, 47, 43.6, 41.6, 45, 51.4, 38.6

Hint: Order the numbers from least to greatest first!

A. 48.4 B. 43.6 C. 45
2. Each of the five math teachers are comparing the number of students in their homeroom classes. The number of boys and girls in each teachers’ classes are recorded in the table below.

Hint: Mean is the average.

Which statement best describes the means of the two sets of data?

A. The mean number of girls in 7 times greater than the mean numbers of boys in the homeroom classes.

B. The mean number of girls is the same as the mean number of bboys in the homeroom classes.

C. The mean number of girls is 7 more than the mean number of boys in the homeroom classes.

Answers

1. 38.6, 41.6, 43, 43.6, 45, (47), 47, 48.4, 51.4
The middle number (median) is 47.

2.The table is not displayed so will explain how you can solve the problem.
→ Mean is the average. Find the sum and divide by the quantity of numbers you added to find the sum.

If you still need help with #2, upload the image of the table or type in the data.

Answer:b

Step-by-step explanation:divided look around the chart

Two triangles have side lengths 3, 4, 5 and 6, _____, 10, respectively. The triangles are similar to each other.
9
7
8
6.6

Answers

Hello!

You have to find out happened between triangles

6 / 3 = 2
10 / 5 = 2

They multiplied the first triangle by 2 to get the second

Apply this to find the missing side

4 * 2 = 8

The answer is 8

Hope this helps!

Answer:

The correct option is: 8

Step-by-step explanation:

Suppose, the missing side length in second triangle is [tex]x[/tex]

So, the side lengths of first triangle: [tex]3, 4, 5[/tex]

and the side lengths of second triangle: [tex]6, x, 10[/tex]

As two triangles are similar, that means their corresponding side lengths will be proportional.

So,

[tex]\frac{3}{6}=\frac{4}{x}\\ \\ 3x= 4*6\\ \\ 3x= 24\\ \\ x=\frac{24}{3}=8[/tex]

So, the missing side length in second triangle is 8.

plz help
(4+3.2)×[(9−2)+2.5]

Answers

The first step for solving this expression is to add the numbers in the first parenthesis.
7.2((9 - 2) + 2.5)
Subtract the numbers in the parenthesis found inside the other parenthesis.
7.2(7 + 2.5)
Add the numbers in the parenthesis.
7.2(9.5)
Now multiply the two numbers together to get your final answer.
68.4
This means the expression (4 + 3.2) × ((9 − 2) + 2.5)is equal to 68.4.
Let me know if you have any further questions.
:)

What is -1 3/5 x -2/3 as a mixed number?

Answers

Convert -1 3/5 to -8/5. Then multiply as follows:

-8 -2
--- * ----- = 16/15 (an improper fraction), or 1 1/15 (a mixed number)
5 3

1 1/15
1 3/5=8/5x2/3=16/15=1 1/15

PLEASE HELP 20 POINTS

Answers

period would be the distance between 2 peaks

looking at the graph there is a peak on x= 1 and then a peak on x= 4
4-1 = 3 so the peak is 3

the amplitude is the midpoint between the highest point and lowest point
on the graph
the high point is y=1 and the low point is y = -2
1 + -3 = 3 spaces, midpoint = 3 / 2 = 1.5 so the amplitude = 1.5

the answer is the first one.

Answer:

Step-by-step explanation:

i put a awnser and that person hacked me lol

The local weather person has been accurate in her predictions within 2 degrees temperature forecast 80% of the time. Find the probability that she is accurate...
a) exactly 3 out of the next 5 days
b) at least 4 of the next 5 days

Answers

A) 0.2048
B) 0.7373

To find the probability that she is correct exactly 3 days, we have
[tex]_5C_3(0.8)^3(1-0.8)^{5-3} \\ \\\frac{5!}{3!2!}(0.8)^3(0.2)^2=0.2048[/tex]

To find the probability that she is right at least 4 of the 5 days, we find the probability she is right 4 days, the probability she is right 5 days, and add them together:
[tex]_5C_4(0.8)^4(1-0.8)^{5-4}+_5C_5(0.8)^5(1-0.8)^{5-5} \\ \\\frac{5!}{4!1!}(0.8)^4(0.2)^1+\frac{5!}{5!0!}(0.8)^5(0.2)^0 \\ \\5(0.8)^4(0.2)+0.8^5=0.4096+0.32768=0.73728\approx0.7373[/tex]

in the box below, enter the value that missing from the table.

Answers

it will take 5 hours for you to get home

For this case we have the following equation:
d = v * t
Where,
d: distance
v: speed
t: time
Clearing the time we have:
t = d / v
Rewriting:
t = d * (1 / v)
We look for the value of d:
For t = 1, v = 75 we have:
1 = d * (1/75)
d = 75
Then, v = 15 we have:
t = 75 * (1/15)
t = 5 hours
Answer:
The value that is missing from the table is:
t = 5 hours

Find 2 numbers that have... a product of 49 and a sum of 14

Answers

Hey there! Two numbers is 7 and 7! (Product=multiply) 7x7=49 and (Sum=add) 7+7=14! Hope this helped! Have a nice day!

Consider the equation x^2 + 12x + c = 0. If c = -28, list the steps to solve the equation by completing the square, and give the solution or solutions.

Answers

x^2+12x-28
(x-2)(x+14)

Solve for x
x-2=0
x=2

x+14=0
x=-14

The solutions of the equation x² + 12x - 28 = 0 are x = 2 or x = -14.

What is quadratic equation?

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

To solve the equation x² + 12x + c = 0, where c = -28, by completing the square.

Substitute c = -28 into the equation to get x² + 12x - 28 = 0.

x² + 12x = 28

Complete the square by adding the square of half the coefficient of x to both sides of the equation:

x² + 12x + (12/2)² = 28 + (12/2)²

x² + 12x + 36 = 64

(x + 6)² = 64

Take the square root of both sides of the equation.

x + 6 = ±8

x=8-6=2

x=-8-6=-14

Hence, the solutions of the equation x² + 12x - 28 = 0 are x = 2 or x = -14.

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f(x) = cos(x)
f'(x) = -sin(x)
f'(π/2) = -sin(π/2)
f'(π/2) = -1

My answer to this question is A. -1, but I am posting it here because several students got B. +1 as their answer. Can anyone confirm the answer as A?

Answers

Your working out is correct. The appropriate answer is ...
A. -1

For confirmation, check a graph of cos(x) at π/2. It has negative slope at that point.

Your answer would be -1.

What is the vertex form, f(x) = a(x − h)2 + k, for a parabola that passes through the point (4, −3) and has (5, 2) as its vertex. What is the standard form of the equation?

Answers

[tex](h;\ k)\ -\ \text{the coordinates of the vertex}[/tex]

[tex]\text{therefore we have:}\ f(x)=a(x-5)^2+2[/tex]

[tex]\text{a parabola that passes through the point (4, −3)}[/tex]

[tex]\text{substitute the coordinates of the point (4;-3) to the equation:}[/tex]

[tex](4;-3)\to x=4;\ y=-3\\\\-3=a(4-5)^2+2\\\\-3=a(-1)^2+2\\\\-3=a+2\ \ \ |-2\\\\a=-5[/tex]

[tex]f(x)=-5(x-5)^2+2=-5(x^2-2\cdot x\cdot5+5^2)+2=-5(x^2-10x+25)+2\\\\=-5x^2+50x-125+2=-5x^2+50x-123[/tex]

Answer:

y = x² - 10x + 27

Step-by-step explanation:

Solve the equation. Check for extraneous solutions

please help!!!

Answers

!z!=a→z=a or z=-a; z=4x+3, a=9+2x

!4x+3!=9+2x
1) 4x+3=9+2x
Solving for x:
4x+3-3-2x=9+2x-3-2x
2x=6
2x/2=6/2
x=3

Checking for extraneous solution:
!4x+3!=9+2x
x=3→!4(3)+3!=9+2(3)
!12+3!=9+6
!15!=15
15=15 Ok, then x=3 is not a extraneous solution

2) 4x+3=-(9+2x)
Solving for x:
4x+3=-9-2x
4x+3-3+2x=-9-2x-3+2x
6x=-12
6x/6=-12/6
x=-2

Checking for extraneous solution:
!4x+3!=9+2x
x=-2→!4(-2)+3!=9+2(-2)
!-8+3!=9-4
!-5!=5
5=5 Ok, then x=-2 is not a extraneous solution

Answer:
x = -2 or 3

A jet plane is descending at a rate of 200 feet per second from an altitude of 36000 feet let x represent the number of seconds of descent and y represent the jet plane’s altitude in feet.

Which expression represents this situation?

A. y = 200x - 36000

B. y = 200x + 36000

C. y = -200x - 36000

D. y = -200x + 36000

Answers

Rate of descend = 200 ft/sec

In x second, the plane will have descended by 200*x ft = 200x ft
The altitude of the plane, y after x seconds will be 36000 - 200x. That is,

y= 36000-200x = -200x + 36000.

Therefore, the correct expression representing this situation is D.

Jane's plane will be modeled using linear equation given by:
y=ax+b
where:
a=slope=rate
b=y-intercept or initial valuegiven:
from the question
a=200 ft per second
b=36000 ft
thus the expression representing the situation will be:
y=200x+36000
where x is time in seconds
thus the answer is:
B. y = 200x + 36000

Jack Watkins earns a base salary of $1500 a month, plus a 4% commission on the sales he makes. What is his gross pay of his sales for the month are $8000.

A. 1520
B. 1532
C. 1700
D. 1820

Answers

Jack Watkins earns a base salary of $1500 a month, plus a 4% commission on the sales he makes. What is his gross pay of his sales for the month are $8000.
solution:
Gross pay=(salary)+(commissions)
base salary=$1500
commission=4%
monthly sales=$8000
commissions earned in cash
=4/100×8000
=$320

thus
Gross salary=320+1500=$1820

Circle P is tangent to the x-axis and the y-axis. If the coordinates of the center are (r, r), find the slope of the line through the origin and the center.

Answers

The origin equals (0, 0) and the center of the circle equal (r, r). We can use the slope formula:
y_2 - y_1/x_2 - x_1
Fill in:
0 - r/0 - r
r/r
1
The answer to this problem is 1.

The value of slope of the line through the origin and the center is,

⇒ Slope = 1

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Circle P is tangent to the x-axis and the y-axis.

And, the coordinates of the center are (r, r),

Now, The value of slope of the line through the (0, 0) and the center (r, r) is,

⇒ Slope = (r - 0) / (r - 0)

⇒ Slope = r/r

⇒ Slope = 1

Thus, The value of slope of the line through the origin and the center is,

⇒ Slope = 1

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There are 158 fourth grade studnets and 139 fifth grade students going on a field trip. There needs to be one caperone for every 8 kids. Explain how to find the number of caperones needed for the trip.

Answers

To find the number of chaperones, you could find the total number of students that are going on the field trip and then break this number into groups of 8.

(158 + 139)/8
297/8 = 37.125

You will need a minimum of 38 chaperones for the 297 students. If there is any remainder(decimal) you will need an extra chaperone so the groups do not exceed 8.

The tank shown is a cylinder with diameter equal to 4 feet and height equal to 12 feet. the tank holds 1130 gallons of rainwater when full. how many gallons of water are in the tank when the depth of the water is 9 feet?

Answers

we know that
volume of the tank=1130 gal

step 1
find the volume of the tank with deep 9 ft
volume of the tank with deep 9 ft=pi*r²*h
r=4/2-----> 2 ft
h=9 ft
volume of the tank with deep 9 ft=pi*2²*9-----> 113.04 ft³

step 2
convert to gal
1 ft³------------------> 7.48052 gal
113.04 ft³--------> x
x=113.04*7.48052-----> x=845.60 gal

the answer is
845.60 gal

alternative method

if the volume of the tank is 1130 gal for ----------> a height of 12 ft
X volume-----------------------------------> 9 ft
x=9*1130/12-----> 847.5 gal

FACTORIZE PLEASE, A LOT OF POINTS

64x^(3)-48x^(2)+12xy^(2)-y^(3)

Answers

=> 64x³ - 48x²y + 12xy² - y³

=> (4x)³ - 3(4x)²(y) + 3(4x)(y)² - y³

We know the formula: (a - b)³ = a³ - 3a²b + 3ab² - b³

By applying this formula above, we will get

=> (4x - y)³. (Ans)

Hope this helps!

or you can just put it in a smaller form by saying (4x - y)³

help please

Sammy is planning a trip to Nashville. He knows the hotel costs $125 per night and the round trip flight is $159. He has a budget of $900 to spend on his trip. Which of the following inequalities represents his budget to determine how many nights he can stay in Nashville?

125n + 159 ≥ 900
125n + 159 ≤ 900
159n + 125 ≤ 900
159n + 125 ≥ 900

Answers

The answer would be 125n + 159 is less than or equal to 900

In short, the second option is correct. Hope this helps!

$900 is the cap, the greatest amount Sam can spend. That immediately rules out the 1st and the 3rd choices. Does that help? How much does the hotel cost per night, and which letter represents the # of nights?

Find the value of the lesser root of x 2-8x+7=0

Answers

Hi there! The answer is x = 1

[tex] {x}^{2} - 8x + 7 = 0[/tex]

[tex](x - 7)(x - 1)[/tex]
Rule AB = 0, gives A = 0 or B = 0

[tex]x - 7 = 0 \: \: or \: \: x - 1 = 0 \\ x = 7 \: \: \: \: \: \: \: \: \: or \: \: x = 1[/tex]
Therefore, the smallest of both roots is x = 1.

Which of the following shows that polynomials are closed under subtraction when polynomial 5x − 6 is subtracted from 3x2 − 6x + 2?
3x2 − 11x + 8 may or may not be a polynomial
3x2 − 11x + 8 will be a polynomial
3x2 − x + 4 may or may not be a polynomial
3x2 − x + 4 will be a polynomial

Tip: Every 2 after 3x is an exponent.. so it would be 3x^2

Answers

The answer is 3x2 − 11x + 8 will be a polynomial
Simply because polynomials have solutions. 3x2 − 11x + 8 does have 2 solutions.

Which point best represents the square root of 15?
A. Point A
B. Point B
C. Point C
D. Point D

Answers

The square root of 15 = 3.87
So point B is the answer it’s between 2 and 4

A tunnel is in the shape of a parabola. The maximum height is 16 m and it is 16 m wide at the base, as shown below.

A parabola opening down with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 16 meters and its width from left to right is 16 meters.

What is the vertical clearance 7 m from the edge of the tunnel?

15.4 m
0.3 m
15.7 m
0.6 m

Answers

Vertex at the origin and opening down → y=ax^2
Width: w=16
x=w/2→x=16/2→x=8
x=8, y=-16→y=ax^2→-16=a(8)^2→-16=a(64)→-16/64=a(64)/64→-1/4=a→a=-1/4

y=ax^2→y=-(1/4)x^2

7 m from the edge of the tunnel → x=w/2-7=8 m-7 m→x=1 m
x=1→y=-(1/4)x^2=-(1/4)(1)^2=-(1/4)(1)→y=-1/4

Vertical clearance: 16-1/4=16-0.25→Vertical clearance=15.75 m

Please, see the attached file.

Answer: Third option 15.75 m

the basic formula of a parabola is;

y -k= 4a (x-h)^2

Solving for this, the vertical clearance 7m forom the edge of the tunnel must be

15.7m

Hope this helps! Goodluck!

The table shows the calories burned during exercise.
(picture of the table attached)

Which statement is true?

A)The y-intercept of the function is (15, 75).

B)The rate of change is 15 calories burned per minute.

C)A linear function to model the calories burned, y, as a function of time in minutes, x, is y = 5x.

D)An exponential function to model the calories burned, y, as a function of time in minutes, x, is y = 5x.

Answers

For this case we observe that the function found in the table is a linear function because the exchange rate is constant.
We have then that the slope of the line is:
[tex]m = \frac{y2-y1}{x2-x1} [/tex]
Substituting values:
[tex]m = \frac{150-75}{30-15} m = 5[/tex]
Then, the equation of the line is:
[tex]y = 5x [/tex]
Answer:
C) A linear function to model the burned calories, and, as a function of time in minutes, x, is y = 5x.

Answer: C. A linear function to model the calories burned, y, as a function of time in minutes, x, is y = 5x.

Step-by-step explanation:

On Tuesday, Mrs. Myles assigned 7 more problems than she did on Monday. If she assigned x problems on Monday, write an expression to represent how many problems Mrs. Myles assigned on Tuesday

Answers

Answer:

Number of problems assigned on Tuesday = x+7

Step-by-step explanation:

Number of problems assigned on Monday = x.

Number of problems assigned on Tuesday is 7 more than that assigned on Monday.

Number of problems assigned on Tuesday = x+7. [In Matha we use + sign for more than]

The expression that will represent the number of problems Mrs. Myles assigned on Tuesday is x+7.

Answer: actually it 7 + x the other way around

Step-by-step explanation:

Given: ABCD is a trapezoid, AC ⊥ CD AB = CD, AC=the square root of 75 , AB = 5 Find: AABCD

Answers

In this attached picture according to the conditions of the problem we have an isosceles trapezoid and since we know that legs are equal (AD=BC=5 cm), we have to calculate bases and height in order to find the area. Working with the triangle BCD, we apply Pythagoras theorem and find that CD = [tex] \sqrt{75+25} [/tex] = 10 cm. Since BDC is a right triangle, applying theorem for the area of triangles, we find that [tex] \frac{1}{2} * BF = \frac{1}{2} * 5 * \sqrt{75} [/tex] and BF= [tex] 0.5\sqrt{75} [/tex]. Since ABCD is an isosceles trapezoid, triangles ADE and BFC are congruent with Angle Side Angle theorem. Then, DE=FC and with the help of Pythagoras theorem, DE=FC=2.5 cm. Then, AB=EF=5 cm and the area of the trapezoid is [tex]A= BF * \frac{AB+CD}{2} = 0.5 \sqrt{75} * \frac{5+10}{2} = 18.75 \sqrt{3} cm^{2} [/tex]

The area of the given trapezoid will be [tex]\frac{75}{4} \sqrt{3}[/tex].

It is given that

In trapezoid ABCD

AE ⊥ CD

AC = √75

AD=BC =5

AB =5

In the triangle ADC

From Pythagoras theorem

AC²+AD²=DC²

(√75)² +5² = DC²

DC=10

Let DE=CF=x (Isosceles trapezoid)

What is isosceles Trapezoid?

Trapezoid in which the base angles are equal and therefore the left and right side lengths are also equal.

AB=EF= DC-2x

5 = DC-2x

x=5/2

AE = [tex]\sqrt({5^{2} } -(5/2)^2)\\\\[/tex]

AE = [tex]\sqrt{75} /2[/tex]

So, the area of the trapezoid ABCD = [tex]\frac{1}{2} *(AB+CD)*AE[/tex]

Area of the trapezoid ABCD = [tex]\frac{1}{2} *(5+10)*\frac{\sqrt{75} }{2}[/tex]

Area of the trapezoid ABCD = [tex]\frac{75}{4} \sqrt{3}[/tex]

Therefore, The area of the given trapezoid ABCD will be [tex]\frac{75}{4} \sqrt{3}[/tex].

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Find two number whose sum is 60 such that the sum of the square of one number plus 12 times the other number is a minimum

Answers

60=x^2+12
x^2=48
x=6.93

Hope this helps

What is the length of AC?

Answers

since both triangles have a right-angle, and the two angles at vertex C are also twins, thus both triangles are similar by AA, therefore,

[tex]\bf \cfrac{small}{large}\qquad \cfrac{DE}{BA}=\cfrac{EC}{CA}\implies \cfrac{7}{84}=\cfrac{x}{156-x}\implies 1092-7x=84x \\\\\\ 1092=91x\implies \cfrac{1092}{91}=x\implies 12=x\qquad \quad \qquad \boxed{AC=156-12}[/tex]

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