Answer:
x = 11
BC = 23
AD = 29
EF = 26
Step-by-step explanation:
Given:
Trapezoid ABCD, having,
median = EF = 4x - 18
base BC = x + 12
base AD = 3x - 4
Required:
Part I: value of x
Part II: Length of BC, AD, and EF.
Solution:
Part I: Value of X
The median length of a trapezoid is said to be the ½ of the sum of the 2 bases of the trapezoid.
Therefore, EF = ½(BC + AD)
4x - 18 = ½((x + 12) + (3x - 4)
4x - 18 = ½(x + 12 + 3x - 4)
4x - 18 = ½(x + 3x +12 - 4)
4x - 18 = ½(4x + 8)
Multiply 2 by both sides
2(4x - 18) = 4x + 8
8x - 36 = 4x + 8
Add 36 to both sides
8x - 36 + 36 = 4x + 8 + 36
8x = 4x + 44
Subtract 4x from both sides
8x - 4x = 4x + 44 - 4x
4x = 44
Divide both sides by 4
x = 11
Part II:
BC = x + 12 = 11 + 12 = 23
AD = 3x - 4 = 3(11) - 4 = 33 - 4 = 29
EF = 4x - 18 = 4(11) - 18 = 44 - 18 = 26
Zach keeps his pet chameleon Pinky in a terrarium with the dimensions shown below. There's sand in the bottom of the terrarium that reaches a height of 8 centimeters. Zach gets a new terrarium for Pinky that is larger. The base of the new terrarium is 25 by 64 centimeters. Zach moved the existing sand to the new terrarium.
Answer:
5cm
Step-by-step explanation:
50cm x 20cm x 8cm = 8000cm^3
25cm x 64cm = 1600cm^2
1600x=8000
x=5cm
A pantry contains 6 shelves each 42 inches long.
The shelves are to be relined with fresh paper.
The paper is sold in 1-yard rolls. The number
of 1-yard rolls needed is:
Answer:
7 1-yard rolls
Step-by-step explanation:
1 yard = 36 inches.
6(42 in) = 252 inches.
252 in/36 in = 7
Therefore, 7 1-yard rolls are needed.
The number of 1-yard rolls needed to sell 6 shelves each of 42 inches is 7.
Given,
A pantry contains 6 shelves.
Each shelves = 42 inches long.
The shelves are to be relined with fresh paper.
The paper is sold in 1-yard rolls.
We need to find the number of 1-yards rolls needed to sell 6 shelves.
How many inches is 1yards?1 yard = 36 inches.
We have,
6 shelves and each shelves is 42 inches.
1 shelves = 42 inches.
6 shelves = 6 x 42 inches
6 shelves = 252 inches.
And since,
36 inches = 1 yard
252 inches = (252/36) yard
252 inches = 7 yard
Thus the number of 1-yard rolls needed to sell 6 shelves each of 42 inches is 7 1-yard rolls.
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1.) Write 7/25 as a percent and decimal.
Answer:
Below
Step-by-step explanation:
● 7/25
Let' write this fraction as a decimal then convert it to a percentage
● 7/25 = 0.28
To get a percentage multiply it by 10
● 0.28 × 100
● 28 %
Answer:
0.28 or 28 percent
Step-by-step explanation:
1)The easiest way to solve this is with a calculator. Just enter in 7/25, and you get 0.28.
2) Now, 0.28 is out of 1, but we also want a percent, so you have to change it to make it out of 100. You do this by multiplying by 100, and to do that you simply move the decimal place 2 places back.
3) You would then get 28, so 28 percent.
Extra) You can also do the part I did with a calculator without, but it is much more time consuming. After you get 0.28, you would go through the steps listed above.
The t distribution approaches the _______________ distribution as the sample size ___________.
Answer:
Normal; increases.
Step-by-step explanation:
In Statistics and probability, a student t-distribution also known as the t-distribution refers to the continuous probability distribution which can be used to estimate population parameters when the population variance or standard deviation is not known (unknown) and the sample population is relatively small. The student t-distribution is a statistical distribution which was published in 1908 by William Sealy Gosset.
The t-distribution approaches the normal distribution as the sample size increases because the parameters becomes negligibly smaller.
This ultimately implies that, when the degree of freedom of a t-distribution curve is increased in comparison with that of a normal distribution, the value of probability becomes significantly similar.
HELPP! QUICKKKK! Lol
Problem:
Last year I attended the Jurassic World Dinosaur Exhibit with my family and my friend and her family. My
family includes 2 adults (including myself) and my child we paid a total of $94. Her family includes 2
adults and 2 children she paid a total of $110. What was the admission price for an adult ticket and how
much was it for the admission price for a child ticket?
Let a represent adult ticket price
Let c represent child ticket price
Answer:
Child ticket = $16.
Step-by-step explanation:
Let adult tickets = a;
child ticket = c.
2a + c = 94 — eq no. 1,
2a + 2c = 110 — eq no. 2,
then,from eq 1,
c = 94 - 2a. —eq no. 3.
Substitute eq 3 into eq 2,
2a + 2(94 - 2a) = 110
2a - 4a = 110 - 188
-2a /-2 = -78 / -2
a = 39.
Substitute value of a into eq 3,
c = 94 - 2(39)
= 94 - 78
c = 16.
Thus, child ticket = $16.
Emanuel was charged \$32$32dollar sign, 32 for a 14\dfrac29 \text{ km}14 9 2 km14, start fraction, 2, divided by, 9, end fraction, space, k, m taxi ride. What was the cost per kilometer? \$Emanuel was charged \$32$32dollar sign, 32 for a 14\dfrac29 \text{ km}14
9
2
km14, start fraction, 2, divided by, 9, end fraction, space, k, m taxi ride.
What was the cost per kilometer?
Answer:
$2.25/km
Step-by-step explanation:
The cost charged for a total taxi ride of [tex]14\frac{2}{9}\ km[/tex] was $32. To get the cost per km, we divide the cost charged for the total taxi ride by the total distance that was traveled by the taxi. The cost per km is given by:
Cost per km = [tex]\frac{Cost \ of\ money\ charged}{Total\ distance}=\frac{\$ 32}{14\frac{2}{9} \ km}=\frac{32}{\frac{128}{9} }= \$2.25/km[/tex]
Therefore the cost per kilometer is $2.25 per kilometer. Each kilometer traveled by the taxi cost $2.25.
(k) 1 + tan 4A . tan 2A = sec 4A.
Please help me.... question from multiple angle of trigonometry!!!!!
it was a long proof...
follow the caption and steps and you'll understand it
proved...
Step-by-step explanation:
this is too easy method to solve this problem
PLEASE HELP!! URGENT
A Giant Redwood tree cast a shadow that is 532 feet long, with an angle of elevation of 25.7° Use the
information provided and the diagram below to determine the height of the tree. Round to the nearest
whole foot.
532 it
256 ft
479 ft
231 ft
13672 ft
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Answer:
The answer is option 1.
Step-by-step explanation:
You have to apply Tangent Rule, tanθ = opposite/adjacent. Then, you have to substitute the following values into the formula :
[tex]tan(θ) = \frac{oppo.}{adj.} [/tex]
[tex]let \: θ = 25.7 \: , \: oppo. = h \: , \: adj. = 532[/tex]
[tex] \tan(25.7) = \frac{h}{532} [/tex]
[tex]532 \tan(25.7) = h[/tex]
[tex]h = 256 \: feet \: (3s.f)[/tex]
The value of height of tree is,
⇒ h = 256 feet
We have to given that,
A Giant Redwood tree cast a shadow that is 532 feet long, with an angle of elevation of 25.7° .
Hence, By given figure we get;
By using trigonometry formula, we get;
⇒ tan 25.7° = Opposite / Adjacent
⇒ tan 25.7° = h / 532
⇒ 0.4812 = h / 532
⇒ h = 0.4812 × 532
⇒ h = 256 feet
Therefore, The value of height of tree is,
⇒ h = 256 feet
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Round the number 53.18474629
a) To the nearest tenth
b) To the nearest thousandth
c) To the nearest whole number
Answer:
Step-by-step explanation:
To the nearest tenth: 53.2
To the nearest thousandth: 53.185
To the nearest whole number: 53
Match each function formula with the corresponding transformation of the parent function y = 3x
1. y = -3^ x Translated up by 1 unit 2.
2.y = 3^ -x Reflected over the y-axis 3.
3.y = 3 ^x - 2 Translated right by 2 units 4.
4. y = 3 ^x + 1 Translated down by 2 units 5.
5. y = 3^ x + 1 Translated left by 1 unit 6.
6. y = 3 ^x - 2 Reflected over the x-axis
Everything is exponents of the three except the -2 at the end and the 4th one is also +1 not an exponent
Answer:
1. y = -3^ x Translated up by 1 unit 2.
2.y = 3^ -x Reflected over the y-axis 3.
3.y = 3 ^x - 2 Translated right by 2 units 4.
4. y = 3 ^x + 1 Translated down by 2 units 5.
5. y = 3^ x + 1 Translated left by 1 unit 6.
6. y = 3 ^x - 2 Reflected over the x-axis
Step-by-step explanation:
An atom consists of electrons, protons, and neutrons. Each electron has a charge of -1, each proton has a charge of +1, and each neutron has no charge. If 3 electrons are removed from each of 4 atoms, what is the combined net change to the charge of the 4 atoms?
Answer:
The net charge on the four atoms is 12
Step-by-step explanation:
The given parameters are;
The charge of each electron = -1
The charge of each proton = + 1
The charge of each neutron = neutral
Therefore, if 3 electrons are removed from each of the three atoms, we have;
The quantity of net negative charge removed from the four atoms = 3 × -1 × 4 = -12
Given that the at the four atoms add equal number of protons and electrons, we have;
Original charge on the four atoms = n×(-1) + n×(+1) = 0
Therefore;
The net charge on the four atoms after removal of the 12 electrons = Original charge - (-12)
The net charge on the four atoms = 0 - (-12) = +12
The net charge on the four atoms = +12.
Find an equation of the line passing through the pair of points. Write the equation in the form Ax+By = C.
(-4,7), (-5,-2)
Choose the equation of the line in the form Ax + By = C.
Answer:
-9x + y = 43
Step-by-step explanation:
We can put the equation into y = mx + b form first, then change it to Ax + By = C
First, we can find the slope by doing rise/run (y2 - y1) / (x2 - x1)
(-2 - 7) / (-5 + 4)
-9/-1 = 9
We can put this into the equation y = mx + b, along with another point, to find b:
y = mx + b
7 = 9(-4) + b
7 = -36 + b
43 = b
Now, we know the equation will be y = 9x + 43, and we can rearrange this:
Subtract 9x from both sides:
-9x + y = 43 will be the equation of the line
The hanger image below represents a balanced equation. Find the value of r that makes the equation true.
Step-by-step explanation:
R is 4 times so the equation will be
32 = 4r
32/4 = r
8 = r
A 40 pound bag of topsoil will
cover a surface area of 12 square
feet.
a. How many pounds of topsoil are
needed to cover a surface area of
480 square feet?
b. How many bags of topsoil must
be purchased to cover a surface
area of 480 square feet?
For number of bags, divide total area by the area 1 bag can cover.
480 / 12 = 40 total bags.
Now for total weight, multiple total bags by weight per bag:
40 bags x 40 pounds = 1,600 total pounds.
A = 40 bags
B = 1,600 pounds
A certain forest covers an area of 2900 km. Suppose that each year this area decreases by 8.5%. What will the area be after 8 years?
Use the calculator provided and round your answer to the nearest square kilometer.
Answer:
1425 square kilometer.
Step-by-step explanation:
2900 - 8.5% = 2653.5
2653.5 - 8.5% = 2427.9525
2427.9525 - 8.5% = 2221.5765375
2221.5765375 - 8.5% = 2032.74253181
2032.74253181 - 8.5% = 1859.95941661
1859.95941661 - 8.5% = 1701.8628662
1701.8628662 - 8.5% = 1557.20452257
1557.20452257 - 8.5% =1 424.84213815 ≈ 1425
Choose a system of equations with the same solution as the following system
arner Home
Classwork for Alge.
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Reade
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The curved parts of the figure are arcs centered at points A and C. What is the approximate length of boundary ABCD? Use the value = 3
and round the answer to one decimal place.
5
С
30°
А
120°
5
Answer:
The correct answer is
C. 23.1
Step-by-step explanation:
i think this is correct
Find the mean of the data in the pictograph below.
Answer:
10.5
Step-by-step explanation:
write the formula used to find length when the breadth height and volume are known........breadth when the length height and volume are known............ height when the breadth length and volume are known ..............Please answer this as fast as possible my homework is due tommorow
Answer: L = V/bh
b= V/Lh and h= V/Lb
Step-by-step explanation: V = Lbh or V= lwh is also used for the Basic form for the Volume of a cube or rectangular prism is
Volume = Length × breadth × height
The volume will be expressed as cubic units such as cubic meters cubic feet. Sometimes abbreviations are used like cm^3 for cubic centimeters.
When you know the Volume, and you need to find a missing dimension, just make a fraction with the V in the numerator and the dimensions you know in the denominator. This means you are dividing the Volume by the area of the dimensions you have been given to find the missing dimension.
Please Answer For Brainliest!!!
Answer:
C
Step-by-step explanation:
They want to find out altogether and the total number so add it up!
Answer: 72,132,204
Step-by-step explanation:
You can choose from the following 15, 16, 24, -88, 75, -62, 151, 88, 1, 30, -5 Also thank you in advance I don't know why I don't get this one so please explain if possible!
Answer:
-88
Step-by-step explanation:
whoever deleted my answer thanks a lot
Help me please!!! This is the last day I can finish this ASAP PLEASE I will comment the solutions
Answer:
See below.
Step-by-step explanation:
1)
[tex]64=x^2\\x=\sqrt{64}\\x=8[/tex]
2)
[tex]64=x^3\\x=\sqrt[3]{64}\\ x=4[/tex]
[tex](4^3=64)[/tex]
3)
[tex]2^x=32\\2^x=2^5\\x=5[/tex]
4)
[tex]x=(\frac{2}{5})^3=\frac{2^3}{5^3}=8/125[/tex]
5)
[tex]\frac{16}{9} =x^2\\x=\sqrt{\frac{16}{9} }\\ x=\frac{\sqrt{16} }{\sqrt{9}} \\x=4/3[/tex]
6)
[tex]2\cdot2^5=2^x\\2^1\cdot2^5=2^x\\2^{(1+5)}=2^6=2^x\\x=6[/tex]
7)
[tex]2x=2^4\\2x=16\\x=8[/tex]
8)
[tex]4^3=8^x\\(2^2)^3=(2^3)^x\\2^6=2^{3x}\\3x=6\\x=2[/tex]
Answer:
1) 8
2) 4
3) 6
4) 6/15
5) 4/3
6) 6
7) 8
8) 2
Step-by-step explanation:
Im about to cook dinner just comment if you want work shown.
PLEASE HELP PLEASE WILL MARK BRAINLY
Answer:
Every 18 miles he uses 3 gallons
divide this:
18 ÷ 3 = 6 miles per gallon
30 miles = 30 ÷ 6 = 5 gallons
7 gallons = 7 x 6 = 42 miles
48 miles = 48 ÷ 6 = 8 gallons
10 gallons = 10 x 6 = 60 miles
Hope this helps :D
if alan had bought a figure at a discount of 5%, he would pay $20 less. How much would he pay if he had bought it at a discount of 20%
Answer:
80
Step-by-step explanation:
5%-->20% is increased by x4, therefore you multiply 20 by 4 which is 80 or you can set an proportion
5/20=20/x5x=400x=80help me plz i dont get this
Answer:
56 [tex]in^2[/tex]
Step-by-step explanation:
We can first break this down into 2 smaller rectangles.
1x2x4 rectangle
4x3x4 rectangle.
Then we can find out the area of each, and we get 8+48 = 56.
You also could find this out by subtracting the area that is missing.
Answer:
The volume of the container is 56 in^3
Step-by-step explanation:
To solve, I split this figure vertically at the corner between the two steps. We know that the formula for volume of a container is V= l*w*h. The first, smaller portion of the container has a length of 4, a width of 1, and a height of 2. 4*1*2= 8 in^3
The second, larger portion of this container has a length of 4, (look at the side of the first portion), a width of 3, (4-1=3), and a height of 4. 4*3*4= 48 in^3.
Finally, add together the volumes of the two portions and that is the volume of the whole figure. V= 56 in^3
can somewon help me plz
Answer:
=1468 in ^3
Step-by-step explanation:
Find the volume of the container as if the corner was still there
V = l*w*h
V = 10 * 10 *15
= 1500
Subtract the missing corner
The volume of the missing piece is
V = l*w*h
= 2*4*4
= 32
V = 1500-32
=1468 in ^3
Answer:
It is 1468 inches cubed.
Step-by-step explanation:
You first want to the volume of the entire shape by multiplying the length, width, and height, which is 10, 10, and 15. They multiply to become 1500 inches cubed. You then want to find the volume of the smaller rectangular shape, so multiply 4, 4, and 2. And that equals 32. So subtract the volume of the big shape that we found, 1500, by the volume of the small one, which is 32. That equals 1468 inches cubed. You want to subtract the volume of the big one by the small one because the volume is just the big shape with a small shape cut out of it. So whenever you get one of these problems, just find the volume of both shapes, the big one and the small one, and subtract the small one from the big one.
A parallelogram has a base of 9 centimeters and a height of 21 centimeters. What is the area of the parallelogram? Please include all work!!
Answer:
A =189 cm^2
Step-by-step explanation:
The area of a parallelogram is found by
A = bh where b is the base and h is the height
A = 9 * 21
A =189 cm^2
please help real quick
Divide total km by the km in the scale:
112 / 16 = 7
The answer is A. 7 cm
Answer:
7 cm
Step-by-step explanation:
1 cm : 16 km :: x cm : 112 km
Product of mean = Product of extreme
16 * x = 1 * 112
x =[tex]\frac{112}{16}[/tex]
x = 7cm
what is the value of a?
a. 55
b. 110
c. 50
d. 100
Answer:
a i think
Step-by-step explanation:
What effect will replacing x with (x−3) have on the graph of the equation y=x2 y = x 2 ? A. slides the graph 3 units down B. slides the graph 3 units right C. shrinks the graph by a factor of 3 D. slides the graph 3 units left
Answer:
B. slides the graph 3 units right
Step-by-step explanation:
Replacing x with x-h moves the graph 'h' units to the right. In this case, the graph is moved 3 units right by replacing x with x-3.