Helen has 48 cubic inches of clay to make a solid square right pyramid with a base edge measuring 6 inches.
A solid right pyramid with a square base has a base edge measuring 6 inches.
Which is the slant height of the pyramid if Helen uses all the clay?
3 inches
4 inches
5 inches
6 inches
Answers
Answer:
the answer is C
Step-by-step explanation:
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Based on the calculations, the slant height of this pyramid is equal to: C. 5 inches.
Given the following data:
Volume of pyramid = 48 cubic inches.Base edge of square = 6 inches.How to calculate the slant height of this pyramid?In order to determine the slant height of this pyramid, we would first find the base area and height of the pyramid by using this formula:
Volume = 1/3 × base area × height
For the base area, we have:
Base area = s²
Base area = 6²
Base area = 36 square inches.
For the height, we have:
Volume = 1/3 × base area × height
48 = 1/3 × 36 × height
48 = 12h
h = 48/12
Height, h = 4 inches.
Next, we would determine the slant height of this pyramid by applying Pythagorean's theorem:
l² = h² + b²/4
l² = 4² + 6²/4
l² = 16 + 36/4
l² = 16 + 9
l = √25
Slant height, l = 5 inches.
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Related Questions
URGENT PLZ SAVE ME
If c varies directly as b and c = 6 when b = 2.
Find
a) the formula for c in terms of b
b) the value of c given b = 14
c) the value of b given c = 39
Answers
Answer:
Hello,
Are you still alive ?
Step-by-step explanation:
a)
c=k*b (c varies directly as b)
6=k*2 ==> k=3 ( c = 6 when b = 2.)
[tex]\boxed{c=3*b }\\[/tex]
b)
b=14 ==> c=3*14=42
c)
c=39
[tex]b=\dfrac{c}{3} =\dfrac{39}{3} =13\\[/tex]
You and your friends have tickets to attend a music concert. While standing in line, the promoter states he will give a gift card for a free album download to each person that is a multiple of 2. He will also give a backstage pass to each fourth person and floor seats to each fifth person. Which person will receive the free album download, backstage pass, and floor seats? Explain the process you used to determine your answer.
Answers
9514 1404 393
Answer:
20th
Step-by-step explanation:
The person will receive all gifts if the are all of a multiple of 2, a multiple of 4, and a multiple of 5. Since 4 is already a multiple of 2, the person who will receive all is the one who is a multiple of 4 and 5.
20 is 4×5, so is a multiple of both numbers. There is no smaller number that is a multiple of both 4 and 5.
The 20th person will receive all gifts.
_____
The value we have determined here is called the "least common multiple" (LCM). It is the product of the unique prime factors of the numbers of interest, raised to the highest power that appears in any of the numbers.
2 = 2¹
4 = 2²
5 = 5¹
LCM(2, 4 5) = 2² × 5¹ = 20
Terms of geometric sequence are found by the formula T n = ar n - 1. If a = 3 and r = 2, find the first 4 terms of the sequence.
Answers
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Answer:
3, 6, 12, 24
Step-by-step explanation:
It helps if the formula is properly written.
Tn = a·r^(n-1)
Fill in the given values for a, r, and use n = 1 to 4.
T1 = 3·2^(1-1) = 3
T2 = 3·2^(2-1) = 6
T3 = 3·2^(3 -1) = 12
T4 = 3·2^(4 -1) = 24
__
Additional comment
The value a=3 tells you the first term is 3. The value r=2 tells you each term is 2 times the previous one. Knowing this, you can write down the sequence based on your knowledge of multiplication tables (×2). You can use the formula as we did above, but it isn't necessary.
3, 6, 12, 24, ...
base:10 height:2.5 what is the slope of the ramp
Answers
Answer:
Slope is B. ¼
Step-by-step explanation:
Slope: is hypotenuse
[tex] = { \sf{ \frac{ \delta \: height}{ \delta \: base} }} \\ \\ { \sf{ = \frac{2.5}{10} }} \\ \\ = { \sf{ \frac{1}{4} }}[/tex]
which means slope = 1/4
What is the equation of the parabola shown in the graph?
Answers
Answer:
[tex]-\frac{x^{2} }{4}[/tex] -2x - 7
Step-by-step explanation:
Never seen a phone with 3 cameras before or something but ok.
Took a while to use brainly's insert character thingie since fractions and the exponent kinda threw me off.
find the answer for 10 points
Answers
Answer:
52.8
Step-by-step explanation:
(3×2.6×2/2)+(3×5×3)
= 7.8+45
= 52.8
Answered by GAUTHMATH
x^{2} +y^{2} =?
cho mình hỏi với
Answers
Answer:
[tex]{ \sf{ {x}^{2} + {y}^{2} = {(x + y)}^{2} - 2xy }}[/tex]
Step-by-step explanation:
[tex]{ \tt{ {(x + y)}^{2} = (x + y)(x + y) }} \\ { \tt{ {(x + y)}^{2} = ( {x}^{2} + 2xy + {y}^{2}) }} \\ { \tt{( {x}^{2} + {y}^{2} ) = {(x + y)}^{2} - 2xy}}[/tex]
Which point on the number line shows the graph
Answers
Answer:
B
Step-by-step explanation:
find the squre of 17
[tex] \sqrt{17} [/tex]
Answers
What is the distance between the following points?
Will give brainliest
Answers
Answer:
√65
Step-by-step explanation:
(-6,4) (-5,-4)
√(x2 - x1)² + (y2 - y1)²
√[-5 - (-6)]² + (-4 - 4)²
√(1)² + (-8)²
√1 + 64
√65
Find the measure of ZJ, the smallest angle in a triangle
with sides measuring 11, 13, and 19. Round to the
nearest whole degree.
O 30°
O 34°
o 42°
O 47°
Answers
2bc.cos(A) = b^2 + c^2 - a^2
cos(A) = (b^2 + c^2 - c^2) / (2bc)
cos(A) = (13^2 + 19^2 - 11^2) / (2 x 13 x 19) = 0.827935
A = 34 degrees
You need 675 mL of a 90% alcohol solution. On hand, you have a 25% alcohol mixture. How much of the 25% alcohol mixture and pure alcohol will you need to obtain the desired solution?
Answers
Answer:
90 ml of the 25 percent mixture and 585 of pure alcohol
Step-by-step explanation:
Firstly, you should find the quantity of alcohol in the desired mixture.
675:100*90= 675*0.9= 607.5
Firstly, define all the 25 percents mixure as x, the pure alcohol weight is y.
1. x+y= 675 (because the first and the second liquid form a desired liquid).
Then find the equation for spirit
The first mixture contains 25 percents. It is x/100*25= 0.25x
When the second one consists of pure alcohol, it contains 100 percents of spirit, so it is x.
2. 0.25x+y=607.5
Then you have a system of equations ( 1.x+y= 675 and 2. 0.25x+y= 607.5)
try 2-1 to get rid of y
x+y- (0.25x+y)= 675-607.5
0.75x= 67.5
x= 90
y= 675-x= 675-90= 585
It means that you need90 ml of the 25percents mixture and 585 0f pure alcohol
if x-y =2 and xy=15, find the value of x cube - y cube.
Answers
Answer:
5³ = 125 : -3³ = -27Step-by-step explanation:
let x= 5 and y= 3x - y = 25 - 3 = 2xy = 155 × 3 = 15x³ = ? : -y³ = ?5³ = 125 : -3³ = -27[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
18 Geometry question: Use an algebraic equation to find the measure of each angle that is representative in terms of X
Answers
Answer:
12x - 28° = 116°
7x + 32° = 116°
Step-by-step explanation:
12x - 28° and 7x + 32° are vertical angles. Vertical angles are congruent.
Therefore, to find the measure of each angle, we have to set each equation equal to each other as follows:
12x - 28° = 7x + 32°
Collect like terms
12x - 7x = 28 + 32
5x = 60
Divide both sides by 5
5x/5 = 60/5
x = 12
✔️12x - 28°
Plug in the value of x
12(12) - 28
= 144 - 28
= 116°
✔️7x + 32°
7(12) + 32
= 84 + 32
= 116°
A certain test preparation course is designed to help students improve their scores on the LSAT exam. A mock exam is given at the beginning and end of the course to determine the effectiveness of the course. The following measurements are the net change in 5 students' scores on the exam after completing the course: 16, 21, 22, 12, 22
Using these data, construct a 90% confidence interval for the average net change in a student's score after completing the course. Assume the population is approximately normal. Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answers
Answer:
The critical value used is [tex]T_c = 2.132[/tex]
The 90% confidence interval for the average net change in a student's score after completing the course is (14.357, 22.843).
Step-by-step explanation:
Before building the confidence interval, we need to find the sample mean and the sample standard deviation.
Sample mean:
[tex]\overline{x} = \frac{16+21+22+12+22}{5} = 18.6[/tex]
Sample standard deviation:
[tex]s = \sqrt{\frac{(16-18.6)^2+(21-18.6)^2+(22-18.6)^2+(12-18.6)^2+(22-18.6)^2}{4}} = 4.45[/tex]
Confidence interval:
We have the standard deviation for the sample, so the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So
df = 5 - 1 = 4
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 4 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 2.132. The critical value used is [tex]T_c = 2.132[/tex]
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.132\frac{4.45}{\sqrt{5}} = 4.243[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 18.6 - 4.243 = 14.357
The upper end of the interval is the sample mean added to M. So it is 18.6 + 4.243 = 22.843.
The 90% confidence interval for the average net change in a student's score after completing the course is (14.357, 22.843).
For the function y=f(x), find f’(a)
Answers
Answer:
-1
Step-by-step explanation:
f(x) = x²+3x+1
f(a) = a²+3a+1
f'(a) = 2a+3
putting a = -2
2×(-2)+3
= -4+3
= -1
5(2x-5) = 1/2(18x+40)
Answers
Answer:
x = 45
Step-by-step explanation:
5 (2x - 5) = 1/2 (18x + 40)
10x - 25 = 9x + 20
10x = 9x + 45
x = 45
please mark this answer as brainlist
Help please 6x + 3 > a if the inequality above is true for the constant a which of the following. coupd be a vakue of z
Answers
Answer:
[tex]\frac{a+3}{6}[/tex]
Step-by-step explanation:
Treat it like any other math problem with a equals sign:
6x + 3 = a
subtract 3 from both sides: 6x = a + 3
divide both sides by 6: [tex]x = \frac{a+3}{6}[/tex]
swap the ≥ back in: [tex]x \geq \frac{a+3}{6}[/tex]
the only time the sign flips is if you divide by a negative
1. Samuel paid #34.20 for a blanket. If the marked price of the blanket is #41.78. What is the discount?
2. A mother buys a dress for her daughter at a discount of 18%. If the price of the dress is #35.00. How does she actually pay for the dress?
Answers
Answer:
1. The discount is 10%
2. 250
ALL I NEED HELP WITH IS WITH PART D, HOW DO I GET THAT
Use the function f(x) = −16x^2 + 22x + 3 to answer the questions.
Part A: Completely factor f(x). (2 points)
Part B: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part C: Describe the end behavior of the graph of f(x). Explain. (2 points)
Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph. (4 points)
Answers
Step-by-step explanation:
Step 1: Factor the equation
[tex]f(x) = -16x^{2} + 22x + 3\\f(x) = -(8x + 1)(2x - 3)[/tex]
Step 2: Find the x-intercepts of the graph of f(x)
[tex]-8x - 1 + 1 = 0 + 1\\-8x / -8 = 1 / -8\\x = -1/8[/tex]
[tex]2x - 3 + 3 = 0 + 3\\2x / 2 = 3 / 2\\x = 3/2[/tex]
Step 3: Describe the end behavior of the graph of f(x)
Since the function is to the power of 2, that means that it is a parabola. And since the leading coefficient is negative, means that the arrows will be pointing down therefore, the end behavior of this graph is as x goes to infinity, f(x) goes to negative infinity and as x goes to negative infinity, f(x) goes to negative infinity.
Step 4: What are the steps you would use to graph f(x)
The first step that I would do is factor the equation. Then I would find the x-intercepts of the graph and plot them on the graph. I would then plug in 0 for all of the x values to get the y intercept. After doing that I would get the vertex using the vertex formula plotting it on the graph. Finally, I would connect all of the dots together to form the graph of the equation.
Answer:
The person above me is correct!
A square piece of cardboard of sides 15 cm is folded to make a cube of sides 5 cm.
Is there enough cardboard?
Answers
Answer:
Step-by-step explanation:
The 15 cm by 15 cm piece of cardboard area = 225 cm².
A cube has six congruent faces. If each edge is 5 cm, the surface area is 6×5² = 150 cm². So there is enough cardboard to make a cube, but not by folding. You'd have to do some cutting and taping.
Use the listing method to represent the following set. Hurry plz!!!
Answers
[tex]\\ \sf\longmapsto \left\{x|x \epsilon I,x\leqslant 3\right\}[/tex]
Here x belongs to set of Integersx is less than or equal to 3In listing
[tex]\\ \sf\longmapsto \left\{\dots,0,1,2,3\right\}[/tex]
The sum of twice a number and 3 times the same number as 40. What is the number?
Answers
Answer:
Let the number be x
According to Question ,
2x + 3x = 40
5x = 40
x = 8
therefore , the number is 8
hope that helps uh...☺
[18].Simplify (TTE): x(2x+y+5) - 2(x²+xy+5) + y(x + y)
Answers
Answer:
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 5x -10 + y\²[/tex]
Step-by-step explanation:
Given
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y)[/tex]
Required
Simplify
We have:
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y)[/tex]
Open brackets
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 2x\²+xy+5x - 2x\²-2xy-10 + xy + y\²[/tex]
Collect like terms
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 2x\²- 2x\²+xy-2xy+ xy+5x -10 + y\²[/tex]
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 5x -10 + y\²[/tex]
X ^2 + 2x + y’ + 6y = 15
Answers
Step-by-step explanation:
x^2+2x+7y=15
7y=15-x^2-2x
y=15/7-1/7x^2-2/7x , x ∈ all real numbers
At what rates did she invest?
$1400 invested at ____%
$900 invested at ____%
Answers
9514 1404 393
Answer:
$1400 at 8%$900 at 10%Step-by-step explanation:
The 1-year interest is simply the invested amount times the interest rate.
Let r represent the lower interest rate. Then r+0.02 is the higher rate, and the total interest earned is ...
1400r + 900(r +.02) = 202
2300r +18 = 202 . . . . . . . . . .simplify
2300r = 184 . . . . . . . . . .subtract 18
r = 184/2300 = 0.08 = 8% . . . . . . divide by the coefficient of r
$1400 was invested at 8%.
$900 was invested at 10%.
$900 invested at 10%
A runner sprinted for 414 feet. How many yards is this?
Answers
Answer:
138 yards
Step-by-step explanation:
1 feet is (1/3) yard
414 feet is (1/3)*414=138 yards
For the following function, one zero is given. Find all other zeros.
f(x)=x3-7x2+17x-15; 2-i
Answers
Answer:
1,-3,-5
Step-by-step explanation:
Given:
f(x)=x^3+7x^2+7x-15
Finding all the possible rational zeros of f(x)
p= ±1,±3,±5,±15 (factors of coefficient of last term)
q=±1(factors of coefficient of leading term)
p/q=±1,±3,±5,±15
Now finding the rational zeros using rational root theorem
f(p/q)
f(1)=1+7+7-15
=0
f(-1)= -1 +7-7-15
= -16
f(3)=27+7(9)+21-15
=96
f(-3)= (-3)^3+7(-3)^2+7(-3)-15
= 0
f(5)=5^3+7(5)^2+7(5)-15
=320
f(-5)=(-5)^3+7(-5)^2+7(-5)-15
=0
f(15)=(15)^3+7(15)^2+7(15)-15
=5040
f(-15)=(-15)^3+7(-15)^2+7(-15)-15
=-1920
Hence the rational roots are 1,-3,-5 !
for any Integer 'a',a ÷ 0 is _______
give me answer
Answers
Answer:
undefined, invalid
and for a limit expression like a/x, x->0 we also say this is infinite.
A woman is 42years old. Her daughter is 1/3 of her age. Three years ago the sum of her age was
Answers
Answer:
50
Step-by-step explanation:
So we know that 42/3=14.
3 years before was:
14-3=11
42-3=39
The sum of 11+39 is 50
