We are Given:
Height of the Pyramid(h) = 2 cm
Volume of the Pyramid = 24 cm³
Base of the Pyramid:
We know that the Volume of a square-based Pyramid:
Volume = a²*(h/3)
24 = a² * (2/3) [Replacing the variables]
24 * 3/2 = a² [Multiplying both sides by 3/2]
a² = 36
a = 6 [taking the square root of both sides]
Hence, the length of base of the Pyramid is 6 cm
Final answer:
The length of the base of the square pyramid is 6 centimeters, which is found by solving the equation V = (1/3) * B * h for the area of the base B and then finding the square root of B to get the length of the side.
Explanation:
To determine the length of the base of the square pyramid, we can use the formula for the volume of a pyramid, which is V = (1/3) * B * h, where V is the volume, B is the area of the base, and h is the height of the pyramid. For a square pyramid, the base is a square, so the area of the base B can be expressed as s2, where s is the length of the side of the square.
We are given that the volume V of the pyramid is 24 cm³ and the height h is 2 cm. Using the formula, we can solve for s:
V = (1/3) * s2 * h
24 cm³ = (1/3) * s^2 * 2 cm
24 cm³ = (2/3) * s^2
s^2 = (24 * 3) / 2
s^2 = 36
s =[tex]\sqrt{36}[/tex]
s = 6 cm
Therefore, the length of the base of the square pyramid is 6 centimeters.
(SAT Prep) In the given figure, find x for which a ∥ b?
A. 50° B. 65° C. 75° D. 95°
Please explain your answer, and thanks in advance :)
Answer:
x= 65 degrees
Step-by-step explanation:
If the triangles vertices are marked CDE (d as the right angle and c as the leftmost vertex) then:
Alternate interior angles
⇒m∠ACE=85 degrees
m∠ACD=25 and m∠ACD+m∠DCE=m∠ACE=85 degrees
⇒ 25 + m∠DCE= 85 ⇒ m∠DCE=60 degrees
Since the sum of the angles in a triangle is 180 degrees
⇒ 60 + 90 + m∠DEC = 180 ⇒ m∠DEC= 30 degrees
Finally, since ∠BEC is supplementary to the given 85 degree angle
⇒ 30 + 85 + x = 180 ⇒ x=65
Answer:
[tex]\huge\boxed{x = 65 \ \text{degrees}}[/tex]
Step-by-step explanation:
We can use angle relationships to find the measure of [tex]x[/tex] here.
Let's assume that the triangle has the points ABC, where m∠a is the leftmost angle, m∠b is the right angle, and m∠c is the rightmost angle (I've labeled it in the attached picture).
We have to realize here that a and b are parallel lines. This means that the angles on one side will be equivalent to the other as long as the triangle in the center is symmetrical along both.
It's not. However, we can make it symmetrical by realizing that the 85° angle is the exact same as Line A AC. These are alternate interior angles, meaning their angle measurements will be the same. So Line A A C is also 85°.
Line A A C covers the area even in the triangle. Since we know the total measure and the measure outside the triangle, we can find the measure of m∠a.
[tex]25 + a = 85\\\\a = 85-25\\\\a = 60[/tex]
Now we know that m∠a is 60°. We also know that m∠b is a 90° angle. All triangle angles add up to 180°. Since we know two out of the three, let's find the measure of m∠c by adding up what we know and subtracting from 180.
[tex]60+90+c=180\\\\150+c=180\\\\c=180-150\\\\c=30[/tex]
Now that we know m∠c, we can note that the 85° angle, m∠a, and x are supplementary. This means their angle lengths add up to 180°. Since we know two out of the three, we can do a process similar to finding the missing triangle angle.
[tex]85+30+x=180\\\\115+x=180\\\\x=180-115\\\\x = 65[/tex]
Therefore, x is 65°.
Hope this helped!
Which are equivalent ratios to 7:13?
Answer:
14:26, 21:39, 28:52, 35:65, 42:78, 41:91
Step-by-step explanation:
All of the above are equivalent ratios. These are only a few. More can be found by just simply multiplying 7 by any amount, and 13 by any amount.
Ratios that are equivalent to 7:13 from the given options are 21:39, 28:52, and 14:26. Option A, C, D is correct.
To find equivalent ratios, we need to multiply or divide both terms of the ratio by the same non-zero number. Let's go through the options provided:
21:39 - If we divide both terms by 3, we get 7:13, which means this is an equivalent ratio.72:128 - If we divide both terms by 8, we get 9:16, which is not equivalent to 7:13.28:52 - If we divide both terms by 4, we get 7:13, which means this is an equivalent ratio.14:26 - If we divide both terms by 2, we get 7:13, which means this is an equivalent ratio.36:48 - If we divide both terms by 6, we get 6:8, which simplifies to 3:4. This is not equivalent to 7:13.Therefore, the equivalent ratios are 21:39, 28:52, and 14:26.
Hence, A. C. D is the correct option.
The complete question is:
Which are equivalent ratios to 7:13?
A) 21:39
B) 72:128
C) 28:52
D) 14:26
E) 36:48
This table gives a few (z,y) pairs of a line in the coordinate plane.
-56 66
-42 58
-28 50
What is the y-intercept of the line?
Answer:
The y-intercept of the line is 34.
Step-by-step explanation:
There are few points on the z-y plane through which a straight line passes.
The points are (-56,66), (-42,58) and (-28,50).
Now, take the first two points to get the equation of the straight line.
The equation is [tex]\frac{y - 58}{58 - 66} = \frac{z - (-42)}{-42 - (- 56)}[/tex]
⇒ [tex]\frac{y - 58}{- 8} = \frac{z + 42}{14}[/tex]
⇒ 14(y - 58) = - 8(z + 42)
⇒ [tex]y - 58 = - \frac{8}{14}z - 24[/tex]
⇒ [tex]y = - \frac{8}{14}z + 34[/tex]
This equation is in slope-intercept form.
Hence, the y-intercept of the line is 34. (Answer)
Solve the following system of equations graphically: y=3x+4 and y=-2x-5
Answer:
(x, y) = (-1.8, -1.4)
Step-by-step explanation:
Modern graphing calculators make it trivially simple to solve many problems by graphing. It has become my favorite method.
The graph shows the solution to be (x, y) = (-1.8, -1.4).
___
If you're graphing by hand, it is usually convenient to start with the y-intercepts, then draw the lines with the required slopes. These equations are written in slope-intercept form, making that approach relatively simple.
The first equation has a y-intercept of (0, 4) and a slope of 3. So, another point on the graph will be left 1 and down 3 (as opposed to right 1 and up 3). That point is (-1, 1).
The second equation has a y-intercept of (0, -5) and a slope of -2. So, another point on the graph of that will be left 1 and up 2, to (-1, -3)
please help
Simplify.
(4a5b6)4
16a9b10
256a9b10
16a20b24
256a20b24
Answer:
256a^20b^24
Step-by-step explanation:
Erica says that 1/5 of the national flag of Thailand shown on the right is blue. what’s wrong?
Answer:
The blue portion of the flag is actually 2/6 or 1/3 of the flag
Step-by-step explanation:
If you look at the size of the blue portion of the line it takes up twice the space as the white part. Imagine a small line drawn through the middle of the blue rectangle, now you can see that the flag is split up into 6 parts, rather then 5! Since we now have 2/6 of the flag being taken up by blue, that can be reduced down to 1/3 of the flag covered in blue.
Which expressions are equivalent to z + (z + 6)z+(z+6)z, plus, left parenthesis, z, plus, 6, right parenthesis?
Answer: [tex]2z^{2} + 14 z +6[/tex] and [tex]2(z^{2} + 7 z +3)[/tex]
Step-by-step explanation:
We have the following expression:
[tex]z+(z+6)z+(z+6)z+(z+6)[/tex]
Let's solve it:
[tex]z+z^{2}+6z+z^{2}+6z+z+6[/tex]
We have this result:
[tex]2z^{2} + 14 z +6[/tex]
However if we apply coomon factor 2, we will have a simplified result:
[tex]2(z^{2} + 7 z +3)[/tex]
Ava and Addison are saving for a new cell phone. Ava is starting at 100$ and adding 5$ each week.Addison is starting with 200$ and is adding 4$ each week. Write and solve a problem that can be used to find out after how many weeks Ava and Addison will have the same amount of money saved?
Answer:
The numbers of weeks for which both Ava and Addison have same amount of money saved is 100 weeks .
Step-by-step explanation:
Given as :
The amount of money having with Ava at starting = $100
The money that Ava is saving each week = $5
The amount of money having with Addison at starting = $200
The money that Addison is saving each week = $4
Now, Let The numbers of weeks for which both Ava and Addison have same amount of money saved = n weeks
Now, According to question
The amount of money having with Ava at starting + (The money that Ava is saving each week × numbers of weeks) = The amount of money having with Addison at starting + (The money that Addison is saving each week × numbers of weeks)
Or, $100 + $5 × n = $200 + $4 × n
Or, $5 × n - $4 × n = $200 - $100
Or, n = 100
So, The numbers of weeks for which both Ava and Addison have same amount of money saved = n = 100 weeks
Hence,The numbers of weeks for which both Ava and Addison have same amount of money saved is 100 weeks . Answer
Help asap, can't figure this out.
Answer:
B. 70
Step-by-step explanation:
[tex]7 \div 12 = \frac{7}{12} \\ 120 \times \frac{7}{12} = 70[/tex]
Answer:
B
Step-by-step explanation:
Given that for every 12 seeds, 7 grew into plants
Then for 120 seeds, that is 120 ÷ 12 = 10 times as many seeds, thus
number growing into plants = 10 × 7 = 70 → B
Factor the expression 3x2 + 2x - 8
Answer:
(3x − 4) (x + 2)
Step-by-step explanation:
3x² + 2x − 8
Factor using AC method.
3 × -8 = -24
Factors of -24 that add up to 2 are -4 and 6
Divide by 3 and reduce: -4/3 and 6/3 = 2/1
(3x − 4) (x + 2)
Please please need help on these two
Answer:
( f + g ) (x) = [tex] 2 x^{2} + x - 4[/tex]
g(x) - f(x) = [tex] x^{2} - 2 x - 4[/tex]
Step-by-step explanation:
f(x) = 4 x - 4 and g(x) = [tex] 2 x^{2} - 3 x[/tex]( f + g ) (x) = f(x) + g(x)
= [tex] 4 x - 4 + 2 x^{2} - 2 x[/tex]
= [tex] 2 x^{2} + x -4[/tex]
2. g(x) = [tex] x^{2} + 1[/tex] and f(x) = 2 x + 5
g(x) - f(x) = [tex] x^{2} + 1 - (2 x + 5)[/tex]
= [tex] x^{2} + 1 - 2 x - 5[/tex]
= [tex] x^{2} - 2 x - 4[/tex]
Two numbers have a sum of 1,212 and a difference of 518. What are the two numbers?
Answer:
The two numbers are
518
694
Step-by-step explanation:
As per requirements the two equations will be
X+Y=1212
X-Y=518
When we subtract these equations we get
X=1212-518
X=694
Now put the X value and find the Y value in any equation
X+Y= 1212
Y=1212-X
Where X = 694
Y=1212-694
Y=518
X=694 and Y=518
Answer:
answer is 865.
Step-by-step explanation:
865+347 is 1212 an the diff is 518.
and the largest number out of 865 and 347 is 865
What is 20 minus 5 as distributive property
Answer:
5(4-1)
Step-by-step explanation:
5(4-1)
20-5
5x4= 20
5x1= 5
plz hurry!!!! thank you!!!!
Answer:
∠A ≈ 19.47°
Step-by-step explanation:
As you know , the angle that tangent makes with the radius at the point of tangency is 90°.
∴∠OKA = 90°
As AO = 15 and OK = 5 ,
[tex]sin(A) = \frac{OK}{AO}[/tex]
[tex]sin(A) = \frac{5}{15} [/tex]
[tex]sin(A) = \frac{1}{3} [/tex]
∠A = [tex]sin^{-1} (\frac{1}{3} )[/tex]
∠A ≈ 19.47°
Answer:
[tex]\mathbf{m\angle A = sin^{-1}(\frac{1}{3}) \approx 19.47^{\circ}}[/tex]
Step-by-step explanation:
This question involves some basic knowledge of trigonometric function. The following formula only works for right angled triangles.
[tex]\mathbf{sin(x) = \frac{perpendicular}{hypotenuse}}[/tex]
In ΔAKO,
m∠AKO = 90°
Therefore ΔAKO is a right angled triangle. If we take ∠A into consideration then base will be AK, perpendicular will be OK and hypotenuse will be AO.
AO = 15
OK = 5
[tex]\therefore \mathrm{sin(\angle A) = \frac{OK}{AO} = \frac{5}{15} = \frac{1}{3}}[/tex]
[tex]\mathrm{sin(\angle A)=\frac{1}{3}}[/tex]
[tex]\mathrm{\angle A=sin^{-1}(\frac{1}{3})}[/tex]
To calculate [tex]\mathrm{sin^{-1}(\frac{1}{3})}[/tex] use scientific calculator
value of [tex]\mathrm{sin^{-1}(\frac{1}{3})}[/tex] is approximately equal to 19.47°
Therefore [tex]\mathbf{m\angle A \approx 19.47}[/tex]
(NOTE : When a line passing through center of a circle, is drawn to a tangent at the point of tangency then the angle made between then is 90°
Therefore m∠AKO = 90°)
which expressions are equivilant to 3x+3(x+y)
Step-by-step explanation:
3×+3(x+y) is equal to 6x+3y
a line intersects the points (13,-4) and (1,12).Find the slope and simplify completely
Answer:
4/-3
Step-by-step explanation:
To find the slope
y2 - y1 / x2 - x1 =
12 - -4 16
---------- = ----
1 - 13 -12
Simplify by dividing both parts by 4
4/-3 is your slope :)
Answer:
Step-by-step explanation:
I've answered this question already.
write the equation of a line that passes through the point -5,-4 and has a slope of 1/5.
What is the equation of a line that passes through points (0,4) and (-4,-8)? Y=2x+4, y=2x-4, y=3x+4, y=3x-4
Answer:
(-8 - 4)/(-4 - 0) = -12/-4= 3
y - 4 = 3(x - 0)
y - 4 = 3x - 0
y = 3x + 4
the answer is c
Find an ordered pair ( x, y ) that is a solution to the equation. 3x+y=7
Answer:
2,1
Step-by-step explanation:
y=-3x+7
y=-3(2)+7
y=-6+7
y=1
so (2,1)
line m passes through the points -2,7 and 4,-5 as shown below.
Answer:
y=-2x
Step-by-step explanation:
Answer:
y+2x=8
Step-by-step explanation:
when you put this in slope intercept form it will equal y=-2x+8 . Parallel lines need to have the same slope
Question 1 of 5
2 Points
What is the simplified fractional equivalent of the terminating decimal 0.25?
O
O A.
CINNICT
O
O c. 1
O D. 25
SUBMIT
Answer:
The simplified fractional equivalent is [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
we know that
A terminating decimal is a decimal that ends. So, it's a decimal with a finite number of digits.
we have
[tex]0.25[/tex]
Let
[tex]x=0.25[/tex]
Multiply by 100 both sides
[tex]100x=25[/tex]
Divide by 100 both sides
[tex]x=\frac{25}{100}[/tex]
Simplify
Divide by 25 both numerator and denominator
[tex]x=\frac{1}{4}[/tex]
Zolt Inc. (zolt) stock is selling for $8.22 per share with an EPS of .45 cents per share. What is Zolt's PE ratio? (Round to nearest tenth.)
rev: 09_19_2013_QC_35406
18.3
19.5
8.3
20.0
None of these
Answer:
18.3 ( when EPS is 45 cents), otherwise there is none of these
Step-by-step explanation:
PE = Current Price / EPS
current Price = $ 8.22 = 822 cents
EPS = .45 cents (?) ... is it 45 cents ?
if it is 45 cents : PE = 822 / 45 = 18.26 ≈ 18.3
The required PE ratio of the Zolt's is given as 18.3. Option A is correct.
Given that,
Zolt Inc. (zolt) stock is selling for $8.22 per share with an EPS of .45 cents per share.
The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
PE = Current Price: EPS
PE = Current Price / EPS
Current Price = $ 8.22 = 822 cents
EPS = 0.45 cents = 45 cents
it is 45 cents per PE
So Ratio = 822 / 45 = 18.3
Thus, the required PE ratio of the Zolt's is given as 18.3. Option A is correct.
Learn more about ratios here:
brainly.com/question/13419413
#SPJ5
If w=45,what is the value of 2(w-7)
Answer:
76
Step-by-step explanation:
if w=45, you'd get 2(45-7) by replacing the variable (w) with its value (45)
so first you'd distribute 2 to the 45 and the 7
now it'd be:
90-14=76
so the answer would be 76! :)
Answer:
The answer is 76
Step-by-step explanation:
First you swap in the number like so: 2(45-7)
Then you figure out what's is the parentheses first going with PEMDAS like so : 2(38)
Finally you multiply the number getting your final answer which is :76
A high school drama club is putting on their annual theater production there is a maximum of 800 tickets for the show the cost of the tickets are six dollars before the day of the show and nine dollars on the day of the show to meet the expenses of the shelf book club must sell at least $5000 worth of tickets
Answer:
Step-by-step explanation:
a.) Let x be the number of tickets sold before the event and y the number of tickets sold on the day of the event. Then x + y =< 800 and 6x + 9y >= 5000. (b.) Suppose the club sold 440 tickets before the event, i.e. x = 440, maximum number of tickets remaining to be sold = 800 - 440 = 360. Maximum amount realized from the sales supposing all tickets were sold = 6(440) + 9(360) = 2640 + 3240 = $5880 which is greater than $5000. Therefore, it is possible for the club to sell enough additional tickets on the day of the show to meet the expenses of the show.
HOPE THIS HELPED ;3
Solve 4^(x+2) = 12 for x using the change of base formula log base b of y equals log y over log b.
Answer:
[tex]x \approx -0.208[/tex]
Step-by-step explanation:
By applying logarithms to each side of the equation and some algebraic handling:
[tex]x+2 = \log_{4} 12[/tex]
[tex]x + 2 = \frac{\log_{10} 12}{\log_{10} 4}[/tex]
[tex]x = \frac{\log_{10}12}{\log_{10}4} - 2[/tex]
[tex]x \approx -0.208[/tex]
Final answer:
To solve the equation
[tex]4^{x+2} = 12[/tex]for x, you can use the change of base formula log base b of y equals log y over log b. By following the steps, you should find the solution to be x ≈ -0.086.
Explanation:
To solve the equation
[tex]4^{x+2} = 12[/tex]for x, we can use the change of base formula log base b of y equals log y over log b. Let's solve it step by step:
Take the logarithm of both sides of the equation using any base (let's use base 10 for this example): [tex]log (4^{x+2})[/tex] = log 12Apply the power rule of logarithms: (x+2) * log 4 = log 12Divide both sides by log 4: x+2 = log 12 / log 4Subtract 2 from both sides to isolate x: x = log 12 / log 4 - 2Use a calculator to evaluate the right side of the equation: x ≈ -0.086Therefore, the solution to the equation
[tex]4^{x+2} = 12[/tex]is approximately x = -0.086.
What is the answer to 2*3(15-5+3)4*4-6
Answer:
1242
Step-by-step explanation:
[tex]1. \: 6(15 - 5 + 3)4 \times 4 - 6 \\ 2. \: 6(10 + 3)4 \times 4 - 6 \\ 3. \: 6(13)4 \times 4 - 6 \\ 4. \: 78 \times 4 \times 4 - 6 \\ 5. \: 312 \times 4 - 6 \\ 6. \: 1248 - 6 \\ 7. \: = 1242[/tex]
Slope is 4 and (4,6) is on the line
Answer:
y-6=4(x-4)
Step-by-step explanation:
y-y1=m(x-x1)
y-6=4(x-4)
What is the quotient of ã and
?
What is the quotient of 3/4 and 5/6?
Answer:
9/10 ( or 0.9)
Step-by-step explanation:
quotient of 3/4 and 5/6
= 3/4 ÷ 5/6
= 3/4 x 6/5
= 18/20
= 9/10 ( or 0.9)
Answer:
9/10
Step-by-step explanation:
10 POINTS!!
Suppose a snow cone has a paper cone that is 8 centimeters deep and has a diameter of 5 centimeters. The flavored ice comes in a spherical scoop with a diameter of 5 centimeters and rests on top of the cone. If all the ice melts into the cone, will the cone overflow? Explain.
Answer:
D
Step-by-step explanation:
We require to calculate the volume (V) of the cone and sphere.
The volume of a cone is calculated as
V = [tex]\frac{1}{3}[/tex]πr²h ( r is the radius and h the height )
Here diameter = 5, hence r = 5 ÷ 2 = 2.5, thus
V = [tex]\frac{1}{3}[/tex]π × 2.5² × 8 ≈ 52.36 cm³
The volume of a sphere is calculated as
V = [tex]\frac{4}{3}[/tex]πr³ ( r is the radius )
Here diameter = 5, hence r = 5 ÷ 2 = 2.5, thus
V= [tex]\frac{4}{3}[/tex]π × 2.5³ ≈ 65.45 cm³
Since volume of the sphere is greater than the volume of the cone
Thus when the ice cream melts it will overflow → D
Whats the Answer y=10 4x-5y=3