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A square pyramid has a base with an area of 20 square meters, and its lateral faces have a slant height of x meters. Sydney is constructing a second square pyramid with the same size base, but the lateral faces of her pyramid have a slant height twice as long, 2x. Which statement best describes how the surface area of Sydney’s pyramid compares to the surface area of the original pyramid?
1. Sydney’s pyramid will have the same surface area because the .5 in the expression for the area of the triangular faces will make up for the slant height being doubled.
2. Sydney’s pyramid will have the same surface area because the slant height is not used when finding surface area.
3. Sydney’s pyramid will have a surface area that is exactly double the original pyramid’s because the slant height is used when finding the area of every lateral face.
4. Sydney’s pyramid will have a surface area that is greater than the original pyramid’s but not double the area because the slant height is not used when finding the area of the base.
30 POINTS
Answers
[tex]A=b^2+2bx[/tex]
note that b²=base area
so, if we say that her original pyramid's surface area is [tex]A_1=b^2+2bx[/tex], then the new one has a slant height of twice that, ie, we replace x with 2x and see what happens
[tex]A_2=b^2+2b(2x)[/tex]
[tex]A_2=b^2+4bx[/tex]
if we try to work [tex]A_1[/tex] back into there
[tex]A_2=b^2+2bx+2bx[/tex]
[tex]A_2=(b^2+2bx)+2bx[/tex]
[tex]A_2=A_1+2bx[/tex]
see our options
option 1 is wrong since the surface area increased by 2bx
option 2 is wrong since the surface area increased by 2bx, also we do use the slant height when finding surface area
option 3 is wrong because we got [tex]A_2=A_1+2bx[/tex] and not [tex]A_2=2(A_1)[/tex]
option 4 is correct since the new surface area is greater than the original by 2bx
answer is option 4
Answer:
Sydney’s pyramid will have a surface area that is greater than the original pyramid’s but not double the area because the slant height is not used when finding the area of the base.
Step-by-step explanation:
Can someone help with this math question
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[tex]y=mx+b[/tex]
being m the slope of the line and b the y-intercept of it.
On the other hand, if x = 0 then y = b.
We will order the equations above without inequalities like this:
[tex]y=-x-6[/tex]
So, the G and J are straight lines with negative slope. We need to find the one that matches the inequality. Taking a point, for example (0, 0), we will analyze Figure J, so in the inequality:
[tex]0+0\ \textless \ -6[/tex]
This is false, so this statement doesn't match the Figure J. Therefore, the answer is G.
2.
Find the annual percentage rate, using the annual percentage rate table.
Amount Financed: $8,900
Finance Charge: $1,030.62
Number of Payments: 24
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Finance Charge: $1,030.62
Number of Payments: 24
(Finance Charge)/(Amount Financed)*100$=($1,030.62)/($8,900)*100$
(Finance Charge)/(Amount Financed)*100$=(0.1158)*100$
(Finance Charge)/(Amount Financed)*100$=$11.58
In the row of number of Payments 24, we look for:
(Finance Charge)/(Amount Financed)*100$=$11.58, and we to which annual porcentage rate it corresponds in the first row
Answer: The annual percentage rate is 10.75%
Solve equation -6/7m=-84
Answers
[tex] \frac{-6}{7m} [/tex] = -84, m ≠ 0
Multiply both sides of the equation by 7m.
-6 = -588m
Now switch the sides of the equation.
-588m = -6
Divide bot sides of the equation by -588.
m = [tex] \frac{1}{98} [/tex], m ≠ 0
Lastly,, check if the solution is in the defined range (it is) to find your final answer.
[tex]m = \frac{1}{98} [/tex]
Let me know if you have any further questions.
:)
To solve the equation -6/7m = -84, multiply both sides by the reciprocal of -6/7, which is -7/6. The solution is m = 98.
To solve the equation -6/7m = -84, we need to isolate the variable m on one side of the equation. We can do this by performing the inverse operation of what is currently being done to m. Since m is being divided by -6/7, we can multiply both sides of the equation by the reciprocal of -6/7, which is -7/6, to cancel out the division on the left side.
The steps to solve the equation are:
Multiply both sides of the equation by -7/6:
-7/6 * (-6/7m) = -7/6 * -84
The left side simplifies to m, and the right side becomes m = 98.
So, the solution to the equation is m = 98.
Can anyone find the Surface Area of E?
Answers
The perimeter of the base of a regular quadrilateral prism is 60 cm, the area of a lateral face is 105 cm2. Find: the volume of the prism
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s = P/4
s = (60 cm)/4 = 15 cm
The area of one lateral face is the product of side length and height.
A = s×h
105 cm² = (15 cm)×h
Then the height of the prism is
h = (105 cm²)/(15 cm) = 7 cm
The area of the base is then
B = s²
B = (15 cm)² = 225 cm²
The volume of the prism is the product of its base area and height.
V = Bh
V = (225 cm²)×(7 cm) = 1575 cm³
The volume is 1575 cm³.
Which values of x would make a polynomial equal to zero if the factors of the polynomial were (x-2) and (x-11)?
Answers
x-2=0
x=2
x-11=0
x=11
A polynomial will be equal 0 if x=2, or x=11.
Answer:
[tex]x=2\text{ (or) }x=11[/tex]
Step-by-step explanation:
We have been given factors of a polynomial as [tex](x-2)[/tex] and [tex](x-11)[/tex]. We are asked to find the values of x that would make the polynomial equal to zero.
We will use zero product property of polynomials to solve our given problem. The zero product property of polynomials states that if any of two factors of a polynomial is zero, then their product will be equal to zero.
Upon equating our given factors to zero, we will get:
[tex](x-2)(x-11)=0[/tex]
[tex](x-2)=0\text{ (or) }(x-11)=0[/tex]
[tex]x-2=0\text{ (or) }x-11=0[/tex]
[tex]x-2+2=0+2\text{ (or) }x-11+11=0+11[/tex]
[tex]x=2\text{ (or) }x=11[/tex]
Therefore, [tex]x=2\text{ (or) }x=11[/tex] will make the polynomial equal to zero.
What situation should be used to rewrite 16(x^3+1)^2 -22(x^3+1)-3=0 as a quadratic equation
Answers
Use substitution: [tex]x^3+1=t[/tex]
[tex]16t^2-22t-3=0\\\\16t^2-24t+2t-3=0\\\\8t(2t-3)+1(2t-3)=0\\\\(2t-3)(8t+1)=0\iff2t-3=0\ \vee\ 8t+1=0[/tex]
[tex]2t-3=0\ \ \ |+3\\\\2t=3\ \ \ |:2\\\\t=\dfrac{3}{2}\\..............................\\8t+1=0\ \ \ \ |-1\\\\8t=-1\ \ \ \ |:8\\\\t=-\dfrac{1}{8}[/tex]
we're going back to substitution:
[tex]x^3+1=\dfrac{3}{2}\ \vee\ x^3+1=-\dfrac{1}{8}\ \ \ \ |subtract\ 1\ from\ both\ sides\ of\ the\ equations\\\\x^3=\dfrac{1}{2}\ \vee\ x^3=-\dfrac{9}{8}\\\\x=\sqrt[3]{\dfrac{1}{2}}\ \vee\ x=\sqrt[3]{-\dfrac{9}{8}}[/tex]
[tex]x=\dfrac{1}{\sqrt[3]2}\ \vee\ x=-\dfrac{\sqrt[3]9}{2}\\\\\boxed{x=\dfrac{\sqrt[3]4}{2}\ \vee\ x=-\dfrac{\sqrt[3]9}{2}}[/tex]
hello can you please help me posted picture of question
Answers
Hey can you please help me posted picture of question
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So,
F(x) shifted to left will be F(x + c), where c is any constant
So,
G(x) will be of the form F(x+c) or (x + c)²
From the given options, only option B lists such an expression.
So the answer is option B
I suck at math lol. Could someone give me the answers in detail? Picture attached! Thanks
Answers
Volume=πr²h
r=1.7m, h=15 m
plugging in the values in our formula we get:
V=π(1.7)²×15
V=43.35π
Answer: 43.35π m³
12]
Volume of the oblique cylinder will be:
V=πr²h
r=4 in, h=8
thus
V=π×4²×8
V=128π in²
Answer: 128π in²
Q is directly proportional to r. q is 76 when r is 20. work out q when r is 45.
Answers
q=kr
thus
k=q/r
when r=20, q=76
hence
k=76/20=
q=76/20r
when r=45 the value of q will be:
q=76/20×45
q=171
Answer:
q=171
Step-by-step explanation:
Hello there!
In this explanation k is constant and it means that q is some constant amount bigger than r.
q=kr
76=k×20
76÷20=k
k= 3.8
q=3.8r
q=3.8×45
q=171
Find an equation in standard form for the ellipse with the vertical major axis of length 16 and minor axis of length 4
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Given the lengths of the major and minor axes of an ellipse, one can derive the standard form equation of the ellipse. In this example, the lengths were 16 and 4, yielding a standard form equation of x²/4 + y²/64 = 1.
Explanation:The subject of this question is about finding the standard form equation for an ellipse given the lengths of the major and minor axes. To find the equation of the ellipse, we need to identify the semi-major axis (a) which is half the length of the major axis, and the semi-minor axis (b), which is half the length of the minor axis.
In this case, the lengths of the major and minor axes are 16 and 4 respectively, which gives us a semi-major axis of 8 and a semi-minor axis of 2. The standard form equation of an ellipse with a vertical major axis is given by:
(x-h)²/b² + (y-k)²/a² = 1
Where (h, k) is the center of the ellipse. In this case, since the center of the ellipse is at the origin (0,0), the equation becomes:
x²/4 + y²/64 = 1
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Someone please help.
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In this case the common ratio is -3.
As,
- 3.49 x -3 = 10.47
10.47 x - 3 = -31.41
and so on...
So, the next number of the series will be:
94.23 x - 3= -282.69
Thus, the answer to this question is - 282.69
What is the slope of the line? A) -3 B) - 1/3 C) 1/3 D) 3
Answers
slope = (y2 - y1)/(x2 - x1)
slope = (4 - 1)/(2 - 1) = 3/1 = 3
answer
D) 3
The foci of the hyperbola are ( 13 , 0) and (− 13 , 0), and the asymptotes are y = 12 x and y = − 12 x. find an equation of the conic section with the given properties. use x and y as the variables in your answer.
Answers
y=-+12x
12=a/b
a=12b
c²=a²+b²
(13,0) and (-13,0)
13²=(12b)²+b²
169=145b²
b= 13/12
169=a²+169/145
a²= 24336/145
x²/a²-y²/b²=1
145x²/24336 + 145y²/169=1
The equation of the conic section is [tex]\frac{145x\²}{24336} - \frac{145y\²}{169}=1[/tex]
The foci of the hyperbola are given as: (13,0) and (-13,0)
The asymptote is given as [tex]y =\pm 12x[/tex]
Divide both sides of [tex]y =\pm 12x[/tex] by x.
[tex]\frac yx = \pm 12[/tex]
Where y/x = a/b.
So, we have:
[tex]\frac ab = \pm 12[/tex]
Make a the subject
[tex]a = \pm 12b[/tex]
Recall that
[tex]c\²=a\²+b\²[/tex]
Where:
[tex]c = \pm13[/tex]
[tex]c\²=a\²+b\²[/tex] becomes
[tex](\pm 13)^2 = (\pm 12b)^2 +b^2[/tex]
[tex]169 = 144b^2 +b^2[/tex]
Evaluate like terms
[tex]169 = 145b^2[/tex]
Make b^2 the subject
[tex]b^2 = \frac{169}{145}[/tex]
Recall that [tex]a = \pm 12b[/tex]
Square both sides
[tex]a^2 = 144b^2[/tex]
Substitute [tex]b^2 = \frac{169}{145}[/tex]
[tex]a^2 = 144 \times \frac{169}{145}[/tex]
[tex]a^2 = \frac{24336}{145}[/tex]
The equation of the conic section is represented as:
[tex]\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1[/tex]
Substitute known values
[tex]\frac{x^2}{24336/145} - \frac{y^2}{169/145} = 1[/tex]
Rewrite as:
[tex]\frac{145x\²}{24336} - \frac{145y\²}{169}=1[/tex]
Hence, the equation of the conic section is [tex]\frac{145x\²}{24336} - \frac{145y\²}{169}=1[/tex]
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hello can you please help me posted picture of question
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Number of women = 6
Probability of selecting 1st women = 6/10
Probability of selecting 2nd women = 5/9
Probability of selecting 3rd women = 4/8
Probability that are 3 selected candidates are women = 6/10 x 5/9 x 4/8 = 1/6
So, the correct answer is option A
a cube with side length s has a volume of 216 cubic centimeters. the equation s^3 = 216 shows the volume of a cube. what is the side length of the cube in centimeters
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So you just need to take cubic root of 216.
Since 6³ = 216, then ∛( 216 ) = 6
So the side length of the cube would be 6 cm.
Hope this helps.
Q9 Q3.) Solve the matrix equation 4X + 5A = B
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See pictures below for the answer! My handwriting isn't that good. Let me know if you can't read it :)
Part A: Explain in words the mistake Juanita made. Part B: Solve the equation 3x + 6 = 24
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3x + 6 = 24
divide all terms by 3
3x/3 + 6/3= 24/3
x + 2= 8
subtract both sides by 2
x= 6
CHECK:
3x + 6 = 24
3(6) + 6= 24
18 + 6= 24
24= 24
ANSWER: She did not divide all terms by 3 when eliminating the x term's coefficient. x= 6
Hope this helps! :)
A triangle has side lengths of 10 centimeters, 2 centimeters, and c centimeters.
Enter a value to complete the inequality that describes the possible values for c, the length of the third side of the triangle.
HELP ASAP I COULD GET A PRESIDENTIAL AWARD FOR THIS!!!
Answers
Answer:
12
Step-by-step explanation:
The possible values of the third side of the triangle can be written as, 8 < c < 12.
What is Triangle?A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.
Sum of the interior angles of a triangle is 180 degrees.
Given a triangle.
Side lengths of the triangle are 10 centimeters, 2 centimeters, and c centimeters.
We have to find the possible values of c.
By the triangle Inequality Theorem,
10 - 2 < c < 10 + 2
8 < c < 12
Hence the possible values of c are 9, 10 and 11.
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HELP ASAP PLEASE
Given that ABC ~ DEC, find the value of x. If necessary, round your answer to two decimal places.
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If these are similar triangles, this means that the ratio of corresponding sides is equivalent. In this case, AB corresponds to DE as CB corresponds to CE. In ratio and proportion form:AB / CB = DE / CE
x / 5 = (18 - x) / 25
5x = 18 - x
6x = 18
x = 3
james just bought a large container of ice cream the label says that there are 16 servings of ice cream write a formula to help james determine the number of grams on one serving of ice cream x=number of grams of ice cream in the container y=number of grams per serving
Answers
Final answer:
To determine the number of grams per serving of ice cream, use the formula y = x / 16, where x is the total number of grams in the container and y is the number of grams per serving.
Explanation:
To determine the number of grams per serving of ice cream, we can set up a formula using the variables x and y. Since the container has 16 servings of ice cream, the total number of grams in the container can be represented as 16y (16 servings multiplied by the number of grams per serving).
So, the formula to determine the number of grams per serving (y) is: y = x / 16
For example, if the total number of grams in the container (x) is 800g, then the number of grams per serving (y) would be 800g / 16 = 50g.
Suppose you have an isosceles triangle, and each of the equal sides has a length of 1 foot. suppose the angle formed by those two sides is 45^\circ. then the area of the triangle is
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The base angles are congruent and measure 67.5 deg.
The congruent sides measure 1 ft.
Use law of sines to find the length of the base.
[tex] \dfrac{\sin 67.5^\circ}{1~ft} = \dfrac{\sin 45^\circ}{b} [/tex]
[tex] b = \dfrac{\sin 45^\circ}{\sin 67.5^\circ}~ft [/tex]
[tex] b = 0.765~ft [/tex]
Draw a height from the vertex of the 45-deg angle to the base.
Half of the base is 0.765 ft/2 = 0.383 ft
We can find the height of the triangle using the small triangles.
0.383^2 + h^2 = 1^2
h = 0.9239 ft
A = bh/2 = 0.765 * 0.9239/2 ft^2
A = 0.354 ft^2
The area of a given isosceles triangle with sides of 1 foot in length and a 45-degree angle between these sides is 0.5 square feet.
Explanation:The area of an isosceles triangle can be calculated using the formula 1/2 base times height. But since we know that the triangle is isosceles and the angle between the equal sides is 45 degrees, this forms a 45-45-90 degree triangle which is a special kind of triangle. In a 45-45-90 degree triangle, the lengths of the sides are in the ratio 1:1:√2. Therefore, the length of the base (which also serves as the height in this case) will be the same length as the equal sides, 1 foot. Substituting these into the formula for area, we get Area = 1/2 * 1 ft * 1 ft = 0.5 square feet.
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What is is the equation of the line perpendicular to y = 3x-7 that contains the point (6,8)?
A. 1/3x - 7
B. 1/3x + 6
C. -1/3x - 7
D. -1/3x + 10
Answers
m = -1/(3) = -1/3
Only choices C and D have this slope. Only choice D goes through the given point. (-1/3)*6 +10 = -2 +10 = 8.
The appropriate selection is ...
D. (-1/3)x + 10
The equation of the line perpendicular to y = 3x -7 that passes through the point (6, 8) is Option D. y = -1/3x + 10. The slope of the perpendicular line is -1/3. Using point-slope form, we determine the final equation.
To find the equation of a line perpendicular to y = 3x - 7 that passes through the point (6, 8), we must determine the slope of the perpendicular line first.
The slope of the given line is 3. The slope of a line perpendicular to this one is the negative reciprocal of 3, which is -1/3.
We now use the point-slope form of the linear equation, which is:
y - y₁ = m(x - x₁)
Substitute m = -1/3 and the point (6, 8):
y - 8 = -1/3(x - 6)
Distribute -1/3:
y - 8 = -1/3x + 2
Add 8 to both sides:
y = -1/3x + 10
Thus, the equation is Option D. -1/3x + 10.
What is the y-intercept of the quadratic y=-2x^2-4x-5 ?
(-5,0)
(0,-2)
(-1,3)
(0,-5)
Answers
We have: [tex]y=-2x^2-4x-5\to f(0)=-2(0)^2-4(0)-5=-5[/tex]
Answer: (0; -5)
Olly drank 1/2 of a 16 fluid ounce bottle of juice how many cups of juice are left in the bottle explain
Answers
Remember the conversion: 8 fluid ounces = 1 cup. Since Olly drank 8 fluid ounces, then using the conversion, we can tell that Olly drank 1 cup of juice.
The total number of cups of juice that are left in the bottle are 8x.
What is division?Division is a process of splitting a number into two or more equal parts.
Given is that Olly drank 1/2 of a 16 fluid ounce bottle of juice.
Assume that 1 fluid ounce of bottle can fill {x} cups. So, we can write -
16 fluid ounce bottle of juice can fill {16x} cups.
So, 1/2 x 16 fluid ounce of juice will fill {1/2 x 16x} cups.
{1/2 x 16x} cups
8x cups
Therefore, the total number of cups of juice that are left in the bottle are 8x.
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A die is continuously rolled until the total sum of all rolls exceeds 375. what is the probability that at least 90 rolls are necessary?
Answers
Final answer:
To find the probability of at least 90 rolls being necessary for the total sum of all rolls to exceed 375, we need to consider the probabilities associated with each roll.
Explanation:
To find the probability of at least 90 rolls being necessary for the total sum of all rolls to exceed 375, we need to consider the probabilities associated with each roll.
The maximum possible sum from a single roll of a six-sided die is 6, so after 90 rolls, the maximum possible sum is 90 * 6 = 540. If the total sum exceeds 375, it means that at least one roll resulted in a value greater than 2.
To calculate the probability, we need to find the complement of the event that the total sum is less than or equal to 375, which is the event of the total sum being greater than 375. Let's assume that the probability of rolling a value greater than 2 is p. The probability of at least 90 rolls being necessary is 1 - (1 - p)^90.
can someone plz help me!!!
Answers
6*5, 3, 8, 4
30, 3, 8, 4
∛64 > ∛27> √ 64 > 6√25
5u exponent 7 - 21u exponent 7
Simply
Answers
Since both algebraic terms are identical (both are using u^7), we can subtract the coefficients directly, as in: 5 - 21 = -16
Therefore, 5u^7 - 21u^7 = -16u^7