Answers
The surface area of the prism is 112 in²
What is surface area of prism?A prism is a solid shape that is bound on all its sides by plane faces.
The surface area of a prism is expressed as;
SA = 2B +pH
where h is the height and B is the base area and p is the perimeter of the base
The perimeter of the base = 2(l+b)
= 2(3+4) = 2×7 =14 in
The area of the base = l× b
= 4× 3 = 12 in²
height = 7
Therefore the surface area = 2 × 12 + 14 × 7
= 14+98
= 112 in²
therefore the surface area of the prism is 112 in²
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Related Questions
How can you eliminate the y-terms in this system?
Answers
To eliminate the y-terms in this system of equations, we can multiply the second equation by 2 and add it to the first equation.
We have,
To eliminate the y-terms in this system of equations, we can multiply the second equation by 2 and add it to the first equation.
This will result in the y-terms canceling out, and we will be left with only x-terms on one side of the equation, which we can then solve for x.
So, multiplying the second equation by 2, we get:
2(3x + 4y) = 2(5)
6x + 8y = 10
Now, adding this to the first equation, we get:
4x - 8y + 6x + 8y = 20 + 10
10x = 30
Dividing both sides by 10, we get:
x = 3
Now, we can substitute this value of x back into either of the original equations to solve for y.
4x - 8y = 2
So,
4(3) - 8y = 20
12 - 8y = 20
-8y = 8
y = -1
Therefore,
The solution to the system of equations is (x, y) = (3, -1).
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What are a) the ratio of the perimeters and b) the ratio of the areas of the larger figure to the smaller figure? The figures are not drawn to scale.
A. 5/2 and 25/4
B. 5/2 and 7/4
C. 7/2 and 25/4
D. 7/2 and 7/4
SOMEONE PLEAS HELP!
Answers
Answer:
The answer to your problem is, A. 5/2 and 25/4
Step-by-step explanation:
In the problem the two similar figures, with side lengths 30 yds and 12 yds.
In order to solve the problem we need to find the ratio of the perimeters and the ratio of the areas of the larger figure to the smaller figure.
Using this information we know the the ratio of the perimeter of similar figure is equal to the scale factor and the ratio of the areas equal to the square of the scale factor.
the scale factor = 30/12 = 5/2
the ratio of the perimeter = 5/2
the ratio of the areas = (5/2)² = 25/4
Thus the answer to your problem is, A. 5/2 and 25/4
What is the surface area of a right cone with a diameter of 15 units and a slant height of 34 units?
Answers
The surface area of the right cone is 800.7 squared unit.
What is surface area?The surface area of a three-dimensional object is the total area of all its faces.
To calculate the surface area of the right cone, we use the formula below
Formula:
S.A = πrl.................. Equation 1From the question,
Given:
π = Pie = Constantr = Radiusl = Slight heightFrom the question,
Given:
r = 15/2 = 7.5 unith = 34 unitSubstitute these values into equation 1
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Peter’s teacher says he may have his report card percentage based on either the mean or the median and he can drop one test score if he chooses.
84%, 71%, 64%, 90%, 75%, 44%, 98%
Which measure of center should Peter choose so he can have the highest percentage possible?
Peter should choose the mean after dropping one test score.
Peter should choose the mean without dropping one test score.
Peter should choose the median after dropping one test score.
Peter should choose the median without dropping one test score.
Answers
Answer:
A.
Step-by-step explanation:
Peter should choose to base his report card percentage on the median if he wants to have the highest percentage possible. To calculate the median, Peter would first order the scores from lowest to highest: 44%, 64%, 71%, 75%, 84%, 90%, 98%. Then, he would select the middle score as the median, which is 75%. If Peter drops his lowest score (44%), his percentage based on the median would be 80% ((64%+71%+75%+84%+90%+98%)/6). If he were to choose the mean, his percentage would also be 80%. However, since the median is not affected by extreme values like the 44% score, it is a more reliable measure of central tendency in this case.
I did this on homework b4 and got It right so this Is 100 percent right.
Answer:
Peter should choose the median after dropping one test score so he can have the highest percentage possible.
If we calculate the mean of all seven test scores, we get:
(84+71+64+90+75+44+98)/7 = 73.14%
If we calculate the median of all seven test scores, we get:
Arrange the scores in ascending order:
44, 64, 71, 75, 84, 90, 98
The median is 75.
If we drop the lowest score (44) and calculate the mean of the remaining six test scores, we get:
(84+71+64+90+75+98)/6 = 80.5%
If we drop the lowest score (44) and calculate the median of the remaining six test scores, we get:
Arrange the scores in ascending order:
64, 71, 75, 84, 90, 98
The median is 79.5%.
Therefore, Peter should choose the median after dropping one test score to have the highest possible percentage.
Instructional Item 2
Use the properties of exponents to create an equivalent expression for the given expression
shown below with no variables in the denominator.
(64x²)-^-1/6(32x^5)^-2/5
Answers
a^m * a^n = a^(m+n)
(a^m)^n = a^(mn)
(a*b)^m = a^m * b^m
a^(-m) = 1/a^m
Using these properties, we can simplify the given expression as follows:
(64x²)^(-1/6) * (32x^5)^(-2/5)
= (2^6 * x^2)^(-1/6) * (2^5 * 2x^5)^(-2/5)
= 2^(-6/6) * x^(-2/6) * 2^(-2/5) * (2x^5)^(-2/5)
= 2^(-1) * x^(-1/3) * 2^(-2/5) * 2^(-4/5) * x^(-2)
= 2^(-9/5) * x^(-7/3)
= (1/2^(9/5)) * (1/x^(7/3))
Thus, an equivalent expression with no variables in the denominator is (1/2^(9/5)) * (1/x^(7/3)).
A lodestone is a natural magnet that attracts iron and steel the force required to pull a magnet free from steel plate is called pull force certain magnet has a pull force of 2.2 pounds right this pull force as a mixed number
Answers
We can write the pull force of the magnet as [tex]2 \frac{1}{5} pounds[/tex].
What is the mixed number representation of the pull force?A mixed number refers to number that contains both an integer (whole number) and a proper fraction (a fraction whose numerator is less than its denominator).
To represent the pull force as a mixed number, we must to convert the decimal 0.2 to a fraction. Since 0.2 is equal to 1/5, we can write it as 2 and 1/5 pounds/ Therefore, the mixed number representation of the magnet's pull force of 2.2 pounds is 2 1/5 pounds.
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Which answers describe the shape below? Check all that apply.
31
A
A. Quadrilateral
B. Rhombus
C. Trapezoid
D. Parallelogram
E. Rectangle
F. Square
Answers
Answer:
A and D are correct. This is a parallelogram, which is a quadrilateral. B is not correct because not all the sides are congruent. C is not correct. E and F are not correct because this parallelogram does not have any right angles.
27. The side length of a cube is (b+7). What is its volume?
HELP WHICH INE IS IT CORRECTT ITS DUE TODAY
Answers
Answer:
Step-by-step explanation:
Please answer these 3 questions
Answers
The Volume of the box is 12 cubic unit.
We have,
Height = 1 unit
Width = 2 unit
Length = 6 unit
So, Volume of box
= l w h
= 1 x 2 x 6
= 12 cubic unit
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please help 3/4 divided by 1/8
Answers
Answer:
6
Step-by-step explanation:
please help 3/4 divided by 1/8
3/4 : 1/8 =
3/4 x 8 =
24/4 =
6
Triangle ABC is congruent to triangle DEF.
Which statement must be true about the triangles?
Responses
AC, = , EF
m∠B=m∠F
m∠A=m∠D
BC = DE
Answers
Answer:
the third one: m<a = m<d
35 fluid ounces equals how many cup and ounces
Answers
Answer: 4.375 Cups and 35 Ounces.
Step-by-step explanation:
The amount of fluid ounces in 1 cup is 8, meanwhile the amount of fluid ounces in an ounce is 1.
Hope that helps
(a) How much stronger is a magnitude 7 earthquake than a magnitude 6 earthquake?
_____ times as strong
(b) How much stronger is a magnitude 9 earthquake than a magnitude 6 earthquake?
_____ times as strong
Answers
a. The magnitude of earthquake 7 is 1.259 times stronger than a magnitude 6 earthquake
b. The magnitude of earthquake 9 is 1.995 times stronger than a magnitude 6 earthquake
What is the magnitude of an earthquake?The magnitude of an earthquake is given by M = 10㏒(A/A₀) where A = intensity of eartquake and A₀ = standard intensity
a. To find out how much stronger is a magnitude 7 earthquake than a magnitude 6 earthquake, we proceed as folllows.
For a magnitude of 7,
M = 7 and intensity = A'So, M = 10㏒(A'/A₀)
7 = 10㏒(A'/A₀) (1)
For a magnitude of 6,
M = 6 and intensity = A"So, M = 10㏒(A'/A₀)
6 = 10㏒(A"/A₀) (2)
Subtracting (2) from (1), we have that
7 - 6 = 10㏒(A'/A₀) - 10㏒(A"/A₀)
1 = 10㏒[(A'/A₀) ÷ (A"/A₀)]
1 = 10㏒[(A'/A")
㏒[(A'/A") = 1/10
Taking inverse logarithm, we have
(A'/A") = ¹⁰√10
= 1.259
So, it is 1.259 times stronger
b. To find out how much stronger is a magnitude 9 earthquake than a magnitude 6 earthquake, we proceed as folllows.
For a magnitude of 9,
M = 9 and intensity = A'So, M = 10㏒(A'/A₀)
9 = 10㏒(A'/A₀) (1)
For a magnitude of 6,
M = 6 and intensity = A"So, M = 10㏒(A'/A₀)
6 = 10㏒(A"/A₀) (2)
Subtracting (2) from (1), we have that
9 - 6 = 10㏒(A'/A₀) - 10㏒(A"/A₀)
3 = 10㏒[(A'/A₀) ÷ (A"/A₀)]
3 = 10㏒[(A'/A")
㏒[(A'/A") = 3/10
Taking inverse logarithm, we have
(A'/A") = 10⁰°³
= 1.259
So, it is 1.995 times stronger
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riangle NMO is drawn with vertices N(−5, 2), M(−2, 1), O(−3 , 3). Determine the image vertices of N′M′O′ if the preimage is reflected over x = −2.
N′(5, −2), M′(2, 1), O′(3, 3)
N′(−2, 2), M′(1, 1), O′(0, 3)
N′(1, 2), M′(−2, 1), O′(−1, 3)
N′(−5, −2), M′(−2, −1), O′(−3, −3)
Answers
The vertices after transformation are N′(1, 2), M′(−2, 1), O′(−1, 3).
We have,
N(−5, 2), M(−2, 1), O(−3 , 3).
We know the rule to reflect over a vertical line x =a is
(x, y) --> (-x-2a, y)
So, for x=2 the rule will be
(x, y) --> (-x-4, y)
Now, the vertices after transformation are
M(-2, 1) -> M'(-2, 1)
N(-5, 2) -> N'(1, 2)
O(-3, 3) -> O'(-1, 3)
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Solve for x:
3x - 3 = 4(x-9)
Show your work
Answers
-3 + 36 = 4x - 3x
33 = x
Therefore, x = 33
Answer:
[tex]\Huge \boxed{\bf{x = 33}}[/tex]
Step-by-step explanation:
To solve for x in the equation [tex]3x - 3 = 4(x - 9)[/tex], we will follow these steps:
1. Distribute the 4 on the right-hand side of the equation:
[tex]3x - 3 = 4x - 36[/tex]2. To isolate x, subtract 3x from both sides:
[tex]-3 = x - 36[/tex]3. Lastly, add 36 to both sides of the equation to solve for x:
[tex]x = 33[/tex]So, the solution to the equation [tex]3x - 3 = 4(x-9)[/tex] is [tex]x = 33[/tex].
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________________________________________________________
What is an equation of the line that passes through the points (0,-8) and (4, -3)?
=00
Answers
Hello!
To find the equation of the line that passes through the points (0,-8) and (4,-3), we can use the slope-intercept form of the equation:
y = mx + b
where m is the slope of the line and b is the y-intercept.
First, find the slope (m) of the line using the formula:
m = (y2 - y1)/(x2 - x1)
where (x1, y1) = (0,-8) and (x2, y2) = (4,-3).
m = (-3 - (-8))/(4 - 0) = 5/4
Now that we have the slope (m), we can use the point-slope form of the equation to find the equation of the line:
y - y1 = m(x - x1)
where (x1, y1) = (0,-8) and m = 5/4.
y - (-8) = (5/4)(x - 0)
Simplify the equation to get the slope-intercept form:
y + 8 = (5/4)x
y = (5/4)x - 8
Therefore, the equation of the line that passes through the points (0,-8) and (4,-3) is y = (5/4)x - 8.
PQRS is a rhombus. ∠ SPQ = 120° and SP = 8.
Find each of the following.
20). ∠ SPO
21). ∠ POS
22). ∠ PSO
23). ∠ PO
24). ∠ SO
25). ∠ The area of PQRS
Answers
In the rhombus PQRS, if angle ∠ SPQ = 120° then ∠SPO is 30°
∠POS is 90° and ∠PSO is 60 degrees, ∠PO is 90° and ∠SO is 150°
PQRS is a rhombus.
∠ SPQ = 120° and SP = 8.
We have to find angles,∠SPO = (180° - ∠SPQ) / 2
= (180° - 120°) / 2
= 30°
∠POS = 90°
Now we have to find angle PSO
∠PSO+∠SPO+∠POS =180
30+90+∠PSO=180
120+∠PSO=180
∠PSO=180-120
∠PSO=60 degrees
∠PO = 360° / 4 = 90°
∠SO = 180° - ∠POS = 180° - 30°
= 150°
The area we find by using formula diagonal 1 × diagonal 2/2
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Solve for x. 3x2−6x+2=0
x=3±23√3
x=3±3√3 x equals fraction numerator 3 plus or minus square root 3 end root end numerator over 3 end fraction x=6±43√3 x equals fraction numerator 6 plus or minus 4 square root 3 end root end numerator over 3 end fraction x=6±23√3 x equals fraction numerator 6 plus or minus 2 square root 3 end root end numerator over 3 end fraction
Answers
The solution of "quadratic-equation" , 3x² - 6x + 2 = 0 is (b) x = (3 ± √3)/3.
A "Quadratic-Equation" is defined as a second-degree polynomial equation of the form : ax² + bx + c = 0,
where x = variable, and "a", "b", and "c" are constants, with a ≠ 0.
We use the "quadratic-formula" to solve : which is ⇒ x = (-b ± √(b²-4ac))/(2a),
In the quadratic equation "3x² - 6x + 2 = 0", We get , a = 3, b = -6, and c = 2.
Substituting the values,
we get,
⇒ x = (-(-6) ± √((-6)²-4(3)(2)))/(2×3),
⇒ x = (6 ± √(36-24))/6,
⇒ x = (6 ± √12)/6,
⇒ x = (6 ± 2√3)/6,
⇒ x = (3 ± √3)/3,
So the two roots of the quadratic equation 3x² - 6x + 2 = 0 are : x = (3 + √3)/3 and x = (3 - √3)/3.
Therefore, the correct option is (b).
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The given question is incomplete, the complete question is
Find the solution of the given quadratic equation , 3x² - 6x + 2 = 0.
(a) x = 3 ± 23√3
(b) x = (3 ± √3)/3
(c) x = 6 ± 43√3
(d) x = 6 ± 23
a+b-c
a + b is equal to what
Answers
The expression a + b cannot be added/evaluated because 2.00x and 1.50y are not like terms
Evaluating the expressionFrom the question, we have the following parameters that can be used in our computation:
a + b is equal to what
The above statement is an addition expression that adds the values of a and b
However, the terms of the expression are not like terms
i.e. a and b are not like terms
This means that the expression cannot be added/evaluated
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At what values of x does f(x)=0?
Answers
Answer:
f(x) = 0 at x = -2, 1, 3
A, B, and D are the correct choices.
Which system of linear equations has no solutions?
a) y = 4x +1 y= -4x + 1
b) y= 2x + 7 y= 2x - 7
c) 3x + y =1 6x + 2y =2
d) 5x + y =3 x + 5y = 15
Answers
Answer:
b)
Step-by-step explanation:
a) y = 4x +1 y= -4x + 1
Different slopes; same y-intercept; lines intersect at 1 point; there is 1 solution.
b) y= 2x + 7 y= 2x - 7
Same slopes; different y-intercepts; parallel lines do not intersect; no solution.
c) 3x + y =1 6x + 2y =2
Equations are the same; infinite number of solutions.
d) 5x + y =3 x + 5y = 15
Different slopes; lines intersect at 1 point; there is 1 solution.
Answer: b)
Triangle ABC has vertices at A(−3, 3), B(0, 7), and C(−3, 0). Determine the coordinates of the vertices for the image if the preimage is translated 3 units up.
A′(−3, 0), B′(0, 4), C′(−3, −3)
A′(−3, 6), B′(0, 10), C′(−3, 3)
A′(−6, 3), B′(−3, 7), C′(0, 0)
A′(0, 3), B′(3, 5), C′(0, 0)
Answers
Answer:
To translate triangle ABC 3 units up, we need to add 3 to the y-coordinate of each vertex:
A' = (-3, 3 + 3) = (-3, 6)
B' = (0, 7 + 3) = (0, 10)
C' = (-3, 0 + 3) = (-3, 3)
Therefore, the coordinates of the vertices for the image triangle A'B'C' are A'(-3, 6), B'(0, 10), and C'(-3, 3).
So the correct answer is: A′(−3, 6), B′(0, 10), C′(−3, 3).
Determine how many liters a right circular cylindrical tank holds if it is 6 m long and 13 m in diameter.
Answers
The tank holds approximately 994,040 liters.
To solve this problem
The volume of a right circular cylinder is given by the formula:
V = πr^2h
Where
r is the radius of the cylinderh is its height π is a mathematical constant approximately equal to 3.14159The cylinder's diameter is specified as 13 m, hence the radius may be computed using the formula: r = d/2 = 13/2 = 6.5 m
The cylinder is described as having a 6 m length.
These values are substituted into the volume calculation to produce the following result:
V = π(6.5)^2(6)
V ≈ 994.04 cubic meters
Since 1 cubic meter equals 1000 liters, we can convert the volume to liters by multiplying by 1000.
V = 994.04 cubic meters x 1000 liters/cubic meter
V = 994,040 liters
Therefore, the tank holds approximately 994,040 liters.
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26). Is Δ EFG ≅ Δ HIJ?
27). What is the scale factor of Δ EFG to Δ HIJ?
28). What is the ratio of their perimeters?
29). What is the ratio of their areas?
Answers
The triangles are not congruent.
Given that, two triangles, EFG and HIJ are similar,
So,
Since, the triangles are similar, but according to the definition of similarity, two objects that are similar are not necessarily congruent,
so the Δ EFG is not congruent to Δ HIJ.
Cos 30° = HI / HJ
√3/2 = 3/HI
HI = 3.5
Therefore, the scale factor Δ EFG to Δ HIJ = EF / HI = 10/3.5 = 2/0.7
The ratio of perimeter of similar objects are same as the scale factor,
so, the ratio of their perimeters = 2/0.7
The ratio of the areas of the similar objects are the ratios of the squares of the scale factor.
So, the ratio of their areas = 4/0.49
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Please helpppppppppp k12and only give an accurate answer
With Geico you get a discount for being a good driver of 10%. You have a six month policy for 1,025. If you pay it in full, you get another 10% discount.
How much would you pay per month if you choose to not pay in full?
Round your answer to the nearest cent and do not put a dollar sign.
Answers
$138.38 you pay per month if you choose to not pay in full
If you pay in full, you get a 10% discount on the six-month policy, which means you would pay:
1,025 - 0.1(1,025) = 922.50
If you choose to not pay in full, you would not get the 10% discount for paying in full.
We get the 10% discount for being a good driver, which would be applied to each monthly payment.
This means that each monthly payment would be:
(1 - 0.1)(922.50) / 6 = 138.38
we get a monthly payment of $138.38.
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you complete your math homework 25 out of 25 school days in April. Describe the likelihood of you completing your math homework.
Answers
Because 25/25=50
Which makes the inequality 100%
Is AB a tangent? Why or Why not? (Hint: use Pythagorean Theorem)
Answers
Answer:
AB is not a tangent. The lengths 4, 12, and 13 do not form a right triangle.
√(4^2 + 12^2) = √160, which is not equal to 13.
Answer:
No
Step-by-step explanation:
if AB is a tangent the the angle BAC = 90°
using Pythagoras' theorem
then square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
BC² = 13² = 169
AB² + AC² = 12² + 4² = 144 + 16 = 160
since BC²≠ AB² + AC²
then Δ ABC is not a right triangle so AB is not a tangent
For each of the shapes below, state whether it is a regular polygon, an
irregular polygon or neither.
ASAAP NEED HELLPPP
Answers
Answer:
regular: Eirregular: A, B, Dneither: CStep-by-step explanation:
You want to identify the given shapes as a regular or irregular polygon, or neither.
Regular polygonA regular polygon is one that has all sides congruent, and all interior angles congruent. Polygon E is marked as having congruent sides and congruent angles.
Polygon E is a regular polygon.
PolygonA polygon is a closed figure formed by line segments connected end-to-end. A simple polygon is one that has no intersecting line segments. A convex polygon is one that has all interior angles measuring 180° or less.
Any simple polygon that is not a regular polygon is an irregular polygon.
Polygons A, B, D are irregular polygons.
CircleA circle is not a polygon. Figure C is neither a regular polygon nor an irregular polygon.
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The height and radius of a cone are each multiplied by 3.
What effect does this have on the volume of the cone?
The volume of the cone is multiplied by
Answers
If both the height and radius of a cone are multiplied by 3, the new radius and height will be 3r and 3h, respectively.
We can substitute these values into the volume formula for the new cone:
V = (1/3)π(3r)^2(3h)
Simplifying the expression gives:
V = (1/3)π(27r^2h)
V = 9πr^2h
So, the volume of the new cone is 9 times larger than the volume of the original cone.
Therefore, if both the height and radius of a cone are each multiplied by 3, the volume of the cone is multiplied by 9
PLEASE HELP ASAPP !!!!!!!!!!!!!!!!!!!!!
Answers
The value of m for the quadratic equation, 2x² - 28x + 7m = 0 to have one solution is 14.
How to solve quadratic equation?She said the quadratic equation 2x² - 28x + 7m = 0 has only one solution for some value of m.
Therefore, the exact value of m which give the quadratic equation exactly one solution can be calculated as follows:
Therefore, a quadratic equation has one solution when the discriminant is zero.
Hence,
b² = 4ac
a = 2
b = -28
c = 7m
Therefore,
(-28)² = 4 (2)(7m)
784 = 56m
divide both sides by 56
m = 784 / 56
m = 14
Therefore,
m = 14
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