Answers
ANSWER:
139 square yards
STEP-BY-STEP EXPLANATION:
We have that the formula for the surface area of a triangular prism is the following:
[tex]A=p\cdot h+2b[/tex]Where p, is the perimeter is the base and h is the height, while b is the area of the base, we replace and calculate the area like this:
[tex]\begin{gathered} p=4+4+5=13 \\ A=13\cdot9.5+2\cdot7.75 \\ A=123.5+15.5 \\ A=139 \end{gathered}[/tex]The area is 139 square yards
Related Questions
Write the equation of the line that passes through the given points.
1,2.5) and (0,-1.5)
Answers
Answer:
y = 4x - 1.5
Step-by-step explanation:
We need to find the slope (m) and the y-intercept (b), if we are writing this in the slop intercept form of a line.
y =mx + b
The slope is the change in y over the change in x.
The two points give us the y's ad x's
The y's are: -1.5 and 2.5
The x's are: 0 and 1
[tex]\frac{-1.5 - 2.5}{0-1}[/tex] = [tex]\frac{-4}{-1}[/tex] = 4 A negative divided by a negative is a positive.
We have the slope. The slope is the point (0,b). We are given that point.
(o, -1.5) The y-intercept is -1.5
y =mx + b
y = 4x - 1.5
this is a 45-45-90 triangle, what is the measure of x? rationalize the denominator
Answers
The value of x in the right triangle is 15√2.
How to find the side of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees.
The sides of a right triangle can be named base on the angle position. This includes hypotenuse side, opposite side and adjacent side.
Therefore, the side x of the right triangle can be found using trigonometric ratios as follows:
cos 45 = adjacent / hypotenuse
cos 45° = x / 30
cross multiply
30 cos 45° = x
Therefore,
x = 30 × 1 / √2
x = 30 / √2 × √2 / √2
x = 30√2 / 2
x = 15√2
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What’s the answer pls
Answers
If I'm not mistaken, the answer is 43.17
Identify pairs of lines which look perpendicular in the diagram. There are more than one answers.
Answers
Answer:
Angles gh, fh, and jh are perpendicular :)
Step-by-step explanation:
perpendicular is when line touch and they make a 90* angle and the three angles that i have listed all touch and make 90*
Let g be a group with normal subgroups m and n. furthermore, assume n is a subste of m. use the first isomorphic theorem to prove that (g/n)/(m/n) is isomorphic to g/m.
Answers
The proof of (g/n)/(g/m) isomorphic to g/m from the first isomorphism theorem is as shown below.
Let a group g with normal subgroups m and n. Furthermore, n is a subset of m.
Proof: We have to prove (g/n)/(m/n) ≅ g/m (1)
g/m and g/n are valid because m and n are normal in g. As normality satisfies the intermediate subgroup condition, n is normal in m. because normality is image-closed m/n is a normal subgroup in g/n. Under the quotient map by n, the normal subgroup m of g is sent to a normal subgroup m/n of g/n. Thus the L.H.S of the statement to prove makes sense.
To describe the isomorphism from the left side to the right side
φ: g/n \to g/m
ψ(gn) = gm
So, a coset of n is taken by the map and it gives the corresponding coset of m. This is well-defined, because if h∈ n, thus h∈ m, hence (gh)m = g(hm) = gm.
The map is a homomorphism. So we observe that it maps the identity element to the identity element, keeps group multiplication preserved, and also preserves the inverse map.
Also, the map is surjective because any coset gm is present as the image of gn under ψ.
Lastly, we need to find the kernel of the map which is given by the set of gn such that gm = m. This is those cosets of n that are in m, and this is the same as the coset space m/n. Thus the kernel of the map is exactly g/m. Thus, the surjective homomorphism ψ: g/n → g/m has kernel m/n. And now by the first isomorphism theorem
(g/n)/(m/n)≅g/m where ≅ shows isomorphism
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Rewrite the expression using only positive integer exponents. (m2/3n-1/3)^5
Answers
When the expression (m²/³ n⁻¹/³)⁵ is rewritten, the equivalent expression is ∛m¹⁰n⁻⁵
How to rewrite the expression?From the question, the expression is given as
(m2/3n-1/3)^5
Rewrite the expression properly
So, we have the following representation
(m²/³ n⁻¹/³)⁵
Express the radicals as roots
So, we have
(m²/³ n⁻¹/³)⁵ = (∛m² ∛n⁻¹)⁵
Remove the brackets in the expression
This is done by multiplying the exponents
So, we have
(m²/³ n⁻¹/³)⁵ = (∛m¹⁰ ∛n⁻⁵)
Combine the roots
(m²/³ n⁻¹/³)⁵ = ∛m¹⁰n⁻⁵
Hence, the equivalent expression is ∛m¹⁰n⁻⁵
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The required simplified expression is given as ∛[m¹⁰/n⁵].
Given that,
For an expression (m²/³n-¹/³)⁵ we have to deduce the function that the solution only consists of the positive integer exponents.
Here,
Rewriting the given expression,
= (m²/³n-¹/³)⁵
Simplifying the expression,
using the property, (xᵃ)ᵇ = xᵃᵇ
= m¹⁰/³n⁻⁵/³
= [m¹⁰n⁻⁵]¹/³
we imply cube root for the exponent 1/3.
= ∛[m¹⁰n⁻⁵]
= ∛[m¹⁰/n⁵] (using the property x⁻¹ = 1 / x )
Thus, the required simplified expression is given as ∛[m¹⁰/n⁵].
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PLEASE HELP!!
Points A(-1, 2) and B(5,8) are the endpoints of AB. What are the coordinates of point C on AB such that AC is 2/3 the length of AB
Answers
The coordinates of the point C on the line AB such that AC is 2/3 the length of AB is (3,6) .
In the question ,
it is given that
the coordinates of the end points of A and B is A(-1,2) and B(5,8) .
also AC = 2/3(AB)
So , AC/AB = 2/3
and given that point C is on the line AB , hence AC+CB=AC
2+CB=3
So , CB=1
hence AC/CB = 2/1
so , the point C divides the line AB in the ration 2:1 .
and we have the coordinates of end points ,
that is x₁[tex]=[/tex] -1 , y₁=2 and x₂=5 , y₂ = 8 and the ratio m=2 and n=1 .
Substituting the above values in the section formula ,
which states that the coordinate of point C will be
((m*x₂+n*x₁)/(m+n) , (m*y₂+n*y₁)/(m+n))
= ((2*5+1*(-1))/(2+1) , (2*8+1*2)/(2+1))
= ((10-1)/3 , (16+2)/3)
= (9/3 , 18/3)
= (3,6)
Therefore , The coordinates of the point C on AB such that AC is 2/3 the length of AB is (3,6) .
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the average number of miles driven on a full tank of gas for a hyundai veracruz before its low fuel light comes on is 320. assume this mileage follows the normal distribution with a standard deviation of 30 miles. what is the probability that, before the low fuel light comes on, the car will travel
Answers
The probability that, before the low fuel light comes on the car will travel is 0.2576
Given,
The average number of miles driven on a full tank of gas before its low fuel light comes on is ( μ )= 320
It follows the standard deviation of ( δ ) = 30
For the normal distribution,
P(X < x) = P( Z < x - μ / δ)
a)
P( X < 330) = P( Z < 330 - 320 / 30)
= P( Z < 0.3333)
= 0.6306
b)
P( X > 308) = P( Z > 308 - 320 / 30)
= P( Z > -0.4)
= P( Z < 0.4)
= 0.6554
c)
P( 305 < X < 325) = P( X < 325) - P( X < 305)
= P( Z < 325 - 320 / 30) - P( Z < 305 - 320 / 30)
= P( Z < 0.1667) - P( Z < -0.5)
= 0.5662 - ( 1 - 0.6915)
= 0.2576
d) P(X = 340) = 0
Since X is a continuous random variable (For normal distribution).
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a student has taken 6 tests and received scores of 88, 73, 81, 80, 79, and 94. the seventh test is coming up and the student wants to know what score is needed on the seventh test to have a mean score of 83. determine the score the student needs. show your work.
Answers
Solution:
Let the score for the seventh test be represented below as
[tex]=x[/tex]The mean score t be attained after the sevent tests is
[tex]mean=83[/tex]The scores from the 6 tests are given below as
[tex]88,73,81,80,79,94[/tex]To figure out the seventh score, we will do the calculation below
[tex]\begin{gathered} mean=\frac{additionofthescores}{number\text{ of tests}} \\ 83=\frac{88+73+81+80+79+94+x}{7} \\ 83=\frac{495+x}{7} \\ cross\text{ multpily} \\ 83\times7=495+x \\ 495+x=581 \\ x=581-495 \\ x=86 \end{gathered}[/tex]Hence,
The final asnwer is
[tex]\Rightarrow86[/tex]Find the indicated part round your answer to the nearest degree
Answers
Solution
For this case we can do the following:
tan x = 35/30
And we can solve for x and we got:
[tex]x=\tan ^{-1}(\frac{35}{30})=49.39[/tex]And rounded to the nearest degree is:
49º
Pls help me. I'm struggling so bad
Answers
The formula for M₁ in terms of [tex]F_{g}[/tex] , G , M₂ , r is M₁ = ( [tex]F_{g}[/tex]*r² ) /(G*M₂ ) .
in the question ,
it is given that the
formula to find , "gravitational force" between two objects is
[tex]F_{g}[/tex] = (G*M₁*M₂)/r²
to express the formula in terms of M₁ ,
we first multiply both the sides by r² ,
on multiplying , we get
[tex]F_{g}[/tex]*r² = G * M₁ * M₂
On dividing both sides by G ,
we get
( [tex]F_{g}[/tex]*r² ) /G = M₁ * M₂
we have to find the formula for M₁ ,
we divide both sides by M₂,
So , on dividing both sides by M₂ , we get
( [tex]F_{g}[/tex]*r² ) /(G*M₂ ) = M₁
hence M₁ = ( [tex]F_{g}[/tex]*r² ) /(G*M₂ )
Therefore , the formula for M₁ in terms of [tex]F_{g}[/tex] , G , M₂ , r is M₁ = ( [tex]F_{g}[/tex]*r² ) /(G*M₂ ) .
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The figure is not drawn to scale. m
Answers
For the given function
The sum of all angles = 360°
So,
[tex]\begin{gathered} y+x+125+90=360 \\ m\angle x=27 \\ So,\text{ } \\ y+27+125+90=360 \\ y+242=360 \\ y=360-242=118 \end{gathered}[/tex]So, the difference between x and y will be:
[tex]y-x=118-27=91[/tex]So, the answer will be:
∠x is 91° smaller than ∠y
Eli has 12 eggs. He uses his grandpa's recipe to bake 4 loaves of challah. Find how many eggs are left over if Eli uses 2 eggs for each loaf of challah?
Answers
Answer:
4 Eggs are left since he uses 2 eggs per 1 loaf so 2x4=8
Step-by-step explanation:
Look at photo down below for question
Answers
The coordinates of the rotated triangle will be (2, - 2) , (3, -8) , (7, 0)
What is translation of graph?Function translation takes a function (and its graph) and, by adding and subtraction, moves the graph around the plane without changing its shape.
Given is a triangle coordinate on x - y plane.
The rule (x, y) → (- x, - y) represents the rotation of a figure by 180 °.
Now, initially the coordinates of the triangle are -
(-2, 2) , (-3, 8) , (-7, 0)
After transforming the graph by the rotation of 180°, the new coordinates will be -
(2, - 2) , (3, -8) , (7, 0)
Plot the coordinates on the graph and you will get the rotated image.
Therefore, the coordinates of the rotated triangle will be (2, - 2) , (3, -8) , (7, 0).
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For the function Rx) = +2, which of these could be a value of Ax) when x isclose to 2? A. 0.01B. 2C. -0.01D. 10,000
Answers
The given function F(x) is,
[tex]F(x)=\frac{1}{x-2}[/tex]Take the limit of the function when x ix close to 2.
[tex]Lt_{x\rightarrow2}\frac{1}{x-2}=\infty[/tex]Hence, the function diverges.
How much would $500 invested at 6% interest compounded monthly be worth after 5 years? Round your answer to the nearest cent. A.$669.11B.$674.43C.$886.41D.$512.63
Answers
Solution:
Given that;
[tex]\begin{gathered} Principal=P=\text{ \$500} \\ rate=r=\frac{6}{100}=0.06 \\ time=t=\text{ 5 years} \end{gathered}[/tex]To find the amount in 5 years, we will apply the compound interest formula below
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ Since,\text{ it is compounded montly, n = 12} \end{gathered}[/tex]Substitute the values of the variables into the formula above
[tex]\begin{gathered} A=500(1+\frac{0.06}{12})^{(5\times12)}=500\left(1+\frac{0.06}{12}\right)^{60}=674.42507 \\ A=\text{ \$}674.43\text{ \lparen nearest cent\rparen} \end{gathered}[/tex]Hence, the answer is B
If ax-3=bx+5 then the solution for x in terms of a and b is
Answers
In this equation the solution for x in terms of a and b is 8.
What is equation?
There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.
Sol- As per the question given that- ax-3= bx+5------(equation 1)
Let ax=3-----(equation 2)
And bx =5------(equation 3)
On adding equation(1)and (2) we get
(ax)+(bx)= 3+5
(ax)+(bx)=8
x(a+b)+y(a+b)=8
(x+y)+(a+b)=8
1×(a+b)=8
Thus
a+b=8
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Solve the equation. -5x + 1 = 31 x=
Answers
we get that:
[tex]\begin{gathered} -5x+1=31\rightarrow-5x=31-1=30 \\ x=-\frac{30}{5}=-6 \end{gathered}[/tex]so the answer is x=-6
-
Bobby photographs a bird. If the bird, that measures 3.4 inches in the photo, is actually 3.75 feet tall, approximately how long is its boak if it measures 0.4 inches in the
photo?
Answers
We need to know about scaling of measurements to solve the problem. The length of the bird's beak is 5.29 inches.
In the given question we know that the height of the bird in the photo is 3.4 inches and the real height of the bird is 3.75 feet. We know that the length of the beak in the photo is 0.4 inches, we need to find out the real length of the beak. We need to find by how much the measurement of the bird is scaled down to fit in the photo. We need to convert feet to inches first to get the scaling factor, we can then divide the length of the beak given by the scaling factor.
3.75 feet= 3.75x12 =45 inches
scaling factor= 3.4/45=0.0756
real length of beak=0.4/0.0756=5.29 inches
Therefore the length of the beak of the bird is 5.29 inches.
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A plumber charges a flat fee of 75 to visit a home and examine a clogged drain. The plumber charges an additional 22 per hour spent fixing the drain. The total cost, (in dollars), for fixing a drain that takes hours is given by the following.
Answers
The expression for the total cost is 75 + 22h
How to calculate the cost?From the information, the plumber charges a flat fee of 75 to visit a home and examine a clogged drain and also charges an additional 22 per hour spent fixing the drain.
Therefore, the amount that will be charged for each hour will be:
= 75 + (22 × h)
= 75 + 22h
where h = number of hours.
For example if the number of hours is 5 hours. This will be:
= 75 + 22h
= 75 + 22(5)
= 75 + 110
= 185
Your information was incomplete but an overview was given.
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Can someone help me please with this !!!!!
Answers
Answer:
A. [tex]9n - 190 = 5n[/tex]
Step-by-step explanation:
Dora earning 5 dollars per song is represented by [tex]5n[/tex].
Gary earning 9 dollars a song but paying the $190 fee is represented by [tex]9n - 190[/tex] because the fee from the coffee shop is subtracted from his total earnings.
Safiya travels at an average speed of 40 mph for 30 miles.
Without stopping, Safiya then travels 50 miles in 1.5 hours.
Find her average speed for the entire journey to 2 dp.
Pls help
Answers
Average speed is 35.56 mph.
Calculating average speed involves dividing the whole distance travelled by the total time it took to cover that distance. Speed is the rate of movement of something at a specific time. Average speed refers to the average speed during the course of a journey.
We have to find the average speed of the whole journey.
First we have to find total distance for whole journey and then total time for whole journey.
Total distance for whole journey = 30 miles + 50 miles = 80 miles
Time for 30 miles = distance/speed = 30/40 = 3/4 hrs = 0.75 hrs
Total time = 1.5 + 0.75 hrs = 2.25 hrs
Average speed = total distance/ total time
= 80/2.25
= 35.56 mph.
The average speed is 35.56 mph.
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What is the slope that passes through these points?
(0, -4) and (-5, -5)
Answers
Answer: m=1/5
Step-by-step explanation:
how to graph y=2x+2 please help
Answers
The graph of the equation is attached to the solution.
We can graph the equation of the line by finding the x and y intercept of the line.
We know that the equation is in the slope intercept form.
Hence, we can write the y-intercept of the line as 2.
The coordinates of the point will be (0,2).
To find the x - intercept, we can put y = 0
0 = 2x + 2
-2 = 2x
x = -2/2 = -1
x = -1
The coordinates of the point will be (-1,0).
We can find another point on the line.
Let x = 1
y = 2(1) + 2
y = 2 + 2
y = 4
The coordinates of the point will be (1,4).
We can plot these points on the graph and get our graph.
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Which of the following ordered pairs is either the x- or y-intercept of the function 3x + 2y = -6?
Answers
Answer:
x-intercept (-2,0)
y-intercept (0,-3)
Step-by-step explanation:
to find the x-intercept we set y=0
so 3x=-6
x=-2
to find the y-intercept we set x=0
so 2y=-6
y=-3
I need help!
Use the given information to select the factors of f(x). f(4)=0 f(-1)=0 f(3/2)=0. Make sure to select all correct answers for full credit.
Answers
Using the information of the factors f ( x ) are
( x + 1 ) ⇒ f ( -1 )( x - 4 ) ⇒ f ( 4 )( 2x - 3 ) ⇒ f ( 3/2 )What is a function in math?The term function as used n math refers to a relation consisting of variables. the variables are of two major types which include
The dependent variableThe independent variableThe given function is substituted in the several equations given but the equations that yielded the desirable result of f ( x ) = 0 are:
option 4option 5option 6Therefore they are the correct choice
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When an integer is subtracted from 2 times the next consecutive odd integer, the
difference is 9. Find the value of the greater integer.
Answers
Answer:
7
Step-by-step explanation:
Let x be the "integer." We'll assume it is odd.
The next consecutive odd integer would be x+2.
(2(x+2) - x) =9 [When an integer is subtracted from 2 times the next consecutive odd integer the difference is 9]
(2(x+2) - x) =9
(2x+4) - x) =9
x+4 =9
x = 5
The greater integer is x+2 or 7
Check:
If 5 is subtracted from 2 times the next consecutive odd integer, 7, is the difference 9?
2*7 - 5 = 9?
14 - 5 = 9?
14 - 5 = 9? YES
-5< x < 5Graph the solution set on a number line
Answers
- 5 < x < 5
Number line:
You have read 4 of the books shown. Which choice shows 2 ways of writing the fraction of these books that you read?
Answers
Using proportions, two ways of writing the fraction of these books that you read is:
4/12 and 1/3.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations, especially multiplication or division.
One example of application of proportions is for relative frequencies, as a relative frequency is given by the number of successes in the sample divided by the sample size.
In the context of this problem, it is found that:
The number of successes on the sample is of 4, as you have read 4 books.The sample size is of 12, as there is a total of 12 books.Hence the relative frequency is:
4/12.
12 is divisible by 4, hence the fraction can be simplified as follows:
1/3.
Missing informationThe number of books is missing, and is of 12. (researching the problem on a search engine).
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What is the value of this expression
Answers
Plug in the values in the right positions. And simplify.
[tex] = \frac{1}{2} (12 \times \frac{1}{4} ) - \frac{1}{2} \\ = \frac{1}{2} (3) - \frac{1}{2} \\ = \frac{3}{2} - \frac{1}{2} \\ = \frac{2}{2} \\ = 1[/tex]
OPTION C IS THE ANSWER .