The expression which represents the volume of the prism, in cubic units, is one-half x³+ x².
What is of volume of prism?Volume of prism is the amount of quantity, which is obtained in it in the 3 dimensional space. The volume of a prism is the product of the area of its base and height.
[tex]V=A_b\times h[/tex]
Here, ([tex]A_b[/tex]) is the area of the base and (h) is the height of the prism.
The side of the base of the triangular prism is x units. Thus the area of the base is,
[tex]A_b=\dfrac{x\times x}{2}\\A_b=\dfrac{x^2}{2}[/tex]
The height of this prism is (x+2) units long. Thus, the volume of the prism is,
[tex]V=\dfrac{x^2}{2}\times (x+2)\\V=\dfrac{1}{2}x^3+x^2[/tex]
Thus, the expression which represents the volume of the prism, in cubic units, is one-half x³+ x².
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Answer:
1. A- 1/2x^3
2. 168
3. 927
4A. 48
4B. 336
5. A D
6. 1 3 3
7. 12 cm
8. 8 , 4
9. B
10. A C D
Step-by-step explanation:
whole thing right on edge
What is the solution of X+8/5x-1
-> O?
5
X5-8 or
x>
O x<-8 or x>5
0x
X
col-
0 -85x<5
0 -8 < x < 1 / 3
x - inf - 8 1/5 + inf
x+8 - 0 + +
5x-1 - - 0 +
result + 0 - ║ +
x+8/(5x-1) > 0 if x € ] -inf ; - 8[ U ] 1/5 ; + inf [
=> x < - 8 and x > 1/5
The solution to the inequality (x + 8)/(5x - 1) ≤ 0 is:
x ∈ (-∞, -8] ∪ [1/5, ∞)
We have,
To solve the inequality (x + 8)/(5x - 1) ≤ 0,
We can use the following steps:
Step 1:
Find the critical values of x where the expression (x + 8)/(5x - 1) is equal to zero or undefined.
The expression is undefined when the denominator is equal to zero:
5x - 1 = 0
x = 1/5
The expression is equal to zero when the numerator is equal to zero:
x + 8 = 0
x = -8
Therefore,
The critical values are x = -8 and x = 1/5.
Step 2:
Create a sign chart to determine the sign of the expression (x + 8)/(5x - 1) for each interval between the critical values.
On the interval (-∞, -8), the expression (x + 8)/(5x - 1) is negative if x + 8 is negative, which means x < -8.
On the interval (-8, 1/5), the expression (x + 8)/(5x - 1) is positive if both the numerator and denominator are negative, or if both are positive.
The numerator is negative on this interval, so the expression is positive if the denominator is negative, which means x < 1/5.
On the interval (1/5, ∞), the expression (x + 8)/(5x - 1) is negative if the numerator is negative and the denominator is positive, which means x > 1/5.
Step 3:
Write the solution in interval notation.
Therefore,
The solution to the inequality (x + 8)/(5x - 1) ≤ 0 is:
x ∈ (-∞, -8] ∪ [1/5, ∞)
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What is the sale price of jeans which regularly cost $32, but now are 10% off?
Answer:
$28.80
Step-by-step explanation:
32 x 0.1 = 3.2
32 - 3.2 =28.8
Hope this helps :)
Answer:
$28.8
Step-by-step explanation:
10% of 32 is 3.2
32 - 3.2 = 28.8
plllsss hhhheelllppp mee pllllsss
Answer:
The theoretical probability states that it should be equal. That is should be 50/50 but the experimental results show that the coin favoured heads.
2. A football is punted into the air. Its height h, in metres, after t seconds is given by the equation
h(t) = -4.91? + 24.5t + 1
a) How high is the ball after 1 second?
b) Find the maximum height of the ball to one decimal place.
c) When does the ball reach its maximum height?
d) When does the ball hit the ground?
Answer:
I'll assume the ? is supposed to be t^2
See the answers below.
Step-by-step explanation:
h(t) = -4.91t^2 + 24.5t + 1
a) How high is the ball after 1 second?
h(1) = -4.91*(1)^2 + 24.5*(1) + 1
h(1) = 20.59 meters
b) Find the maximum height of the ball to one decimal place.
We can find the maximum height by graphing or by taking the first derivative and setting it equal to zero (the slope is zero at the top of the curve):
First Derivative
h(t) = -4.91*(t)^2 + 24.5*(t) + 1
'h(t) = -9.82*(t) + 24.5
0 = -9.82*(t) + 24.5
9.82t = 24.5
t = 2.49 seconds is the time the ball reaches maximum height. Use that is the equation to find the height:
h(2.49) = -4.91*(2.49)^2 + 24.5*(2.49) + 1
h(2.49) = 31.6 meters
Graph
See attached graph. The maximum height occurs at t = 2.49 seconds and the height is 31.6 meters.
c) When does the ball reach its maximum height?
From the first derivative calculation above, t = 2.49 seconds to reach maximum height. The graph also shows 2.49 seconds. Better hurry.
d) When does the ball hit the ground?
The can be determined by either direct calculation of from the graph (attached).
Calculation:
h(t) = -4.91t^2 + 24.5t + 1
0 (ground) = -4.91t^2 + 24.5t + 1
4.91t^2 - 24.5t - 1 = 0 Solve with the quadratic equation. I get t = 5.04 seconds
Graph:
The graph shows 4.95 seconds. Both agree when rounded to one decimal point: 5.0 seconds.
Noah says, "If I try to write ten to the zero power expanded, it should have zero factors that are 10, so it must be equal to 0." Do you agree? Why or why not?
Answer:
No, I do not agree. This is because 10⁰ is equivalent to 1.
Step-by-step explanation:
any number to the power of 0 is equal to 1
Complete a Proportion Web for the following situation
A candy-wrapping robot can wrap 434 pieces of candy in 5 minutes. How many pieces of candy can it wrap in and number of minutes
Answer:
It can produce about 86 candy.
Step-by-step explanation:
434 divided by 5 = 86 with a remainder of 0.8
If you are asked to factorize only, can you also expand the brackets ? Or you can’t u less you are asked to? Please answer..
Jade wants to buy a $200,000 term life insurance policy. she is 34 years old. using the premium table, what is her annual premium for a 10 year policy? a 5-column table with 6 rows titled annual life insurance premium (per 1,000 dollars of face value). column 1 is labeled age with entries 30, 31, 32, 33, 34, 35. column 2 is labeled 5-year term male with entries 3.98, 4.08, 4.19, 4.30, 4.42, 4.54. column 3 is labeled 5 year term female with entries 3.66, 3.76, 3.87, 3.98, 4.10, 4.22. column 4 is labeled 10-year term male with entries 6.06, 6.13, 6.30, 6.38, 6.45, 6.53. column 5 is labeled female with entries 5.72, 5.79, 5.85, 5.93, 6.01, 6.09. a. $1,290 b. $1,202 c. $6,010 d. $820
Premium rates are often referred to as premium per fixed face value. Jade's annual premium for a 10-year policy of $200,000 is $1,202.
How to calculate the total annual premium for $x?
When it's given that the annual premium is $p per $y face value, then we can calculate the annual premium for $1 face value and then use it to calculate the annual premium for $x. Therefore using proportions, we can write,
$y face value : $p annual premium
[tex]\text{\$1 face value} : \$\dfrac{P}{y}\ \rm annual\ premium[/tex]
[tex]\text{\$x face value} : \$\dfrac{P\times x}{y}\ \rm annual\ premium[/tex]
In the given case, from the tables, we see that for age 34, and 10-year life insurance for the female gender, there is an annual premium of 6.01 per $1000 face value.
Therefore, we will get the value of p = 6.01, and y = 1000.
As mentioned that Jade wants to buy Life insurance for $200,000, therefore, x = $200,000
Putting it in the above-derived formula, we get:
[tex]\text{\$x face value} : \$\dfrac{P\times x}{y}\ \rm annual\ premium[/tex]
[tex]\text{\$200,000 face value} : \$\dfrac{6.01\times 200,000}{1,000}\ \rm annual\ premium = \$1,202\ \rm annual\ premium[/tex]
Hence, Jade's annual premium for a 10-year policy of $200,000 is $1,202.
Learn more about Annual Premium Cost:
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Answer:
b 1,202 on edge 2022
Step-by-step explanation:
Find x. Perimeter.
What is the value of x?
What is the perimeter of this triangle?
Step-by-step explanation:
the distance of a vertex on the 2 outgoing sides to the touching points with the inscribed circle is the same for both sides.
and that applies to all 3 vertexes.
so, we know for the top left vertex the distance to both touching points is 4.
that means the distance to the touching points from the bottom left vertex is 7-4 = 3.
and that means that the distance to the touching points from the bottom right vertex is 16-3 = 13.
so, x = 13
it is the distance to one of the touching points for the bottom right vertex.
and the perimeter of the triangle is therefore
7 + 16 + (13 + 4) = 40
Find the 10th term of the following geometric sequence 6,24,96,384,…
Answer:
1572864
Step-by-step explanation:
the nth term of a geoemtric series can be calculated using the following rule : [tex]a_n=a_1(r)^n^-^1[/tex]
where an = nth term, a1 = first term , r = common ratio and n = term position.
here, the first term is 6, the common ratio is 4 and the term position is 10 ( because we want to find the 10th term )
so a1 = 6 , r = 4 and n = 10
using these values we plug them into the rule
recall rule : [tex]a_n=a_1(r)^n^-^1[/tex]
==> plug in a1 = 6 , r = 4 and n - 10
[tex]a_1_0=6(4)^1^0^-^1[/tex]
==> subtract 10 and 1
[tex]a_1_0=6(4)^9[/tex]
==> simplify exponent
[tex]a_1_0=6(262144)[/tex]
==> simplify multiplication
[tex]a_1_0=1572864[/tex]
and we are done!
Note:
the common ration was found by dividing the first term by the next term
What is the solution to the inequality?
12 < 8 + x
O A. x < 20
O B. x>4
O c. x> 20
O D. x<4
Answer:
B. x > 4
Step-by-step explanation:
12 < 8 + x
12-8 < 8-8 +x
12-8 < x
4 <x
x > 4
The graph of a function g is shown below.
Find g (2) and find one value of x for which g(x) = -2.
Answer:
a. 1
b. 1
Step-by-step explanation:
by looking at the graph you can deduce the answer.
The equation for the given graph is g(x) = x²-3, and the value of g(2) will be 5.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The equation for the function is,
g(x) = x²-3
The graph of a quadratic function that has something bowl-shaped. Any equation of the form ax²+bx+c=0 where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
(x - h)² = 4a(y - k)
(h, k) is the vertex of the parabola:
a = √[(c-h)² + (d-k²]
(c, d) is the focus of the parabola:
To find the value of g (2) the value of the function is,
g(2) = 2²-3
g(2) =8-3
g(2) =5
Thus, the equation for the given graph is g(x) = x²-3, and the value of g(2) will be 5.
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Precal unit 4 sample work-
I need help converting the polar to rectangular. I already solved just needing to convert it.
Thank you!
Answer:
(3√26, 0)
Step-by-step explanation:
Finish your work by evaluating the sine and cosine. The imaginary part corresponds to the y-coordinate in (x, y) form.
3√26(cos(360°) +i·sin(360°)) = 3√26(1 +0i)
In rectangular form, that is ...
(3√26, 0)
what is 2+2+1+3+4+6+8+1 and divided 10 + 4 +3+ 4=
Answer:
9/7
Step-by-step explanation:
2+2+1+3+4+6+8+1/10+4+3+4
Hope this helps!!!
BIG IDLAS MATH
#19 i
Evaluate the expression. Write your answer in scientific notation.
(6 x 10-3) + 0.23 – (5 x 10-2) =
Answer:
Step-by-step explanation:
9.23
HELP MeMe M3 i dont get it
Fill in the table and graph the parametric equation
Answer:
Shown above
Step-by-step explanation:
Sorry for my untidy handwriting
Which set of algebra tiles represents the sentence below?Carlton earned 3 more stamps
Micheal is planting a garden in the shape of a right triangle. He wants 4 plants for each square meter area. How many plants does Michael want in the garden?
PLEASE answer this today because it is due tomorrow
Hence, required answer is 336
See the picture for the solution
SOMEONE PLSLPLSSLSLS HELP ITS JUST 3 QUESTIONS BRO PLEASE ITS SO CONFUSING ILL BRAINLIST.
The length and width of a rectangle is 3x + 4 and x + 3 respectively.
a) write the perimeter of the rectangle in simplified form.
b) find the perimeter of the rectangle if x = 5.
c) the area of a rectangle is given by the formula area = length x width. Find the area of this rectangle when x = 4.
Step-by-step explanation:
a) Perimeter is equal to 2w + 2L
2(3x + 4) + 2(x + 3)
6x + 8 + 2x + 6
8x + 14
b) Put 5 in x's place
8×5 + 14
40 + 14
54
c) Area = (3x + 4) * (x + 3)
Put 4 in x's place
(3×4 + 4) * (4 + 3)
12 + 4 * 7
16 * 7
112
Jimmy just left the movies. The
movie ended at 4:47 p.m. The
movie was two hours long.
What time did the movie start?
?
Eva is solving the equation 4(x+32)=8
She says, “I can subtract 32 from each side to get 4x=132 and then divide by 4 to get x=138."
Dakota says, “I think you made a mistake.”
Determine the correct value for x.
x=
Answer:
The correct answer is -30
Step-by-step explanation:
4(x+32)=8 basically you multiply 4 times the numbers that are in the parentesis which that will equals to 4x+128 because 4x1= 4x and 4x32 = 128. then you subtract 128 from 8 which equals to -120. you divide -120 by 4 which equals to -30.
What is the approximate volume of the cone? Use 227
22
7
for π. Enter your answer in the box.
Answer:
132 cm³
Explanation:
[tex]\sf volume \ of \ cone = \dfrac{1}{3} \pi r^2h[/tex]
put radius: 3 cm, height: 14 cm, π as 22/7
[tex]\sf \rightarrow \dfrac{1}{3} *\dfrac{22}{7} * (3)^2(14)[/tex]
[tex]\sf \rightarrow 132 \ cm^3[/tex]
What is the value of x? (angle bisector problem)
Answer:
47Step-by-step explanation:
According to angle bisector theorem we get the following ratio:
VT/KT = VY/KYSubstitute the lengths and solve for x:
77/87.5 = 22/(x - 22)77(x - 22) = 87.5*2277x - 77*22 = 192577x = 1925 + 169477x = 3619x = 3619/77x = 47Use angle bisector theorem
77/87.5=22/x-2277x-1694=192577x=3619x=3619/77x=47Solve 34x−5<8. Round your answer to the nearest thousandth
Answer:
x < 0.382
Step-by-step explanation:
because we know that 34x is smaller than 13. therefore after division we can find out that x must be smaller than 0.382
Part A: Describe a transformation (or series of transformations) that one could do to get from the
original to image below. Be as specific as possible.
Part B: Are these figures congruent? how do you know?
Quadrilateral ABCD was rotated 180 degrees about the origin to form A'B'C'D. The two figures are congruent to each other.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.
Quadrilateral ABCD was rotated 180 degrees about the origin to form A'B'C'D. The two figures are congruent to each other.
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Consider a rectangle with a side length of (2y + 6) and a perimeter of (10y + 4). What is the length of its base?
Select one:
A. 6y - 8
B. 3y - 4
C. 6y - 4
D. 8y - 2
Answer:
D Because other options do not have integration constants
Answer:
The answer is b) 3y-4
Step-by-step explanation:
Owen went shopping for a new pair of sneakers because of a sale. The price on the tag was $32, but Owen paid $16 before tax. Find the percent discount.
Answer:
50% discount
Step-by-step explanation:
Given the following question:
50% of 32
To find the answer we will use the formula to calculate percentages, and then solve by subtracting the answer from the initial cost of the sneakers.
[tex]\frac{p\times n}{100}[/tex]
[tex]\frac{50\times32}{100}[/tex]
[tex]50\times32=1600[/tex]
[tex]1600\div100=16[/tex]
[tex]=16[/tex]
Or...
[tex]32\div2=16[/tex]
[tex]=16[/tex]
50% of 32 is 16 which means the shoes has a "50% discount."
Hope this helps.
how do you find the circumference, radius, and diameter in area?
Answer:
Sample Respond: Let's assume it's equal to 14 cm. Substitute this value to the formula for circumference: C = 2 * π * R = 2 * π * 14 = 87.9646 cm . You can also use it to find the area of a circle: A = π * R² = π * 14² = 615.752 cm² . Finally, you can find the diameter - it is simply double the radius: D = 2 * R = 2 * 14 = 28 cm .
Step-by-step explanation:
I got 100% on the quiz
Prism M is a dilation of Prism N. The height of Prism M is 4 3/4 ft, and the volume of Prism M is 68 2/5 ft³. The height of Prism N is 2 3/8 ft. What is the volume of Prism N?Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer:
8 11/20 ft³
Step-by-step explanation:
For dilated figures, the ratio of volumes is the cube of the ratio of corresponding linear dimensions.
Vn/Vm = (Hn/Hm)³
Vn = Vm(Hn/Hm)³ = (68 2/5 ft³)((2 3/8 ft)/(4 3/4 ft))³
Vn = (342/5 ft³)((19/8)/(19/4))³ = (342/5 ft³)(1/2)³ = 342/40 ft³
Vn = 8 11/20 ft³
The volume of Prism N is 8 11/20 ft³.
Answer:
The answer is 8 11/20.