Answer:
8 inches
Step-by-step explanation:
Surface area of a prism is:
S = 2A + Ph
where A is the area of the base, P is the perimeter of the base, and h is the height of the prism.
The base is a square, so A = s² and P = 4s:
S = 2s² + 4sh
Given that S = 512 and h = 12:
512 = 2s² + 4s(12)
512 = 2s² + 48s
256 = s² + 24s
0 = s² + 24s - 256
0 = (s + 32) (s - 8)
s = -32, s = 8
Since s must be positive, s = 8 inches.
Follow below steps;
To find the length of the square base of the right prism:
First, calculate the lateral surface area: 512 in² = 4s * 12 where s is the side length of the square base.
Then, solve for s: 512 = 48s, s = 512 / 48 = 10.67 in.
Therefore, the length of the square base is 10.67 inches.
What is the center point
Answer:
Center of the circle= (-9,6)
Radius = 5 units
Step-by-step explanation:
Once the equation of the circle has been written in the format
(x-h)²+(y-k)²=r² , (h,k) is the center while r is the radius of the circle.
From the given equation, -h=9 therefore h= -9.
-k = -6 therefore k = 6. r² = 25 therefore r= √25=5
Center of the circle= (-9,6) radius = 5 units
What is the fourth term of the sequence?
ar = 2.41-2
Enter your answer in the box.
HELPPPP!!!!
Answer:
32
Step-by-step explanation:
Substitute n = 4 into the formula
[tex]a_{4}[/tex] = 2 × [tex]4^{4-2}[/tex] = 2 × 4² = 2 × 16 = 32
Which method would you use to prove that the two triangles are congruent?
Answer:
AAS
Step-by-step explanation:
Given one pair of congruent angles and one pair of congruent sides.
When two lines intersect they form a pair of congruent angles (vertical angles are equal)
So the two triangles are congruent by AAS.
Answer: AAS
Step-by-step explanation:
By the figure we can say that the have one side equal. Now for the angles we have that in the part of the triangles are touching we have an oposite angles then these two angles have to be equals. Finally the two triangles have two equal angles and ones equal side. we can conclude that the correct method is AAS.
two square regions have an area of 125 and 5 how many yards of fencing is needed to enclose? ( assume regions fenced separately)
Answer:
[tex]24\sqrt{5}\ yards[/tex]
Step-by-step explanation:
Let A1 be the area of one square and A2 be the area of second square
So,
A1 = s^2
where s is side of square
[tex]s^2=125\\\sqrt{s^2}=\sqrt{125}\\s=\sqrt{25*5}\\ s= \sqrt{5^2 * 5}\\ s= 5\sqrt{5}[/tex]
So side of one square is [tex]5\sqrt{5}[/tex]
To calculate the length of fence we need to find the perimeter of the square
So,
P1 = 4 * s
[tex]=4*5\sqrt{5} \\=20\sqrt{5}[/tex]
For second square:
[tex]A_2=s^2\\5=s^2\\\sqrt{s^2}=5\\{s}=\sqrt{5}[/tex]
The perimeter will be:
[tex]P_2 = 4*s\\=4 * \sqrt{5} \\=4\sqrt{5}[/tex]
So the total fence will be: P1+P2
[tex]= 20\sqrt{5}+4\sqrt{5} \\= 24\sqrt{5}\ yards[/tex]
What is the explicit formula for this sequence -7, -4, -1, 2, 5
[tex]a_n=3n-10[/tex]
Answer:
an = -7 + (n - 1) 3
Step-by-step explanation:
find the sum of 7 E 3i - 15
i =2
answers :
9
0
-9
6
Answer:
-9
Step-by-step explanation:
find the value of i2, which is -9, find the value of i7, which is 6
Then, add them together and multiply by the number of terms in the sequence divided by 2 (6/2=3)
what is the fifth term in the geometric sequence described by this explicit formula y=40×(-2)^(n-1)
Answer:
The fifth term is 620
Step-by-step explanation:
y=40×(-2)^(n-1)
The 5th terms means n=5
y = 40 * (-2) ^ (5-1)
= 40 * (-2) ^4
= 40 * (16)
= 640
find the inverse function of f x equals 2x / 3 - 17
Answer:
[tex]\large\boxed{f^{-1}(x)=\dfrac{3x+51}{2}=\dfrac{3}{2}x+\dfrac{51}{2}}[/tex]
Step-by-step explanation:
[tex]f(x)=\dfrac{2x}{3}-17\to y=\dfrac{2x}{3}-17\\\\\text{exchange x to y and vice versa:}\\\\x=\dfrac{2y}{3}-17\\\\\text{solve fro y:}\\\\\dfrac{2y}{3}-17=x\qquad\text{add 17 to both sides}\\\\\dfrac{2y}{3}=x+17\qquad\text{multiply both sides by 3}\\\\2y=3x+51\qquad\text{divide both sides by 2}\\\\y=\dfrac{3x+51}{2}=\dfrac{3}{2}x+\dfrac{51}{2}[/tex]
Let v=−3i
v
=
−
3
i
and w=2−4i
w
=
2
−
4
i
. Find v−w
v
−
w
.
Answer:
-2 + i
Step-by-step explanation:
v = -3i
w = 2 - 4i
v - w =
= -3i - (2 - 4i)
= -3i - 2 + 4i
= -2 + i
The given value of v = -3i and w = 2-4i, so v-w = -2 + i.
Given: v = -3i, w = 2-4i
To find: v - w
Solution:
Substitute the values of v and w into the expression v - w.
v - w = -3i - (2-4i)
v - w = -3i - 2 + 4i
v - w = -2 + i
whats 9 plus 10
ps its 21
Answer:
it is 21 because 9+10=19+2=21-10=11+10=21 its magic
Step-by-step explanation:
Answer:
19
Step-by-step explanation:
9 + 10 = 19
It is impossible for it to be 21.
10
9
----
1 9
Hope this helps.
Alice.
find (fof)(0) f(x)=x^2
a.1
b.0
c.-8
d.-1
Answer:B
f(0)=0
Step-by-step explanation:
when 0 is squared it’s just 0
Answer: option b.
Step-by-step explanation:
Given the function f(x):
[tex]f(x)=x^2[/tex]
In order to find [tex](fof)(x)[/tex], the first thing you must do is to substitute the function f(x) into the same function f(x). Observe the procedure:
[tex](fof)(x)=(x^2)^2[/tex]
Now, you need to simplify:
[tex](fof)(x)=x^4[/tex]
Finally, to find [tex](fof)(0)[/tex] you need to substitute [tex]x=0[/tex] into [tex](fof)(x)=x^4[/tex], then you get:
[tex](fof)(0)=(0)^4[/tex]
[tex](fof)(0)=0[/tex]
Which equation is the inverse of 2(x - 2)^3=8(7+y)
Answer:
[tex]\large\boxed{y=2\pm\sqrt{28+4x}}[/tex]
Step-by-step explanation:
[tex]2(x-2)^2=8(7+y)\\\\\text{exchange x to y, and vice versa:}\\\\2(y-2)^2=8(7+x)\\\\\text{solve for y:}\\\\2(y-2)^2=(8)(7)+(8)(x)\\\\2(y-2)^2=56+8x\qquad\text{divide both sides by 2}\\\\(y-2)^2=28+4x\iff y-2=\pm\sqrt{28+4x}\qquad\text{add 2 to both sides}\\\\y=2\pm\sqrt{28+4x}[/tex]
Answer:
y is inverse: 2 ±[tex]\sqrt{28+ 4x}[/tex] .
Step-by-step explanation:
Given: 2(x - 2)²=8(7+y).
To find: Find inverse.
Solution : We have given
2(x - 2)²=8(7+y).
Step 1: inter change the x and y.
2(y - 2)²=8(7+x).
Step 2:
Solve for y
On dividing both sides by 2
(y - 2)² = 4 (7+x).
Distributes 4 over ( 7 + x)
(y - 2)² = 28 + 4x
Taking square root both sides.
[tex]\sqrt{(y-2)^{2} } = ±\sqrt{28+ 4x}[/tex].
y - 2 = ±[tex]\sqrt{28+ 4x}[/tex].
On adding both sides by 2
y = + 2 ±[tex]\sqrt{28+ 4x}[/tex] .
Therefore, y is inverse : 2 ± [tex]\sqrt{28+ 4x}[/tex].
What is the slope of the equation y - 3 = -4(X - 5)?
Answer:
Step-by-step explanation:
y - 3 = -4(x - 5)
Add 3 to both sides to isolate y
y = -4 ( x - 5 ) + 3
Distribute
y = -4x +20 + 3
Combine like terms
y = -4x + 23
y = mx + b is standard form for which m is slope
m = -4
Please mark for brainliest!! :D Thanks!!
If you have any questions or need more information, please comment below and I'll respond asap!!
Answer:
-4
Step-by-step explanation:
Distribute -4 into the parenthesis and get -4x + 20. The number paired with x is the slope, usually represented by m in y = mx + b. So, the slope is -4. For the full slope intercept format, move the -3 on left side to the right by adding 3. The new equation is y = -4x + 23.
Which expression is equivalent to sqrt10/4sqrt8
Answer:
Step-by-step explanation:
Since it's a division we need to look for a common factor to cancel
so first we try to break the numbers to there prime factors
[tex]\frac{\sqrt{10} }{4\sqrt{8} } = \frac{\sqrt{2.5} }{4\sqrt{2.2.2} }[/tex]
So , now we try to factors that are common in top and bottom
[tex]= \frac{\sqrt{2} \sqrt{5}}{4\sqrt{2}\sqrt{4} }[/tex]
common factor is sqrt 2 so lets cancel it
we get
[tex]\frac{\sqrt{5} }{4\sqrt{4} }[/tex]
[tex]\frac{\sqrt{5} }{8}[/tex]
A company makes globes with a radius of 11 inches. The material to make the globes costs the company $0.04 per square inch. To the nearest cent, how much does the company pay for the material to create one globe? Use 3.14 for pi.
Recall the formula SA=4 pi r^2.
$11.05
$60.79
$243.16
$607.90
Answer:
One globe costs $60.79
Step-by-step explanation:
The area of the globe is
A = 4.π.r^2
Since the radius is 11 inches
A = 4*(3.14)*(11 in)^2 = 1519.76 in^2
We apply a rule of three
1 in^2 --------------------------------- $0.04
1519.76 in^2 ------------------------- x
x = (1519.76 in^2/ 1 in^2)*$0.04
x = (1519.76)*$0.04
x = $60.79
x ≈ $60.8
Answer: Second Option
$60.79
Step-by-step explanation:
To solve this problem let's suppose that the balloons are spherical
Then the surface area of a sphere is given by the formula:
[tex]SA=4\pi r^2[/tex]
Where r is the radius of the sphere
In this case we know that the radius of each globes is 11 inches, then:
[tex]SA=4(3.14) (11)^2[/tex]
[tex]SA=4(3.14)(121)[/tex]
[tex]SA=1519.76\ in^2[/tex]
If the material to make globes costs $ 0.04 per square inch then the cost of a globes is:
[tex]C=1519.76*0.04[/tex]
[tex]C=\$60.79[/tex]
27. A watch cost $75.99. If the sales tax
rate is 6.25%, what is the amount of
sales tax?
A $0.48
B $2.19
C $4.75
D $474.94
Step-by-step explanation:
75.99 ×.0625=4.749
75.99+4.75(because I rounded)=
$80.74 total cost incase you have another step
75.99 ×.0625 = 4.749
I rounded to get 4.75.
75.99 + 4.75 = $80.74
$80.74 - $75.99 = $4.75
Answer: $4.75
What is the value of x?
[tex]x+40=3x\\2x=40\\x=20[/tex]
For this case we have by definition of angles between secant lines that:
[tex]x + 40 = 3x[/tex]
Also, the angle between T and V is equal to the angle between S and W.
Returning to the question, we have to:
[tex]x + 40 = 3x[/tex]
We must know the value of "x":
Subtracting 3x on both sides of the equation we have:
[tex]x-3x + 40 = 0[/tex]
Subtracting 40 from both sides of the equation:
[tex]-2x = -40[/tex]
Dividing between -2 on both sides of the equation:
[tex]x = \frac {-40} {- 2}\\x = 20[/tex]
So, the value of x is 20
Answer:
[tex]x = 20[/tex]
Which is a correct classification for the triangle?
Step-by-step explanation:
All three sides are equal, so this is an equilateral triangle.
Answer:
This is an equilateral triangle
Step-by-step explanation:
All three sides are equal, making it equilateral
Solve for z :2x+6yz=2xz+2y
Answer:
z = [tex]\frac{y-x}{3y-x}[/tex]
Step-by-step explanation:
2x+6yz=2xz+2y (rearrange so that z is on one side)
6yz - 2xz = 2y - 2x (divide both sides by 2)
3yz - xz = y - x (factor our z from LHS)
z (3y - x) = y - x
z = [tex]\frac{y-x}{3y-x}[/tex]
Identify the law illustrated by: 4(3x-7) is equivalent to 12x-28.
Answer:
Distributive law of multiplication
Step-by-step explanation:
Answer:
Step-by-step explanation
A: No it is not the inverse law of multiplication which has something to do with division.
B: is your answer.
C: It is not the commutative Law. An example of that would be a*b =b*a
D: Identity of multiplication is 1.
Graph y = -|x| + 2. Click on the graph until the correct one appears.
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]y=-\left|x\right|+2[/tex]
we know that
The graph is inverted V-shaped.
The x-intercepts are the points (-2,0) and (2,0)
The vertex is the point (0,2)
The domain is all real numbers
The range is all real numbers less than or equal to 2
using a graphing tool
The graph in the attached figure
Last year amusement park received 236,758 visitors it was open every day of the year but 7 Holliday’s what was the average number of visitors to the park per day
Answer:
An average of 661 people per day.
Step-by-step explanation:
1. 365-7= 358
2. 236,758/ 358= 661.3351
3. Round to 661
PLEASE HELP !!!!
ivanna's earnings vary directly with the number of hours she works. suppose that she worked 7 hours yesterday and earned $77. if she earned $99 today, how many hours did she work today
Answer:
9 hr
Step-by-step explanation:
vary directly means you should think about a constant being multiply to one variable to get another variable.
So we have E=kH
where E=earnings and H=hours and k is the constant of proportionality
So they give us when H=7 we have E=77 giving us 77=k(7) which means the constant of proportionality is 11
So that means no matter what the E and H are k is 11
So we have the equation is E=11H
Replace E with 99 and solve for H
99=11(H)
So H=9
9 hours
What is the 8th term of the geometric sequence with this explicit formula?
an= 6.(-2)(n-1)
Answer:
- 768
Step-by-step explanation:
Substitute n = 8 into the explicit formula, that is
[tex]a_{8}[/tex] = 6 × [tex](-2)^{7}[/tex] = 6 × - 128 = - 768
Solve for
5(x + 1) = 4x + 8)
Answer:
x =3
Step-by-step explanation:
5(x + 1) = 4x + 8
Distribute the 5
5x+5 = 4x+8
Subtract 4x from each side
5x-4x+5 = 4x-4x+8
x+5 =8
Subtract 5 from each side
x+5-5 = 8-5
x =3
The area of a circle with radius r is given by A = π r2. Find the area of a circle with radius 7 centimeters. Use 3.14 for π.
Answer:
The area is 0.015m²
Step-by-step explanation:
Step one
Given that the expression for area of the circle is A = π r²
Step two
Now our raduis r= 7cm - - - meter =7/100= 0.07
And Pi = 3.142
Step three
Substituting r in the formula for area we have
A= 3.142*(0.07)²
A=3.142*0.0049
A= 0.015m²
The graph below plots the values of y for different values of X:
Which correlation coefficient best matches the data plotted on the graph? (1 point)
Answer:
0.50
Step-by-step explanation:
we know that
Observing the graph
we have the following points
(1,3),(2,4),(3,9),(4,7),(5,2),(6,18)
Using a Excel tool (Correl function)
The correlation coefficient is equal to r=0.605639
see the attached table
therefore
The correlation coefficient that best matches the data plotted on the graph is 0.50
What is the following quotient? 2/sqrt13+sqrt11
Answer:
Answer is [tex]\sqrt{13}-\sqrt{11}[/tex]
Step-by-step explanation:
We need to divide
[tex]\frac{2}{\sqrt{13}+\sqrt{11}}[/tex]
For solving this, we need to multiply and divide the given term with the conjugate of [tex]{\sqrt{13}+\sqrt{11}[/tex]
The conjugate is: [tex]{\sqrt{13}-\sqrt{11}[/tex]
Solving
[tex]=\frac{2}{\sqrt{13}+\sqrt{11}} *\frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}} \\=\frac{2(\sqrt{13}-\sqrt{11})}{(\sqrt{13}+\sqrt{11})(\sqrt{13}-\sqrt{11})}\\We\,\, know\,\, that\,\, (a+b)(a-b) = a^2-b^2\\=\frac{2(\sqrt{13}-\sqrt{11})}{(\sqrt{13})^2-(\sqrt{11})^2}\\=\frac{2(\sqrt{13}-\sqrt{11})}{13-11}\\=\frac{2(\sqrt{13}-\sqrt{11})}{2}\\=\sqrt{13}-\sqrt{11}[/tex]
So answer is [tex]\sqrt{13}-\sqrt{11}[/tex]
Answer:
The correct Answer is D[tex]\sqrt{13} - \sqrt{11}[/tex]
Step-by-step explanation:
Kevin is responsible for delivering sacks of grains to a grocery shop on the tenth floor of a departmental store. Each sack weighs 364 pounds and Kevin weighs 150 pounds. The capacity of the elevator is 2,000 pounds.
If six sacks are to be taken at a time, what should be the weight of each sack?
Final answer:
Kevin can safely take sacks weighing up to 308.33 pounds each in the elevator, provided he takes six sacks at a time and the elevator's capacity is 2,000 pounds with Kevin weighing 150 pounds.
Explanation:
The student's question is asking for the maximum weight of each sack of grain that Kevin can deliver on the elevator, given the elevator's weight capacity and the additional weight of Kevin himself. To answer this question, we need to consider the weight that the elevator can hold minus Kevin's weight, and then determine how much weight is left for the sacks of grain.
The elevator has a capacity of 2,000 pounds, and Kevin weighs 150 pounds. This means the total weight that the elevator can carry in addition to Kevin is:
2000 pounds (elevator capacity) - 150 pounds (Kevin's weight) = 1850 pounds (available for sacks)
If Kevin needs to deliver six sacks at a time, we can divide the total available weight by six to find the maximum weight for each sack:
1850 pounds / 6 sacks = approximately 308.33 pounds per sack
Therefore, the weight of each sack must be 308.33 pounds or less for Kevin to safely use the elevator without exceeding its capacity.
Susan is paying $0.30 per $100 on her $483,000 home in homeowners insurance annually. If her annual homeowners insurance premium is divided into twelve equal monthly installments to be included on each of her monthly mortgage payments of $2128.00, what is her total monthly payment? a. $2,248.75 b. $2,409.75 c. $3,381.00 d. $3,577.00 Please select the best answer from the choices provided
Answer:
a) $2248.75
Step-by-step explanation:
Susan pays $0.3 per $100
For $483000, she pays $1449 insurance annually : Calculation shown below
483000/100 x 0.3 = $1449
Monthly instalments of the insurance premium for 12 months :
annual insurance premium/ 12 months
1449/12 = $120.75
Monthly mortgage payments = $2128
Monthly total payments = monthly mortgage payments + monthly insurance premium instalment.
= 1449 + 120.75
= $2248.75
!!