Answer:2
Step-by-step explanation:
A triangular prism that has a volume of 24 cubic inches is changed by a scale factor of 5. Find the volume of the dilated cube.
A. 120
B. 600
C. 3000
D. 3600
==========================================================
Reason:
If the linear scale factor is 5, then the volume scale factor is 5^3 = 125
Meaning we'll multiply the old volume by 125 to get the new volume
new volume = 125*(old volume)
new volume = 125*(24)
new volume = 3000
---------------
A more in-depth look:
Consider a 2 by 2 by 2 block. Its volume is 2*2*2 = 8
Now multiply each dimension by 5, so we now have a 10 by 10 by 10 block. The new larger volume is 10*10*10 = 1000
The volume ratio is 1000/8 = 125, which matches with the value found earlier.
Since we multiplied each piece by 5, and did so three times, we're really multiplying the volume by 5*5*5 = 125.
The radio of the base of two cylindrical tins are r and 3r respectively .if the water level in A is 18cm high , what would be the height of the same quantity of water in B
Answer:
2 cm.
Step-by-step explanation:
Volume of the water is the same in the 2 cyinders,
Volume of water in A = π r^2 * 18.
Volume in B = π (3r)^2 * h.
So 18πr^2 = 9π r^2 h
18 = 9h
h = 18 / 9
= 2
2. Noah is solving the equation x² + 8x + 15 = 3. He begins by rewriting the
expression on the left in factored form and writes (x + 3)(x + 5) = 3. He
does not know what to do next.
Noah knows that the solutions are x = -2 and x = -6, but is not sure how
get to these values from his equation.
Solve the original equation by completing the square.
Answer:
The solution set is {-6, -2}.
Step-by-step explanation:
x^2 + 8x + 15 = 3
x^2 + 8x = -12
Completing the square:
(x + 4)^2 - 16 = -12
(x + 4)^2 = 4
Taking square roots of both sides:
x + 4 = +/- 2
x = 2 - 4 = -2 or x = -2-4 = -6.
Building a Storage Container
You are being asked to design an enclosed water storage container. You are given a budget of
$100 to build the container. It has been determined that the best material to make the container
costs $10 per m². (In other words your surface can not cost more than $100.) What is the
largest amount of water your container can hold? You will need to explain to your boss the
reasoning because they have a business degree and do not really remember any of their
geometry work from school.
Answer:
2973.5 liters
Step-by-step explanation:
You are being asked to find the volume of the largest possible container that has a given surface area. The volume will depend on the shape. If shape is not specified, we know a sphere has the largest volume for a given area.
__
areaThe available area is ...
($100) / ($10/m²) = 10 m²
diameterThe area of a sphere with diameter d is ...
A = πd²
Then the diameter for the given area is ...
10 m² = πd²
(10/π) m² = d² . . . . . divide by π
√(10 m²/π) = d ≈ 1.78412 m . . . . . . diameter of the largest sphere
volumeThe volume of a sphere is given by ...
V = 4/3πr³ = (π/6)d³
For the diameter found above, the volume of the sphere will be ...
V = (π/6)(1.78412 m)³ ≈ 2.97354 m³
There are 1000 liters in a cubic meter, so the largest amount of water that can be contained is ...
2.97354 m³ × (1000 L/m³) = 2973.54 L
The largest amount of water the container can hold is about 2973.5 liters.
An elementary class consists of 8 boys and 10 girls. A child is chosen at random and it is a girl. A second child is randomly chosen again from the remaining children, and it is a boy. Was the probability of choosing the boy dependent on choosing a girl first
Answer:
Yes
Step-by-step explanation:
So we know the second child was a boy however if the first child was a boy, the probability of getting a second boy would be 7/17 since one boy is missing and one person is missing from the total.
However, if a girl was chosen as the first child, the probability of getting a boy second would be 8/17 since no boys would be missing but one person would be missing from the original total.
PLEASE HELP!!!
Solve for x using the Quadratic Formula: x2 + 2x + 1 = 0
-b+Vb2-4ac
X=
2a
Ox=2
Ox= 1
O x = 0
O x = -1
Answer:
last option, x = -1
Step-by-step explanation:
[tex]x^{2} + 2x + 1 = 0\\x_{1} = \frac{-2 + \sqrt{2^{2} - 4(1)(1) } }{2(1)}\\x_{2} = \frac{-2 - \sqrt{2^{2} - 4(1)(1) } }{2(1)}\\x_{1} = \frac{-2 + \sqrt{0} }{2}\\x_{2} = \frac{-2 - \sqrt{0} }{2}\\x = \frac{-2}{2} \\x = -1[/tex]
The value of x by using the Quadratic Formula is,
⇒ x = - 1
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
Given that;
Equation is,
⇒ x² + 2x + 1
Now, We can use the Quadratic Formula for x as;
⇒ x² + 2x + 1
⇒ x = - 2 ± √2² - 4×1×1 / 2
⇒ x = - 2 ± √4 - 4 / 2
⇒ x = - 2 / 2
⇒ x = - 1
Thus, The value of x by using the Quadratic Formula is,
⇒ x = - 1
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The length of AB is four times the length of BC.
AC = 75 cm.
=
The equation of a straight line is given a x = 2y - 1 Write the equation in the form y = mx + c
Answer:
2y = x - 1
Step-by-step explanation:
y = 2y
mx = x
c = -1
What is the area of a triangle whose vertices are R(3, 4), S(6, 2), and T(7, 10)?
Enter your answer in the box.
According to Heron's formula, the area of a triangle whose vertices are R(x, y) = (3, 4), S(x, y) = (6, 2) and T(x, y) = (7, 10) has a value of approximately 14.525 units.
How to calculate the area of a triangle by knowing its sides
In this question we must determine the lengths of the three sides of the triangle by Pythagorean theorem and then the area is determined by Heron's formula.
First, we determine the length of each side:
[tex]RS = \sqrt{(6-3)^{2}+(2-4)^{2}}[/tex]
[tex]RS = \sqrt{3^{2}+(-2)^{2}}[/tex]
[tex]RS = \sqrt{13}[/tex]
[tex]ST = \sqrt{(7-6)^{2}+(10-2)^{2}}[/tex]
[tex]ST = \sqrt{1^{2}+8^{2}}[/tex]
[tex]ST = \sqrt{65}[/tex]
[tex]RT = \sqrt{(7-3)^{2}+(10-4)^{2}}[/tex]
[tex]RT = \sqrt{4^{2}+6^{2}}[/tex]
[tex]RT = \sqrt{80}[/tex]
Now we calculate the area of the triangle by Heron's formula:
[tex]s = \frac{\sqrt{13}+\sqrt{65}+ \sqrt{80}}{2}[/tex]
s ≈ 10.306
[tex]A = \sqrt{10.306 \cdot (10.306 - \sqrt{13})\cdot (10.306 - \sqrt{65})\cdot (10.306 - \sqrt{80})}[/tex]
A ≈ 14.525
According to Heron's formula, the area of a triangle whose vertices are R(x, y) = (3, 4), S(x, y) = (6, 2) and T(x, y) = (7, 10) has a value of approximately 14.525 units.
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help me whats 93458 divided by 19435
scan qr code for assignment question!
Answer:
[tex]\frac{93458}{19435}[/tex] ≈ 4.81
Step-by-step explanation:
[tex]\frac{93458}{19435}[/tex] can not be simplified
(a) The angle pitch of a roof is safest when measuring between 18° – 27°. According to these guidelines, is the roof pictured in the image safe?
(b) What is length of the roof line (segment PR)? Round answer to the nearest tenth of a foot and show all your work.
Find Q
tanQ=Perpendicular/BasetanQ=4/15tanQ=0.26Q=tan^-¹(0.26)Q=14.6°Not safe
Apply Pythagorean theorem
PR²=4²+15²=16+225=241
PR=√241Answer:
a) not safe
b) 15.5 ft (nearest tenth)
Step-by-step explanation:
Part (a)Tan trig ratio
[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleGiven:
[tex]\theta[/tex] = xO = PV = 4 ftA = RV = VQ = 15 ftSubstituting the given values into the formula and solving for x:
[tex]\implies \sf \tan(x)=\dfrac{4}{15}[/tex]
[tex]\implies \sf x=\tan^{-1}\left(\dfrac{4}{15}\right)[/tex]
[tex]\implies \sf x=14.9^{\circ}\:(nearest\:tenth)[/tex]
As 14.9° is not between 18° and 27°, the roof is not safe.
-------------------------------------------------------------------------------------------------
Part (b)Pythagoras’ Theorem
[tex]\sf a^2+b^2=c^2[/tex]
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
Given:
a = RV = VQ = 15 ftb = PV = 4 ftc = PRSubstituting the given values into the formula and solving for PR:
[tex]\implies \sf 15^2+4^2=PR^2[/tex]
[tex]\implies \sf 225+16=PR^2[/tex]
[tex]\implies \sf PR^2=241[/tex]
[tex]\implies \sf PR=\sqrt{241}[/tex]
[tex]\implies \sf PR=15.5\:ft\:(nearest\:tenth)[/tex]
[tex]\log _ { 5 } ( 2 m + 5 ) = 3log5(2m+5)=3[/tex]
solution needed
with briefly explained
Answer:
m = 60
Step-by-step explanation:
log is another way to write an exponent.
Example:
exponent form:
7^2 = 49
log form:
log_7 (49) = 2
In your question, we need to change to exponent form, from log form.
log_5 (2m+5)=3
5 is the base. 3 is the exponent.
Now it can be solved.
5^3 = 2m+5
125 = 2m + 5
120 = 2m
60 = m
Which statement is true about the end behavior of the
graphed function?
• As the x-values go to positive infinity, the function's
values go to negative infinity.
• As the x-values go to zero, the function's values go
to positive infinity.
• As the x-values go to negative infinity, the function's
values are equal to zero to
O As the x-values go to positive infinity, the function's
values go to positive infinity.
Answer:
D. As the x-values go to positive infinity, the function's values go to positive infinity.
Step-by-step explanation:
the answer on edge 2022
As the x-values go to positive infinity, the function's values go to positive infinity. The correct option is D.
What is a function?A function is a mathematical formula that describes how the dependent variable and independent variable are related. The dependent variable's value varies in the function together with the independent variable's value.
The correct option is D that as the x-values go to positive infinity, the function's values go to positive infinity.
In mathematics, a function is a rule that gives each input value in a set a distinct output value. A function is, more precisely, a collection of ordered pairs (x, y), where each x-value is matched with precisely one y-value.
The variable x normally represents the input values, also known as the independent variable, while the variable y typically represents the output values, also known as the dependent variable. Typically, a symbol like f(x), where f is the function's name and x is the input variable, is used to represent a function.
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The expression 3200(1.06)^t represents the
enrollment of a high school t years after 2000.
describe how the enrollment changes
each year.
a. increases 1.06%
b. increases 6%
c. decreases 1.06%
d. decreases 6%
Expression 3200(1.06)^t represents the enrollment of a high school t years after 2000 will increase by 6%.
What is the percentage?The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.
The given expression is as follows:-
= 3200 ( 1.06 ) [tex],^t[/tex]
Here when the time has increased the percentage is also increased by 6%.
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What's the square root of Pi times the c length of a right triangle with the a measurement of 12 and the b measurement of 10?
Answer:
[tex]2\sqrt{61\pi }[/tex]
Step-by-step explanation:
Let's find c by using the Pythagorean Theorem: [tex]10^2 + 12^2 = c^2[/tex] so [tex]c = \sqrt{10^2 + 12^2}[/tex]. I'm going to leave c like this so it is easier to multiply by [tex]\sqrt{\pi }[/tex]. [tex]c\sqrt{\pi } = \sqrt{10^2 + 12^2}\sqrt{\pi } = 2\sqrt{61\pi }.[/tex]
Hope this helped! :)
5-2i-2(3+i) can you help me with this answer
Answer:
-1 - 4 i
Step-by-step explanation:
5 - (2 * i) - (2 * (3 + i)) =
-1 - 4 i
The length of a rectangle is three times the width. The sum of the length and the width is 24 inches. What is the length of the rectangle?
Answer:
Length: 18 inches
Width: 6 inches
Step-by-step explanation:
l+w=24
l=3w w=1w
3w+w=24
w=6
Length: 3*6=18 inches
Width: 6 inches
someone please help me and solve for the unknowns and give reasons please
or can you just solve for the unknowns please
Answer:
Step-by-step explanation:
The angles labeled with 2x, 4x, and 3x are on a straight line so their sum is equal to 180
2x + 4x + 3x = 180 add like terms
9x = 180 divide both sides by 9
x = 20
The angle represented with 3x - 30 and the angle represented with 2x + 10 are alternate and their measurement is same
3x - 30 = 2x + 10 export like terms to same side of the equation
3x - 2x = 10 + 30
x = 40
to find the angles replace x with the value found for each.
Please Help! I need This quickly!!!
The area of the smallest box that a circular pizza will fit into = 1661 squared cm.
What is Area of Circle?
The area of a circle is the amount of space enclosed within the boundary of a circle. The region within the boundary of the circle is the area occupied by the circle.
The circular pizza requires the same amount of dough as the square pizza.
Area of the square pizza =40 cm * 40 cm
= 1600 [tex]cm^{2}[/tex].
Area of circle= [tex]\pi\; r^{2}[/tex]
1600 = 3.14 *[tex]r^{2}[/tex]
[tex]r^{2}[/tex] = 510
r= 22.58
r = 23 cm approx.
Area of circle= [tex]\pi\; r^{2}[/tex]
= [tex]3.14 * (23)^{2}[/tex]
= 1661.06 squared cm
The area of the smallest box that a circular pizza will fit into = 1661 squared cm.
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Sydney is considering two jobs. One job pays $45,000 per year. The other job pays a
weekly salary of $950. Which job pays better?
Answer:
The first job pays more
Step-by-step explanation:
950 x 3 = One month pay = 2,850
2,859 x 12 = One year = 34,308 Per Year
Comparing them both
$45,000 One Year, First Job
$34,308 One Year, Second Job
6 erasers cost $6.60.
Which equation would help determine the cost of 3
erasers?
Answer:
answer is a
Step-by-step explanation:
u just look at 6 and 6.60 thats 1 and 10 every eraser but for 3 its 1.30
-2(8f+9)-6n use f=5 and n=7
Answer: Correct me if I am wrong, but this is how I think you should solve it.
Step-by-step explanation:
1. Simplify 8×5 to 40.
−2×(40+9)−6×7
2. Simplify 40+9 to 49.
−2×49−6×7
3. Simplify −2×49 to −98.
−98−6×7
4. Simplify 6×7 to 42.
−98−42
5. Simplify
−140
Your all done! Hope this helps.
please help!! i’ll give brainliest
Solve for x.
x = [?]
Answer:
3x +18+4x+15=180
7x+33=180
7x=180-33
7x=147
7x÷7=147÷7
x=21
Answer:
[tex]\boxed{\bf x = {21}^{o} }[/tex]
Step-by-step explanation:
We know that the sum of angles of a linear pair is always equal to 180°, they are also known as supplementary angles.
[tex]\sf 3x + 18 + 4x + 15 = {180}^{o} [/tex][tex]\sf 7x = 180 - 18 - 15[/tex][tex]\sf 7x = 147[/tex][tex]\sf \cfrac{ 7x}{7} = \cfrac{147}{7} [/tex][tex]\sf x = {21}^{o} [/tex]«•••••••••••••••«»•••••••••••••••»
in the figure below lines p and q are parallel. what do you notice? IREADY
100 points
Answer:
alternate interior anglesthe sameStep-by-step explanation:
The problem is concerned with angles 4 and 5, which lie between the lines given as parallel. They are on opposite sides of the line cutting across those parallel lines (the transversal), so they are ...
alternate interior anglescongruent__
Being congruent angles, their measures are ...
equalthe same_____
Additional comment
For questions like this, there are many descriptions that are true. It would be helpful to know the possible answer choices.
PLEASE HELP ! <3 !!!!!!!!!!!!!!!!!!!!!!!
Answer:
7 things an investor should consider when picking stocks:
Trends in earnings growth.
Company strength relative to its peers.
Debt-to-equity ratio in line with industry norms.
Price-earnings ratio as an indicator of valuation.
How the company treats dividends.Effectiveness of executive leadership.
Step-by-step explanation:
somebody please help me with this
Answer:
P(A) = 13/18
P(B) = 7/18
Step-by-step explanation:
A) Sum greater than 5
If the sum needs to be >5, then it can be 6, 7, 8, 9, 10, 11, and 12.
There are 26 out of 36 events where the sum is >5, thus P(A) = 26/36 = 13/18.
B) Sum divisible by 4 or 6
The sum ranges from 2 to 12, there are two methods to calculate this:
B1) Method 1: Calculate the frequency one by one
The sums divisible by 4 or 6 are S = {4, 6, 8, 12}. There are 9 of them, n(S) = 14. Thus P(B) = 14/36 = 7/18.
B2) Method 2: Use the rule of not mutually exclusive events
Not mutually exclusive events (might also be called mutually inclusive) happens when two events can happen together at the same time. In this problem, the sum might be divisible by 4 and 6 at the same time, i.e. the number 12.
The common formula for not mutually exclusive events is P(A∪B) = P(A) + P(B) - P(A∩B). Nb: P(A) isn't talking about the previous problem, nor does P(B) talk about the second section as a whole; the terms P(A) and P(B) will be utilized next, explained with their uses.
P(A) = probability of the sum being divisible by 4, i.e. the number 4, 8 and 12
P(A) = (3+5+1) / 36 = 9/36 = 1/4
P(B) = probability of the sum being divisible by 6, i.e. the number 6 and 12
P(B) = (5+1) / 36 = 6/36 = 1/6
P(A∩B) = probability of the sum being divisible both by 4 and 6, i.e. the number 12
P(A) = 1 / 36 = 1/36
Here comes the use of formula P(A∪B) = P(A) + P(B) - P(A∩B)
P(A∪B) = 1/4 + 1/6 - 1/36 = 7/18
Nb: As you can see, both method B1 and B2 give the same answer. Method B1 is usually easier to use when facing simpler problems like this. I'd recommend using method B2 for more complex and difficult questions, such as when you can't visualize the problem with a table because there are too much sets of variables.
Image of table for reference: https://qph.fs.quoracdn.net/main-qimg-1283a98bd649f522986e2f91a592ffd3
Please help me if really appreciate it!!
Solve the system of equations by the substitution method.
10x + 2y = 2
- 5x = y + 10
Select the correct choice below and, if necessary, fill in the answ
What is 8.92 cm² Converted To Meters?
[tex]8.92 ~ \text{cm}^2\\\\=8.92 \times \left( 1 ~ \text{cm} \right)^2\\\\=8.92 \times \left(10^{-2}~ \text{m} \right)^2~~~~~~;\left[1~ \text{cm} = \dfrac{1}{100}~ \text m} = 10^{-2}~ \text{ m} \right]\\\\=8.92 \times 10^{-4}~ \text{m}^2\\\\=0.000892~ \text{m}^2[/tex]
5.
—-
help please
—
math geniuses pls help!!!
pls check other questions too!
Answer:
The mean is greater than median
Step-by-step explanation:
Option D