You must use Pythagorean theorem, which is [tex]a^{2} +b^{2} =c^{2}[/tex]
a and b are both legs (the two legs are the sides that form a perpendicular right angle) while c is the hypotenuse (side opposite the right angle)
In this case...
a = y
b = 8
c = 12
^^^Plug these numbers into Pythagorean theorem
[tex]y^{2} +8^{2} =12^{2}[/tex]
Simplify as much as possible
[tex]y^{2}[/tex] + 64 = 144
Isolate y by subtracting 64 to both sides
[tex]y^{2}[/tex] + (64 - 64) = 144 - 64
[tex]y^{2}[/tex] = 80
Further isolate y by taking the square root of both sides. This will take away the square from the left side
y = [tex]\sqrt{80}[/tex]
[tex]\sqrt{80}[/tex] <<< Can be further simplified
4√5 = y
Hope this helped!
~Just a girl in love with Shawn Mendes
The graph represents the height y, in feet above the ground of a rock x seconds after it is dropped from a building. Which statement is true? Select each correct answer.
-the rock hits the ground in 45 s.
-the rock rises above 45 ft before falling toward the ground.
-the maximum height of the rock occurs at x=0
-the rock is in the air for 3 s.
-the Maximum height of the rock is 45 ft.
Answer:
B.
Step-by-step explanation:
If you look at the graph carefully, the graph/line is starting to fall at (0,45) which is the starting point or dropping point.
I hope this helped =)
Round 378,903.97 to the nearest thousand
Answer:
Step-by-step explanation:
378,903,970.
A rectangle has an area of 40,if the length and width are doubled. What is the new area ?
Answer:
160
Step-by-step explanation:
e.g. 5×8 --> 10×16 =160
4×10 --> 8×20 =160
2×20 --> 4×40 =160
160
When you double both the length and width, you are multiplying by 2 twice. Whatever you do to one side of an equation, you have to repeat on the other.
l * w = 40; This is the original equation.
2l * 2w = 40 * 2 * 2; This is when you double the length and the width.
The 2 * 2 on the end can be simplified.
2l * 2w = 40 * 4
Now, simplify 40 * 4.
2l * 2w = 160
So, when you double both the length and the width, you multiply the area by 4, making the area 160.
y=4x-2, y=3x-1
pllllleeaaasssseee heeeelllpppp meeeee
Answer:
x=1
y=2
Step-by-step explanation:
Hope this helps (3
What is the effect on the volume of a sphere if the radius is divided by 2?
Answer:
volume of sphere if radius is divided by 2 is 1/8 of volume of sphere with r radius.
Step-by-step explanation:
The formula to find volume of sphere is:
Volume of sphere = 4/3 π r^3
if radius is divided by 2 i.e r/2
Volume of sphere if r/2 = 4/3 π (r/2)^3
= 4/3 π r^3/8
= (4/3 π r^3) / 8
= (Volume of sphere 1)/8
So, volume of sphere if radius is divided by 2 is 1/8 of volume of sphere with r radius.
Answer:
The volume become 1/8 th of the initial volume
Step-by-step explanation:
Points to remember
Volume of sphere V = 4/3(πr³)
Where r is the radius of sphere
It is given that radius of sphere is r/2
To find the effect in volume
Here r = r/2
V = 4/3(πr³)
V = 4/3(π(r/2)³)
= 4/3(πr³/8)
= 1/8( 4/3(πr³)
New volume = 1/8(V)
what the midpoint (2,3) and (12,3)
Answer:
(7, 3)Step-by-step explanation:
The formula of a midpoint:
[tex]\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)[/tex]
We have (2, 3) and (12, 3).
Substitute:
[tex]x=\dfrac{2+12}{2}=\dfrac{14}{2}=7\\\\y=\dfrac{3+3}{2}=\dfrac{6}{2}=3[/tex]
Answer: (7,3)
Step-by-step explanation:
See the paper attached. (:
A 4-foot piece of aluminum wire costs $6.72. What is the price per inch?
Answer:
the answer is 14 cents
Step-by-step explanation:
12 time 4 equal 48 ( this is converting the feet into inches)
48 divided by 6.72 to get 0.14
Answer:
$0.14
Step-by-step explanation:
There are 12 inch in 1 foot.
You are given 4 foot. Find the amount of inch in 4 feet.
1 ft x 12 in/ft = 12 in
4 ft x 12 in/ft = 48 in
There are 48 in. in 4 ft. Divide 48 from $6.72
(6.72)/48 = $0.14
$0.14 is the price per inch.
~
Classify the following triangle as acute, obtuse, or right.
Answer:
A. Obtuse
F. Scalene
Step-by-step explanation:
There are two ways to classify a triangle:
by angles:
Obtuse - has one angle that is greater than 90°
Right - has one angle that is 90°
Acute - has all angles less than 90°
and by side lengths:
Equilateral - all sides are equal
Isosceles - two sides are equal
Scalene - no sides are equal
In this triangle, there is an obtuse angle (A. Obtuse).
∡ = 132°, which is greater than 90°.
There are no equal sides (F. Scalene).
6 ≠ 7 ≠ 11.9
Jenna uses the Fermi process to estimate the number of stickers it would take to cover her bedroom floor. Both her stickers and her floor are rectangular in shape. . She estimates her stickers to be about 2 in. long and 1 in. wide . She estimates her bedroom floor to be about 20 ft long and 10 ft wide Which expression should Jenna use in the process?
Answer:
3x10^4/2x10^0
Step-by-step explanation:
just took the test!!
The expression that Jenna should use in the process is area of floor/area of sticker
How to find the surface area of a figureThe surface area is defined as the sum of area of the faces.
Area of rectangle = lengh * width
Determine the area of the rectangular sticker
The area of the rectagular sticker = 2in * 1in
The area of the rectagular sticker = 2 square inches
Determine the area of the bedroom floor
Area of the floor = 20ft * 10ft
Area of the floor = 200 square feet = 28800 square in
Determine the number of stickers needed
Number of stickers needed = area of floor/area of sticker
Number of stickers needed = 28800/2
Number of stickers needed = 14400 stickers
The expression that Jenna should use in the process is area of floor/area of sticker
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HEEEEELLLLPPPPPPP
THE VALUE OF X IS __
Answer:
x=3
Step-by-step explanation:
25x+57+x=45x
26x+57=45x
57=19x
x=57/19
x=3
ANSWER
x=3
EXPLANATION
Use the exterior angle theorem:
25x°+(57+x)°=45x°
Group similar terms,
57=45x-25x-x
19x=57
Divide both sides by 19.
x=3
What is the value of |−25|? Numerical Answers Expected! Answer for Blank 1:
Answer:
25
Step-by-step explanation:
The absolute value function always returns a positive result which represents the magnitude of the input.
The magnitude of -25 is 25. The magnitude of 25 is 25.
Thus, |−25| = 25.
ANSWER: 25
Every time you see that sign ( | | )is the number without a sign example: |-56|= 56 ; |-37282|=37282.
In the diagram, lines r and s are parallel to each other and perpendicular to transversal line t. Line w is a transversal to lines r and s. Use properties of special angles, formed by parallel lines, perpendicular lines and their transversals, to describe the relationship between the angles. Choose all of the situations that correctly describe the relationship between the angles. Note: Figure is not drawn to scale
s || r ; s ⊥ t ; r ⊥ t
line w is a transversal
same side interior angles
alternate interior angles
equal angles
alternate exterior angles
supplementary angles
right angles
corresponding angles
vertical angles
The angles do not share a special relationship.
Answer:
equal angles and vertical angles
Step-by-step explanation:
we know that
Vertical Angles are the angles opposite each other when two lines cross. They are always equal
In this problem
∠14=∠16 -----> by vertical angles
therefore
The answer is
equal angles and vertical angles
Answer:
Vertical angles, equal angles
Step-by-step explanation:
when a transversal passes through two lines, then,
Angles formed in the same side and inside the two lines are same side interior angles.
Angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles.
Angles formed on opposite sides of the transversal and outside the two lines are alternate exterior angles.
Angles with the same relative position at each intersection are corresponding angles,
While, when two lines intersect each other then the opposite angles formed called vertical angles,
supplementary angles : When the sum of two angles are 180°,
Right angles : angle that has the measurement of 90°,
Equal angles : angles with the same measurement.
Now, vertical angles are always equal angles,
Also, when two parallel lines are cut by the same transversal then the pair of alternate interior angles, alternate exterior angles, corresponding angles are always equal.
Hence, by above definitions it is clear that,
∠16 and ∠14 are vertical and equal angles.
If the reserve rate is 4% and the bank receives a deposit of 12000 how much of the 12000 is the bank free to Loan
Answer:
11,520
Step-by-step explanation:
The reserve rate simply refers to the amount the bank sets aside as reserves. In this case, the bank sets aside 4% of deposits made by its customers implying the bank would loan out 96% of all deposits made; so we have
12000x 0.96 = 11,520 is free to loan out
write an equation that would allow you to solve the following problem. mart'a jump rope is 10 inches shorter than 3 times the length of dilbert's rope. if both of their ropes laid together end-to-end measure 120 inches long, how long is Marta's jump rope?
Answer:
Step-by-step explanation:
m=marta's rope
d=dilbert's rope
3d-10=m
m+d=120
Then you can substitute equation 1 into the second one
(3d-10)+d=120
3d-10+d=120
4d-10=120
4d=130
d=32.5
m+d=120
m+32.5=120
m=120-32.5
Helppppppppppppppppppppp!
Answer:
±(√35 i)
Step-by-step explanation:
[tex]\pm\sqrt{-35}[/tex]
We need to solve the above equation using the imaginary unit i.
We know i= √-1
Solving
±√-35 =±( √-1 √35)
= ±(√35 i)Since 35 = 5*7 or 35*1 it cannot be further simplified
So our answer is ±(√35 i).
Maria want to make a footstool in the shape of a cylinder, as show below. She wants to fill the footstool with foam and cover it with fabric. r=12in by h=18in
Answer:
She'll need 8143 cubic inches of foam and 1,809.6 square inches of fabric.
Step-by-step explanation:
Assuming you want to know how much foam and fabric she will need...
First the foam... so we need to determine the volume of that footstool. The Volume of a cylinder is given by:
V = π * r² * h
So, we plug in the numbers:
V = π * 12² * 18 = π * 144 * 18
V = 2,592 π = 8143 cubic inches.
Now for the fabric... we'll assume Maria wants to cover the side of the stool and the top, but not the bottom.
The side of the stool is basically a rectangle of width of 18 inches and a length of the circumference of the base of the stool. The circumference is given by: C = 2 π * r of course, so C = 24π = 75.14 inches.
So the lateral surface of the cylinder is:
LS = 18 * 75.14 = 1,357.2 sq inches.
Then we need to calculate the area of the top... which is easy:
A = π * r² = π * 12² = 144 π = 452.4 sq inches
So, to cover the lateral side of the footstool and its top, she needs to use:
TA = 1,357.2 + 452.4 = 1,809.6 sq inches of fabric.
(04.01 LC)
Which of the tables represents a function
Answer:
Table 2
For every input, there is one output.
Why table 1 is not a function:
The input 5 has two outputs, 3 and 2
Why table 3 is not a function:
The input 1 has two outputs, 2 and 3
Why table 4 is not a function:
The input 4 has three outputs, 2, 3, and 4
Hope this helps!
Craig earns the same amount of money each month. His electric bill is 1/15 his monthly earnings, and he pays a total of $1,320 each year for his electric service. How much does Craig earn each month, in dollars?
Answer:
1650
Step-by-step explanation
1320/12=110
110x15=1650
In this triangle, what is the value of x?
Enter your answer, rounded to the nearest tenth, in the box.
Answer: x = 75.7 cm
Step-by-step explanation:
In the given picture, we are given a right triangle.
The length of hypotenuse = 85 cm
Angle opposite to x= [tex]63^{\circ}[/tex]
Using trigonometry,
[tex]\sin\theta=\dfrac{\text{Side opposite to }\theta}{\text{Hypotenuse}}\\\\\Rightarrow\ \sin63^{\circ}=\dfrac{x}{85}\\\\\Rightarrow\ x=85\times\sin63^{\circ}\\\\\Rightarrow\ x=85\times0.89100652418\\\\\Rightarrow\ x=75.7355545553\approx75.7\ cm[/tex]
Hence, the value of x = 75.7 cm
A quarter is approximately 0.07 inches thick. A dollar bill is approximately 4.3 × 10-3 inches thick.
A is thicker than a by m × 10n inches, where m = and n = .
Answer:
m = 6.57 and n = -2
Step-by-step explanation:
To answer this question you will covert the thickness of a dollar to standard notation and then compare the two values.
0.07 =compared to 0.0043 = 0.0657
0.0657 = 6.57 x 10^-2
A quarter is thicker than a dollar by 6.57 x 10^-2.
m = 6.57 and n = -2
m = 6.57 and n = -2
Step-by-step explanation:
To answer this question you will covert the thickness of a dollar to standard notation and then compare the two values.
0.07 =compared to 0.0043 = 0.0657
0.0657 = 6.57 x 10^-2
A quarter is thicker than a dollar by 6.57 x 10^-2.
m = 6.57 and n = -2
The question is in the picture. Help please.
Answer:
≈ 2.1 m
Step-by-step explanation:
Given
v = [tex]\sqrt{9.8d}[/tex] ← substitute v = 4.5
4.5 = [tex]\sqrt{9.8d}[/tex] ← square both sides
4.5² = 9.8d
20.25 = 9.8d ← divide both sides by 9.8
d = 2.0663 ≈ 2.1 m ( nearest tenth )
Marge has a flat tire and needs to change it. To loosen the lug nuts, she has two wrenches: one is 12 inches long and the other is 18 inches long. Which wrench will generate more torque and make her job easier? Explain why using calculations to back you up.
For items requiring calculations, either show your work or describe how to calculate it
Answer: Hey i am single and ready to mingle
Step-by-step explanation:
I need someone
The 18-inch wrench will generate more torque and make it easier for Marge to loosen the lug nuts because torque is the product of the force applied and the lever arm, and the longer wrench provides a larger lever arm.
The wrench that Marge should use to generate more torque and make her job easier when changing a flat tire is the one that is 18 inches long. This is because torque (au) is calculated as the product of the force (F) applied and the distance (r) from the pivot point, with the equation torque (au) = force (F) × lever arm (r). Since the wrenches provide the lever arm and assuming the same force is applied to both, the longer wrench will provide greater torque due to a larger r.
For example, if Marge exerts a force of 100 newtons, the torque generated by each wrench would be:
12-inch wrench: au = 100 N × 0.305 m = 30.5 N.m (since 12 inches is approximately 0.305 meters)
18-inch wrench: au = 100 N × 0.457 m = 45.7 N.m (since 18 inches is approximately 0.457 meters)
The 18-inch wrench generates 45.7 N.m of torque, compared to 30.5 N.m with the 12-inch wrench, thus the 18-inch wrench will make loosening the lug nuts easier.
How do I write these circles in standard form?
Answer:
A: [tex](x-0)^{2} +(y-0)^{2} = 2^{2}[/tex]
or [tex]x^{2} +y^{2} =4[/tex]
B: [tex](x-5)^{2} +(y+4)^{2} =9[/tex]
Check the picture below.
[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad radius=\stackrel{}{ r} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{small}{circle}~~ \begin{cases} r=2\\ h=0\\ k=0 \end{cases}\implies (x-0)^2+(y-0)^2=2^2\implies x^2+y^2=4 \\\\\\ \stackrel{large}{circle}~~ \begin{cases} r=3\\ h=5\\ k=-4 \end{cases} \\[3em] [x-5]^2+[y-(-4)]^2=3^2\implies (x-5)^2+(y+4)^2=9[/tex]
Can Someone Help me with my Algabra 2 Homework 4a-c
Answer:
Step-by-step explanation:
Sigma notation is:
n
∑ ak
k=1
The n on top is the number of terms. ak is the expression for the kth term.
Let's look at the first one. The series is:
-2+4+-8+...+64+-128
There's two things to notice. One, the sign changes back and forth between + and -. Two, the magnitude doubles with each next term. Therefore:
ak = (-2)ᵏ
Next we need to find the number of terms. -128 is the last term, so:
128 = 2ⁿ
n = 7
So the answer is:
7
∑ (-2)^k
k=1
Now the second one. Notice the numerators are all 1 and the denominators are all perfect squares. Therefore:
ak = (1/k)²
The last term is 1/100, so n = 10.
So the answer is:
10
∑ (1/k)²
k=1
Now the last one. Notice that each term is 5 plus the previous term. This is an arithmetic series. So we can say:
ak = 4 + 5(k-1)
ak = 4 + 5k - 5
ak = 5k - 1
The last term is 49, so:
49 = 5n - 1
n = 10
So the answer is:
10
∑ (5n-1)
k=1
Carlos graphs the equations y=-1/2 x^2+4 and and y=-1/2 x^2-2x+2 generates the graph below. Which conclusion is supported by the graph?
Answer: The answer is B the second option. I just took the test.
Step-by-step explanation:
Answer:
2nd Option is correct.
Step-by-step explanation:
Given Functions:
[tex]y=\frac{-1}{2}x^2+4[/tex]
[tex]y=\frac{-1}{2}x^2-2x+2[/tex]
We need to find which conclusion supported by graph.
From the given, it is clear that both graph intersecting only at one point.
Also, One graph is translation of another graph.
So, the equation [tex]\frac{-1}{2}x^2+4=\frac{-1}{2}x^2-2x+2[/tex] has only one solution.
Therefore, 2nd Option is correct.
A point is chosen at random in the larger circle. What percent of the time will the point be in the shaded region? Round to the nearest tenth of a percent.
Please help me!!
Answer:
The dot will land on red 74.8% of the time
Step-by-step explanation:
To start off we need to find the Area of the whole circle. We can calculate this by using the Area of a Circle Formula on the larger circle measurement.
[tex]A = \pi r^{2}[/tex] .... A is Area, and r is radius.
[tex]A = \pi 8.01^{2}[/tex]
[tex]A = \pi *64.1601[/tex]
[tex]Aw = 201.56in^{2}[/tex] .... rounded to the nearest hundredth
So now we know that the area of the WHOLE circle is [tex]201in^{2}[/tex]. Now we need to find the area of the inner white circle.
[tex]Aw = \pi 4.02^{2}[/tex]
[tex]Aw = \pi *16.1604[/tex]
[tex]Aw = 50.77in^{2}[/tex] .... rounded to the nearest hundredth
Now that we have the area of the whole circle and the area of the smaller inner circle we subtract them to find the area in red.
[tex]Ar = 201.56in^{2} - 50.77in^{2}[/tex]
[tex]Ar = 150.79in^{2}[/tex]
Lastly, we divide the Area in Red by the total Area to get the percentage of time the dot will land on red.
[tex]d = \frac{150.79in^{2} }{201.56in^{2} }[/tex]
[tex]d = 0.748 * 100[/tex] .... multiply by 100 to turn decimal into a percent.
[tex]d = 74.8[/tex]
Finally, we can see that the dot will land on red 74.8% of the time.
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
To find the percent of the time that the point will be in the shaded region of the larger circle, we need to find the ratio of the area of the shaded region to the area of the larger circle and convert it to a percentage.
Explanation:To find the percent of the time that the point will be in the shaded region, we need to find the ratio of the area of the shaded region to the area of the larger circle. Let's say the radius of the larger circle is R, and the radius of the smaller shaded circle is r. The area of the larger circle is πR2 and the area of the shaded circle is πr2. So the ratio is πr2 / πR2 = r2 / R2. The percentage is then (r2 / R2) * 100. Round this to the nearest tenth of a percent to get the final answer.
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the length of a varies string varies inversely as the frequency of its vibrations. A violin string 10 inches long vibrates at a frequency of 512 cycles per second. Find the frequency of an 8-inch string.
Answer:
10(512) = 5,120
8f = 5,120
f = 640 cycles per second
50.
Belinda has 10 cups of flour. She uses 3 cups of it to make a loaf of bread.
She uses 1/4 cup of the remaining flour for each biscuit she wants to make. How
many biscuits can she make with the remaining flour?
Answer:
28 biscuits.
Step-by-step explanation:
Belinda has 10 cups of flour
She uses 3 cups to make a loaf of bread
She uses [tex]\frac{1}{4}[/tex] cup of the remaining flour for each biscuit she wants to make.
There are 10 - 3 = 7 cups of flour remaining
[tex]\frac{1}{4}[/tex] cup of flour makes -> 1 biscuit
7 cups of flour will make;
7 × 1 ÷ [tex]\frac{1}{4}[/tex] = 7 × 4 = 28 biscuits
what is 2 3/5 × -4/3
Answer:
- 52/15 your welcome
Step-by-step explanation:
the angle of elevation necessary for a hit ball to just clear the center field fence is not the only factor that goes into determining whether the ball clears the fence what might be some other determining factors, and how do they play a role on the ball’s final destination? Provide at least two other determining factors
Answer:
Step-by-step explanation:
Along with the angle of elevation, the initial velocity of the ball will determine how far and how high it goes.
Also, the initial height that the ball is hit from, as well as the horizontal distance from the fence, will affect whether the ball clears the fence.
There's also the acceleration of gravity, but here on Earth, that doesn't change much near the surface.