Answer:
6/7
Step-by-step explanation:
all fractions have a common denominator which allows us to add all numerators and maintain the same denominator. 2+3+1=6, and put it back over 7. so 6/7.
Isabella has a total of 150 music cds .she love rock music and alternative music .the number of alternative music cds is three that of the rock music cds that she owns. write the two equations that represent this information .
The two equation that represents the information is x + y = 150
y = 3x
How to form an equation?
let
the number of rock music = x
the number of alternative music = y
Therefore,
x + y = 150
y = 3x
The two equation that represent the information are as follows:
x + y = 150
y = 3x
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A wire of length 4x is bent into the shape of a circle. A. Express the circumference of the circle as a function of 4x. B. Express the area of the circle as a function of 4x.
The circumference of the wire is 4x and the area of the circle is 4x^2/π
How to determine the circumference?The length of the wire is given as;
Length = 4x
This represents the circumference.
Hence, the circumference of the wire is 4x
How to determine the area?In (a), we have:
Circumference = 4x
Calculate the radius using:
2πr = 4x
Divide through by 2π
r = 2x/π
The area is:
Area = πr^2
This gives
Area = π(2x/π)^2
Evaluate
Area = 4x^2/π
Hence, the area of the circle is 4x^2/π
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Find the value of x.
please explain because I'm confused
Answer:
40
Step-by-step explanation:
The sum of exterior angles of a convex polygon is 360°. This relation lets you write an equation for x.
__
Clockwise from the bottom, the sum of exterior angles is ...
90° +(x +35)° +(x +15)° +(2x -20)° +(2x)° = 360°
120° +6x° = 360° . . . . . . . simplify
6x = 240 . . . . . . . . . . divide by °, subtract 120
x = 40 . . . . . . . . . . divide by 6
The value of x is 40.
Answer:
x = 40°
Explanation:
The shape is a pentagon. Any polygon's exterior angles sum up to 360°.
Now, they all sum up to 360° :
⇒ (x + 35) + (x + 15) + (2x - 20) + 2x + 90 = 360°
⇒ x + x + 2x + 2x + 35 + 15 -20 + 90 = 360°
⇒ 6x + 120° = 360°
⇒ 6x = 360° - 120°
⇒ 6x = 240°
⇒ x = 240°/6
⇒ x = 40°
Which inequality represents the domain of the exponential piece?
a x>3
b x greater than or equal to -1
c x>1
d x less than or equal to -2
Using it's concept, it is found that the inequality represents the domain of the exponential piece is:
d) [tex]x \leq -2[/tex].
What is the domain of a function?The domain of a function is the set that contains all possible input values.
Researching this problem on the internet, we have that the function is divided as follows:
For [tex]x \leq -2[/tex], it has exponential behavior.For x > 2, it has polynomial behavior.Hence, for the domain of the exponential piece, option d is correct.
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Find the sum of the first 200 terms of the arithmetic sequence that begins: 12, 18, 24, ...
Answer:
S₂₀₀ = 121800
Step-by-step explanation:
the sum to n term of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
here a₁ = 12 and d = a₂ - a₁ = 18 - 12 = 6 , then
S₂₀₀ = [tex]\frac{200}{2}[/tex] [ (2 × 12) + (199 × 6) ]
= 100(24 + 1194)
= 100 ×1218
= 121800
In a video game, the player can choose a character from 4 animal characters and 3 human characters. Players can also let the computer randomly select a character for them. The player will have the computer randomly select his character. What is the probability it will pick a human character? Enter your answer as a fraction in simplest form in the box. PLEASEEEEEEEEEEEEEEEEEEEEEEEEE
The probability of selecting the human characters will be equal to 3 / 7.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Given that:-
The player can choose a character from 4 animal characters and 3 human characters.The probability will be calculated as:-
Probability = 3 / (3+4)
Probability = 3 / 7
Therefore the probability of selecting the human characters will be equal to 3 / 7.
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Find the area and the area of the figure.
Answer:
352
Step-by-step explanation:
sssplit the shapes and then do regular formula
a = lh
In a random sample survey of 80 students at Ned's middle school, 32 students said that math was their favorite subject. There are a total of 900 students at this middle school. Based on this survey, how many students would you expect to say that math is their favorite subject?
Answer:
360
Step-by-step explanation:
from the survey:
32/80 - 0.4 love math
0.4*900
= 360
What is the common difference between successive terms in the sequence? 2, 8, 14, 20, 26,. –6 –4 4 6.
Answer:
The common difference is the difference between any two consecutive terms in an arithmetic sequence.
The formula which is used to find the common difference in AP is
d = an - an-1
Here the common difference is
d = a2 - a1 = 8 - 2 = 6
d = a3 - a2 = 14 - 8 = 6
d = a4 - a3 = 20 - 14 = 6
d = a5 - a4 = 26 - 20 = 6
2, 8, 14, 20, 26 … = 2, (2 + 6), (8 + 6), (14 + 6), (20+ 6) …
Therefore, the common difference is 6.
Step-by-step explanation:
How do the average rates of change for f(x) = -0.5x² and g(x) = -1.5x² over the interval -5 ≤ x ≤ -2 compare?
Find KE the answer is 40 I just need help getting to it.
Answer:
EK = 8
Step-by-step explanation:
Intersecting Chords Formula: a • b = c • d
BK * KD = EK * KC
4 * 10 = (x+1) * (x-2)
40 = x^2 +x-2x-2
40 = x^2 -x -2
0 = x^2 - x-2-40
0 = x^2 -x -42
Factor
0 = (x-7) (x+6)
Using the zero product property
x-7 = 0 x+6 =0
x=7 x=-6
X is not negative
x=7
EK = x+1
EK = 7+1
EK = 8
Find f(4) given f(x) = 2x^2 - 7
Answer:
f(4) = 25
Step-by-step explanation:
substitute x = 4 into f(x)
f(4) = 2(4)² - 7 = 2(16) - 7 = 32 - 7 = 25
When you use the slope formula, does it matter what point you choose as (x1 , y1) and what point you choose as (x2, y2)? Explain why or why not.
Answer:
It does not matter.
Step-by-step explanation:
How to find a slope with just two points,
Step One: Identify two points on the line.
Step Two: Select one to be (x1, y1) and the other to be (x2, y2).
Step Three: Use the slope equation to calculate the slope.
Example
Let's say that points (15, 8) and (10, 7) are on a straight line. What is the slope of this line?
Step One: Identify two points on the line.
In this example, we are given two points, (15, 8) and (10, 7), on a straight line.
Step Two: Select one to be (x1, y1) and the other to be (x2, y2).
It doesn't matter which we choose, so let's take (15, 8) to be (x2, y2). Let's take the point (10, 7) to be the point (x1, y1).
Step Three: Use the equation to calculate the slope.
Once we've completed step 2, we are ready to calculate the slope using the equation for a slope:
[tex]slope=\frac{y2-y1}{x2-x1} =\frac{8-7}{15-10} =\frac{1}{5}[/tex]
We said that it really doesn't matter which point we choose as (x1, y1) and the which to be (x2, y2). Let's show that this is true. Take the same two points (15, 8) and (10, 7), but this time we will calculate the slope using (15, 8) as (x1, y1) and (10, 7) as the point (x2, y2). Then substitute these into the equation for slope:
[tex]slope=\frac{y2-y1}{x2-x1} =\frac{7-8}{10-15} =\frac{-1}{-5}=\frac{1}{5}[/tex]
We get the same answer as before!
Often you will not be given the two points but will need to identify two points from a graph. In this case, the process is the same, the first step being to identify the points from the graph. Below is an example that begins with a graph.
So therefore it does not matter.
No, it does not matter which point you choose as (x₁, y₁) and which point you choose as (x₂, y₂) when using slope formula. Slope between two points on line remains same regardless of order in which you choose points.
The slope formula is given by slope = (y₂ - y₁) / (x₂ - x₁)
This is because the slope represents the rate at which the y-coordinate changes with respect to the x-coordinate.
If you swap the points (x₁, y₁) and (x₂, y₂), the change in y and the change in x will simply swap as well, but their ratio, which is the slope, will remain unchanged. For example, if the slope between (x₁, y₁) and (x₂, y₂) is m, then the slope between (x₂, y₂) and (x₁, y₁) will also be m.
This property of the slope formula makes it convenient and efficient to calculate the slope between two points, regardless of their order, as it will yield the same result.
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For each graphically defined function below, state the domain, the range, and the intervals on which the function is increasing, decreasing, or constant.
Domain:
Range:
Increasing:
Decreasing:
Constant Intervals?
Answer:
Domain: [tex]-3\leq x\leq 3[/tex]
Range: [tex]0\leq y\leq 1.5[/tex]
Increasing: [tex]0\leq x\leq 3[/tex]
Decreasing: [tex]-3\leq x\leq 0[/tex]
No constant intervals
Step-by-step explanation:
Hope this helped
Math ahh need done ASAP
Answer:
a) 3Step-by-step explanation:
Use the nth tern equation of the AP
[tex]a_n=a_1+(n-1)d[/tex]We have
[tex]a_1=-2[/tex] and [tex]a_{10}=25[/tex]Find the value of d
25 = - 2 + (10 - 1)d25 + 2 = 9d27 = 9dd = 27/9d = 3Correct choice is a)
Now
a_n=a+(n-1)d25=-2+9d9d=27d=3If YV = 23 ft, find the length of VYX to the nearest tenth.
The length of EC shown in the diagram is 66.2.
"To understand the calculation, check below."
TrianglesΔBE - ΔAE = ΔAB
ΔAB = 180°- 117°
ΔAB = 63°
Δ[tex]BE-[/tex] Δ[tex]AB-[/tex] Δ[tex]BC[/tex] = Δ[tex]CD[/tex] (Congruent angles)
Δ[tex]CD= 180 - 63 - 15[/tex]
Δ[tex]CD=102[/tex]
[tex]EC = 102 + 63[/tex]
[tex]EC=165[/tex]
[tex]L = 165[/tex] • [tex]2\pi23/360[/tex]
[tex]L = 66.2[/tex]
Therefore, EC = 66.2
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Find the gradient of the line joining (-1,9) and (3,5)
[tex]\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]
Find the gradient of the line joining (-1,9) and (3,5)
[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]
Use the slope formula:-
[tex]\boxed{\frac{y_2-y_1}{x_2-x_1}}[/tex]
Replace the letters with the numbers:-
[tex]\boxed{\frac{5-9}{3-(-1)}}[/tex]
[tex]\circ[/tex] On simplification,
[tex]\boxed{\frac{-4}{3+1}}[/tex]
[tex]\circ[/tex] On further simplification,
[tex]\boxed{\frac{-4}{4}}[/tex]
[tex]\circ\sf{SLOPE=-1}[/tex]
Good luck with your studies.[tex]\rule{300}{1}[/tex]
Quick please!
Tell whether a triangle with the given side lengths is a right triangle.
16 in, 34 in, 30 in
Answer:
It's a right triangle ..
Step-by-step explanation:
By using Pythagoras theorem , we can know that it's a right angled triangle or not ..
so , H² = P² + B²
=> 34² = 16² + 30²
=> 1,156 = 256 + 900
=> 1,156 = 1,156
Hence , it's a right triangle
the number of ducks living at the pond increased by 40%
50/9 as a mixed fraction
Answer:
5 5/9
Step-by-step explanation:
9 goes into 50 4 times and the subtract that from 50
Answer :
5 [tex]\frac{5}{9}[/tex]
Explanation:
50/9= 5.5555555555556 = 5
Now that we have our whole number for the mixed fraction, we need to find our new numerator for the fraction part of the mixed number.
Step 2: Get the new numerator
To work this out we'll use the whole number we calculated in step one (5) and multiply it by the original denominator (9). The result of that multiplication is then subtracted from the original numerator:
50 - (9 x 5) = 5
Step 3: Our mixed fraction
We've now simplified 50/9 to a mixed number. To see it, we just need to put the whole number together with our new numerator and original denominator:
5 [tex]\frac{5}{9}[/tex]
i need some help with this question.
The scale factor will be 1.5. The corresponding angles are congruent because the size is changed not the angles.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
Adnan wants a larger garden.
He draws the triangle ΔPQR to show his original garden.
He wants to enlarge a garden, so he uses a dilation to form the image of the triangle ΔPQ'R'.
He uses vertex P as the center of the dilation.
The ratio of the corresponding sides will be given as
PQ'/PQ = Q'R'/QR = R'P/RP = 1.5
The scale factor will be 1.5.
The corresponding angles are congruent because the size is changed not the angles.
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PLEASE EASY 20 POINTS A new park in the shape of a hexagon will have 6 sides of equal length.
On a scale drawing, the coordinates of the vertices of the park are (26.5, 12), (38.5, 7), (26.5, 2), (13.5, 2), (1.5, 7), and (13.5, 12).
How long is each side of the park?
Using the distance formula, each side of the park is 13 units long
How to determine the length of each side?The vertices of the park are given as:
(26.5, 12), (38.5, 7), (26.5, 2), (13.5, 2), (1.5, 7), and (13.5, 12).
The length of each side is calculated using the following distance formula:
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]
Using any consecutive points, we have:
[tex]d = \sqrt{(13.5 - 1.5)^2 + (12 -7)^2} = 13[/tex]
Hence, each side of the park is 13 units long
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Need help please answer ASAP!
Perimeter of larger sail
10+24+2660ftNow
Let shorter sail's Perimeter be x
x/6=60/10x/6=6x=36#2
Let they be 2x and 7x
2x+7x=1809x=180x=20Smaller angle
20(2)=40Select all angle measures for which
sin 0=-
❌
✅
✅
❌
✅
If the trigonometric expression is sin θ = -√2/2. Then the value of angle θ will be 5π/4, 7π/4, and 13π/4.
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
The trigonometric expression is given below.
sin θ = -√2/2
The expression can be written as
sin θ = -1/√2
Then the value of angle θ will be
θ = sin⁻¹ (-1/√2)
θ = 5π/4, 7π/4, and 13π/4.
Thus, the correct options are B, C, and E.
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Answer:
B,C,E
Step-by-step explanation:
Find the value of x in the given figure
[tex]~~~~~~(2x+34)+(x+71) = 180\\\\\implies 3x + 105=180\\\\\implies 3x = 180-105\\\\\implies 3x = 75\\\\\implies x = \dfrac{75}3\\\\\implies x = 25[/tex]
The graph of a sinusoidal function intersects its midline at (0, 1) and then has a maximum point at
Write the formula of the function, where is entered in radians.
f(x) =
Answer:
f(x) = 4·sin(2/7x) +1
Step-by-step explanation:
The sinusoidal function y = a·sin(kx) +b will have cross its midline at (0, b), and a peak value of (x, y) = (π/(2k), a+b). We can use these facts to find the values of a, k, and b for the sinusoidal function.
__
midline(0, b) = (0, 1) ⇒ b = 1
peak value(7π/4, 5) = (π/(2k), a+1)
This gives rise to two equations:
7π/4 = π/(2k)
k = π/(2(7π/4)) = 2/7
and
a+1 = 5
a = 4
equationUsing the found values for the parameters of the function, we have ...
f(x) = 4·sin(2/7x) +1
12.3 Write the first five terms of the sequence whose general term is [tex]a_{n}=3^{n}+4[/tex] .
Answer:
7,13,31,85,247......
Step-by-step explanation:
[tex]a_n =3^n + 4[/tex]
[tex]\sf a_1=3^1 + 4 = 3 + 4 = 7\\\\a_2 = 3^2 + 4 = 9 + 4 = 13\\\\a_3 = 3^3 + 4 = 27 + 4 = 31\\\\a_4 = 3^4 + 4 = 81 + 4 = 85\\\\a_5 = 3^5 + 4 = 243 + 4 = 247[/tex]
The given sphere has a radius of 2 inches. a sphere with radius of 2 inches. what happens to the volume if the radius is doubled? the volume of the new sphere is times larger than the volume of the original sphere.
Answer:
8 times larger than original
Step-by-step explanation:
the volume (V) of a sphere is calculated as
V = [tex]\frac{4}{3}[/tex]πr³
when r = 2 , then
V = [tex]\frac{4}{3}[/tex]π × 2³ = [tex]\frac{4}{3}[/tex]π × 8
when r is doubled , that is r = 4 , then
V = [tex]\frac{4}{3}[/tex]π × 4³ = [tex]\frac{4}{3}[/tex]π × 64
64 is 8 times larger than 8
then new sphere is 8 times larger than original sphere
Answer:
8 times
Step-by-step explanation:
Find the equation of the line shown
In parallelogram HIJK, the measure of angle H is 45∘.
Find the measure of angle J. Explain how you know.
Find the measure of angle K. Explain how you know.
Answer:
Step-by-step explanation: