Answer:
The required absolute inequality is |x - 78| ≤ 20.
Step-by-step explanation:
Consider the provided information.
Let $x is monthly charge.
The monthly charges for a basic cable plan = $78
it is given that it could differ by as much as $20
So, the maximum charges can be $78 + $20,
And, the minimum charges can be $78 - $20,
The value of x is lies from $78 - $20 to $78 + $20
Which can be written as:
78 - 20 ≤ x and x ≤ 78 + 20
-20 ≤ x - 78 and x - 78 ≤ 20
Change the sign of inequality if multiplying both side by minus.
20 ≥ -(x - 78) and x - 78 ≤ 20
⇒ |x - 78| ≤ 20
Thus, the required absolute inequality is |x - 78| ≤ 20.
A cylinder has a height of 16cm and a radius of 5cm. A cone has a height of 12cm and a radius of 4cm. If the cone is placed inside the cylinder as shown, what is the volume of the air space surrounding the cone inside the cylinder? (Use 3.14 as an approximation of ‘pi’.)
Radius of cylinder = 5cm
Radius of cone = 4cm
Answer:
1055.04
Step-by-step explanation:
Cylinder
h = 16 cm
r = 5 cm
Volume = ?
Formula
V=pi * r^2 * h
Solution
V = pi r^2*h
V = 3.14 * 5*5*16
V = 1256 cm^3
Cone
h = 12 cm
r = 4 cm
Formula
V = (1/3) pi r * r * h
Solution
V = (1/3) 3.14 * 4 * 4 * 12
V = (1/3) 602.88
V = 200.96
Answer
Volume of unoccupied region = Cylinder - Cone
Volume of unoccupied region = 1256 - 200.96
Volume of unoccupied region = 1055.04
You will have to round it to the number of digits required.
If y* 4x+1 were changed to y = 2x + 6, how would the graph of the new line
compare with the first one?
The new line with the equation y = 2x + 6 will be less steep than the original line y = 4x + 1 due to its lower slope, and will start higher on the y-axis with a y-intercept of 6 compared to the original line's y-intercept of 1.
When comparing the graph of the equation y = 4x + 1 with the new graph of the equation y = 2x + 6, there are two main features to consider: slope and y-intercept. For the original line, the slope is 4, meaning that for every one unit increase in x, y increases by 4 units.
The y-intercept, where the line crosses the y-axis, is at (0,1). On the other hand, the new line has a slope of 2, which indicates a less steep incline; for every one unit increase in x, y increases by only 2 units. Additionally, the y-intercept of this new line is at (0,6), which is higher on the y-axis as compared to the original line.
Which line segment is a chord of o Pin the diagram below?
A. RS
B. PQ
C. QR
D. ST
C or QR
Step-by-step explanation:
Suppose y varies directly with x. If y = -4 when x = 8, what is the equation of direct variation?
Complete the steps to write the equation of direct variation.
1. Start with the equation of direct variation y = kx.
2. Substitute in the given values for x and y to get
3. Solve fork to get
4. Write the direct variation equation with the value found for k. The equation is
[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{we also know that }~~ \begin{cases} y=-4\\ x=8 \end{cases}\implies -4=k(8)\implies \cfrac{-4}{8}=k\implies -\cfrac{1}{2}=k \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=-\cfrac{1}{2}x~\hfill[/tex]
Answer:
k = -1/2
y= -1/2x
Step-by-step explanation:
y = kx
We know y = -4 and x=8
-4 = k*8
Divide each side by 9
-4/8 = 8k/8
-1/2 =k
y= -1/2x
Another engineer is tiling a new building. A square tile is cut along one of its diagonals to form two triangles with two congruent angles. What are the measurements of the interior angles of the triangles? Explain how you calculated them.
Answer:
The measurements of the interior angles of the triangles are 45°-90°-45°
Step-by-step explanation:
we know that
A square is a quadrilateral with 4 equal sides and 4 interior angles of 90 degrees
The diagonal of a square bisect the square into two congruent isosceles right triangles
The two congruent legs of each isosceles right triangle is equal to the length side of the square
The measure of the base's angles of each isosceles right triangle is equal to 45 degrees, because the diagonal bisect the right angle of the square
therefore
The measurements of the interior angles of the triangles are 45°-90°-45°
Answer:
Sample Explanation:
Since the triangle shares an angle with the original square, the triangle has a right angle. Since the triangle has two angles that are congruent, the equation for the measures of all three angles is 90 + 2x = 180, and I found that x = 45. The angles in the triangle are 90°, 45°, and 45°.
Step-by-step explanation:
Finding Unknown Angle Measures Assignment
Finding Unknown Measurements
Solve log525 = x 2 1/2 -2
Answer:
x = 1/2
Step-by-step explanation:
The equation in correct format is:
[tex]log_{5}(25)=x[/tex]
We have to solve this logarithmic equation to find the value of x. This can be done by using the rules of logarithm i.e the power rule and same base rule shown below:
[tex]log(a)^{b}=b \times log(a)\\\\log_{a}(a)=1[/tex]
Using these rules on our equation, we get:
[tex]log_{5}(25)=x\\\\log_{5}(5^{\frac{1}{2} })=x\\\\ \frac{1}{2} log_{5}(5)=x\\\\ \frac{1}{2} (1)=x\\\\ x=\frac{1}{2}[/tex]
Thus the value of x would be 1/2
Answer:
x = 2Step-by-step:
Log5 (25)= xWrite in exponential form
Log5 (5^2)= xSimplify the expression
2= xSwap sides
x = 2
Calculate (Round two decimal places for final answer): 650 mL = _______________ oz.
Answer:
6.5
Step-by-step explanation:
For this case we must perform a conversion of milliliters to ounces.
By definition we have to:
1 US liquid ounce equals 29.5735 milliliters. Then, making a rule of three:
1 oz. ---------> 29.5735 milliliters
x -------------------> 650 milliliters
Where "x" represents the number of oz equivalent to 650 mL.
[tex]x = \frac {650 * 1} {29.5735}\\x = 21.9791[/tex]
Thus, 650 mL equals 21.9791 oz.
Answer:
650 mL equals 21.9791 oz.
If the value of “y” varies directly with “x” and y = -51 when x = 3, find “y” if x = 2
Y =
Answer:
y = - 34
Step-by-step explanation:
Given y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = - 51 when x = 3
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{-51}{3}[/tex] = - 17
y = - 17x ← equation of variation
When x = 2, then
y = - 17 × 2 = - 34
Final answer:
To find the value of y when x = 2 in a direct variation relationship, determine the constant of variation first and then substitute the given values to find the unknown.
Explanation:
The relationship given is that y varies directly with x. To find y when x = 2, you can use the direct variation formula.
First, find the constant of variation by using the values given: y = kx. Plug in y = -51 and x = 3 to find k.
Once you have k, solve for y when x = 2 using y = kx.
Therefore, when x = 2, y = -34.
I’m trying to find the missing fraction for this 1/3 + blank =7/12
[tex]\dfrac{1}{3}+x=\dfrac{1}{12}\\\\\dfrac{4}{12}+x=\dfrac{1}{12}\\\\x=-\dfrac{3}{12}=-\dfrac{1}{4}[/tex]
Answer:
1/4
Step-by-step explanation:
The LCD here is 12. Subtract 1/3, or 4/12, from 7/12, to obtain the missing fraction. 7/12 - 4/12 = 3/12, or 1/4. The missing fraction is 1/4.
If point C is inside AvB, then __+m CvB= m AvB
Answer: OPTION A
Step-by-step explanation:
It is important to remember the "Angle Addition Postulate" in order to solve this exercise.
You have this larger angle:
[tex]\angle AVB[/tex]
According to the "Angle Addition Postulate", if the point "C" is in the interior of [tex]\angle AVB[/tex], then the measure of this angle can be obtained by adding the angle [tex]\angle AVC[/tex] and the angle [tex]\angle CVB[/tex].
You can observe in the figure that:
[tex]m\angle AVC=39\°\\\\\mangle CVB=23\°[/tex]
Then you get that:
[tex]m\angle AVC+m\angle CVB=m\angle AVB\\\\39\°+23\°=62\°[/tex]
Therefore, the correct answer is Option A.
Answer:answer is actually C
What is the difference of the two polynomials (9x^2+8x)-(2x^2+3x)
Answer:
7x² + 5x
Step-by-step explanation:
Given
(9x² + 8x) - (2x² + 3x) ← distribute parenthesis, second by - 1
= 9x² + 8x - 2x² - 3x ← collect like terms
= (9x² - 2x² ) + (8x - 3x)
= 7x² + 5x
Distribute the negative sign:
[tex](9x^2+8x)-(2x^2+3x)=9x^2+8x-2x^2-3x[/tex]
Gather like terms:
[tex]9x^2+8x-2x^2-3x = (9x^2-2x^2) + (8x-3x) = 7x^2+5x[/tex]
Which description from the list below accurately describes the relationship between
Answer
Congruent by dilation
Step-by-step explanation:
They are not the same size, nor have the same area and are not currently congruent because they are different sizes.
Answer:
D. Congruent after dilation.Step-by-step explanation:
From the figures, you can observe that the triangles don't have the same size or area, that means they cannot be congruent.
However, if we dilate the first triangle by a scale factor of 2, then both triangles will be congruent, because 5 x 2 = 10, 4 x 2 = 8 and 3 x 2 = 6.
Therefore, the right answer is D. Because if you dilate the first triangle, both would be congruent. Also, because they don't have the same area, size, and they aren't congruent.
Nico has conducted an observational study to learn about how different personal experiences affect car purchases. Nico surveyed 300 new car buyers at the auto mall and found that 75% of the buyers were shopping for the same model of a car they have owned before. What conclusion can Nico make from his study?
A.Owning the same model of a car previously causes a buyer to purchase that car again, but he cannot draw a cause-and-effect conclusion from an observational study.
B. There may be a link between owning a model of a car and buying that model again, but he cannot draw a cause-and-effect conclusion from an observational study.
C.There may be a link between owning a model of a car and buying that model again, and he can draw a cause-and-effect conclusion from an observational study.
D.Owning the same model of a car previously causes a buyer to purchase that car again, but he can draw a cause-and-effect conclusion from an observational study.
Answer:
Option B is correct.
Step-by-step explanation:
Nico surveyed 300 new car buyers at the auto mall and found that 75% of the buyers were shopping for the same model of a car they have owned before.
This is 225 customers out of 300.
When people are satisfied with their car's current company and brand and model, they can prefer the same thing again for the same better experience. But this is not 100% proven. We can only say that there may be a link between the two things.
Hence, the conclusion that can be drawn here is :
B. There may be a link between owning a model of a car and buying that model again, but he cannot draw a cause-and-effect conclusion from an observational study.
The conclusion of the given study is that; Option B
What is the conclusion of the study?We are told that;
Number of new cars Nico surveyed = 300
Percentage of buyers that surveyed the new cars = 75% .
Thus, number of customers surveying this cars = 75% * 300 = 225 customers
If people are satisfied with their car's current company and brand and model,it means that they can also prefer the same thing again for the same better experience. Thus, the conclusion is that;
B. There may be a link between owning a model of a car and buying that model again, but he cannot draw a cause-and-effect conclusion from an observational study.
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Does anyone know what (-2)^-3 equals? By the way it has to be simpified.
Answer:
-1/8
Step-by-step explanation:
(-2)^-3
The negative exponent means it's the inverse.
1 / ((-2)^3)
-2 cubed is -8.
1 / (-8)
So the simplified answer is -1/8.
Answer:
-8
Step-by-step explanation:
=(-2)^-3
= -2 ×-2 ×-2
= -8
If f(c)=0, which of the following statements must be true?
___________________________________________
○A. The point (-c, 0) lies on the graph of f(x)
○B. The point (0, c) lies on the graph of f(x)
○C. x-c is a factor of f(x)
○D. x+c divides evenly into f(x)
Answer:
C.
Step-by-step explanation:
If f(c)=0 then (c,0) is on the graph.
In general, if f(a)=b then (a,b) is on the graph.
By factor theorem if f(c)=0 then x-c is a factor.
If x-c is a factor then x-c will divide f(x) evenly. We know this because the remainder will be 0 because we know x-c is a factor of f.
The only choice that I have said in this whole thing that is true is C.
Answer: The correct option is
(C) x-c is a factor of f(x).
Step-by-step explanation: Given that for a function f(x), f(c) = 0.
We are to select the true statement from the given options.
We have the factor theorem as follows :
Factor theorem : If p(a) = 0 for a polynomial function p(x), then (x-a) is a factor of p(x).
According to the given information, we have
f(c) = 0.
Therefore, (x-c) is a factor of f(x).
Thus, (C) is the correct option.
i need help step by step
0=x²-7x +10
Answer:
x=2 or x=5
Step-by-step explanation:
0−(x^2−7x+10)
=x^2−7x+10−(x^2−7x+10)
−x^2+7x−10=0
(−x+2)(x−5)=0
−x+2=0 or x−5=0
x=2 or x=5
Answer:
x = 2 or x = 5
Step-by-step explanation:
Several ways to do this.. but i'll use completing the square:
x²-7x +10 = 0
x²-7x = -10 (take the x coefficient , divide that by two and then square the result and add it back to both sides)
x² - 7x + ( -7/2 )² = -10 + ( -7/2 )² (simply the left side using the property (a + b)² = a² + 2ab + b² )
[x + (-7/2)]² = -10 + ( -7/2 )²
[x - (7/2)]² = -10 + ( 49/4 )
[x - (7/2)]² = 9/4
x - (7/2) = ±√(9/4)
x - (7/2) = ±(3/2)
x = (7/2) ± (3/2)
x = 2 or x = 5
A sphere has a diameter of 10 inch. What is the volume of the sphere?
Answer:
≈ 523.6 in³
Step-by-step explanation:
The volume (V) of a sphere is
V = [tex]\frac{4}{3}[/tex] π r³ ← r is the radius
here diameter = 10, hence r = 5, so
V = [tex]\frac{4}{3}[/tex] π × 5³
= [tex]\frac{4}{3}[/tex] π × 125
= [tex]\frac{4\pi (125)}{3}[/tex] ≈ 523.6 ( to 1 dec. place )
The area of a rectangle is (x^3 - 5x^2 + 3x - 15), and the width of the rectangle is (x^2 + 3). If area = length c width, what is the length of the rectangle?
Answer:
Length = x-5
Step-by-step explanation:
Length= Area/width
Length = x³-5x²+3x-15/ x²+3
Re-arrange the numerator:
Length=x³+3x-5x²-15/x²+3
Take common from the numerator:
Length=x(x²+3) -5(x²+3)/x²+3
Length=(x²+3)(x-5)/x²+3
Length = x-5
Thus the answer is x-5 ....
what fraction of the positive integer factors of 1000^3, are perfect squares?
Answer:
25/81
Step-by-step explanation:
1000³ = (10³)³ = 10⁹ = 2⁹ × 5⁹
For a factor to be a perfect square, the exponents must be even. For example:
2⁰ × 5⁰, 2⁰ × 5², 2² × 5⁰, etc.
There are 5 even exponents between 0 and 9 for each 2 and 5. So the number of perfect square factors is 5×5 or 25.
The total number of factors is 9×9 or 81.
So the fraction of positive integer factors that are perfect squares is 25/81.
25/81 is the fraction of the positive integer factors of 1000^3,
What is perfect square ?When you multiply an integer (a "whole" number, positive, negative, or zero) by itself, the resulting product is known as a square number, perfect square, or simply "a square." For example, 0 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on are all square numbers.A perfect square is a number that can be written as the product of two integers or as an integer's second exponent. 25 is a perfect square because it is the product of the integer 5 and itself, 5 5 = 25.Perfect squares are significant because they demonstrate how to calculate the square root of a completely exact natural number. A perfect square's square root1000^3 = (10^3)^3 = 10^9 = 2^9 x 5^9
Perfect square factors have even exponents.
There are 5 even exponents between 0 and 9 for each 2 and 5.
Number of perfect square factors: 5x5 =25
Total number of factors: 9x9 =81
Fraction: 25/81
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Need help on the stretch problem.
Step-by-step explanation:
ΔACX is an isosceles triangle, so ∠AXC = ∠XAC. We'll call the measure of this angle x°.
∠AXC and ∠BXC are supplementary, so ∠AXC + ∠BXC = 180. That means ∠BXC = 180 − x.
ΔBXC is an isosceles triangle, so ∠XBC = ∠XCB. We'll call the measure of this angle y°.
Angles of a triangle add up to 180, so:
y + y + (180 − x) = 180
2y = x
y = x/2
∠ACX and ∠XCB are complementary, so ∠ACX + ∠XCB = 90.
x + y = 90
x + x/2 = 90
3/2 x = 90
x = 60
Therefore, ∠AXC = ∠XAC = 60°.
Write parametric equations of the line with the equation 3x + 2y = 5.
Answer:
a. x = t, y = -[tex]\frac{3}{2}t[/tex] + [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
The answer is a. x = t, y = -3/2t + 5/2
The parametric equations of the line with the equation 3x + 2y = 5 is mathematically given as
x=t
y = (5-3t)/2
What is the parametric equations of the line with the equation 3x + 2y = 5.?Question Parameter(s):
the line with the equation 3x + 2y = 5.
Generally, the equation for the equation in slope-intercept is mathematically given as
y = 3x -5/ 2
Therefore
y = (5-3t)/2
While
x=t
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what is the equation of the following line? (7,2) (0,0)
Let m = slope
m = (0-2)/(0-7)
m = -2/-7
m = 2/7
y - 0 = (2/7)(x - 0)
y = (2/7)x
Did you follow?
The equation of the line for the given coordinates [tex](7,2) , \ (0,0)[/tex] is equal to [tex]y= \frac{2}{7}x[/tex].
What is equation?"Equation is defined as the relation between the variables using the sign of equality."
Formula used
Slope [tex]'m' = \frac{y_{2} -y_{1}}{x_{2} -x_{1}}[/tex]
Equation of line passing through a point
[tex]y- y_{1} = m (x- x_{1})[/tex]
According to the question,
Given coordinates,
[tex](x_{1} ,y_{1}) = (7,2)\\\\(x_{2} ,y_{2}) = (0,0)[/tex]
Substitute the value in the formula to get slope,
[tex]m = \frac{0-2}{0-7}[/tex]
[tex]= \frac{2}{7}[/tex]
Substitute the value in the formula to get equation of the line,
[tex]y-2= \frac{2}{7} (x-7)\\\\\implies y-2 = \frac{2}{7}x -2\\ \\\implies y = \frac{2}{7}x[/tex]
Hence, the equation of the line for the given coordinates [tex](7,2) , \ (0,0)[/tex] is equal to [tex]y= \frac{2}{7}x[/tex].
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Find the value of angle E Need help Asap 10 minutes left
Answer:
D
Step-by-step explanation:
the question not give enough explanation and clue
For this case we have that the sum of the internal angles of a quadrilateral is 360 degrees.
In the figure they only give us the measure of an angle. We can not say that the angles C and D or E and F are the same because they do not say it.
Thus, we do not have enough information to solve the problem.
Answer:
Option D
Solve (X-3)^2/3=9 (the ^ is an exponent)
Step-by-step explanation:
Step-by-step explanation:
To answer the question you have t the square of the differences.
So this means that (x-3)^2= x^2-9x+9
Next youmultiply 3 on both sides which says…
x^2-9x+9=27
x^2-9x=18
So, x equals
9/2+3/2 square root 17
OR
9/2-3/2 square root 17
Analyze the graph which inequality represents the graph
For this case, we must find two points that belong to the line and thus find the slope.
We have:
[tex](x1, y1) :( 1,1)\\(x2, y2) :(0,4)[/tex]
We found the slope:
[tex]m = \frac {y2-y1} {x2-x1} = \frac {4-1} {0-1} = \frac {3} {- 1} = - 3[/tex]
It is also observed that the cut-off point with the y-axis is 4.
In this way, we discard options A and B.
We evaluate option C:
[tex]y> -3x + 4[/tex]
We substitute the point (0,0) that belongs to the shaded region and verify the inequality:
[tex]0> -3 (0) +4\\0> 4[/tex]
It is not fulfilled!
Thus, the correct option is option D.
ANswer:
Option D
Answer:
For this case, we must find two points that belong to the line and thus find the slope.
We have:
We found the slope:
It is also observed that the cut-off point with the y-axis is 4.
In this way, we discard options A and B.
We evaluate option C:
We substitute the point (0,0) that belongs to the shaded region and verify the inequality:
It is not fulfilled!
Thus, the correct option is option D.
ANswer:
Option D
To convert 10 kilometers to meters, you would use the ratio 1000 meter/1 kilometer
A. True
B. False
Answer:
True
Step-by-step explanation:
Since 1 km is 1000 metres that is the correct ratio to use
1 : 1000
( × 10 to get 10 km )
10 : 10000
Answer:
Step-by-step explanation:
Let's actually do the work:
10 km 1000 m
--------- * --------------- = 10^4 m
1 1 km
Answer: TRUE
Which figure can be transformed into figure P by a translation 2 units to the right followed by a reflection across the x-axis?
Answer:
Figure M
Step-by-step explanation:
Figure P has vertices at points (-2,4), (-2,8), (-6,8) and (-6,6).
Consider figure M with vertices (-4,-4), (-4,-8), (-8,-8) and (-8,-6).
1. Translate figure M 2 units to the right. This translation has the rule:
(x,y)→(x+2,y),
so
(-4,-4)→(-2,-4);(-4,-8)→(-2,-8);(-8,-8)→(-6,-8);(-8,-6)→(-6,-6).2. Reflect the translation image figure M across the x-axis according to the rule
(x,y)→(x,-y)
Thus,
(-2,-4)→(-2,4);(-2,-8)→(-2,8);(-6,-8)→(-6,8);(-6,-6)→(-6,6).kt over k+t for k=13 and t=8
Answer:4.95
Step-by-step explanation:
so you multiply (13*8) because its k*t and then the bottom of the formula is 13+8 because its k+t so 13*8 equals 104 and 13+8 is 21 then you divide 104/21=4.95
Which graph represents a geometric sequence?
Geometric sequence--
The sequence is said to be geometric if each of the term of the sequence is obtained by multiplying the preceding term of the sequence by a fixed constant.
This fixed constant is known as a common ratio and is denoted by r.
i.e. the sequence is given by:
a,ar,ar²,ar³,.....
The graph which represents the geometric sequence is attached to the answer.
Since the table of values are as follows:
x y
1 1
2 2
3 4
4 8
i.e. the sequence 1,2,4,8
form a geometric sequence.
Since the common ratio of the sequence is: 2 with first term as: 1
(first term is: 1
second term is: 1×2=2
Third term is: 2×2=4
and fourth term is: 4×2=8 )
Answer:
It's B. Second Graph.
Step-by-step explanation:
20 POINTS! WILL GIVE BRAINLIEST!
Bryce had a $25 gift card to use on songs and games at an online media store. Songs cost $2 each and games cost $5 each. Bryce spent all the money on the gift card to download 8 items. Solve the system to determine how many games he purchased. Let s represent the number of songs and g represent the number of games.
s + g = 8
2s + 5g = 25
Bryce purchased _____ games.
Answer:
Bryce purchased 3 games.
Step-by-step explanation:
To find the number of songs and games that Bryce downloaded, we need to solve the following system of equations:
s + g = 8
2s + 5g = 25
We know that:
s + g = 8 → 2s + 2g = 16 → 2s = 16 -2g
2s + 5g = 25 → 16 - 2g + 5g = 25
→3g = 25 - 16
→3g = 9
→ g = 3
Therefore, bryce downloaded 3 games and 5 songs!
Answer: 3
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