Answers
y >-x + 4
y <= 2(x - 1)^2 - 18
Comment
Let's establish what we are talking about. The question says purple and to me purple means the shaded area above the blue and to the upper right of the parabola.
Not so. It is the wine colored area right above the parabola according to the direction of he inequalities.
Second thing: the question is trying to see if you can read all he information you need from a graph.
Step One
Find the equation of the line.
We can read 2 points right away the x and y intercepts.
(4,0) is the x intercept
(0,4) is the y intercept
The general equation for the slope intercept equation is
y = mx + b So when x = 0 then b = y
4 = m*0 + b
b = 4
This far we have
y = mx + 4
when x = 4, y = 0
0 = m*4 + 4 Subtract 4 from both sides.
-4 = m*4 Divide by 4
-4/4 = m
m = - 1
Complete equation is y = -1x + 4
The inequality is y > -x + 4 Top answer block.
Step Two
Find the equation for the parabola
You could just read the minimum point which is (1,-18) There is a catch. (Isn't there always?) This may have a constant in front of the (x - a)^2 term. We'll check that out in the next step.
y = (x - 1)^2 - 18 is the basic vertex solution
Step Three
Find the value of a in
y = a(x - 1)^2 - 18
You have to do this because the answer has a space before the brackets. We need another point. The y intercept might work.
y = a(0 -1)^2 - 18
Use the point (0,-16)
-16 = a(1) - 18
-16 = a - 18 Add 18 to both sides.
2 = a
So the equation of the quadratic is
y <= 2(x - 1)^2 - 18 <<<<<< answer second section down on your question sheet.
Related Questions
The surface areas of two similar cones are 20 ft^2 and 125 ft^2. What is the scale factor?
A. 1/5
B. 2/5
C. 3/5
D. 4/5
Answers
The scale factor between two similar cones with surface areas of 20 ft² and 125 ft² is found by taking the square root of the ratio of the surface areas, which is [tex]\frac{1}{6.25}[/tex], resulting in a scale factor of B. [tex]\frac{2}{5}[/tex].
The question is asking about the scale factor between two similar cones with given surface areas. In the case of similar figures, the ratio of their surface areas is equal to the square of the scale factor. To find the scale factor, we take the square root of the ratio of the surface areas.
First, find the ratio of the surface areas: surface area of smaller cone : surface area of larger cone = [tex]\frac{20 ft^2}{125 ft^2}[/tex] = [tex]\frac{1}{6.25}[/tex].
Then, we take the square root of the ratio to find the scale factor: [tex]\sqrt{ (\frac{1}{6.25})}[/tex] = [tex]\frac{1}{2.5}[/tex], which simplifies to [tex]\frac{2}{5}[/tex]. Therefore, the scale factor is [tex]\frac{2}{5}[/tex], making option B the correct answer.
To find the scale factor between two similar cones, you can use the ratio of their corresponding lengths.
The surface area of a cone is proportional to the square of its height.
Let's denote the scale factor as kk. If A1A1 and A2A2 are the surface areas of the first and second cone respectively, then:
A1/A2=(k/1)^2
Given A1=20 ft^2 and A2=125 ft^2, we have:
20/125=(k/1)^2
Solving for k:
k= √ 20/125=√ 4/25=2/5=52
So, the correct answer is B. 2/5
complete question;
The surface areas of two similar cones are 20 ft^2 and 125 ft^2. What is the scale factor?
A. 1/5
B. 2/5
C. 3/5
D. 4/5
Another term for mean is the arithmetic mean. Why is this so?
Answers
Answer:
It helps distinguish it from other means, such as the geometric mean and the harmonic mean. When someone asks for the average of a group of numbers, they’re most likely asking for the arithmetic mean. An arithmetic mean is calculated by adding several quantities together and dividing the sum by the number of quantities.
Step-by-step explanation:
I got a 100% for this answer :)
Suppose that a stove and a freezer together weigh at least 370 pounds. The weight of the stove is 170 pounds. Which inequality correctly describes these conditions for the weight of the freezer,
Answers
We know that
x + y = 370
and
x = 170
To find the weight of the freezer (y)
you subtract the stove weight from the total weight
370 - 170 = 200
the freezer is 200 lbs
I'd assume the inequality you'd be looking for in this question is
stove + freezer > freezer > stove
If you are still having issues please post the answer choices and I can further aid you.
The inequality representing the weight of the freezer when the stove weighs 170 pounds and the combined weight of both is at least 370 pounds is 170 + F ≥ 370.
To find the correct inequality for the weight of the freezer, given that the stove weighs 170 pounds and the combined weight of the stove and freezer is at least 370 pounds, you can represent this as an inequality.
Let F represent the weight of the freezer.The inequality that correctly describes the conditions is:170 + F ≥ 370
In this inequality, 170 represents the weight of the stove and F represents the weight of the freezer.
Therefore, the correct inequality is 170 + F ≥ 370.
What’s the point-slope form of a line with slope 2/5 that contains the point (-3,6)
Answers
Answer:
The equation of this line is y - 6 = 2/5(x + 3)
Step-by-step explanation:
To find this, start with the base form of point-slope form.
y - y1 = m(x - x1)
Now put the slope in for m and the two coordinates in for (x1, y1).
y - 6 = 2/5(x + 3)
find the surface area of each figure. Round your answers to the nearest tenth, if necessary
Answers
h₁=8.4 cm
h₂=7.8 cm
b= 9 cm
A= 3(1/2bh₁)+1/2 bh₂
A=3(1/2(9)(8.4))+1/2 (9)(7.8)
A= 148.5 cm³
Which products are greater than 2 5/6?
A.
1/8 × 2 5/6
B.
2 5/6 × 2 5/6
C.
2 5/6 × 1 5/8
D.
5/6 × 2 5/6
E.
6/5 × 2 5/6
Answers
After converting mixed numbers to improper fractions and completing the multiplication, options B, C, and E yield products that are greater than 2 5/6. Options A and D are less than 2 5/6.
Explanation:The question asks to evaluate which of the given products are greater than 2 5/6.
We will convert the mixed numbers to improper fractions to make the multiplication easier and then compare the products with 2 5/6 (= 17/6).
For option A (1/8 × 2 5/6), multiplying by 1/8 will clearly result in a product smaller than 2 5/6.For option B (2 5/6 × 2 5/6), squaring 2 5/6 will definitely give a product larger than 2 5/6 itself.For option C (2 5/6 × 1 5/8), since both numbers are greater than 1, their product will be greater than either of the numbers.For option D (5/6 × 2 5/6), 5/6 is less than 1, so the product will be less than 2 5/6.For option E (6/5 × 2 5/6), 6/5 is a reciprocal of 5/6 and is greater than 1, hence their product will be greater than 2 5/6.Therefore, the correct answers are options B, C, and E.
The value of -4^2 is _____?
16
-16
8
-8
Answers
multiplying to negative numbers will make a positive number
How much 30% paint thinner solution should be added to a gallon of 10% paint thinner solution to make a solution that is 20% paint thinner
Answers
Explanation:
You can set an equation in this way:
1) Number of gallons of 30% thinner solution to be added: x gallons
2) Amount of thineer in the x gallons: 0.30x
3) Amount of thineer in the 1 gallon solution of 10% thinner: 0.10 (1) = 0.10
4) Number of gallons of the final solution, which is 20%: 1 + x
5) Amount of thineer in the final 20% solution: 0.2 (1 + x)
6) Equality:
Amount of thinner in the 30% solution + amount of thinner in the 10% solution = amount of thinner in the 20% solution
0.30x + 0.1 = 0.2 (1 + x)
7) Solve
0.3x - 0.2x = 0.2 - 0.1
0.1x = 0.1
x = 1
That is 1 gallon of 30% thinner solution should be added.
11) Write the equation of the circle with center (7, 3) and a radius of 2.
Answers
Answer:
(x - 7)² + (y - 3)² = 4
Step-by-step explanation:
The equation formula of a circle is (x - h)² + (y - k)² = r², where the center is at ordered pair (h, k) and r represents the radius in units.
With the information given in the question itself, we plug and play, simplifying if need be:
center (7, 3), h = 7, k = 3
radius = 2
(x - 7)² + (y - 3)² = (2)²
(x - 7)² + (y - 3)² = 4
The equation of this circle is (x - 7)² + (y - 3)² = 4
A street light is mounted on a pole. The tip of the shadow of a man who is standing on a street a short distance from the pole has an angle of elevation to the top of his head of 28°. A woman standing in the opposite direction of the pole as the man was standing on the same street has a angle of elevation from the tip of her shadow to her head of 24°. If the two people are 20 feet apart, how far is the street light from the head of the woman?
Answers
h=height of street light
x=distance of woman from pole, 20-x=distance of man from pole
tan 24=x/h=0.445
tan 28=(20-x)/h=0.532
re-arranging the above we get:
x=0.445h
20-x=0.532h
thus the value of h will be given by:
20=0.977h
hence
h=20.5 ft
substituting the values we get:
x=woman's position =9.1 ft from the pole and the man is 10.9 ft away.
the statement cot theta=12/5 sec theta= -13/5 and the terminal point determined by theta is in quadrant 4
Answers
NEED HELP ASAP I will give you Brainly
Can someone please help me with this??
(PLEASE USE THE PICTURES ABOVE)
And please do what it says.
Thanks soo much
thanks
Answers
For ax +by = c, you can solve for y to put the equation into slope-intercept form.
by = -ax +c . . . . . . subtract the x-term
y = (-a/b)x +c/b . .. divide by the coefficient of x
The slope is the x-coefficient, -a/b; the y-intercept is c/b. The function is an odd-degree polynomial function, so its domain and range are both "all real numbers."
2x+3y=18
Slope-intercept form: y = (-2/3)x +6
Domain: all real numbers
Range: all real numbers
Slope: -2/3
Y-intercept: 6
3x-4y > 16
Slope-intercept form: y < (3/4)x -4
Domain: all real numbers
Range: all real numbers
Slope: 3/4
Y-intercept: -4
_____
You will note that the inequality symbol in y < (3/4)x -4 is reversed from that in 3x -4y > 16. That is because in solving for y, we divided by -4. When you multiply or divide an inequality by a negative number, you must reverse the sense of the inequality.
Make a the subject of the formula:p=2a-3
Answers
p=2a-3
add 3 on both sides
3+p=2a-3+3
simplifying the above gives us:
3+p=2a
divide both through by 2
3/2+p/2=(2a)/2
thus
a=3/2+p/2
Is 23 a prime number or a composite number? Plzz help
Answers
*PLEASE NEED HELP* (50 POINTS)
Find (f/g)(x)
f(x)= sqrt(x^2-1)
g(x)= sqrt(x-1)
_____________________________________________
a) sqrt(x+1)
b) sqrt(x-1)
c) sqrt((-x^2)/(-x+1))
d) sqrt((1)/(x+1))
Answers
1² = 1
1³ = 1
1⁴ = 1
1¹⁰⁰⁰⁰⁰⁰⁰⁰⁰ = 1
then
[tex]\bf \begin{cases} f(x)&=\sqrt{x^2-1}\\ g(x)&=\sqrt{x-1}\\ \left( \frac{f}{g} \right)(x)&=\frac{f(x)}{g(x)} \end{cases} \\\\\\ \cfrac{f(x)}{g(x)}\implies \cfrac{\sqrt{x^2-1}}{\sqrt{x-1}}\implies \sqrt{\cfrac{x^2-1}{x-1}}\implies \sqrt{\cfrac{x^2-1^2}{x-1}} \\\\\\ \sqrt{\cfrac{\stackrel{\textit{difference of squares}}{\underline{(x-1)}(x+1)}}{\underline{x-1}}}\implies \sqrt{x+1}[/tex]
If f(x) = 5x, what is f–1(x)?
Answers
================================
Explanation:
Think of f(x) = 5x as y = 5x
The idea is to swap x and y, and then solve for y
y = 5x
x = 5y
5y = x
5y/5 = x/5
y = x/5
Making the inverse function [tex]f^{-1}(x) = \frac{x}{5}[/tex]
In simpler terms, we're basically undoing what we do to x originally. We multiplied x by 5, so the inverse will undo that and divide x by 5
Example:
Take the value x = 10 and plug it into the function to get
f(x) = 5*x
f(10) = 5*10
f(10) = 50
So the output is 50
If we take that output and plug it into the inverse g(x) we get
g(x) = x/5
g(50) = 50/5
g(50) = 10
which is the original input
What is the greatest common factor of 73, 47, 74, and 79?
Answers
4(3x-12)=5 (2x+6)
Break down how to solve this
Answers
9514 1404 393
Answer:
x = 39
Step-by-step explanation:
The usual approach is ...
12x -48 = 10x +30 . . . . use the distributive property to eliminate parentheses
2x -48 = 30 . . . . . . . . . subtract 10x from both sides [1]
2x = 78 . . . . . . . . . . . . add 48 to both sides [2]
x = 39 . . . . . . . . . . . . divide both sides by the coefficient of x
The solution is x = 39.
__
Check
4(3x -12) = 5(2x +6) . . . . given
4(3·39 -12 = 5(2·39 +6) . . . . substitute for x
4(117 -12) = 5(78 +6) . . . . . . . multiply
4(105) = 5(84) . . . . . . . . . . . . add
420 = 420 . . . . . . . . . . . . . . multiply
The found value of x makes the equation true, so is the solution.
_____
Additional Notes
[1] The point of the solution process is to put the variable on one side of the equal sign and a constant on the other side. To that end, we subtract the smallest variable term from both sides of the equation. The net result is a variable term on one side of the equal sign that has a positive coefficient.
We could have subtracted either of the constant terms first, and subtracted the variable term second. In this latter approach, the variable term subtracted is the one on the same side of the equation as the remaining constant term. Unless care is taken to select the constant on the side of the largest variable term (for subtraction), the net result may be a negative variable term. Technically, that works just as well, but can tend to increase the probability of an error being made.
__
[2] We notice that all of the terms in the equation after the last step have the x-coefficient as a common factor. This gives us the opportunity to divide by that coefficient at this stage. Doing this would give x-24=15. Then adding 24 would give the same final solution. Sometimes I like to work equations this way so the variable is "bare" (has a coefficient of 1) sooner, and the numbers are smaller.
__
In this discussion, when we talk about subtracting or dividing, we mean the entire equation is involved. The properties of equality tell us the equal sign remains valid if the same operation is performed on both sides of the equation. Our discussion here takes for granted that understanding. We have occasionally said "[do such and such] to both sides". Even where it isn't stated, the "to both sides" always applies.
Rewrite the equation below so that it does not have fractions.2/3x-3=3/4Do not use decimals in your answer
Answers
2 / 3x-3 = 3/4
Rewriting we have:
We multiply both sides of the equation by 3:
3 * (2 / 3x-3) = 3 * (3/4)
2x-9 = 9/4
We multiply both sides of the equation by 4:
4 * (2x-9) = 4 * (9/4)
8x-36 = 9
Answer:
The equation is quivalent to:
8x-36 = 9
The equation without fractions is 8x - 36 = 9.
To eliminate fractions from the equation 2/3x - 3 = 3/4, you can multiply both sides of the equation by the least common multiple (LCM) of the denominators, which is 12:
(12) * (2/3x - 3) = (12) * (3/4)
This will clear the fractions:
2(4x) - 3(12) = 3(3)
Now, simplify each term:
8x - 36 = 9
So, the equation without fractions is:
8x - 36 = 9
To know more about fractions:
https://brainly.com/question/10354322
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A rectangular prism has a volume of 150 cm3. if the height measures 3 cm and the width measures 2 cm, what must the length be to achieve the given volume?
Answers
3 x 2 x 25 = 150
perform the indicated operation 1/3 divide 3/8
Answers
------- = ------- = ---
3 × 3 3 × 3 9
So, your answer is [tex] \frac{8}{9} [/tex]
Answer:
[tex]\frac{8}{9}[/tex]
Step-by-step explanation:
perform the indicated operation 1/3 divide 3/8
divide the fraction 1/3 and 3/8
When we divide the fractions, we flip the second fraction and multiply with first fraction.
[tex]\frac{\frac{1}{3} }{\frac{3}{8} }[/tex]
When we flip 3/8 it becomes 8/3
[tex]\frac{1}{3} \cdot \frac{8}{3}[/tex]
Multiply numerator with numerator and denominator with denominator
1 times 8 is 8
3 times 3 is 9
So final answer is [tex]\frac{8}{9}[/tex]
The area of triangle ABC is 24 square centimeters. If B = 30° and a = 6 cm, what is the measure of side c? 4 cm 8 cm 16 cm 32 cm
Answers
Answer:
16 cm
Step-by-step explanation:
Given : The area of triangle ABC is 24 square centimeters.
To Find: If B = 30° and a = 6 cm, what is the measure of side c?
Solution:
Formula : [tex]Area = \frac{1}{2} \times a \times c \times sin B[/tex]
a = 6
Area = 24
B = 30°
Substitute the values in the formula
[tex]24 = \frac{1}{2} \times 6 \times c \times sin 30[/tex]
[tex]24 = \frac{1}{2} \times 6 \times c \times \frac{1}{2}[/tex]
[tex]24 =3 \times c \times \frac{1}{2}[/tex]
[tex]\frac{24 \times 2}{3} =c[/tex]
[tex]16=c[/tex]
Hence the measure of side c is 16 cm
So, Option c is correct.
What is the transformation that occurs to the equation y = 2^x if it changes to y = 2^(x - 8)?
The graph moves 8 units to the right.
The graph moves 8 units to the left.
The graph moves 8 units up.
The graph moves 8 units down.
Answers
Write a percent proportion for which the percent is greater than 100 and the part is known. Use the percent equation to solve your problem to find the whole.
Answers
yepAnswer:
Step-by-step explanation:
Write p(x) = 21 + 24x + 6x2 in vertex form.
Answers
p(x) = 21 + 24x + 6x2 => p(x) = 6x2 + 24x + 21
Rewrite the first 2 terms as
6(x^2 + 4x)
then you have p(x) = 6(x2 + 4x ) + 21
Now complete the square of x^2 + 4x:
p(x) = 6(x^2 + 4x + 4 - 4) + 21
= 6(x+2)^2 - 24 + 21
p(x) = 6(x+2)^2 - 3 this is in vertex form now.
We can read off the coordinates of the vertex from this: (-2, -3)
Answer:
p(x) = 6(x+2)^2 - 3
Step-by-step explanation:
Which of the following segments is a radius of K?
A) RT
B) MT
C) KM
D) MR
Answers
Observe the given figure, we have to determine the segments which is a radius of K.
1. RT is a diameter of a circle K as it is a straight line passing from side to side through the center of a circle.
2. MT is a chord of a circle K as it is the line segment connecting two points on a circle's circumference.
3. KM is a segment which is a radius of circle K as it is the length of the line from the center to any point on its edge.
4. MR is a chord of a circle K as it is the line segment connecting two points on a circle's circumference.
So, KM segment is a radius of circle K.
Therefore, option 3 is the correct answer.
Answer: KM
Step-by-step explanation:
The area of a trapezoid is 144 square inches. if the height is 12 inches, find the length of the median.
Answers
Answer: 12 inches
Step-by-step explanation: In this problem, since we're asked to find the length of the median, let's use our formula for the area of a trapezoid that involves the median which is shown below.
Area = median · height
We know that the area is 144 and the height is 9 so we can set up the equation 144 = M · 12. Now to solve for m, we divide both sides of the equation by 12 and we find that 12 = M.
So the length of the median of the trapezoid is 12 inches.
Given an area of 144 square inches and a height of 12 inches, the median is found to be 24 inches.
To find the length of the median of a trapezoid, we can use the formula for the area of a trapezoid, which is:
Area = 0.5 × (Base1 + Base2) × Height
We are given that the area is 144 square inches and the height is 12 inches. The formula can be rearranged to solve for the average of the two bases or the median (M):
144 = 0.5 × M × 12
Simplifying this equation, we get:
M = (144 × 2) / 12
M = 288 / 12
M = 24 inches
Thus, the length of the median is 24 inches.
Anyone know the answer?
Answers
Note: It started at A. Flip the right shape over so that it matches how it looks with the left one. AB is congruent with SR, therefore, A is congruent with S. Because of this, (with A starting for the first shape), you're congruent shape will have to start with S.
hope this helps
Use the graph below to answer the question that follows: cosine graph with points at 0, 3 and pi, negative 5 and 2 pi, 3 What are the amplitude, period, and midline of the function?
Amplitude: 4; period: 2π; midline: y = −1
Amplitude: 8; period: 2π; midline: y = 1
Amplitude: 8; period: π; midline: y = −1
Amplitude: 4; period: π; midline: y = 1
Answers
A = (l-5l + 3) / 2
A = 8/2
A = 4
The middle line is given by:
y = -1
The period of the function is given by:
T = l x2 - x1 l
T = l 0 - 2pi l
T = l - 2pi l
T = 2pi
Answer:
Amplitude: 4; period: 2π; midline: y = -1
Final answer:
The amplitude of the cosine function is 4, the period is 2π, and the midline is y = -1.
Explanation:
The question asks to determine the amplitude, period, and midline of a cosine function based on its graph. The amplitude is the maximum distance from the midline to the peak of the wave, which from the given points (0, 3) and (π, -5) is |-5 - 3| / 2 = 4. The period is the length of one complete cycle of the wave, which appears to be 2π since it starts repeating after (0, 3) to (2π, 3). The midline is the horizontal line that bisects the wave into two equal parts, which from the given points is at y = -1 since it's the average of the maximum and minimum values. The correct answer is: Amplitude: 4; period: 2π; midline: y = − 1.
Can someone help meh with this math question? I will award brainliest. For a standard-position angle determined by the point (x,y). what are the values of the trigonometric functions. For the point (6,8), find csc theta and sec theta?
Answers
sin θ = opposite leg/hypotenuse, so
csc θ= hypotenuse/opposite leg
hypotenuse =√((leg1)² +(leg2)²) =√(6²+8²)=√(36+64)=√100=10
csc θ = 10/8=5/4
cscθ =5/4
sec θ is inverse of cos θ , cos θ =adjacent leg/hypotenuse, so
sec θ =hypotenuse/ adjacent leg =10/6=5/3
sec θ =5/3