Answers
Answer:
a. A(x) = 3x² - 8x + 5
b. x = ⁸/₃
Step-by-step explanation:
a.
A(x) = shaded area
A(x) = (2x - 3)² - (x - 2)²
= 4x² - 12x + 9 - (x² - 4x + 4)
= 4x² - x² - 12x + 4x + 9 - 4
= 3x² - 8x + 5
b.
ΔABF area = ⁵/₄ cm²
A(x) = 4(⁵/₄)
= 5
Substitution:
3x² - 8x + 5 = A(x) = 5
3x² - 8x + 5 = 5
3x² - 8x = 0
x(3x - 8) = 0
3x - 8 = 0
x = ⁸/₃
x = 0
Since x > 2, x = 0 is not valid;
So, x = ⁸/₃
Related Questions
Read Fred's conclusion. If the sum of the digits of a number is a multiple of 3. then the number is a multiple of 6. Which statement best summarizes Fred's conclusion? The conclusion is true.
A .The number 42 is an example The conclusion is true.
B There are no counterexamples The is false.
C There are no counterexamples. The conclusion is false.
D The number 45 is a counterexample
Answers
Answer:
the answer would be a because 42÷6=7 and 42÷3=14.
The correct answer is option A) The number 42 is an example The conclusion is true.
42 is a multiple of both 3 and 6.
How many does multiple mean?
Containing more than once, or more than one; consisting of more than one; manifold; repeated many times; having several, or many, parts.
What is a multiple in math?A multiple in math is the number you get when you multiply a certain number by an integer. For example, multiples of 5 are: 10, 15, 20, 25, 30…etc. Multiples of 7 are: 14, 21, 28, 35, 42, 49…etc.
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Jake ran 4% miles in % of an hour. How fast did he run in one hour?
Answers
Solve the following inequalities. Graph the solution on a number line and express it in interval notation. You can use the back page for your solution. 26. x+47 > 36 27. x-8 -2x PLEASE HELP ME
Answers
[tex]\\ \sf\longmapsto x+47>36[/tex]
[tex]\\ \sf\longmapsto x>36-47[/tex}
[tex]\\ \sf\longmapsto x>-11[/tex]
Graph attached
x and y simplifying problem. Please explain how to do thiese. I will gove 15 points
Answers
[tex]\dfrac 56 x + \dfrac25 y - \dfrac14 x + \dfrac3{10} y[/tex]
First, combine like terms:
[tex]\left(\dfrac 56 - \dfrac14\right) x + \left(\dfrac25 + \dfrac3{10}\right)y[/tex]
Now just simplify the coefficients of x and y. We do this by converting each pair of fractions to ones with a common denominator. Then we can combine them easily.
[tex]\dfrac56 - \dfrac14 = \dfrac56\cdot\dfrac22 - \dfrac14\cdot\dfrac33 = \dfrac{5\cdot2}{6\cdot2} - \dfrac{1\cdot3}{4\cdot3} = \dfrac{10}{12} - \dfrac3{12} = \dfrac{10-3}{12} = \dfrac7{12}[/tex]
[tex]\dfrac25 + \dfrac3{10} = \dfrac25\cdot\dfrac22 + \dfrac3{10} = \dfrac{2\cdot2}{5\cdot2} + \dfrac3{10} = \dfrac4{10} + \dfrac3{10} = \dfrac{4+3}{10} = \dfrac7{10}[/tex]
So the simplified expression would be
[tex]\dfrac7{12} x + \dfrac7{10} y[/tex]
I NEED HELP PLEASE 15 POINTS
13) Given that m∠EFJ = 70°, find m∠KFG. A) 10° B) 20° C) 30° D) 40°
Answers
Answer:
20°
Step-by-step explanation:
∡EFJ = 70°
∡JFK = 90°
So, ∡KFG = 180 - ∡JFK - ∡EFJ = 180 - 90 - 70 = 20°
Answer:
60
Step-by-step explanation:
i put 30 then it said the answer was 60
Solve the inequality below for t.
3 - 13t >/= -9 - 9t
Answers
Answer:
T is =/> 3
Step-by-step explanation:
Add 9t to both sides, 3-4t>/= -9 . Subtract 3 from both sides. -4t>/=-12
divide 12 by 4 for 3. Because 3 results in equality between both sides, it is equal, however if t is greater than 3, the lefthand side becomes greater than the right.
Based on the scatterplot, what is the best prediction of the amount of $ in sales when the temperature is at 21°C?
Answers
Answer:
Between 400$ and 500$
Step-by-step explanation:
Draw a straight line that follows the scatterplot - either by guesstimating (best choice) or by applying any known method to extrapolate a line. Then it's just a matter of reading the y value corresponding to that x. Hardly a perfect image, but close enough since it's a prediction
The equation x + y = z relates the whole numbers x, y, and z. How does z compare to x?
If it helps, consider an example where you substitute 3 for x, 5 for y, and 8 for z.
y is z less than x.
y is z more than x.
x is y less than z.
x is y more than z.
Answers
Answer:
C. x is y less than z
Step-by-step explanation:
x+y=z
by using transposition
x = z-y
whatever x is, it is equal to the value of y taken from z
Find the equation for the circle with center (8,−8) and radius of length 2
Answers
Step-by-step explanation:
(x-8)²+(y--8)²=(2)²
x²-16x+64+y²+16y+64=4
x²+y²-16x+16y+124=0
can someone plzzz help me with this (multiple choice ) i have more if anyone is good at this
Answers
A rectangular swimming pool is 4 ft deep. One side of the pool is 4.5 times longer than the other. The amount of water needed to fill the swimming pool is 1800 cubic feet.
Find the dimensions of the pool.
Answers
Answer:
19 x 23.5 x 4
Step-by-step explanation:
4 * x * (x + 4.5) =1800
Divide both sides by 4
x * (x + 4.5) = 450
Use distributive property
x^2 + 4.5x = 450
Move all terms to one side
x^2 + 4.5x - 450 = 0
Use quadratic formula to solve a = 1, b = 4.5, c = -450
-4.5 +- [tex]\sqrt{4.5^2 - 4 * 1 * -450}[/tex]/2
=-4.5 + - [tex]\sqrt{1820.25}[/tex] / 2
= -4.5 +- 42.664 / 2
=19.08 and -23.582. You can't have a negative length, so it is 19.08, or 19
19 x 23.5 x 4
Help me with this question
Answers
Answer:
I don't have any idea of that question
Step-by-step explanation:
I'm sorry
The table shows the height of water in a pool as it is being filled. A table showing Height of Water in a Pool with two columns and six rows. The first column, Time in minutes, has the entries, 2, 4, 6, 8, 10. The second column, Height in inches, has the entries, 8, 12, 16, 20, 24. The slope of the line through the points is 2. Which statement describes how the slope relates to the height of the water in the pool? The height of the water increases 2 inches per minute. The height of the water decreases 2 inches per minute. The height of the water was 2 inches before any water was added. The height of the water will be 2 inches when the pool is filled
Answers
Answer:
The height of the water increases 2 inches per minute.
Step-by-step explanation:
14 divided 4 and 7/8 written in simplest form
Answers
Answer:
7 and that is its simplest form
Step-by-step explanation:
thank me later
Answer:
4
Step-by-step explanation:
14 ÷ 4 = 3.5
3.5 and 7/8 = 4
20x^5 y^3 + 8x^6 y^3 - 4x^5 y^2
———————————————
4x^5 y^2
Answers
Answer:
1) 4x^{5} y^{2} (5y+2xy-1)
2) Implied to have no solution based on given context.
Step-by-step explanation:
Problem 1:
1) Find the Greatest Common Factor (GCF).
[tex]GCF=4x^{5} y^{2}[/tex]
2) Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
[tex]4x^{5}y^{2} (\frac{20x^{5} y^{3} }{4x^{5}y^{2} } +\frac{8x^{6}y^{3} }{4x^{5} y^{2} } +\frac{-4x^{5} y^{2} }{4x^{5} y^{2} } )[/tex]
3) Simplify each term in parentheses.
[tex]4x^{5} y^{2} (5y+2xy-1)[/tex]
Problem 2:
From the way the problem is given, there is no solution.
Christina says the graph for the inequality r < -5 will be the same as the graph for the inequality -5 > r. Do you agree or disagree? Justify your reasoning. (Explain) HELP ME
Answers
Answer:
you are in the 45 and 56 zone so yes
Step-by-step explanation:
Plz help I need help
Answers
14 - 2, because of the +2, get 12
Divide 12 by 2, because of 2x, get 6
You would then get x<6
Hope this helps!
I NEED HELP WITH THESE
I am pretty sure of my answers, so I just need someone to double check. Explanation is not needed because I know how to solve it, just needs to be checked. You can put one it you want.
Answers
Answer:
(b) 500 km (b) 6 secondsStep-by-step explanation:
1.The semi-major axis length is √47196900 = 6870 km. That distance from the center of the Earth means the satellite is ...
6780 -6370 = 500 . . . km
from the surface of the Earth.
The satellite is a maximum of 500 km from the Earth.
(It is a minimum of 250 km from Earth.)
__
2.The equation has a zero at t=6. When the car's velocity is zero, it is at a complete stop.
The car comes to a complete stop when time is 6 seconds.
(The car is still being accelerated, so it doesn't stay stopped.)
__
I prefer a graphing calculator for a quick solution. You can also solve this equation algebraically.
0 = 0.5t^2 -10.5t +45 . . . . t when v(t) = 0
t^2 -21t +90 = 0 . . . . . . . multiply by 2
(t -6)(t -15) = 0 . . . . . . . . factor
t = 6 or t = 15 . . . . . . . only t=6 is in the domain of the function
How do you divide fractions? Can someone please explain step by step to get marked as brainliest!
Answers
When diving fractions, use KFC:
K eep the first fraction the same
F lip the second fraction upside down
C hange the divide sign to a multiply
After, just work it out multiplying the denominators and the numerators together getting your answer
Hope this helped you, have a good day bro cya)
K: Keep ( keep the first fraction the same)
C: Change (change your division sign to a multiplication sign)
F: Flip (flip your second faction numbers)
Ex.
Equation: 3/5 divided by 2/6
KCF: 3/5 multiplied by 6/2
Hope this helps!
PLEASE HELP ME WITH GEOMETRY <3
Answers
Answer:
answer is 25
Step-by-step explanation:
EKJ = 90, same as JHF, and EJK is 65 (because EJF =115 and 180-115=65
65+90=155
180-155=25
There are 8 triangles and 6 circles. What is the simplest ratio of total circles to total shapes
Answers
Ratio of total circles to total shapes is 4 : 7
An equation is an expression that shows the relationship between two or more variables and numbers.
There are 8 triangles and 6 circles. The ratio of total circles to total shapes is given by:
Ratio of total circles to total shapes = 8 circles : (8 + 6) shapes
Ratio of total circles to total shapes = 8 : 14 = 4 : 7
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The points (8, 1) and (6, 0) fall on a particular line. What is its equation in slope-intercept form?
Answers
Answer:
y=-3/2 x + 6Step-by-step explanation:
Let f(x) = x+2/x+6
f^-1(-6) =
Answers
We can explicitly find the inverse. If [tex]f^{-1}(x)[/tex] is the inverse of [tex]f(x)[/tex], then
[tex]f\left(f^{-1}(x)\right) = \dfrac{f^{-1}(x)+2}{f^{-1}(x)+6} = x[/tex]
Solve for the inverse :
[tex]\dfrac{f^{-1}(x) + 2}{f^{-1}(x) + 6} = x[/tex]
[tex]\dfrac{f^{-1}(x) + 6 - 4}{f^{-1}(x) + 6} = x[/tex]
[tex]1 - \dfrac4{f^{-1}(x) + 6} = x[/tex]
[tex]1 - x = \dfrac4{f^{-1}(x) + 6}[/tex]
[tex]f^{-1}(x) + 6 = \dfrac4{1-x}[/tex]
[tex]\implies f^{-1}(x) = \dfrac4{1-x} - 6[/tex]
Then when x = -6, we have
[tex]f^{-1}(-6) = \dfrac4{1-(-6)} - 6 = \dfrac47-6 = \boxed{-\dfrac{38}7}[/tex]
Alternatively, we can first solve for x such that [tex]f(x) = -6[/tex]. Then taking the inverse of both sides, [tex]x = f^{-1}(-6)[/tex]. (The difference in this method is that we don't compute the inverse for all x.)
We have
[tex]\dfrac{x+2}{x+6} = -6[/tex]
[tex]x + 2 = -6 (x + 6)[/tex]
[tex]x + 2 = -6x - 36[/tex]
[tex]7x = -38[/tex]
[tex]\implies x = \boxed{-\dfrac{38}7}[/tex]
Which of the following is most likely the next step in the series?
A.
B.
C.
D.
Answers
Each consecutive element of the series has one less blue points than the before element, with that, we conclude that the correct option is D, where there is only one blue point.
Which of the following is most likely the next step in the series?
Here we can see a series of 3 elements.
the first element is a circle with 4 blue points on its circumference, such that the points are connected to form a rectangle.
The next element is a circle with 3 blue points on it, such that when the points are connected a triangle is formed.
The third element is a circle, this time with 2 points, and the connection forms a segment.
So what we can see is that in each consecutive element the number of blue points on the circumference of the circles decreases by one, so the logical conclusion is that the next element will have only one point on its perimeter, then the correct option is D, where we can see only one blue point on the perimeter of the circle.
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A builder makes a certain type of concrete by mixing together 1 part portland cement (made from lime and clay), 3 parts sand, and 5 parts crushed stone. If 765 ft^3 of concrete are needed, how many cubic feet of each ingredient does he need?
Answers
Answer:
85 ft^3 portland cement255 f^3 sand425 ft^3 crushed stoneStep-by-step explanation:
The total number of parts is 1+3+5 = 9. The relevant fractions of the mix are ...
1/9 = portland cement
3/9 = 1/3 = sand
5/9 = crushed stone
Since the total is 765 ft^3, the ingredients required are ...
(1/9)(765 ft^3) = 85 ft^3 portland cement
(1/3)(765 ft^3) = 255 f^3 sand
(5/9)(765 ft^3) = 425 ft^3 crushed stone
The perimeter of the equilateral triangle drawn below is 9b + 12.
The shape below is made of four of these triangles.
Find a simplified expression for its perimeter.
Answers
If the perimeter of a triangle is 9b+12 then one side equals 3b+4 (divide by 3 because there are 3 sides
In the big triangle there are 6 sides so multiply 3b+4 by 6
=18b+24
Can someone please help me solve this
Answers
Answer:
all the numbers +
Step-by-step explanation:
Henry's garden which is 1/4 of an acre is to be divided into 12 equal size areas what is the size of each area?
Answers
The size of each area is 3x
Word problems in mathematics involve arithmetic operations and algebraic equations employed to solve real-life cases.
From the given parameters.
Henry's garden is said to be 1/4 of an acre.If an acre = xThen, Henry's garden is (1/4)xSo, Henry's garden is said to be divided into 12 equal size areas.
∴
The size of each area is;
[tex]\mathbf{= \dfrac{\dfrac{1}{4}x}{12}}[/tex]
[tex]\mathbf{= \dfrac{1}{4}(x) \times \dfrac{12}{1}}[/tex]
= 3x
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Help help help help
Answers
Answer:
-1
Step-by-step explanation:
What is -3/4+2 3/4 O 3 1/2 O 3 3/4 O 2 1/2 O 2
Answers
Answer:
D. 2
Step-by-step explanation:
Common denominator is already presented which is 4.
-3/4 and 3/4 cancel each other out.
you can also convert to decimal form -3/4 + 2 3/4 is the same as:
-0.75 + 2.75 = 2.