Which function matches the graph?
-5
-2
3/
7
A. f(x) =
(x + 3)(x - 5)(x + 7)²(x - 2)²
B. f(x) = (x - 3)²(x + 5)²(x-7)(x + 2)
C. f(x) = (x - 3)(x + 5)(x - 7)²(x + 2)²
D. f(x) = (x - 3)²(x + 5)(x-7)(x + 2)²
E. f(x) = (x + 3)²(x - 5)(x-7)²(x + 2)
Answers
Answer: B
Step-by-step explanation:
The root at [tex]x=-5[/tex] cuts through the x-axis, and has a multiplicity of one. So, it corresponds to a factor of [tex](x+5)[/tex].
The root at [tex]x=-2[/tex] bounces off the x-axis, and has a multiplicity of two. So, it corresponds to a factor of [tex](x+2)^2[/tex].
The root at [tex]x=3[/tex] cuts through the x-axis, and has a multiplicity of one. So, it corresponds to a factor of [tex](x-3)[/tex].
The root at [tex]x=7[/tex] bounces off the x-axis, and has a multiplicity of two. So, it corresponds to a factor of [tex](x-7)^2[/tex].
Related Questions
Finding Slope
Help mee
Answers
Answer: The slope is [tex]\frac{2}{3}[/tex].
Step-by-step explanation:
[tex]Slope = \frac{y_{2} -y_{1} }{x_{2}-x_{1} } =\frac{-8-(-6)}{-2-1} =\frac{-2}{-3} =\frac{2}{3}[/tex]
[tex]11/16 - 2/3[/tex]11/16 - 2/3=
Answers
Step by step Explanation :
11/16 - 2/3
= 33/48 - 32/48 (Common denominator is 48 so we multiplies 11 and 16 by 3, and 2 and 3 by 16)
=1/44
suppose the number of hours of sleep students get per night has a unimodal and symmetric distribution with a mean of 7 hours and a standard deviation of 1.5 hours. approximately what percent of students sleep more than 8.5 hours per night?
Answers
Approximately 34% of people sleep more than 8.5 hours per night.
According to the Empirical Rule states for a normally distributed random variable: 68% of the measures are within 1 standard deviation of the mean, 95% of the measures are within 2 standard deviations of the mean and 99.7% of the measures are within 3 standard deviations of the mean. According to the question, Mean = 7 and Standard deviation = 1.5. Also, in the question the normal distribution is symmetric, which means that 50% of the measures are below the mean and the rest 50% are above the mean. Now, the mean is 7 and 8.5 is 1 one standard deviation above the mean. So, by the Empirical Rule, of the 50% of the measures that are above the mean, 68% are within 1 standard deviation of the mean (more than 8.5 hours). So, we get
0.5*0.68 = 0.34 which is equal to 34%.
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5. Which might be your first step if you want to solve the
system by elimination?
1st equation: 5x + 4y = 7
2nd equation: 2x - 3y = 3
A) Substitute -10y + 7 for x in the second equation.
B) Substitute 3y + 3 for x in the second equation.
C) Multiply the first equation by 3, multiply the second
equation by 4, then add the resulting equations
together.
D Multiply the first equation by 2, multiply the second
equation 5, then add the resulting equations together.
Answers
Answer:
C)
Step-by-step explanation:
elimination is not substitution.
therefore, A and B are out.
D does not work, because in the described way the x terms don't get different signs, and the addition does not eliminate any variable.
C brings both y terms to the same absolute value, and their signs are different, so the addition will eliminate the y terms leaving us with one equation in x that we can solve :
15x + 12y = 21
8x - 12y = 12
---------------------
23x 0 = 33
23x = 33
x = 33/23
Answer:
a is the right answer for you
The largest y-value of the function is called thefunction.value of the
Answers
As the y-values of a function are the values that the function takes, the largest y-value of a function is called the maximum value of the function
Answer: maximumWrite the equation of the line that is perpendicular to the line y=3x+5 and passes through point (9,5)
Answers
The equation of the required perpendicular line is x + 3y = 24.
What is the slope relation for two perpendicular lines?
For two perpendicular lines on a plane, the product of their slopes always equals (-1).
What is the equation of line with slope 'm' and passing through the point (x₁, y₁)?
The standard equation of the line with slope 'm' and passing through the point (x₁, y₁) is y - y₁ = m(x - x₁).
Given, the required line is perpendicular to line given by y = 3x + 5 with slope, m₁ as 3, on analysis with standard equation of line; also the line passes through the point (9, 5) i.e. (x₁, y₁).
Let the slope of the required line be = m₂
As per statement established in the literature above, we have:
Slope of two perpendicular lines = -1
∴m₁ × m₂ = -1 ⇒ 3m₂ = -1 ⇒ m₂ = (-1)/3
Again, equation of the required perpendicular line is:
y - 5 = [(-1)/3][x - 9] ⇒ 3y - 15 = 9 - x ⇒ x + 3y = 24
Thus, the equation of the required perpendicular line is x + 3y = 24.
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Simplify the expression.
2/5y−4+7−9/10y =
Answers
Answer:
[tex]\frac{1}{2}[/tex] y +3
Step-by-step explanation:
You want to combine like terms
[tex]\frac{2}{5}[/tex] y and [tex]\frac{-9}{10}[/tex] y are like terms because they both have a variable y
-4 and + 7 are like terms because they are both constants. (numbers without letters)
We combine these
[tex]\frac{4}{10}[/tex] means the same as [tex]\frac{2}{5}[/tex] I just multiplied the numerator (top) and the denominator (bottom) by 2. I did this so that I could add it to [tex]\frac{-9}{10}[/tex]
[tex]\frac{4}{10}[/tex]y - [tex]\frac{9}{10}[/tex]y = [tex]\frac{-5}{10}[/tex] y (4-9 = -5) or [tex]\frac{-1}{2}[/tex] y simplified
-4 + 7 = 3
4 2/15 / 3.1 (I NEED HELP NOW!!!!!!!!!!!)
Answers
Answer:
The answer would be 1.3, and the three is repeating.
Step-by-step explanation:
First, make 4 2/15 into a improper fraction.
4 2/15= 62/15
Now, when we divide fraction, use the rule Keep, Change, Flip.
Keep the 62/15.
Change the division sign into a multiplication sign.
To make the 3.1 into a fraction, put a one over it.
3.1/1
Now, flip the fraction.
3.1/1= 1/3.1
Your equation will look like this:
62/15x1/3.1
Multiply across.
62/46.5
Now simplify.
The answer would be 1.3, and the three is repeating.
I need help with math identify the vertex of the parabola
Answers
The vertex of a parabola is the extreme point (maximum or minimum, depending on the the sign of the quadratic coefficient).
In the graph, we can see that the x-coordinate of the vertex is x=-1 and the y-coordinate is y=3.
Then, we can write the coordinates of the vertex as (h,k) = (-1,3)
Answer: The coordinates of the vertex are (-1,3)
The perimeter of a rectangle is to be between 140 and 220 inches. FindThe range of values for its length when its width is 20 inches
Answers
The lower value of the perimeter is 140 inches .
Width of the rectangle is 20 inches .
The length of the rectangle is calculated as ,
[tex]\begin{gathered} \text{Perimeter = 2 ( Length + width )} \\ 140=\text{ 2 ( Length + }20\text{ )} \end{gathered}[/tex]Rearranging the terms ,
[tex]\begin{gathered} \text{Length + 20 = }\frac{140}{2} \\ \text{Length + 20 = 70} \\ \text{Length = 50 inches} \end{gathered}[/tex]The higher value of perimeter is 220 inches .
Width of the rectangle is 20 inches .
The length is calculated as,
[tex]\begin{gathered} \text{Perimeter = 2 ( Length + width )} \\ 220=\text{ 2 ( Length + }20\text{ )} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \text{Length + 20 = 110} \\ \text{Length = 110 - 20} \\ \text{Length = 90 inches} \end{gathered}[/tex]Thus the range of values for the length of the given rectangle are 50 and 90 .
this is NOT a test or Quiz its a homework pic is below
Answers
From the information given,
Jack wants to eat 2 1/5 of his plate in 1/3 hour. The first step is to convert 2 1/5 to improper fraction. It becomes 11/5
The statement would be
Jack wants to eat 11/5 of his plate in 1/3 hour.
Let x represent how much of his plate that he will eat in 1 hour. Therefore
11/5 = 1/3
x = 1
By cross multiplying, it becomes
x * 1/3 = 1 * 11/5
x/3 = 11/5
x = 11/5 * 3
x = 33/5
Converting to mixed fraction, it becomes
6 3/5
The correct option is the first one
WILL GIVE BRAINLIEST!!! solve the problem fill in the blanks to show your work
Answers
By performing mathematical operations, the answer to the given expression (- 1.2(2/5) ÷ -2) is 0.24.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands. The four mathematical operations are functions that take input values, or numbers, and turn them into output values, or yet another number. They are multiplication, division, addition, and subtraction.So, the values in the blank will be:
= - 1.2(2/5) ÷ -2= -1.2(0.4) ÷ -2= - 0.48 ÷ -2= 0.24Therefore, by performing mathematical operations, the answer to the given expression (- 1.2(2/5) ÷ -2) is 0.24.
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If Susie's age is 8 less than 3 times her brother's age, and Susie is 13. How old is her brother?
Answers
Answer:
correct me if im wrong but my answer is x=7, or in other words, 7.
Step-by-step explanation:
Answer:
7 years old
Step-by-step explanation:
You would start by going backward. If 13 is 8 less, then you would first add 8. You would have 21. Now all you have to do is divide by three. So your answer would be 7. If you would want to check you could plug it back in. 7 multiplied by 3 is 21. 21 - 8=13
The Answer, 7 years old
O is the center of the regular decagon below. Find its perimeter. Round to the nearest
tenth if necessary.
16
Answers
Based on the center of the regular decagon, we can find that the perimeter of the decagon would be 98.9 units.
How to find the perimeter of a decagon?When given the midpoint of a decagon and the measurement of the radius, the perimeter can be found by the formula:
= 10 x ( ( 2 x Radius of the decagon) / (1 + √5)))
Given a radius of 16 units, the perimeter of this decagon is:
= 10 x ( (2 x 16) / (1 + √5)))
= 10 x ( (32 / (1 + √5)))
= 98.9 units
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Perimeter of Decagon with radius and midpoint given is 100 units.
What is Polygon?Polygon can be defined as a flat or plane, two-dimensional closed shape bounded with straight sides.
Given polygon is a decagon. A decagon is a polygon which have ten sides with same length with centre o.
The radius of the decagon is 16.
When radius and midpoint is given the perimeter can be given by formula
Perimeter= 10 x ( ( 2 x Radius of the decagon) / (1 + √5)))
=10×((2×16) / (1 + √5)))
=10×((32) / (1 + √5)
=320/1+√5
=320/1+2.2
=320/3.2
=100 units.
Hence perimeter of Decagon with radius and midpoint given is 100 units.
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What percentage of the numbers from 1 to 20 contain the digit 2?
Answers
3/20 = 0.15
Answer: 15%
Sydney picked 28 raspberries and 35 blueberries to make two desserts.
She needs 4 raspberries for each raspberry tart and 5 blueberries for each
blueberry tart. She wants to know how many desserts she will be able to
make with the berries.
Answers
To find out how many raspberry tarts Sydney can make, we need to take the total number of raspberries (28) and divide it by how many raspberries are needed per tart (4).
28 ÷ 4 = 7, which means she can make 7 raspberry tarts.
The same logic applies to the blueberry tarts, so we do the total (35) divided by how many we need for 1 tart (5):
35 ÷ 5 = 7, so she can make 7 blueberry tarts.
need this asap 50 points for it
Answers
Answer:
the subtraction property of equality
Step-by-step explanation:
trust
Answer:
Subtraction
Step-by-step explanation:
Jim sits on a seesaw. If Jim weighs 100 pounds, what mass in kilograms does the person on the other side need to be for the seesaw to be balanced?
Answers
The weight of the other person has to be the same in order for the seesaw to be balanced, then the person on the other side weighs 100 pounds as well. Now, we know that:
[tex]1\text{ lb=}0.45\text{ kg}[/tex]Then to find the mass we just multiply the weight in pounds by 0.45:
[tex]100\cdot0.45=45[/tex]Therefore the other person has a mass of 45 kg.
The weight of the other person has to be the same in order for the seesaw to be balanced, then the person on the other side weighs 100 pounds as well. Now, we know that:
[tex]1\text{ lb=}0.45\text{ kg}[/tex]Then to find the mass we just multiply the weight in pounds by 0.45:
[tex]100\cdot0.45=45[/tex]Therefore the other person has a mass of 45 kg.
x-4y=-2
Determine if the given ordered pair, (2, 1), satisfies the given equation.
O YES
O NO
Answers
Answer:
Yes.
Step-by-step explanation:
Replace x with 2 and y with 1 and see if the equation is true
x - 4y = -2
2 - 4(1) = -2
2 - 4 = -2
-2 = -2
The statement is true so the point is on the line.
a group of friends is taking part in a two-day walking event for charity. yesterday, they walked 28 miles in 9 hours and 44 minutes. today, they finished the last 10 miles in 2 hours and 55 minutes. what was the group's average speed for the two-day event?
Answers
Average speed of the group for the two day event is 0.105 miles\min.
The average is defined as the mean value that is equal to the ratio of the total sum of the number of a given set of values to the total number of values present in that set.
Time taken on day 1 in minutes = 9x60 + 44
= 540 + 44 = 584 minutes.
Time taken on day 2 in minutes = 2x60 + 55
= 120 + 55 = 157 minutes
Now we will be applying speed-distance formula we get,
Speed= Distance/time
On day 1,
[tex]Speed_{1}[/tex]= 28/584 = 0.0479 miles/min
On day 2,
[tex]Speed_{2}[/tex]= 10/175 = 0.0571 miles/min
Thus,the average speed is:
Average = [tex]Speed_{1} + Speed_{2}[/tex] = 0.0479 + 0.0571= 0.105 miles/min
Hence,the average speed is 0.105 miles/min
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Given
\qquad \overline{BA}\perp\overline{BD}
BA
⊥
BD
start overline, B, A, end overline, \perp, start overline, B, D, end overline
\qquad m \angle CBD = 4x + 52^\circm∠CBD=4x+52
∘
m, angle, C, B, D, equals, 4, x, plus, 52, degrees
\qquad m \angle ABC = 8x - 10^\circm∠ABC=8x−10
∘
m, angle, A, B, C, equals, 8, x, minus, 10, degrees
Find m\angle CBDm∠CBDm, angle, C, B, D:
Answers
The value of ∠CBD is 68° and the value of ∠ABC is 22°
Given
Angle CBD = 4x + 52
Angle ABC = 8x − 10
If BA is perpendicular to BD, then ∠BAD = 90°
∠BAD = ∠CBD + ∠ABC
On substituting this values into the formula:
4x + 52 + 8x − 10 = 90
12x + 42 = 90
Add -42 to both sides
12x + 42 - 42 = 90 -42
12x = 48
x = 48/12
x = 4°
Here,
∠CBD = 4x + 52
∠CBD = 4 x 4 + 52 = 16 + 52 = 68°
Then,
∠ABC = 8x − 10
∠ABC = 8 x 4 − 10 = 32 - 10 = 22°
That is,
The value of ∠CBD is 68° and the value of ∠ABC is 22°
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Answer:
68 degrees
Step-by-step explanation:
got it right on khan academy
Could I please get help with this this problem, and find out their answers?
Answers
The image of triangles are given .
a.
[tex]\angle J\cong\angle E,\angle K\cong\angle G,\angle L\cong\angle F[/tex]b. Find the ratio,
[tex]\frac{EG}{JK}=\frac{15}{10}=\frac{3}{2}[/tex][tex]\frac{GF}{KL}=\frac{24}{16}=\frac{6}{4}=\frac{3}{2}[/tex][tex]\frac{EF}{GL}=\frac{21}{14}=\frac{3}{2}[/tex]c.Hence the triangles are similar .
[tex]\Delta\text{JKL}\cong\Delta\text{EGF}[/tex]The correct option is A.
PLS BE DONE RIGHT AWAY, VERY APPRECIATED
Answers
B: the square root of 144 would be 12 because 12x12=143
Match each ratio to an equal ratio. Drag the items on the left to the correct location on the right.
Answers
Answer:
30
Step-by-step explanation:
it doesn't seem to be correct question
x=3
An aquarium has dimensions 2x feet, (x â€" 1) feet, and (x 2) feet. The aquarium volume must be no more than 280 cubic feet. What are the possible values of x? (1, 5) (1, 5] [1, 5) [1, 5]
Answers
The possible values of x that satisfies the given dimensions and the condition that the volume must be no more than 280 cubic feet is x = [1,5]
The dimensions of the aquarium is: 2x ft , (x -1) ft, and (x + 2) ft. Since the volume must be no more than 280 ft³, it means:
V = 2x (x - 1) (x + 2) ≤ 280
Divide both sides by 2:
x (x - 1) (x + 2) ≤ 140
x³ + x² - 2x - 140 ≤ 0
(x - 5) (x² + 6x + 28) ≤ 0
Since x² + 6x + 28 is always greater than zero then x that satisfies the above inequality is:
x - 5 ≤ 0
or x ≤ 5
Using the interval notation, x = (-∞, 5]
However, remember that the dimension is always a positive number.
Hence,
x - 1 ≥ 0
or x ≥ 1
Therefore, the solution is [1, 5]
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Suppose we are buying beans and rice to feed a large gathering of people, and we plan to spend $120 on the two ingredients. Beans cost $2 a pound and rice costs $0.50 a pound.
If x represents pounds of beans and y pounds of rice, the equation 22 + 0.50y = 120 can represent the constraints in this situation.
The line below shows the graph of this equation (ignore the points not on the line).
Please help me I would appreciate it so much
Answers
The true statements about the constraints in this situation are:
If we buy 30 pounds of beans we can buy with 120 pounds of rice.If we buy no beans we can buy 240 pounds of rice.If we buy 20 more pounds of rice, we would have to buy 5 less pounds of beans.How to determine the true statements?In order to determine the true statements, we would substitute the value of x and y into the given linear equation and then evaluate. From the information provided, the constraints in this situation are modeled or represented by this linear equation:
2x + 0.50y = 120
Where:
x represents pounds of beans.y represents pounds of rice.When x = 40 and y = 60, we have:
2x + 0.50y = 120
2(40) + 0.50(60) = 120
80 + 30 = 120
110 ≠ 120 (Not a solution).
When x = 30 and y = 120, we have:
2x + 0.50y = 120
2(30) + 0.50(120) = 120
60 + 60 = 120
120 = 120 (True solution).
Therefore, if we buy 30 pounds of beans we can buy with 120 pounds of rice.
When x = 0 and y = 240, we have:
2x + 0.50y = 120
2(0) + 0.50(240) = 120
0 + 120 = 120
120 = 120 (True solution).
Therefore, if we buy no beans we can buy 240 pounds of rice.
When x = 0 - 5 and y = 240 + 20, we have:
2x + 0.50y = 120
2(0 - 5) + 0.50(240 + 20) = 120
-10 + 130 = 120
120 = 120 (True solution).
Therefore, if we buy 20 more pounds of rice, we would have to buy 5 less pounds of beans.
When x = 0 + 10 and y = 240 - 60, we have:
2x + 0.50y = 120
2(0 + 10) + 0.50(240 - 60) = 120
20 + 90 = 120
110 = 120 (Not a solution).
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Can someone tell me what x and y is and how to solve for it
Answers
[tex]2x = 76[/tex]
Due to alternate angles
[tex] \frac{2x}{2} = \frac{76}{2} \\ x = 38[/tex]
40°+(y-8)°+76°=180°(sum of angles in a triangle)
[tex]40 + y - 8 + 76 = 180 \\ y + 108 = 180 \\ y = 180 - 108 \\ y = 72[/tex]
ATTACHED IS THE SOLUTION.
Answer:
x = 38 ; y = 72
Step-by-step explanation:
180 = 76 + 40 + (y - 8)
180 = 108 + y
72 = y
The triangle has parallel lines, so the uppermost right angle is also 90 degrees.
90 - 76 = 14
180 = 90 + 14 + 2x
180 = 104 + 2x
76 = 2x
38 = x
3x+y-77=0
Can anyone help me with this question it would really help me out
Answers
the answer is in the photo I took of solving it
Please help me I only have 3 minutes left to do this
Answers
486lb of grass seed is required to cover the field on the right.
What is Area of Rectangle?The area of Rectangle is length times of width
Let us find the areas of two rectangle larger and smaller.
Area of the larger rectangle:
60×90=5400 square feet.
Now divide the larger square area by the smaller square area:
Area of the smaller rectangle
40×50=200 square feet.
Now divide larger rectangle with smaller
5400/200 =27
27 is the ratio of the difference
27×18=486 lb.
Hence 486lb of grass seed is required to cover the field on the right.
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Subtract.
−3−6−(−1) = ?
Answers
Answer:
-8
Step-by-step explanation: