If [tex]f(x)=0[/tex] at [tex]x=-11[/tex] and [tex]x=-13[/tex], then we can factorize
[tex]f(x) = ax^2 + bx + c = a (x + 11) (x + 13)[/tex]
Now,
[tex]f(x-9) = a((x-9)+11) ((x-9)+13) = a(x+2)(x+4)[/tex]
which means the zeros of [tex]f(x-9)[/tex] are [tex]x=-2[/tex] and [tex]x=-4[/tex].
how to find percentage
Answer:
The easiest way to find percentage is to multiply the number by 100. Like if you were required to find the percentage of 0.87 you multiply it by 100 and get 87 there for 0.87 is equal to 87%.
Step-by-step explanation:
Hope it helps! =D
Help me do a histogram for this
High
Temperatures
(F)
21 to 30
degrees
31 to 40
degrees
41 to 50
degrees
51 to 60
degrees
61 to 70
degrees
71 to 80
degrees
Frequency
18
32
68
74
63
41
SAT scores are normally distributed, with a mean of 500 points and a
standard deviation of 100 points. Suppose you take the SAT. Several weeks
later, you receive your results, which show that you reached the 90th
percentile for the math portion.
Recalling that SAT scores are always expressed as multiples of 10, how many
points did you get on the test?
A.600
B.630
C.130
D.590
E.690
Recalling that SAT scores are always expressed as multiples of 10, then the points we get on the test will be 628.
What do you mean by standard deviation?In statistics, Standard deviation is a measure of the variation of a set of values.
σ = standard deviation of population
N = number of observation of population
X = mean
μ = population mean
WE have been given that SAT scores are normally distributed, with a mean of 500 points and a standard deviation of 100 points.
The solution as follows;
Let be X: scores of SAT
P(X ≥ x) = 0.9
P((X - 500)/100 ≥ (x - 500)/100) = 0.9
P(Z ≥ z) = 0.9
z = 1.28
1.28 = (x - 500)/100
128 + 500 = x
x = 628
Recalling that SAT scores are always expressed as multiples of 10, then the points we get on the test will be 628.
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The length of a rectangle is 7yd more than twice the width x. The area is 555yd2.
(a) Write an equation in terms of x that represents the given relationship.
The equation in terms of x that represents the given relationship is (7 + x)x = 555
Write an equation in terms of x that represents the given relationship.The given parameters are
Length = L
Width = x
Area = 555 yd^2
From the question, we have
L = 7 + x
The area of a rectangle is
A = Lx
Substitute 7 + x for L
So, we have
A = (7 + x)x
Substitute 555 for A
So, we have
(7 + x)x = 555
Hence, the equation in terms of x that represents the given relationship is (7 + x)x = 555
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Help
Please help
I appreciate it
a raindrop falls at the rate of 4/50 mile in 1/20 hour. at this rate how far will the raindrop travel in 1 hour
Answer:
Step-by-step explanation:
4/50 * 20 = 8/5 miles
Which expressions are equal to 0 when x=-1? Check all that apply.
Answer:
The answer A,B,C
The total number of goals scored in a hockey game was 29. Team B scored 5 more goals than team A. How many goals did each team score
Answer:
Team A scored 12 pts
Team B scored 17 pts
Use the table below to answer questions on the number of TV sets per household in the United States. # TV Sets 0 1 2 3 4 5 or more Prob. 0.092 0.275 0.101 0.194 0.035 0.303 a. Verify that this is a probability model. b. Find (3 4) c. Find ( ) d. Find (4) e. Is (4) an unusual event? Why?
From the given discrete probability distribution, we have that:
a) Because the sum of all probabilities is of 1, we can verify that this is a probability model.
b) P(3 or 4) = 0.229.
c) P(at least one) = 0.908.
d) P(4) = 0.035.
e) Since both P(X ≤ 4) and P(X ≥ 4) > 0.05, 4 is not an unusual event.
What is the discrete probability distribution?The probability distribution in this problem gives the probability of a household having a number of TV sets, given as follows:
P(X = 0) = 0.092.P(X = 1) = 0.275.P(X = 2) = 0.101.P(X = 3) = 0.194.P(X = 4) = 0.035.P(X = 5) = 0.303.For item a, we have to add all the probabilities, hence:
0.092 + 0.275 + 0.101 + 0.194 + 0.035 + 0.303 = 1.
Because the sum of all probabilities is of 1, we can verify that this is a probability model.
For item b, we take the probabilities from the table as follows:
P(3 or 4) = P(X = 3) + P(X = 4) = 0.194 + 0.035 = 0.229.
For item c, we follow a similar procedure to item b, taking the probabilities from the table as follows:
P(at least one) = 1 - P(X = 0) = 1 - 0.092 = 0.908.
For item d, from the table, we have that:
P(4) = 0.035.
For item e, we have that:
P(X ≥ 4) = 0.338.P(X ≤ 4) = 0.662.Since both P(X ≤ 4) and P(X ≥ 4) > 0.05, 4 is not an unusual event.
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Round the number to the nearest thousandth.
0.3244
Answer:
.324
Step-by-step explanation:
.3244 if underlined digit >= 5 round the thousandth digit up o/w leave it as is
1=1cm x 1\2 cm x 2cm
There isn't a ton of info provided in your question, however, I believe the solution is 1 = 1.
URGENT PLEASE HELP!!!!! WILL GIVE BRAINLIEST!!!
The coordinates of parallelogram ABCD are A(0, 0), B(a, 0), C(
,
), and D(0, b).
The coordinates of the midpoint of AC¯¯¯¯¯ are (
,b2).
The coordinates of the midpoint of BD¯¯¯¯¯ are (a2,
).
The midpoints of the diagonals have the same coordinates.
Therefore, AC¯¯¯¯¯ and BD¯¯¯¯¯ bisect each other.
Answer:
a, b, a/2, b/2
Step-by-step explanation:
The coordinates of C are (a,b).
You find the midpoint by taking the averages of the coordinates.
The third blank is a/2.The fourth blank is b/2.Note the image.
9,077
9,884
1,303
1,055
3,222
Which number have a digit in the ones place that is 1/10 the value of the digit in the tens place
The number that have a digit in the ones place is 1/10 of the value in the tens place are 3,222 and 1,055.
What is Place value?
The value of each digit is called place value.
The given condition to find the number is;
Number that have a digit in the ones place is 1/10 of the value in the tens place.
Now, In the number 3,222;
2 is 1/10 of the 20 in the tens place.
And, In the number 1,055
5 is 1/10 of the tens value of 50.
So, The number that have a digit in the ones place is 1/10 of the value in the tens place are 3,222 and 1,055.
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The diagram shows a circle inside a square work out the area of this circle
16cm is the square
The area of the circle inscribed inside the square is 64π cm²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The circle inside the square as shown in the diagram have a diameter of 16 cm. Hence:
Radius = diameter / 2 = 16/2 = 8 cm
Area of circle = π * radius² = π * 8² = 64π cm²
The area of the circle inscribed inside the square is 64π cm²
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8 There are 3 horses in a field.
Each horse has 4 legs. Write
an addition equation and a
multiplication equation to find
the number of legs on 3 horses.
Add:
Multiply:
chapter 8
1.Find the surface area of each figure. Round your answers to the nearest hundredth, if necessary.
The surface area of the sphere is approximately equal to 615.752 square miles.
How to determine the surface area of a solid
The surface area of a solid is the area comprised by all faces of a solid, in the case of a sphere, there is only one face whose extension is determined by the following formula:
A = 4π · r²
Where:
A - Area of the sphere, in square miles.r - Radius of the sphere, in miles.If we know that r = 7 miles, then the surface area of the sphere is:
A = 4π · (7 mi)²
A ≈ 615.752 mi²
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3x + y =4 and x - 3y = 8 solve using substitution method and elimination method
Answer:
×=2 , y= -2
Step-by-step explanation:
3x+y=4______(1)
x-3y=8_______(2)
by substitution method...
multiplying eq (1) by 3..
9x+3y=12_____(3)
x-3y=8_______(4)
10x=20
x=2
putting the value of x in eq (1)
3x+y=4
3(2)+y=4
6+y=4
y=4-6
y=-2
×=2 , y= -2
How high is a tree that casts a 24 ft shadow at the same time a 5-ft pole casts a shadow 14 ft-long the tree height
Answer:
60/7 ft
Step-by-step explanation:
Using similar triangles, if we let the height of the tree in ft be x,
[tex]\frac{x}{24}=\frac{5}{14} \\ \\ x=\frac{60}{7}[/tex]
Let a = any rational number. Is the absolute difference if a is a positive or a negative number? Explain
Answer: Is the absolute difference if a is a positive number, when a = any rational number.
Step-by-step explanation:
Define Positive numbers:
Positive numbers are the numbers which are greater than zero that lies on the right side of the number line.
Example: 0, 1, 2, 3, 4…
Define Negative numbers:
Negative numbers are the numbers which are less than zero that lies on the left side of the number line.
Example: … -5, -4, -3, -2, -1, 0.
Given data,
Let a = any rational number. Is the absolute difference if a is a positive number.
Because,
Let us take, a = any rational number
We have to know → Is the absolute value of a different if a is a positive number or negative number.
Define Modulus (|x|) of a number :
The modulus or absolute value of a number means the distance that goes from the number to its origin, this is, to the point 0 (zero) that makes part of the real straight line. For instance, the distance from point 6 to its origins is 6, but the distance from point -6 to its origins is also 6.
The modulus operator formula is :
|x| = { x if x ≥ 0 and -x if x ≤ 0
Given question,
Assume any rational number x/y
Using the Modulus property :
|x| = { x/y if x/y ≥ 0 and -x/y if x/y ≤ 0
Therefore, if the rational number is less then zero (say -2).
Then the absolute value will be = - (- 2) = 2
and for any rational number greater than 0 (say 2)
Then its absolute value will be = 2 only.
Hence,
Is the absolute difference if a is a positive number, when a = any rational number.
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Find the general expression for the slope of a line tangent to the curve of y=x2+2x at the point P(x,y). Then find the slopes for x=−3 and x=0.5. Sketch the curve and the tangent lines.
The general expression for the slope of the tangent line is m = y'(x) = 4x + 2. the value of m is - 10 for x = - 3 and is 4 for x = 0.5.
A line that only touches a curve once is said to be tangent to it. The point (x₀ , y₀) where a line with the equation of a tangent to a curve
y = f ( x ) is given by:
T' (x) = f'(x) (x ₋ x₀) ₊ y₀
The slope of the tangent line to a curve at a point is computed by getting the first derivative of the curve.
y(x)=2x²y
y'(x) = (2)2x²⁻¹ ₊ (1)2x¹⁻¹
y'(x) = 4x¹ ₊ 2x°
y'(x) = 4x ₊ 2(1)
y'(x) = 4x ₊ 2
The slope at a point
P (x, y) is computed by substituting the x-coordinate of the point to the first derivative. This is the general expression for the slope:
m = y'(x) = 4x + 2
For x = - 3
m = 4 (- 3) + 2
m = - 12 + 2
m = - 10
For x = 0.5
m = 4 (0.5) + 2
m = 2 + 2
m = 4
Therefore, the general expression for the slope of the tangent line is m = y'(x) = 4x + 2. the value of m is - 10 for x = - 3 and is 4 for x = 0.5.
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Amir buys a car for £13155 which depreciates in value at a rate of 1.5% per year.
How much Amir's car will be worth in 9 years.
Answer: $11,379 i believe
Step-by-step explanation: Multiplying 9 times the percentage value at which the cars value depreciates it gives you, 13.5%. Dividing 13155 by that 13.5% will give you the absolute value of $11379.075 in which would be $11,379.
Hope this helps!
Review each problem below and determine if it is a future value question or a present value question. Choose the correct match.
Note: do not solve the problems, simply determine if the problem is a future value question or a present value question.
Claudia deposited $1,000 today. Assuming 7% annual interest, how much will the $1,000 be worth in one year?
Steven White plans to retire in 15 years with $400,000 saved. He thinks his savings can earn 10 percent per year. How much does Steven White have to deposit today in order to have $400,000 in 15 years?
What will a deposit of $4,500 today at 10% compounded semiannually be worth if left in the bank for six years?
If Joe deposits every payment in an account paying a nominal annual interest rate of 6% compounded monthly, how much will he have at the end of three years?
If you want $1,000 five years from now and you earn 5 percent on your savings, how much do you need to deposit today?
The distinction between present value and future value is that the former is required now and the latter is needed at a future period
What is the difference between present value and future value?
The present value indicates today's worth or dollars of a future value of a flow whereas the future value determines the future worth of an investment or deposit made today or deposits over a number of years at a time in the future
The amount that Claudia would have in a year's time is future value because the present value is the initial deposit made today
The amount that Steven would have to deposit today in order to accumulate $400,000 in 15 years is the present value
The amount that a deposit of $4,500 made today would worth in 6 years is the future value because the initial deposit is the present value.
Joe would have to deposit payments in expectation of future value after 3 years and the deposit required today to earn a rate of return of 5% in order to have $1000 in 5 years is a present value
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Select the values that are solutions to the inequality x2 + 3x – 4 > 0.
I need help with geometry
Answer:
Step-by-step explanation:
The area of a triangle is equal to half the product of the base by the height drawn to that base
Hence,
1)
[tex]\displaystyle\\S_\triangle=\frac{1}{2}(4)(1.5)\\\\S_\triangle=2(1.5)\\\\S_\triangle=3 \ square\ inches[/tex]
2)
[tex]\displaystyle\\S_\triangle=\frac{1}{2}(16)(9.4)\\\\S_\triangle=8(9.4)\\\\S_\triangle=75,2 \ square\ km[/tex]
3)
The area of a trapezoid is equal to the product of the half sum of the trapezoid bases by the height
Hence,
1 ft=12 in
[tex]\displaystyle\\S_{trapezoid}=\frac{a+b}{2}h \\\\S_{trapezoid}=\frac{16.8+33.6}{2}(12)\\\\ S_{trapezoid}=\frac{50.4}{2} (12)\\\\S_{trapezoid}=25.2(12)\\\\S_{trapezoid}=302,4 \ square \ inches[/tex]
4)
[tex]\displaystyle\\S_{trapezoid}=\frac{7.9+2.3}{2}(4.6)\\\\S_{trapezoid}=\frac{10.2}{2}(4.6)\\\\ S_{trapezoid}=5.1(4.6)\\\\ S_{trapezoid}=23.46\ square\ meters[/tex]
5)
The area of a rectangle is equal to the length times the width of its sides
Hence,
[tex]S=ab\\\\S=6(5.1)\\\\S=30.6\ square\ meters[/tex]
6)
[tex]S=6(4)-2(4-3)\\\\S=24-2(1)\\\\S=24-2\\\\S=22 \ square\ cm[/tex]
-4 + 8[tex]\frac{3} {8}\frac{6} {7}[/tex]
It should be noted that the value of -4 + 8 36/87 will be 4 12/29.
How to calculate the fraction?It should be noted that based on the information illustrated, the fraction given is illustrated as:
= -4 + 8 36/87
= -4 + 8 12/29
= 4 12/29
Therefore, it should be noted that the value of -4 + 8 36/87 will be 4 12/29.
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Find 3 ratios that are equivalent to the given ratio 12:16
Answer:
answer.3.4,6.8,9.12
Step-by-step explanation:
get 12+16=28.
12/28=6/14=3/7
16/28=8/14=4/7.
now get 3/7and 4/7.
subtruct 3 from 12 and also subtract 4 from 16 to get 9.12
Find an equation of the circle that satisfies the given conditions. Center (−1, 8); passes through (−3, −5)
Answer:
[tex](x + 1)^2 + (y-8)^2 = 173[/tex]
Step-by-step explanation:
[tex]\textsf{The standard form of the equation of a circle is }\\\\ \sf (x -h)^2 + (y-k)^2 = r^2 \;where\; (h, k) \textsf{ are the coordinates of the center of the circle and \;r\; is the radius}[/tex]
Here h = -1, k = 8
So we get
[tex](x - (-1)) ^2 + (y - 8)^2 = r^2[/tex]
[tex](x + 1)^2 + (y - 8)^2= r^2\\\\[/tex]
Since the circle passes through the point (-3, -5) we can plug in these values of x = -3 and y = -5 to get r squared
[tex](-3 + 1)^2 + (-5 -8)^2 = r^2\\\\(-2)^2 + (-13)^2 = r^2\\\\4 + 169 = r^2\\\\r^2 = 173\\\\\\[/tex]
So the equation of the circle is
[tex](x + 1)^2 + (y-8)^2 = 173[/tex]
m(n) = 3n³ - 4n
evaluate m(-1)
Step-by-step explanation:
If n= -1
input -1 for n in the equation
e.g. 3(-1)³-4(-1)
From there solve for n and you should get -23n
(-1, 8) and (5,-2) equation must be in slope intercept form
The linear equation that passes through (-1, 8) and (5,-2) is:
y = (5/3)*x + 29/3
How to find the linear equation?
A general linear equation in the slope-intercept form is:
y = a*x + b
Where a is the slope, and b is the y-intercept.
If we know that this line passes trhough the points (-1, 8) and (5, -2) then we can write the slope as:
a = (-2 - 8)/(5 + 1) = -10/6 = 5/3
Then we can write:
y = (5/3)*x + b
Now to find the value of b we can replace the values of one of the points in the line, if we use (-1, 8) we will get:
8 = (5/3)*-1 + b
8 + 5/3 = b
24/3+ 5/3 = b
29/3 = b
We conclude that the linear equation is:
y = (5/3)*x + 29/3
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Answer please
Picture is include
Don’t worry about part b just do part A