After solving the equation x^2-2x-7=0, values of x are -1 + 2√2 and
-1 - 2√2.
A quadratic equation has a leading coefficient of the second degree.
What is a quadratic equation?
A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers.
It is written in the form of ax²+bx+c.
After applying the quadratic formula to it we get,
[tex]x = \frac{-b +\sqrt{b^{2} - 4ac } }{2a} \\ x = \frac{-b -\sqrt{b^{2} - 4ac } }{2a}[/tex]
where a = 1
b = 2
c = -7
After putting the values of a,b, and c, we get
x = -1 + 2√2 and,
x = -1 - 2√2 .
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Which property is demonstrated below?
a(b+c)=(a.b)+(a.c)
O Inverse property
O Distributive property
O Communitive property
O Identity property
( and 15 points for this and will make brainliest to best answer) Please be fast!
Which property is demonstrated below?
a(b + c) = (a*b) + (a*c)
O Inverse property
O Distributive property
O Communitive property
O Identity property
Modeling with Mathematics:
A square-shaped parking lot with 100-foot sides is reduced by x feet on one side and extended by x feet on an adjacent side.
a) The area of the new parking lot is represpresented by (100+ x)(100 – x).
Find this product.
b) Does this area of the parking lot increase, decrease, or stay the same? Explain your thinking. (You can use example values for x to help explain.)
Answer:
a) Difference of squares:
[tex]10000 - {x}^{2} [/tex]
b) The area of the parking lot decreases because x^2 is subtracted from 10,000.
[tex]10000 - {1}^{2} = 10000 - 1 = 9999[/tex]
[tex]10000 - {2}^{2} = 10000 - 4 = 9996[/tex]
the heights of men in a certain population follow a normal distribution with mean 69.7 inches and standard deviation 2.8 inches. (a) if 10 men are selected at random, what is the probability their average height is above 72 inches? (b) if exactly one man is selected at random, what is the probability his average height is above 72 inches? (c) what is the 80th percentile for the average height of 10 men? (d) what is the probability the average height of 10 men is between 70 and 71 inches?
a) 10 men are selected at random, the probability their average height is above 72 inches is 0.0122.
b) Exactly one man is selected at random, the probability his average height is above 72 inches is 0.0122.
c) The 80th percentile for the average height of 10 men is 0.0097%.
d) The probability the average height of 10 men is between 70 and 71 inches is 0.13607.
Mean = 69.7 inches
Standard Deviation = 2.8 inches
a) Using normal distribution,
P(Y > 72) = P(Y - mean > 72 - mean)
P(Y > 72) = P((Y - mean ÷ SD) > (72 - mean ÷ SD))
P(Y > 72) = P(Z > (72 - mean ÷ SD))
P(Y > 72) = P(Z > (72 - 69.7 ÷ 2.8))
P(Y > 72) = P(Z > 2.25)
P(Y > 72) = 1 - P(Z ≤ 2.25)
P(Y > 72) = 0.0122
b) P(man's height is above 72 inches) = 0.0122
c) (80 × 0.0122) ÷ 100
= 0.0097%
d) P( 70 > Y > 71) = P(70 - mean > Y - mean > 71 - mean)
P( 70 > Y > 71) = P((70 - mean ÷ SD) > (Y - mean ÷ SD) > (71 - mean ÷ SD))
P( 70 > Y > 71) = P((70 - mean ÷ SD) > Z > (71 - mean ÷ SD))
P( 70 > Y > 71) = P((70 - 69.7 ÷ 2.8) > Z > (71 - 69.7 ÷ 2.8))
P( 70 > Y > 71) = P(0.107 > Z > 0.464)
P( 70 > Y > 71) = 0.13607
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What is the midpoint of A B if A = (−2, 2) and B = (3, −1)? Enter your answer in the boxes below. Midpoint of A B = ( , )
The coordinate of the midpoint AB is (1/2, 1/2)
How to determine the midpoint?From the question, the coordinates of the points are given as
A = (-2, 2)
B = (3, -1)
The midpoint of a line or points is then calculated using the following midpoint formula
Midpoint = 1/2 * (x₂ + x₁, y₂ + y₁)
Where x and y are the coordinates of A and B
Substitute the known values in the above equation
So, we have the following equation
AB = 1/2 * (-2 + 3, 2 - 1)
Evaluate the sum
AB = 1/2 * (1, 1)
Evaluate the products
AB = (1/2, 1/2)
Hence, the midpoint is (1/2, 1/2)
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pls help due nowwwwwwwwwwwwwww
Answer:
A
Step-by-step explanation:
once tearra started buying games her money decreased by $35.50
Paul biked 7 miles on Saturday and 15 miles on Sunday. What was the total distance, in miles, Paul biked during those 2 days?
We have that:
Paul biked 7 miles on Saturday.
Paul bike 15 miles on Sunday.
The total distance, in miles, the Paul biked during Saturday and Sunday is:
[tex]T=7+15=22[/tex]Using the drawing tools to form the correct answer on the provided graph
Horizontal line with the given function: y = 4
Explanation:
Since the midline of a sine function is the horizontal centerline about which the functions oscilliart above and below, the corresponding line here is y = 4 with x = 0.
NB:
The midline is parrallel to y = 0 ~ the x-axis.
Consider the inequality y > -1.25. Which if the following statements are the?
we have the inequality
y > -1.25
the solution is the interval (-1.25, infinite)
Note that the number -1.25 is not included in the solution
so
Verify each statement
1) 1 is a solution --------> true2) -1.75 is a solution ------> false
3) all the solutions are negative -------> false
4) they're are infinitely many solutions to this inequality -----> true5) the inequality -1.25 < y represents the same solution set to given the inequality ----> trueFind the reminder when 2 to the 100th power is divided by 5 explain your work
The remainder when 2 to the 100th power is divided by 5 is 8.
What is the remainder when 2 to the 100th power is divided by 5?The remainder when 2 to the 100th power is divided by 5 is 8. We can achieve the accurate result by using the exponential formula where:
a^mn = a^m(n)
So, applying this here, we will have
2^10 (10)/5
Recall that multiplying 10 by 10 will give us 100. What was done in this case is simply splitting the figures up to make the division simpler. The exponential law was applied here.
Now, 2^10/5
204.8
The remainder as we can see from this result is 8. Thus we arrive at the answer 8.
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what is 1/3 of 9 cookies and lollipops
∵ 1/3 of 9 means multiply it by 9
[tex]\begin{gathered} \because\frac{1}{3}\times9=\frac{1\times9}{3}=\frac{9}{3} \\ \therefore\frac{1}{3}\times9=3 \end{gathered}[/tex]3 is 1/3 of 9 cookies and lollipops
Answer:
1/3 of 9 is 3.
Step-by-step explanation:
Think of it like this: what number can be added to itself 3 times to get 9? The answer is 3! 3 + 3 + 3 = 9. So, 1/3 of nine is 3 because 9 split into 3 sections would be 1/3 + 1/3 + 1/3 = 1 and 3 + 3 + 3 = 9. So, 1/9 simplified is 1/3!
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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)
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].
Please help!! Math is not my cup of tea and I’m really struggling!! ASAP
Given the function:
f(x)=x²-3x - 4
Find the following values.
a) f(2)
f(2)=
b) f(4)
ƒ(4)=
c) f(-3)
ƒ(-3) =
The values of f(2), f(4) and f(-3) for the function, f(x) = [tex]x^{2} -3x-4[/tex], are -6, 0 and 14 respectively.
According to the question,
We have the following information:
f(x) = [tex]x^{2} -3x-4[/tex]
Now, to find the values of each function we will put the values in place of x.
We will find the value of f(2) by putting 2 in place of x.
f(2) = [tex](2)^{2} -3(2)-4[/tex]
f(2) = 4-6-4
f(2) = -2-4
f(2) = -6
(We know that the numbers with negative sign are added but the result always remains in negative.)
We will find the value of f(4) by putting 4 in place of x:
f(4) = [tex](4)^{2} -3(4)-4[/tex]
f(4) = 16-12-4
f(4) = 4-4
f(4) = 0
Now, we will find the value of f(-3) by putting -3 in place of x:
f(-3) = [tex](-3)^{2} -3(-3)-4[/tex]
f(-3) = 9+9-4
f(-3) = 18-4
f(-3) = 14
Hence, the values of f(2), f(4) and f(-3) are -6, 0 and 14 respectively.
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You decide to use a scale of 1 in: 7 ft to make a scale drawing of your classroom. If the actual length of your classroom is 49 feet, what should the length of the classroom in the drawing be?
The dimension of the length of the classroom in the drawing is calculated to be 7 ft
What is scale of a map?The scale of a map represents by how much a map is reduced or increased. Most of the times the map is smaller than what is being represented hence the scale is usually a reduction.
How to find the length of the classroom in the drawingGive that
1 in in drawing represent 7 ft in actual length
If the actual length of your classroom is 49 feet then we solve as follows to get the dimension in the drawing:
1 in = 7 ft
? in = 49 ft
cross multiplying gives
7 * ? = 49 * 1
? = 49 / 7
? = 7 in
Hence, the conclusion is that the unknown dimension in the drawing represented as ? is equal to 7 in.
This implies that 7 in in the drawing represents actual distance of 49 ft and this is a reduction
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Can someone please answer this!
Considering the situation described, it is found that:
a) The numeric values of the piecewise function are as follows:
W(30) = $300.W(40) = $400.W(47) = $505.W(52) = $580.b) The new piece-wise function is:
W(h) = 10h, 0 ≤ h ≤ 38.W(h) = 15(h - 38) + 380, h > 38.c) The new piece-wise function is:
W(h) = 12h, 0 ≤ h ≤ 40.W(h) = 18(h - 40) + 480, h > 40. What is a piecewise-defined function?A piecewise-defined function is a function that has different definitions, depending on the input of the function.
In this problem, the rule is one for times up to 40 hours, and another for times greater than 40 hours, hence the numeric values are given as follows:
W(30) = 10 x 30 = $300.W(40) = 10 x 40 = $400.W(47) = 15 x (47 - 40) + 400 = $505.W(52) = 15 x (52 - 40) + 400 = $580.For item b, the new reference is of 38 hours, hence the function is:
W(h) = 10h, 0 ≤ h ≤ 38.W(h) = 15(h - 38) + 380, h > 38. (the earnings for the first 38 hours are of 38 x 10 = $380).For item c, the new hourly wage is of 12 hours, hence the rule is:
W(h) = 12h, 0 ≤ h ≤ 40.W(h) = 18(h - 40) + 480, h > 40. (pay and half = 12 x 1.5 = 18, wage for the first 40 hours of 40 x 12 = 480).More can be learned about piecewise functions at brainly.com/question/19358926
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How do you find ratios?
For example, if there are 5 blue balls and 7 red balls. the ration of the blue balls with the red balls is
[tex]5\colon7[/tex]it can also be written as a fraction :
[tex]\frac{5}{7}[/tex]It is important to put the one that was mentioned first in the numerator. in this case is blue ball, that's why 5 came first. If we are asked what is the ratio of the red balls with the blue balls , then we will have to indicate 7 first. The ratio will have to be
[tex]\begin{gathered} 7\colon5 \\ or \\ \frac{7}{5} \end{gathered}[/tex]The sequence is important.
round your answer to the nearest tenth.
The next place value on the right should be used to round a number to the closest tenth (the hundredths). Simply take away all the digits to the right if it's 4 or fewer. Remove all the digits to the right after adding 1 to the digit in the tenths position if the number is five or above.
To what decimal place do you round?
Examine the hundredth number to determine the decimal number's nearest tenth. Add one to the tenth value if the number is more than 5. Remove all the numbers that are present after the tenth place if the value is less than 5, but keep the tenth place value in place otherwise. As an illustration, if you want to round up to the nearest.
Triangle Area Solver
A=hbb
2
b Base
Enter value
hb Height
Enter value
γ
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H(x)=-5/6x;h(x)=10
Find the value of x so that the function has the given value
The value of x = -12.
Define Function.
A special relationship where each input has a single output. It is often written as "f(x)" where x is the input value. Example: f(x) = x/2 ("f of x equals x divided by 2")
The given expression is
H(x)=-5/6 x
also, H(x) = 10
so, put H(x) value in given expression,
10 = -5/6 x
Now, solve for 'x'
-5x = 60
x = 60/(-5)
x = -12
Therefore, the value of x = -12
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Which is the better buy? 2-gallon container of laundry detergent for $23.36. or 17-cup container of laundry detergent for $20.06
we gotta know the conversion between cups and gallons
We know
1 cup (US) = 0.0625 gallons
So, 2 gallon would be 2/0.0625 = 32 cups
So, the problem in cups is:
32 cups = $23.36
17 cups = $20.06
Definitely 32 cups for 23.36 is better buy
2 gallons for $23.36 is the better buy
Note:
23.36/32 = $0.73 per cup
20.06/17 = $1.18 per cup
Given f(x) = -3x + 1, solve for x when f(x) = −5.
Answer:
x=2
Step-by-step explanation:
-3x+1=-5
Subtract 1 from both sides.
-3x=-6
Divide -3 from both sides.
x=2
If f(x)=-5 and f(x)=-3x+1, x=2.
For each sequence, determine whether it appears to be arithmetic. If it does, find the common difference.
We are to determin if the following sequence are arithmetic and also fin their common difference if they are arithmetic.
(1) -3, -9, -27, -81, ................
This sequence is not an arithmetic sequence because theere is no common difference.
-9 - -3 = -27 - -9
-9 + 3 = -27 + 9
-6 ≠ -18
Therefore is not an arithmetic sequcence.
(2) 13, 17, 21, 25, ......................
This sequence is an arithmetic sequence.
It has a commdon difference of 4
17 - 13 = 21 - 17
4 = 4
Therefore, the sequence is an arithmetic sequence.
(3) -6, -2, 2, 6, .........................
This sequence is an arithmetic sequence.
It has a common difference of 4
-2 - -6 = 2 - -2
-2 + 6 = 2 + 2
4 = 4
Therefore, the sequence is an arithmetic sequence
Identify a pair of lines that looks parallel in the diagram.
pls help me
Lines f and g look to be parallel to each other.
Answer:
Lines G and F
Step-by-step explanation:
Parallel means never touching, and they usually run alongside eachother, that's why G and F look parallel.
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What would the transformation be for this figure and what does the transformation result in a figure that is congruent to the original?
Solution
Transform figure using the rule (x , y) = (-x , y - 8)
A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure. The original shape of the object is called the Pre-Image and the final shape and position of the object is the Image under the transformation.
[tex](x_1,y_1)-->(-x_1,y_1-8)[/tex]You downloaded a video game to your computer. You have a 60-minute free block of time for the game. It
takes 5 minutes to set up the game and 7 minutes to play each level of the game. Write an inequality to
determine the number of levels you can play in 60 minutes. How many levels can you play for free? Write an Inequality
An inequality to determine the number of levels you can play in 60 minutes is 5 + 7l ≤60
What is a linear equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Here, it is given that :
Time for setting up the game = 5 minutes
Time to play each level = 7 minutes
Let l represent the number of levels played.
So, Time to play l levels = 7l
So, b = 5+7l
Now we are required to Write an inequality to determine the number of levels you can play in 60 minutes.
So, the inequality becomes :
5 + 7l ≤60
Hence an inequality to determine the number of levels you can play in 60 minutes is 5 + 7l ≤60
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find regular and irregular polygons
Answer:
Regular Polygon:
D
Irregular Polygon:
A, B, F
Not a Polygon:
E, C
Step-by-step explanation:
Polygons are shapes with straight lines.
Regular polygons have uniform side lengths and angles.
2. WRITING Describe the relationship between the angle measures of
angles, supplementary angles, vertical angles, and
complementary
linear pairs.
Please help
Answer:
yes
Step-by-step explanation:
a farmer needs to enclose three sides of a meadow with a fence (the fourth side is a cliff wall). the farmer has 34 feet of fence and wants the meadow to have an area of 140 sq-feet. what should the dimensions of the meadow be? (for the purpose of this problem, the width will be the smaller dimension (needing two sides); the length with be the longer dimension (needing one side). additionally, the length should be as long as possible.)
The dimensions are Width = 7 feets ; length = 20 feets
As given,
Meadow area is 140 square feet.
Height = W (smaller dimension and 2 sides)
Height = L (longer dimension and 1 side)
Fence yards equal 34 feet;
Hence,
L + W = 34
L + 2W = 34
L = 34 - 2W - - - (1)
Recall:
Area = L * W = 140
Substitute value of L
140 = (34 - 2W) * W
140 = 34W - 2W²
2W² - 34W + 140 = 0
W² - 17W + 70 = 0
W² - 10W - 7W + 70 = 0
W(W - 10) - 7(W - 10) = 0
(W - 10) = 0 or (W - 7) =0
W = 10 or W = 7
We choose the shorter width because length should be as long as possible:
W = 7
L + 2W = 34
L = 30 - 14
L = 20 feets
Therefore, The measurements are 7 feet wide and 20 feet long.
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The distance between the points (-2,y) and (3, -7) is 13 units.What are the possible values of y?
To calculate hte possible values of y you have to apply the Pythagoras theorem:
[tex]a^2+b^2=c^2[/tex]Where
c will be the distance between the given points, and the hypothenuse of a right triangle
a will be the base of a theoretical triangle below the hypothenuse, you calculate it as (x2-x1)
b= will be the heigth of said triangle, you calculate it using the y-coordinates (y2-y1)
So:
[tex]\begin{gathered} c^2=a^2+b^2 \\ c^2=(x_2-x_1)^2+(y_2-y_1)^2 \\ c=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \end{gathered}[/tex]Replace the expression with the given measurements to calculate the y-coordinate of the first point:
[tex]\begin{gathered} c=\sqrt[]{(3_{}-(-2))^2+(-7-y)^2} \\ 13=(3+2)+(-7-y) \\ 13=5-7-y \\ 13=-2-y \\ 13+2=-y \\ -15=y \end{gathered}[/tex]The possible values for y, since its
39% of 80 74% of 240 91% of 82 66% of 160
9% of 71 126% of 80 234% of 145 97.9% of 39
52% of 57.9 33% of 15.3
Answer:
39% of 80 = 39.2
74% of 240 = 177.6
91% of 82 = 74.62
66% of 160 = 105.6
9% of 71 = 63.9
126% of 80 = 100.8
234% of 145 = 339.3
97.9% of 39 = 38.181
52% of 57.9 = 30.108
33% of 15.3 = 5.049
Step-by-step explanation:
In order to find the percentage of each equation, we will use the first one as an example. We take the 39%, and convert it to 0.39 and get rid of the %. Then, "of" means multiplication.
So, we have:
0.39 x 80 = 39.2
in the diagram below , the measure of arc SQ is 160 degrees and the measure of arc PR is 102 degrees . find the value of x .
Given:
The measure of angle of arrc SQ is 160°.
The measure of angle of arc PR is 102°.
The objective is to find the measure of angle x.
Since, the angle x is away from te center of the circle.
Then, the formula to find the value of angle x is,
[tex]x=\frac{PR+SQ}{2}[/tex]Now, substitute the given values in the above formula.
[tex]\begin{gathered} x=\frac{102+160}{2} \\ =\frac{262}{2} \\ =131\degree \end{gathered}[/tex]Hence, the value of x is 131°.
an oil prospector will drill a succession of holes attempting to find a productive well. assume the probability of being successful on any drilling is 0.15, and that outcomes of drillings are independent. what is the expected number of drilling attempts needed in order to find a productive well? what is the probability that the first productive well is found on the third attempt? if the prospector can only afford to drill five holes, what is the probability that the prospector will fail to find a productive well
The oil prospector drills wells with a success probability of 0.15. The probability of finding the first productive well in the third attempt is 0.108375 and the probability that the prospector fails to find productive well in the first 5 attempts is 0.26724 or 26.724%
Let Y be the number of drilling trials on which the prospector will find the first productive well. As Y is a geometric random variable with p=0.15 where p is the probability of being successful on any drilling. Let q = 1- p be the probability of being unsuccessful in drilling a well. q = 1 - 0.15 = 0.85
The probability that the first productive well is found on the third attempt is when outcomes are independent
P(Y=3) = q * q * p = 0.85^2* 0.15 = 0.108375
We want to find the probability that 5 wells are drilled and not a productive one is found. That is we need to find p(Y>5). Y is a binomial random variable with several wells drilled at most as n. Given n=5 and p=0.15, q = 0.85
We know the geometric probability is p(y) = [tex]q^{y-1}[/tex]p
Then corresponding probabilities are added
p(Y≤ 5 ) = p(0) + p(1) +p(2) + p(3) +p(4) +p(5)= 0.73276
Using the complement rule:
p(Y>5) = 1 - p(Y≤5) = 1- 0.73276 = 0.26724 = 26.724 %
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