Answer: 1. [-8, 8]
2. [-27, 27]
Step-by-step explanation:
1. |X|≤8
x≤8 or x>=-8
-8<=x<=8 ==> [-8, 8]
2. |X|≤27
x≤27 or x>=-27
-27<=x<=27 ==> [-27, 27]
What is the area??? Please help!!!
Answer:
169 squared I think,hope this helps
9. M (2, 1) is the midpoint of segment AB. If the endpoint A has coordinates (5,6), find
the coordinates of endpoint B.
Answer:
(-1, -4)
Step-by-step explanation:
To find the missing endpoint, we can multiply the midpoint coordinates by 2, so we can get 4 and 2. Then we can subtract the coordinates from the endpoint we have, which is A, to those numbers.
4-5 is -1
2-6 is -4
Put them together and we get (-1, -4) as our endpoint B.
Answer:
Step-by-step explanation:
(5+x)/2=2, (6+y)/2=1
for the x value
5+x=4
x=-1
then for the y value
6+y=2
y=-4
then your answer would be (-1,-4)
Multiply and simplify completely
√6 x 3√54
Answer:
54
Step-by-step explanation:
using the rule of radicals
[tex]\sqrt{ab}[/tex] = [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] and [tex]\sqrt{a}[/tex] × [tex]\sqrt{a}[/tex] = a , then
[tex]\sqrt{6}[/tex] × 3[tex]\sqrt{54}[/tex]
= [tex]\sqrt{6}[/tex] × 3 × [tex]\sqrt{9(6)}[/tex]
= [tex]\sqrt{6}[/tex] × 3 × [tex]\sqrt{9}[/tex] × [tex]\sqrt{6}[/tex]
= [tex]\sqrt{6}[/tex] × [tex]\sqrt{6}[/tex] × 3 × 3
= 6 × 9
= 54
[tex]{ \qquad\qquad\huge\underline{\boxed{\sf Answer}}} [/tex]
Here's the solution ~
[tex]\qquad \sf \dashrightarrow \: \sqrt{6} \times 3 \sqrt{54} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{2 \times 3} \times \sqrt{2 \times {3}^{3} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{ {2}^{2} \times {3}^{4} } [/tex]
[tex]\qquad \sf \dashrightarrow \:2 \times {3}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \:2 \times 9[/tex]
[tex]\qquad \sf \dashrightarrow \:18[/tex]
you're given a fair coin. you flip the coin until either heads heads tails (hht) or heads tails tails (htt) appears. is one more likely to appear first? if so, which one and with what probability?
The HHT is more likely to appear first with a probability of 2/3.
What is probability?The probability is an estimation of the likelihood that an event will occur. It assesses the event's certainty.
The formula for probability is given as;
P(E) = Number of Favourable Outcomes/Number of total outcomes.
Now according to the given question;
Only the second and third flips in the sequence matter. We understand the first flip is an H, and we're not interested in sequences that begin with T.
Lets start with the given format;
H _ _
If we get an HH_, the game is over and HHT will surely win (regardless of the number of heads we get, the next T is an automatic win). If we get an HTT, the game is over.
If we get an HTH, the game is a tie, and we must restart it.
Thus,
P(HHT) = 1/2
P(HTT) = 1/4
P(Draw) = 1/4
P(HHT wins) = P(HHT) / [1-P(Draw)]
= (1/2) / (1-1/4)
P(HHT wins) = 2/3
Thus, the probability of occurrence of HHT has more chances with 2/3.
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What is the slope of a line parallel to the line whose equation is 18x + 15y = 90. Fully simplify your answer.
Answer:
6/5
Step-by-step explanation:
Rise
_____
Run
The slope of parallel line is -6/5
What is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx
where, m is the slope
given:
Equation: 18x + 15y = 90.
Now, writing the given equation in slope intercept form
15y= 90- 18x
y= 90/15 - 18/15 x
y= 6 - 6/5x
So, the slope of given line is -6/5
Now, the slope of parallel and given is same.
Thus, the slope of parallel line is -6/5
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You want to enlarge a 4 x 5 inch photo to fit into a 1 inch wide frame
that has an outer perimeter of 53 inches.
a. Write and simplify an equation for the outer perimeter of the
picture frame.
b. Determine the factor by which you must enlarge the picture to have it completely fill the inside of the picture frame
The 4•x by 5•x inner dimensions of the 53 inches outer perimeter picture frame, the 1 inch wide frame and the 4 × 5 inch picture to be enlarged, gives;
a. The outer perimeter equation is presented as follows;
18•x + 8 = 53 inches
b. The scale factor required for the enlargement of the picture is 2.5
Which method can be used to write the equation and find the scale factor?The dimensions of the photo = 4 × 5 inch
Width of the frame = 1 inch
Outer perimeter of the frame = 53 inches
The width of the inside of the picture frame = 4•x
The height of the inside of the picture frame = 5•x
a. The equation for the outer perimeter of the picture frame is therefore;
2 × (4•x + 1 + 1) + 2 × (5•x + 1 + 1) = 53
Which gives;
2 × (4•x + 2) + 2 × (5•x + 2) = 53
8•x + 4 + 10•x + 4 = 53
A simplified equation for the outer perimeter of the picture frame is therefore;
18•x + 8 = 53b. Solving the above equation, we have;
18•x + 8 = 53
18•x = 53 - 8 = 45
18•x = 45
Therefore;
x = 45 ÷ 18 = 2.5
x = 2.5
The width and height of the picture frame are therefore;
Width = 4•x = 4 × 2.5 = 10
Height = 5•x = 5 × 2.5 = 12.5
Which gives;
Width = 10 inches
Height = 12.5 inches
The enlargement factor, sf, is given by the ratio of a side of the picture frame to a side of the picture as follows;
sf = 12.5/5 = 2.5
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two years ago, paul was 7 times as old as matt was. two year from now, paul will be five times as old as matt will be. find the present age of each
The present age of Paul is 52 years and the present age of Matt is 10 years.
We are given that two years ago, Paul = 7 times as Matt
Let the current age of Matt be x and of Paul be y
2 years ago, we will have that:
Age of Matt = x - 2
So, we get the equation as:
Age of Paul = 7 ( x - 2) = 7 x - 14
y - 2 = 7 x - 14
y = 7 x - 14 + 2
y = 7 x - 12
Also, we are given that to year from now, Paul = five times Matt
We get that:
y + 2 = 5 ( x + 2)
y + 2 = 5 x + 10
y = 5 x + 10 - 2
y = 5 x + 8
So, we get:
7 x - 12 = 5 x + 8
7 x - 5 x = 8 + 12
2 x = 20
x = 20 / 2
x = 10
y = 5 (10) + 2
y = 50 + 2
y = 52
Therefore, the present age of Paul is 52 years and the present age of Matt is 10 years.
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PLEASE help with this problem in math!!
the jazz band has b members. to raise money for a tour, each member sold 12 raffle tickets. write an expression that shows the number of raffle tickets sold. submit
The term or expression 12b represents the number of raffle tickets sold by the members of the band.
Expression: An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.
There are b number of members in a jazz band. The jazz band wants to take a tour.
Each of the members sold 12 raffle tickets to raise money for the tour.
Therefore, the number of raffle tickets sold will be the product of the number of jazz members and the number of raffle tickets sold by each member.
So, the expression for the number of raffle tickets sold by the members of the jazz band will be:
= 12 × b
= 12b
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WILL GIVE BRAINLIEST
To pay for a home improvement project that totals $11,000, Genesis is choosing between taking out a simple interest bank loan at 6% for 3 years or paying with a credit card that compounds monthly at an annual rate of 16% for 6 years. Which plan would give Genesis the lowest monthly payment?%0D%0A%0D%0A The monthly credit card payment would be $396.49, which is lower than the monthly payment on the bank loan.%0D%0A The monthly payment on a bank loan would be $360.56, which is lower than the monthly credit card payment.%0D%0A The monthly credit card payment would be $354.44, which is lower than the monthly payment on the bank loan.%0D%0A The monthly payment on a bank loan would be $323.89, which is lower than the monthly credit card payment.
Using the monthly payment formula, it is found that the best plan is given by:
The monthly credit card payment would be $238.37, which is lower than the monthly payment on the bank loan.
What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.For the simple interest payment method, the parameters are given as follows:
r = 0.06, n = 3 x 12 = 36, P = 11000, r/12 = 0.06/12 = 0.005.
Hence:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 11000(0.005)\frac{(1.005)^{36}}{(1.005)^{36} - 1}[/tex]
A = 334.64.
For the credit card payment method, the parameters are given as follows:
r = 0.16, n = 6 x 12 = 72, P = 11000, r/12 = 0.16/12 = 0.0133.
Hence:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 11000(0.0133)\frac{(1.0133)^{72}}{(1.0133)^{72} - 1}[/tex]
A = 238.37.
The monthly credit card payment would be $238.37, which is lower than the monthly payment on the bank loan.
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square root 71 in math
Answer: 8.4261
Step-by-step explanation:
HELP ME QUICK!!
Joe wants to wallpaper the back wall of his bedroom. The wall is in the shape of a rectangle its length of 17 feet and its width is 13 feet suppose wallpaper cost five dollars for each square foot how much will paper cost for the wall
Based on the shape of the back wall of Joe's bedroom and the dimensions of the rectangle, and the cost per square foot, the paper cost of the wall would be $1,105
What is the paper cost of the wall?First, find the area of the back wall of Joe's bedroom because this is the area that would need to be covered by the wall paper:
Area of rectangle = Length x Width
Solving gives:
= 17 x 13
= 221 square foot
The cost to cover the wall based on the cost in dollars of each square foot is:
= Number of square feet x Cost per square foot
= 221 x 5
= $1,105
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Keisha has $585.43 in her checking account. She must maintain a balance of $300 to avoid a fee. She wrote a check for $302.05 today. Write an inequality, using x for the variable, that would be used for the least amount of money she needs to deposit to avoid a fee.
The inequality that would be used for the least amount of money she needs to deposit to avoid a fee will be 585.43 + x - 302.05 ≥ 300.
How to calculate the value?From the information, it was stated that Keisha has $585.43 in her checking account and that she must maintain a balance of $300 to avoid a fee and then she wrote a check for $302.05 today.
The inequality that would be used for the least amount of money she needs to deposit to avoid a fee will be:
585.43 + x - 302.05 ≥ 300
Collect like terms
x ≥ 300 - 585.43 + 302.05
x ≥ $16.62
She's needs to deposit at least $16.62.
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Add. Write your answer in scientific notation. (1.38×104)+(8×103) 9.38×1049 point 3 8 times 10 to the 4th power 2.18×1042 point 1 8 times 10 to the 4th power 9.38×1079 point 3 8 times 10 to the 7th power 2.18×107
The addition of the expression (1.38×10⁴) + (8×10³) written in scientific notation is "9 point 3 8 times 10 to the 7th power". option C
Scientific notation(1.38×10⁴) + (8×10³)
= (1.38 + 8) × 10^(4 + 3)
= 9.38 × 10^7
Options:
9 point 3 8 times 10 to the 4th power9.38×10⁴
2 point 1 8 times 10 to the 4th power2.18×10⁴
9 point 3 8 times 10 to the 7th power9.38×10^7
2.18×10^7Therefore, the addition of the expression (1.38×10⁴) + (8×10³) written in scientific notation is "9 point 3 8 times 10 to the 7th power".
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if f(x) = x and g(x) = 2, what is (f.g) (x)?
The value of (f.g) (x) is 2. Option B
What is a function?A function can be defined as an expression or rule that explains the relationship between an independent and dependent variable.
Given the functions;
f(x) = xg(x) = 2To determine (f.g) (x), we need to know that it is a composite function
We substitute the value of g(x) = 2 as x in f(x)
But we have f(x) = x
Then,
(f.g) (x) = 2
Thus, the value of (f.g) (x) is 2. Option B
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when constructing a congruent line segment to cd the ray needed for the construction must be shorter
This statement is false. when constructing a congruent line segment to cd the ray needed for the construction it must be not shorter.
Why configured line segment to CD the ray never can be shorter?Because when constituting a configured line segment to CD the ray never can be shorter. The reason is when we constitute a configured it's Ray line is always increase that mean it's go up Hight and it's must be longer . That's why this statement is false.
What is a congruent line segment?Congruent line segments are geometrical figures in one dimension with identical dimensions. In terms of congruent lines, the word "congruent" refers to the equality of the two line segments. When two lines are the same length, they are said to be congruent. Superimposable figures that entirely enclose each other when stacked one atop the other are congruent segments. The congruent segments continue to be congruent even after being turned, flipped, or rotated.
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(4)^2(-7)-(-7)^2
This is all
Solve the inequality -5/2 (3x-2)<6-2x. For full credit, you will need to show and explain every step. You may add more lines if you need them.
The solution to the inequality, -5/2(3x - 2) < 6 - 2x is: x > -2/11.
How to Solve an Inequality?To find the solution to the inequality given, follow the steps explained below:
-5/2(3x - 2) < 6 - 2x [given]
-5/2(3x) -5/2(-2) < 6 - 2x [distribution property]
-15x/2 + 5 < 6 - 2x [simplify]
-15x/2 + 5 - 5 < 6 - 2x - 5 [subtraction property]
-15x/2 < 1 - 2x
-15x/2 + 2x < 1 - 2x + 2x [addition property]
-11x/2 < 1 [simplify]
-11x/2 × 2 < 1 × 2 [multiplication property]
-11x < 2
-11x/-11 > -2/11 [division property]
x > -2/11
Note: the inequality sign would change if we are dividing both sides by a negative number.
Therefore, the solution to the inequality, -5/2(3x - 2) < 6 - 2x is: x > -2/11.
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Which postulate proves the two triangles are congruent
Based on the side-angle-side congruent theorem/postulate, both triangles are congruent. the answers is SAS.
What is the Side-angle-side Congruence Theorem (SAS)?The side-angle-side congruence theorem (SAS) means that two triangles have two pairs of sides that are congruent to each other with a pair of included congruent angles in between the two pairs of congruent sides of both triangles, and thus, both triangles must be congruent to one another.
The diagram shows two triangles that share a common side which is a pair of congruent sides. It also shows a pair of another congruent sides that is marked congruent.
Also, we have a pair of included congruent angles that both triangles have.
Therefore, based on the side-angle-side congruent theorem/postulate, both triangles are congruent. the answers is SAS.
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19. The football game was attended by 237 people, down 40% from last week. How many
people attended last week's game?
(a) 332
(b) 395
(c) 142
(d) 379
Answer:
(a) 332
Step-by-step explanation:
Find 40% of 237
94.8, Round to 95
237 + 95 = 332
What is the quotient?
StartFraction (negative 7) squared Over (negative 7) Superscript negative 1 EndFraction
Negative 343
Negative 7
7
343
The quotient of the given division operation is -343. and The correct option is the first option -343.
According to the statement
We have to find that the value of the quotient.
So, For this purpose, we know that the
Quotient can be defined as the result of the division of a number by any divisor.
In other words, The result of the division is the quotient.
From the given information:
we are to determine the quotient of the given division operation
And
The statement become is:
[tex]\frac{-7^{2} }{-7^{-1} }[/tex]
Then we have to solve this
Then
[tex]\frac{49}{-7^{-1} }[/tex]
Then
49*-7
-343.
the quotient of the given division operation is -343.
So, The quotient of the given division operation is -343. and The correct option is the first option -343.
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Answer:
-343
Step-by-step explanation:
Edge
Solve: 1 1/8 - 3/4
pls answer in fraction!!
Answer:
3/8
change to an improper fraction
1 1/8=9/8
3/4 times 2 equals
6/8
9/8-6/8
3/8
Answer: I think the answer is 3/8 or it can be 5/8.
explanation: I hope this helps.
suppose a survey of 979 business owners found that more than % bought . which part of the survey represents the descriptive branch of statistics? make an inference based on the results of the survey.
In this problem, descriptive statistics is used because the survey percentage is used to make inference for all business owners.
What is descriptive statistics?
Descriptive statistics is used when data from a sample, which is a sub-set of a population, is used to make inferences about the entire population.
In this problem, the data 979 business owners sampled is used to make inference about the population, which is composed by all business owners, hence descriptive statistics is used.
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A sum of £350 is invested at simple interest and amounts to £476 after 3 years. Calculate
(a) the total interest
(b) the rate per cent per annum.
Answer:
(a) $126
(b) .453333%
Step-by-step explanation:
(a) 476 - 350 = $126
(b)
[tex]si = p \times r\times t \\ 476 = 350 \times r\times 3 \\ 476 = 1050r \\ \frac{476}{1050} = r \\ r = 0.453333\%[/tex]
prove 2/sqrt3cosx+sinx=sec(pi/6-x)
Thus L.H.S = R.H.S that is [tex]\frac{2}{\sqrt{3} cosx + sinx }[/tex] = [tex]sec(\frac{\pi }{6-x} )[/tex] is proved
According to the question we have been given that
[tex]\frac{2}{\sqrt{3} cosx + sinx }[/tex] = [tex]sec(\frac{\pi }{6-x} )[/tex]
And we need to prove that left hand side is equal to the right hand side.
To prove this we will solve the right-hand side of the equation first with the help of trigonometry identity. The right hand side of the equation is :
R.H.S = [tex]sec(\frac{\pi }{6-x} )[/tex]
= [tex]\frac{1}{cos(\frac{\pi }{6-x} )}[/tex]
[As secƟ = 1/cosƟ)
= [tex]\frac{1}{\frac{cos\pi }{6cosx} + \frac{sin\pi }{6sinx} }[/tex]
[As cos (X-Y) = cosXcosY + sinXsinY , which is a trigonometry identity where X = Π/6 and Y = x]
[tex]=\frac{1}{\frac{\sqrt{3} }{2}cosx + \frac{1}{2}sinx } \\= \frac{1}{\frac{\sqrt{3}cosx + sinx }{2} }\\=\frac{2}{\sqrt{3}cosx + sinx}[/tex]
R.H.S = L.H.S
or L.H.S = R.H.S
Hence [tex]\frac{2}{\sqrt{3} cosx + sinx } = sec(\frac{\pi }{6-x})[/tex] is proved
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What reasoning shows correctly how to rewrite 4 to the power of 3 over 2 end exponent?
The reasoning which shows the given statement correctly is [tex]4^{\frac{3}{2}}[/tex].
Given the statement is "4 to the power of 3 over 2 end exponent".
In mathematics, an expression is defined as a set of numbers, variables, and operations that are formed according to context-dependent rules.
In the given statement 3 over 2 means, 3 is divisible by 2 and it can be written as 3/2.
And it is also given that 4 to the power of 3 over 2 that means we have to write 3/2 in the power of 4 and it can be written as
[tex]4^{\frac{3}{2}}[/tex]
Hence, the reasoning which shows the given statement "4 to the power of 3 over 2" correctly is [tex]4^{\frac{3}{2}}[/tex].
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The graph shown corresponds to someone who makes ___
help quick pls
Answer:B $20 an hour
Step-by-step explanation:
if you look at the graph, in one hour he made $20
Help I have no clue what are the answers I tried 30 times!
The correct options for the linear combinations of the vectors are given by:
A, B, C, D, E and F.
What is a span between two vectors?The span between two vectors is the set that contains all linear combinations between these two vectors.
Supposing we have two vectors u1 and u2, as is the case in this problem, the infinitely many linear combinations have the following format:
k1u1 + k2u2
In which k1 and k2 are real numbers.
With k1 = 4 and k2 = -7, we get that option A is correct.
For option B, we have to see if it is possible to solve the following system.
k1 + 4k2 = 0.5k1 + 22k2 = 0.-4k1 - 11k2 = 0.The solution is k1 = k2 = 0, which are real numbers, hence option B is correct.
Both vectors u1 and u2 are part of the span, hence options D and F are correct. The size of the span is of infinity, hence option E is correct while option G is not.
The dimension of the span is of 3, as the vectors have 3 elements, hence option C is correct.
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are there any points with integer coordinates on a line if a line passes through (5,-8.5) and (13.8, 6.9)?
please provide a yes or no and examples.
There are at least two integer points in the line that passes through (5, - 8.5) and (13.8, 6.9).
Does a line contain coordinates with only integers?
In this problem we have a line that passes through two points on a Cartesian plane and herein we must check if that line contains at least one point with integer coordinates. First, determine the equation of the line:
Slope
m = [6.9 - (- 8.5)] / (13.8 - 5)
m = 7 / 4
Intercept
b = - 8.5 - (7 / 4) · 5
b = - 69 / 4
The equation of the line is y = (7 / 4) · x - 69 / 4.
Second, evaluate the equation of the line at different integers:
x= 6
y = (7 / 4) · 6 - 69 / 4
y = - 27 / 4
x = 7
y = (7 / 4) · 7 - 69 / 4
y = - 5
x = 8
y = (7 / 4) · 8 - 69 / 4
y = - 13 / 4
x = 9
y = (7 / 4) · 9 - 69 / 4
y = - 3 / 2
x = 10
y = (7 / 4) · 10 - 69 / 4
y = 1 / 4
x = 11
y = (7 / 4) · 11 - 69 / 4
y = 2
x = 12
y = (7 / 4) · 12 - 69 / 4
y = 15 / 4
x = 13
y = (7 / 4) · 13 - 69 / 4
y = 11 / 2
There are at least two integer points in the line that passes through (5, - 8.5) and (13.8, 6.9).
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10. Sam earns a salary of $25,000 while Charlie earns a salary of $30,000. They each receive
a $2000 raise. Which of the following is true?
(a) Sam's raise is larger than Charlie's in both absolute and relative terms.
(b) The raises are the same in absolute terms, but Sam's is larger in relative terms.
(c) The raises are the same in relative terms, but Sam's is larger in absolute terms.
(d) The raises are the same in absolute terms, but Charlie's is larger in relative terms.
If the salary of Sam is $25000 and Charlie earns $30000 and each get a raise of $2000 then the statement "The raises are the same in absolute terms, but Charlie's is larger in relative terms" is true.
Salary of Sam = $25000
Raise in Sam's Salary = $2000
New Total Salary = $25000 + $2000 = $27000
Salary of Charlie = $30000
Raise in Charlie's Salary = $2000
New Total Salary = $30000 + $2000 = $32000
Hence the absolute value of their salaries are same but Charlie will get more in relative terms.
Hence, option d is correct.
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