The slope of the line perpendicular to the line given by equation 2x+2y=-12 is found as 1.
What is the definition of line slope?The slope of a line measures its steepness as well as direction.The slope of a line is defined as the change throughout y coordinate in relation to the transitions in x coordinate.The net change in y coordinates is Δy, while the net change in x coordinates is Δx.So m represents the change in y coordinate in relation to a shift in x coordinate.The slope can be calculated using the following formula:
m = Δy/Δx
Where, m is the slope.
The equation of the line is; 2x+2y=-12
Write the equation in slope-intercept form.
2x + 2y = -12
Divide by 2.
x + y = -6
y = -x - 6
Slope m₁ = -1 and y-intercept = -6.
As, both line are perpendicular.
Thus,
m₁ x m₂ = -1
m₂ = -1/m₁
Put the value.
m₂ = -1/(-1)
m₂ = 1
The slope of the perpendicular line is found as 1.
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Which ratio is equivalent to 9/78.
A: 1/8
B: 3/26
C: 1/3
D: 3/18
Answer:
3/26
Step-by-step explanation:
you simply divide both numbers by there largest lcm which is 3
9/3=3
78/3=26
Together 3/26
A figure is dilated by a factor of 3. Which of following statements about the image of the figure is true?
When an image is dilated by a factor of 3, the statement about the image of the figure that is true is Both the area and the perimeter increase.
What happens when a shape is dilated?When a shape is dilated, the effect on the shape is that its dimensions are made to be longer. For instance, a shape dilated by 2 would see all its dimensions increase by 2.
In the case of a figure that is dilated by a factor of 3, it means that the shape would increase by 3 in size.
The effect of this is that the perimeter would increase by 3. The area of the figure would also increase thanks to the increase in dimensions by 3.
Options for this question include:
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Find 2 conservative numbers whose square differs by 25
The 2 conservative numbers whose square differs by 25 are 12 and 13.
How to illustrate the information?It should be noted that consersative numbers simply refer to the numbers hat follow each other continuously in a particular order. They include 1, ,2, 3, etc.
In this case, the two conservative numbers whose square differs by 25 are 12 and 13. This will be illustrated as:
= 13² - 12²
= 169 - 144
= 25
Therefore, the numbers are 12 and 13
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find the slope of line passing through each of the following pairs of points and draw the graph of the line. (4,3), (2,2)
The slope of line passing through the pair of points (4,3) and (2,2) is 1/2.
What is the slope of the line with the given coordinates of points?Slope is simply expressed as change in y-values over the change in x-values.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Given the data in the question;
Point 1( 4,3 )
x₁ = 4y₁ = 3Point 2( 2,2 )
x₂ = 2y₂ = 2Slope m = ?
Plug the given coordinates into the slope formula and solve for m.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 2 - 3 )/( 2 - 4 )
Slope m = ( -1 )/(-2 )
Slope m = ( 1 )/( 2 )
Slope m = 1/2
Therefore, the slope of the line segment with the given coordinates is 1/2.
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Consider the matrices.
What operations are defined for these matrices?
Drag the operation to the boxes to correctly complete the table.
[0]. and Q = []
00
Answer:
Defined: M-N
Not defined: Q+P, M+P, L-N
Step-by-step explanation:
Just took the test
You are considering a 5/1 arm what does 5 represent
Your rate is temporarily fixed for a total of five years under a 5/1 ARM, indicated by the "5".
An adjustable-rate mortgage is what?A loan for a home is a mortgage with an adjustable interest rate (ARM). An ARM's initial interest rate is fixed for a specific period of time.
The "1" indicates the number of times the rate may change after the initial fixed-rate term expires; in this instance, the "1" equals one year, therefore the rate changes once a year.
The "5" in the word represents the period during which the rate will be fixed, and the "1" denotes the interval between adjustments after that (once per year). Therefore, it is already apparent how crucial insurance is.
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Name all transformations of the following function
Notice that the parent function of y is:
[tex]f(x)=\sqrt{x}.[/tex]Now, recall that a function h(x) translated n units to the left is represented by:
[tex]h(x+n),[/tex]translated m units up :is represented by
[tex]h(x)+m,[/tex]reflected across the x-axis :is represented by
[tex]-h(x),[/tex]vertically compressed by a factor of 1/k :is represented by
[tex]\frac{1}{k}h(x).[/tex]Therefore, y is f(x) translated 3 units to the left, reflected over the x-axis, vertically compressed, and translated 2 units up.
Answer:y is its parent function translated 3 units to the left, reflected over the x-axis, vertically compressed, and translated 2 units up.
The table below displays results from experiments with polygraph instruments. Find the positive predictive value for the test. That is, find the probability that the subject lied, given that the test yields a positive result.
_ No_(Did_Not_Lie) Yes_(Lied)
Positive_test_results 10 45
Negative_test_results 34 12
Using it's concept, the probability that the subject lied, given that the test yields a positive result is of 9/11 = 0.8182 = 81.82%.
What is a probability?The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.
In this problem, we want to find the probability that the subject lied, given that the test yields a positive result, hence:
The total outcomes are the tests resulting in a positive.The desired outcomes is the number of tests out of those positive in which the subject lied.From the table, we have that:
There were 10 + 45 = 55 positive test results.In 45 of those tests, the subject lied.Hence the probability is given as follows:
p = 45/55 = 9/11 (simplifying by 5)
p = 9/11 = 0.8182 = 81.82%.
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10. An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 4 cm long. A second side of the triangle is 7.4 cm long. Find the longest and shortest possible lengths of the third side of the triangle.
Round answers to the nearest tenth of a centimeter.
O 44.4 cm, 11.1 cm
11.1 cm 49 cm
O 24 cm 49 cm
444 cm, 3.2 cm
The longest and shortest possible lengths of the third side of the triangle are 4.9 cm and 11.1 cm.
What does the Angle Bisector Theorem state?It states that the opposite side of a triangle is divided into segments by each angle bisector that are proportional in length to the adjacent sides.
Given:
An angle bisector divides the opposite side of the triangle into segments 6 cm and 4 cm long.
Second side of the triangle is 7.4 cm.
We have to calculate the longest and shortest possible lengths of the third side of the triangle.
By Angle Bisector Theorem we can solve this problem,
In the triangle ABC, AD is the angle that bisects angle A, placing D on side BC.
Now, BD / DC = AB / AC
BC = 6 + 4 = 10 cm
Angle bisector divides BC into 2 segments,
BD = 6 cm
CD = 4 cm
If AB = 7.4 cm,
6/4 = 7.4 / AC
AC = 7.4(4) / 6
AC = 29.6 / 6
AC = 4.94 cm (shortest possible length of the third side of the triangle)
If AC = 7.4 cm
6/4 = AB/7.4
AB = 6(7.4)/4
AB = 44.4/4
AB = 11.1 cm (longest possible length of the third side of the triangle)
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m - a + n + p , for a
The expression m = a + n + p can be written as a = m - n - p after making the subject a.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
The expression is:
m = a + n + p
To solve for a make the subject as a:
a = m - n - p
Thus, the expression m = a + n + p can be written as a = m - n - p after making the subject a.
The question is incomplete.
The complete question is:
Solve for a, if the expression is m = a + n + p.
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The mean per capita income is $21,604 per annum with the standard deviation of $727 per annum. What is the probability that the sample mean will be less than $21,635 if a sample of 193 persons is randomly selected? Round your answer to four decimal places
Explanation
In the question, we are given that
[tex]\begin{gathered} \mu=21,604 \\ \sigma=$ 727 $ \\ n=193 \end{gathered}[/tex]First, we will get the standard deviation of the sample mean as
[tex]\sigma_x=\frac{\sigma}{\sqrt{n}}=\frac{727}{\sqrt{193}}=52.3306[/tex]Then, we can find the probability that the sample mean will be less than $21,635 for a sample of 193 persons
[tex]\begin{gathered} P(\bar{X}<21635)=P(z<\frac{\bar{X}-\mu}{\sigma_x})=P(z<\frac{21635-21604}{52.3306}) \\ =P(z<0.59238) \end{gathered}[/tex]Therefore, using the z score calculator
[tex]P(z<0.59238)=0.7232[/tex]Answer: 0.7232
Convert (2,210 °) to rectangular form.
A. (1,-√3)
B. (-√3,-1)
C. (-√3,1)
D. (-1,-√3)
E. (√3,-1)
The answer is D. -1,-3. i just finished and got it right
A small order coffee company charges $12 for each bag of coffee +3 dollars shipping no matter how many bags are ordered. Describe the function that this situation gives rise to. make a table for this function, sketch a graph for this function, and find an equation for this function. Is the function linear or not? How can you tell?
A small order coffee company charges $12 for each bag of coffee +3 dollars shipping no matter how many bags are ordered. Describe the function that this situation gives rise to. make a table for this function, sketch a graph for this function, and find an equation for this function. Is the function linear or not? How can you tell?
Step 1
Describe the function,
.
Let
x, the number of bags
shipping = 3 dollars
Charges=$12 for each bag, then
charges=12*x
Now, the total is
total=charges + shipping
total=12x +3
now, we have a function ( the total (y) depends on the number of bags)
[tex]y=12x+3[/tex]where
y is the total charge, and x is the numbers of bags
Step 2
assume values for x, replace and find y
x=-3
then y=12(-3)+3, y=-36+3, y=-33
so, when x=-3, y=-33
2
then y=12(-2)+3, y=-24+3, y=-21
so, when
x=-2, y=-21
1
then y=12(-1)+3, y=-12+3, y=-9
so, when
x=-1, y=-9
0
then y=12(0)+3, y=+3, y=3
so, when
x=0, y=3
1
then y=12(1)+3, y=12+3, y=15
so, when
x=1, y=15
the table is
x y
-3 -33
-2 -21
-1 -9
0 3
Step 3
, just sepick two cooridnadinates from the table mak, then mark those pintsoints, and finally, dwr in the planeaaw a line conceeecting he connectingnts
Step 4
as you can see, when we take the points of the table and we unite them, a line appears
so , this is a linear function
Also, the exponent of the variable ( x) is cero, which means it is a linear function.
Marie is calculating an annuity payment. Her mortgage of $200,000 compounds monthly for 30 years. What is the nt value she will use in her formula?
Based on the annuity payment that Marie will make and the number of years, the nt value that she will use in her formula is 360 months.
How to find the nt value?The nt value is the number of periods that Marie will need to pay her annuity payment. This value can be yearly, monthly, weekly and even daily.
As the mortgage compounds monthly in this instance, the nt value will need to be monthly as well.
To find the nt value, the formula is:
= Number of years x number of compounding periods per year
= 30 x 12 times a year
= 360 months
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Answer:
360
Step-by-step explanation:
i did that and i got it right
what is equivalent to (x+7)^2 ?
1. x^2+49
2. (x-7)(x+7)
3. (x+7)(x+7)
4. (7x)(7x)
⇒In this case what is in the brackets is being treated as being the term . so this means that if we are to expand then we expand the whole term in full detail.
⇒In this case we have x+7 as the term of the expression which means when we expand we are going to expand the whole term x+7
[tex]=(x+7)^{2} \\=(x+7)(x+7)[/tex]
The third option is the answer.
GOODLUCK!!
Use synthetic division to find the quotient and remainder when
2x^3-9x² +14x-2 is divided by x-1.
Dividing (2x³ - 9x² + 14x - 2) by (x - 1) with synthetic division method given the remainder 5 and the quotient 2x² - 7x + 7 + (5/x-1).
What is synthetic division?One unique way to divide polynomials is by using the synthetic division method. This approach, where the leading coefficient should be equal to 1, is a special case of multiplying a polynomial expression by a linear factor. In the specific case of dividing by a linear factor, the synthetic division is a shorthand, or shortcut, method of polynomial division. However, the synthetic division is typically used to locate polynomial zeroes (or roots), not to divide out factors.So, 2x³ - 9x² + 14x - 2 ÷ x - 1 by synthetic division as follows:
(Refer to the images attached below for calculations)2x³ - 9x² + 14x - 2 ÷ x - 1:
Remainder: 5Quotient: 2x² - 7x + 7 + (5/x-1)Therefore, dividing (2x³ - 9x² + 14x - 2) by (x - 1) with synthetic division method given the remainder 5 and the quotient 2x² - 7x + 7 + (5/x-1).
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List 3 points that are on the line 5y= 3x - 7.
List 3 points that are on the line 5y= 3x - 7.
We know that the y-intercept is (0, -7)
We know that slope = 3 and slope = rise / run or 3 y for every 1 x
We can add 1 for the x and 3 for the y: (0, -7) to (1, -4).
We can do that again:add 1 for the x and 3 for the y: (1, -4) to (2, -1).
(0, -7)
(1, -4)
(2, -1)
answer this question please
a. Absolute value function the reference beam is g(x) = |8x/5|.
b. g(x) = +8x/5 ; x < 5 and g(x) = -8x/5 > 5.
What is defined as the absolute value function?An absolute value function is one that has an algebraic expression enclosed in absolute value symbols. Remember that a number's absolute value is its distance from 0 just on number line.For the given function;
Part a: The reference beam is passing from the points;
(x₁, y₁) = (5, 8)
(x₂, y₂) = (0, 0)
Then the slope of the line is -
m = (y₂ - y₁)/(x₂ - x₁)
Put the values ;
m = (0 - 8)/(0 - 5)
m = 8/5
The equation of the line is;
y - y₁ = m(x - x₁)
Put the values;
y - 0 = 8/5(x - 0)
y = 8x/5
Or in absolute modulus function for the path of reference beam; y = |8x/5|.
Part b: absolute function in terms of piecewise function;
g(x) = +8x/5 ; x < 5 as the slope is increasing.
and g(x) = -8x/5 > 5.; as the slope is decreasing.
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The recipe for junk crunchies requires a total of 8 cups of sugar and flour together. If the recipe had called for 1/4 cup more sugar, the amount of sugar would be half the amount of flour. How many cups of sugar does the recipe call for?
The recipe of the junk calls for 16/7 cups of sugar
How to determine the number of cups of sugar in the recipe?From the question, the given parameters are:
Total number of cups = 8
Let the number of cups of sugar be x and the number of cups of flour be y
So, we have the following equation
x + y = 8
Also, we have:
The recipe uses 1/4 cup more sugar, so the amount of sugar equals half the amount of flour
This means that
(1 + 1/4) * x = 1/2 * y
Evaluate the sum and the products
So, we have
5/4x = 1/2y
Make y the subject
y = 5/2x
Substitute y = 5/2x in x + y = 8
x + 5/2x = 8
Evaluate the sum
3.5x = 8
Divide by 3.5
x = 16/7
Hence, the cups of sugar is 16/7
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The sum of 5 times the first number and 6 times the second number is 235. The difference between 7 times the first number and 17 is 2 times the second number. Find both the numbers.
a) Using the variable x to represent the first number and y to represent the second number, write the information given in the first sentence, "The sum of 5 times the first number and 6 times the second number is 235."
Correct
b) Using the variable x to represent the first number and y to represent the second number, write the information given in the second sentence, "The difference between 7 times the first number and 17 is 2 times the second number."
Correct
c) Find both the numbers.
The first number is:
Correct
The second number is:
Correct
By using the elimination method, the numbers are 11 and 30
Consider the first number as x and the second number as y
Sum of 5 times the first number and 6 times the second number is 235
The linear equation will be
5x+6y = 235
The difference between 7 times the first number and 17 is 2 times the second number
7x-17 = 2y
Rearrange the terms
7x-2y = 17
The both equations are
5x+6y = 235
7x-2y = 17
Multiply the first equation by 2 and second equation by 6
10x+12y = 470
42x-12y = 102
Here we have to use the elimination method
Add both equation and y term will cancelled
10x+42x = 470+102
52x = 572
x = 11
Substitute the value of x in any equation
5x+6y =235
5(11)+6y = 235
55+6y = 235
6y = 180
y = 30
Hence, by using the elimination method, the numbers are 11 and 30
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What is the value of c?
14=-2c-6-3c
Answer:
-4
Step-by-step explanation:
14= -5c-6
+6 +6
________
20 = -5c
÷-5 ÷-5
________
-4 = c
The graph shows the number of states and Washington, DC, within each range of electoral votes for the 2020 presidential election. Which interval contains 11 states? Check all that apply.
0 to 3
3 to 6
6 to 9
9 to 12
12 to 15
15 to 18
18 to 21
Based on the number of states and their electoral votes in the 2020 presidential election, the intervals with 11 states are:
3 to 66 to 9How to find the intervals?The graph on electoral votes by state in 202, gives the number of electoral votes as a range from 0 to 21 but in intervals of 3.
In 0 - 3 electoral votes, the number of states is 16.
In 3 - 6 electoral vote interval, number of states is 11.
In 6 - 9 electoral vote interval, number of states is 11.
In 9 - 12 electoral vote interval, number of states is 3.
In 12 - 15 electoral vote interval, number of states is 3.
In 15 - 18 electoral vote interval, number of states is 3.
In 18 - 21 electoral vote interval, number of states is 4.
The two intervals with 11 states are therefore 3 - 6 and 6 - 9.
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[tex]5(\frac{x+5}{9} )-9[/tex]
Answer:
I don't know
Step-by-step explanation:
I don't know
Solve each equation mentally.
a. ½ ·x = 1
b.x = 1
c. 1 + 1 = x
A.) [tex]x = 2[/tex]
B.) [tex]x=1[/tex] (Nothing further can be done with this.)
C.) [tex]x=2[/tex]
_____________________________________
Hope this helps! If not, feel free to comment below on the matter and I'll see what else I can do to assist you further. If it did help though, feel free to lmk! Thanks and good luck!
The total body surface area, or BSA, of a human is difficult to calculate. There are various models that estimate BSA based on a person's weight and height. One simpler model is
the height in the first case will be 191 cm and the weight in the second case will be 106 kg.
We are given the function as:
BSA = √( w h / 3600)
where:
h = height
w = weight
BSA = body surface area
1) Now, for w = 68 kg and BSA = 1.9, we get the height as:
1.9 = √( (68) h / 3600)
3.61 = 68 h / 3600
12,996 = 68 h
h = 12996 / 68
h = 191.12 cm
h ≈ 191 cm
2) for h = 165 cm and BSA = 2.2, we get the weight as:
2.2 = √( w (165) / 3600)
4.48 = 165 w / 3600
17424 = 165 w
w = 17424/ 165
w = 105.6 kg.
w ≈ 106 kg
Therefore, we get that, the height in the first case will be 191 cm and the weight in the second case will be 106 kg.
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based on the infomation in the table , is the cost of the apples proportional to the weight of apples?
pounds of apples cost of apples
2 3.76
3 5.64
4 7.53
5 9.40
The given table shows that does not show a proportional relationship, as the ratio between the output and the input is not the same for all terms of the table.
What is a direct proportional relationship?A direct proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality k, as defined below.
y = kx
In this problem, we have that:
The input x is the number of pounds of apples.The output y is the cost of the apples.To verify if it shows a proportional relationship, we have to divide the output by the input in each case, hence:
k = 3.76/2 = 1.88.k = 5.64/3 = 1.88.k = 7.53/4 = 1.8825.k = 9.40/5 = 1.88.Due to the different constant for 4 pounds, the table does not show a proportional relationship,
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6. The table shows the equations Ms. Valer discussed in math class
Equations
6 x 10° 6
6 10¹ -60
6 x 10-600
6x 10³6,000
Explain the pattern of zeros in the product when multiplying
by powers of 10.
The product when multiplying by powers of 10 is 6 ×[tex]10^{10}[/tex] = 60000000000
What is multiplication ?The fundamental concept of repeatedly adding the same number is embodied in the process of multiplication. The outcome of multiplying two or more numbers is known as the product of those numbers, and the factors that are multiplied are referred to as the factors. The process of repeatedly adding the same number is made easier by multiplication.
Finding the product of two or more numbers is done by multiplication. It is a fundamental mathematical operation that is frequently applied in everyday situations. When combining groups of similar sizes, multiplication is utilized.
Given that :The table shows the equations Ms. Valer discussed in math class Equations
6 x 10°= 6
6× 10¹ =60
6 x 10=600
6x 10³=6,000
6 ×[tex]10^{10}[/tex] = 60000000000
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y varies directly with x, and y = 40in when x = 15in
If y varies directly with x, that means there is going to be a constant that connects both the x and y variable.
[tex]\begin{gathered} \text{When x=15, and y=40, then} \\ k=\frac{y}{x} \\ k=\frac{40}{15} \\ k=\frac{8}{3} \\ \text{Therefore, the equation is going to be;} \\ y=\frac{8}{3}x \end{gathered}[/tex]The appropriate direct variation equation is stated above, and that is;
y = 8/3x
A restaurant is having a deal for Valentine's day and is offering a 4-course meal for $27.00. If there is a sales tax of 8 percent, what is the actual cost of the meal?
Answer:
$29.16
Step-by-step explanation:
You want the total cost of a $27 meal after 8% tax is added.
TaxThe amount of added tax is found by multiplying the meal cost by the tax rate:
0.08 × $27.00 = $2.16
TotalThe total cost is the meal cost plus the tax:
$27 +2.16 = $29.16 . . . . actual cost of the meal
__
Additional comment
The sum 27 + 0.08×27 can also be found by factoring out the 27:
= 27(1 +0.08) = 27×1.08
what is the slope and y intercept of 4x + 7y=18?
Answer:
-4/7, 18/7
Step-by-step explanation:
[tex]4x+7y=18 \\ \\ 7y=-4x+18 \\ \\ y=-\frac{4}{7}x+\frac{18}{7}[/tex]