Two lines are perpendicular if the product of their slopes is equal to -1.
Find the slope of the given line. Then, use that result to find the slope of a line perpendicular to it. Use the slope of the line perpendicular to the given line to find the equation of the one that passes through the point (-8,7).
To find the slope of the given line, write it in slope-intercept form by isolating y:
[tex]\begin{gathered} y+1=-x \\ \Rightarrow y=-x-1 \end{gathered}[/tex]The coefficient of x is -1. Then, the slope of the given line is -1.
Let m be the line perpendicular to y+1=-x.
Since the product of the slopes of perpendicular lines is equal to -1, then:
[tex]\begin{gathered} -1\times m=-1 \\ \Rightarrow m=\frac{-1}{-1} \\ \therefore m=1 \end{gathered}[/tex]The equation of a line with slope m that passes through the point (a,b) in slope-point form is:
[tex]y=m(x-a)+b[/tex]Replace m=1, a=-8 and b=7 to find the equation of the line perpendicular to y+1=-x that passes through the point (-8,7):
[tex]\begin{gathered} y=1(x-(-8))+7 \\ \Rightarrow y=(x+8)+7 \\ \therefore y=x+15 \end{gathered}[/tex]Therefore, the equation of the line perpendicular to y+1=-x that passes through (-8,7) is:
[tex]y=x+15[/tex]Hello! Question is in photo please help me out.
The value of x for the given similar triangle will be 5 units.
What is the similarity?If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.
If two figures have three sides similar then they will be similar by side-by-side property which is written as SSS.
From the similarity concept, the value of x will be calculated as:-
( 10 / x ) = ( 6 / 3 )
10 = 2x
x = 10 / 2
x = 5
Therefore, the value of x for the given similar triangle will be 5 units.
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A sequence is defined recursively using the formula f(n+1) =-0.5f(n) . If the first term of the sequence is 120, what is f(5)?
−15
−7.5
7.5
15
Suppose we have the recursive formula of sequence, [tex]\displaystyle{f(n+1)=0.5f(n)}[/tex]. From this formula, we know that:
[tex]\displaystyle{f(2)=0.5f(1)}\\\\\displaystyle{f(3)=0.5f(2)}\\\\\displaystyle{f(4)=0.5f(3)}\\\\\displaystyle{f(5)=0.5f(4)}[/tex]
Since the first term of sequence is 120. Therefore, [tex]\displaystyle{f(1)=120}[/tex]. Since [tex]\displaystyle{f(4)=0.5f(3)}[/tex] then substitute in [tex]\displaystyle f(5)[/tex]:
[tex]\displaystyle{f(5)=0.5\cdot 0.5f(3)}[/tex]
Then substitute f(3) down to f(1):
[tex]\displaystyle{f(5)=0.5\cdot 0.5 \cdot 0.5 \cdot 0.5 \cdot 120}\\\\\displaystyle{f(5)=(0.5)^4\cdot 120}\\\\\displaystyle{f(5)=7.5}[/tex]
Therefore, f(5) = 7.5
Solve for x:
3(x+1)-22+13=12
Answer:
x=6
Step-by-step explanation:
3 (x+1) -22 +13=12
3x+3 -22+13=12
3x+3-9=12
3x-6= 12
3x= 12+6
3x= 18
x= 18/3
x= 6
Pick a number 1 through 20. Now do it again.Now do it a third time. I am going to writedown my prediction of what numbers youpicked. Assuming no magic was used, what isthe probability I guessed right? Put youranswer in fraction form. (Note: Numbers CANbe used more than once.)
There are 20 numbers to choose from. Thus, the total sample space is 20.
If you choose one number, the probability of choosing that number is:
[tex]\frac{1}{20}[/tex]Now, if after choosing one number in the first round, you proceed to choose another number in the second round.
The probability of choosing a number for this second round will be:
[tex]\frac{1}{20}[/tex]Note that you are allowed to repeat numbers, so therefore, this is a probability problem with replacement.
For the third round, you choose another number from 1 to 20. The probability is the same as the previous two:
[tex]\frac{1}{20}[/tex]The probability that a person guesses these 3 numbers is the same as the probability of actually choosing the numbers randomly.
Thus the final answer:
[tex]\frac{1}{20}\times\frac{1}{20}\times\frac{1}{20}=\frac{1}{8000}[/tex]Therefore, the final answer is:
[tex]\frac{1}{8000}[/tex]ABC is shown . D is a point on AB,AC =7, AD=6, and , BC=18.
ok
AC = 7
AD = 6
BC = 18
It must be 12, because the sum of two sides of a triangle is higher than the other side.
And 6 + 5 = 11
AB + AC = 11 + 7 = 18
A crate of medicine with a density of 2,200 kilograms per cubic meter will be shipped from England to the U.S. What is the crate's density in pounds per cubic foot?
The crate's density in pounds per cubic foot = 137.28 lb/ft³
What is density?Density is defined as the quantity that shows the relationship between the mass and volume of an object which is measured in kilograms per cubic meter or in pounds per cubic foot.
The density of the given crate of medicine = 2,200 kg / m³
To convert to pounds per cubic foot;
1 kg/m³ = 0.0624 lb/ft³
2,200 kg/m³ = X
Make X the subject of formula;
X = 2,200 × 0.0624/1
X = 137.28 lb/ft³
Therefore, when converter to pounds per cubic foot the density of the crate of the medicine= 137.28 lb/ft³.
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The five number summary of a dataset is given as
0, 4, 8, 12, 17
An observation is considered an outlier if it is below:
An observation is considered an outlier if it is above:
An observation is considered an outlier if it is below -16.75
An observation is considered an outlier if it is above 33.25
Extremely low or high values in a data set are considered outliers. Outliers are a product of statistical observational errors and variability. They frequently produce significant statistical issues, hence they are frequently left out of the study.
We must think about if it meets the following criteria in order to identify an outlier:
Q₁ - 1.5 (IQQ) ⇒ for lower value
Q₃ + 1.5 (IQR) ⇒ for higher value
Q₁ stands for the lower quantile, Q₃ for the higher quantile, and IQR for the inter-quantile range. Using the previous data,
Q₁ and Q₃ come from:
Q₁ = (0 + 4) / 2 = 4 / 2 = 2
Q₃ = (12 + 17) / 2 = 29 / 2 = 14.5
IQR = Q₃ - Q₁ = 14.5 - 2 = 12.5
(a) An observation is considered an outlier if it is below:
Q₁ - 1.5 (IQR) = 2 - 1.5 (12.5) = 2 - 18.75 = -16.75
An outlier is a number that is less than -16.75
(b) An observation is considered an outlier if it is above:
Q₃ + 1.5 (IQR) = 14.5 + 1.5 (12.5) = 14.5 + 18.75 = 33.25
An outlier is a number that is greater than 33.25
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A doll’s house has an original price of $x. It is sold for $350 after its original price has been decreased by 5% and then by 10%. Find x.
Answer:
Step-by-step explanation:
0.95x*0.9=0.855
350/0.855=409.35
x=409.35
Please explain and help me get the correct answer. Thank you. Practice work that is not graded.
First, from the formula given we solve the equation for D:
[tex]\begin{gathered} 4PD=D^2LN\pi, \\ \frac{4PD}{LN\pi}=D^2, \\ \sqrt{\frac{4PD}{LN\pi}}=D^{}. \end{gathered}[/tex]Now, substituting the given data:
(a) PD=405 cu in, L=4.7 in, and N=7,
in the above equation we get:
[tex]D=\sqrt[]{\frac{4\times405}{4.7\times7\times\pi}}in=\sqrt[]{15.6736175}in\approx3.96\text{ in}[/tex](b) PD=399.4 cu in, L=2 in, and N=6,
in the above equation we get:
[tex]D=\sqrt[]{\frac{4\times399.4}{2\times6\times\pi}}in=\sqrt[]{42.37765618}in\approx6.51\text{ in}[/tex]Answer:
(a) 3.96 in.
(b) 6.51 in.
After 12 weeks, how much more will he made in sales of buttered popcorn than the sales of caramel popcorn
We have two functions for the sales of popcorn:
[tex]\begin{gathered} B(w)=8w+9 \\ C(w)=6w-1 \end{gathered}[/tex]being B(w) the number of buttered popcorn sold over "w" weeks and C(w) the number of caramel popcorn sold over "w" weeks.
We now have to calculate how much more he would have made after 12 weeks in sales of buttered popcorn than the sales of caramel popcorn.
We can calculate this as the difference of sales of buttered popcorn and the sales of caramel popcorn for w = 12.
Each sale will be the product of the cost per unit (in this case, is $11 for both types) and the number of units sold (B(w) or C(w), depending on the ytpe of popcorn).
Then, we can calculate the difference in sales as:
[tex]\begin{gathered} D=11\cdot B(12)-11\cdot C(12) \\ D=11\cdot(8\cdot12+9)-11\cdot(6\cdot12-1) \\ D=11\cdot(96+9)-11\cdot(72-1) \\ D=11\cdot105-11\cdot71 \\ D=1155-781 \\ D=374 \end{gathered}[/tex]Answer: he would have made $374 more in sales from buttered popcorn than from caramel popcorn.
Find the solution of the system of equations.6x – 3y = -303x – 6y = 12
6x - 3y = -30 -------------------------------(1)
3x - 6y = 12 ---------------------------------(2)
Multiply through equation(1) by 3 and then multiply through equation (2) by 6
18x - 9y = - 90 ---------------------------------(3)
18x - 36y = 72 ----------------------------------(4)
subtract equation (4) from equation (3)
Elijah and his brother ran a race. Elijah reached the finish line in 60.26 seconds and his brother reached the finish line 6 seconds later. How long did it take Elijah's brother to run the race?
Evaluate. 43⋅(100÷25)−50 Enter your answer in the box.
Answer:
122
Step-by-step explanation:
43 * (100/25) - 50
43 * 4 - 50
172 - 50
122
Hope this helps! :)
A combined total of 598 hamburgers and cheeseburgers were sold. There were 52 fewer cheeseburgers sold in hamburgers. How many hamburgers were sold
Find the value of f(7) y = f(x) 10 6 4 -10 -8 -6 -4. -2 4 10 -4 -6 GO -10 Answer: Submit Answer
Answer:
f(7) = -5
Step-by-step explanation:
To find f(7), we would need to first find on the graph 7 on the x-axis.
We would next need to see where 7 on the x-axis meets with the graph. In this case, we would go down.
Now that we see where 7 on the x-axis meets with the graph, we would now look at the number on the y- axis that spot on the graph matches with.
In this case, we would go left from the graph all the way to the y-axis, where the correspo ding number would be -5.
Quadrilatral ABCD has the following vertices
A(-6,-2)
B(-4,4)
C(8,1)
D(6,-6)
Angle a is right angle
is ABCD a rectangle
pls help i will give brainliest
From the calculations below, we can tell that quadrilateral ABCD is not a rectangle because AB is not parallel to CD
How to Identify a rectangle?
We are given that the quadrilateral is ABCD with the vertices as;
A(-6,-2)
B(-4,4)
C(8,1)
D(6,-6)
We are further told that Angle A is a right angle. Thus;
AB must be perpendicular to AD.
Secondly, for ABCD to be a rectangle, AB must be parallel to CD. Thus;
By slope formula, for AB and CD are gotten from the formula;
Slope = (y₂ - y₁)/(x₂ - x₁)
Slope of CD = (-6 - 1)/(6 - 8)
Slope of CD = -7/-2 = 7/2
Slope of AB = (4 - (-2))/(-4 - (-6))
Slope of AB = 6/2
Slope of AB = 3
Since Slope of AB and AC are not equal then ABCD is not a rectangle.
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For each relation, decide whether or not it is a function.
Relation 1 and Relation 3 are functions while Relation 2 and Relation 4 are not functions.
Function is a relation which maps a set to another set with some criteria.
It includes a property that one element of the domain set should only be related to exactly one element in the range set. That is, same element from the domain cannot be related to different elements in the range. Also all elements in the domain should have images in the range also.
Now we will check all the relations given one-by-one.
In relation 1, the relations are:
Chair ---------> 0
Pencil --------> 0
Paper ---------> 4
Star ------------> 1
Here All the domain elements are mapped only once to one element from the range. So it is a function.
In relation 2, the relations are:
4 ----------------> 5
4 ----------------> 9
0 ----------------> -9
1 -----------------> 4
8 -----------------> -4
Here 4 is mapped to both 5 and 9. So it does not satisfy the definition of a function and hence is not an function.
In relation 3, the relations are:
z -----------------> c
k -----------------> a
a -----------------> k
c ------------------> c
Here also all elements in the domain are mapped only once to an element from the range. So it is a function.
In relation 4, the relations are:
-4 -----------------> m
-4 -----------------> d
-4 -----------------> c
9 -----------------> s
Here, -4 is mapped to m, d and s. So it cannot be a function as it has more than one images.
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The quotient of 1 and the square of a number. Write it as an expression
Answer:
1 ÷ [tex]\sqrt{n\\}[/tex] = x
Step-by-step explanation:
For the given, "the quotient of 1 and the square of a number", the expression is 1+√n
What is a mathematical expression?
A sentence qualifies as a mathematical expression if it comprises one or more mathematical operations, at least two numbers, Mathematicians have the ability to multiply, divide, add, and subtract. A mathematical operator, a number or variable, and an expression make up an expression.
The phrase "The quotient of 1 and the square of an integer" is presented.
The dividend and the amount being divided by the divisor are, respectively, referred to as the dividend and the amount being divided by it. The quotient is created by dividing the result.
If n is the number the expression can be written as,
=1+√n
Thus, for the given expression the expression is 1+√n.
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Convert compressions to simplified faction or integer. If it’s not a real number, enter None
Given an expression:
[tex](-81)^{\frac{1}{4}}[/tex]We have to simplify the expression, if it does not result in a real number then the answer is NONE.
Let:
[tex]x=(-81)^{\frac{1}{4}}[/tex]Then,
[tex]\begin{gathered} x=(-81)^{\frac{1}{4}} \\ \Rightarrow x^4=((-81)^{\frac{1}{4}})^4 \\ \Rightarrow x^4=-81 \end{gathered}[/tex]There is no real number whose power 4 is a negative number.
Thus, the answer is not a real number. The answer is NONE.
Pythagorean Theorem• Create a real-world problem involving threelengths that form a right triangle• Give the measurement of the "legs", then solvefor the missing side
SOLUTION
Find the perimeter of a rectangle whose length is 150 m and the diagonal is 170 m.
The problem can be modeled using the figure below
Notice that the triangle formed is a right triangle:
Therefore using Pythagorean theorem it follows:
[tex]x^2+150^2=170^2[/tex]Solve for x
[tex]\begin{gathered} x^2=170^2-150^2 \\ x^2=6400 \\ x=80 \end{gathered}[/tex]Therefore the other leg no miss
I NEED HELP ON TRIG PROOFS, SOMEONE PLEASE HELP!!!! URGENT!!!!
Step-by-step explanation:
:)))))))))))))))))))))
A bag contains 42 red, 45 green, 20 yellow, and 32 purple candies. You pick one candy at random. Find the probability that it is not yellow
P(not yellow)
The probability that it is not yellow candies will be 119/139.
What is mean by Probability?
The term probability refers to the likelihood of an event occurring.
Given that;
A bag contains;
Number of red candies = 42
Number of green candies = 45
Number of yellow candies = 20
Number of purple candies = 32
Now,
Total number of candies in a bag = 42 + 45 + 20 + 32
= 139
And, The number of candies in a bag not contain yellow candy
= 139 - 20
= 119
Thus, The probability that it is not yellow candies will be;
Probability = Number of not yellow candies / Total candies
= 109 / 139
Therefore, The probability that it is not yellow candies will be 119/139.
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Bill Jensen deposits $8500 with Bank of America in an investment paying 5% compounded semiannually. Find the compound amount in 6 years
Given:
Initial deposit = $8500
rate of interest = 5% compounded annuallly
time (t) = 6 years
If Ao is invested at an annual interest rate r and compounded semiannually, the amount At after t years is given by the formula:
[tex]A_t\text{ = }A_0(1\text{ + }\frac{r}{2})^{2t}[/tex]The compound amount in 6 years:
[tex]A_t\text{ = 8500 }\times\text{ (1 + }\frac{0.05}{2})^{2\times6}[/tex]Simplifying we have:
[tex]\begin{gathered} A_t\text{ = 8500 }\times1.025^{12} \\ =\text{ 11431.56} \end{gathered}[/tex]Answer:
$11431.56
Which graph best represents 16≤x²+y²≤25
The most appropriate choice for annular region will be given by
This graph represents an annular region shown in the figure
What is annular region?
Annular region represents the space between two concentric circles of different radii.
Equation of annular region centered at (0, 0) is
[tex]a^2 \leq x^2+y^2\leq b^2[/tex]
Here,
[tex]x^2 + y^2\geq 16\\x^2 + y^2 \geq 4^2\\[/tex]
It denotes the outside of a circle of radius 4 centered at (0, 0)
[tex]x^2 + y^2\leq 25\\x^2 + y^2 \leq 5^2\\[/tex]
It denotes the inside of a circle of radius 5 centered at (0, 0)
So the complete graph is being attached here.
This region is known as annular region
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Find the percent change. Round to the nearest tenth of a percent when necessary. From 50 to 94.
Percent change of 88%
1) Consider 50 as equivalent to 100% as well as 94 to x.
50 ----------- 100%
94 ------------ x
2) Now we can set the ratios and cross multiply then:
[tex]\begin{gathered} \frac{50}{94}=\frac{100}{x} \\ 50x=94\cdot100 \\ 50x=9400 \\ \frac{50x}{50}=\frac{9400}{50} \\ x=188 \\ \end{gathered}[/tex]So 94 corresponds to 188%. Then we can see that there was an increase. Since 94 >50.
But we need to subtract from 100% to find out the percent change from 50 to 94.
188%-100%= 88%
3) Hence, the answer is an increase of 88%
Solve for X picture include
The sum of angles of a triangle is equal to 180 degree.
Determine the value of x, by using angle sum for the triangle.
[tex]\begin{gathered} 2x-4+3x-4+3x-4=180 \\ 8x=180+12 \\ x=\frac{192}{8} \\ =24 \end{gathered}[/tex]The value of x is 24
Write and equation for each of the following problems and solve. (40 points each)3. The length of a rectangle is 5 cm more than three times the width. If the width is 12, what is thelength of the rectangle?
It is given that,
The length of a rectangle is 5 cm more than three times the width.
That is, l=3w+5
Put width, w=12.
Therefore, the length becomes,
l=3(12)+5
l=36+5
l=41 cm.
Hence, the length of the rectangle is 41 cm.
Help solve this problem it's 8th grade math identifying coordinates on a graph
Answer:
C -9, -4
E -8, 4
G-4, 0
I-6, -8
B0, 0
D-16, 4
F-2, 9
H0, 7
J9,-2
A sequence is defined by the recursive formula f(n + 1) = 1.56(0). Which sequence could be generated using the formula? 0 -12 -18, -27 ! EE 0 -20, 30, -45, -18, -16.5, -15, ... 0-16, -17.5, -19, ...
f(n+1) is
[tex]f(n+1)=\frac{3}{2}^nf(n-(n-1)[/tex]Therefore, substitutig, we get, option c.
Write two expressions that represent the volume of the cube, one with exponents and one without. The side of the cube is the fraction 3/5.
(3/5)^3 and (3/5 × 3/5 ×3/5) are the two expressions that represent the volume of the cube having side 3/5.
1.) For the first expression with exponents:
(3/5)to the power of 3 can be written as , where the number 3/5 is called the base, and 3 is the power or exponent of the expression. So (3/5) times 3 .
Where, Side of the cube (a) = 3/5
⇒ (3/5)^3
⇒ 0.216 cube.units
2.) For the second expression without exponents:
The formula of volume of the cube is given by volume(side) =a*a*a, where a is the length of its sides or edges.
Cube ⇒ ( 3/5 × 3/5 × 3/5)
Cube ⇒ 0.216 cube.units
Cube of having side (3/5) = 0.216 cube.units
Hence, (3/5)^3 and (3/5 × 3/5 ×3/5) are the two expressions that represent the volume of the cube having side 3/5 .
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