The equation of a line is: y = 4/7x - 12Which equation would have a line that is perpendicular to this line?1. y = - 4/7x - 12. y = - 7/4x - 53. y = 7/4x - 84. y = 4/7x - 2
Answers
Let's recall the framework of the equation of a line:
We say that two lines are perpendicular if the slope of one line is minus the multiplicative inverse of the slope of the other one; mathematically, this amounts to the following equation:
[tex]m_1=-\frac{1}{m_2}.\leftarrow\begin{cases}m_1=\text{Slope of one line} \\ m_2=\text{ Slope of the other line}\end{cases}[/tex]In this case, the slope of our line is 4/7. Then the slope (m) of any line perpendicular to it must satisfy
[tex]m=-\frac{1}{\frac{4}{7}}\text{.}[/tex]Solving this equation for m, we get
[tex]\begin{gathered} m=-\frac{1}{\frac{4}{7}}, \\ m=-\frac{\frac{1}{1}}{\frac{4}{7}}, \\ m=-\frac{1}{1}\cdot\frac{7}{4},\leftarrow\text{ Flipping rule when dividing fractions} \\ m=-\frac{7}{4}. \end{gathered}[/tex]AnswerThe answer is 2.
Related Questions
Solve the equation p + 7 = −15 for p. −22 22 −8 8 need help
Answers
An equation is a collection of variables and constants. The value of p for the given equation p + 7 = −15 is p = -22 so option (A) is correct.
What is the equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
The equation must be constrained with some constraints.
As per the given equation,
p + 7 = -15
Subtract both sides by 7
p + 7 - 7 = -15 - 7
p + 0 = -22
p = -22
Hence "An equation is a collection of variables and constants. The value of p for the given equation p + 7 = −15 is p = -22 so option (A) is correct".
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please break down 145 + 216 with the hundreds tens and ones.
Answers
Step 1:
Sum the numbers
[tex]145+216=361[/tex]Step 2:
Express the number in Hundreds, Tens, and Ones
3 has a value of 300
6 has a value of 60
1 has a value of 1
Therefore, to express 361 in hundreds, tens and ones
Help me to find the measure of angles 1 2 and 3!
Answers
Given:
Given the diagram
Required: The measure of angles 1, 2 and 3.
Explanation:
The sum of interior angles of a triangle is 180 degrees. So,
[tex]\begin{gathered} x+55^o+70^o=180^o \\ x=180^o-55^o-70^o \\ =55\degree \end{gathered}[/tex]The angles x and 1 are supplementary angles, that is, the sum of angles 1 and x gives 180 degrees.
[tex]\begin{gathered} x+m\angle1=180\degree \\ 55\degree+m\angle1=180\degree \\ m\angle1=180\degree-55\degree \\ =125\degree \end{gathered}[/tex]The angle 2 is the opposite angle of 55 degrees. Hence angle 2 equals 55 degrees, that is,
[tex]m\angle2=55\degree[/tex]Angle y and 150 degrees are supplementary angles. So,
[tex]\begin{gathered} y+150\degree=180\degree \\ y=180\degree-150\degree \\ =30\degree \end{gathered}[/tex]The sum of the interior angles of a triangle equals 180 degrees.
[tex]\begin{gathered} m\angle2+m\angle3+y=180\degree \\ 55\degree+m\angle3+30\degree=180\degree \\ m\angle3=180\degree-55\degree-30\degree \\ =95\degree \end{gathered}[/tex]Final Answer:
[tex]m\angle1=125\degree,m\angle2=55\degree,m\angle3=95\degree[/tex]The angel pitch of a roof is safest when measuring between 18 - 27. According to these guidelines, is the roof pictured in the image safe? I cannot figure out where to start with this question nor how to solve it.
Answers
we know that
YZ=RV+VQ ----> by addition segments postulate
substitute given values
30=RV+15
so
RV=30-15=15 ft
that means
Point V is the midpoint of the segment RQ
triangle RPQ is an isosceles triangle
mFind out the value of angle x
tan(x)=4/15 ------> by TOA
x=tan^-1(4/15)
x=14.93 degrees
The angle x is not between 18 - 27
therefore
The roof Is not safeWhat is the concentration of hydrogen ions in a solution with a pH of 2?
Answers
When pH is 2, the hydrogen ion concentration in [tex]litre^{-1}[/tex] is [tex]10^{-2}[/tex]
What is pH?The pH value of water indicates how acidic or basic it is. The negative log of the hydrogen ion concentration is defined as pH. The pH scale starts from 0 and ends at 14. A pH of 7 is considered neutral because pure water has a pH of exactly 7. Acidic values are less than 7; basic or alkaline values are greater than 7.
Given that,
pH = 2 for HCl acid
We know that,
The relation between concentration of acid and pH is,
pH = -log[[tex]H^{+}[/tex]]
2 = -log[[tex]H^{+}[/tex]]
[tex][H^{+} ][/tex] = [tex]10^{-2}[/tex]
Hence, the hydrogen ion concentration in a solution with a pH of 2 is [tex]10^{-2}[/tex].
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For each system choose the best description of a solution if applicable give the solution
Answers
ANSWER
The system has no solution
EXPLANATION
We want to find the solution to the system of equations given:
[tex]\begin{gathered} x+4y-4=0 \\ -x-4y=4 \end{gathered}[/tex]From the first equation, make x the subject of the formula:
[tex]x=4-4y[/tex]Substitute that into the second equation and simplify:
[tex]\begin{gathered} -(4-4y)-4y=4 \\ -4+4y-4y=4 \\ \Rightarrow4y-4y=4+4 \\ 0=8 \end{gathered}[/tex]As we can see, the two sides of the equality sign have two different values.
This implies that the system of equations has no solution.
After 6 weeks, a plant is 11 inches tall. After 8 weeks, it is 13 inches tall. After 10 weeks, it is 15 inches tall.
Write an equation to describe the relationship between the height of the plant, y, and the number of weeks it has been growing, x
Answers
The equation to describe the relationship between the height of the plant and the number of weeks is
y = x + 5
Given,
The height of the plant = x
The number of weeks = y
The height of plant at 6th week = 11 inches
The height of plant at 8th week = 13 inches
The height of plant at 10th week = 15 inches
We have to find the equation to describe the relationship between the height of the plant and the number of weeks.
Lets see,
x = 6 and y = 11, y – x = 11 – 6 = 5
x = 8 and y = 13, y – x = 13 – 8 = 5
x = 10 and y = 15, y – x = 15 – 10 = 5
That is,
y – x = 5.
y = x + 5
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(g) distance from the x-axis is equal to the distance to the y-axis.
Answers
Part a
Remember that the ordinate is the y-coordinate and the abscisa is the x-coordinate
so
(x, 2x+1)
y=2x+1
Part b
[tex](\frac{1}{2}y^2,y)[/tex]x=(1/2)y^2
Part c
x^2+y^2=25
Part e
y=2
Part f
x=7
Part g
x=y
Part h
[tex]\sqrt[\square]{x^2+y^2}=5[/tex]Part i
[tex]\sqrt[\square]{(x-2)^2+(y-3)^2}=5[/tex]f(x)=4x^{2}-8x-5 f(x)=4x 2 −8x−5 \text{Find }f(-7) Find f(−7)
Answers
The value of given quadratic equation at -7 is 247.
What is quadratic equation?
The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics. It is expressed in the form of:
ax² + bx + c = 0
where x is the unknown variable and a, b and c are the constant terms.
given ,f(x) = [tex]4x^{2} -8x-5[/tex] to find f(-7)
f(-7)= 4(49)-8(-7)-5
=196+56-5
=247
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TRIGONOMETRY Find the magnitude and the direction of the resultant vector
Answers
Step 1:
Write the given vectors
[tex]\begin{gathered} \bar{V}\text{ = ( 10 , 9 )} \\ \bar{W}\text{ = (-6 , -2 )} \end{gathered}[/tex]Step 2
Resultant vector = [ 10 + (-6) , 9 + (-2) ]
= ( 4 , 7 )
Resultant vector = 4i + 7j
Step 3
[tex]\begin{gathered} \text{Magnitude = }\sqrt[]{4^2+7^2} \\ \text{Magnitude = }\sqrt[]{16\text{ + 49}} \\ \text{Magnitude = }\sqrt[]{65} \\ \text{Magnitude = 8.1} \end{gathered}[/tex]Step 4:
[tex]\begin{gathered} \text{Direction }\theta=tan^{-1}(\frac{4}{7}) \\ \text{Direction = 29.7} \end{gathered}[/tex]Find the domain & range(Select the correct answer below & fill in the box to complete the choice.)A. The domain is the interval ____(Write your answer in interval notation.)B. The domain is the set {_____}(Use a comma to separate answers as needed. Write each answer only once.)——————————————————A. The range is the set {_____}(Use a comma to separate answers as needed. Write each answer only once.)B. The range is the interval ____(Write your answer in interval notation.)
Answers
The domain of a function is the set of x values the function uses as inputs; from a graph the domain is the x-values that the graph take on the x-axis; in this case, since we have an infinite amount of x-valeus the function uses we will write the domain as an interval. The domain is:
[tex](-\infty,\infty)[/tex]Similarly, the range is the set of values the function takes on the y-axis, from the graph we notice that the range is:
[tex](-\infty,6\rbrack[/tex]
Which of the following represent(s) the commutative law of addition?1.6 X 5 = 5 x62.6 + 5 = 5 + 63.6–5 = 5-64.2 and 33 only1 and 42 only
Answers
Given:
Commutative law of addition.
[tex]6+5=5+6[/tex]2 only is the correct answer.
A coffee shop collected the following information regarding purchases from 110 of its customers. 67 purchased coffee. 41 purchased donuts. 19 purchased coffee and donuts. Complete parts a) through c) . a) Of those surveyed, how many purchased only coffee? (Type a whole number.)
Answers
We have the next information
Let X be the number of customer purchased coffee
Let Y be the number of customer pwho urchased donuts
X∩Y Then is the number of customers who purchased both coffee and donuts
X∪Y is the number of customers who purchased both coffee or donuts
The number of customers who purchase only coffee is
[tex]67-19=48[/tex]48 customers purchased only coffee
The number of customers who purchase only donuts is
[tex]41-19=22[/tex]22 customers purchased only donuts
In order to know how many customers did not purchase either of these items
First we will calculate the customers that purchase something
[tex]67+41-19=89[/tex]then we know that the total number of customers is 110
[tex]110-89=21[/tex]21 customers did not purchase either of these items
Can anyone put on these on a table
y=4x-7 and y + x =6
Answers
Answer:
4x_7+x=6 4x_x=7+6 3x=13 x=13÷3
Find the total surface area of the following cone. leave your answers in terms of PI
Answers
Given
height of cone = 4cm
Base radius of cone = 3cm
Find
TSA of cone
Explanation
[tex]l=\sqrt{4^2+3^2}=\sqrt{16+9}=5[/tex]We know that TSA of cone is
[tex]\begin{gathered} TSA=\pi r(r+l) \\ =\pi(3)(3+5) \\ =\pi(3)(8) \\ =24\pi cm^2 \end{gathered}[/tex]Final Answer
[tex]TSA=24\pi cm^2[/tex]how do I solve 9-2x=35
Answers
In order to solve the expression:
[tex]9-2x=35[/tex]We operate inn such a manner that x is left alone, that is:
[tex]9-2x=35\Rightarrow9=35+2x\Rightarrow9-35=2x[/tex][tex]\Rightarrow-26=2x\Rightarrow-13=x[/tex]We have our expression 9 - 2x = 35.
In order to solve for x, we try and leave x alone, that is, we sustract 9 from both sides of the operation:
9 - 9 - 2x = 35 -9 => -2x =26
Now that we have this, we proceed to eliminate -2 from the side of x, for that we divide both sides by -2, that is:
(-2/-2)x=(26/-2) => x = -13
what is the ansss??? btw this is a practice assignment.
Answers
A) Check the graph below, please. B) Horizontal translation to the left in 2 units. C) Vertical shift 4 units
1) Given that we have the function h(x) = |x+2| and g(x)= |x| + 4
A) Let's set a pair of tables, and pick 3 arbitrary values for x and then plug into each one
h(x) = |x+2|
x | y = |x+2|
-1 | 1 y =|-1 +2| = |1| = 1
0 | 2 y =|0+2| = |2| = 2
1 | 3 y =|1+2| = |1| = 1
g(x) =|x| + 4
x | y
-1 | 5
0 | 4
1 | 5
Let's plot those absolute value functions:
B) Considering the parent function f(x) =|x| we can notice that h(x) is a translation to the left, in two units. This we can see better this way:
Note that f(x) is in red, and h(x) in pink or light red.
C) Considering that f(x) = |x| we can see that g(x) = is a vertical shift 4 units up.
A man walked 5 miles right and read a sign that said "20 miles north to Atlanta". How far is Atlanta from the starting point?
Answers
ANSWER
Atlanta is 20.62 miles away from the starting point
EXPLANATION
This is a diagram of this problem
We're looking for the hypotenuse of this right triangle. Using the Pythagorean theorem:
[tex]\begin{gathered} d^2=5^2+20^2 \\ d=\sqrt[]{25+400} \\ d=\sqrt[]{425} \\ d\approx20.62\text{ miles} \end{gathered}[/tex]A cyclist rides his bike at the speed of 11 ft per second what is the speed in miles per hour how many miles will the cyclist travel in 5 hours in your computations use the fact that one mile is equal to 5280 ft do not round your answers
Answers
The speed of the cyclist in miles per hour is 7.5 miles per hour. The distance covered by the cyclist in 5 hours is 30 miles.
According to the question,
We have the following information:
A cyclist rides his bike at the speed of 11 ft per second.
Now, it is given that we have to use 1 mile = 5280 ft.
So, we have:
1 ft = 1/5280 miles
We know that there 3600 seconds in 1 hour.
1 seconds = 1/3600 hour
So, we have the speed in miles per hour:
11*(1/5280)/(1/3600)
(11*3600)/5280
7.5 miles per hour
Time taken = 5 hours
Speed = 7.5 miles per hour
Distance = speed*time
Distance = 7.5*5
Distance = 30 miles
Hence, the speed of the cyclist in miles per hour is 7.5 miles per hour. The distance covered by the cyclist in 5 hours is 30 miles.
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Please help me!! The question is in the attachment!!
Answers
Using it's concept, the probabilities are given as follows:
b) P(B|C) = 0.1429.
c) P(not A|B) = 0.8.
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.
For item b, the conditional probability can be written as follows:
P(B|C) = P(B and C)/P(C).
From the diagram, we have that:
P(B and C) = P(5) = 0.05.P(C) = P(5) + P(6) = 0.05 + 0.3 = 0.35.Hence:
P(B|C) = 0.05/0.35 = 0.1429.
For item c, the conditional probability is:
P(not A|B) = P(not A and B)/P(B).
From the diagram, these probabilities are:
P(not A and B) = P(4) + P(5) = 0.15 + 0.05 = 0.20.P(B) = P(3) + P(4) + P(5) = 0.05 + 0.15 + 0.05 = 0.25.Hence:
P(not A|B) = 0.20/0.25 = 0.8.
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Find the numerical value if x=4 and y=34x2(squared)+7y=?
Answers
To find the numerical value of the expression, we have to replace the variables for their given values. This way:
[tex]\begin{gathered} 4x^2+7y \\ 4(4)^2+7(3) \\ 4\cdot16+21 \\ 64+21 \\ 85 \end{gathered}[/tex]The numerical value of the expression is 85.
Balloon A is released 5 feet above the ground. Balloon B is released at ground level. Both balloons rise at a constant rate. Which situation can you represent using an equation of the form y = kx? Explain.
Table for Balloon A shows that the balloon reaches 9ft in 1s, 13ft in 2s, 17ft in 3s. Table for Balloon B shows that the balloon reaches 4ft in 1s, 8ft in 2s and 12ft in 3s.
Answers
Answer: Balloon B
Step-by-step explanation:
The distance, in feet, is always four times the time, in seconds.
The surface areas of the circular cylinder shown in the figure is given by S = 2π(25) + 2π(5h).
Find the heighth of the cylinder if the surface area is 942 square feet. Use 3.14 for 7t.
h =
Answers
The heighth of the cylinder if the surface area is 942 square feet is 25 feet.
How to calculate the height?From the information given, the S = 2π(25) + 2π(5h). We are to find the heighth of the cylinder if the surface area is 942 square feet.
This will be:
S = 2π(25) + 2π(5h).
2π(25) + 2π(5h) = 942
50π + 10πh = 942
(50 × 3.14) + (10 × 3.14 × h) = 942
157 + 31.4h = 942
Collect like terms
31.4h = 942 - 157
31.4h = 785
h = 785/31.4
h = 25
The height of the cylinder is 25 feet
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Y-Intercept: x-intercept: y 소 4 3+ 2+ 1- HX 1 2 3 4 -2+ -3 -47 -1413121110-9-8-7-6-5-4-3-2 -61 - 77 -8+ -9+ -10 -11+ -12+ -13+ -141
Answers
Input data
Graph
Procedure
y-intercept
Y-Intercept of a Straight Line. Where a line crosses the y-axis of a graph.
(0, -6)
x-intercept
The x-intercept is the point where a line crosses the x-axis
(-8,0)
-r + 23 = -7r+ 3(2r + 8)
Ned help solving….Please help
Answers
The equation has no solution.
How to find the solution of the given equation?
-r + 23 = -7r + 3(2r + 8)
Applying distributive property A(B+C) = AB+AC
⇒ -r + 23 = -7r + 6r + 24
Combining like terms,
⇒ 7r - 6r -r = 24 - 23
⇒ 7r - 7 r = 1
⇒ 0 = 1
L.H.S ≠ R.H.S
Since the two sides are unequal , there is no solution.
What is the distributive property ?
In mathematics, the rule governing addition and multiplication operations is known as distributive law or distributive property.It is shown as A(B+C) = AB+AC.This law makes it simple to demonstrate that multiplying a sum of numbers by a certain number after adding multiple numbers has the same result as multiplying each number by the same amount independently before adding the results. It claims that multiplying a collection of significant two or three digit numbers will produce the same result as partitioning, multiplying, and adding the numbers individually.To learn more about distributive property, refer:
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Determine the equation of the line that passes through the point (1/7,1) and is parallel to the line −4y−3x=−3
Answers
SOLUTIONS
The parallel line will be of form
[tex]m_1=m_2[/tex]the equation of the line that passes through the point (1/7,1) and is parallel to the line −4y−3x=−3
[tex]\begin{gathered} -4y-3x=-3 \\ -4y=3x-3 \\ y=\frac{3x}{-4}-\frac{3}{-4} \\ y=-\frac{3}{4}x+\frac{3}{4} \\ y=mx+c \\ m_1=-\frac{3}{4} \end{gathered}[/tex]The equation of the line parallel to point(1/7 , 1)
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ x_1=\frac{1}{7},y_1=1 \\ y-1=-\frac{3}{4}(x-\frac{1}{7}) \\ y-1=-\frac{3}{4}x+\frac{3}{28} \\ y=-\frac{3}{4}x+\frac{3}{28}+1 \\ multiply\text{ through by 28} \\ 28y=-21x+3+28 \\ 28y=-21x+31 \end{gathered}[/tex]The next nine births at a hospital all being girls
Answers
Answer:
There is a chance it could happen. Rare occurrence though.
Step-by-step explanation:
(a) Rewrite as a logarithmic equation.e^y=2(b) Rewrite as an exponential equation.In x=9
Answers
Let's rewrite it the first one
[tex]e^y=2[/tex][tex]\begin{gathered} \log _ee^y=\log _e2 \\ y=\log _e2 \end{gathered}[/tex]When we apply, log on both sides. We have the logarithm of a power equal to its exponent that is why we have y on the left side.
Rewriting the second one:
[tex]\begin{gathered} \ln (x)=9 \\ \log _ex=9 \\ x=e^9 \end{gathered}[/tex]Since the Natural Logarithm is log in the base "e" we can say that x is equal to e raised to 9
M) Point K is the midpoint of JL. JK = 6x + 9 andKL = 5x + 12. Find JK.1) 272) 303) 18
Answers
Answer:
The right option is 1) 27
Explanation:
According to the given data we have the following:
K is the midpoint of JL.
JK = 6x + 9
KL = 5x + 12
K is the midpoint of JL, hence, JL=JK+KL
So, to find JK we would equal JK with KL
So, 6x + 9=5x + 12
6x-5x=12-9
x=3
Therefore, JK=6(3)+9
JK=18+9
JK=27
Therefore, the right option is 1) 27
In a study of randomly selected women science majors, the following data were obtained on two groups, those who left their profession within a few months after graduation (leavers) and those who remained in their profession after they graduated (stayers). Test the claim that those who stayed had a higher science grade point average than those who left. Use α = 0.05.
Answers
X₁: science GPA for those who left their profession after graduation
X₂ science GPA for those who remained in their profession after graduation.
The working hypothesis is that the GPA of those who stayed is higher than those who left.
Which is the same as saying that the GPa of those who left is less than those who stayed.
μ₁ represents the population mean of the science GPA of those who left.
μ₂ represents the population mean of the science GPA of those who remained.
Part one
You can express the working hypothesis as follows:
[tex]\mu_1<\mu_2[/tex]The hypothesis does not include the equal sign, so this hypothesis can be considered as the alternative hypothesis.
The null hypothesis of this test will be the complement of the alternative hypothesis, and always carries the equal sign within. So if the alternative hypothesis states that "the mean of the leavers is less than the mean of the stayers", then the null hypothesis will be that "the mean of the leavers is greater than or equal to the mean of the stayers" you can symbolize this as:
[tex]\mu_1\ge\mu_2[/tex]Since the null hypothesis carries the equal sign you can also write it as:
[tex]\mu_1=\mu_2[/tex]Both options are equally valid.
So, the second answer is null hypothesis.
Part two
Considering that we are studying the population means of two normal variables and that we know the population standard deviation for both populations, the test statistic to use is the standard normal for the difference of means which is defined as follows:
[tex]Z=\frac{(\bar{X_1}-\bar{X_2})-(\mu_1-\mu_2)}{\sqrt[]{\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2}}}N(0,1)[/tex]Subindex 1 indicates the values corresponding to the "leavers":
X₁bar= 3.16
n₁= 103
σ₁= 0.52 → σ₁²= 0.2704
Subindex 2 indicates the values corresponding to the "stayers":
X₂bar= 3.28
n₂= 225
σ₂= 0.46 → σ₂²= 0.2116
Under the null hypothesis both population means are equal, which means that their difference is equal to zero:
If μ₁ = μ₂, then μ₁ - μ₂ = 0
Replace all values on the formula to determine the Z-value under the null hypothesis, i.e. the test statistic:
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