May you write a equation of a line that is perpendicular to, " y = 1/3x + 3" and passes through (-1, -2)?
Answers
the general equation of a graph is y= mx + c
m is the gradient and c is the intercept
from the first line equation, m = 1/3
condition for perpendicularity is that if two lines are perpendicular
the gradient of the first line is equal to the negative of the reciprocal of the second line gradient
so
\(\begin{gathered} \text{if m}_{1\text{ }}is\text{ the gradient of the first line and } \\ m_{2\text{ }}is\text{ the gradient of the second line} \end{gathered}\)\(\frac{-1}{m_2}=m_1\)\(\begin{gathered} m_1=\text{ }\frac{1}{3},\text{ then } \\ m_2=\text{ -}\frac{\frac{1}{1}}{3}\text{ =- }\frac{1}{1}\times\frac{3}{1}=-3 \end{gathered}\)\(\begin{gathered} \text{if it passes through the points (-1,-2)} \\ x\text{ = -1, y=-2} \\ \text{use y= mx +c to obtain the value of c by substituting m, x and y} \end{gathered}\)\(\begin{gathered} y=mx\text{ + c} \\ -2\text{ = -3 }\times-1\text{ +c} \\ -2\text{ = 3 + c} \\ -2-3\text{ =c} \\ -5\text{ =c} \\ c=\text{ -5} \end{gathered}\)so the equation of the line is obtain by substituting the values of the gradient (m2) and the intercept (c) in y = mx +c
so the equation is y = -3x + (-5)
y = -3x -5
Related Questions
Given the points P (3, 5) and Q (-5, 7) on the cartesian plane such that R (x, y) is
the midpoint of PQ, find the equation of the line that passes through R and
perpendicular
to PQ.
Answers
Answer:
-22=22
Step-by-step explanation:
3,5-5,7=
-22/22
The equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.
To find the equation of the line passing through the midpoint R and the points P and Q, we first need to find the coordinates of the midpoint R. The midpoint coordinates can be found by taking the average of the x-coordinates and the average of the y-coordinates of P and Q.
The x-coordinate of the midpoint R is (3 + (-5)) / 2 = -1/2.
The y-coordinate of the midpoint R is (5 + 7) / 2 = 6.
So, the coordinates of the midpoint R are (-1/2, 6).
Next, we can use the two-point form of the equation of a line, which states that the equation of the line passing through points (x₁, y₁) and (x₂, y₂) is given by:
(y - y₁) = (y₂ - y₁) / (x₂ - x₁) \(\times\) (x - x₁)
Substituting the coordinates of R (-1/2, 6) and P (3, 5) into the equation, we have:
(y - 6) = (7 - 5) / (-5 - 3) \(\times\)(x - (-1/2))
Simplifying the equation:
(y - 6) = (2 / -8) \(\times\)(x + 1/2)
(y - 6) = -1/4 \(\times\)(x + 1/2)
4(y - 6) = -x - 1/2
Therefore, the equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.
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A store owner buys sweatshirts for $16 and marks them up 20% to make a profit. The sales tax where his store is located is 7.5%. A customer considers buying one or two sweatshirts from the store. Select all the statements that apply. (choose 3)
One sweatshirt before tax costs $19.20.
One sweatshirt before tax costs $12.80.
he sales tax for two sweatshirts is $1.92.
The sales tax for two sweatshirts is $2.88.
Total cost for two sweatshirts is $41.28.
Total cost for two sweatshirts is $27.52.
Answers
The statements that apply to the store, based on the cost of the sweatshirts and the markup are:
One sweatshirt before tax costs $19.20.The sales tax for two sweatshirts is $2.88.Total cost for two sweatshirts is $41.28.How to find the selling price of the sweatshirt?The cost of a single sweatshirt before tax can be found by the formula:
= Cost of sweatshirt to store owner x ( 1 + markup)
= 16 x ( 1 + 20%)
= $19.20
The sales tax on this sweatshirt would then be:
= 19.20 x 7.5%
= $1.44
On two sweatshirts would be:
= 1.44 x 2
= $2.88
The total cost of two sweatshirts is therefore:
= 19.20 + 19.20 + 2.88
= $41.28
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can someone help what landmark id landed
Answers
Answer:
FBI building
Step-by-step explanation:
suppose h(t)=(3t+5)/t and k(t)=5/(t-3). Show that h(t) and k(t) are inverse functions using algebra.
Answers
We will see that the functions are inverses by proving that the composition is equal to the identity.
How to show that h(t) and k(t) are inverse functions?Two functions are inverses if their composition is equal to the identity, this means that if h(t) and k(t) are inverses, then we can write:
h(k(t)) = t
and
k(h(t)) = t
Proving one of these will be enough.
Here the functions are:
h(t) = (3t + 5)/t
k(t) = 5/(t - 3)
Let's find h(k(t))
We will get:
h(k(t)) = (3*k(t) + 5)/k(t)
Now we can replace the function k(t) there.
h(k(t)) = (3*5/(t - 3) + 5)/(5/(t - 3))
Now we can simplify this using algebra.
h(k(t)) = ( 15/(t - 3) + 5)*(t - 3)/5
h(k(t)) = (15/(t - 3))*(t - 3)/5 + 5*(t - 3)/5
h(k(t)) = 3 + (t - 3) = t
h(k(t)) = t
So yes, the two functions are inverses.
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which value of x makes the question true?
x+7=-9
Answers
x+7=-9
One way to find the variable in an addition problem is to subtract.
-9-7
This can be solved by adding 9 and 7 and then slapping a '-' sign in front.
9+7=16
-16
hope it helps!
Expon
Question
Which sets of the radical expressions listed could be considered like terms as written?
A. 5√2x
B. -4x√2
C. 5√/2x
D. -3√2x
E. 5x√2x
Select all the correct answers.
A and D
B and E
C and E
A and C
A, C, D, and E
Answers
A and D , that is, 5∛2x and -3∛2x are sets of the radical expressions listed that could be considered like terms. This can be obtained by understanding what like radicals are.
Which sets of the radical expressions listed could be considered like terms as written?Radical expression: Radical expression is an equation that has a variable in a radicand (expression under the root) or has a variable with a rational exponent.For example, √128, √16
Like radicals: Radicals that have the same root number and radicand (expression under the root)For example, 2√x and 5√x are like terms.
Here in the question radical expressions are given,
5∛2x-4x∛25√2x-3∛2x5x√2xBy definition of like radicals we get that 5∛2x and -3∛2x are like terms since root number and radicand are same, that is, root number is 3 and radicand is 2x.
Hence A and D , that is, 5∛2x and -3∛2x are sets of the radical expressions listed that could be considered like terms.
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Answer:
Step-by-step explanation:
A and D
C and E
From edmentum
10. A rectangle has a perimeter of 22 cm. If the length of the rectangle is 2 cm more than two times the
width, what are its dimensions?
Answers
Answer:
w = 3 cm
l = 8 cm
Step-by-step explanation:
let 'w' = width
let '2 + 2w' = length
P = 2l + 2w
22 = 2(2 + 2w) + 2w
22 = 4 + 4w + 2w
22 = 4 = 6w
18 = 6w
w = 3
length = 2 + 2(3) = 18
You can transform V to V' by translating it and then performing a dilation centered at V'. Find the translation rule and scale factor of the dilation. Simplify the scale factor and write it as a proper fraction, improper fraction, or whole number. Translation: (x, y) -> (___,___) Scale factor: ___
Answers
Answer:
Translation rule → (x + 10, y + 1)
Scale factor = 4
Step-by-step explanation:
Coordinates of V → (-8, -2)
Coordinates of V' → (2, -1)
Therefore, point V has been translated from x = -8 to x = 2,
Translation on x-axis → 2 - (-8) = 10 units
Translation on y-axis → -1 - (-2) = -1 + 2
= 1 unit
If the point V is translated 10 units right and 1 unit upwards,
Rule for the translation → (x + 10, y + 1)
Radius of the circle V = 2 units
Radius of the circle V' = 8 units
Scale factor = \(\frac{\text{Dimension of the image}}{\text{Dimension of the original}}\)
= \(\frac{\text{Radius of the image}}{\text{Radius of the original}}\)
= \(\frac{8}{2}\)
= 4
Therefore, circle V has been dilated by a scale factor of 4 to form circle V'.
10 POINTS! Answer ASAP. In the diagram shown, line p is parallel to line q. What is the measure of Angle 1? Answer Choices: 45, 75, 63, 52
Answers
Answer:
Step-by-step explanation:
It's 75° b/c of complementary angles.... understand? :∫
Answer is 75
Alternate Angle:
Alternate angle theorem states that when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent.
Here, angle-1 is the sum of alternate angles
=> i.e., sum of angle 45 degrees and 30 degrees
=> 45 + 30 = 75
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How many shipments had at least 10 broken tiles but less than 20 broken tiles ?
Answers
Answer:
5 shipments had at least 10 broken tiles but less than 20 broken tiles.
Lilly has a piece of string that is 36 inches long. She wants to cut it into 9 equal pieces.
How long will each piece of string be?
A 4 inches
B. 6 inches
c. 25 inches
D. 27 inches
E.45 inches
Answers
Answer: A, 4 inches.
Step-by-step explanation: 36 divided by 9 is 4.
you can use the finger trick if you learned it
The frame of a bicycle weighs 16 pounds. Each tire weighs 9 ounces. The seat weighs 12 ounces. The handlebars weigh 24 ounces. How many pounds does the bicycle weigh?
Answers
The weight of the bicycle is 19.375 pounds.
Define weight.In physics and engineering, the weight of an object refers to the gravitational force that pulls on it. Weight is frequently described as a scalar quantity that measures the gravitational force's strength.
The weight of the frame of the bicycle= 16 pounds
1 pound= 16 ounces
Therefore, 16 pounds= 16 x 16 = 256 ounces
The weight of one tire= 9 ounces
Therefore, the weight of two tires= 9 x 2 = 18 ounces
The weight of the seat= 12 ounces
The weight of handlebars= 24 ounces
Therefore, the total weight of the bicycle = 256 + 18 + 12 + 24
= 310 ounces
Therefore, the bicycle weighs 310 ounces
That is 310/ 16 = 19.375 pounds
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Which of the following is a biconditional statement?
Question 17 options:
A)
If x ≠ 5 then x2 ≠ 25
B)
If x2 = 25, then x = 5 or x = –5
C)
x = 5 if x2 = 25
D)
x = 5 if and only if x + 5 = 10
Answers
It is D
I just took the test and got it right
The biconditional statement is x = 5 if and only if x + 5 = 10.
Option D is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Biconditional statement.
This means,
The statement and its converse are both true.
Now,
x = 5 if and only if x + 5 = 10
This shows that both the statement and its converse are true.
Thus,
x = 5 if and only if x + 5 = 10 is a biconditional statement.
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How can you check if a line belongs to a plane (Cartesian equation of the line and the equation of the plane is given)?
Answers
For example, suppose you have the Cartesian equation of a line in the form:
y = mx + b
and the equation of a plane in the form:
ax + by + cz + d = 0
To check if the line belongs to the plane, you can substitute a point (x, y) on the line into the equation of the plane and solve for z. If the resulting value of z satisfies the equation of the plane, then the line belongs to the plane.
Here's an example:
Suppose the Cartesian equation of the line is y = 2x + 1, and the equation of the plane is 2x + 3y + 4z + 5 = 0.
If we substitute a point on the line, such as (1, 3), into the equation of the plane, we get:
2(1) + 3(3) + 4z + 5 = 0
Solving for z, we find that z = -1.5.
Since the resulting value of z satisfies the equation of the plane, the line belongs to the plane.
If the resulting value of z does not satisfy the equation of the plane, then the line does not belong to the plane.
Which of the following is not a really number ?
Answers
Answer;
\(D\)Explanation;
Broadly, numbers can be real or complex.
When numbers are real, they can be represented only by the use of the conventional figures and can be evaluated as such in their simplest form.
When mumbers are complex, then comes the use of selected alphabets in conjuction with the numbers for identification
Popular amongst complex numbers are square roots of negative numbers
The last option is a root of a negative number and that is our answer
Solve 3x + 6 = 34
Answers:
−2
4
6
10
Answers
Answer:
To solve the equation 3x + 6 = 34, we need to isolate x on one side of the equation.
First, we can start by subtracting 6 from both sides of the equation to get:
3x + 6 - 6 = 34 - 6
Simplifying this, we get:
3x = 28
Next, we divide both sides by 3 to isolate x:
3x/3 = 28/3
Simplifying this, we get:
x = 28/3
This is not one of the answer choices listed. However, we can approximate the answer to the nearest integer. Using a calculator, we get:
x ≈ 9.333
Rounding to the nearest integer, we get:
x ≈ 9
Therefore, the answer closest to the solution of the equation 3x + 6 = 34 is 10.
HELP ME OUT PLEASE!!!!
Answers
Answer:
the first option is correct
y= 3/2x + 3
Step-by-step explanation:
Is -4,488/24 positive or negative?
Answers
-4488/24 = -187
Answer:
negative
Step-by-step explanation:
positives and negatives make a negative
4a. Squeaky-Clean Dry Cleaner dry cleans 93 garments per week. If 32%of those garments are dresses and 45% are suits, how many pairs ofpants does the dry cleaner clean?4b. How many dresses does the dry cleaner clean?
Answers
The cleaner dry cleans 21 pairs of pants
The cleaner dry cleans 30 dresses
Explanation:Number of garments dry-cleaned per week = 93
32% of the garments are dresses, and 45% are suits
Percentage of pairs of pants contained in the garments = 100% - 32% - 45%
Percentage of pairs of pants contained in the garments = 23%
Number of pairs of pants = 23% of 93
Number of pairs of pants = (23/100) x 93
Number of pairs of pants = 21.39
Number of pairs of pants = 21 (to the nearest whole number)
32% of those garments are dresses
Number of dresses = 32% of 93
Number of dresses = (32/100) x 93
Number of dresses = 29.76
Approximate to the nearest whole number
Number of dresses = 30
What is angle
Enter your answer in the box
Answers
Answer:
CAB is 37 degrees
Step-by-step explanation:
90 + 53 = 143
180 - 143 = 37
-3(x+1)=-4 what is the property
Answers
The distributive property of multiplication over addition states:
\(a\cdot(b+c)=a\cdot b+a\cdot c\)where a, b, and c can be numbers or variables.
Applying this property to the left side of the
PLEASE HELP ASAP. Name the marked angle in 2 different ways.
Answers
2.) ∠MKN
As long as the vertex is the middle letter, the angles can be identified in a couple different ways. Notice that “K” is in the middle of both names? That’s because point K is the vertex and is always the middle letter of an angle name.
According to this author, the stories about Nancy Hart . As a result, they are to the study of Georgia’s past.
ill mark you brailiest
Answers
Answer:
According to this author, the stories about Nancy Hart
✔ likely have some basis in truth
.
As a result, they are
✔ very important
to the study of Georgia’s past
Step-by-step explanation:
I just took it on Edge 2020
Joyce saved $220 on an item that was 75% off what was the original price
Answers
Answer:
$880
Step-by-step explanation:
Use the equation:
\(P=(1-d)x\) with d being the discount in a decimal form, and P being the price that was bought at.
220=(1-0.75)x
simplify parenthesis terms
220=0.25x
divide both sides by 0.25
880=x
So, the original price was $880.
Hope this helps! :)
Suppose P(x) = 3x 2−4x−7 is a quadratic function and we suspect that 8 3 is a zero of P(x). How can we confirm our suspicion?
Answers
P(8/3) is not equal to zero, we can conclude that 8/3 is not a zero of P(x). Therefore, our suspicion was incorrect.
What is quadratic equation and how to solve it ?
A quadratic equation is a second-degree polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable.
To solve a quadratic equation, there are different methods, such as factoring, completing the square, and using the quadratic formula. The quadratic formula is the most general method and can be used for any quadratic equation.
It states that the solutions to the equation ax^2 + bx + c = 0 are given by the formula
x = (-b ± sqrt(b^2 - 4ac)) / (2a).
We can use this formula to find the roots of the equation by substituting the values of a, b, and c into the formula and simplifying.
To confirm if 8/3 is a zero of the quadratic function P(x) = 3x^2 - 4x - 7, we can substitute 8/3 for x in the equation and check if the resulting expression is equal to zero. If P(8/3) equals zero, then we can confirm that 8/3 is indeed a zero of P(x).
P(8/3) = 3(8/3)^2 - 4(8/3) - 7
= 3(64/9) - 32/3 - 7
= 64/3 - 32/3 - 21/3
= 11/3
Since P(8/3) is not equal to zero, we can conclude that 8/3 is not a zero of P(x). Therefore, our suspicion was incorrect. If we want to find the zeros of P(x), we can use the quadratic formula or factor the equation into (3x + 1)(x - 7) = 0 to get the roots x = -1/3 and x = 7.
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…aniwwjwwjaoqkqwgahw qjauaaj
Answers
Answer:
Undefined
Step-by-step explanation:
Lim x - - > 1(1 /In(2-x) + 1/(x-1))
To find the limit as x tends to 1
Substitute x = 1 into the function ;
(1 / In(2 - 1) + 1 / (1 - 1))
(1 / In 1) + (1 / 0)
1 / 0 + 1 / 0
Undefined
Ken owns 500 shares of LaceNBrace, which makes hockey equipment. He receives a notice stating the company will be paying $0.15 dividend per share. What is the total dividend payment he receives for that quarter? O $750 O $8.50 O $7.55 O $75
Answers
Ken will receive a total dividend payment of $75 for that quarter.
We have to given that,
Ken owns 500 shares of LaceNBrace, which makes hockey equipment.
And, He receives a notice stating the company will be paying $0.15 dividend per share.
Now, For the total dividend payment Ken receives for that quarter, we can multiply the dividend per share by the total number of shares he owns:
= $0.15 per share x 500 shares
= $75
Therefore, Ken will receive a total dividend payment of $75 for that quarter.
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Evaluation the following:
A.
\( \sqrt{ \frac{32 {y}^{2} }{72 {x}^{2} } } \)
B.
\( \sqrt[3]{ \frac{125 {m}^{3} }{36 {m}^{2} } } \)
C. if
\( x1 = 2 \: and \: x2 = 1 \\ and \: y1 = 3 \: and \: y2 = - 1\)
then find the value of :
\( \sqrt{ \frac{x2}{y2} - \frac{y2}{x2} } \)
Answers
Answer:
A. √32y²/72x²= 32y/72x
Step-by-step explanation:
√32y²/72x²= 32²/72²
= 32/72.
B. √125m³/36m²
=4192.6/108
=38.8203.
C. √x²/y²-y²/x²
therefore, x²=1, y²=-1
that is, √1/-1 - -1/1= -1(-)-1=0.
(PLEASE ANSWER 50 POINTS)Write an equation of a line slope-intercept form with the given slope and y-intercept. Slope:3, y-intercept:2
Answers
the slope (mx) is 3
the y-intercept (b) is 2.
the equation form is y=mx+b
HELPPP ME PLEASE I NEEDA HELP
p.s if u see this please answer look at the picture
Answers
Answer:
-5+2
Step-by-step explanation:
Answer:
I would say 6 cm too, also can anyone help me on my math? its powers and exponents