The line on the graph passes through the points A (0, 6) and B (3, 0).
YA
a) Calculate the gradient of line AB.
b) Find the gradient of a line perpendicular
to AB.
c) Find the equation of the line passing
through point A and perpendicular
to AB.
B
Answers
The equation for the line passing through point A and perpendicular to AB will be y-0.5x=6, the gradient of line AB is -2, and the gradient of a line perpendicular to AB is 0.5.
What is the slope or gradient?A numerical assessment of a line's angle relative to the ground is known as the slope.
Given data;
m₁ is the slope of line AB
m₂ is the slope of a line perpendicular to AB
The coordinate points are,
A,(x₁,y₁)= (0, 6)
B,(x₂,y₂)=(3, 0).
The gradient of line AB;
[tex]\rm m_{{1} }= \frac{y_2-y_1}{x_2-x_1} \\\\ \rm m_{{1} }= \frac{0-6}{3-0} \\\\ m_{{1} }=-2[/tex]
The slope of the lines has a perpendicular relation is -1;
m₁ × m₂ = -1
(-2) × m₂ = -1
m₂ = 1/2
m₂ = 0.5
The equation of the line passing through point A and perpendicular to AB;
(y - y₁) = m₂(x-x₁)
(y-6)=0.5(x-0)
y-6 = 0.5 x
y-0.5x=6
Hence, the gradient of line AB, the gradient of a line perpendicular to AB, and the equation of the line passing through point A and perpendicular to AB will be -2,0.5 and y-0.5x=6.
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Related Questions
What is the length of the hypotenuse of right ΔDEF shown? A) √5041 B) √2545 C) √497 D) √1063
Answers
The length of the hypotenuse of right triangle ΔDEF is 50.44 units
How to find hypotenuse of a right triangle?The hypotenuse side can be found using Pythagoras theorem,
Therefore,
c² = a² + b²
where
c = hypotenusea and b are the other legs.Therefore,
x² = 39² + 32²
x² = 1521 + 1024
x = √2545
x = 50.4479930225
x = 50.44
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I need help with this math question
Answers
Answer:
D = 12
Step-by-step explanation:
Side ST is corresponding to side QT. 9" / 3" = 3
3 is the proportion between the two triangles.
Side PT is the corresponding side to side RT.
PT = 4" x 3 = 12"
The mean annual income of certified welders is normally distributed with a mean of $50,000 and a population standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $50,000 annually. The alternate hypothesis is that the mean is not $50,000. If the level of significance is 0.10, what is the decision rule
Answers
Using the p-value method, the decision rule is:
|z| < 1.645: do not reject the null hypothesis.|z| > 1.645: reject the null hypothesis.What is the relation between the p-value and the test hypothesis?Depends on if the p-value is less or more than the significance level:
If it is more, the null hypothesis is not rejected.If it is less, it is rejected.In this problem, we have a two-tailed test, as we are testing if the mean is different of a value. For a significance level of 0.1, the critical value of z(when a p-value of 0.1 is obtained) is of |z| = 1.645, hence the decision rule is:
|z| < 1.645: do not reject the null hypothesis.|z| > 1.645: reject the null hypothesis.More can be learned about p-values at https://brainly.com/question/13873630
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ABC is an equilateral triangle whose vertex A has the co-ordinates (0, √3). Find the co- ordinates of B and C.
Answers
Answer:
B = (-1, 0)
C = (1, 0)
Step-by-step explanation:
Properties of an Equilateral Triangle
Three sides of equal lengthAll interior angles are 60°Given:
ΔABC is an equilateral triangleVertex A is at (0, √3)Drawing an altitude from vertex A divides the triangle into two 30-60-90 triangles.
A 30-60-90 triangle is special right-angled triangle where:
Angles are in the ratio 1 : 2 : 3Sides are in the ratio 1 : √3 : 2Therefore, the formula for the sides is: b : b√3 : 2b, where:
b = shortest side opposite the 30° angleb√3 = side opposite the 60° angle2b = longest side (hypotenuse) is opposite the right angleAs Vertex A has the co-ordinates (0, √3), the side opposite the 60° angle is √3 units.
Using the ratios to find b (shortest side length):
b√3 = √3 ⇒ b = 1
As the altitude divides BC into two equal line segments, and the length of the shortest side of the right triangles is 1 unit, the coordinates of B are C are:
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Evaluate 43 – 3m for m = 6.
Answers
Original Equation: 43 - 3m; m = 6
Substitute 6 in for m
43 - 3(6)
Multiply 3*6
43 - 18
Subtract 43 - 18
25
Your answer is: 25
Answer:
= 43 - 3×6= 43 - 18Therefore , 25 ans.
Which could be used to evaluate the expression negative 6 (4 and two-thirds)? (negative 6) (4) (negative 6) (two-thirds) (negative 6) (4) times (negative 6) (two-thirds) (negative 6 4) (negative 6 two-thirds) (negative 6 4) times (negative 6 two-thirds)
Answers
Hence, the required expression is (Negative 6) (4) + (negative 6) (two-thirds).
What is an expression?expression is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.). This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/Variable, Math Operator, Number/Variable)
How to solve?LHS,
(-6)([tex]\frac{14}{3}[/tex]) = -28
RHS,
(-6)()[tex]4+\frac{2}{3}[/tex]) = -28
LHS=RHS
Hence, the required expression is (Negative 6) (4) + (negative 6) (two-thirds).
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5 quick algebra 1 questions for 50 points!
Only answer if you know the answer, shout-out to subtomex0, tysm for the help!
Answers
[tex]x {}^{2} - 8x - 9 = 0 \\ x + y = 8 \\ xy = - 9[/tex]
Two numbers who sum up to 8 and multiply to -9 are: 9 and -1Q 4 - d -[tex]g(x) = x {}^{2} - 7x + 12 \\ g(6) = 36 - 42 + 12 = 6 \\ g( - 7) = 49 + 49 + 12 = 110 \\ g( - 3) = 9 + 21 + 12 = 42 \\ g(4) = 16 - 28 + 12 = 0[/tex]
x=4 is a rootThese problems can be approached in many ways: completing the square/factoring/using the quadratic formula...Q 1 - c -h(x)= -2x+10h(0)=10 ( 0 , 10 )h(x)=0x=5 ( 5 , 0 )Q 5 - True -f(x) = 2x²+3x-2f(x)=02x²+3x+2=0x=-2 x=1/2Q 4 - 3 is the zero -b
Answer:
Question 1:The correct answer is C. -1 and 9
Question 2: The correct answer is D.4
Question 3: The correct answer is C. The x-intercept of (5,0) and y-intercept of (0,10)
Question 4: The correct answer is B. True
Question 5: The correct answer is b.
Fill the empty slots by dragging tiles from the left to show the next step for solving the equation. Solve the two-step equation. -9x + 0.4 = 4
Which operation must be performed to move all the constants to the right side of the equation?
Answers
In order to move a the constant terms to the right hand side, we need to subtract 0.4 from both sides of the equation.
What are the constant terms?In an equation, the constant terms are those terms that do not have any alphabet attached to them. In this case, 4 and 0.4 are constant terms.
In order to move a the constant terms to the right hand side, we need to subtract 0.4 from both sides of the equation thus;
-9x + 0.4 - 0.4 = 4 - 0.4
-9x = 3.6
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Classify the polynomial by its degree and number of terms. Select all choices that apply for each polynomial.
(which is correct ??)
Answers
Step-by-step explanation:
The polynomial highest degree is 2 so the degree is 2.
The binomial have three terms so it is a trinomial.
Given the following linear function sketch the graph of the function and find the domain and range. f( x ) = 2/7 x− 2
Answers
Answer:
Domain: All Real Numbers Range: All Real Numbers
Step-by-step explanation:
The domain and range is going to be infinite. The linear function will be using the x and y- axis in order to continue being a function. The y-intercept will be -2 on the y-axis. I recommend using the rise-over-run method for your slope value. from the point (0, -2) on the y-axis. Go up two on the y-axis, and right 7 on the x-axis.
Sorry, it may be difficult to explain through words.
A tire on a car has an outside diameter of 36.30 in. Through what angle (in radians) does the tire turn while traveling 1 mile?
Answers
Answer: 3491.91 radians
Step-by-step explanation:
The total distance in inches traveled by car = 63,360 inches (1 mile)
Total Revolution made by tire through traveling =
[tex]=\frac{63360}{\pi *36.30}[/tex]
We know 1 revolution angle made by tire = 2π radian (360 degrees/1 revolution of unit circle)
In [tex]\frac{63360}{\pi *36.30}[/tex] ,
the revolution angle made by the tire =
[tex]=2\pi * \frac{63360}{\pi 36.60}[/tex]
[tex]=2 * \frac{63360}{ 36.60}[/tex]
[tex]= 3491.91[/tex] radian
Calculate the area of triangle OPQ.
Answers
Thus, we need information about the sides OQ and PQ to solve the triangle and find the area. The information given is not enough to determine the area of the triangle.
Is this triangle solvable?
In this question we must analyze if the area of the triangle OPQ can be found by all information given. By the law of the cosines we understand that lengths of two sides and the measure of an angle should be known to construct a triangle and by the law of the sines we understand that either two angles and a side or two sides and an angle must be known.
Thus, we need information about the sides OQ and PQ to solve the triangle and find the area. The information given is not enough to determine the area of the triangle.
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Pauley graphs the change in temperature of a glass of hot tea over time. he sees that the function appears to decrease quickly at first, then decrease more slowly as time passes. which best describes this function?
Answers
Non-linear graph best describes this function.
Why nonlinear?
As described in the question, Pauley graphs the change in temperature of a glass of hot tea over time. He sees that the function appears to decrease quickly at first, then decrease more slowly as time passes. It is linear because the graph decreases over time. It is linear because there is both an independent and a dependent variable but it doesn't satisfies one condition of being linear. Thus, It's Nonlinear because linear functions are increasing functions. It is nonlinear because linear functions increase or decrease at the same rate.
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Answer:
B
Step-by-step explanation:
NEED HELP ASAP!!!!!!!!
PLEASE
For which set of data are the median and mode the same number?
(A) 4, 5, 7, 8, 9, 9
(B) 4, 5, 7, 7, 8, 10
(C) 3, 5, 6, 8, 8, 9
(D) 5, 5, 6, 8, 9, 10
Answers
Answer:
b
Step-by-step explanation:
The steps to derive the quadratic formula are shown below:
Step 1 ax2 + bx + c = 0
Step 2 ax2 + bx = − c
Step 3 x2 + b over a times x equals negative c over a
Step 4 x2 + b over a times x plus b squared over 4 times a squared equals negative c over a plus b squared over 4 times a squared
Step 5 x2 + b over a times x plus b squared over 4 times a squared equals negative 4 multiplied by a multiplied by c, all over 4 multiplied by a squared plus b squared over 4 times a squared
Step 6
Provide the next step to derive the quadratic formula. (1 point)
x plus b over 2 times a equals plus or minus b squared minus 4 times a times c all over the square root of 4 times a squared
x plus b over 2 times a equals plus or minus b minus 2 times a times c all over square root of 2 times a
x plus b over 2 times a equals plus or minus the square root of the quantity b squared minus 4 times a times c all over the square root of 4 times a squared
x plus b over 2 times a equals plus or minus the square root of the quantity b squared minus 4 times a times c all over the square root of 2 times a
Answers
Answer: [tex]x+\frac{b}{2a}=\pm \frac{\sqrt{b^2 - 4ac}}{\sqrt{4a^2}}[/tex]
Step-by-step explanation:
We can rewrite the left hand side as a perfect square, more specifically
[tex]\left(x+\frac{b}{2a} \right)^2[/tex]
So, taking the square root of both sides,
[tex]x+\frac{b}{2a}=\pm \frac{\sqrt{b^2 - 4ac}}{\sqrt{4a^2}}[/tex]
Eight years ago, Marilyn invested $1000 in a stock. The table shows the
value of the stock over time.
Year
0
1
2
3
4
5
6
7
8
Value
$1000
$1095
$1200
$1314
$1440
$1580
$1730
$1890
$2070
Which is closest to the rate of change modeled by the function?
Leaming Inc.
Helo 13
Answers
Answer: 1.095
Step-by-step explanation:
The function is increasing, so the rate of change must be greater than 1.
John lives in Vermont and Julie lives in Florida. One January day, it was 52°F in Florida and 9°F in Vermont. What was the difference in temperature.
Answers
Answer:
43
Step-by-step explanation:
52-9=43
Find the length of the midsegment .
A.15
B.44
C.22
D.13
Answers
Answer: 22
Step-by-step explanation:
Using the triangle midsegment theorem,
[tex]2(5x+2)=3x+32\\\\10x+4=3x+32\\\\7x+4=32\\\\7x=28\\\\x=4[/tex]
So, the length of the midsegment is 5(4) + 2 = 22
In which year did Eugene, Oregon have the greatest difference between high and low temperatures in November?
A)November 2009
B)November 2010
C)November 2011
D)November 2008
Answers
An architect's sketch of plans for the front of a garage in the shape of pentagon is shown below. What is the approximate perimeter of the
front of the garage?
-8
-6 -4 -2
A. about 36 ft
B. about 21 ft
C. about 10 ft
D. about 77 ft
Answers
Using it's concept, it is found that the approximate perimeter of the front of the garage is:
A. about 36 ft.
What is the perimeter of a figure?The perimeter of a figure is given by the total length of it's boundary.
In this problem, we have that:
The bottom boundary has length of 10 units.The two lateral boundaries have lengths of 7 units.There are two top boundaries, which are the hypotenuses of a right triangle with legs 3 and 5, hence:[tex]t = \sqrt{3^2 + 5^2} = 5.83[/tex]
Hence the perimeter of the figure is:
P = 10 + 2 x 7 + 2 x 5.83 = 35.66.
Rounding, it is of about 36 ft, hence option A is correct.
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Express a) 36 b) 80 as sum of two prime numbers
Answers
⊱________________________________________________________⊰
Answer:
See below.Step-by-step explanation:
[tex]\large\begin{gathered} \sf{36=19+17. 19 \ and \ 17 \ are}\\ \sf{\ both \ primes, \ because \ they're \ only \ divisible \ by \ 1 \ and \ themselves} \\ \sf{ 80=73+7. \ Again, \ 73 \ and \ 7 \ \underline{ARE} \ prime. \end{gathered}}[/tex].
Done!!
⊰________________________________________________________⊱
CαlligrαphyIn the falcon's nest ice cream cost 20 cents. if the school pays 15 cents, what percent mark-up is it?
Answers
Answer: 25% off
Step-by-step explanation:
1= 0.25 + 0.75
25% is off is the equivalency of multiplying the value of the original cost with 0.75.
20*0.75=15
The______is the set of inputs For a fraction
Answers
The set of all input values of a function is the domain of the function
What is a function?A function relates an input to an output.
A function defines a relationship between one variable (the independent variable) and another variable.
The set of all input values of a function is the domain of the function.
The domain of a function are also called independent variables.
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change the unit of weight 1,000 lb =___ t ?
Answers
Answer:
0.5 t
Step-by-step explanation:
Since we know that 2,000lbs=1 t
1,000lbs is half a ton, which makes it 0.5 tons
Question is on the picture:)
Answers
Answer:
Z = 90 degrees
Step-by-step explanation:
Reason is a diameter subtends angle of 90 degrees on the circumference
Compared to continental crust, oceanic crust is:
A. mostly granite
B. more dense
C. All of these
D. thicker
Answers
Answer:
B. more dense
Try it
Which graph represents the function h(x) = 5.5|x]?
LIV
-2
2 4
-4-2
Intro
2
-4-2
O
2 4
-4-2
2
Answers
[tex]take \: some \: values \\ h(1) = 5.5 \times |1| = 5.5 \times 1 = 5.5 \\h(2) = 5.5 \times |2| = 5.5 \times 2 = 11 \\ h(4) = 5.5 \times |4| = 5.5 \times 4= 22[/tex]
It's clearly the second option since the other ones aren't steep enough.Which of the following could be rewritten as an addition problem of two integers with the same sign?
8 - 10
-8 - 10
-8 + 10
-8 - (-8)
Answers
because it can also be written as -8 + -10 instead of -8 - 10
I need answer fast!!
3. Write the rule that describes the second transformation. (5 points)
Answers
The rule that describes the second transformation is; Rotated at 90° clockwise
How to Interpret Transformations?From the given diagram we can see that;
The transformation from Rectangle ABCD to A'B'C'D' follows the transformation sequence of;
Shift 1 unit downwards then translate 5 units to the right.
However, for the transformation of A'B'C'D' to A"B"C"D", we see that the transformation is; Rotated at 90° clockwise
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In a large population, 76% of the households have cable tv. A simple random sample of 225 households is to be contacted and the sample proportion computed. What is the mean and standard deviation of the sampling distribution of the sample proportions
Answers
0.017559
It is given that:
Probability of Households Having cable TV, p₀ = 76% = 0.76
Therefore,
The probability that the Households not having cable TV = 1 - 0.76 = 0.24
Sample size, n = 225 households
sample proportions is less than 82% i.e p = 0.82
Now,
The standard error, SE = [tex]\sqrt{} \frac{0.76(1-0.76)}{225}[/tex]
= 0.02847
Z = [tex]\frac{0.82-0.76}{0.02847}[/tex]
Z = 2.107
therefore, P(sample porportions < 0.82) = P(Z < 2.107)
now from the p value from the Z table we get P(sample porportions < 0.82) = 0.017559
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