Which equation is perpendicular to y= -5/3x - 6y= -5/3x - 3y= 5/3x + 7y= -3/5x + 4y= 3/5x - 10
Answers
Two lines are perpendicular if and only if their slopes fulfil:
\(m_1m_2=-1\)All of the equations are given in the form:
\(y=mx+b\)Then, the equation
\(y=-\frac{5}{3}x-6\)has slope:
\(m_1=-\frac{5}{3}\)Plugging this in the perpendicular relation we have that:
\(\begin{gathered} -\frac{5}{3}m_2=-1 \\ m_2=\frac{-1}{-\frac{5}{3}} \\ m_2=\frac{3}{5} \end{gathered}\)this means that any perpendicular line to the one given has to have slope 3/5.
From the options given we notice that the only line that has this slope is:
\(y=\frac{3}{5}x-10\)Therefore, the perpendicular line is the last option.
Related Questions
Write a multiplication expression and a
division expression that would havе
result.
a)-8
b) -15
help please
Answers
Step-by-step explanation:
a. 8 × -1 = -8 or -2 × 4 = -8
8 ÷ -1 = -8 or 32 ÷ -4 = -8
b. -3 × 5 = 15 or 15 ×(-1) = -15
45 ÷ -3 = -15 or 225 ÷ -15 = -15
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At what value of x does the graph of the following function F(x) have a vertical asymptote?A.0B.-3C.6D.3
Answers
The Solution:
Given:
We are asked to determine the value of x at which the function f(x) has its vertical asymptote.
Below is the graph of the given function f(x):
Thus, from the above graph, the vertical asymptote of f(x) is at x = 3.
Therefore, the correct answer is [option D]
Find SP please and thank you
Answers
\(\\ \sf\longmapsto 3x+5=6x-7\)
\(\\ \sf\longmapsto 6x-3x=5+7\)
\(\\ \sf\longmapsto 3x=12\)
\(\\ \sf\longmapsto x=4\)
SP=6(4)-7=24-7=17Answer:
17 units.Step-by-step explanation:
We know that:
MS = SPGiven:
MS = 3x + 5SP = 6x - 7Solution:
3x + 5 = 6x - 7Taking the "-7" on the LHS and the "3x" on the RHS:
=> 7 + 5 = 6x - 3xAdding/Subtracting:
=> 12 = 3xDividing:
=> 3x/3 = 12/3=> x = 4Now, let's substitute the value of x into the expression of SP.
6x - 7=> 6(4) - 7=> 24 - 7=> 17 units.Hence, the measure of SP is 17 units.
Each square below represents one whole.
A square divided in 4 equal parts, all 4 of which are shaded
Another square divided in 4 equal parts, 3 of which are shaded
What percent is represented by the shaded area?
Answers
Answer:
SQUARE 1:
100% ; 75%
Step-by-step explanation:
SQUARE 1:
If each square represents a whole ; the percentage of a whole = 100%
Dividing the square into 4 equal parts :
Percentage of each part :
100% ÷ 4 = 25%
Percentage represented by the shaded part:
(Percentage of each shaded part * number of shaded part)
(25% * 4) = 100%
SQUARE 2:
each square represents a whole ; the percentage of a whole = 100%
Dividing the square into 4 equal parts :
Percentage of each part :
100% ÷ 4 = 25%
Percentage represented by the shaded part:
(Percentage of each shaded part * number of shaded part)
(25% * 3) = 75%
Answer:175%
Step-by-step explanation:
Percent means per hundred.
So, we need an equivalent ratio that will tell us how many pieces would be shaded out of 100100100 pieces per whole.
7 shaded parts times 25 equals 175 shaded parts. 4 parts per whole times 25 equals 100 parts per whole. 7 to 4 is equivalent to 175 to 100.
Sketch and label a net of the right triangular prism. Each square on the grid represents
1 square centimeter. Calculate the surface area of the prism by using its net.
Answers
The total surface area of the prism is determined as 216 cm².
What is the surface area of the prism?The surface area of the prism is calculated by applying the following formula.
The area of the two triangular faces is calculated as follows;
Area of the two triangles = 2 (¹/₂ x base x height )
Area of the two triangles = 2 (¹/₂ x 6 cm x 4 cm )
Area of the two triangles = 24 cm²
The area of rectangular faces is calculated as follows;
A = ( 5 cm x 12 cm ) + (5 cm x 12 cm ) + ( 6 cm x 12 cm )
A = 192 cm²
The total surface area of the prism is calculated as follows;
Area = 24 cm² + 192 cm²
Area = 216 cm²
The sketch of the triangular prism is in the image attached.
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Determine the equation for the line that has a slope of -2 and a y intercept of 5
Answers
Please help im new and i need help!
Please help me if you onlw the answers please!!
Answers
9514 1404 393
Answer:
a) 2.038 seconds
b) 5.918 meters
c) 1.076 seconds
Step-by-step explanation:
For the purpose of answering these questions, it is convenient to put the given equation into vertex form.
h = -4.9t² +9.2t +1.6
= -4.9(t² -(9.2/4.9)t) +1.6
= -4.9(t² -(9.2/4.9)t +(4.6/4.9)²) +1.6 +4.9(4.6/4.9)²
= -4.9(t -46/49)² +290/49
__
a) To find h = 0, we solve ...
0 = -4.9(t -46/49)² +290/49
290/240.1 = (t -46/49)² . . . . subtract 290/49 and divide by -4.9
√(2900/2401) +46/49 = t ≈ 2.0378 . . . . seconds
The ball takes about 2.038 seconds to fall to the ground.
__
b) The maximum height is the h value at the vertex of the function. It is the value of h when the squared term is zero:
290/49 m ≈ 5.918 m
The maximum height of the ball is about 5.918 m.
__
c) We want to find t for h ≥ 4.5.
h ≥ 4.5
-4.9(t -46/49)² +290/49 ≥ 4.5
Subtracting 290/49 and dividing by -4.9, we have ...
(t -46/49)² ≥ 695/2401
Taking the square root, and adding 46/49, we find the time interval to be ...
-√(695/2401) +46/49 ≤ t ≤ √(695/2401) +46/49
The difference between the interval end points is the time above 4.5 meters. That difference is ...
2√(695/2401) ≈ 1.076 . . . . seconds
The ball is at or above 4.5 meters for about 1.076 seconds.
__
I like a graphing calculator for its ability to answer these questions quickly and easily. The essentials for answering this question involve typing a couple of equations and highlighting a few points on the graph.
_____
Additional comment
I have a preference for "exact" answers where possible, so have used fractions, rather than their rounded decimal equivalents. The calculator I use deals with these fairly nicely. Unfortunately, the mess of numbers can tend to obscure the working.
"Vertex form" for a quadratic is ...
y = a(x -h)² +k . . . . where the vertex is (h, k) and 'a' is a vertical scale factor.
In the above, we have 'a' = -4.9, and (h, k) = (46/49, 290/49) ≈ (0.939, 5.918)
How do you Solve t/−5=−7.
Answers
Step-by-step explanation: 35/-5 = -7
T= 35 hope this helps
Write a two-step inequality that could be represented by the number line.
Answers
Answer:
0
Step-by-step explanation:
Renting a pony for a birthday party costs $200, plus $40 per hour. Write an equation to represent the total cost, c, of renting a pony for hours.
Answers
Answer:
200+ 40h= c
Step-by-step explanation:
Solve the following equations for x (5 points each). (a) -3x+10=34 and (b) 13x-4=11x+10-8
please show work
Answers
Answer:
A)x=-8 B)x=3
Step-by-step explanation:
A)-3x+10=34 -3x+10-10=34-10 -3x/-3=24/-3 x=-8
B) 13x-4=11x+10-8 13x-4+4=11x+10-8+4 13x-11x=11x-11x+6 2x/2=6/2 x=3
From the set {1, 4, 6}, use substitution to determine which value of x makes the equation true. 10 x + 8 = 48
Answers
Thank you hope this helps
What is the slope of the line below?
(2, 2)
(1,-1)
A. negative
B. positive
C. Zero
D. undefined
Answers
Step-by-step explanation:
Use the slope formula:
m=(y2-y1)/(x2-x1)
m=(-1-2)/(1-2)
m=(-3)/(-1)
m=3
consider the series 1/4+1/16+1/64+1/256
Answers
The expression that defines Sn is option (A), Sn = lim n->∞ (1/4)^n is the correct answer.
What is a series?A sequence is defined as an arrangement of numbers in a particular order. A series is the cumulative sum of a given sequence of terms. Typically, these terms are real or complex numbers.
For the given situation,
The series is 1/4 + 1/16 + 1/64 + 1/256.
⇒ \(\frac{1}{4}+\frac{1}{16} +\frac{1}{64} +\frac{1}{256}\)
⇒ \(\frac{1}{4}+\frac{1}{4^{2} } +\frac{1}{4^{3} } +\frac{1}{4^{4} }\)
Thus the sum of this series can be obtained by the expression,
\(S_{n}= \lim_{n \to \infty} (\frac{1}{4^{n}})\)
⇒ \(S_{n}= \lim_{n \to \infty} (\frac{1}{4})^{n}\)
Hence we can conclude that the expression that defines Sn is option (A), Sn = lim n->∞ (1/4)^n is the correct answer.
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5.064 divide by 8???
Answers
Answer:
0.663
Step-by-step explanation:
Answer:
0.633
Step-by-step explanation:
Find the surface area of a triangular prism. 16 cm., 20cm.,12cm.,10cm.
Answers
A bookshelf contains 6 German books, 4 Spanish books and 7 French books. Each book is different from one another. How many different arrangements can be done of these books if
Answers
Answer:
17 different arrangements
Step-by-step explanation:
6+4+7=17
round off all answer in to two decimal places A=p(1+in) Steven won a portion of the local lottery.the price money is to the value of R18000.he wants to invest the money but does not know which bank to choose. FNB offers Steven 5,6/% for 8 years simple interest per annum, Nedbank offers Steven 6,6% for 6 years simple interest per annum and standard bank offers 7,2% for 5 years simple interest determine each bank future value to help Steven decide which bank he should choose FNB NEDBANK STANDARD BANK
Answers
Answer:
FNB bank
Step-by-step explanation:
FNB = 18000 * 0.056* 8 = 8064
Nedbank = 18000*0.066* 6 = 7128
Standard = 18000*0.072*5=6480
FNB is the best choice for Steven
Please show me the steps to solve this problem
Answers
This is a pre-algebra problem. I'll go through the steps with you. If you don't get it, don't be afraid to ask!
Step One - Cross Multiply
These are fractions, but that doesn't mean you have to add them. Fractions are just the numerator divided by the denominator. So to 'remove' the 9, multiply both sides by 9. To 'remove' the 6, multiply both sides by 6. (We multiply both sides of the equation by the same number because we need to make each side the same). Note that when you multiply both sides by 9 or 6, you have to multiply the whole part.
(2x+1)×6 = (1-1)×9
Distribute.
12x+6 = 9-9
Step Two - Solve the Equation
So we are left with this equation after cross multiplying:
12x+6 = 9-9
First, we can start by subtracting 9 from 9, because those are the same types of numbers.
12x+6 = 0
Now, we have to 'remove' the 6. We can do that by subtracting each side by 6.
(12x+6)-6 = 0-6
12x = -6
Now we are left this this.
We need to 'remove' the 12 now, so we can isolate the x. Since 12 is multiplied to x, we divide each side by 12.
(12x)÷12 = -6÷12
We get x = -1/2
x = -1/2 or -0.5
Hope this helped!
Craig has a building block in the shape of a rectangular pyramid. A net of which is shown below.
If a measures 16 cm, b measures 8 cm, and d measures 17 cm, what is the surface area of the rectangular pyramid?
Answers
Looking at the net, we can see that the rectangular pyramid has one rectangular base and four triangular faces.
The dimensions of the rectangular base are a = 16 cm and b = 8 cm, so the area of the rectangular base is A_base = a * b.
The dimensions of the triangular faces are given by the sides of the rectangle and the slant height of the pyramid, which is represented by d = 17 cm. Each triangular face has a base equal to one side of the rectangle and a height equal to d.
The area of each triangular face can be calculated as A_triangle = 0.5 * (base * height) = 0.5 * (a * d) or 0.5 * (b * d).
Since there are four triangular faces, the total area of the triangular faces is A_triangles = 4 * A_triangle.
Finally, the surface area of the rectangular pyramid is the sum of the area of the rectangular base and the area of the triangular faces:
Surface Area = A_base + A_triangles = A_base + 4 * A_triangle.
Substituting the given values:
A_base = 16 cm * 8 cm = 128 cm².
A_triangle = 0.5 * (16 cm * 17 cm) = 136 cm².
A_triangles = 4 * 136 cm² = 544 cm².
Surface Area = 128 cm² + 544 cm² = 672 cm².
Therefore, the surface area of the rectangular pyramid is 672 cm².
I hope this helps! :)
Find simple interest. The rate is an annual rate unless otherwise noted. Assume 365 days in a year and 30 days per month. $1,300 at 4.25% for a year
Answers
Answer:
$55.25
1,300×0.0425=$55.25
What is the 15% of 20
Answers
Answer:
Step-by-step explanation:
15% of 20 is 3
in how many ways can the letters of MCHNLRN be arranged
Answers
Answer:
2520
Step-by-step explanation:
There are 7 letters in MCHNLRN and they can be arranged into 7 ways:
7! = 5040 ways in total
However, the letter 'N' is repeated so we have to divide it by 2.
5040 ÷ 2 = 2520 ways
Answer:
2,520 ways
Step-by-step explanation:
MCHNLRN has 7 letters with one repetition.
therefore, =7!/2!
=2,520 ways
A company produces steel rods. The lengths of the steel rods are normally distributed with a mean
of 117.6-cm and a standard deviation of 2.5-cm.
Find the probability that the length of a randomly selected steel rod is greater than 114.1-cm.
PIX> 114.1-cm) =
Enter your answer as a number accurate to 4 decimal places. Answers obtained using exact z-scores
or z-scores rounded to 3 decimal places are accepted.
Help
Answers
Answer:
Step-by-step explanation:
A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 142.7-cm and a standard deviation of 2.2-cm.
Find the probability that the length of a randomly selected steel rod is between 137.6-cm and 143.6-cm.
P(137.6-cm < X < 143.6-cm) =
Enter your answer as a number accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
Diven {x) = 3x- 1 and 9(x) = 2x-3, for which value of x does g(X) = {2)?
Answers
The calculated value of x at g(x) = 2 is x = 2.5
How to determine the value of x at g(x) = 2from the question, we have the following parameters that can be used in our computation:
f(x) = 3x - 1
Also, we have
g(x) = 2x - 3
When g(x) - 2, we have
2x - 3 = 2
So, we have
2x = 5
Divide by 2
x = 2.5
Hence, the value of x at g(x) = 2 is x = 2.5
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Question 4 O Mark this question Megan was conducting a study to determine if there was a relationship between eating a whole foods diet and general overall health. For her study Megan's null hypothesis was that a whole foods diet would not have any impact on general health. Megan's alternate hypothesis was that eating a whole foods diet would cause improvements in health. If Megan completed her study, which of the following statements would indicate a Type I error? Megan's results show that a whole foods
Answers
Type I error is "Megan's results show significant improvements in health associated with a whole foods diet."
A Type I error occurs when the null hypothesis is rejected, even though it is true.
In this case, the null hypothesis states that a whole foods diet would not have any impact on general health.
Therefore, a Type I error would occur if Megan's results show significant improvements in health associated with a whole foods diet.
This means that Megan would reject the null hypothesis and conclude that a whole foods diet does have an impact on general health, even though it is not true.
So, the statement that would indicate a Type I error is "Megan's results show significant improvements in health associated with a whole foods diet."
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5x - 10y = 2 what is the y Intercept
Answers
Answer:
(0, -1/5)
Y= -1/5
Step-by-step explanation:
15% of 9 is what number and how to solve using proportions
Answers
Answer:
Step-by-step explanation
Okay so lets solve step by step/
15% can be written as a fraction: 15/100
The of in the equation means multiplying.
15/100= 3/20
3/20*9= 270/20
27/2 is answer
x-1/x^2 - x - 20 Give the equivalent numerator if the denominator is (X - 5)(x + 4)(x + 3)
x^2 + 2x + 3
x^2 + 2x - 3
x^2-3
Answers
Answer:
\(x^2+2x-3\)
Step-by-step explanation:
Note that \(x^2-x-20=(x-5)(x+4)\), so, if the denominator is \((x-5)(x+4)(x+3)\), we need to multiply the numerator by \((x+3)\). And \((x-1)(x+3)=x^2+2x-3\).
Find the area of a regular octagon with side lengths of 17.2 m and an apothem length of 20.8 m.
Answers
Answer:
Pentagon a = 4.9 in. s = 7.1 in. /l ;/ >cvr'-. ~ j-?.1· '19~~. 5) Octagon a = 20.8 m s= 17.2m. ,4 ~;.>a-rt. ::: i, 17. z • t~f "g. ~ :::::, l'/?1 ,0 nt z, ... What is the length of the apothem to the nearest whole number
Step-by-step explanation:
Pentagon a = 4.9 in. s = 7.1 in. /l ;/ >cvr'-. ~ j-?.1· '19~~. 5) Octagon a = 20.8 m s= 17.2m. ,4 ~;.>a-rt. ::: i, 17. z • t~f "g. ~ :::::, l'/?1 ,0 nt z, ... What is the length of the apothem to the nearest whole number