Mathematics High School

Write the equation of the line that is perpendicular to 5x+8y=16 and passes through (-5,7).

Answers

Answer 1
In order to do this problem, we should first put the equation in slope-intercept form, and then consider the relationship between the slopes of perpendicular lines. 
Slope Intercept form (y=mx + b), m=slope, b=y-intercept
5x + 8y = 16         Subtract 5x from both sides
8y=-5x + 16          Divide both sides by 8
y= (-5/8)x  + 2

This is our line in slope-intercept form. What will the slope be of a line that is perpendicular to this one? It will be the opposite inverse of the slope of our equation. The opposite inverse means flipping the numerator and denominator, and multiplying by negative one.
Our slope = -5/8, so the opposite inverse is 8/5.

The slope of our perpendicular line will be 8/5
In slope intercept form, our line will be 
y=(8/5)x + b
We know it passes through the point (-5,7), so we can plug in -5 for x and 7 for y in order to find b:
7 = (8/5) * -5 + b
7 = 8 *-1 + b        Add 8 to both sides
15 = b
Plugging in b, we can get our general function in slope-intercept form:

y= (8/5)x + 15

Related Questions

the area of the a rectangular painting is 4902 cm squared. if the length of the painting is 86 cm, what is it’s width?

Answers

the width of the painting is 57 cm

Any nonzero number to the power of zero is equivalent to _____.

Answers

the answer to this question is 0          



The sum of 2 consecutive numbers is 97. Find the numbers

Answers

For two consecutive numbers :

let the first number is a, and of course the next number to it would be a+1

adding these two numbers: (a) + (a+1) = 97

then solve for a:

a+a+1=97
2a+1=97
2a=96
a=48


so the first number is 48 and the second number is the next one to it (49)

The two numbers are  48 and 49

Find a equation for the line, in point-slope form, that contains (5,1) and is perpendicular to 6x − 3y = 2.

Answers

hello : 
let the slope : a    and ; b the slope of the line : 6x - 3y = 2
the line that is perpendicular to 6x-3y=2  so : a×b = - 1 
but : 
6x - 3y = 2...      y = 2x-2/3  when : b = 2
 in point - form form of the equation of the line that is perpendicular
 to 6x-3y=2 is : y = (-1/2)x +c
contains (5,1) : 1 =  (-1/2)(5) +c
c = 7/2
an equation is : y= (-1/2)x +7/2

Find three consecutive integers with a sum of -36

Answers

The formula for this is:
 x + (x +1) + (x+2) = -36
3x + 3 = -36
3x  = -39
x = -13

-13,-12,-11

Hope this helps!

Please help me out!! ☮✌

Answers

a linear pair would equal 180 degrees

so 180-28 = 152

What is the reciprocal of 6 3/7?

Answers

I believe your answer is going to be -6 7/3. Reciprocals are the opposites of a number, so I switched the sign on the 6 and made it -. When dealing with fractions, the reciprocal is essentially just flipping the numerator and denominator, which is how I got 7/3. 

I hope I helped. Best of luck!

45/7 is the correct answer

How do you know that 6:14 is equivalent to 15:35 using a multiplication table?

Answers

Answer:Sample answer: Using a multiplication table, you would see that 6 and 15 are multiples of 3 by factors 2 and 5. You would also see that 14 and 35 are multiples of 7 by factors 2 and 5.

The required equivalency of the ratios 6:14 and 15:35 is 3 / 7 = 3 / 7.

Given that,
To determine that 6:14 is equivalent to 15:35 using a multiplication table.

What is the Ratio?

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
the given ratios are,
1) 6 : 4 = 6/4 = 2* 3/ 2 *7
2) 15:35= 15 / 35 = 5 * 3 / 5 *  7

Implies both the ratios are equivalent, by
6 : 14 = 15 : 35
2[ 3 : 7] = 5 [ 3 : 7 ]

Thus, the required equivalency of the ratios 6:14 and 15:35 is  3 / 7 = 3 / 7.

Learn more about ratio here:

brainly.com/question/13419413

#SPJ2

Which of the following is rational?
A. 3 x pie
B. 2/3 + 9.26
C. root 45 + root 36
D. 14.333... + 5.78765239...

Answers

The correct answer is B
2/3 is a rational number + 9.26 (also rational) = rational answer

Based on this excerpt, we can conclude that autism

Answers

I'm guessing you want a definition of autism if so "a mental condition, present from early childhood, characterized by difficulty in communicating and forming relationships with other people and in using language and abstract concepts."
Hope this helps. (ﾉ◕ヮ◕)ﾉ*:･ﾟ✧


solve for x. 3x-r=r(-3+x)

Answers

3x-r=r (-3+x)
3x-r=-3r+xr
3x-r+r=-3r+xr+r
3x=-2r+xr
3x-xr=-2r+xr-xr
3x-xr=-2r
x (3-r)=-2r
x (3-r)/(3-r)=-2r/(3-r)
x=-2r/(3-r)

Felicity's insurance company pays for 65% of her elbow surgery, after she pays a $500 deductible.
How much will Felicity pay for her elbow surgery if it costs $9400?

A. $3290
B. $3465
C. $3615
D. $3790

Answers

C

9400 – 500(deductible)

The remainder is 8900, and the company pays for 65% of that. That means Felicity pays 35%.

35% of 8900 is 3115. Add on the 500 deductible and she pays 3615 in total.
Its going to be D. $3790
Because you first have to take 9400•0.65= 6110
Then you subtract that from the total amount and the deductible like so:
9400-6110-500=3790
And that is how you come up with D as the answer

Triangles are congruent if they have the same ______________.

Answers

Triangles are congruent if they have the same (Shape and Size).
Triangles are congruent if they have the same size and shape.

Which expression is equivalent to 32⋅32⋅32⋅32 ? (Also All The 32s Are Fractions, The Lines Just Wont Come Up.)

Answers

Answer:

If this is 1/32 for all of them the answer would be (1/32)^4 or (1/32) to the 4th power. if this is 3/2 it would be (3/2)^4 or (3/2) to the 4th power.

Step-by-step explanation:

If this is 1/32 for all of them the answer would be (1/32)^4 or (1/32) to the 4th power. if this is 3/2 it would be (3/2)^4 or (3/2) to the 4th power. I hope this helps : )

Which equation illustrates the commutative property of addition?

Answers

the correct answer is A or the first one
yes answer is A.
first one

a + b = b +a
so in this case

12 + 6 + 15 = 12 + 15 + 6

Determine the relationship between the lines that pass through the given points: line
a.(-3, 5) and (0, 7) line
b.(6, 2) and (9, 4)

Answers

a. (-3,5)(0,7)
    slope = (7 - 5) / (0 - (-3) = 2/3

y = mx + b
slope = 2/3
(0,7)...x = 0 and y = 7
sub and find b, the y int
7 = 2/3(0) + b
7 = b....this is ur y int (0,7)
so ur equation for this line is : y = 2/3x + 7

b. (6,2)(9,4)
    slope = (4 - 2) / (9 - 6) = 2/3

y = mx + b
slope(m) = 2/3
(6,2)...x = 6 and y = 2
sub and find b, the y int
2 = 2/3(6) + b
2 = 4 + b
2 - 4 = b
-2 = b...this is ur y int (0,-2)
so this equation is : y = 2/3x - 2

so " a " has a slope of 2/3 and a y int of 7 and " b " has a slope of 2/3 and a y int of -2.

ur lines are parallel lines.....parallel lines will have the same slope and different y intercepts <===

The longer leg of a right triangle is 4cm longer than the shorter leg. the hypotenuse is 8cm longer than the shorter leg. find the side lengths of the triangle

Answers

Longer leg = x + 4

Shorter leg = x

Hypotenuse = x + 8


Using Pythagorean Theorem:

a^2 + b^2 = c^2

(x + 4)^2 + x^2 = (x + 8)^2

x^2 + 8x + 16 + x^2 = x^2 + 16x + 64

2x^2 + 8x + 16 = x^2 + 16x + 64

2x^2 +8x = x^2 + 16x + 48

2x^2 - 8x = x^2 + 48

x^2 - 8x = 48

x^2 - 8x - 48 = 0

You can complete the square from here or use the quadratic formula.

Completing the square:

x^2 - 8x = 48

x^2 - 8x + (-8/2)^2 = 48 + (-8/2)^2

x^2 - 8x + 16 = 48 + 16

(x - 4)(x - 4) = 64 or (x - 4)^2 = 64

x - 4 = +√64 OR x - 4 = -√64

x - 4 = +8 OR x - 4 = -8

x = 12 OR x = -4

However, you can't use negative 4 as a length because your length needs to be a positive.

So x will be 12.


Shorter leg: 12

Longer leg: 12 + 4

Hypotenuse: 12 + 8

Final answer:

To find the side lengths of the right triangle, we let the shorter leg be x cm, resulting in the longer leg and hypotenuse being (x + 4) cm and (x + 8) cm, respectively. Using the Pythagorean theorem, we establish the equation x² + (x + 4)² = (x + 8)², then solve for x to determine the side lengths.

Explanation:

The problem involves solving for the lengths of the sides of a right triangle using the Pythagorean theorem. Let the shorter leg of the triangle be x cm. According to the problem statement, the longer leg would then be x + 4 cm, and the hypotenuse would be x + 8 cm. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).

Using the theorem we can set up the equation:

x² + (x + 4)² = (x + 8)²

Solving for x will give us the lengths of the sides of the triangle:

Shorter leg: x cmLonger leg: x + 4 cmHypotenuse: x + 8 cm

PLEASE HURRY!! 30 POINTS

Simplify
73+3(23−13)2

Answers

if exponent 2

73+3(23−13)^2
= 73 + 3(10)^2
= 73 + 3(100)
= 73 + 300
= 373

if not exponent 2, but multiply 2 then

73+3(23−13) 2
= 73 + 3(10)2
= 73 + 3(60)
= 73 + 180
= 253

Answer:

1976

Step-by-step explanation:

Study the products shown. Is there a pattern?

(x + 3)2 = x2 + 6x + 9

(x + 4)2 = x2 + 8x + 16

(x + 5)2 = x2 + 10x + 25

(x + 6)2 = x2 + 12x + 36

Each product is in the form ax2 + bx + c.

Which of the following describes the relationship between b and c?

c is 1.5 times that of b.

c is double b.

c is the square of half of b.

c is the square of b.

Answers

c is the square of half of b.

This is evident in all products,

(6/2)² = 3²
= 9
(8/2)² = 4²
= 16
(10/2)² = 5²
= 25
(12/2)² = 6²
= 36
(b/2)² = c

Answer:

The correct option is 3. c is the square of half of b.

Step-by-step explanation:

The given equations are

[tex](x+3)^2=x^2+6x+9[/tex]

[tex](x+4)^2=x^2+8x+16[/tex]

[tex](x+5)^2=x^2+10x+25[/tex]

[tex](x+6)^2=x^2+12x+36[/tex]

These are the perfect square. According to this pattern,

[tex](x+y)^2=x^2+2xy+y^2[/tex]           .... (1)

Each product is in the form

[tex](x+y)^2=ax^2+bx+c[/tex]         .... (2)

From (1) and (2), we get

[tex]b=2y[/tex]

[tex]c=y^2[/tex]

[tex]c=(\frac{b}{2})^2[/tex]                    [tex][\because b=2y][/tex]

It means c is the square of half of b.

Therefore the correct option is 3.

One side of trapezoid is 10 inches. The side parallel to this is twice as long as this side. The height is half as long as the given side length. Find the area of the trapezoid.

Answers

the formula for area of a trapezoid is: 1/2 (b1+b2) h
b1=10
b2=10·2=20 because it stated the side parallel is twice as long as the side above
h=10/2=5 because the height is half as long as the give side length
area of the trapezoid is: 1/2 (10+20) 5
(5·10)·5
50·5
area of the trapezoid is 250 in²

The cost of 1 movie ticket is $7.50. The cost 2 movie tickets is $15.based on this constant rate of change what is the cost of 4 movie tickets

Answers

The cost of 4 tickets is 30 dollars 4 x 7.50 = 30

You found 6.60 on the ground at school, alpl in nickels, dimes, and quarters. you have twice as many quarters as dimes and 42 coins in all. how many of each type of coin do you have?

Answers

Let the number of nickel coins be n, the number of quarter coins be q and the number of dimes be d.

We know that 1 nickel= $0.05, 1 dime= $0.1 and 1 quarter= $0.25,


We found $6.60 means that : i) 0.05n+0.1d+0.25q=6.60

we have 42 coins in all mean: ii) n+d+q=42

we have twice as many quarters as dimes mean that iii) q=2d


using the last relation we can reduce the number of unknowns by writing all q's in terms of d's as follows:

i) 0.05n+0.1d+0.25q=6.60
ii) n+d+q=42

substitute q with 2d:

i) 0.05n+0.1d+0.25(2d)=6.60
ii) n+d+(2d)=42

i) 0.05n+0.1d+0.5d=6.60
ii) n+d+2d=42


i) 0.05n+0.6d=6.60
ii) n+3d=42

multiply the second equation by -0.2, to eliminate the d's:

i) 0.05n+0.6d=6.60
ii) -0.2n-0.6d=-8.4
---------------------------

i+ii)  

-0.2n+0.05n=6.60-8.4
-0.15n=-1.8
n=-1.8/(-0.15)=12

substitute in i):

0.05n+0.6d=6.60
0.05*12+0.6d=6.60
0.6+0.6d=6.60
0.6d=6.0
d=10


finally, from equation n+d+q=42:

12+10+q=42
22+q=42
q=42-22=20


Answer: # nickels=12, # dimes=10, # quarters=20

If the parent function is y = 2x, which is the function of the graph?




A. y = 0.5(2)x + 1 − 3


B. y = 0.5(2)x + 1 + 3


C. y = 0.5(2)x − 1 − 3


D. y = 0.5(2)x − 1 + 3


Description

Answers

Answer is C but if its on grad point your answer is 0.5(2)^x

What's the missing side

Answers

x = 35/sin(40) = 54.4503

 round answer as needed.

Simplify: (sin θ − cos θ) − (sin θ + cos θ)2 (5 points)

Answers

I'll use x instead of theta

(sin(x) - cos(x)) - (sin(x) + cos(x))^2
(sin(x) - cos(x)) - (sin^2(x) + 2*sin(x)*cos(x) + cos^2(x))
(sin(x) - cos(x)) - (sin^2(x) + cos^2(x) + 2*sin(x)*cos(x))
(sin(x) - cos(x)) - (1 + 2*sin(x)*cos(x))
sin(x) - cos(x) - 1 - 2*sin(x)*cos(x)
- 2*sin(x)*cos(x) - cos(x) + sin(x) - 1 

The final answer is choice D



Show work on simply 2+(3g-4)-(8g+3)

Answers

2 + 3g - 4 -8g - 3

2 - 7 -5g

-5g - 5 is your answer

hope this helps

A motor racing circuit has the length of 5 5/6 milesa straight section of the circuit has the length 1 1/4 mileswhat fraction of the circuit is the straight section?

Answers

The straight section is 3/14 of the total circuit. This is mostly a problem of adjusting fractions to have common denominators. The fraction of the total circuit is ( length of straight section ) / ( length of total racing circuit ) = ( 1 1/4 ) / ( 5 5/6 ) first, convert the integer parts to a fractions with the same denominator as the fractional part: = ( (1x4)/4 + 1/4 ) / ( (5x6 / 6) + 5/6 ) combine the fractions to make a single fraction in numerator & denominator: = ( 4/4 + 1/4 ) / ( 30/6 + 5/6 ) = ( 5/4) / ( 35/6 ) the division by 35/6 can be done by instead multiplying by the inverse of 35/6: = 5/4 x 6/35 which is done by multiplying the numerators and denominators, and then simplifying by factoring out common divisors from top and bottom: = ( 5 x 6 ) / ( 4 x 35 ) = 30 /140 = 6 / 28 = 3/14

Answer:

3/14

Step-by-step explanation:

Three eggs are required to make two dozen muffins. how many eggs are needed to make 12 dozen muffins using a proportion

Answers

18 eggs are required to make 12 dozen muffins
Amount of eggs needed to make 2 dozen muffins
= 3

Amount of eggs needed to make 1 dozen muffins
=3/2
=1.5

Amount of eggs need to make 12 dozen muffins
=1.5x12
=18

The plate is rotated 90° about the origin in the counterclockwise direction. In the image trapezoid, what are the coordinates of the endpoints of the side congruent to side FG?

Answers

[tex] (x, y) --\ \textgreater \ (-y, x) (-2, 5) --\ \textgreater \ (-5, -2)[/tex]
The answer to ur question is (x, y) --\ \ < \ (-y, x) (-2, 5) --\ \ < (-5, -2). Hope this helps you!!

Solve the equation 1-|1/3q-5| = -6

Answers

q=1/36 or q=-1/6, for the question
q=36 hope this helps!!!
Other Questions
Juanita is making necklaces to give as presents. She plans to put 15 beads on each necklace. Beads are sold in packages of 20. What is the least number of packages she can buy to make necklaces and have no beads left over really need a answer and explanation for this As disciples of Jesus Christ, how are we called to strive for, stand up for, labor for, and nurture peace? The seventh grade class contributed $60 toward refreshments and the sixth grade contributed $50. How much money did the seventh grade class contribute for each dollar contributed by the sixth grade class Este objeto se usa para poner la comida con los platos, las cucharas, los tenedores y los cuchillos. Usualmente, la familia se sienta alrededor de este objeto para comer juntos. la mesa de comedor la alfombra el sof la silla A personal experience timeline is used to help the writer do what P = W/t solve for W? In the equation b= a-2, which is the independent variable and which is the dependent variable ? Explain???? need help i don't understand An athlete trains on a circular track of radius 40 m and jogs 10 laps each day, 5 days a week. How far does he jog each week? Round the answer to the nearest whole number of metres. A car dealership increased the price of a certain car by 13% . The original price was $41,200 Use the partial quotient strategy to solve 74 3 the sum of twice a number and 15 is -42 Which correctly shows where a comma is needed in the sentence? A. Neither light nor moisture, is good for food preservation so most food products are packaged immediately after they are processed. B. Neither light nor moisture is good for food preservation, so most food products are packaged immediately after they are processed. C. Neither light nor moisture is good for food preservation so most food products are packaged, immediately after they are processed. D. Neither light nor moisture is good, for food preservation so most food products are packaged immediately after they are processed. Read the passage that Gabriel wrote for his narrative essay. Once we arrived at the local pool, I looked around to see who else was there. Normally, I would have found the kids frolicking and splashing in the water hilarious, but not today. They were cute, but the fact that they were half my age and swimming around like so many ducks just made me feel worse. You nervous? my mom asked. I swallowed the lump in my throat. Not really, I mumbled, trying to hide my shaking hands in my pockets. I dont think I fooled my mom, but she didnt comment on the fact that I looked a little green. Instead, she tried to encourage me, saying, Well, I think its really impressive that youre going to confront your fear of water and learn to swim. Which is bigger 1/3 or 0.33 Napoleon's Continental System was designed to __________. According to the table how many points did the two countries agreed I say 4 am I right Figurative language in Carry Your Own Skis The sum of a number and 12 is 20. What is the number? suppose 255,113 people live in a city is it reasonable to say that about 300,00 live in the city? use the number line to help you solve the problem . Steam Workshop Downloader