what is the equation in standard form of the line that passes through the point (6, -1) and is parallel to the line represented by 8x + 3y =15?
The equation in standard form of the line is given by:
[tex]\frac{8}{3}x + y = 15[/tex]
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, the line is parallel to 8x + 3y =15, hence the slope is given by:
[tex]m = -\frac{8}{3}[/tex]
It passes through the point (6, -1), hence:
y = mx + b
[tex]-1 = -\frac{8}{3} \times 6 + b[/tex]
b = 15
Hence:
[tex]y = -\frac{8}{3}x + 15[/tex]
In standard form:
[tex]\frac{8}{3}x + y = 15[/tex]
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The difference of two numbers is 4 and their product is 60. Find the numbers.
Answer:
x = 10; y = 6
Step-by-step explanation:
Let's list the factors of 60 because the product of those numbers is 60.
⇒ Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60The following possibilities of x and y are possible using (x × y = 60):
60 and 1 ⇒ x = 60; y = 1 ⇒ 60 × 1 = 6030 and 2 ⇒ x = 30; y = 2 ⇒ 30 × 2 = 6020 and 3 ⇒ x = 20; y = 3 ⇒ 20 × 3 = 6015 and 4 ⇒ x = 15; y = 4 ⇒ 15 × 4 = 6012 and 5 ⇒ x = 12; y = 5 ⇒ 12 × 5 = 6010 and 6 ⇒ x = 10; y = 6 ⇒ 10 × 6 = 60Let's check each possibilities using the equation (x - y = 4):
60 and 1 ⇒ 60 - 1 = 59 ≠ 430 and 2 ⇒ 30 - 2 = 28 ≠ 420 and 3 ⇒ 20 - 3 = 17 ≠ 415 and 4 ⇒ 15 - 4 = 11 ≠ 412 and 5 ⇒ 12 - 5 = 7 ≠ 410 and 6 ⇒ 10 - 6 = 4 = 4 (Correct)Thus, the values of x and y are 10 and 6 respectively.
NEED ANSWER ASAP How many people drive less than 30 km to work?
Answer:
20 peopleStep-by-step explanation:
According to the graph we have
10 km = 11 people20 km = 9 peopleTheir sum is
11 + 9 = 20 peopleI need help with Function Operations please
Answer:
30
Step-by-step explanation:
The ring operator signifies a composition of functions. The composition is evaluated right-to-left. That means the composition ...
[tex](f\circ g)(x)[/tex]
should be interpreted to mean ...
[tex]f(g(x))[/tex]
___
To evaluate f(g(6)), we first evaluate g(6):
g(6) = 6² -5 = 31
Then we evaluate the function f using that as its argument:
f(31) = 31 -1 = 30
f(g(x)) = 30
please help :)))))) <33
Answer:
56
Step-by-step explanation:
You need to divide 20/16 and 70*z to find the missing length.
The yearbook club had a meeting. The meeting had 8 people, which is one-fourth of the club. How many people are in the club?
Answer:
32
Step-by-step explanation:
Since we know 8 = 1/4
We can convert the 1/4 into a percentage:
8 = 25%
To get to 100% which is the full club we have to multiply both sides by 4:
8×4 = 25% ×4
32 = 100%
So there are 32 people in the club.
please help me i don't get it
Area = length x width
area of files = 30 x 20 = 600 square feet
area of unmoved field = 16 x 26 = 416 square feet
area that was mowed = 600 - 416 = 184 square feet
answer: 184 square feet
Answer:
184 ft
Step-by-step explanation:
so, for this, the key is the smaller dimentions on the inside, they are the area of the smaller inner rectangle (416 ft) and the bigger dimentions on the outside, are for the entire rectangle including the mowed area (600 ft), but you dont know the exact value of the mowed area, so you would simply subtract the areas (600-416=184) and that number, 184, is the area of the mowed area that you didnt know.
hope this helps
kleann
A triangle has one side of length 5 and another of length 9. Which of the following are possible lengths of the third side?
Answer:
Anything between 4 and 14
Step-by-step explanation:
When two lengths of a triangle are added together, they must be greater than the third side. Therefore the unknown length cannot be equal to or less than 4 nor equal to or greater than 14.
Need help on this. can anyone help please?
Answer:
it is B
Step-by-step explanation:
that's because line goes through (0,0)
The area of a rectangle is 5 x cubed + 19 x squared + 6 x minus 18 with length x + 3. using synthetic division, what is the width of the rectangle?
5 x squared + 4 x minus 6
5 x squared + 34 x + 108 + startfraction 306 over x + 3 endfraction
5 x cubed + 4 x squared minus 6 x
5 x squared + 34 x + 108 + startfraction 306 over x minus 3 endfraction
A rectangle is a 2-dimensional shape having 4 sides. The width of the rectangle is 5x^2 + 4x - 6
How to find the quotient of a function using synthetic division?A rectangle is a 2-dimensional shape having 4 sides
The formula for calculating the area of the rectangle is given as:
A = lw
Given the following
Area = 5x^3+19x^2+6x-18
Length = x + 3
Using the synthetic division:
5x^2 + 4x - 6
x + 3 | 5x^3+19x^2+6x-18
5x^3 + 15x^2
________________________
4x^2 + 6x
4x^2 + 12x
__________________________
-6x - 18
-6x - 18
Hence the width of the rectangle is 5x^2 + 4x - 6
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Answer:
A
Step-by-step explanation:
Please help me with this please and thank you please actually help me with this please
Answer:
easy ok first 0 -3 1 -4 2 -5
Step-by-step explanation:
ask me another
What is the answer to this?
Answer:
-8
Step-by-step explanation:
[tex]\ \ \ \ \ \ \dfrac{-9 -7}{2} \\\\\\= \ \ \ \dfrac{-16}{2} \\\\\\= \ \ \dfrac{-(2^{4} )}{2^{1} } \\\\\\= \ \ -(2^{4 - 1}) \\\\\\ = \ \ -(2^{3})\\\\\\= \ \ - (2 \times 2 \times 2) \\\\\\= \ \boxed{-8}[/tex]
Answer:
-8
Step-by-step explanation:
Pls I need it for a testI’ll give out 20 points
Answer:
It should be D.
Step-by-step explanation:
a scientist plans to study exotic birds in the rain forest. the helicopter flight to and from the rain forest costs$499. supplies costs $122 for each day. how many days can the scientist spend in the rain forest on $1,283 budget ?
Answer:
The scientist would be able to go to the rain forest for only 2 days.
Step-by-step explanation:
The scientist only has 1,283. You subtract 1,283 by 122 and 499 and you are left with 662. The scientist wants to go to the rain forest again so he spends 122 and 499 with 662. All he has left now is 41. He can't afford it anymore.
What's 19 to the power of 63? Brain fart-
Answer:
2.5782963e+29
Step-by-step explanation:
basically 19 times itself 63 times
Answer:
19^63 , 3.6431483821774E+80
Step-by-step explanation:
completing the square k^2-2k-8=0
[tex]~~~~k^2-2k-8=0\\\\\implies k^2 - 2k +1^2-1-8=0\\ \\\implies ( k-1)^2-9=0\\\\\implies (k-1)^2-3^2 =0\\\\\implies (k-1-3)(k-1+3)=0\\\\\implies (k-4)(k+2)=0\\\\\implies k=4,~~ k= -2[/tex]
What is the equation, in slope-intercept form, of the line that contains the points (4, 11) and (-4, -5)? A. y = 2x + 3 B. y = -2x - 3 C. y = 3x + 2 D. y = 3x - 2
Answer:
A. y = 2x +3
Step-by-step explanation:
Find the number that makes the ratio equivalent to 36:81.
4:
Answer:
9
Step-by-step explanation:
9*4 = 36
9*9 = 81
divide both by 9 and you get 4:9
Find the mean of the data set without the outlier.
Then, find the mean of the data set with the outlier.
Answer:
The median is 8.1
Step-by-step explanation:
You add up all the numbers and divide it by how much numbers there are.
1) Add. 1 + 7+ 16 + 18 + 40 = 81
2) Count. There are 10 numbers.
3) Divide 81/10
4) 8.1
The median is 8.1
A certain third-degree polynomial function has zeros at-5, -1, and 2. Which could NOT be a factor of the expression that defines the function?
7 - 1
Answer:
I am pretty sure it is the second option
Step-by-step explanation:
Hope this helps
Find the measures of all angles and sides
Answer:
See attached image. 82 and 98 degrees.
Step-by-step explanation:
On attached document.
Enter the missing numbers in the boxes to complete the table of equivalent ratios of lengths to widths.
Answer:
for number 6 the width is 24 and the blank after the length of 9 is 12 and after 48 width it is 60. your welcome.
HELP!!! On 4 6 and 7
Show that x = -5 is a solution to the inequality 18x − 42 ≠ 7x
Answer:
See Below
Step-by-step explanation:
Put -5 in place of x
18(-5)-42 does not equal 7(-5)
-90-42 does not equal -35
-90-42=-132, not -35
The value x = -5 is a solution to the inequality 18x − 42 ≠ 7x.
What is inequality?The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than, or < ‘less than.
For showing x =-5 is a solution of the inequality 18x − 42 ≠ 7x put x =-5 in the solution if it satisfies the condition then it is a solution of the given inequality.
18x − 42 ≠ 7x
18 x ( -5 ) - 42 ≠ 7 x ( -5 )
-132 ≠ -35
The value x = -5 is satisfying the given inequality. Hence, x = -5 is a solution to the inequality 18x − 42 ≠ 7x.
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The cake that Larry is baking requires 1 cup of sugar. Larry is adding sugar to a bowl using a measuring scoop. In the first scoop, he adds 7/8 cup of sugar. In the second scoop, he adds another 7/8 cup of sugar. Has Larry measured the sugar correctly?
Howdoyouwrite
4
5
asapercentage?
Answer:
80%
Step-by-step explanation:
4/5 as a percentage would be 8/10ths, or 80%
By multiplying the fraction to get a denominator of 10, you get 8 over 10. Therefore it would be 80 percent of 100.
What is the range of the fallowing numbers 29, 47, 32, 36, 57, 20, 39, 38, 52, 51, 28, 24, 44, 40, 45, 35, 50, 50, 32, 31
Answer: 37
Step-by-step explanation:
range = max - min
max = maximum value in a data set
min = minimum value in a data set
Maximum value: 57
Minimum value: 20
Range: 37
Answer:
37
Step-by-step explanation:
First of all, let's define what range is. The range is the highest value of a set of numbers minus the lowest value of the same set. In this case, your highest value is 57 and your lowest value is 20. The sum would be 57 - 20 which would equal 37 and that is your answer.
Hope I helped you out :)
I’m just trying to check my math, I got 159
Wellington city engineers are designing two parallel roads by the International Polo Club to help with traffic flow during tournaments.
Answer:
159°
Step-by-step explanation:
Angle 21° and <4 are supplementary angles!
21 + x = 180
x = 159°
Hope this helps!
The measure of angle ∠4 is 159.
What are corresponding angles?The angles that are in the same position on a given two parallel lines intersected by a transversal line are called the corresponding angles.
Corresponding angles are always equal.
We can also have alternate angles which are always equal.
We can also have alternate interior and exterior angles which are equal.
The angles on the same side make upto 180 degrees
We have,
From the figure,
The angle opposite to 21° and ∠4 sum is 180.
This means,
Angles on the same side.
Now,
Opposite angles are equal.
So,
21 + ∠4 = 180
∠4 = 180 - 21
∠4 = 159
Thus,
The measure of angle ∠4 is 159.
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A windowpane is 12 inches by 5 inches. What is the distance between opposite corners
of the windowpane? ( it’s the pythagorean theorem )
Which statement best describes the "cult of domesticity" that emerged in the late 19th century?
A. A movement to allow women into medical schools.
B. Groups of women who gathered to discuss matters of the home and family.
C A widespread set of values relating to women, their behavior, and their place in the home.
D. The movement to attain voting rights for women citizens.
Answer:
a movement one single movement cultivating one group
Answer: C
Step-by-step explanation:
