The line that passes through (-2, 1) and (8, 2) is:
y = (1/10)*x + 12/10
How to find the equation of the line?I assume you want to find the equation of the line that passes through (-2, 1) and (8, 2).
A general linear equation is written as:
y = a*x + b
If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope can be written as:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
In this case, we know that it passes through (-2, 1) and (8, 2), then:
[tex]a = \frac{2 - 1}{8 - (-2)} = 1/10[/tex]
Then the line is:
y = (1/10)*x + b
To find the value of b, we use one of the given points, for example if we use (8, 2), it means that when x = 8, we must have y = 2.
2 = (1/10)*8 + b
2 - 8/10 = b
20/10 - 8/10 = b
12/10 = b
Then the linear equation is:
y = (1/10)*x + 12/10
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which statement is true about fiction
Answer:
The function is even because of symmetry over x axis
Round 0.90 decimal to the nearest tenth
0.90 nearest tenth is 9 since there is no other number to help round it over.
Give the equation of a line that goes through the point ( 4 , 9 ) and is parallel to the line − 3 x + 7 y = 21 .
Answer:
[tex]\sf y=\dfrac{3}{7}x+\dfrac{51}{7}[/tex]
Step-by-step explanation:
Given equation: -3x + 7y = 21
Slope-Intercept Form: y = mx + b -
where:
m is the slopeb is the y-intercept (when x = 0)Note: parallel lines have the same slope.
1. Rewrite the given equation in slope-intercept form:
[tex]\sf -3x + 7y = 21\ \textsf{[add 3x to both sides]}\\\\-3x + 3x + 7y = 21 + 3x\\\\7y = 3x + 21\ \textsf{[divide both sides by 7]}\\\\\dfrac{7y}{7}=\dfrac{3x+21}{7}\\\\\implies y=\dfrac{3}{7}x+3[/tex]
Here, this equation has a slope of ³⁄₇ and a y-intercept of 3.
2. Find the equation of the parallel line:
substitute the point (4, 9) into the equation to find the value of b
[tex]\sf y=\dfrac{3}{7}x+b\\\\9=\dfrac{3}{7}(4)+b\\\\9=\dfrac{12}{7}+b\\\\\dfrac{63}{7}-\dfrac{12}{7}=\dfrac{12}{7}-\dfrac{12}{7}+b\\\\\dfrac{51}{7}=b[/tex]
[tex]\sf \textsf{Equation:}\ y=\dfrac{3}{7}x+\dfrac{51}{7}[/tex]
3. Check your work:
[tex]\sf y=\dfrac{3}{7}x+\dfrac{51}{7}\\\\9=\dfrac{3}{7}(4)+\dfrac{51}{7}\\\\9=\dfrac{12}{7}+\dfrac{51}{7}\\\\9=\dfrac{63}{7}\\\\9=9\ \checkmark[/tex]
[tex]\sf \textsf{Therefore, the equation of the parallel line is:}\ y=\dfrac{3}{7}x+\dfrac{51}{7}[/tex]
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Answer:
[tex]\sf y=\dfrac{3}{7} x+\dfrac{51}{7}[/tex]
Step-by-step explanation:
First, write the given equation in slope-intercept form. That is, you can make y the subject in the given equation.
Slope intercept form
y = mx + c
Here,
m = slope
c = y-intercept
Let us write the given equation in slope-intercept form.
− 3x + 7y = 21
Add 3x to both sides.
7y = 3x + 21
Divide both sides by 7.
[tex]\sf y=\dfrac{3}{7}x +\dfrac{21}{7} \\\\y=\dfrac{3}{7}x +3[/tex]
We know that the slopes of parallel lines are equal. Therefore, the slope(m) of the new line is 3/7.
The new line is going through ( 4, 9 ). Using that, let us find the value of c (y-intercept), by substituting the values of m, y, and x.
( 4, 9 ) → ( x , y )
m → 3/7
Let us find the value of c
[tex]\sf y = mx+c\\\\9 =\dfrac{3}{7}*4+c\\\\ 9=\dfrac{12}{7}+c\\\\ 9-\dfrac{12}{7}=c\\\\\dfrac{63-12}{7} =c\\\\\dfrac{51}{7} =c[/tex]
And now let us write the equation of the new line.
[tex]\sf y =mx+c\\\\\sf y=\dfrac{3}{7} x+\dfrac{51}{7}[/tex]
hey! Solving linear equations with integers! i don’t think it should be that hard since it’s practice, I just need some help with a bit more problems! :’)
1) -3 ( 3 - x ) = 2x + 5
2) -6 - 9p = + 3p
3) -5 (-4 - a ) = 3a + 8
4) s - 6 = -5s
that should be it! Ty
Solution 1 :-
>> -3 (3 - x) = 2x + 5
>> -3 × (3 - x) = 2x + 5
>> -9 + 3x = 2x + 5
>> 3x - 2x = 9 + 5
>> x = 14
Solution 2 :-
>> -6 - 9p = 3p
>> -9p - 3p = 6
>> -12p = 6
>> p = -1/2
Solution 3 :-
>> -5 (-4 - a) = 3a + 8
>> -5 × (-4 - a) = 3a + 8
>> 20 + 5a = 3a + 8
>> 5a - 3a = 8 - 20
>> 2a = -12
>> a = -12 / 2
>> a = -6
Solution 4 :-
>> s - 6 = -5s
>> s + 5s = 6
>> 6s = 6
>> s = 6 / 6
>> s = 1
Answer:
1) x = 14
2) p = - [tex]\frac{1}{2}[/tex] (- 1/2)
3) a = -6
4) s = 1
work shown in image :)
hope this helps!!
18
1 point
The scatter plot shown below would best be modeled by a line of best fit.
True
False
G
0
The statement about using the line of best fit for the given scatter plot is; False
How to interpret a scatter plot?When we have a scatter plot, it is always best to look for the line of best fit or curve of best fit depending on the nature of the variation of the plotted points.
Now, from the scatter plot image attached, we can see that the points are already looking like a curved plot form and so what we will need her will be a curve of best fit and not a line of best fit plot and as such the statement about using a line of best fit plot is false.
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A company designs a logo using a kite figure around the letter t. The logo is 12 centimeters wide and 16 centimeters tall. What is the area of the logo?
The area of the logo using the length and the width is 162 cm²
Area of logoLength of logo = 16 cm
Width of logo = 12 cm
Area of logo = length × width
= 16 cm × 12 cm
= 192 cm²
Therefore, the area of the logo using the length and the width is 162 cm²
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Which of the following describe an angle with a vertex at E.
Answer:
A and B are correct
Step-by-step explanation:
The middle letter represents the vertex of an angle. For instance, angle ABC has a vertex at B. Because the letter "e" is in the middle of angle FED and angle DEF, it represents the vertex of those angles. Hope this helps
A website sells a dress at £50 and shoes at £43.
The website has an offer:
Buy a dress and shoes together and get
1
3
off the price.
There is also a shipping and handling charge of £7 added at the end, after any discount.
If Ruth buys both a dress and shoes, how much will she actually pay?
Answer:
£69
Step-by-step explanation:
Given information:
Cost of dress = £50Cost of shoes = £43Discount offer: Buy a dress and shoes together and get 1/3 off the price.Shipping & handling charge = £7 (added after the discount is applied)Cost of buying a dress and shoes:
⇒ £50 + £43 = £93
Discount:
⇒ 1/3 of £93 = 1/3 × 93 = £31
Cost of goods after discount is applied:
⇒ £93 - £31 = £62
Addition of shipping and handling:
⇒ £62 + £7 = £69
Therefore, Ruth will pay £69 if she buys a dress and shoes.
HELP ANSWER FOR 30 POINTS
A cone has a volume of 24 cubic inches. What is the volume of a cylinder that the cone fits exactly inside of?
Answer: 72 cubic inches
Step-by-step explanation:
The formula for the volume of a cone: [tex]\dfrac{1}{3}\pi r^{2}h[/tex]
Formula for the volume of a cylinder: [tex]\pi r^{2}h[/tex]
We are given that a cylinder should fit exactly inside the cone
Upon comparing the two equations above, we get:
[tex]$$Volume of cone = \dfrac{1}{3}\text{Volume of cylinder}[/tex]
Since we are given the volume of cone is 24 cubic inches, we can write down the below:
[tex]24 = \dfrac{1}{3}\text{Volume of cylinder }\\ \text{Volume of cylinder = 72 cubic inches}[/tex]
Therefore, we can conclude that if the volume of the cylinder is 72 cubic inches, then the cone with volume of 24 cubic inches can fit exactly in.
Answer:
[tex]V_{cylinder}=72\:in^3[/tex]
Step-by-step explanation:
[tex]V_{cone}=24\: in^3[/tex] (Given)It is given that: Cone fits exactly inside the cylinder.[tex]\implies V_{cylinder}=3*V_{cone}[/tex][tex]\implies V_{cylinder}=3*24[/tex][tex]\implies V_{cylinder}=72\:in^3[/tex]A diver sits on a boat at the surface of the ocean preparing to dive. She dives in and descends to -128 feet. After a few minutes, she ascends 45 feet to swim with a pod of dolphins that has appeared. What integer represents the diver's position in feet (depth) when she swims with the dolphins?
HELP WILL NAME BRAINLIEST
Answer:
The diver's position in feet (depth) when she swims with dolphins is -83 feet.
Step-by-step explanation:
First highlight the important information from the question.
A diver sits on a boat at the surface of the ocean preparing to dive. She dives in and descends to -128 feet. After a few minutes, she ascends 45 feet to swim with a pod of dolphins that has appeared. What integer represents the diver's position in feet (depth) when she swims with the dolphins?
So, first she descends -128 feet, then she ascends 45 feet to swim with dolphins. So, now that we have the important information highlighted we can solve the problem.
-128+45=-83.
The diver's position in feet (depth) when she swims with dolphins is -83 feet.
Hope this helps!
If not, I am sorry.
Write an equation in slope intercept form with the given information.
Slope = 4 and goes through point (3,0)
Answer:
y = 4x - 12
Step-by-step explanation:
Helppp! Which linear inequality is represented by the graph
WILL GIVE BRAINLIEST!!!! *20 points*
Answer:
g(-0.0001) = -9
g(0.0001) = -1
g(0) = -1
g(9) undefined
Step-by-step explanation:
g(9) undefined .because the graph have an empty circle
at (9 , 0) which means g is not defined at 9.
insert one rational number between 5 and 5.25
Answer:
5.1
Step-by-step explanation:
A rational number is any number that can be written as a fraction, or is a decimal that terminates or repeats.
Find the length of side AB.
Give your answer to 3 significant figures.
Answer:
[tex]\huge\boxed{\sf AB = 8.86 \ cm}[/tex]
Step-by-step explanation:
Given:θ = 41°
Hypotenuse = BC = 13.5 cm
Required:opposite = AB = ?
We will use the trigonometric ratio of sin.
Solution:[tex]\displaystyle sin \ \theta = \frac{opposite }{hypotenuse} \\\\sin \ 41=\frac{AB}{13.5} \\\\0.656 = \frac{AB}{13.5} \\\\0.656 \times 13.5 = AB\\\\8.86 \ cm = AB\\\\\boxed{ AB = 8.86 \ cm}\\\\\rule[225]{225}{2}[/tex]
please hurry its due in 5 mins
Answer:
Divide the shape in two pieces:
A rectangle and a triangle
Find area of rectangle:
A=length*width=5*4=20m^2
Find area of triangle:
base of triangle=5-2=3m
height of triangle=8-4=4m
Area=(1/2)*base*height
=(1/2)(4)(3)=6m^2
Total area=6+20=26m^2
Hope it helps!
If 1=3 2=3 3=5 4=4 5=4 then 6=?
The value of the 6 is 3.
If you write 1 in word then you will write one and if you count the letter it will give you 3
Similarly, if you write the numbers 2,3,4,5 in word and count the number you will get 3,5,4,4 respectively.
What are the counting letters?counting Letters provides a perfect way to introduce number words to beginning readers, as well as discuss the concepts of letters and words.
So, if you write 6 in words you will write six and on counting the letter you will get 3.
Hence, 6 = 3 ans.
Therefore the value of the 6 is 3.
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A circle representing a pool is graphed with a center at the origin. Grant enters the pool at point A and swims over to a friend who is located at point B.
Find the nature of the graph of the function y = -9x3 + 5x2 - 2x using end behavior.
The graph goes upwards on the left side and downwards on the right side, so the correct option is the first one.
How is the end behavior of the function?
We have the function:
[tex]y = -9*x^3 + 5*x^2 -2x[/tex]
This is a cubic polynomial with a negative leading coefficient.
So, when x takes large negative values, because the leading coefficient is negative, y will take large positive values.
And when x takes large positive values, because the leading coefficient is negative, y will take large negative values.
So the nature is:
The graph goes upwards on the left side and downwards on the right side. The correct option is the first one.
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4. Solve: 8−2n−6n=−16
A. n=11
B. n=9
C. n=10
D. n=3
Answer:
D. n=3
Step-by-step explanation:
8-2n-6n= –16
Take 8 to the other side
-2n-6n= -16-8
Solve them
-8n = -24
Take -8 to the other side
[tex]n \: = \frac{ - 24}{ - 8} [/tex]
n = 3
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathbf{8 - 2n - 6n = -16}[/tex]
[tex]\huge\textbf{Solving for the answer:}[/tex]
[tex]\mathbf{8 - 2n - 6n = -16}[/tex]
[tex]\huge\textbf{Combine the like terms:}[/tex]
[tex]\mathbf{(-2n - 6n) + 8 = -16}[/tex]
[tex]\mathbf{-2n - 6n + 8 = -16}[/tex]
[tex]\mathbf{-8n + 8 = -16}[/tex]
[tex]\huge\textbf{Subtract \boxed{\bf 8} to both sides:}[/tex]
[tex]\mathbf{-8n + 8 - 8 = -16 - 8}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathbf{-8n = -16 - 8}[/tex]
[tex]\mathbf{-8n = -24}[/tex]
[tex]\huge\textbf{Divide \boxed{\bf -8} to both sides:}[/tex]
[tex]\mathbf{\dfrac{-8n}{-8} = \dfrac{-24}{-8}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathbf{n = \dfrac{-24}{-8}}[/tex]
[tex]\mathbf{n = -24 \div -8}[/tex]
[tex]\mathbf{n = 3}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\textsf{Option D. \boxed{\frak{n = 3}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Answer:
In the given Triangle problem, the three options are:
1. m∠5 + m∠6 = 180°
2. ∠2+ ∠3 = ∠6
3. m∠2 + m∠3 + m∠5 = 180°
Step-by-step explanation:
Concept: Consider Δ ABC with Exterior angles ∠1, ∠4 and ∠6.
Use the Exterior angle Property of Triangle which says that an exterior angle of a triangle is equal to the sum of the opposite interior angles.
For Exterior angle ∠1 we have:
∠1 = ∠5 + ∠3
Similarly, for Exterior ∠4 we have:
∠4 = ∠5 + ∠2
Similarly, for Exterior ∠6 we have:
∠6 = ∠2 + ∠3
Now, use the Triangle Sum Property which states that in a triangle sum of the measures of angles is equal to 180°
m∠2 + m∠3 + m∠5 = 180°
Linear Pair:
The measure of a straight angle is 180°, so a linear pair of angles must add up to 180°.
m∠5 + m∠6 = 180°
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2m² + 2m – 12 = 0
m=?
a. 2,-12
b. 3,1
c. 1.-3
d. -2.2
Step-by-step explanation:
F1/A1 = F2/A2
10/2=F2/4
5=F2/4
F2=5x4
F2=20
How many solutions are there to the system of equations graphed below if
the lines are parallel?
O A. Zero
O B. Two
C. Infinitely many
O D. One
HELP MEE ,25 POINTS !!!!
Celina says that each of the following expressions is actually a binomial in disguise:
5abc-2a^2+6abc
5x^3∙2x^2-10x^4+3x^5+3x∙(-2) x^4
(t+2)^2-4t
5(a-1)-10(a-1)+100(a-1)
(2πr-πr^2 )r-(2πr-πr^2)∙2r
Based on the four expressions written above (image attached) one can say that She is right about the remaining four expressions as they all can shown or expressed as binomials.
What is Binomial Distribution?
Binomial distribution is known to be a kind of probability distribution whos models or show the probability of getting one of two outcomes in any said number of points or parameters.
Note that:
5abc -2a² + 6abc
Add like terms
= 11abc - 2a²
5x³∙ 2x² -10x⁴ +3x⁵+ 3x∙(-2) x⁴
Simply
=5 . 2x³⁺² - -10x⁴ +3x⁵+ 3x∙ 2x⁴
=10x³⁺² -10x⁴ +3x⁵+ 3∙ 2xx⁴
= 7x⁵ + 10x⁴
(t+2)²-4t
Simply
= (t² + 2t.2 + 2²) - 4t
= (t² + 2t.2 + 4) - 4t
= t² + 4
The same applies for the rest. Therefore, one can say that Based on the four expressions written above (image attached) one can say that She is right about the remaining four expressions as they all can shown or expressed as binomials.
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The number of days to renovate a house, with 6 men, doing the job is 8 days. How many men need to work on the job if it takes 12 days to complete it ?
Answer:
9 men
Step-by-step explanation:
If 6 men are required to complete a job in 8, than 9 men would be required for a 12 day job.
12-8=4 which is half of 8
Half of 6 is 3
6+3=9
Answer:
4 men
Step-by-step explanation:
• Let x be the number of men needed to do the work I need 12 days.
•• it’s clear that the two variables (number of men and number of hours are in inverse proportion)
•• Which means their product is always equal to a constant.
Therefore
12 × x = 6 × 8 = 48
Then
x = 48 ÷ 12
= 4
Pythagorean Theorem and its Converse
I need number 6
Answer:
x = 14.02 units
Step-by-step explanation:
Finding unknown value using Pythagorean theorem:
This is an isosceles trapezium. The two perpendiculars divide the trapezium into two congruent triangles and a rectangle. Let the base of the triangle by 'y'. We can find the value of 'y' using Pythagorean theorem.
In ΔABC,
AC² = AB² + BC²
19² = 17 ² + y ²
361 = 289 + y ²
361 - 289 = y ²
y ² = 72
y =√72
y = 8.49
x = 31 - 8.49 - 8.49
x = 14.02
If P = 160 meters and w = 34 meters, find I. P = 21+ 2w
Hey there!
ASSUMING:
p = 2l + 2w
IF SO:
• We already have our perimeter (p) & our width (w), now you have to find our length (l)
160 = 2l + 2(34)
CONVERT TO:
2l + 2(34) = 160
SIMPLIFY IT:
2l + 68 = 160
SUBTRACT 68 to BOTH SIDES:
2l + 68 - 68 = 160 - 68
SIMPLIFY IT:
2l = 160 - 68
2l = 92
DIVIDE 2 to BOTH SIDES:
2l/2 = 92/2
SIMPLIFY IT:
l = 92/2
l = 46
Therefore, your answer should be:
l = 46
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
What is -4(5x-3)+12 simplified
Answer:
20x+24Step-by-step explanation:
-4(5x-3)+12
-20x+12+12
20x+24
my answer is 20x+24.
The simplified form of the given expression -4(5x-3)+12 would be 20x+24.
What is a simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Simplification usually involves making the expression simple and easy to use later.
Given;
-4(5x-3)+12
Open the bracket
-20x+12+12
Solve the like terms;
20x+24
Hence, the simplified form of the given expression -4(5x-3)+12 would be 20x+24.
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The table below shows a relationship between x and y values. Which of the following equations describes this relationship?
Answer:
y=2x+1
Step-by-step explanation:
Find the sum.
-110 + (-102) + (-94) + ... + 66 + 74
Answer:
Step-by-step explanation:
a=-110
d=-102-(-110)=-102+110=8
let n be the number of terms.
74=-110+(n-1)×8
74=-110+8n-8
74+118=8n
192=8n
n=192/8=24
[tex]s=\frac{n}{2} [2a+(n-1)d]\\s=\frac{24}{2} [2(-110)+(24-1)\times8]\\=12[-220+184]\\=12(-36)\\=-432[/tex]
