The slope-intercept form of the equation of the line described is y = -10/9x + 4/3.
Given the following data:
Points on x-axis = (-6, 4).
Points on y-axis = (8, -1).
What is a slope?A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.
How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Substituting the given points into the formula, we have;
Slope = (4 + 6)/-1 - 8)
Slope = -10/9
Mathematically, the standard form of the equation of a straight line is given by;
y = mx + c
Where:
x and y are the points.m is the slope.c is the intercept.At point (-6, 8), we have:
8 = -10/9(-6) + c
8 = 60/9 + c
72 = 60 + 9c
9c = 72 - 60
c = 12/9
c = 4/3
Therefore, the slope-intercept form of the equation of the line described is y = -10/9x + 4/3.
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2. B.C.E. is the same as... A. Before Christ C. Anno Domini B. After Death D. Before Christmas
Answer:
Before Christ
Step-by-step explanation:
While in the past it was before Christ, its been moving to Before the Common Era
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Algebra 2 question. Gives 100 points. Please help.
Answer:
x = 4
Step-by-step explanation:
[tex] \sqrt{11x + 5} = 7 [/tex]
Square both sides. This step may introduce extraneous solutions, but we will deal with that after we find the solution.
[tex] (\sqrt{11x + 5})^2 = (7)^2 [/tex]
[tex] 11x + 5 = 49 [/tex]
Subtract 5 from both sides.
[tex] 11x = 44 [/tex]
Divide both sides by 11.
[tex] x = 4 [/tex]
Now we check for extraneous solutions. We substitute the value of the solution into the original equation, and we see if it makes the original equation true.
[tex] x = 4 [/tex]
[tex] \sqrt{11x + 5} = 7 [/tex]
[tex] \sqrt{11(4) + 5} = 7 [/tex]
[tex] \sqrt{44 + 5} = 7 [/tex]
[tex] \sqrt{49} = 7 [/tex]
[tex] 7 = 7 [/tex]
7 = 7 is a true equation; therefore, our solution, x = 4, is not an extraneous solution and is the correct solution of the given equation.
Answer: x = 4
What is the formula to find the height of a triangle when you are just given coordinates, like in the picture.
Im guessing it is Base x Height ÷ 2? My answer is 12, i aplogise if i am incorrect.
Step-by-step explanation:
Just subtract the y coordinate of B with the y coordinate of A (or C).
so since B has a y of 9 and A has a y of 5 the height is
9 - 5 =
4
How had the New Deal given the government an advantage in preparing for war?
A. The New Deal focused on creating jobs in the weapons industry.
B. Farmers had been encouraged to plant more crops, making more food
C. The government owned a lot of the peoples' debt, and could ask for favors.
D. The government had become closely involved in social and economic affairs
Let PQRS be a quardilateral in a plane, where QR=1, ∠PQR=∠QRS=70°, ∠PQS=15° and ∠PRS=40°. If ∠RPS=θ°, PQ=α and PS=β, then the intervals that contains the value of 4αβ sinθ° are
(A) (0, √2)
(B) (1, 2)
(C) (√2, 3)
(D) (2√2, 3√2)
The intervals that contains the value of 4αβ sinθ° are
(A) (0, √2)
(B) (1, 2)
What is the Interval Angle of the quadrilateral?Given that, PQRS be a quadrilateral in a plane, where;
QR = 1
∠PQR =∠QRS = 70°
∠PQS = 15°
∠PRS=40°.
Further given that, ∠RPS = θ°, PQ = α and PS = β
Now, In triangle PQR
Using sine law, we have;
PQ/sin R = QR/sin P
α/sin 30 = 1/sin 80
Thus;
α = 1/2sin80
Now, In triangle PRS
Using sine law, we have;
PS/sin R = RS/sin P
∠RPS = ∠RSQ = 55
QR = RS = 1
β/sin 40 = 1/sinθ
βsinθ = sin40
Now, Consider 4αβ sinθ° = 4 * 1/2 sin 80 * sin 40 = 2 sin 40/(2 sin 40 cos 40)
Since sin 2x = 2 sin x cos x, then;
= 1/cos 40 = sec 40
Now, we know secx is an increasing function.
Thus;
sec 40 ∈ (2/√3, √2)
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In triangle PQR, we have by the law of sines,
[tex]\dfrac{\sin(30^\circ)}\alpha = \dfrac{\sin(80^\circ)}1 \\\\ ~~~~ \implies \alpha = \dfrac{\sin(30^\circ)}{\sin(80^\circ)}[/tex]
and by the law of cosines,
[tex]PR^2 = 1 + \alpha^2 - 2\alpha \cos(70^\circ)[/tex]
In triangle PQS, the law of sines gives
[tex]\dfrac{\sin(15^\circ)}\beta = \dfrac{\sin(85^\circ-\theta)}\alpha \\\\ ~~~~ \implies \beta = \dfrac{\sin(15^\circ)\sin(30^\circ)}{\sin(85^\circ-\theta)\sin(80^\circ)}[/tex]
In triangle PRS, again with the law of sines,
[tex]\dfrac{\sin(40^\circ)}\beta = \dfrac{\sin(140^\circ - \theta)}{\sqrt{1 + \alpha^2 - 2\alpha\cos(70^\circ)}} \\\\ ~~~~ \implies \beta = \sqrt{1+\alpha^2 - 2\alpha\cos(70^\circ)} \dfrac{\sin(40^\circ)}{\sin(140^\circ-\theta)}[/tex]
Together, these give
[tex]\dfrac{\sin(15^\circ) \sin(30^\circ)}{\sin(85^\circ-\theta) \sin(80^\circ)} = \sqrt{1 + \alpha^2 - 2\alpha \cos(70^\circ)} \dfrac{\sin(40^\circ)}{\sin(140^\circ - \theta)}[/tex]
Carefully, we can rearrange terms and invoke identities (half-angle, product-to-sum) to reduce this equation to
[tex]\dfrac{\sin(140^\circ - \theta)}{\sin(85^\circ - \theta)} = \dfrac{\sqrt{2 - 3\sin(10^\circ) - \sin^2(10^\circ) + 2\sin^3(10^\circ)}}{\sin(15^\circ)}[/tex]
On the left, substitute [tex]\phi=85^\circ-\theta[/tex], and on the right, [tex]\sigma=\csc(15^\circ)\sqrt{2-3\sin(10^\circ)-\sin^2(10^\circ)+2\sin^3(10^\circ)}[/tex]. Expand the left side and rearrange terms.
[tex]\dfrac{\sin(55^\circ-\phi)}{\sin(\phi)} = \sigma \\\\ ~~~~ \implies (\sigma + \sin(35^\circ))\sin(\phi) - \cos(35^\circ) \cos(\phi) = 0[/tex]
Condense this using the identity
[tex]R\sin(\phi-\xi) = R\cos(\xi)\sin(\phi) - R\sin(\xi)\cos(\phi)[/tex]
Solve for [tex]R,\xi[/tex].
[tex]\begin{cases}R\cos(\xi) = \sigma+\sin(35^\circ) \\ R\sin(\xi) = \cos(35^\circ)\end{cases} \implies \begin{cases}R^2 = (\sigma+\sin(35^\circ))^2 + \cos^2(35^\circ) \\\\ \tan(\xi) = \dfrac{\cos(35^\circ)}{\sigma+\sin(35^\circ)} \end{cases}[/tex]
So our equation becomes
[tex]\sqrt{(\sigma+\sin(35^\circ))^2 + \cos^2(35^\circ)} \, \sin\left(\phi - \tan^{-1}\left(\dfrac{\cos(35^\circ)}{\sigma+\sin(35^\circ)}\right)\right) = 0[/tex]
Solve for [tex]\phi[/tex], bearing in mind that [tex]40^\circ<\theta<100^\circ[/tex] so [tex]-15^\circ<\phi<45^\circ[/tex], then evaluate the target expression. (Forgive the sudden switch to approximations; I do think there is a nice analytical solution.)
[tex]\phi = \tan^{-1}\left(\dfrac{\cos(35^\circ)}{\sigma+\sin(35^\circ)}\right) \approx 8.88311^\circ \\\\ ~~~~ \implies \theta \approx 76.1169^\circ \\\\ ~~~~ \implies \beta \approx 0.68309 \\\\ ~~~~ \implies 4\alpha\beta\sin(\theta) \approx 0.91334 < 1 < \sqrt2 < 2\sqrt2[/tex]
which makes (A) the correct choice.
What is the value of x that makes the given equation true?
x − 3x = 2 (4+x)
x = − 4
x = − 3
x = − 2
x = − 1
Answer:
-2
Step-by-step explanation:
[tex]x-3x=2(4+x) \\ \\ -2x=2(4+x) \\ \\ -x=4+x \\ \\ -2x=4 \\ \\ x=-2[/tex]
If h(x) = 5, what is h(2)?
I can't tell if the entire question is here or not, it appears to be missing something.
If you did put all of the information here, h(2) = 5 because there is no x input.
The volume of a cube is 500 m^3.
How long is each edge?
BRAINLIST FOR ANYONE WHO GETS IT RIGHT PLS HURRY
The edge length of the cube is a approximately 8.
According to the statement
We have to find that the edge of the cube.
So, For this purpose, we know that the
The edge of a cube is the line segment joining the two vertices.
From the given information:
The volume of a cube is 500 m^3.
The formula for volume of the cube is a :
volume of a cube formula: V = a^3.
v = a^3
500 = a^3
Take cube root of the volume to find the edge length
a = (500)^1/3
a = 7.93
a = 8 (approx.)
The length of the edge of the cube is a approximately 8.
So, The edge length of the cube is a approximately 8.
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A raffle offers a first prize of $ and second prizes of $ each. One ticket costs $, and tickets are sold. Find the expected payback for a person who buys 1 ticket. Is this a fair game?
The expected payback for a person who buys 1 ticket is 1.23. Yes, the game is fair.
Given that, A raffle offers a first prize of $500 and 3 second prizes of $80 each. One ticket costs $2, and 600 tickets are sold.
What is the probability?The probability formula defines the likelihood of the happening of an event. It is the ratio of favourable outcomes to the total favourable outcomes. The probability formula can be expressed as, P(E)=Number of favourable outcomes/Total number of outcomes.
Now,
Expected value = sum of ( amount won ) × probability of winning
= expected value of 1st place + expected value of 2nd place + expected value of losing
= (1/600) (500) + (3/600) (80) + (596/600) × 0
= 500/600 + 240/600
= 740/600
= 740/600
= 1.23
Therefore, the expected payback for a person who buys 1 ticket is 1.23. Yes, the game is fair.
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"Your question is incomplete, probably the complete question/missing part is:"
A raffle offers a first prize of $500 and 3 second prizes of $80 each. One ticket costs $2, and 600 tickets are sold. Find the expected payback for a person who buys 1 ticket. Is this a fair game?
Pls Help!
Find the Greatest Common Factor of 18 and 27, show all your work!
Answer:
9
Step-by-step explanation:
Factor for 18 are:
1,2,3,6,9,18
Factors for 27 are:
1,3,9,27
Hope I helped <3
Which of the following
is the inverse of y = 3^x
Answer: f-1(x) = 1/3x.
Step-by-step explanation:
The inverse of y = 3x is f-1(x) = 1/3x.
To find the inverse, interchange the variables and solve for y
f ^− 1 (x) = In(x)/In(3)
WILL GIVE BRAINLIEST PLEASE HELP ASAP!!
You are solving a measurement problem where the numbers 4.5160 x 10^−3, 2.09 x 10^7, and 5.8 x 10^3 are multiplied. How many significant digits should the product have?
A. 2
B. 1
C.5
D. 3
The number of significant digits: 2
The correct answer is an option (A)
In this question, we have been given three numbers 4.5160 x 10^−3, 2.09 x 10^7, and 5.8 x 10^3
We need to find the number of significant digits of the product of above numbers.
First we find the product of given numbers.
4.5160 x 10^−3 × 2.09 x 10^7 × 5.8 x 10^3
= (4.5160 × 2.09 × 5.8) × (10^−3 × 10^7 × 10^3)
= 54.742952 × 10^(-3 + 7 + 3)
= 54.7 × 10^7
= 5.5 × 10^8
Here, the number of significant digits: 2
The correct answer is an option (A)
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If 40% of a population is 4500, what is the total population?
Answer:
11,250
Step-by-step explanation:
In order to find the total population just divide 4500 by 40%
[tex] = \sf \: 4500 \div \frac{40}{100} [/tex]
[tex] = \sf \: 4500 \times \frac{100}{40} [/tex]
[tex] = \sf \frac{450000}{40} [/tex]
[tex] = \sf \: 11,250[/tex]
Given that f(x) = x-5, g(x)=-4x and h(x)=2f(x+1)-g(x-2), then what is the value of h(4)?
hi
f(x) = x-5, then f(5) = 0
g(x)=-4x . g(2) = -4*2 = -8
and
h(x)=2f(x+1)-g(x-2)
then
h(4) = 2* 0 - (-8) = 8
Does the square of a binomial always include only positive terms?
No, the square of a binomial does not include only positive terms.
How is a binomial expression defined?A mathematical expression with two terms known as a binomial expression cannot be merged unless a variable-eliminating input is provided. Positive integer exponents must be unique for each of the binomial terms. Any exponents must not be negative, zero, or a fraction.
Simplify and combine any "like" terms to add binomials. Different exponents or variables cannot be used in "like" phrases. Add, for instance, the binomials (12x + 3) and (3x - 1).
The square of a binomial may contain negative terms.
For example, (a - b)² = a² + b² - 2ab
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Which of the following are expressions with numbers only.
Select all options that apply
1) x - 3
2) 6
3) (8 x 20) d
4) (14÷2) x 2
5) (a + 6) 4
hey theyre help me please
Answer:
15
Step-by-step explanation:
because it's diving the 2nd role number and that equals the numbers on the 3rd role so u do the inverse and u get 15
Using the graph, determine the coordinates of the vertex of the parabola.
The coordinates of the vertex of the parabola are (-1, -9)
Coordinate of a vertexFrom the question, we are to determine the coordinates of the vertex of the parabola
The vertex of a parabola is the point where the parabola crosses its axis of symmetry.
In the given graph, the axis of symmetry is x = -1
Thus,
The vertex of the parabola in the given graph is the point where x = -1 on the curve
At this point on the parabola, x = -1 and y = -9.
Hence, the coordinates of the vertex of the parabola are (-1, -9)
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kayla buys a new pair of shoes for $39.99 the sales tax is 6%. what is the total with tax ?
Answer:
$42.38
Step-by-step explanation:
$39.99 x 0.06= 2.39
39.99 + 2.39= $42.38 (total with tax)
Answer:
Step-by-step explanation:
39.99 * 0.06 = 2.4
The total tax equals = 2.4
6% in decimal form is 0.06 multiplied by the total cost of shoes to get the total tax. 2.4
add that to the total to get the total cost with tax = $42.39
find a pattern for a sequence 17, 13, 9, 5,
Answer: an=21-4n
Step-by-step explanation:
17, 13, 9, 5, ...
13-17=-4
9-13=-4
5-9=-4
This sequence is an arithmetic progression a₁=17 d=-4
Hence,
[tex]a_n= a_1+(n-1)d\\\\a_n=17+(n-1)(-4)\\\\a_n=17-4n+4\\\\a_n=21-4n,\ \ \ \ n=1, 2, 3, 4, ...[/tex]
Find the line of best fit for this graph
Write the equation of the line of best fit using the slope-intercept formula y=mx+b. Show all your work, including the points used to determine the slope and how the equation was determined.
What does the slope of the line represent within the context of your graph? What does the y-intercept represent?
Test the residuals of two other points to determine how well the line of best fit models the data.
Answer:
Look, I can't solve these for you: but for now Y = x + 3
Step-by-step explanation:
we know that
The linear equation in slope intercept form is equal to Y=mx+b
where
m is the slope
b is the y-intercept
step 1
Find the slope
Take two points from the graph
see the attached figure
about (37,40) and (47,50)
The formula to calculate the slope between two points is equal to
m=y2-y1
Find the y-intercept
we have
substitute in the linear equation
solve for b
therefore
The linear equation is y=x+3
If Norman iqvested $100,000 for 3 years at 12%, how much interest on interest will he earn? (Do not round intermediate calculations. Round the final answer to two decimal places.)
A. $4,585.32
B. $4,303.36
C. $4,856,32
D. $4,492.80
If Norman invested $100,000 for 3 years at 12%, the amount of interest earned on interest is $4,492.80
What is the future value of the investment?
The future value of the investment after 3 years is its future worth at the end of year 3 which comprises of the initial investment and the interest earned over the 3-year period as captured thus:
FV=PV*(1+r)^N
FV=future value after 3 years=unknown
PV=amount invested=$100,000
r=annual interest rate=12%
N=number of years of investment=3
FV=$100,000*(1+12%)^3
FV=$ 140,492.80
compound interest=$140,492.80-$100,000
compound interest=$40,492.80
interest on principal only=$100,000*12%*3=$36,000
interest on interest=$40,492.80-$36000
interest on interest=$4,492.80
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find the solution for variables x, y, and z
The solution for variables x, y, and z are -
x = 100y = 3z = -3What is defined as the elimination method?The elimination method is the procedure of eliminating one of the variables in a system of linear equations by using addition or subtraction methodologies in conjunction with variable coefficient multiplication or division. Because it allows us to eliminate or remove one of the variables, allowing us to solve a much more simplified equation.The given linear equation are-
x - 6y - 2z = -8 .......equation 1.
-x + 5y + 3z = 2 ......equation 2.
3x - 3y - 4z = 15 .......equation 3.
Add equation 1 and 2; gives
-y + z = -6 .....equation 4
multiply equation 2 and subtract it with equation 3;
12y + 5z = 21 ......equation 5
multiply equation 4 with 5 and subtract it from equation 5.
17 y = 51
y = 3.
Put y = 3 in equation 4 and find z.
z = -6 + 3
z = -3
Put the value of y and z in equation 1 and find x.
x = -8 + 18 + 6
x = 100
Therefore, the solution for variables x, y, and z are -
x = 100y = 3z = -3To know more about the elimination method, here
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Olivia and ray walk to school olivia walks 1/4 of a mile to school her walk is 2/3 of the distance that ray walk to school what is the total distance in miles that ray walks to school
Based on the distance that Olivia has to walk to school, the total distance that Ray walks to school in miles is 3 / 8 miles
How to find the number of miles walked?Olivia walks 1/4 of a mile to school which means that the number of miles she walks to school is:
= 1/4 x 1
= 1/4 miles
= 0.25 miles
This 0.25 miles represents 2/3 of the distance that Ray walks to school. The total distance that Ray walks to school is therefore:
= Number of miles Olivier walks to school / Proportion of distance to Ray
= 0.25 ÷ 2/3
= 0.375
= 3 / 8 miles
In conclusion, Ray walks 3/8 miles to school.
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Answer:
Ray walks to school in miles is 3 / 8 miles.
Someone please help
Answer:
4/3 (x) = 28/3
*divide both sides by 4/3
4/3 (x) ÷ 4/3 = 28/3 ÷ 4/3
x = 7
I don't really know how to multiply decimals and i'm really confused on it and need some help on 2.4 x 2.5. Help ASAP!!
Answer:
you could use a calculator but if you don't you can follow these steps
Step 1 : to avoid confusion it is easier to remove the decimal points then multiply them (i.e. 24 × 25)
Step 2: After you've gotten the answer (600), count how many decimal places both numbers are (i.e. 2.4 is one decimal place and 2.5 is also one decimal place.. making it two decimal places)
Step 3: Move your answer to 2 decimal places (i.e 600 → 6.00 or 6)
Answer is 6
Calculations
2.4 × 2.5
= 24 × 25
= 600 to 2 decimal places
= 6
+Hope this helps
Perform the indicated operation. (-7) · (-5)
Answer:
1/(2 – 4i)
Explanation:
Use geeksforgeeks.org or another website
5 divided by 1319 and find each quotient to two places
The value of 5 divided by 1319 to two places is 3.79 × [tex]10^{-3}[/tex] .
The way of find answer is the divide 5 by 1319
If the number you're dividing by has a decimal, move the decimal point all the way to the right counting the number of places you've moved it to. Then move the decimal point in the number you're dividing the same number of places to the right.Insert a decimal point in the quotient (answer) space, exactly above the decimal point in the number under the division bar.Divide until the remainder is zero, or until you have enough decimal places in your answer. You can also stop if the remainder repeats because this indicates that your answer is a repeating decimal.We have to find 5 divided by 1319 and find each quotient to two places
To find answer = 5/1319 = 0.00379075
quotient to two places = 3.79 × [tex]10^{-3}[/tex]
The main answer is 3.79 × [tex]10^{-3}[/tex].
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Karoline needs to jog 30.5 miles over the next 7 days to train for a race.
She plans to jog 4.25 miles each day.
Use the drop-down menus to complete the statements about her race training
Answer:
If she plans to jog 4.25 miles each day then 4.25 * 7 would equal 29.75. This is the first answer.
In order to get the second answer, we need to subtract 30.5 (What she needs to jog) over 29.75 (how much she is planned to job over the next 7 days). So 30.5 - 29.75 = 0.75
Here is the math I did to get 0.75:
= 30.5 - 29.75
= 30.5 + -29.75
= 0.75 (Answer)
Hopefully this helped :D
Step-by-step explanation:
A. positive nonlinear association
B. positive linear association
C. no association
D. negative nonlinear association
E. negative linear association
Answer:
C. no association?
Step-by-step explanation:
Looks like there's no association to me. Association usually are in a linear line or curves. The data points given do not form such shapes. Hope that's right.
Here's some clarification: https://open.lib.umn.edu/macroeconomics/chapter/nonlinear-relationships-and-graphs-without-numbers/