Answer for A. (-8,-2)
answer for B. (4,-7)
the sum of two times x and 3 times y is 5. the difference of x and y is 5 write two equations and fine the value of y
Answer:
y = -1
Step-by-step explanation:
Details have been given in the question, we need to break them apart and create our equations accordingly.
"the sum of two times x and 3 times y is 5"
2x + 3y = 5
"the sum of two times x and 3 times y is 5"
x - y = 5
So, our two equations are:
2x + 3y = 5
x - y = 5
Solve using substitution method, by moving y to the other side.
x = y + 5
2(y + 5) + 3y = 5
2y + 10 + 3y = 5
Combine like terms
5y + 10 = 5
Subtract 10 from both sides
5y = -5
y = -1
The sum of 5 consecutive even numbers is 310.
What is the third number in this sequence?
Answer:62
Step-by-step explanation:
The differance between 2 consecutive even number is 2...so if the first consecutive even number is x, then the next 4 consecutive even number will(x+2),(x+4),(x+6),(x+8)
So
X+(x+2)+(x+4)+(x+6)+(x+8)=310
5x+20=310
So,x=58
As the third number is (x+4)
Putting the value of x the final result comes(58+4)=62.
2,2n+2,2n+4,2n+6,2n+8 - 5 consecutive even integers
2n+4 - 3rd number
[tex]2n+2n+2+2n+4+2n+6+2n+8=310\\10n+20=310\\10n=290\\n=29\\\\2n+4=2\cdot29+4=62[/tex]
quadrilateral ABCD is inscribed in circle 0. Chords BA and CD are extended to intersect at point E. A tangent at B intersects line DA where line
DA is extended to point F. Diagonals BD and AC of quadrilateral ABCD are drawn.
arch ĀB =128
arch BC =144°
arch DC = 64
arch DA = 32
Find the measure of angle 1,2,5 and 6
Check the picture below.
let's notice the "white" ∡1 is an inscribed angle with an intercepted arc of (x-32), and the "green" ∡5 is also an inscribed angle with an intercepted arc of (2x).
the ∡6 and ∡2 are both external angles, however they intercepted two arcs, a "far arc" and a "near arc", thus we'll use the far arc - near arc formula, as you see in the picture, and we'll use the inscribed angle theorem for the other two.
[tex]\bf \measuredangle 1=\cfrac{x-32}{2}\implies \measuredangle 1 =\cfrac{32}{2}\implies \measuredangle 1 = 16 \\\\[-0.35em] ~\dotfill\\\\ \measuredangle 5 =\cfrac{2x}{2}\implies \measuredangle 5 = x\implies \measuredangle 5 = 64 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \measuredangle 2 = \cfrac{(2x+8)~~-~~(x-32)}{2}\implies \measuredangle 2=\cfrac{2x+8-x+32}{2} \\\\\\ \measuredangle 2=\cfrac{x+40}{2}\implies \measuredangle 2=\cfrac{104}{2}\implies \measuredangle 2=52 \\\\[-0.35em] ~\dotfill\\\\ \measuredangle 6=\cfrac{[(2x+8)+(x)]~~-~~(2x)}{2}\implies \measuredangle 6=\cfrac{3x+8-2x}{2}\implies \measuredangle 6=\cfrac{x+8}{2} \\\\\\ \measuredangle 6=\cfrac{72}{2}\implies \measuredangle 6=36[/tex]
Use the information given below, to compare the cost of operating two different vehicles for one month (4 weeks) You
are considering two different cars. You drive to work, a 20 mile round trip, five days a week. Gasoline costs you $1.50
per gallon
Car Agets 28 miles per gallon, would have $300 a year in maintenance costs, and would cost you $1,500 per year to
insure
Car B gets 19 miles per gallon, would have $500 a year in maintenance costs, and would cost you $1,000 per year to
insure
Costs
Car A
Car B
Gas cost per month
Insurance cost per month
Maintenance cost per month $
Total cost per month
Answer:
Gas Cost Per Month: Car A $21.43, Car B $31.58
Insurance Cost Per Month: Car A $125, Car B $83.33
Maintenance Cost Per Month: Car A $25, Car B $41.67
Total Cost Per Month: Car A $171.43, Car B $156.58
Step-by-step explanation:
Gas Cost Per Month:
It is a 20 mile round trip per day, so five days a week would be 100 miles. This means that you drive 400 miles to work in one month. So for Car A, 400/28 = 14.29 gallons. 14.29 gallons times $1.50 = $21.43 per month. For Car B, 400/19 = 21.05 gallons. 21.05 Gallons times $1.50 = $31.58 per month.
Insurance Cost Per Month:
Car A costs $1,500 to insure for one year. So if we take 1,500 and divide it by 12 we get $125 per month. Car B costs $1,000 to insure for one year. So taking 1,000 and dividing by 12 gives us roughly $83.33.
Maintenance Cost Per Month:
Car A costs $300 per year, so taking 300 and dividing by 12 gives us $25 per month. Car B costs $500 per year, so taking 500 and dividing by 12 gives us roughly $41.67 per month.
Total Cost Per Month:
Now all we need to do is add everything together. For Car A, we have $21.43 in gas, $125 in insurance, and $25 in maintenance. This gives a grand total of $171.43 per month. For Car B, we have $31.58 in gas, $83.33 in insurance, and $41.67 in maintenance, leaving a grand total of $156.58.
Hope this helps!
To compare the monthly operating costs of Car A and Car B, calculate and sum up the gas, insurance, and maintenance costs for each car. Car B, with a total monthly cost of $156.58, is less expensive to operate than Car A, which costs $171.43 per month.
To compare the cost of operating two different vehicles for one month, we need to calculate the monthly gas, insurance, and maintenance costs for each vehicle and then add them up to get the total monthly cost.
Calculating Costs for Car A
Gas Cost per Month: You drive 20 miles a day for 5 days a week, that's 100 miles a week or 400 miles for 4 weeks (1 month). At 28 miles per gallon, you would need roughly 14.29 gallons (400/28) per month. At $1.50 per gallon, the monthly gas cost is 14.29 gallons * $1.50/gallon = $21.43.Insurance Cost per Month: $1,500 per year translates to $125 per month ($1,500/12 months).Maintenance Cost per Month: $300 a year equates to $25 per month ($300/12 months).Total Cost for Car A per Month = Gas + Insurance + Maintenance = $21.43 + $125 + $25 = $171.43.Calculating Costs for Car B
Gas Cost per Month: With the same driving pattern, you would need roughly 21.05 gallons (400/19) per month. At $1.50 per gallon, the monthly gas cost is 21.05 gallons * $1.50/gallon = $31.58.Insurance Cost per Month: $1,000 per year is about $83.33 per month ($1,000/12 months).Maintenance Cost per Month: $500 a year is about $41.67 per month ($500/12 months).Total Cost for Car B per Month = Gas + Insurance + Maintenance = $31.58 + $83.33 + $41.67 = $156.58.Comparing the total monthly costs, Car B is less expensive to operate than Car A.
triangle JLK be a right triangle with right angle L. If JM=3 and and MK equals 6 find LM show work
Answer:
The length of LM is 4.24
Step-by-step explanation:
* Lets revise the rules in the right angle triangle when we draw the
perpendicular from the right angle to the hypotenuse
- In triangle ABC
# Angle B is a right angle
# The hypotenuse is AC
# BD ⊥ AC
∴ (AB)² = AD × AC
∴ (BC)² = CD × AC
∴ (BD)² = AD × CD
∴ BD × AC = AB × BC
* Lets use one of these rules to solve the problem
∵ Δ JLK is a right triangle
∵ ∠L is a right angle
∵ LM ⊥ JK
- We can find LM by one of the rule above
∵ JM = 3
∵ MK = 6
∵ (LM)² = JM × KM
∴ (LM)² = 3 × 6 = 18 ⇒ take a square root for both sides
∴ LM = √18 = 3√2 ≅ 4.24
* The length of LM is 4.24
write the following equation in standard form 8/7x^3+x^4+6x+1
Answer:
[tex]\large\boxed{x^4+\dfrac{8}{7}x^3+6x+1}[/tex]
Step-by-step explanation:
In order to write any polynomial in standard form, you look at the degree of each term. You then write each term in order of degree, from highest to lowest.
We have:
[tex]\dfrac{8}{7}x^3+x^4+6x+1[/tex]
Look at the degrees for each term in the expression:
[tex]\dfrac{8}{7}x^3[/tex] has a degree of 3
[tex]x^4[/tex] has a degree of 4
[tex]6x[/tex] has a degree of 1
[tex]1[/tex] has a degree of 0
Write this trinomial in order by degree, highest to lowest
[tex]x^4+\dfrac{8}{7}x^3+6x+1[/tex]
The standard form of given equation is 8/7x^3 + x^4 + 6x + 1 is 7x^4 + 8 x^3 + 4 x + 7 = 0.
To write the equation 8/7x^3 + x^4 + 6x + 1 in standard form, you need to rearrange the terms in descending order of exponents.
Standard form for a polynomial is where the terms are written from the highest power to the lowest power of the variable.
So, 8/7x^3 + x^4 + 6x + 1 = 0
7x^4 + 8 x^3 + 4 x + 7 = 0.
A cylindrical rainwater tank is 1.5 m tall with a diameter of 1.4 m. What is the maximum volume of rainwater it can hold??
I need answer.. please help me.... please
To work out the volume of a prism, you multiply the area of cross-section by the height (or length).
So for a cylinder, you work out the area of the circle and then multiply it by the height.
Area of circle (or cross-section) = π × radius²
= π × 0.7²
= 0.49π m²
Now to get the volume of the cylinder, you times this area of the cross-section by the height of the cylinder:
Volume = 0.49π × 1.5
= 2.3 m³ (accurate to 2 decimal places)
---------------------------------------------------------------
Answer:
The maximum volume of rainwater the cylinder can hold is:
2.3 m³
The maximum volume of rainwater will be "2.3 m³".
Volume of Cylinder:Given values are:
Height = 1.5 m
Diameter = 1.4 m
The Area of circle will be:
= [tex]\pi\times radius^2[/tex]
= [tex]\pi\times 0.7^2[/tex]
= [tex]0.49 \pi \ m^2[/tex]
hence,
The volume of cylinder be:
= [tex]0.49 \pi\times 1.5[/tex]
= [tex]2.3 \ m^3[/tex]
Thus the answer above is correct.
Find out more information about volume here:
https://brainly.com/question/9554871
What is the remainder when 58 is divided by 7?
Answer:2
Step-by-step explanation:
If you devide 58 by 7,you will get 8 as quotient..so 7×8=56..
So you will find (58-56)=2 as remainder..
Answer:
The Remainder of 58÷7 is 2
Step-by-step explanation:
The Remainder of a Division Operation is calculated by finding how many times the denominator goes into the numerator without going over and then subtracting that from the numerator.
For Example : [tex]58/7 = 8.28[/tex] ......which means 7 goes into 58 , 8 times.
Next we multiply 7*8 to give us 56.
Lastly, we subtract 58-56 to give us a remainder of 2.
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
Subtract.
–46 – (–19)
A.
–65
B.
–27
C.
27
D.
65
Answer:
B because u will have to first open the bracket according to BODMAS: bracket of division multiplication addition and subtract trust me before solving something like this use this BODMAS
Which statement is true regarding the parallel and
perpendicular lines in the diagram?
Answer:
W is parallel to N and N is perpendicular to M
Step-by-step explanation:
If r = the number of roses, which algebraic expression represents the phrase
below?
the difference of the number of roses and 18 lilies
The algebraic expression that represents the phrase 'the difference of the number of roses and 18 lilies' is 'r - 18'. The term 'difference' in math denotes subtraction operation.
Explanation:In algebra, the phrase 'the difference of the number of roses and 18 lilies' is represented as a subtraction operation between two variables or a variable and a number. In this case, the expression can be represented as r - 18, where 'r' represents the number of roses and '18' represents the number of lilies. However, in this scenario, the type of the flower doesn't really matter, it's just about the quantity which is represented by the term '18'. The key term difference denotes subtraction in mathematical terms.
Learn more about Algebraic expressions here:https://brainly.com/question/953809
#SPJ2
find the perimeter of the following.
Answer:
24.997 = 25.00 (rounded off to 2 decimal figures)
Step-by-step explanation:
By observation, we can see that both straight lines are of equal length and that the angle between the lines is 90°. Hence we can conclude that this is a quadrant of a circle with radius, r = 7 cm.
length of the curved section
= 1/4 x circumference of the circle
= 1/4 x 2πr
= 1/4 x 2 x 3.142 x 7
= 10.997 cm²
HEnce circumference = 10.997 + 7 + 7 = 24.997 = 25.00 (rounded off to 2 decimal figures)
Find the product
x^5•x^4•x^3
If you are multiply, and all of the numbers are the same, then you add the powers. And if you divide, you subtract the powers.
Since all of the base numbers are the same (there are all x), then you add the powers:
x⁵ * x⁴ * x³ = x¹² ( 5 + 4 + 3 = 12)
--------------------------------------------------------
Answer:
x¹²
The total mass of 8 cereal boxes is 4 kilograms. What is the mass of each box of cereal in grams?
Answer:
The mass of each cereal box is 500 grams
Step-by-step explanation:
Remember that
1 K=1,000 g
we know that
The total mass of 8 cereal boxes is 4 kilograms
4 k=4*1,000=4,000 g
therefore
The total mass of 8 cereal boxes is 4,000 grams
To find the mass of each box, divide the total mass by eight
so
[tex]\frac{4,000}{8}=500\ g[/tex]
What are the units of the volume of the figure? Please help
Answer: Cubic Inches
Step-by-step explanation: Because its measured in inches, that would eliminate the choice of centimeters. Its a cube so you use inches cubed. Square inches are for a 2-dimensional object. Such as square feet of a house, as the floor is technically 2-dimensional.
Answer:
Ello mate !
The answer would be cubic inches !
Solve for x.
2x^2 − 4x = 0
Answer:
First, find a constant that can help you solve the equation. Note the equal sign, what you do to one side, you do to the other.
Remember, you are trying to do the following, changing: (note that y = constant)
x² - xy + y = (x - y)(x - y)
First, solve for the obvious answer. Plug in 0 to x:
2(0²) - 4(0) = 0
2(0) - 0 = 0
0 - 0 = 0
x = 0 is one of your answer choices.
Solve for the more complicated answer by doing what I put on the top:
2x² - 4x + 0 (+2) = 0 (+2)
2x² - 4x + 2 = 2
Divide 2 from both sides & all terms:
2(x² - 2x + 1) = 2(1)
x² - 2x + 1 = 1
Solve. Remember to set the equation = 0. Subtract 1 from both sides:
x² - 2x + 1 = 1
x² - 2x + 1 (-1) = 1 (-1)
x² - 2x + 0 = 0
x² - 2x = 0
Isolate the -2x. Add 2x to both sides.
x² - 2x (+2x) = 0 (+2x)
x² = 2x
Isolate the variable x. Divide x from both sides.
(x²)/x = (2x)/x
x = 2x/x
x = 2
x = 2 is your other answer choice.
x = 0, 2 is your answer.
~
Answer:
(0,2)
Step-by-step explanation:
x² - xy + y = (x - y)(x - y)
2(0²) - 4(0) = 0
2(0) - 0 = 0
0 - 0 = 0
2x² - 4x + 0 (+2) = 0 (+2)
2x² - 4x + 2 = 2
2(x² - 2x + 1) = 2(1)
x² - 2x + 1 = 1
x² - 2x + 1 = 1
x² - 2x + 1 (-1) = 1 (-1)
x² - 2x + 0 = 0
x² - 2x = 0
x² - 2x (+2x) = 0 (+2x)
x² = 2x
(x²)/x = (2x)/x
x = 2x/x
x = 2
x = 0, 2 is your answer.
Write the equation of the line that passes through (3, 4) and (2, −1) in slope-intercept form
Answer:
[tex]y = 5x - 11[/tex]
Step-by-step explanation:
1) Find slope
2) Substitute 1 point back into formula to find y-intercept, aka c
ANSWER
[tex]y = 5x - 11[/tex]
EXPLANATION
The given line passes through:
(3,4) and (2,-1).
The slope is given by:
[tex]m = \frac{ - 1 - 4}{2 - 3} [/tex]
[tex]m = \frac{ - 5}{ - 1} = 5[/tex]
The equation can be found using
[tex]y-y_1=m(x-x_1)[/tex]
We plug in the point and slope to get:
[tex]y - 4 = 5(x - 3)[/tex]
[tex]y - 4 = 5x - 15[/tex]
[tex]y = 5x - 15 + 4[/tex]
[tex]y = 5x - 11[/tex]
This is the slope-intercept form
Solve the system of equations y=2x-3 y=x^2-2x-8
Answer:
[tex]\boxed{x = -1; \, x = 5}[/tex]
Step-by-step explanation:
(a) Set the two functions equal to each other
[tex]\begin{array}{rcl}y & = & 2x - 3\\y & = & x^{2} - 2x - 8\\2x - 3 & = & x^{2} - 2x - 8\\2x & = & x^{2} -2x - 5\\x^{2} - 4x - 5 & = & 0\\\end{array}[/tex]
(b) Factor the quadratic equation
Find two numbers that multiply to give -5 and add to give ₄9.
Possible pairs are 1, -5; -1, 5;
By trial and error, you will find that 1 and -5 work:
1 × (-5) = -5 and 1 - 5= -4
x² - 4x - 8 = (x + 1)(x - 5)
(c) Solve the quadratic
[tex]\begin{array}{rlcrl}x+ 1 & =0 & \qquad & x - 5 & =0\\x & = -1 & \qquad & x & = 5\\\end{array}\\\text{The solution to the system of equations is }\boxed{\mathbf{x = -1; x = 5}}[/tex]
the solutions to the equations is (-1, -5) and (5, 7)
The graph Of y= x2 + 11x + 24 is equivalent to the graph of which equation?
Answer:
Step-by-step explanation:
Please use " ^ " to indicate exponentation: y= x^2 + 11x + 24. Thanks.
Because x^2 is positive, the graph of this parabola opens up.
We can find the vertex and roots (zeros) as follows, using the quadratic formula:
With a = 1, b = 11 and c = 24,
-11 ± √ [ (11^2-4(1)(24) ] -11 ± √25
x = ------------------------------------ = --------------- = -3 and x = -8
2(1) 2
This tells us that the x-intercepts are at (-3, 0) and (-8, 0). The minimum value is at x = -b / (2a), which here is x = -11 / [2] = -5 1/2 (which is halfway between the zeros).
The vertex (and thus, the minimum) is at (-5 1/2, f(-5 1/2) ).
Answer: a on edge 2021
Step-by-step explanation:
COMPLETE THIS STATEMENT THE SUM OF THE MEASURES OF THE MEASURES OF THE EXTERIOR ANGLES OF AN N-GON, ONE AT EACH VERTEX IS
Answer:
360 degrees
Step-by-step explanation:
we know that
The sum of the n exterior angles for any convex polygon with n sides is always 360 degrees
Example
An equilateral triangle has three equal interior angles measures 60 degrees
Each exterior angle measures 120 degrees
The sum of the exterior angles is equal to 120+120+120=360
Will Mark Brainiest!!!
Answer:
B. ¾π
Step-by-step explanation:
This radian measure is in the top negative side of the unit circle --> [-x, y].
Which is the equivalent to 641/4
Answer:
32 1/2
2
or
160.25
Step-by-step explanation:
the equivalent to 641/4
is 160.25 in decimal
32 1/2
2
32 whole number 1/2 over or divided by 2
For this case we must indicate an expression equivalent to the following:
[tex]\frac {641} {4}[/tex]
It is observed that the fraction can not be simplified, so, its decimal form is given by:
[tex]\frac {641} {4} = 160.25[/tex]
We can convert to a mixed number, for this, We convert the decimal number to a fraction by placing it on a power of ten. Since there are 2 numbers to the right of the decimal point, we place the decimal on [tex]10 ^ 2 = 100[/tex]. So:
[tex]160 \frac {25} {100}[/tex]
We simplify:
[tex]160 \frac {1} {4}[/tex]
Answer:
[tex]160.25\\160 \frac {1} {4}[/tex]
What is the value of y in the solution to the system of equations 1/3x+1/4y=1, 2x-3y=-30
Answer:
x = -3 and y = 8
Step-by-step explanation:
1/3 (-3) + 1/4 (8) = 1
-1+2=1
2(-3)-3(8)=-30
-6 - 28=-3
Answer:
The value of y in the solution to the system of equations is:
[tex]y=8[/tex]
Step-by-step explanation:
We have the following system of equations
[tex]\frac{1}{3}x+\frac{1}{4}y=1\\2x-3y=-30[/tex]
To solve the system multiply the first equation by -6 and add it to the second equation
[tex]-6*\frac{1}{3}x-6*\frac{1}{4}y=-6[/tex]
[tex]-2x-\frac{3}{2}y=-6[/tex]
+
[tex]2x-3y=-30[/tex]
---------------------------------------------------
[tex]0 - 4.5y=-36[/tex]
[tex]y=\frac{-36}{-4,5}[/tex]
[tex]y=8[/tex]
Write an equation in slope intercept form of the line passing through (8,1) and (1,8)
Answer: y = -x + 9
Step-by-step explanation:
First, to find the slope of the line we will use: (y₂-y₁)/(x₂-x₁)
Using the two points, we get: (8-1)/(1-8)
Simplify it: 7/-7
Finally, the slope is -1
We can now write: y = -x + b
Next we will plug in a point into the equation we have:
(8,1) --> 1 = -8 + b Then solve algebraically
b = 9
Then finish the equation:
y = -x + 9
The equation in slope-intercept form for the line passing through the points (8,1) and (1,8) is y = -x + 9, calculated by first finding the slope and then using it to determine the y-intercept.
To write an equation in slope-intercept form of the line passing through the points (8,1) and (1,8), we first calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1). Substituting the given points gives us m = (8 - 1) / (1 - 8) = 7 / -7 = -1. With the slope and one of the points, we can then find the y-intercept (b) by rearranging the slope-intercept equation y = mx + b to b = y - mx, using one of the given points, for example, (8,1), which gives us b = 1 - (-1)(8) = 1 + 8 = 9. Therefore, the equation of the line in slope-intercept form is y = -x + 9.
which point on the number line best represents 22
Answer:
Where is the point?
Step-by-step explanation:
Answer:
B at 4.7
Step-by-step explanation:
Find the missing term
The sum of -3x^2 or 3x^2 and 7x^2 is 10x^2
Answer:
Step-by-step explanation:
"The sum of -3x^2 or 3x^2 and 7x^2 is 10x^2" is false as it now stands.
If we combine -3x^2 and 3x^2, we get 0, so:
"The sum of -3x^2 or 3x^2 and 7x^2 is 10x^2" is equivalent to
"The sum of (expression) and 7x^2 is 10x^2".
Subtracting 7x^2 from both sides yields (expression) = 3x^2.
So: Although "The sum of -3x^2 or 3x^2 and 7x^2 is 10x^2" is false,
"The sum of 3x^2 and 7x^2 is 10x^2" is true, and the formerly missing term is 3x^2.
can someone please help me with equating coefficients?
(x+4)(ax^2 + bx + c) = -2x^3 -7x^2 + 3x -4
ANSWER
a=-2,v=1,c=-1
EXPLANATION
[tex](x + 4)(a {x}^{2} + bx + c) = - 2 {x}^{3} - 7 {x}^{2} + 3x - 4[/tex]
We expand the left hand side to get,
[tex]a {x}^{3} + b {x}^{2} + cx + 4ax^{2} + 4bx + 4c = - 2 {x}^{3} - 7 {x}^{2} + 3x - 4[/tex]
Simplify further to get:
[tex]a {x}^{3} +(4a + b) {x}^{2} +( 4b + c)x + 4c = - 2 {x}^{3} - 7 {x}^{2} + 3x - 4[/tex]
Comparing the coefficients of the cubic terms , we have
[tex]a {x}^{3}=-2{x}^{3} [/tex]
[tex]a =- 2[/tex]
Comparing the quadratic terms,
[tex](4a + b) {x}^{2} = - 7 {x}^{2} [/tex]
[tex]4a + b = - 7[/tex]
[tex]4( - 2) + b = - 7[/tex]
[tex] - 8 + b = - 7[/tex]
[tex]b = - 7 + 8 = 1[/tex]
Comparing the constant terms,
[tex]4c = - 4[/tex]
[tex]c = - 1[/tex]
Answer:
[tex]\large\boxed{a=-2,\ b=1,\ c=-1}[/tex]
Step-by-step explanation:
[tex](x+4)(ax^2+bx+c)\qquad\text{Use FOIL}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(x)(ax^2)+(x)(bx)+(x)(c)+(4)(ax^2)+(4)(bx)+(4)(c)\\\\=ax^3+bx^2+cx+4ax^2+4bx+4c\qquad\text{combine like terms}\\\\=ax^3+(b+4a)x^2+(c+4b)x+4c\\\\ax^3+(b+4a)x^2+(c+4b)x+4c=-2x^3-7x^2+3x-4\\\\\text{Comparing coefficients of terms with the same exponents:}[/tex]
[tex]\left\{\begin{array}{ccc}a=-2&(1)\\b+4a=-7&(2)\\c+4b=3&(3)\\4c=-4&(4)\end{array}\right\\\\(4)\\4c=-4\qquad\text{divide both sides by 4}\\c=-1\\---------------------\\(2)\\\text{From (1) put}\ a=-2\\b+4(-2)=-7\\b-8=-7\qquad\text{add 8 to both sides}\\b=1\\---------------------\\(3)\\\text{From (4) put}\ c=-1\\-1+4b=3\qquad\text{add 1 to both sides}\\4b=4\qquad\text{divide both sides by 4}\\b=1[/tex]
use the substitution method to solve the system of equations. y=7x +8 y=x +20
Answer:
x = 2, y = 22 → (2, 22)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}y=7x+8&(1)\\y=x+20&(2)\end{array}\right\qquad\text{substitute (1) to (2):}\\\\7x+8=x+20\qquad\text{subtract 8 from both sides}\\7x=x+12\qquad\text{subtract x from both sides}\\6x=12\qquad\text{divide both sides by 6}\\x=2\\\\\text{put the value of x to (2):}\\\\y=2+22\\y=22[/tex]
Which of the following is a key property of the linear parent function? A-it does not go through the origin. B-it is a curved line. C- it is in quadrants ll and lV. D- it has a slope of 1.
Answer:
c
Step-by-step explanation:
A line has a slope of -3/2 and has a Y intercept of 3 what is the X intercept of the line
Answer: [tex]x=2[/tex]
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
We know that the slope of this line is:
[tex]m=-\frac{3}{2}[/tex]
And the y-intercept is:
[tex]b=3[/tex]
Since the line intersects the x-axis when [tex]y=0[/tex], we can substitute values into [tex]y=mx+b[/tex]:
[tex]0=-\frac{3}{2}x+3[/tex]
The final step is to solve for "x", then:
[tex]-3=-\frac{3}{2}x\\\\(-3)(-2)=3x\\\\6=3x\\\\x=\frac{6}{3}\\\\x=2[/tex]
The x-intercept of the line is 2.
We must figure out the value of x when the y-coordinate is 0, in order to identify the x-intercept of a line.
We can express the equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept,
Given that the slope of the line is -3/2 and the y-intercept is 3.
Substituting the given values into the equation, we have y = (-3/2)x + 3.
To find the x-intercept, we set y = 0 and solve for x:
0 = (-3/2)x + 3
Subtracting 3 from both sides:
(-3/2)x = -3
To isolate x, we multiply both sides by -2/3:
x = (-3)(-2/3)
x = 2
Therefore, the x-intercept of the line is 2.
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