The equation of the line in slope-intercept form and standard form that passes through the line are y = -5 / 6x - 43 / 6 and 5x + 6y = -43 respectively.
Slope intercept equationThe Slope intercept equation is use to represent a linear table or graph. Therefore, the formula is represented as follows
y = mx + b
where
m = slope
b = y-intercept
Hence,
(-5, -3)(1, -8)
m = -8 + 3 / 1 + 5 = - 5 / 6
Using (1, -8) let's find b
-8 = -5 / 6 (1) + b
-8 + 5 / 6 = b
-48 + 5/6 = b
b = -43 / 6
Therefore, the slope intercept equation is y = -5 / 6x - 43 / 6
The equation in standard form is represented as Ax + By = C. Therefore,
y + 5 / 6 x = - 43/6
5x + 6y = -43
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The table shows the sales receipt for your purchase.
a) the items with a "t" next to the price are subject to sales tax. what percent sales tax did you pay?
b) calculate the price of the top.
c) the price you paid for the top was 60% of the original price. what was the original price of the top?
The sales receipt for the purchase includes the sales tax
The sales tax is 6%The price at the top is $7.50The original price at the top is $12.50How to determine the percent of sales tax?The sales tax is calculated as:
Percentage sales tax * (Sum of Items subjected to tax) = Sales tax.
So, we have:
T * (3 + 0.5) = 0.21
Evaluate the sum
T * (3.5) = 0.21
Divide both sides by 3.5
T = 6%
Hence, the sales tax is 6%
The price at the topThe price (p) at the top is calculated using:
p = 13 - 3 - 2 - 0.5
Evaluate the difference
p = 7.5
Hence, the price at the top is $7.50
The original price at the top60% of the original price (P) is p.
So, we have:
60% * P = p
Substitute 7.5 for p
60% * P = 7.5
Divide both sides by 60%
P = 12.5
Hence, the original price at the top is $12.50
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determine if the relationships are linear and if so are they proportional
Draw a picture to answer.
what is 1/4 of 12?
Answer:
3
Step-by-step explanation:
1/4 x12= 12/4
12/4=3
Solve this system of equations.
3x + 4y = 36
y = -1/2x + 8
What is x?
Answer: Between 1 and 3.
Step-by-step explanation:
You have to Think about y too, y can be anything, but let's say y is 1. Then x should be 3
x = 4, y = 6
In this case, you can solve the equation by substitution.
3x + 4y = 36
We are given that y = -1/2x + 8
Plug in that value assigned to y.
3x + 4(-1/2x + 8) = 36
3x -2x + 32 = 36
x + 32 = 36
x = 4
Now, we can return back to y
y = -1/2x + 8
y = -1/2(4) + 8
y = -2 + 8
y = 6
Solve the System of equations x = -2 ; y = 3 .(Choose from a,b, or c. Show your work step by step).
a) x+y=1
2x+y=5
b) x+2y = 4
x +y = 1
c) x-y=-5
x+y= 11
Pls show your work as I want to understand how to solve this type of equation.
Answer:
B is a the answers for the question
please mark me as brainlest
If we want to know if diagonals or sides are congruent we would use the
formula.
distance
midpoint
slope
When we want to know if the diagonals or sides are congruent we would use the D. Slope.
What is congruent?It should be noted that congruent in geometry simply means when two objects have same shapes and size.
In this case, when we want to know if the diagonals or sides are congruent we would use the slope. This can show the equality in the shape.
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The bearing of a point K from a point L is 084 degrees. What is the bearing of L from K
Answer:
if point bearing of k-l is 084 degree so the bearing of point l-k is 84 degree
The bearing of a point L from a point K is 264 degrees.
What is Addition?
A process of combining two or more numbers is called addition.
Given that;
The bearing of a point K from a point L is 084 degrees.
Now,
Since, The bearing of a point K from a point L is 084 degrees.
Hence, The bearing of a point L from a point K = 180° + 84°
= 264°
Thus, The bearing of a point L from a point K is 264 degrees.
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#SPJ2
The algebra tiles represent the perfect square trinomial x2 10x c. what is the value of c? c =
The value of c for which the considered trinomial becomes perfect square trinomial is: 20 or -20
What are perfect squares trinomials?They are those expressions which are found by squaring binomial expressions.
Since the given trinomials are with degree 2, thus, if they are perfect square, the binomial which was used to make them must be linear.
Let the binomial term was ax + b(a linear expression is always writable in this form where a and b are constants and m is a variable), then we will obtain:
[tex](ax + b)^2 = a^2x^2 + b^2 + 2abx[/tex]
Comparing this expression with the expression we're provided with:
[tex]x^2 + 10x + c[/tex]
we see that:
[tex]a^2 = 1 \implies a = \pm 1\\b^2 = 10\\b = \pm 10\\2ab = c\\\pm2(10)1 = c\\c = \pm 20\\[/tex]
Thus, the value of c for which the considered trinomial becomes perfect square trinomial is: 20 or -20
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helppp plsss. i have to turn this in asap
Answer:
y= 2x-5
Step-by-step explanation:
The slope formula is m=(y2-y1)/(x2-x1)
-3-1 / 1-3 = -4/-2= 2=m
The Y interception- y=mx+b using coordinates (3,1)
1=2(3)+b
1=6+b (subtracting 6 on both sides to isolate b)
-5=b
plug it in
y=2x-5
A polynomial p(x) has 3, 2-i, and √3 as its roots and goes through (0,-90), find p(x)
Answer:
p(x) = -2x⁵ +14x⁴ -28x³ -12x² +102x -90
Step-by-step explanation:
Assuming the desired polynomial has real and rational coefficients, each of the complex and irrational roots has a corresponding conjugate. That is, the roots of p(x) must include ...
{3, 2 -i, 2 +i, √3, -√3}
Each of these roots corresponds to a linear factor. Root p corresponds to factor (x -p), for example.
__
Factored formThen the factored p(x) will be ...
p(x) = k(x -3)(x -(2 -i))(x -(2 +i))(x -√3)(x +√3) . . . . for some scale factor k
Simplifying a bit, we have ...
p(x) = k(x -3)((x -2)² +1)(x² -3) = k(x -3)(x² -4x +5)(x² -3)
__
Scale factorAt x=0, this evaluates to ...
p(0) = k(0 -3)(0² -4·0 +5)(0² -3) = 45k
We want p(0) = -90, so we require ...
45k = -90
k = -2
__
Then the function p(x) factored to integers is ...
p(x) = -2(x -3)(x² -4x +5)(x² -3)
When we multiply this out, we find the standard form equation is ...
p(x) = -2x⁵ +14x⁴ -28x³ -12x² +102x -90
Photo attached with instructions
Step-by-step explanation:
using cosine rule,
BC²= AC² + BC² - 2*AC*BC*COSc
= 13² + 6² - 2*13*6*-cos(180-91)
= 169 + 36 - (-2.72)
= 202.28
√BC² = √202.28
BC = 14.22
BC = 14.20cm to nearest tenth
Solve the equation for x:
3x+5=20
Answer:
x = 5
Step-by-step explanation:
3x+5=20
Subtract 5 from both sides.
3x=20−5
Subtract 5 from 20 to get 15.
3x=15
Divide both sides by 3.
x= 15/3
Divide 15 by 3 to get 5.
x=5
An isosceles triangle has an angle that measures 38degrees. What measures are possible for the other two angles? Choose all that apply.
Answer:
71° and 71°.⠀
Step-by-step explanation:
The triangle having two sides equal along with one different side is called an isosceles triangle.
⠀
So, Let us assume the other sides (two equal sides) of the isosceles triangle as x. As the different side is already given in the question.⠀
We know that,
The sum of all angles of a triangle is 180°⠀
So, According to the question :
⠀
[tex]{\longrightarrow \it\qquad { \ { { 38 \: }^{ \circ} + x + x = 180{}^{ \circ} }}}[/tex]
⠀
[tex]{\longrightarrow \it\qquad { \ { { 38 \: }^{ \circ} + 2x = 180{}^{ \circ} }}}[/tex]
⠀
[tex]{\longrightarrow \it\qquad { \ { 2x = 180{}^{ \circ} - { 38 \: }^{ \circ}}}}[/tex]
⠀
[tex]{\longrightarrow \it\qquad { \ { 2x = 142{}^{ \circ} }}}[/tex]
⠀
[tex]{\longrightarrow \it\qquad { \ { x = \dfrac{142{}^{ \circ}}{2} }}}[/tex]
⠀
[tex]{\longrightarrow \it\qquad { \pmb { x = 71^{ \circ} }}}[/tex]
⠀
Therefore,
The measure of the two other angles of the isosceles triangle are 71° and 71°.Identify the correct explanation for why the triangles are similar. Then find TO and US.
Answer:
The correct explanation is option B;B. ∠L ≅ ∠L By Reflexive Prop. ≅.
Since ║ , ∠LOP ≅ ∠LMN by the Corr. ∠s Post. Therefore, ΔLOP ~ ΔLMN by AA ~. OP = 2 and MN = 6
Step-by-step explanation:
The given parameters are;
= 5
= 10
= + = 15
= x - 3
= x + 1
A two column proof is presented as follows;
Statement Reason
∠L ≅ ∠L By Reflexive property of congruency
║ Given
∠LOP ≅ ∠LMN By the Corresponding angles Postulate
Therefore
ΔLOP ~ ΔLMN By AA similarity Postulate
Where we have that ΔLOP and ΔLMN, we get;
/ = / = 5/15 = 1/3
∴ (x - 3)/(x + 1) = 1/3
3·(x - 3) = 1·(x + 1)
3·x - 9 = x + 1
3·x - x = 1 + 9 = 10
2·x = 10
x = 10/2 = 5
x = 5
= (x - 3) = 5 - 3 = 2
= 2
= x + 1 = 5 + 1 = 6
= 6
Therefore, the correct option is ∠L ≅ ∠L By Reflexive Prop. ≅.
Since ║ , ∠LOP ≅ ∠LMN by the Corr. ∠s Post. Therefore, ΔLOP ~ ΔLMN by AA ~. OP = 2 and MN = 6.
/TO/ and /US/ are parallel so the angles at TOS (©)and the external angle at OSU (©) are equal ( Z angles) therefore the internal angle at OSU will be 180 - © similarly the angle at POT is also 180 - ©
if there are 15 plane 2 crash 1 breakdown how many planes are left
Answer:
15 planes
Step-by-step explanation:
none disappear, just change shape/ability. its a riddle.
Answer:
15-2-1 = 15-3 = 12.
there are 12 planes left.
Step-by-step explanation:
hope this helped have a nice day
Alex just started college and has taken a 10-year subsidized loan out for $5,500 with 6.5% deferred interest. He plans on graduating in 4 years. Determine the money payment alex will pay upon graduation.
Given that the 6.5% interest on the $5,500 loan is deferred during college, the amount Alex will pay upon graduation is $81.67 monthly.
How can the amount Alex will pay be found?The number of years for the loan = 10-year
The loan amount = $5,500
The number of years for the interest = 6 years
The monthly payment formula is presented as follows;
[tex]a = \frac{p \times \frac{r}{12} \times {(1 + \frac{r}{12} )}^{84} }{({1 + \frac{r}{12} )}^{84} - 1}[/tex]
Which gives;
[tex]a = \frac{5500 \times \frac{0.065}{12} {(1 + \frac{0.065}{12} })^{84} }{{(1 + \frac{0.065}{12} })^{84}} = 81.67[/tex]
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Ramona went to a theme park during spring break she was there for 7 hours and rode 21 rides at what rate did I Ramona ride rides in rides per hour
Answer:
57393487
Step-by-step explanation:
un kilo por hora espero que te ayude
Answer:
3 rides/hour
Step-by-step explanation:
Not sure what ^^ guy was saying... And I don't understand why?
The correct answer is number of rides / hours.
21 / 7 = 3
Best answer gets brainliest
Answer:
The answer is 30.
Step-by-step explanation:
12+12+6= 30
I got 6 because it shows a semi circle, and half of 12 is 6.
Answer:
30
Step-by-step explanation:
one circle = 12
two circle = 12 × 2 = 24
half circle = 12/2 = 6
so
two circle + half circle = 24 + 6 = 30
Quick!!! Solve for the missing lengths using trigonometric ratios.
*
110m
42°
Х
Answer:
see explanation
Step-by-step explanation:
using the tangent ratio in the right triangle to find x
tan42° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{10}{x}[/tex] ( multiply both sides by x )
x × tan42° = 10 ( divide both sides by tan42° )
x = [tex]\frac{10}{tan42}[/tex] ≈ 11.1 ( to 1 dec. place )
-------------------------------------------------
using the sine ratio to find the hypotenuse h
sin42° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{10}{h}[/tex] ( multiply both sides by h )
h × sin42° = 10 ( divide both sides by sin42° )
h = [tex]\frac{10}{sin42}[/tex] ≈ 14.9 ( to 1 dec. place )
PLEASE HURRY! (once more)
A cooler contains three colas, seven root beers, and three ginger ales. Three people grab a drink at random, one at a time.
a) What is the probability that the first person grabs a cola, the second person grabs a ginger ale, and the third person grabs a cola?
b) What is the probability that the third person grabs a root beer given that the first two grabbed colas?
Answer:
a) 3/286
b) 7/286
Step-by-step explanation:
We start with 13 drinks. After the first person takes one drink, there are 12 drinks left, After the second person takes one drink, there are 11 drinks available for the third person.
a) From the 13 drinks, there are 3 colas, From the 12 remaining drinks, there are 3 ginger ales. From the 11 remaining drinks, there are 2 colas. We have:
[tex] \frac{3}{13} \times \frac{3}{12} \times \frac{2}{11} = \frac{3}{286} [/tex]
b) From the 13 drinks, there are 3 colas. From the 12 remaining drinks, there are 2 colas. From the 11 remaining drinks, there are 7 root beers. We have:
[tex] \frac{3}{13} \times \frac{2}{12} \times \frac{7}{11} = \frac{7}{286} [/tex]
Ms. Lee takes out a loan to start a business. She borrows $5,000 of a simple annual interest rate of 6. 5% for 5 years. What is the total amount of interest Ms Lee must pay
Answer:
A = $6,625.00
Step-by-step explanation:
A = P(1 + rt)
A = 5000(1 + (0.065 × 5)) = 6625
For a lab experiment, Jeremy needs to know the volume of a sample of tin with a mass of 189.8 grams.
Use the chart to find the volume of this sample of tin.
Answer:
26 cm^3
Step-by-step explanation:
189.8 gm / ( 7.3 gm / cm^3) = 26 cm^3
Answer:
C) 26cm
Step-by-step explanation:
hope it helps!
PLSSSSSS HELP ME WITH THISS!!!
Answer:
Her total would be $59 so, we would be a dollar extra.
The answer is Yes, the total will be $59.
Step-by-step explanation:
$58 - $18.50 = You need to earn $39.5.
Garden = $6.50 per hour
Cakes = $5.25 per hour
$6.50 X 3 hours = $19.50
$5.25 X 4 hours = $21
$21 + $19.50 = $40.50 totall
$18.50 + $40.50 = $59
Which transformations are needed to change the parent cosine function to y = 0. 35 cosine (8 (x minus StartFraction pi Over 4 EndFraction))? vertical stretch of 0. 35, horizontal stretch to a period of 16 pi, phase shift of StartFraction pi Over 4 EndFraction units to the right vertical compression of 0. 35, horizontal compression to a period of 4 pi, phase shift of StartFraction pi Over 4 EndFraction units to the left vertical compression of 0. 35, horizontal compression to a period of StartFraction pi Over 4 EndFraction, phase shift of StartFraction pi Over 4 EndFraction units to the right vertical stretch of 0. 35, horizontal stretch to a period of StartFraction pi Over 4 EndFraction, phase shift of StartFraction pi Over 4 EndFraction units to the right.
The transformations that are needed to change the parent cosine function to y = 0.35×cos(8(x-π/4)) are:
vertical stretch of 0.35horizontal compression of period of [tex]\pi/4[/tex]phase shift of [tex]\pi/4[/tex] to rightHow does transformation of a function happens?The transformation of a function may involve any change.
Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.
If the original function is [tex]y = f(x)[/tex], assuming horizontal axis is input axis and vertical is for outputs, then:
Horizontal shift (also called phase shift): Left shift by c units: [tex]y = f(x+c)[/tex]earlier)Right shift by c units: [tex]y = f(x-c)[/tex]output, but c units late)Vertical shift:Up by d units: [tex]y = f(x) + d[/tex]Down by d units: [tex]y = f(x) - d[/tex]Stretching:Vertical stretch by a factor k: [tex]y = k \times f(x)[/tex]Horizontal stretch by a factor k: [tex]y = f(\dfrac{x}{k})[/tex]For this case, we're specified that:
y = cos(x) (the parent cosine function) was transformed to [tex]y = 0.35\cos(8(x-\pi/4))[/tex]
We can see its vertical stretch by 0.35, right shift by [tex]\pi/4[/tex]horizontal stretch by 1/8
Period of cos(x) is of [tex]2\pi[/tex] length. But 1.8 stretching makes its period shrink to [tex]2\pi/8 = \pi/4[/tex]
Thus, the transformations that are needed to change the parent cosine function to y = 0.35×cos(8(x-π/4)) are:
vertical stretch of 0.35horizontal compression to period of [tex]\pi/4[/tex] (which means period of cosine is shrunk to [tex]\pi/4[/tex] which originally was [tex]2\pi[/tex] )phase shift of [tex]\pi/4[/tex] to rightLearn more about transformation of functions here:
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Help pleaseee i am awful at math
Step-by-step explanation:
use the above process and answer is $3.60
-2x + 1 = 4x + 9
I don’t know what to solve for x?
Answer:
x = -1.33333333333
Step-by-step explanation:
[tex]\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}[/tex]
[tex]-2x+1-1=4x+9-1[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]-2x=4x+8[/tex]
[tex]\mathrm{Subtract\:}4x\mathrm{\:from\:both\:sides}[/tex]
[tex]-2x-4x=4x+8-4x[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]-6x=8[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}-6[/tex]
[tex]\frac{-6x}{-6}=\frac{8}{-6}[/tex]
[tex]x=-\frac{4}{3}[/tex]
[tex]x=-1.33333333333[/tex]
~Lenvy~
jeff is 1.67 meters tall how many centimeters tall is jeff
Answer:
167
Step-by-step explanation:
Round to the ten millions place.
3,025,285,000
o a. 3,025,290,000
o b. 3,020,000,000
c. 3,025,000,000
d. 3,030,000,000
o e. 3,030,285,000
Please help! Will mark brainliest <3. (Click on the photo too see the question!) you need to select all angle pairs that are vertical angles.
Answer:
B and D
Step-by-step explanation:
vertical angles are ones that are formed by intersecting lines, and they are also equal to each other and opposite of each other.
its not A because they are not equal to each other.
B is correct because they are formed by intersecting line and equal to each other
C is incorrect since theres some random line that doesnt completely pass through on either side
D is correct
2. You are building a fence around your vegetable garden in your backyard. If
the garden is 12'8" long and 4'6" wide, what is the total length of fencing you
will need?
The length of fencing required is 34.34 feet.
Data;
Length = 12 feet 8 inch long = (12 + 0.67) feet = 12.67 feetWidth = 4 feet 6 inch wide = (4+0.5)feet = 4.5 feetPerimeter of the GardenTo find the total length of fencing required, we have to find the perimeter of a rectangle since the garden has a rectangular shape.
[tex]P = 2(L + W)[/tex]
We can substitute the values in the formula of perimeter above and proceed to solve.
[tex]P = 2(L+W) \\P = 2(12.67 + 4.5) \\P = 2(17.17)\\P = 34.34ft[/tex]
The length of fencing required is 34.34 feet.
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