Answer:
[tex]y=-\frac{3}{2}x+1[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0)Parallel lines always have the same slope1) Determine the slope (m)
[tex]3x+2y = 10[/tex]
First, we must organize this given equation in slope-intercept form. This will help us identify its slope.
[tex]3x+2y = 10[/tex]
Subtract 3x from both sides
[tex]2y = -3x+10[/tex]
Divide both sides by 2
[tex]y = -\frac{3}{2} x+5[/tex]
Now, we can identify clearly that [tex]-\frac{3}{2}[/tex] is in the place of m in [tex]y=mx+b[/tex], making it the slope. Because parallel lines have the same slope, this makes the slope of the line we're currently solving for [tex]-\frac{3}{2}[/tex] as well. Plug this number into [tex]y=mx+b[/tex]:
[tex]y=-\frac{3}{2}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=-\frac{3}{2}x+b[/tex]
Plug in the given point (8,-11) and solve for b
[tex]-11=-\frac{3}{2}(8)+b\\-11=-\frac{24}{2}+b\\-11=-12+b[/tex]
Add 12 to both sides
[tex]1=b[/tex]
Therefore, the y-intercept of the line is 1. Plug this back into [tex]y=-\frac{3}{2}x+b[/tex]:
[tex]y=-\frac{3}{2}x+1[/tex]
I hope this helps!
A plumber charges $50 for the first visit plus $8 per hour of work. If the total bill is $290, how many hours did the plumber work?
30 hours
40 hours
80 hours
None of these choices are correct.
Answer:
Step-by-step explanation:
50 + 8x = 290
8x = 240
x = 30 hours
add 7/8 + 2 3/24 + 6 1/6
Answer:
9 4/24 or 9 1/6
Find the LCM(lowest common multiple) of 8, 24 and 6.The LCM of 8, 24 and 6 is 24.We now want to turn all the denominators into 24 so we are going multiply 7/8 by 3 and 1/6 by 4. We won't need to turn the denominator of 3/24 into 24 because it's already 24Whatever you do to the denominator you have to do to the numerator, so you also have to multiply the numerator of 7/8 by 3 and the numerator of 1/6 by 4That now results in 21/8 + 2 3/24 + 6 4/24Now you have to add all the fractions together which is going to equal to 28/24Because 28/24 is more than the whole, subtract 28 from 24 which gives us 4. That 4 is now our new numeratorWe are now going to all the whole numbers 6+2+1=9. Incase you're wondering, the '1' came from the 28/24The answer you should get should be 9 4/24 or if it should be simplified it would be 9 1/6
Suppose the mean income of firms in the industry for a year is 95 million dollars with a standard deviation of 11 million dollars. If incomes for the industry are distributed normally, what is the probability that a randomly selected firm will earn less than 114 million dollars
Answer:
95.73%
Step-by-step explanation:
Given data:
mean μ= 95
standard deviation, σ = 11
to calculate, the probability that a randomly selected firm will earn less than 114 million dollars;
Use normal distribution formula
[tex]P(X<114)=P(Z<\frac{X-\mu}{\sigma} )[/tex]
Substitute the required values in the above equation;
[tex]P(X<114)=P(Z<\frac{114-95}{11} )\\P(X<114)=P(Z<1.7272)\\P(X<114)=0.9573[/tex]
Therefore, the probability that a randomly selected firm will earn less than 114 million dollars = 95.73%
The graph below has the same shape as the graph of G(x) = x, but it is
shifted three units to the left. Complete its equation. Enter exponents using
the caret (-); for example, enter x as x^4. Do not include "G(x) =" in your
answer.
G(x) =
Answer:
G(x) = x+3
Step-by-step explanation:
The equation of the graph is G (x) = (x - 3)⁴
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
A relation between a set of inputs having one output each is called a function.
An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The graph of function G (x) is shown in image.
Here, the graph is 3 units left to function F (x) = x⁴.
The equation of the graph is G (x) = (x - 3)⁴
Hence, the equation of the graph is G (x) = (x - 3)⁴
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In the following diagram HI || JK.
HELP MATES PLEASE WILL GIVE 15 POINTS
What is the measure of Zx?
Angles are not necessarily drawn to scale.
67°
H
K
46°
2°
I
A
Answer:
m∠ x = 67
Step-by-step explanation:
∠AJK = ∠AHI = 67 Corresponding Angles
180 - 67 - 46 = x
x = 67
Triangle Sum Theory - the sum of all angles in a triangle = 180
Also, when you see parallel lines look for Corresponding,
Alternate Interior or Same side Interiors.
The sum of two six-digit numbers is a seven-digit number
Answer
500,000 + 500,000 = 1,000,000
Step-by-step explanation:
Given a parametric curve
{x = 2 cost
{y = 4 sint 0 <= t <= π
a. Set up but do NOT evaluate an integral to find the area of the region enclosed by the curve and the x-axis.
b. Set up but do NOT evaluate an integral to find the area of the surface obtained by rotating the curve about the x-axis.
(a) The area of the region would be given by the integral
[tex]\displaystyle\int_0^\pi y(t)\left|x'(t)\right|\,\mathrm dt = 8 \int_0^\pi \sin^2(t)\,\mathrm dt[/tex]
(b) The area of the surface of revolution would be given by
[tex]\displaystyle\int_0^\pi y(t)\sqrt{x'(t)^2+y'(t)^2}\,\mathrm dt = 4\int_0^\pi\sin(t)\sqrt{4\sin^2(t)+16\cos^2(t)}\,\mathrm dt[/tex]
what are the following proof triangle LMN equals triangle OPQ
Answer:
D. SSS
Step-by-step explanation:
Was given to us that the corresponding sides are congruent so is SSS.
Side Side Side Theorem tells us that if am the sides of a triangle are having the same measurement with the corresponding sides of another triangle then the two triangles are congruent.
2 triangles are shown. The first triangle has side lengths 35, 20, and 20. The second triangle has side lengths x, 44, 44.
What value of x will make the triangles similar by the SSS similarity theorem?
15.9
59
77
96.8
Answer:
[tex]x = 77[/tex]
Step-by-step explanation:
Given
[tex]First \to Second[/tex]
[tex]35 \to x[/tex]
[tex]20 \to 44[/tex]
[tex]20 \to 44[/tex]
Required
Find x by SSS
Represent the triangle sides as a ratio
[tex]35 : x = 20 : 44[/tex]
Express as fraction
[tex]\frac{x}{35} = \frac{44}{20}[/tex]
Multiply by 35
[tex]x = \frac{44}{20} * 35[/tex]
[tex]x = \frac{44 * 35}{20}[/tex]
[tex]x = \frac{1540}{20}[/tex]
[tex]x = 77[/tex]
Answer:
ccccccccccccccccccccccccccc
Step-by-step explanation:
What is the length of my
?
M
3x
X + 8
7639
630
N
¿
O
A. 8
B. 4
C. 16
a
D. 12
Answer:
The length of MN is 4
Choose B
The sum of 7/3 and four times a number is equal to 2/3 subtracted from five times the number?
Answer:
-3
Step-by-step explanation:
Help asap please!!..
Answer:
9x² - 4/3x + ¼
Step-by-step explanation:
(3x - ½)²
(3x - ½)(3x -½)
9x² - ⅔x - ⅔x + ¼
9x² - 4/3x + ¼
625^1+1 *125^-1-1 *25^-1+2
Answer:
626.968
Step-by-step explanation:
EMDAS rule
Pls help this is rlly important!! You’ll get branliest bc this is hard and I’m stuck.
the median of restaurant b's cleanliness ratings is 2.
the median of restaurant b's food quality ratings is 4.
the median of restaurant b's service ratings is 3.
:))
if y = k where k is a constant and y =24 when x =6 what is the value of y when x= 5
Answer:
20
Step-by-step explanation:
y=kx
24=6k
k=4
y=4*5=20
Practice Question
1) VAT (value-added tax) is paid on things that you buy.
The table on the right shows the 2019 VAT rates.
This is how much VAT is charged on certain items
as a percentage of the item's cost.
VẬT (%)
20
5
0.
Items
Chocolate and crisps
Gas and electric
Fruit and vegetables
Currena
Before VAT is added, Simon pays 12p per unit of
electricity plus a fixed charge of £87 per year.
How much does Simon pay in VAT if he uses 3000 units of electricity in one year?
er hour
Shane and Space
Simon will pay £18 in VAT for using 3000 units of electricity in one year.
The VAT rate for gas and electric is 5%.
Therefore, Simon will pay VAT on his electricity usage.
Let's calculate Simon's annual electricity cost without VAT:
Cost per unit of electricity = 12p
= £0.12
Number of units used in one year = 3000
Electricity cost without VAT = Cost per unit × Number of units
= £0.12 × 3000
= £360
Now, let's calculate the VAT amount:
VAT rate = 5% = 0.05
VAT amount = Electricity cost without VAT × VAT rate
= £360 × 0.05
= £18
Therefore, Simon will pay £18 in VAT for using 3000 units of electricity in one year.
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Express the following composite numbers as products of prime factors 64
Answer:
64 is a composite number, and it is 8 squared. 64 = 1 x 64, 2 x 32, 4 x 16, or 8 x 8. Factors of 64: 1, 2, 4, 8, 16, 32, 64. Prime factorization: 64 = 2 x 2 x 2 x 2 x 2 x 2, which can also be written 64 = 2⁶.
Please ignore the writing in blue as I tried to work it out but couldn’t
Answer:
[tex]k=35[/tex]°
Step-by-step explanation:
The degree measure of a straight line is (180) degrees. Therefore, when a line intersects another line, the sum of angle measures on any one side of the line is (180). One can apply this here to find the supplement (the angle on the same side of the line) of the angle with a measure of (130) degrees, and (85) degrees.
[tex]130 + (unknown_1)=180\\unknown_1=50\\\\85+(unknown_2)=180\\unknown_2=95[/tex]
The sum of angle measures in a triangle is (180) degrees, one can apply this here by stating the following;
[tex](unknown_1)+(unknown_2)+(k)=180[/tex]
Substitute,
[tex]50+95+k=180[/tex]
Simplify,
[tex]50+95+k=180\\\\145+k=180\\\\k=35[/tex]
[tex]\sf \bf {\boxed {\mathbb {TO\:FIND :}}}[/tex]
The measure of angle [tex]k[/tex].
[tex]\sf \bf {\boxed {\mathbb {SOLUTION:}}}[/tex]
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {k\:=\:35°}}}}}}[/tex]
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}[/tex]
We know that,
[tex]\sf\pink{Sum\:of\:angles\:on\:a\:straight\:line\:=\:180°}[/tex]
➪ [tex]x[/tex] + 85° = 180°
➪ [tex]x[/tex] = 180° - 85°
➪ [tex]x[/tex] = 95°
Also,
Exterior angle of a triangle is equal to sum of two opposite interior angles.
And so we have,
➪ 130° = [tex]k[/tex] + [tex]x[/tex]
➪ [tex]k[/tex] + 95° = 130°
➪ [tex]k[/tex] = 130°- 95°
➪ [tex]k[/tex] = 35°
Therefore, the value of [tex]k[/tex] is 35°.
[tex]\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}[/tex]
[tex]\sf\blue{Sum\:of\:angles\:of\:a\:triangle\:=\:180°}[/tex]
➪ 50° + 35° + 95° = 180°
( where 50° = 180° - 130°)
➪ 180° = 180°
➪ L. H. S. = R. H. S.
Hence verified.
(Note: Kindly refer to the attached file.)
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{ヅ}}}}}[/tex]
Restaurants sales totaled $38,676 for the week your customer count was $7,325 what did the average customer spend for the week
1.3 hectoliters is how many liters
Answer: 130 liters
Step-by-step explanation:
1 hectoliter = 100 liters
1.3 hectoliters = 1.3 · 100 = 130 liters
Ed decided to build a storage box. At first, he was planning to build a cubical box with edges of length n inches. To increase the amount of storage, he decided to make the box 1 inch taller and 2 inches longer while keeping its depth at n inches. The volume of the box Ed built has a volume how many cubic inches greater than the box he originally planned to build?
Answer:
The new volume is 3n^2+2n inches greater.
Step-by-step explanation:
Volume of a cube = s^3 where s is side of cube
Original volume = n^3
Volume of a Rectangular Prism = LBH
New Volume = (n+1)(n+2)(n)= n^3+3n^2+2n
DIfference = New- original = 3n^2+2n
Use cylindrical shells to find the volume of the solid generated when the region
R under y = x2 over the interval (0,2) revolved about the line y = -1
Answer:
[tex]\displaystyle V = \frac{176 \pi}{15}[/tex]
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
Terms/CoefficientsExpandingFunctionsFunction NotationGraphingExponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Calculus
Integrals
Definite IntegralsArea under the curveIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Shell Method:
[tex]\displaystyle V = 2\pi \int\limits^b_a {xf(x)} \, dx[/tex]
[Shell Method] x is the radius[Shell Method] 2πx is the circumference[Shell Method] 2πxf(x) is the surface area[Shell Method] 2πxf(x)dx is the volumeStep-by-step explanation:
Step 1: Define
Identify
Graph of region
y = x²
x = 2
y = 4
Axis of Revolution: y = -1
Step 2: Sort
We are revolving around a horizontal line.
[Function] Rewrite in terms of y: x = √y[Graph] Identify bounds of integration: [0, 4]Step 3: Find Volume Pt. 1
[Shell Method] Find distance of radius x: [tex]x = y + 1[/tex][Shell Method] Find circumference variable f(x) [Area]: [tex]\displaystyle f(x) = 2 - \sqrt{y}[/tex][Shell Method] Substitute in variables: [tex]\displaystyle V = 2\pi \int\limits^4_0 {(y + 1)(2 - \sqrt{y})} \, dy[/tex][Integral] Rewrite integrand [Exponential Rule - Root Rewrite]: [tex]\displaystyle V = 2\pi \int\limits^4_0 {(y + 1)(2 - y^\bigg{\frac{1}{2}})} \, dy[/tex][Integral] Expand integrand: [tex]\displaystyle V = 2\pi \int\limits^4_0 {(-y^\bigg{\frac{3}{2}} + 2y - y^\bigg{\frac{1}{2}} + 2)} \, dy[/tex][Integral] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle V = 2\pi \bigg( \frac{-2y^\bigg{\frac{5}{2}}}{5} + y^2 - \frac{2y^\bigg{\frac{3}{2}}}{3} + 2y \bigg) \bigg| \limits^4_0[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle V = 2\pi (\frac{88}{15})[/tex]Multiply: [tex]\displaystyle V = \frac{176 \pi}{15}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Applications of Integration
Book: College Calculus 10e
hello can anyone help with this?
Answer:
<2 and <13 are alternate exterior angles.
In simple form, alternate exterior angles are the opposite angle on the opposing parallel line. So, to make you understand better, <4 and <15 are alternate exterior angles.
Hope this helps :D
Instructions: Solve the following linear
equation
4(n + 5) – 2(5 + 7n) = -70
n =
Answer:
Step-by-step explanation:
4*(n +5) - 2*(5 + 7n) = -70
4*n + 4*5 + 5*(-2) + 7n*(-2) = -70
4n + 20 - 10 - 14n = -70
4n - 14n + 20 - 10 = -70
- 10n + 10 = -70
Subtract 10 from both sides
-10n = -70 - 10
-10n = -80
Divide both sides by (-10)
n = -80/-10
n = 8
Step-by-step explanation:
sjbsbsbeekejebebheebebejekek
help with this question pleaseee !
Answer:
Add equations A and C to eliminate y and add B and C to eliminate y
Step-by-step explanation:
From the equation given, we can see that the coefficient of y in A and C are alternating values 5 and -5 which cancels out on adding same for B and C. Hence t eliminate y, we will add B and C and A and C
Therefore the correct answer will be to eliminate add equations A and C to eliminate y and add B and C to eliminate y
What is the m GE bisects Find m
Answer:
DGF = 106
Step-by-step explanation:
Bisects means to divide in half, with two equal parts
DGF = DGE + EGF
DGE = EGF
DGF = DGE + DGE
DGF = 53+53
DGF = 106
GE bisects ∠DGF, so it divides ∠DGF into 2 equal parts.
So, m∠EGF = m∠DGE
=> m∠EGF = 53°
m∠DGF = m∠EGF + m∠DGE
=> m∠DGF = 53° + 53°
=> m∠DGF = 106°
Help me plz I can’t figure it out
Answer:
m = 60
Step-by-step explanation:
The context is very important, the 'm' represents the minutes late the parents are and from this we can eliminate some options :
- The last one because then a parent would drop their child off earlier
- The first one and the third one because it is too long
what was the original price of the car? MUST SHOW ALL STEPS OF THE PROCESS.
Answer:
19219.48
Step-by-step explanation:
16540x0.162+16540
The original price would be 100%
It was marked down 16.2%
100 % - 16.2% = 83.8%
The price you paid was 83.8% of the original price.
To find the original price divide the amount you paid by the percentage of the original price:
16,540 / 0.838 = 19.737.47
Original price: $19,737.47
what is the graph of this function?
Answer:
You MADE IT EASY
Step-by-step explanation:
[tex] {y - 5 \times 9}^{2} \: times \: sevem \\ n \: equals \sec(x + {}^{2} ) [/tex]
Can someone help me please! Thanks
Answer:
hello again.. I think you have a problem about figures
Step-by-step explanation:
please be brave when you try to solve..try to draw new lines to get angle and then look at the overall of shape.. the photo helps you good bye
