Solve each equation. SHOW WORK ANSWER PLEASE
A. P-1=5p+3p-8
B. 5n+34=-2(1-7n)
C. 3x-2=3x+5
D. 4(2x-8)=8(x-4)
Answers
-7p=-7
-7/-7p=-7/-7
P=1
B. 5n+34=-2+14n
5n-14n=-34-2
-9n=-36
-9/-9n=-36/-9
n=4
C. 3x-3x=5+2
0=7 (There is no solution)
D. 8x-32=8x-32
8x-8x=32-32
0=0
The solution to each of the equations are as follows;
A. p = 1
B. n = 4.
C. x = no solution.
D. x = no solution.
What is no solution?In Mathematics, no solution is sometimes referred to as zero solution, and an equation is said to have no solution when the left hand side and right hand side of the equation are not the same or equal.
Next, we would solve each of the equations as follows;
p - 1 = 5p + 3p - 8
p - 1 = 8p - 8
8p - p = 8 - 1
7p = 7
p = 7/7 = 1.
5n + 34 = -2(1 - 7n)
5n + 34 = -2 + 14n
14n - 5n = 34 + 2
9n = 36
n = 36/9 = 4
3x - 2 = 3x + 5
3x - 3x = 5 + 2
0 = 7 (no solution).
4(2x - 8) = 8(x - 4)
8x - 32 = 8x + 32
8x - 8x = 32 + 32
0 = 64 (no solution).
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Related Questions
a rectangular lawn of sides 400m and 300m is surrounded by a path of width 3 m . find the area of path
Answers
Answer:
2109 meter squared
Step-by-step explanation:
\(Area \: of \: path \\ = (400+3)(300+3)-400 \times 300 \\ = 403 \times 303 - 120000 \\ = 122,109 - 120000 \\ = 2109 \: {m}^{2} \)
Dionne Washington wants to sell natural fruit flavored water at her neighborhood block party. She wrote the amount of money she spent as a function of the number of bottles sold. Which set of numbers would be an appropriate domain for Dionne’s function?
0, 1, 2, 3, 4, …
…, −4, −3, −2, −1, 0
…, −3, −2, −1, 0, 1, 2, 3, …
…, −3.5, −2.5, −1.5, 0, 1.5, 2.5, 3.5, …
Answers
Answer:
Option A: {0,1, 2, 3, 4,....}
Step-by-step explanation:
Domain is simply a set of input while the range is a set of output values.
For example, if we have a function named f(x) = x², the domain will be all possible values of x being inputed while the range will be the value of f(x) for all possible values of x inputed.
Now, from the question, we are told that she wrote the amount of money she spent as a function of the number of bottles sold.
If the number of bottles sold is denoted by "x", it means the function is; f(x).
Now, number of bottles has to be a non-negative whole number or simply a non-negative integer. Thus, the possible values of x are all non-negative whole numbers like, 0,1, 2, 3, 4, 5....
Thus,domain is {0,1, 2, 3, 4,....}
Cole is an urban planner. He wants to create a small scale drawing of a city block. The block is a square with sides of length 100\text{ m}100 m100, start text, space, m, end text.
Draw the city block such that 111 unit on the grid below represents 5\text{ m}5 m5, start text, space, m, end text.
Answers
Answer:
Make all sides 3.0
Answer:3.0
Step-by-step explanation:
Which type of transformation could cause a change in the period of a tangent or cotangent function?.
Answers
There is one specific type of transformation that can cause a change in the period of a tangent or cotangent function, and that is a dilation.
A dilation is a transformation that stretches or compresses a function horizontally or vertically. When a tangent or cotangent function is dilated horizontally, the period of the function changes. The period of a tangent function is π, while the period of a cotangent function is also π.
If the function is dilated by a factor of k, then the new period will be π/k. This means that the function will oscillate faster if it is compressed horizontally (k > 1) and slower if it is stretched horizontally (k < 1). Therefore, it is important to consider the effects of dilations when analyzing the period of a tangent or cotangent function.
The type of transformation that could cause a change in the period of a tangent or cotangent function is called a "horizontal stretch" or "horizontal compression." These transformations affect the frequency of the function by scaling it horizontally, which in turn alters the period of the tangent or cotangent function.
In mathematical terms, the general form of a tangent function is y = A * tan(B(x - C)) + D, and for a cotangent function, it's y = A * cot(B(x - C)) + D. In these expressions, A represents the amplitude, B determines the horizontal stretch or compression, C is the phase shift, and D is the vertical shift.
The factor B directly affects the period of the function. For a tangent or cotangent function, the standard period is π. To find the new period after a horizontal transformation, you can use the formula: new period = (standard period) / |B|. Thus, by changing the value of B, the period of the tangent or cotangent function will be affected accordingly.
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What is an equation of the line that passes through the points
(6,1) and (7,2)? Put your answer in fully reduced form.
Answers
Answer (assuming it can be in slope-intercept form):
y = x - 5
Step-by-step explanation:
1) First, find the slope of the equation. Use the slope formula, \(m = \frac{y_2-y_1}{x_2-x_1}\), and substitute the x and y values of the given points into it. Then, solve:
\(m = \frac{(2)-(1)}{(7)-(6)} \\m = \frac{2-1}{7-6} \\m = \frac{1}{1} \\m = 1\)
2) Now that we know the slope and at least one point the line crosses through, we can write an equation of the line in point-slope form, or \(y-y_1 = m (x-x_1)\). Substitute \(m\), \(x_1\), and \(y_1\) for real values.
Since \(m\) represents the slope, substitute 1 for it. Since \(x_1\) and \(y_1\) represent the x and y values of a point the line intersects, use any one of the given points (either one is fine, either way the equation will represent the same line) and substitute its x and y values into the equation. (I chose the point (6, 1), as seen below.) Finally, isolate y to put the equation in slope-intercept form.
\(y-1 = 1(x-6)\\y -1 = x-6\\y = x -5\)
Pls
Assistance and steps
What is the inverse of y = 3/2x?
Answers
Answer:
option (1)
Step-by-step explanation:
rearrange making x the subject, then x is the inverse
y = \(\frac{3}{2}\) x ( multiply both sides by 2 to clear the fraction )
2y = 3x ( isolate x by dividing both sides by 3 )
\(\frac{2}{3}\) y = x
change y back into terms of x , then inverse is
\(f^{-1}\) (x) = \(\frac{2}{3}\) x , or
y = \(\frac{2}{3}\) x
Sony's utility function is U(q
1
,q
2
)=q
1
+Aq
1
a
q
2
b
+q
2
. The letters A,a,b are all positive constants. a) Find the marginal utility functions U
1
,U
2
of the two goods. b) Find the MRS. (Dorrit worry about reducing the math expression, it's not simplifiable in this example.)
Answers
The marginal utility functions for the given utility function are \(U_{1} = 1 + Aaq_{1} ^{(a-1)}q_{2}^{b}\) and \(U_{2} = Abq_{1} ^{a} q_{2}^{(b-1)}+ 1\). The MRS is equal to the ratio of the marginal utilities, or MRS = U₁/U₂ = \(1 + Aaq_{1} ^{(a-1)}q_{2}^{b}\)/ \((Abq_{1}^aq_{2}^{(b-1)} + 1)\).
a) The marginal utility functions can be obtained by taking the partial derivatives of the utility function with respect to each good. For the given utility function U(q₁, q₂) = \(q_{1} + Aq_{1}^{(a)}q_{2}^{(b)} + q_{2}\) the marginal utility of good 1 (U₁) is equal to\(1 + Aaq_{1}^{(a-1)}q_{2}^{(b)}\), and the marginal utility of good 2 (U₂) is equal to \(Abq_{1}^{(a)}q_{2}^{(b-1)} + 1\).
b) The marginal rate of substitution (MRS) represents the rate at which a consumer is willing to exchange one good for another while maintaining the same level of utility. It is defined as the ratio of the marginal utilities of the two goods. In this case, the MRS can be calculated as MRS = U₁/U₂, which gives \(\frac{(1 + Aaq_{1}^{(a-1)}q_{2}^{(b)})}{(Abq_{1}^{(a)}q_{2}^{(b-1)} + 1)}\).
The explanation above summarizes the process of obtaining the marginal utility functions and the MRS for the given utility function. The utility function is differentiated with respect to each good to find the marginal utilities. The MRS is then calculated as the ratio of the marginal utilities. The specific expressions for the marginal utilities and the MRS are provided based on the given utility function.
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use the number line to help you find which fraction is less than 0.5.
Answers
Any fraction that falls to the left of 1/2 on the number line is considered to be less than 0.5.
On the number line, fractions are represented as points between 0 and 1. The fraction 1/2 represents the halfway point on the number line.
Fractions to the left of 1/2 are smaller or less than 0.5.
The fraction 1/4 is to the left of 1/2, so it is less than 0.5.
This means that if you were to convert 1/4 into a decimal, it would be a number smaller than 0.5.
Similarly, the fraction 3/8 is also to the left of 1/2, so it is less than 0.5. When you convert 3/8 to a decimal, it is equal to 0.375, which is less than 0.5.
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Write and solve a system of equations for each problem situation. Interpret the solution in terms of context.
Pedro has 97 athlete cards. In his collection, he has 39 more baseball player cards than football player cards. How many of each type of card does Pedro have?
Answers
Number of each type of cards after solving system of equations for given situation of Pedro cards are 29 and68.
Interpretation is Pedro collected 29 football cards and 68 baseball cards.
As given,
Total number of cards=97
Let y=football cards
x=baseball cards
System of equations are
x + y=97 __(1)
x=y +39 __(2)
Substitute (2) in (1)
y+ 39 +y=97
⇒2y=58
⇒y=29
Substitute y=29 in (2),
x=29 +39
=68
Therefore, number of each type of cards after solving system of equations are football cards 29 and baseball cards 68.
Interpretation is Pedro collected 29 football cards and 68 baseball cards.
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2. Find the surface area of the regular pyramid shown to the nearest whole 2. number. 6m 3-√√3 m |—6 m →|
Answers
Therefore, the surface area of the regular pyramid is approximately 103 m^2.
To find the surface area of a regular pyramid, we need to consider the base and the lateral faces.
Given the dimensions of the pyramid:
Base edge length (a) = 6 m
Slant height (l) = 3 - √3 m
To find the surface area, we need to calculate the area of the base and the area of the lateral faces.
Area of the base:
The base of the pyramid is a regular hexagon, so we can use the formula for the area of a regular hexagon:
Area of base = (3√3/2) * a^2
Substituting the value of a = 6 m into the formula:
Area of base = (3√3/2) * (6 m)^2
Area of base ≈ 93.53 m^2 (rounded to the nearest whole number)
Area of the lateral faces:
The lateral faces are congruent triangles, so we can use the formula for the area of an isosceles triangle:
Area of each lateral face = (1/2) * base * height
The base of each lateral face is the same as the base edge length, a = 6 m.
The height of each lateral face is the slant height, l = 3 - √3 m.
Substituting the values into the formula:
Area of each lateral face = (1/2) * 6 m * (3 - √3 m)
Area of each lateral face ≈ 9.89 m^2 (rounded to the nearest whole number)
To find the surface area, we add the area of the base to the combined area of the lateral faces:
Surface area = Area of base + Total area of lateral faces
Surface area ≈ 93.53 m^2 + 9.89 m^2
Surface area ≈ 103.42 m^2 (rounded to the nearest whole number)
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Simplify the expression -4x(6x − 7).
Answers
Answer: -24x^2+28x
Step-by-step explanation: -4x*6x-(-4x)*7 to -24x^2+28x
maths
1. 24÷ (-6)
2. -15 ÷ 0.3
3. -4 ÷ (-20)
Answers
Answer:
hope it helps
Step-by-step explanation:
1) -72
2) -50
3) 0.2
Answer:
1. 24÷ (-6)=− 4
Factor the numerator and denominator and cancel the common factors.
2. -15 ÷ 0.3=− 50
3. -4 ÷ (-20)=
Reduce the expression, if possible, by cancelling the common factors.
Exact Form:
1/5
Decimal Form:
0.2
here you go! :) hope I am right
Assume that TDW Corporation (calendar year-end) has 2022 taxable income of $650,000 for purposes of computing the §179 expense. The company acquired the following assets during 2022: (Use MACRS Table 1, Table 2, Table 3, Table 4 and Table 5. ) Asset Placed in Service Basis Machinery September 12 $ 2,270,000 Computer equipment February 10 263,000 Furniture April 2 880,000 Total $ 3,413,000 a. What is the maximum amount of §179 expense TDW may deduct for 2022?
Answers
The maximum amount of §179 expense TDW may deduct for 2022 is $257,000.
To determine the maximum amount of §179 expense that TDW Corporation can deduct for 2022, we first Add up the cost of all the assets acquired in 2022:
$2,270,000 (machinery) + $263,000 (computer equipment) + $880,000 (furniture) = $3,413,000
Now we determine the amount of the §179 deduction limit for the tax year.
For tax year 2022, the §179 deduction limit is $1,050,000.
Check if the cost of the assets exceeds the §179 deduction limit.
Since the cost of the assets ($3,413,000) is greater than the §179 deduction limit ($1,050,000), we need to calculate the phase-out limit.
Now we determine the phase-out limit.
For tax year 2022, the phase-out limit is $2,620,000.
Calculate the §179 expense deduction.
Since the cost of the assets ($3,413,000) is greater than the phase-out limit ($2,620,000), we need to reduce the §179 deduction by the excess over the phase-out limit.
The excess over the phase-out limit is $793,000 ($3,413,000 - $2,620,000).
The §179 expense deduction is the lesser of the §179 deduction limit and the cost of the assets reduced by the excess over the phase-out limit.
The §179 expense deduction is $1,050,000 - $793,000 = $257,000.
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Can someone plz help me? :(
Answers
Answer:
The second option since its specifically asking abt the 58 equation
Step-by-step explanation:
DEA if the diameter is 7 in
Answers
CAN SOMEONE HELP :) IF YOU CAN TYSM!
Answers
Answer:
i. x = -0.5 and 1.5; ii. x = 1.5
Step-by-step explanation:
For part i, we can take a look at the x-intercepts of the parabola. When a quadratic equation equals 0, this means that we are taking a look at its roots, or solutions.
The parabola intersects the x-axis at approximately -0.5 and 1.5. We can say this is an estimate to the solutions.
For part ii, the question is asking the x value that makes the function equal 2. We just look at the point where y = 2, which happens to be 1.5. So when x = 1.5, y = 2, which is what we want.
I hope this helps!
Which expression is equivalent to -11 - (-7)?
Answers
sanjay purchased 4 3/4 kg pulses and 5 1/2 kg sugar. what is the total weight of material purchased by him?
Answers
Answer with a step by step explanation:
Sanjay purchased = 4 3/4 kg pulses
He also purchased = 5 1/2 sugar
Total:
Here we'll need to add both weights.
19/4 + 11/2 ← Convert into fractionLCM of 4 & 2 is 4.
19 + 22 /441/4 kgConvert into mixed fraction:
10 1/4 kgWe can conclude that:
Sanjay purchased 10 1/4 kg of material.
You buy a pair of jeans at a department store. A receipt, titled "Department Store". It shows the bill for a pair of jeans. Jeans, 39.99; Discount, negative 10.00; Subtotal, 29.99; Sales Tax, 1.95; Total, 31.94. The line at the bottom reads, Thank You. a. What is the percent of discount to the nearest percent? The percent of discount is %. b. What is the percent of sales tax to the nearest tenth of a percent? The percent of sales tax is %. c. The price of the jeans includes a 60% markup. After the discount, what is the percent of markup to the nearest percent? The percent of markup is %.
Answers
Answer:
25%
6.5%
35%
Step-by-step explanation:
Given the invoice :
Bill for a pair of Jean
Jeans ______39.99
Discount ___ - 10.00
Subtotal ____ 29.99
Sales tax ____ 1.95
Total _______ 31.94
A) % of discount to the nearest %
Discount amount = % discount * price
10 = x% * 39.99
10/39.99 = x%
0.2500625 = x%
x = 0.2500625 * 100%
% discount = 25%
% of sales tax:
Sales tax amount = % tax * Subtotal
1.95 = x% * 29.99
1.95/29.99 = x%
0.06502 = x%
x = 0.06502 * 100%
x = 6.5%
Markup before discount = 60%
Markup after discount = (60 - 25)% = 35%
a lawyer researched the average number of years served by 45 different justices on the supreme court. the average number of years served was 13.8 years with a standard deviation of 7.3 years. what is the 95% confidence interval estimate for the average number of years served by all supreme court justices? place your limits, rounded to 1 decimal place,
Answers
"a lawyer researched the average number of years served by 45 different justices on the supreme court. the average number of years served was 13.8 years with a standard deviation of 7.3 years.
The 95% confidence interval estimate for the average number of years served by all supreme court justices is [11.2, 16.4].According to the central limit theorem , a sampling distribution of the means is usually distributed in a normal distribution, given a big enough sample size, which means that it has a bell-shaped curve. It has a standard deviation that can be estimated by dividing the population standard deviation by the square root of the sample size. Using the formula below,
we can calculate the 95% confidence interval for the population average.= 13.8 ± (1.96 × 7.3 / √45)
= 13.8 ± (1.96 × 1.088)
= 13.8 ± 2.13The limits are calculated by adding and subtracting the calculated value from the sample mean.13.8 + 2.13
= 15.9313.8 - 2.13
= 11.67Therefore, the 95% confidence interval estimate for the average number of years served by all supreme court justices is [11.2, 16.4].
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12 people are waiting at a subway stop to get on the train. However, the train only has space for 9 people to board. How many different combinations of people can get on the train?
220
220
1,320
1,320
13,305,600
13,305,600
79,833,600
79,833,600
Skip to navigation
Answers
This figure is made up of a rectangle and half a circle find perimeter of the figure to the nearest 10th show your work please use 3.14 for pi
Answers
The required perimeter of the given figure will be 60.84 m.
We have been given the figure which is made up of a rectangle and half a circle.
We have to determine the perimeter of the given figure.
As per the given figure, the required solution would be as:
The required perimeter = 2 × (rectangle's length) + rectangle's width + circumference of half a circle
The required perimeter = 2 × 15 + 12 + π × 6
The required perimeter = 30 + 12 + 3.14 × 6
The required perimeter = 30 + 12 + 18.84
Apply the addition operation, and we get
The required perimeter = 60.84 m
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for f(x)=3/8x-7, find f(-16)
Answers
The given function is
\(f(x)=\frac{3}{8}x-7\)The expression f(-16) means we have to evaluate the function when x = -16.
\(\begin{gathered} f(-16)=\frac{3}{8}(-16)-7 \\ f(-16)=-3\cdot2-7=-6-7=-13 \end{gathered}\)Therefore, f(-16) is equal to -13.you generate electricity with your own personal wind turbine? That depends on whether you have enough wind on your site. To produce enough energy, your site should have an annual average wind speed of at least 8 miles per
ding to the Wind Energy Association. One candidate site was monitored for a year, with wind speeds recorded every 6 hours. A total of 1114 readings of wind speed averaged 8.019 mph with a standard deviation of 3.813 mph. Youl
I asked to make a statistical report to help the landowner decide whether to place a wind turbine at this site. Complete parts a and b below.
Answers
The 95% confidence interval of the statistics is (7.795, 8.243).
How to illustrate the information?Based on the information given, the 95% confidence interval will be:
= 8.019 + (1.962 × 3.183/✓1114)
= 8.243 and
= 8.019 - (1.962 × 3.183/✓1114)
= 7.795
In conclusion, the 95% confidence interval of the statistics is (7.795, 8.243).
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Hi please help me in this onei don't know how to solve itfind the value of x
Answers
EXPLANATION
If the measure of ∠2= x+78 and the other ∠=40 degrees, by definition we know that sum of interior angles of a triangle is equal to 180 degrees.
Furthermore, we have two congruent legs, so this is an Isosceles triangle with two congruent angles (with the same measure).
Thus,
180 = 40 + 2* m∠2
Substituting m∠2 by the equation as follows:
180 = 40 + 2(x + 78)
Subtracting -40 to both sides:
180 - 40 = 2(x+78)
Simplifying:
140 = 2(x+78)
Dividing both sides by 2:
140/2 = x + 78
Simplifying:
70 = x + 78
Subtracting -78 to both sides:
70 - 78 = x
Simplifying:
-8 = x
Switching:
x = -8
Answer: The value of x is -8.
What is the mapping rule for a 180° rotation?
O (x, y) - (y, x)
O (x, y) - (-y, x)
O (x, y) - (y, -x)
O (x, y) - (-x, -y)
Answers
Answer: D
Step-by-step explanation:
(x,y)—> (-x, -y)
Students are going to conduct an experiment to study the effect of a net force applied to an object on the object’s motion. In each trial of the experiment, the students will apply a net force on the object. They also need to take two other measurements. What are the other quantities they should measure in each trial of the experiment?.
Answers
For conducting experiment based on effect of a net force , to apply net force on the object two other quantities should be measured in each trial of the experiment is given by velocity and time.
As given in the question,
To conduct a experiment based on the effect of net force applied to an object the dependable quantities are as follow:
Force = mass × acceleration
As object remain same ⇒ mass is constant as object remain same.
And there is change in the acceleration.
Acceleration depends change in velocity over total time taken.
Acceleration depends on velocity and time.
Net force also depends on velocity and time.
Two measurements need to know while conducting trail experiments are velocity and time.
Therefore, to conduct experiment based on effect of a net force , to apply net force on the object two other quantities should be measured in each trial of the experiment is given by velocity and time.
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(b) how many people would you need to interview to be 73% sure that at least seven of these people can read and write (are not illiterate)? (enter the smallest number of people needed to be at least 73% sure.)
Answers
0.3193 is the probability of your 73% surity that at least seven of these people can read and write ( are not illiterate ).
What is probability ?Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. A probability is a number between 0 and 1, where 1 indicates certainty and 0 indicates impossibility of the event.
Calculationp = 0.73
q = 1 - p = 1 - 0.73 = 0.27
n = 8
Using binomial probability formula ,
P(X = x) = (n C x) * px * (1 - p)n - x
P(X > 7) = (8 C 7) * 0.737 * (0.37)8-7 +(8 C 8) * 0.738 * (0.37)8-8
= 0.238624 + 0.080646
Probability = 0.3193
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what is the simple interest of $16000 interested for 5 years at 4% p.a?
Answers
Answer:
3200
Step-by-step explanation:
Simple interest = PRT/100
= (16000 × 5 × 4%\)/100
= 320000/100
= 3200
One rectangular solid with a square base has twice the height of another rectangular solid with a square base with the same side length. which statements about the two rectangular solids are true? check all that apply.
Answers
The correct statements about the solids are:
(A) The bases are congruent.(D)The volume of the first solid is twice as much as the volume of the second solid.(E) If the dimensions of the second solid are x by x by h, the first solid has 4xh more.What are solids?Solid geometry or stereometry is the standard name for the geometry of three-dimensional Euclidean spaces in mathematics. Stereometry is concerned with the volume measurements of various solid forms, such as pyramids, prisms, and other polyhedrons; cylinders; cones; truncated cones, and balls bordered by spheres.To find which statements are correct:
Congruent base: This is used to indicate that the triangles' bases are the same and that they have the same shape.
The volume of the first triangle is: \(2x^{2} h\)
The volume of the second triangle is: \(x^{2} h\)
Therefore, the correct statements about the solids are:
(A) The bases are congruent.(D)The volume of the first solid is twice as much as the volume of the second solid.(E) If the dimensions of the second solid are x by x by h, the first solid has 4xh more.Know more about solids here:
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The complete question is given below:
One rectangular solid with a square base has twice the height of another rectangular solid with a square base with the same side length. Which statements about the two rectangular solids are true? Check all that apply.
A) The bases are congruent.
B) The solids are similar.
C) The ratio of the volumes of the first solid to the second solid is 8:1.
D)The volume of the first solid is twice as much as the volume of the second solid.
E) If the dimensions of the second solid are x by x by h, the first solid has 4xh more
surface area than the second solid.