The system of linear equations, y = 2x + 4 ;
2y = x + 6 has a unique solution and it is a consistent system of linear equations.
What is linear System of Equations and it's solution?An ordered pair that satisfies all equations of the system is the solution of the system. A system of linear equations can have one solution, no solution, or an infinite number of solutions. The systems of equations can be classified according to the number of solutions. If a system has at least one i.e unique solution, it is called consistent. We have, the system of equations is
y = 2x + 4 => 2x - y + 4 = 0 --(1)
2y = x + 2 => x - 2y + 6 = 0 --(2)
Comparing the equation (1) with a₁x + b₁y + c₁=0
and equation(2) with a₂x + b₂y + c₂=0
We get, a₁ = 2 , a₂= 1 , b₁ = -1 , c₁= 4 , b₂= -2 , c₂ = 2
Now, compute the ratio of coefficients of variables .
a₁/a₂ = 2/1 , b₁/b₂ = -1/-2 = 1/2 , c₁/c₂= 4/6 = 2/3
=> a1/a2 ≠ b1/b2 ,
here, both lines are intersect at a point and a unique solution exist for pair of linear equations. In such a case , the pair of linear equations is said to be consistent. Thus, system is consistent.
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Complete question:
Is the system of equation is consistent and
independent consistent and dependent or inconsistent?
y = 2x + 4 , 2y = x + 6
A toy hop purchae 125 identical tuffed animal for total cot of 312. 50 and ell them for $7 each. What i the percent markup?
When they buy 125 identical stuffed animals for $312.50 and sell them for $7 a piece, the percent markup is 64.2%.
What is percentage?A percentage is a figure or ratio that may be stated as a fraction of 100 in mathematics. If we need to compute the percentage of a number, divide it by the entire and multiply by 100. As a result, the percentage denotes a part per hundred. The term % refers to one hundred percent. The sign "%" represents it. To compute a percentage, divide the value by the entire amount and multiply the result by 100. (value/total value)100% is the formula for calculating percentage.
Here,
Total cost=$312.50
Total sell price=7*125
=$875
Markup Price=(875-312.5)/875*100
=0.642*100
=64.2%
The percent markup is 64.2% when they purchase 125 identical stuffed animal for total cost of 312. 50 and sell them for $7 each.
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Help pls 50 ptssssssssssssss
Area of a square:
A = s², where s - side lengthWe have s = 6⁴, then the area is:
A = (6⁴)² cm²Or, apply the power of the power rule (xᵃ)ᵇ=xᵃᵇ to get:
A = 6⁸ cm²calculate the perimeter of the irregular shape 4cm 3cm 2cm 3cm 5cm 6cm 9cm
Answer:8 cm 6 cm 8 cm 6 cm The perimeter of the shape is 8 + 6 + 8 + 6 = 28cm.
Step-by-step explanation:
the following set of ordered pairs defines a function. complete the following {(-26,10), (-30,10),(15,10),(10,10),(-9,10)} add one additional ordered pair to this set such that the set of the ordered pairs still define a function
Answer:
(0,10)
Step-by-step explanation:
You could put any ordered pair, as long as the y value is 10.
The equation of this function is
y = 10 It is a horizontal line going through. The y intercept is (0,10)
What values x and y prove that triangles ABC ~= BAD?
By using congruency, it can be calculated that
x = 6, y = 5
What are congruent triangles?
Two triangles are said to be congruent if their corrosponding sides and corrosponding angles are same. There are different axioms of congruency. They are-
AAS axiom, SAS axiom, ASA axiom, SSS axiom, RHS axiom
It is given that [tex]\Delta[/tex] ABC [tex]\cong[/tex] [tex]\Delta[/tex] BAD
So [tex]\angle[/tex]CAB = [tex]\angle[/tex]ABD [Corrosponding parts of congruent triangles are congruent]
4y = 20
y = [tex]\frac{20}{4}\\[/tex]
y = 5
Also,
AC = BD [Corrosponding parts of congruent triangles are congruent]
5x - 3 = 3x + 9
5x - 3x = 9 + 3
2x = 12
x = [tex]\frac{12}{2}[/tex]
x = 6
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4. Javier bought a microwave for $105. The cost
was 30% off the original price. What was the
price of the microwave before the sale?
The price of the microwave before sales is 350 dollars.
How to find the price of the microwave?Javier bought a microwave for $105. The cost was 30% off the original price. Therefore, the price of the microwave before sales can be calculated as follows:
let
x = price before sales(original price)
Therefore,
105 = 30% of x
105 = 30 / 100 × x
105 = 30x / 100
cross multiply
10500 = 30x
divide both sides by 30
10500 / 30 = 30x / 30
x = 350 dollars
Therefore, the original price is 350 dollars.
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Help, please!!!!! Major point for this assignment
Step-by-step explanation:
45° is an alternate angle with 5y+10. All alternate angles are equal. opposite sides of a parallelogram are equal, we equate to find x.
source: A tutor on another math app. (Brainly doesn't recognize the name)
12. A job pays $25.00 per day plus $5.00 for each additional hour worked. Let x represent the number of hours
worked and y represent the total amount paid.
a. Write an equation in slope-intercept form to represent the amount paid for one day. (3 points)
b. What is the amount paid for one day if you work an 8 hour shift? (2 points)
c. How many hours do you need to work to make $100 in a day? (2 points)
Answer:
Step-by-step explanation:
Calculating Average Weekly Pay for Uneven Work Hours Some professions like nurses & doctors in the healthcare industry might work longer shifts where they are on for 12 hours
assume you wanted to save$2000 to buy a used car 18 months from now.How much money do you need to save every week to accomplish your goal
Answer: $28 per week
Step-by-step explanation:
1 month = 4 weeks
18 times 4 = 72 weeks
So you know you want to save 2000 to buy a car 72 weeks from now.
So take 2000 divided by 72 = $27.77 per week
So you need to save about $28 per week.
14. Jackie borrows $1,500 at 5.75% compound
interest for five years. If she makes monthly
payments, how much is her loan amount after
five years? Round answer to the nearest dollar.
[A] $1,536
[D] $1,725
[B] $2,073
[E] $1,998
[C] $2,050
16 Robert
To find the loan amount after five years, we need to calculate the compound interest on the loan. The compound interest is calculated by multiplying the principal (the initial amount borrowed) by the compound interest rate, raised to the power of the number of compounding periods. In this case, the compound interest rate is 5.75%/12 = 0.475% per month, and there are 12*5 = 60 compounding periods (12 months per year for 5 years).
The compound interest is therefore calculated as follows:
Compound interest = $1,500 * (1 + 0.475%)^60 - $1,500
= $1,725 - $1,500
= $225
So the loan amount after five years is $1,725. Therefore, the correct answer is [D] $1,725.
What is the simplest form of this expression? (X - 4) (x^2 +3x -5)
The simplest expression is x³ - x² - 17x + 20.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
(x - 4) (x² + 3x - 5)
x³ + 3x² - 5x - 4x² - 12x + 20
x³ - x² - 17x + 20
Thus,
The final expression is
x³ - x² - 17x + 20
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the distribution of salaries of teachers is approximately normal. which measure of central tendency would be the best measure to determine the location of the center of the distribution?
The best measure of central tendency to determine the center of the distribution of teacher salaries is the mean.
The mean is the average of all values in a set and is calculated by adding up all the values and dividing them by the number of values. This measure is particularly useful for data that follows a normal distribution, as teacher salaries are likely to do.
The mean is the most commonly used measure of central tendency and is a good indicator of the center of the data set. It is also relatively easy to calculate. So mean will be the measure of the central tendency to determine the center of the distribution of teacher salaries.
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evaluate the iterated integral by converting to polar coordinates. a 0 0 6x2y dx dy − a2 − y2
The iterated integral by converting to polar coordinates [tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] is 7a^4/12.
In the given question, we have to evaluate the iterated integral by converting to polar coordinates.
The given integral is
[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex]
Let polar coordinate.
x = rcosθ, y = rsinθ, x^2 + y^2 = r^2
So dxdy = rdrdθ
r from 0 to a and θ from π/2 to π
Now the integral is
[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]\int_{\pi/2}^{\pi}\int_{0}^{a}7(r\cos\theta)^2(r\sin\theta)drd\theta[/tex]
[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]\int_{\pi/2}^{\pi}\int_{0}^{a}7(r^2\cos^2\theta)(r\sin\theta)drd\theta[/tex]
[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]7\int_{\pi/2}^{\pi}\int_{0}^{a}r^3\cos^2\theta\sin\theta drd\theta[/tex]
Now integrating the first integral
[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]7\int_{\pi/2}^{\pi}\left[\frac{r^4}{4}\right]_{0}^{a}\cos^2\theta\sin\theta d\theta[/tex]
[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]7\int_{\pi/2}^{\pi}\left[\frac{a^4}{4}-\frac{0^4}{4}\right]\cos^2\theta\sin\theta d\theta[/tex]
[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]\frac{7a^4}{4}\int_{\pi/2}^{\pi}\cos^2\theta\sin\theta d\theta[/tex]
Let cosθ = t
So -sinθ = dt/dθ
So sinθdθ = -dt
[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]-\frac{7a^4}{4}\int_{\pi/2}^{\pi}t^2dt[/tex]
[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]-\frac{7a^4}{4}\left[\frac{t^3}{3}\right]_{\pi/2}^{\pi}[/tex]
[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]-\frac{7a^4}{4}\left[\frac{\cos^3\theta}{3}\right]_{\pi/2}^{\pi}[/tex]
[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]-\frac{7a^4}{12}\left[\cos^3\pi-\cos^3(\pi/2)\right][/tex]
[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = -7a^4/12[(-1)^3 - 0]
[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = 7a^4/12
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The complete question is:
Evaluate the iterated integral by converting to polar coordinates.
[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex]
How tall is the table?
1- D
120 cm
90 cm
Answer:
Step-by-step explanation:
105 cm
Please help!!
In the diagram, ΔMTD ≅ ΔGLS . Which statement is true?
∠M ≅ ∠G
DT ≅ LG
DM ≅ SL
∠T ≅ ∠S
Answer:
∠M ≅ ∠G
Step-by-step explanation:
Given:
ΔMTD ≅ ΔGLSThis means that triangle MTD is congruent to triangle GLS.
Two triangles are said to be congruent if:
all three corresponding sides are equal.all three corresponding angles are equal.Therefore:
∠M ≅ ∠G∠T ≅ ∠L∠D ≅ ∠SSimilarly:
TM ≅ LGDT ≅ SLDM ≅ SGTherefore, the true statement is ∠M ≅ ∠G.
As a social media employee, Darla is paid $150 a week plus $10 for every person that
he gets to subscribe to the website. This week, Darla wants her pay to be more than
$450. Website subscribers is defined by w.
Part A. Given 150 + 10w > 450 solve for the number of subscribers Darla needs to make.
Answer:
30
Step-by-step explanation:
Write the inequality as 150 + 10w > 450.
Then, solve. Draw a line on the inequality symbol, and cross out the 150. Subtract 150 from the other side. Then, divide the 10w by 10, to get w by itself. Since it's inverse operations, divide 450 by 10 as well.
You will get an answer of w > 30.
Thus, Darla needs 30 more subscribers.
In the ale the original price are reduced by 15%
a. Calculate the ale price of a book that ha an original price of $12
b. Calculate the original price of a jacket that ha a ale price of $38. 25
Answer:b
Step-by-step explanation:
A triangle has sides with lengths of 15 kilometers, 17 kilometers, and 20 kilometers. Is it a right triangle?
Answer: no
Step-by-step explanation:
use pythagorean theorem.
you can use a^2+b^2=c^2
the biggest value is always c(the hypotenuse) -> c=20
a and b would be 15 and 17(doesn't matter which is which)
plug it into the equation -> 15^2+17^2=20^2
225+289=400
514≠400
so no, it's not a right triangle
A jazz band wants to sell $2,800 worth of tickets. If each ticket costs $70, how many tickets will the band have to sell to meet its goal?
Answer: 40 tickets
Step-by-step explanation:
Divide 2,800 by 7
40
7| 2800|
28
0
You get 40. The jazz band would need to sell 40 tickets to meet its goal.
Hope This Helps!:)A rubber ball is dropped from an initial height of 40 feet. The ball consistently rebounds to 80% of its previous height
Answer:
The ball travels (exactly) 75 feet.
Step-by-step explanation:
Assuming the balls comes to rest:
S = a1 / (1 - r)
Now a1 is the first bounce, 20 ft (10 feet up, 10 feet down.
r is 2/3
S = 20 (1 / (1 - 2/3)
S = 20 / (1/3)
S = 60
Yet that is only the bounce. The drop of 15 feet must be added.
Based on the graph below, what are the new dilation vertices of triangle JKLM with vertices J(-6,2), K(-4,4), L(0,0) M(-2,-2): K= 5/2
The new dilation vertices of the rectangle are J'(-15, 5), K'(-10, 10) L'(0, 0) and M'(-5, -5).
What is the Dilation of the rectangle?
Dilation occurs when a polygon grows or shrinks while maintaining its overall shape. It's similar to zooming in or out on a camera. The polygon in the figure above is a rectangle JKLM. As you move the slider on the right, the transformed rectangle J'K'L'M' grows and shrinks but retains its shape.
We have,
Rectangle JKLM with vertices:
J(-6,2), K(-4,4), L(0,0) M(-2,-2): K= 5/2
New dilation vertices of the rectangle are:
J'(-15, 5), K'(-10, 10) L'(0, 0) and M'(-5, -5)
Hence, the new dilation vertices of the rectangle are J'(-15, 5), K'(-10, 10) L'(0, 0), and M'(-5, -5).
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What symbols do I need for 5 23 18 8 4 to equal 10?
Arithmetic operations can be used to solve this question by using the topic of order of operations. We need to use × and - operators to get the correct answer.
How do we solve inequalities using Arithmetic operations?Many straightforward inequalities can be resolved by adding, taking away, multiplying, or dividing both sides until the variable is all that remains. However, these factors will shift the direction of inequality: Using a negative number to multiply or divide both sides. switching the left and right sides. When resolving an inequality, you can do one of the following:
• Add the same amount to each side;
• Subtract the same amount from each side;
• Multiply or divide each side by the same positive amount. You must flip the inequality sign if you multiply or divide each side by a negative number.
Calculation:5 x (23-18) x (8-4)=100
So we can subtract 23 from 18 where we will get 5 and by subtracting 4 from 8 you will get 4. By multiplying the numbers using × operator you will get the final answer.
Arithmetic operations can be used to solve this question by using the topic of order of operations. We need to use × and - operators to get the correct answer.
Arithmetic operations can be used to solve this question by using the topic of order of operations. We need to use × and - operators to get the correct answer.
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write the expression using exponents. a⋅a⋅c⋅c =
The expression when expressed in its exponent is a²+c²
how to express a number in exponent form?In mathematics, we should understand that exponent tell the power to which a number is raise.
It shows the number of times a number multiplies itself to get the certain member.
The given expression is a*a*c*.
Using the law of multiplication that says when two or more numbers in the same base are multiplied, we add their powers.
Here a appeared twice a*a=a²
And c appeared twice that is c*c=c²
Combining the two exponents together we have that
a²+c²
In conclusion, the exponent of a*a*a*a is a²+c²
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what would the slope of a line parrallel to 2x-y=-1 be?
Answer:
2
Step-by-step explanation:
2x - y = -1
-y = -2x - 1
y = 2x + 1
parallel line = same slope
A city has a 5% sales tax. A book costs $32.55 after tax. How much did it cost before tax?
Answer:
$31
Step-by-step explanation:
x=cost before tax
$32.55 = x + x * 5% ==> solve for x
$32.55 = x + x * 5/100
$32.55 = x + 5x/100
$32.55 = 100x/100 + 5x/100 ==> make common denominators
$32.55 = (100x+5x)/100
$32.55 = 105x/100 ==> simplify
100 * $32.55 = 100 * 105x/100 ==> multiply by 100 on both sides to remove
fractions
$3255 = 105x
x = $3255/105
x = $31
Esteban purchased an iphone 13 which are projected to decrease in value 20% each year. If Esteban purchased the iphone at $1000, which equation represents the value, V, over the course of years, t?
The equation with value V indicating the decrease in value of iPhone 13 with years t is V = [tex] {1000 (1 - 0.02)}^{t} [/tex].
The equation to be used for the calculation of decreased value is -
A = [tex] {P (1 - r)}^{t} [/tex]. In this formula, A is amount, P is principal, r is rate and t represents time. Based on the information in question, A will be replaced with V. So, the required formula will be -
V = [tex] {P (1 - r)}^{t} [/tex]
Now keeping the values in formula for numerical equation -
V = [tex] {1000 (1 - 0.02)}^{t} [/tex]
Since two values are unknown here, the equation can not be solved further.
Therefore, the required equation is V = [tex] {1000 (1 - 0.02)}^{t} [/tex].
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from a square cadrboard sheet, a 5cm wide strip was cut away. the area of the remaining rectangle is 266 cm. find the original dimensions of the square cardboard sheet.
Answer: S=19cm
Step-by-step explanation:
area = s^2
s(s-5)=266
s^2-5s=266
s^2-5s-266=0
(s-19)(s+14)=0
s=19cm
19 x 19 = 266
The original dimensions of the square cardboard sheet is 19 x 19.
What is Quadratic Equation?ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable, a≠0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
Given:
Let the length of each side of the original square cardboard be x cm.
After cutting off a strip of 3cm wide its dimension becomes
length = x cm and breadth= (x−5) cm
So, Area = x² - 5x
266 = x² - 5x
x² - 5x - 266= 0
x² - 19x + 14x - 266= 0
x(x - 19) + 14 (x - 19)= 0
(x- 19)( x + 14) = 0
x= 19, -14.
Hence, the original dimensions of the square cardboard sheet is 19 x 19.
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determine whether the geometric series is convergent or divergent. 8 + 7 + 49 8 + 343 64 +
The given geometric series [tex]$\quad 8+7+\frac{49}{8}+\frac{343}{64}+\cdots$[/tex] is convergent in nature.
[tex]$\quad 8+7+\frac{49}{8}+\frac{343}{64}+\cdots$[/tex]
Since it is geometric series. (As it is given in the question)
A series is considered to be convergent if the partial sums gravitate to a certain value, also known as a limit. In contrast, a divergent series is one whose partial sums do not reach a limit. Divergent series typically go to ∞, go to −∞, or don't approach one specific number.
Here the value of a=8, while the value of the common ratio [tex](r)=\frac{a_2}{a_1}=\frac{7}{8}=\frac{7}{8}[/tex]
since [tex]$|r|=\frac{7}{8} < 1$[/tex]
So the given series is convergent.
The sum of geometric series with infinite terms is equal to [tex]$\frac{a}{1-r}$$$[/tex]
Sum[tex]=\frac{8}{1-\frac{7}{8}}=\frac{8}{\frac{1}{8}}=64[/tex]
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According to the IRS, taxpayers calling the IRS in 2017 waited 13 minutes on average for an IRS telephone assister to answer. Do callers who use the IRS help line early in the day have a shorter wait? Suppose a sample of 50 callers who placed their calls to the IRS in the first 30 minutes that the line is open during the day have a mean waiting time of 11 minutes before an IRS telephone assister answers. Based on data from past years, you can assume that the standard deviation of waiting times is 8 minutes. Using these sample results, can you conclude that the waiting time for calls placed during the first 30 minutes the IRS help line is open each day is significantly less that the overall mean waiting time of 13 minutes? Use alpha=0.05
Establish the two hypotheses
Calculate the test statistic
Make a decision using the critical value approach
Make a decision using the p-value approach
P-value = 0.0384
As P-value < 0.05, reject the null hypothesis.
What is test statistic?
A statistic (a number obtained from the sample) used in statistical hypothesis testing is known as a test statistic. Usually, a hypothesis test is described in words.
A test statistic is a figure obtained from a statistical analysis. It explains how distant your observed data is from the null hypothesis, which states that there is no correlation between the variables or distinction between the sample groups.
The alternative and null hypotheses are listed below.
Lack of hypothesis H0: μ = 13
Ha: 13 Alternative Hypothesis
Statistical test, z = (xbar - mu)/(sigma/sqrt(n))
z = (11 - 13)/(8/sqrt(50))
z = -1.77
Region of Rejection
For α= 0.05, this is a left-tailed test.
Z has a critical value of -1.645.
Therefore, if z -1.645, reject H0 and accept the null hypothesis.
P-value Approach
P-value = 0.0384
As P-value < 0.05, reject the null hypothesis
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Marg Cardo Started to depet P1000 Quarterly in A Fund that pay 5% compounded Quarterly. How much will be Hi Fund affec 7 year
-What Will be the Future
The right response is C. Only X-values inside the original data's range give meaning to the prediction values.
A statistical model that depicts the relationship between two variables is a regression line. It is utilized to forecast the value of a dependent variable depending on the value of an independent variable (independent variable).
The degree to which the regression line matches the data determines how accurate these forecasts are. For values of the independent variable that are similar to the values used to fit the model, the regression line will typically offer the most precise predictions. Prediction values therefore typically only have significance for X-values that fall within or very near the range of the original data set.
The predictions might not be correct if you use the regression line to construct them for independent variable values that are far outside the original data range. This is because, outside of the range of the data that was used to construct the model, the model may not effectively represent the connection between the two variables.
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