Yes, quadrilateral ABCD is a parallelogram.
What are the properties of parallelogram?
A parallelogram is a particular sort of polygon. It is a quadrilateral in which the opposite side pairs are parallel to one another.
Properties:
1. Opposite sides are congruent.
2. Opposite angels are congruent.
3. Consecutive angles are supplementary.
4. If one angle is right, then all angles are right.
5. The diagonals of a parallelogram bisect each other.
6. Each diagonal of a parallelogram separates it into two congruent
It is given that the coordinates of the vertices of quadrilateral ABCD are A (8, -3), B(-2, 1), C (-4,-4), and D(6, -8).
According to distance formula,
If A(a,b) and B(x,y) are two coordinates then
AB = [tex]\sqrt{(x-a)^{2}+(y-b)^{2}}[/tex]
Now, using this distance formula in quadrilateral ABCD
AB = [tex]\sqrt{(-2-8)^{2}+(1+3)^{2}}= \sqrt{(-10)^{2}+(4)^{2}}=\sqrt{100+16}=\sqrt{116}[/tex]
CD = [tex]\sqrt{(6+4)^{2}+(-8+4)^{2}}=\sqrt{10^2+(-4)^2}=\sqrt{100+16}=\sqrt{116}[/tex]
Now, If we have two coordinates A(a,b) and B(x,y) then
Slope of AB = [tex]\frac{y-b}{x-a}[/tex]
Using this formula , finding slope of AB and CD of quadrilateral ABCD we get ,
Slope of AB = [tex]\frac{1+3}{-2-8}=\frac{4}{-10}=\frac{2}{-5}[/tex]
Slope of CD = [tex]\frac{-8+4}{6+4}=\frac{-4}{10}=\frac{-2}{5}[/tex]
As slope of both AB and CD is equal therefore, we can say that AB and CD are parallel.
As AB = CD and AB is parallel to Cd Therefore, ABCD is a parallelogram as opposite sides of parallelogram are equal and parallel.
Hence, quadrilateral ABCD is a parallelogram.
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(-3, -2) and (x, 6); m = 2
Answer:
1
Step-by-step explanation:
(y2-y1)/(x2-x1) is the formula for slope (aka m)
6-(-2)/1-(-3) = 8/4 = 2
On a number line if A is at 9 and B is at 20. Find the length of AB
Answer:
11units (Brainliest?)
Step-by-step explanation:
(20-9)²
(11)²
(cancel squares by square rooting both sides)
11
Enola opened a savings account with $8400 that earns 1.8% simple interest annually. After how many years will the balance of the account be $9600? Round to the nearest tenth, if necessary.
After 8 years the balance of the account would be $9600.
What is simple interest?
Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
Simple Interest =(P×r×t)/100
where:
P =Principal
r = interest rate
t = time
Given:
Principal, P = $8400
Rate of interest, r = 1.8%
Final amount, A = $9600
Simple interest, S.I = Final amount - Principal = 9600 - 8400 = $ 1200
Now, 1.8% of 8400 = (1.8/100) × 8400 = 151.2
⇒ Interest of 1 year = $151.2
Interest after x years = $1200
x = 1200/151.2 = 7.94 ≈ 8 years
Therefore, after 8 years the balance of the account would be $9600.
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. a survey of first-time home buyers found that the sample mean annual income was $51,000. assume that the survey used a sample of 28 first-time home buyers and that the sample standard deviation was $1,200. compute and explain a 95% confidence interval estimate of the population mean.
The 95% confidence interval estimate of the population mean is between $50,555.51 and $51.444.49.
Confidence interval is defined as the range of values where a parameter might fall at a given confidence level. It can be calculated using the formula below.
CI = μ ± z x (SD / √n)
where CI = confidence interval
μ = sample mean
z = found by using a z-score table
SD = sample standard deviation
n = sample size
At 95% confidence level, the area in each tail of the standard normal curve is 2.5, and the cumulative area up to the second tail is 97.5.
(100 - 95) / 2 = 2.5
100 - 2.5 = 97.5
Find 0.975 in the z-table to get the value of z.
At p = 0.95, z = 1.96
Plug in the values and solve for the confidence interval.
CI = μ ± z x (SD / √n)
CI = $51,000 ± 1.96 x ($1,200 / √28)
CI = $51,000 ± $444.49
CI = [$50,555.51, $51.444.49]
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A triangle has sides of length of 39 mm 56 mm and 37 mm is it a right triangle
By Pythagoras theorem, The given triangle with sides 37 mm, 39 mm, 56 mm is not a right triangle as the theorem is false in this case.
What is Pythagoras theorem?The Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relationship between a right triangle's three sides in Euclidean geometry. In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. The Pythagorean Theorem demonstrates how the side lengths of a right triangle can be calculated from the sum of the areas of three intersecting squares. This theorem is a very helpful tool that serves as the foundation for more intricate trigonometry theories like the Pythagorean theorem's opposite.
Here,
We can prove this by Pythagoras theorem,
b²+p²=h²
b=39 mm
p=37 mm
h=56 mm
=39²+37²
=2,890
56²=3,136
As 2890≠3136,
The triangle is not a right triangle. The triangle with sides of 37, 39, and 56 millimeters is not a right triangle according to Pythagoras' theorem because the theorem is incorrect in this case.
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On the grid below, draw the graph of y = 2 – 3x for values of x from – 3 to 3
The graph of the linear function f(x) = 2 - 3x is a straight line attached below
Graph of Linear FunctionA linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with f(x), this function can be written as f(x) = 3x - 2.
A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. Here,
m = slope of the lineb = y-intercept of the linex = is the independent variabley (or f(x)) = dependent variableThe function given y = 2 - 3x can be plotted on a graph using function table
When x = -3
f(-3) = 2 - 3(-3)
f(-3) = 11
when x = -2
f(-2) = 8
when x = - 1
f(-1) = 1
when x = 0
f(0) = 2
when x = 1
f(1) = -1
when x = 2
f(2) = -4
when x = 3
f(3) = - 7
We can use this data and plot a graph.
Kindly find the attached graph of the function below
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Select all of the equations below that have no solutions.
Select 2 correct answer(s)
3x + 5 = 3x + 8
3(x + 5) = 3x + 15
2(x + 1) = 2x + 1
2x + 1 = 2x + 1
Answer:
3x + 5 =3x + 8
Step-by-step explanation:
3x - 3x = 8-5
x = 3
Step-by-step explanation:
we have to soft the ones that have no solutions.
3x + 5 = 3x + 8
5 = 8
that is never true, and therefore there is no solution.
3(x + 5) = 3x + 15
3x + 15 = 3x + 15
that is always true, and it has therefore infinitely many solutions.
2(x + 1) = 2x + 1
2x + 2 = 2x + 1
2 = 1
this is never true, so, there is no solution.
2x + 1 = 2x + 1
this is always true, so this has infinitely many solutions.
What is the equation of the function that is graphed as line b?
y = -2 x - 1
y = 1/2x + 1
y = 3 x
y = 2 x - 1
Answer:
A
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 1) and (x₂, y₂ ) = (0, - 1) ← 2 points on the line
m = [tex]\frac{-1-1}{0-(-1)}[/tex] = [tex]\frac{-2}{0+1}[/tex] = [tex]\frac{-2}{1}[/tex] = - 2
the line crosses the y- axis at (0, - 1 ) ⇒ c = - 1
y = - 2x - 1 ← equation of line b
What is the intermediate step in the form (x+a)^2=b(x+a)
2
=b as a result of completing the square for the following equation?
x^2-28=12x
The intermediate step in the form (x + a)² =b as a result of completing the square for the given equation is (x - 6)² = 64
Given,
The equation x² - 28 = 12x
We need to find the intermediate step in the form (x + a)² =b as a result of completing the square for the given equation
Equation; x² - 28 = 12x
Arrange the equation;
x² - 12x = 28
Take the coefficient of x
k = -12
Divide it by 2
k/2 = -6
Square both sides
(k/2)² = 36
Add 36 to both sides of x² - 12x = 28
x² - 12x + 36 = 28 + 36
(x - 6)² = 64
Therefore,
The intermediate step in the form (x + a)² =b as a result of completing the square for the given equation is (x - 6)² = 64
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hi! could i get some help on this pls! ty
Left Blue Dot (5,9)
Right Blue Dot (7,0)
m = (y2 - y1)/(x2-x1)
= (9-0)/(5-7)
=9/-2
m = -9/2
Don't know the y-intercept so use the formula below to calculate equation of line
y-b = m(x-a)
y-9 = -9/2(x-5)
y-9 = -9x/2 + 45/2
y = = -9x/2 + 45/2 + 18/2
y = -9x/2 + 63/2
10. Find point W on the y-axis so that VW + XW is a minimum given V(2, 3) and
X(-2, -1).
The point on the y-axis is (0,1) such that the distance is minimum.
Let the coordinate of the point W be (0,a)
We know that the distance from any point on the coordinate place is calculated using the distance formula.
Now let us calculate the distance of VW = √[(2-0)²+(3-a)²]
Distance XW = √[(-2-0)²+(-1-a)²]
Now the sum of the distances is given by:
VW + XW
=√[(-2-0)²+(-1-a)²] + √[(2-0)²+(3-a)²]
This can be written in the form of a function in a such that:
f(a) = √a²+2a+5 + √a²-6a+25
Now we will differentiate with respect to a to get the required first degree
f'(a) = [tex]\frac{a+1}{\sqrt{a^2+3a+5}} + \frac{a-3}{\sqrt{a^2-6a+25}}[/tex]
Now at f'(a)=0
we get a=1.
Hence the required point on the y-axis that is at a minimum distance is (0,1) .
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What is the absolute value of +4?.
The absolute value of +4 will be 4 units as it is the distance from (0,0) to (4,0) in coordinate plane.
What is absolute value?Without taking into account direction, absolute value defines how far a number is from zero on the number line. A number's absolute value can never be negative. Look at some illustrations. 5 is the sum of its absolute values. There are 5 units between 5 and 0. A number's absolute value is determined by how far it is from zero on the number line. For instance, the absolute value of -7 would be 7, as it is 7 units away from zero. Additionally, since 0 is 7 units distant, the value of 7 would likewise be 7.
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The amount owed is $10865, based on the given parameters
How to determine the amount owed in six years?The given parameters about the compound interest are
Principal Amount, P = $5300
Interest Rate, R = 8%
Time, t = 6 years
To calculate the amount owed, we make use of the following formula
A = P + CI
Where
Compound interest, CI = P(1 + R)^t - P
So, the equation becomes
A = P + P(1 + R)^t - P
Evaluate the like terms
A = P(1 + R)^t
In this question, the formula is given as
A = P(1 + r/n)^nt
Where
n = 12, i.e compounded monthly
Substitute the known values in the above equation
A = 5300 * (1 + 8%/12)^(6*12)
Express 8% as decimal
A = 5300 * (1 + 0.08/12)^(6*12)
Evaluate the sum
A = 5300 * (1.01)^(6*12)
Evaluate the exponent
A = 5300 * 2.05
Evaluate the product
A = 10865
Hence, the value of the amount after 6 years is $10865
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Each day last week you sold 32, 45, 47, 63, and 72 product accessories. What was the median number of accessories you sold for the week?".
The answer is 47.
Step-by-step explanation:
To find the median, you need to write the numbers in order from least to greatest. However, that is already done.
Then, you need to count the numbers from the ends to the middle.
For example, if the numbers were 2, 4, 8, 9, and 10, you would do it like this (see the example below)
So, you would go from 32 to 45 and 72 to 63, and from 45 to 47 and 63 to 47.
This means that the median is 47.
I attached th eproblem.
Answer:
[tex]\frac{7}{b+4}[/tex]
Step-by-step explanation:
[tex]\frac{7}{b^2+5b+4}[/tex] × [tex]\frac{b^2+8b+7}{b+7}[/tex] ← factor quadratics on numerator/ denominator
= [tex]\frac{7}{(b+1)(b+4)}[/tex] × [tex]\frac{(b+1)(b+7)}{b+7}[/tex]
cancel factors (b+ 1) and (b + 7) on numerator/ denominator
= [tex]\frac{7}{b+4}[/tex] × 1
= [tex]\frac{7}{b+4}[/tex]
A study of the population of deer in a park finds that the population decreases by 1.2% each year. The deer population at the beginning of the study is 525. Write an equation to model the population of deer in the park after x years. After how many years will the population of deer in the park be less than 200?
The exponential decay of the function shows it will take approximately 81 years for the population to decrease to 200
Exponential FunctionAn exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x. This could also be an exponential growth or exponential decay which depends on the situation.
The exponential function is an important mathematical function which is of the form f(x) = ax
The details given in this question are;
Rate = 1.2% Initial population (P) = 525Final population = 200Number of years = x.The exponential function to represent this will be given as
200 = 525(1 + 0.012)⁻ˣ
x = number of years
This can be simplified as
200 = 525(1.012)⁻ˣ
x = 80.9 years
It will take approximately 81 years
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Which list of minerals is grouped based on color?
bornite, chalcopyrite, and hematite
chalcopyrite, pyrrhotite, and pyrite
hematite, bornite, and pyrite
pyrrhotite, goethite, and hematite
The list of minerals that is grouped based on color is B. chalcopyrite, pyrrhotite, and pyrite.
What minerals does chalcopyrite share a color with?Chalcopyrite is a mineral that has a high concentration of copper ore. As a result, it has a golden yellow color due to the copper in it. It also has crystals of a tetragonal form.
Pyrrhotite is a mineral with iron in it. It has the color of bronze yellow which means that it is similar in color to Chalcopyrite. We also have Pyrite which is brass yellow in color and looks golden. This puts it in the same color group as Chalcopyrite.
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In Quadrilateral ABCD , AB¯¯¯¯¯∥CD¯¯¯¯¯ and m∠2=31°. What is m∠5? Enter your answer in the box. ° Trapezoid A B C D with segment B D. Angle A D B is angle 1. Angle B D C is angle 2. Angle C is angle 3. Angle A is angle 4. Angle A B D is angle 5. Angle C B D is angle 6.
The measure of m∠5 is 31 degrees.
What are alternate angles?
Alternate angles are angles that occur on opposite sides of the transversal line and have the same size. Alternate angles are equal
Given that,
The AB is perpendicular to CD.
And, the m∠2=31°.
Based on the above information, the following information should be considered:
The alternate angles should be equal i.e. ∠2 = ∠5 and ∠1 and ∠6.
So, ∠5 = ∠2 = 31 degrees.
Therefore we can conclude that the measure of m∠5 is 31 degrees.
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A contractor needs to buy nails to build a house. The nails come in small boxes and large boxes. Each small box has 100 nails and each large box has 450 nails. The contractor bought 3 more small boxes than large boxes, which altogether had 2500 nails. Determine the number of small boxes purchased and the number of large boxes purchased.
The total number of small boxes is 1.72 and the large boxes is 5.1.
Given;
To build a house, a contractor has to purchase nails. Both small and large boxes of nails are provided. There are 100 nails in each small box and 450 in each large box. The contractor purchased 3 more tiny boxes—totaling 2500 nails—than large boxes.
To calculate the proportion of small and large boxes that were bought,
Let's assume the small boxes as 's' and the big boxes as '3s'.
∴ s(100) + 3s(450) = 2500
100s + 1350s = 2500
1450s = 2500
s = 2500/1450
s = 1.72
∴ 3s = 1.72 * 3
= 5.1
Hence, the total number of small boxes is 1.72 and the number of large boxes is 5.1.
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The number of small boxes purchased is 7 and the number of large boxes purchased is 4 by the contractor.
Let the number of large boxes purchased = x
then the number of small boxes purchased = x + 3
It is also given that,
small box contains = 100 nails
large box contains = 450 nails
According to the question:
450x + 100(x + 3) = 2500
450x + 100x + 300 = 2500
550x = 2500 - 300 = 2200
x = 2200/550
x = 4
and x + 3 = 4 + 3 = 7.
Thus, Let the number of small boxes purchased = 4 and the number of small boxes purchased = 7.
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Question 1(Multiple Choice Worth 1 points)
(03.01 MC)
Simplify √5(6-4√3)
09
30√3
06√5-4√15
O√30-20√3
Answer:
6√5 - 4√15
Step-by-step explanation:
√5(6 - 4√3) =
Distribute √5
= 6√5 - 4√3√5
= 6√5 - 4√15
2(-4x + 2) + 5x - 2 = -19
Solve for x.
Answer:
x = 7
Step-by-step explanation:
2 (-4x + 2) + 5x - 2 = -19 Distribute 2 to -4x and 2
-8x + 4 + 5x - 2 = -19 Combine like terms
-3x + 2 = -19 Subtract 2 from both sides
-3x = -21 To get x by itself, divide -3 on both sides
x = 7
Which values are part of the solution set based on the result of the inequality?
-4x + 24 < -2x + 2
Step-by-step explanation:
Which values are part of the solution set based on the result of the inequality?
-4x + 24 < -2x + 2
add 2x to both sides:
-4x + 24 + 2x < -2x + 2 + 2x
-2x + 24 < 2
subtract 24 from both sides:
-2x + 24 - 24 < 2 - 24
-2x < -22
divide both sides by -2: [remember to flip the sign direction because you are dividing by a negative number]
-2x/-2 > -22/-2
x > 11
or (11 , ∞)
you take a random sample of 605 iphones off an assembly line and find that 0.07 proportion to be defective. what is a lower bound for a 95% confidence interval for the proportion
The lower bound for a 95% confidence interval for the proportion of defective iphones from this assembly line is 0.0524.
With the probability of a success of π , and a confidence level of 1-α, we have the following confidence interval of proportions:
π± z[tex]\sqrt{\frac{\pi (1-\pi }{n} }[/tex]
z is the z-score having a p-value of 1-α/2.
we have η = 605 and ρ = 0.07
So, α = 0.1 and z is the value of Z that has a pvalue of:
1 - 0.1/2 = 0.95
Z= 1.645
Now the lower limit:
π - z[tex]\sqrt{\frac{\pi (1-\pi }{n} }[/tex]
= 0.07-1.645[tex]\sqrt\frac{(0.07*0.93)}{605}[/tex]
= 0.07 - 0.01706
= 0.0524
The lower bound for a 95% confidence interval for the proportion of defective Galaxy phones from this assembly line is 0.0524
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Write an equation in slope-intercept form of the line that passes through (6,
-1) and (3,
-7).
Answer: y = 2x - 13
Step-by-step explanation:
y=mx + b
[tex]m= \frac{-7-(-1)}{3-6}[/tex]
[tex]= \frac{-6}{-3}[/tex]
[tex]m = 2[/tex]
y = 2x + b
(6, -1) <-- use to find "b" by substituting either one of the coordinates
-1 = 2(6) + b
-1 = 12 + b
-13 = b
y = 2x - 13
solve 2^(x+3)=(1/8)^(x+2) for x
Answer:
-9/4 Negative As a Fraction
How I got the answer:
2 (x+3) = (1/8) (x+2)
x+ 3 = -3 (x+ 2)
x = -9/4
I helped you so mark me BRAINLIEST
Cd is the perpendicular bisector of ab. Ad ≅ bd by definition of a bisector. ∠ cda and ∠ cdb are both right angles based on the definition of perpendicular lines. Cd ≅ cd by the reflexive property of congruence. Δ adc ≅ δ bdc by the _____. So ca ≅ cb because corresponding parts of congruent triangles are congruent.
Answer:
YesTheorem 8.3: If two angles are complementary to the same angle, then these two angles are congruent.
A and B are complementary, and C and B are complementary.
in the parallelogram pqrs shown below, ps is 7 centimeters long. if the parallelogram's perimeter is - 40 centimeters, how many centimeters long is pq?
13 cm long is PQ in parallelogram .
What does parallelogram mean in a nutshell?
A parallelogram is a geometric shape with parallel sides that exists in two dimensions. The pair of parallel sides in this sort of polygon with four sides, also known as a quadrilateral, are of equal length. In a parallelogram, the sum of the adjacent angles is 180 degrees.Perimeter of ∥gm = - 40 cm
2(PQ+ PS) = - 40
2 ( PQ + 7 ) = 40
PQ + 7 = 20
PQ = 20 - 7
PQ = 13 cm
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Find the -intercept and -intercept of the line.
3x + 5y = -6
Answer:
The intercept would be -6/5
Step-by-step explanation:
Answer:
y=-3 x=-3
Step-by-step explanation:
4/5(-7x-1/2)=-2x-(4x-1)
Answer:
x = 7/2
Step-by-step explanation:
-28/5 x -2/5 = -2x -4x + 1
-28/5 x -2/5 = -6x + 1
-28 x -2 = -30x + 5
30 x -28 x = 5 + 2
2x = 7
2/2 x = 7/2
x = 7/2
Answer:
(7/2)
Step-by-step explanation:
I'll rewrite "4/5(-7x-1/2)=-2x-(4x-1)" to (4/5)(-7x-1/2)=-2x-(4x-1) to clarify the fraction (I am not interpreting it as 4/(5(-7x-12))). [The five is not part of the denominator in my rewrite]
(4/5)(-7x-1/2)=-2x-(4x-1)
(-28x-2)= 5*((-6x+1)) [multiply the numerator by 4 on the left side, and multiply both sides by 5]
-28x-2= -30x + 5 [Combine like terms]
2x = 7 [Put like terms together by adding 30x and +2 to both sides]
x = (7/2) This satidfies the equation.
John wants to buy a new TV. The price is , and the sales tax is 5 percent.
Store A is offering a 10 percent discount and Store B is offering a rebate.
What would John's total cost be at each store? Make sure to record your answers to the nearest cent.
Total cost at Store A = $
Total cost at Store B = $
Price of Tv at Store A = $ 94.5
Price of Tv at Store B = $ 95
How to calculate the price?Given that
Price of tv player = $ 100
Sales Tax = 5%
The price of tv at store A after 10% discount = 100 - 10% of 100
The price of tv at store A after 10% discount:
= 100 - 0.1x100
= 100 - 10 = $90
Price of tv at store A after sales tax = 90 + 5% of 90
= 90 + 0.05x90
= 90 + 4.5
= $94.5
Now, lets calculate price of of tv at store B.
The price of tv at store B= 100
Price of tv at store B after sales tax:
= 100 + 5% of 100
Price of tv at store B after sales tax = 100 + 0.05x100
= 100 + 5
= $105
Price of tv at store B $10 rebate
= 105 - 10
= $95
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Complete questions
John wants to buy a tv. The price is $100, and the sales tax is 5 percent. Store A is offering a 10 percent discount and Store B is offering a $10 rebate. What would John's total cost be at the two stores? Total cost at Store A = Total cost at Store B =
