Answer:
3^-2
Step-by-step explanation
Subtract the exponent on the denominator from the exponent on the numerator
5-7=-2
keep the 3 and apply the -2 exponent
You decide to save money to purchase an automobile. You save $1,500 and the total cost of the
new automobile is $27,890. The dealership offers to loan you the remaining amount, in order to
purchase the automobile, at 5.25% annual interest for 66 months.
3. What is the principal of the loan?
Show your work here:
4. What is the total amount of interest that you will have paid on the loan when the
automobile is paid off?
Show your work here:
The principal for the loan is $27,890.
The total amount of interest to be paid on the loan, at a rate of 5.25% after 66 months is $8053.24
How to find the principalThe principal is the amount of money to be paid for the automobile which is $27,890.
How to find the interest
from simple interest formula = ( principal * time * rate ) / 100
given data
principal = $27,890
time = 66 months
rate = 5.25%
converting the time to years gives
time = 66 / 12
time = 5.5 years
simple interest = ( 27 890 * 5.5 * 5.25 ) / 100
simple interest = 805 323.75 / 100
simple interest = $8053.24
We can therefore say that the amount of interest paid on the loan at a rate of 5.25% after 66 months is $8053.24
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HII HELP PLEASE! I DONT UNDERSTAND
Answer:
C
Step-by-step explanation:
3x^2-30x=72
3(x^2-10x)=72
x^2-10x=24
Then do the subtitules
Answer:C
Give me brainlliest
Answer: C x = -2
Step-by-step explanation:
[tex]3x^{2} - 30x - 72 = 0[/tex]
[Add 72 on both sides]
[tex]3x^{2} - 30x = 72[/tex]
[Factorise Left Hand Side of equation to get 3 on one side of a bracket]
[tex]3(x^{2} -10x) = 72[/tex]
[Divide each side by 3 to just get the brackets and the x's on one side]
[tex]x^{2} -10x = 24[/tex]
[Minus 24 on both side as the equation must = 0]
[tex]x^{2} -10x-24=0[/tex]
[Solve the square on the left hand side]
[tex](x-12)(x+2)=0[/tex]
[Solve for x on left hand side - two possible answers]
[tex]x-12=0 \\ x=12[/tex]
[tex]x+2=0\\x=-2[/tex]
[The answer '12' is not in the option for the question so '-2' is the answer]
PLEASE HELP!! i’ll give brainliest
AE = EB and CF = FB
ca = 18
de = 7
cb = 14
fe = [?]
Answer:
by comparing the two triangles,
we take the ratio of each side to be equal
Step-by-step explanation:
By comparing the sides of the triangles,
we take the ratio of each sides to each other
de/cb = fe/ca
de.ca = fe.cb
fe = (de.ca)/cb
fe = (7* 18)/14
fe = 9
The measure of side FE of triangle DEF is FE = 9
What are similar triangles?If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the first triangle be represented as ABC
Now , let the second triangle be DEF
And triangle ABC and DEF are similar triangles
So , corresponding sides of similar triangles are in the same ratio
And , AE = EB and CF = FB
From the similar triangle theorem ,
EF / AC = DE / CB
Substituting the values in the equation , we get
EF / 18 = 7 / 14
Multiplying by 18 on both sides of the equation , we get
EF = ( 7 x 18 ) / 14
EF = 18/2
EF = 9
Therefore , the value of EF is 9
Hence , the measure of side EF is 9
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please tell me the additive invers of -25, 18, and -4.5!! Thanks!
Answer:
-1/25, 1/18, -2/9
Step-by-step explanation:
The additive inverse of a number is also called the reciprocal. The reciprocal is the number that is multiplied to get 1.
Simplify the following equation shown in the picture below :
Answer:
D
Step-by-step explanation:
2x - 14x = 12x
3x²
6y + 7y = 13y
3²-12x-13y
9. The volume of a box in cubic feet can be expressed as V(x) = x³ - 3x² - 10x or as the product of three linear factors with integer coefficients. The width of the box is 5-x. What is the length, width, and height of the box in factored form? A. -x(5-x)(x+2) B. X(5-x)(x+2) C. X(5-x)(x-2) D. -x(5-x)(x-2)
The length, width, and height of the box in factored form is -x (x-5)(x +2) which is option A
The box is in the shape of a cuboid
The volume of a cuboid = l b h, where l is the length, b is the breath or width and h is the height
Putting the values of width and volume in the formula
x³ - 3x²-10x = l ×(5-x) × h
This becomes a cubic equation
l × h = (x³-3x²-10x)/ 5-x
l × h = -x²-2x
l × h = -x(x+2)
Now, putting the value of l × h in the equation we get
v= -x ( x+ 2) (5-x)
v = -x (x-5)(x +2)
Hence, the length, width, and height of the box in factored form is -x (x-5)(x +2) which is option A
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Suppose M is the midpoint of FG. Find the missing measure FM = 3x - 4, MG = 5x - 26
Answer:
FG=58 X=11
Step-by-step explanation:
I'm assuming your looking for the whole segment. What I did was 3x-4=5x-26. We first have to find X. So just use the equation to find X. You should get X=11 if you did it the way I set it up. Then you plug it in with the measures you got. So FM = 3(11)-4 and 5(11)-26. You should get 29 for both. If your looking for FG, you would add those two together. So 29+29= 58. FG=58. there you go.
Numbers from greatest to least
yall help me pwease im so bad at math
Answers are in bold
4x-62x/5x - 74/e6(9+x)x(13-6)10x+12(20/x) + 7(x - 16)/2==========================================================
Explanations:
"Four times a number" gives us "4x". We then subtract off 6.The expression 2x represents "2 times a number", aka "the product of 2 and a number". We then divide that expression over 5 to get the quotient.Take any number x, and subtract off 7. For instance, if x = 10, then x-7 = 10-7 = 3, which shows that 3 is 7 less than 10.The term "quotient" means "result of division". So we divide 4 over 'e'The expression 9+x is the sum of 9 and some unknown number. The 6 out front means we multiply 6 with (9+x).The term "difference" means we'll be subtracting the terms."ten times a number" translates to 10x, in which we increase that by 12 to get 10x+12The portion 20/x is the quotient of 20 over x. This is similar to problem 4. Then we increase the (20/x) by 7 to get (20/x) + 7The x-16 part is the difference of x and 16. That result is then divided in half.Two tankers contain 850 litres and 680 litres of kerosene oil respectively. find the maximum capacity of a container which can measure the kerosene oil of both the tankers when used an exact number of times
The maximum capacity of a container which can measure the kerosene oil of both the tankers when used an exact number of times is 170 Litres.
Amount of kerosene in first tanker = 850 litres
Amount of kerosene in Second tanker = 680 litres
The maximum capacity of a container which can measure the kerosene oil of both the tankers when used an exact number of times will be the HCF of amount of kerosene in first tanker and amount of kerosene in second tanker i.e., HCF of 850 litres and 680 litres.
To calculate HCF of 850 and 680 , we can write
850 = 2 × 5 × 5 × 17
680 = 2 × 2 × 2 × 5 × 17
HCF of 850 and 680 = 2 × 5 × 17 = 170
The maximum capacity of a container which can measure the kerosene oil of both the tankers when used an exact number of times is 170 Litres.
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write 101 in binary form
Answer:
1100101
Step-by-step explanation:
(4^6) (4^−8)?????????????
Answer:
1/16
in decimal form it is:
0.0625
Step-by-step explanation:
PLS HELP!!!
John simplified the expression
-3 X (3 + 12 ÷ 3) - 4.
Word Pro
For his first step, he added 3 + 12 to get 15. What
was John's error? Find the correct answer.
Answer:
Correct answer : -21x - 4
John's error : He added the number inside the parenthesis, instead he should've divided first then added the number.
I hope you get it
5w + 10x . quick answer!
Answer:
you can not do that. They are not like terms. Even though they are raised to the same power, they don't have the same variable
Step-by-step explanation:
Members of a baseball team raised $1128.75 to go to a tournament. They rented a bus
for $856.50 and budgeted $24.75 per player for meals. Write and solve an equation
which can be used to determine x, the number of players the team can bring to the
tournament.
solve the following absolute equation 2|3x-4|+8=6
Answer:
"No solution" is the answer
Step-by-step explanation:
A triangle has two sides of lengths 10 and 14. What value could the length of
the third side be? Check all that apply.
A triangle having two sides of lengths 10 and 14 will have the third side length less than 24.
As per the question statement, We are given a triangle that has two sides of lengths 10 and 14 and we are asked about the length of the third side.
Before solving the question, we should be well aware of the the theorem of triangle side sum property.
"According to the "sum of sides of a triangle rule," any two triangle sides' sums must be bigger than the length of the third side."
The sum of length of two sides are = [tex]10+14=24[/tex]
Hence the length of third side has to be less than 24 as per the theorem.
Triangle side sum property: "According to the "sum of sides of a triangle rule," any two triangle sides' sums must be bigger than the length of the third side."To learn more about triangles and its properties, click on the link given below:
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Give an example of each type of number.
18. a real number between √13 and 14
19. an irrational number between 5 and 7 pleaseee!!!!!!
Examples of each type of number are shown:
A real number between √13 and √14: 3.61An irrational number between 5 and 7: 5.1234567What are real numbers and irrational numbers?Real numbers are made up of both rational and irrational numbers. Real numbers include integers (-2, 0, 1), fractions (1/2, 2.5), and irrational numbers such as 3, (22/7), and so on.Irrational numbers are all real numbers that are not rational numbers in mathematics. Irrational numbers, in other words, cannot be expressed as the ratio of two integers.(A) A real number between √13 and √14:
We can say that many real numbers lie between √13 and √14.3.61, 3.62, 3.63, 3.64, 3.65, 3.66, 3.67, 3.68, 3.69, 3.70, 3.71, 3.72, and 3.73.(B) An irrational number between 5 and 7:
Consider the following irrational numbers between 5 and 7: 5.1234567, 5.5768576, 6.12134567, and so on.Between 5 and 7, there are an infinite number of irrational numbers.Therefore, examples are:
A real number between √13 and √14: 3.61An irrational number between 5 and 7: 5.1234567Know more about real numbers here:
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A sampling interval of 5 (selecting every fifth unit) was used to select a sample from a population of 1000. how many elements are to be in the sample?
200 elements are required to be in the sample.
What is a sampling interval of a population?The sampling interval is the frequency with which data is collected. The sampling interval is computed by the division of the total population size by the required sample size.
So, from the information given:
The total population N = 1000The sampling interval (i) = 5The elements that are required to be in the sample i.e. the sample size (n) can be computed by using the formula:
[tex]\mathbf{i = \dfrac{N}{n}}[/tex]
[tex]\mathbf{ n= \dfrac{N}{i}}[/tex]
[tex]\mathbf{ n= \dfrac{1000}{5}}[/tex]
n = 200 elements.
Therefore, we can conclude that 200 elements are required to be in the sample.
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The points (–5, 4) and (9, –2) are on a line. Find the intercepts to the nearest tenth.
Answer:
The y-intercept = (0, 13/7).
The x-intercept = (13/3, 0).
To the nearest tenth they are
y-intercept (0, 1.9)
x-intercept (4.3, 0)
Step-by-step explanation:
First find the equation oif the line joining these points:
Slope of line = (4 - (-2)) / (-5-9))
= 6/-14
= -3/7
y - y1 = m(x - x1)
Using m = -3.7 and (x1, y1) = (-5, 4)
y - 4 = -3/7(x - (-5)
y = -3/7x -15/7 + 4
y = -3/7x + 13/7 is the equation of the line.
The y-intercept (when x = 0)
= 0 + 13/7
= (0, 13/7)
The x-intercept:
0 = -3/7x + 13/7
x = -13/7 / -3/7
= 13/3.
x intercept is (13/3, 0)
N is an even number
(B) what type of number is n+ 1?
Answer:
Odd
Step-by-step explanation:
If n is even, we can assign it any even number, like 2. after every even comes an odd, so 2+1=3. Just like 4+1=5, the next number after any even is odd.
Of the 200200 parking spaces in a parking lot, 6\%6% of the spaces are reserved for handicapped parking. Of those parking spaces NOT reserved for handicapped parking, 2020 are suitable for compact cars only. How many spaces that are NOT reserved for handicapped parking are suitable for non-compact cars?
Using proportions, it is found that 38 spaces are suitable for non-compact cars.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
For this problem, we have that:
94% of the spaces are not reserved for handicapped parking, hence this number is of 0.94 x 200 = 188.Of those, 20% are suitable for compact cars, hence 0.2 x 188 = 38.38 spaces are suitable for non-compact cars.
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Last week, Jaime spent 34, 30,45,30,40,38,
and 28 minutes practicing for football. Find
the ________________
.Round to the
nearest whole number,
Answer:
35 average minutes at practice.
Step-by-step explanation:
Answer:
What do I find?
If it's the mean then the answer is 35.
Step-by-step explanation:
34, 30, 45, 30, 40, 38, 28 ==> 7 numbers
34+30+45+30+40+38+28=245
245/7=35
What is the probability of not drawing a queen from a standard deck of 52 cards?
The probability of not drawing a queen from a standard deck of 52 cards is 12/13
How to determine the probability of not drawing a queen from a standard deck of 52 cards?In a standard deck of 52 cards, we have
Total number of cards = 52
Queen cards = 4
The probability of not drawing a queen from a standard deck of 52 cards is calculated as
P = 1 - P(Queen)
Where
P(Queen) = Queen cards/Total number of cards
So, we have
P(Queen) = 4/52
Substitute P(Queen) = 4/52 in the equation P = 1 - P(Queen)
This gives
P = 1 - 4/52
Evaluate the difference
P = 48/52
Simplify
P = 12/13
Hence, the probability of not drawing a queen from a standard deck of 52 cards is 12/13
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Answer:
12/13
Step-by-step explanation:
Got it right on the test.
Find the measures of the angles of following triangle. The ratio of the measures of the three angles is 5: 4: 7 .
Answer:
56.25º, 45º and 78.75º respectively
Step-by-step explanation:
Diane cycled a total distance of 71,808 feet on a bicycle path surrounding a lake she cycled eight laps where each lap was the same length what was the length of each lap around the lake
The length of each lap around the lake is 8976 feet.
We are informed that Diane cycled 8 laps around the lake. Also, Diane covered total distance of 71,808 feet. So, length of 8 laps = total distance covered by Diane. Hence, the length of each lap will be calculated by performing division.
Length of 1 lap = total distance covered by Diane ÷ length of 8 laps
Keep the values in formula to find the length of each lap.
Length of each lap = 71,808 ÷ 8
Performing division to find the length of each lap
Length of each lap = 8976 feet
Thus, the length of each lap around the lake is 8976 feet.
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Which of the following statements are true about a reflection? Select all that apply. © An image created by a reflection will always be congruent to its pre-image. • Corresponding angles and segments are always congruent in a reflection of a figure. • Reflections can only be constructed across horizontal or vertical lines. D Reflections may change the size of a pre-image. • An image and its pre-image are always the same distance from the line of reflection.
True statements about reflection are:
(A) A reflection's image will always be congruent to its pre-image.(B) In a figure reflection, corresponding angles and segments are always congruent.(E) The distance between an image and its pre-image from the line of reflection is constant.What do we mean by reflection?The change in direction of a wavefront at an interface between two different media that causes the wavefront to return to the medium from which it originated is referred to as reflection. Light, sound, and water wave reflections are common examples. A reflection's image will always be congruent to its pre-image.In a figure reflection, corresponding angles and segments are always congruent.The distance between an image and its pre-image from the line of reflection is constant.The description of reflection is similar to three options given in the question which are option (A), (B) and (E).
Therefore, true statements about reflection are:
(A) A reflection's image will always be congruent to its pre-image.(B) In a figure reflection, corresponding angles and segments are always congruent.(E) The distance between an image and its pre-image from the line of reflection is constant.Know more about reflections here:
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The correct question is given below:
Which of the following statements are true about a reflection?
Select all that apply.
A. An image created by a reflection will always be congruent to its pre-image.B. Corresponding angles and segments are always congruent in a reflection of a figure.C. Reflections can only be constructed across horizontal or vertical lines.D. Reflections may change the size of a pre-image.E. An image and its pre-image are always the same distance from the line of reflection.Answer:
A. An image created by a reflection will always be congruent to its pre-image.
B. Corresponding angles and segments are always congruent in a reflection of a figure.
E. An image and its pre-image are always the same distance from the line of reflection.
Are correct !!
The formula C = P(1-d) is used to find the cost of an item that is discounted.
C represents the cost of an item after a discount. P represents the original price of an item, and d is the amount of the discount
written as a percent in decimal form.
Solve for d.
A d-1-
B d-1-2
C d=1+%
D d=-1
The value of the discount d is given by [tex]\\\\d=1-\frac{C}{P}[/tex] .
A reduction in price that is often offered for early or quick payment or to a select group of customers is called discount.
The amount that results from subtracting the cost of production from the purchasing price is called the profit.The cost is the total amount needed to create a good or provide a service.Selling price is the cost at which something actually sells.Profit = sell price-cost priceDiscount = Marked price - sell priceGiven expression for the Profit , cost price and discount as
[tex]or, C = P(1-d)[/tex]
Here d is the discount , P is the profit and C is the cost price.
Now solving the equation for d we get:
[tex]or, C = P(1-d)\\\\or,\frac{C}{P} =1-d\\\\or, d+\frac{C}{P}=1\\\\or, d=1-\frac{C}{P}[/tex]
Hence the expression for calculating the discount d is given by
[tex]\\\\d=1-\frac{C}{P}\\[/tex] .
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Answer:
A
Step-by-step explanation:
what would the sum of x and 16 is less than 32 look like in a problem?