To isolate the variable on one side of the equal sign, divide both sides of the equation by the coefficient of the variable.
use prime factors to explain why 15 x 375 is a perfect square
Answer:
A perfect square can always be expressed as a product of pairs of equal factors
if we resolve 15x 375(which equals 5625)
225x25 = 9x25x25 = 3x3x5x5x5x5 = 3x5x5x3x5x5 or 3 to the power of 2 x 5 to the power of 4 which can also equal to 75 squared
which means that 75 is the number whose square is 5265
equilateral triangle with 48 inches on each side with the height of 38 inches..how much space does it cover?
Answer:An equilateral triangle with sides of length 48 inches can be divided into two right triangles by drawing a line from one vertex to the midpoint of the opposite side. The height of the equilateral triangle, or the length of the line segment from the vertex to the midpoint of the opposite side, is equal to the height of each of these right triangles.
Using the Pythagorean theorem, the length of the altitude of each right triangle can be found:
sqrt(48^2 - 24^2) = sqrt(2304) = 48 inches.
The area of each right triangle is 1/2 base * height, or 1/2 * 24 * 48 = 576 square inches.
Since the equilateral triangle is made up of two of these right triangles, the total area of the equilateral triangle is 2 * 576 = 1152 square inches.
Step-by-step explanation:
An equilateral triangle with sides of length 48 inches can be divided into two right triangles by drawing a line from one vertex to the midpoint of the opposite side. The height of the equilateral triangle, or the length of the line segment from the vertex to the midpoint of the opposite side, is equal to the height of each of these right triangles.
Using the Pythagorean theorem, the length of the altitude of each right triangle can be found:
sqrt(48^2 - 24^2) = sqrt(2304) = 48 inches.
The area of each right triangle is 1/2 base * height, or 1/2 * 24 * 48 = 576 square inches.
Since the equilateral triangle is made up of two of these right triangles, the total area of the equilateral triangle is 2 * 576 = 1152 square inches.
Nice Drink Company produces many types of soft drinks, including Cola. The amount of soda in each can of Cola has a normal distribution with a mean of 12 ounce and a standard deviation of 0.50 ounce. What is the probability that a randomly selected can of Cola contains
(a) less than 10.50 ounce of cola?
The probability that a randomly selected can of cola contains less than 10.50 ounce of cola is 0.14%
What is an equation?An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.
The z score is given by:
z = (raw score - mean) / standard deviation
Given that mean = 12 ounce, standard deviation = 0.5 ounce
For x < 10.50:
z = (10.5 - 12) / 0.5 = -3
From the normal distribution table:
P(z < -3) = 0.0014 = 0.14%
0.14% of the can of cola contains less than 10.50 ounce of cola
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An artist plans to use a tile that is shaped as a parallelogram as one of the tiles in a design. To determine the other tiles that can be used in the design the artist uses a computer program where she inputs measurements that will match different tiles to the design. The artist labels the parallelogram as MBKR.
Some of the measurements of parallelogram MBKR are shown.
RM = 3x + 11.2
MB = 7x - 3.8
KR=5x+7
Determine the perimeter of the tile.
The perimeter of parallelogram MBKR is 18x + 26.6.
How to solve the problem?The perimeter of the parallelogram is equal to the sum of the lengths of its sides. Given RM = 3x + 11.2, MB = 7x - 3.8 and KR = 5x + 7, we can find the perimeter by adding the lengths of RM, MB, KR and KB (the length of the fourth side). To find KB, we can use the property of a parallelogram that opposite sides are equal in length.
RM + MB + KR + KB = (3x + 11.2) + (7x - 3.8) + (5x + 7) + KB
= 15x + 15.4 + KB
= 15x + 15.4 + RM
= 15x + 15.4 + (3x + 11.2)
= 18x + 26.6
So, the perimeter of parallelogram MBKR is 18x + 26.6.
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15% increase in grade, which integers represents it?
15% increase in grade is a positive integer.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Positive Is about the number higher than 0 or basically "increase"
While, Negative is about lower than 0 or "decrease"
1. Is below than 0°C (negative)
2. Increase in grade (positive)
3. above sea level (positive)
4. increase of 100 pesos (positive)
5. decrease of 15 pesos (negative)
Hence, 15% increase in grade is a positive integer.
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The number 0.000 000 000 034 2 is equivalent to which of the following
expressions?
A. 3.42 x 10^-18
B. 3.42 x 10^-11
C. 3.42 x 10^-10
D. 3.42 x 10^11
E. 3.42 x 10^13
Answer: 3.42x10^11
Step-by-step explanation:
The number 0.0000000000342 is equivalent to 3.42 × 10^-11. Hence, option B is the correct answer.
This type of conversion is called scientific notation.
Firstly we have to place a decimal between the two non-zero numbers which is 3.42.
And then, count the number of decimals that were moved. That is 11.
And then, determine whether the decimal point is to be moved to the left or right to return to the original number. If the decimal is moved right then the exponent is negative. If the decimal is moved left then the exponent is positive.
Here, the exponent is moved right and the decimal will be negative.
In this case, it is written as 3.42 × 10^-11.
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Find the value(s) of c such that the area of the region bounded by the parabolae y = x^2-c^2 and y = c^2 - x^2 is 4608
Answer (separate by commas): c= ??
Answer:
Either [tex]c = 12[/tex] or [tex]c = (-12)[/tex].
Step-by-step explanation:
Find the [tex]x[/tex]-coordinate of the intersection of the two curves by equating their [tex]y[/tex]-values and solving for [tex]x[/tex]:
[tex]x^{2} - c^{2} = c^{2} - x^{2}[/tex].
[tex]x^{2} = c^{2}[/tex].
[tex]x = c[/tex] or [tex]x = (-c)[/tex].
In other words, the two curves intersect both when [tex]x = c[/tex] and when [tex]x = (-c)[/tex].
Assume that [tex]c \ge 0[/tex]. The area enclosed would be over the range [tex](-c) < x < c[/tex]. Note that over this range, [tex]x^{2} \le c^{2}[/tex], so [tex]x^{2} - c^{2} \le 0 \le c^{2} - x^{2}[/tex]. The curve [tex]y = c^{2} - x^{2}[/tex] would be above [tex]y = x^{2} - c^{2}[/tex].
Integrate the upper curve minus the lower curve [tex](c^{2} - x^{2}) - (x^{2} - c^{2})[/tex] over this interval to find the area enclosed:
[tex]\begin{aligned}& \int\limits_{-c}^{c} \left((c^{2} - x^{2}) - (x^{2} - c^{2})\right)\, dx \\ =\; & \int\limits_{-c}^{c} \left(2\, c^{2} - 2\, x^{2}\right)\, dx \\ =\; & {\left[2\, c^{2}\, x - \frac{2}{3}\, x^{3}\right]}_{-c}^{c} && (\text{power rule}) \\ =\; & \left(2\, c^{2}\, c -\frac{2}{3}\, c^{3}\right) - \left(2\, c^{2}\, (-c) - \frac{2}{3}\, (-c)^{3}\right) \\ =\; & \frac{8}{3}\, c^{3} \end{aligned}[/tex].
In other words, assuming that [tex]c \ge 0[/tex], area enclosed between these two curves would be [tex](8/3)\, c^{3}[/tex]. Since this area is given, the value of [tex]c[/tex] can be found as:
[tex]\begin{aligned}c &= \sqrt[3]{\frac{3}{8}\, (\text{Area})} = 12\end{aligned}[/tex].
However, note that if [tex]c < 0[/tex], the order of limits of the integral would need to be reversed:
[tex]\begin{aligned}& \int\limits_{c}^{-c} \left((c^{2} - x^{2}) - (x^{2} - c^{2})\right)\, dx \\ =\; & \cdots \\ =\; & {\left[2\, c^{2}\, x - \frac{2}{3}\, x^{3}\right]}_{c}^{-c} \\ =\; & \left(2\, c^{2}\, (-c) - \frac{2}{3}\, (-c)^{3}\right) - \left(2\, c^{2}\, c -\frac{2}{3}\, c^{3}\right) \\ =\; & \left(-\frac{8}{3}\, c^{3}\right) \end{aligned}[/tex].
Hence, [tex]c = (-12)[/tex] would also be a solution to this question.
una parte de $4000.00 fue invertida a un 3% de interés anual y el resto a un 4%, al finalizar el año tuvo un rendimiento de $155.00 ¿Qué cantidad de dinero fue invertida al 3% y que cantidad al 4%? R=
The amounts of each investment are given as follows:
3% interest: $3875.4% interest: $125.How to obtain the balance using simple interest?The balance of an account after t years, using simple interest, that is, a single compounding per year, is given by the equation presented as follows:
A(t) = P(1 + rt).
In which the parameters of the equation are explained as follows:
P is the value of the initial deposit.r is the interest rate, as a decimal.The interest accrued is given as follows:
I(t) = Prt.
An amount of x was invested at 3% during one year with a return of R, hence:
R = 0.03x.
An amount of 4000 - x was invested at 4% during one year with a return of 155 - R, hence:
155 - R = 0.04x.
From the first equation, we have that:
x = R/0.03.
x = 33.3R.
Replacing into the second equation, the value of R is obtained as follows:
155 - R = 0.04(33.3R)
1.332R = 155
R = 155/1.332
R = $116.37.
Hence the value of x, representing the amount invested at 3%, is given as follows:
x = 33.3 x 116.37
x = $3875.
The value invested at 4% is given as follows:
4000 - 3875 = $125.
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How many solutions does 3(4x - 8) = -24 + 12x have?
Group of answer choices
a. infinitely many solutions
b. no solution
c. one solution
d. two solutions
Answer:
a) Infinitely many solutions
Step-by-step explanation:
3(4x-8) = -24+12x
12x - 24 = -24 + 12x
0 = 0
infinitely many solutions
:] hope this helps
ABCD is a quadrilateral.
Work out the length of CD.
Give your answer correct to
3 significant figures.
Optional working
Answ
cm
+
35%
D
12 cm
B
102°
(52°
The length of DC is 26.1 cm.
What is Trigonometry?The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).
Given:
BDC is a triangle and angles in a triangle sum up to 180° .
180 - 102° + 52° = ∠BDC
180 - 154 = 26°
∠BDC = 26°
and, <ABD can be found same way since sum of interior angles in a triangle is 180°.
∠ABD = 180 - 90 - 35
∠ABD = 55°
Using Trigonometry
sin 35° = opposite/hypotenuse
sin 35° = 12/BD
BD sin 35° = 12
BD = 12/sin 35°
BD = 12/0.57357643635
BD = 20.9213615475
BD ≈ 21 cm
Using sine formula
21/sin 52° = DC/sin 102°
DC sin 52° = 21 sin 102°
DC = 21 sin 102°/sin 52°
DC = 0.97814760073 × 21/0.7880107536
DC = 20.5410996154 /0.7880107536
DC = 26.0670295696
DC ≈ 26.1 cm(3 significant figures)
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Below is the graph of f ( x ) f(x)f, left parenthesis, x, right parenthesis. The function has a maximum point at (-4,2) and a minimum point at (-1,-3) find a formula for f(x)
f(x)=-5/3x-14/3 is the formula for the function.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The function has a maximum point at (-4,2) and a minimum point at (-1,-3)
We have to find the formula for f(x).
Let the slope m=-3-2/-1+4
m=-5/3
Now let us find the y intercept
2=-5/3(-4)+b
2=20/3+b
2-20/3=b
-14/3=b
f(x)=-5/3x-14/3 is the formula for the function.
Hence, f(x)=-5/3x-14/3 is the formula for the function.
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Which of the following tables represents a linear relationship that is also proportional? x −1 0 1 y −4 −2 0 x −1 0 1 y −2 0 2 x −1 0 1 y 0 1 2 x −1 0 1 y 1 3 5
The x = -1, 0, 1 and y = 1, 3, 5 represents a linear relationship that is also proportional.
What is linear relationship?
Linear relationship is a statistical term used to describe a straight-line relationship between two variables.
A relationship is proportional if there is a constant of proportionality (k) such that for any x and y in the relationship, y = kx.
The table x = -1, 0, 1 and y = 1, 3, 5 represents a linear relationship that is proportional because we can see that for every increase in x by 1 unit, y increases by 2 units (the constant of proportionality).
This is a linear relationship because the values of x and y change in a consistent straight-line pattern.
Therefore, x = -1, 0, 1 and y = 1, 3, 5 represents a linear relationship that is also proportional.
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Answer:
A is the answer
Step-by-step explanation:
A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is red.
Spinner divided evenly into eight sections with three colored blue, one red, two purple, and two yellow.
Determine the theoretical probability of the spinner not landing on blue, P(not blue).
0.375
0.625
0.750
0.875
The theoretical probability of the spinner not landing on blue is 5/8
How to determine the theoretical probability of the spinner not landing on blue?Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
The probability of an event A is defined as the number of favorable outcomes divided by the number of total outcomes.
Since sections 1 and 8 are purple. Probability of purple = 2/8 = 1/4
Sections 2 and 3 are yellow. Probability of yellow = 2/8 = 1/4
Sections 4, 5, and 6 are blue. Probability of blue = 3/8
Section 7 is red. Probability of red = 1/8
The theoretical probability of the spinner not landing on blue can be determined by subtracting the probability of the spinner landing on blue from 1. That is:
P(not blue) = 1 - 3/8 = 5/8
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What is the quotient
3.60/1.80
Answer:
2
Step-by-step explanation:
3.6 / 1.8 = 2.
Answer:
The answer is 2
Step-by-step explanation:
A student is graduating from college in one year but will need a loan in the amount of $4,980 for the last two semesters. The student may receive either an unsubsidized Stafford Loan or a PLUS Loan. The terms of each loan are:
Unsubsidized Stafford Loan: annual interest rate of 6.25%, compounded monthly and a payment grace period of six months from time of graduation
PLUS loan: annual interest rate of 7.25%, compounded monthly, with a balance of $5,353.29 at graduation
Which loan will have a higher balance and by how much at the time of repayment?
The Stafford loan will have a higher balance by $114.84 at the time of repayment.
The PLUS loan will have a higher balance by $114.84 at the time of repayment.
The Stafford loan will have a higher balance by $52.97 at the time of repayment.
The PLUS loan will have a higher balance by $52.97 at the time of repayment.
The Stafford loan will have a higher balance of $114.84 at the time of repayment.
What is compound interest?Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.
We know the formula for compound interest is,
A = P(1 + r/100)ⁿ.
Where, A = amount, P = principle, r = rate, and n = time in years.
The formula for compound interest compounded monthly is
A = P(1 + (r/12)/100)¹²ⁿ.
So, For Unsubsidized Stafford Loan,
A = 4980(1 + (6.25)/12/100)¹⁸. (12 times 1.5 years two semesters and 6
months)
A = 4980(1 + 0.0052)¹⁸.
A = 4980(1.0052)¹⁸.
A = $5467.
So, Unsubsidized Stafford Loan will give a higher balance.
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Answer: The Stafford loan will have a higher balance by $114.84 at the time of repayment.
Step-by-step explanation:
On any right triangle, which trigonometric function would you use to determine the opposite side if you knew the angle measure and the length of the hypotenuse?
Sine
Cosine
Tangent
Brady is making snack bags with 18 juice boxes and 27 cookies. He wants each bag to have the same number of juice boxes and the same number of cookies. (a) What is the maximum number of snack bags he could make? (b) How many juice boxes and (c) how many cookies could he put in each bag? Show your work!
a) The maximum number of bags is 9.
b) 2 per bag.
c) 3 per bag.
What is the maximum number of snack bags?To find that, we need to find the maximum common factor between the numbers of snackbags and juice boxes.
We can rewrite these as:
18 = 2*3*3
27 = 3*3*3
Then the maximum common factor is 3*3 = 9
So that is the maximum number of bags.
b) It is given by the quotient between the number of juice boxes and the number of bags:
18/9 = 2
c) Exactly the same computation than above, this time with the number of boxes:
27/9 = 3
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Find the Volume of the following cone.
A. 150.72 in3
B. 16.75 in3
C. 8.37 in3
D. 75.36 in3
Answer:
8.73in³
Step-by-step explanation:
volume =⅓πrh
⅓×3.142×2×4=
8.37 in³
Maeve currently has $130 and plans to earn more money each of the 8 weekends this summer. She wants at least $1,250 by the end of the summer. How much does she need to earn each weekend? Assume she earns the same amount each weekend. Solve her problem, and then graph the solution on a number line.
1) Maeve needs to earn $140 each weekend to get at least $1,250, using a linear inequality.
2) The graph on a number line that solves her problem is number line D, showing Maaeve's earnings per weekend.
What is a linear inequality?A linear inequality is a first-order term inequality that compares two values by the inequality symbols such as, '<', '>', '≤', '≠' or '≥'
In a linear inequality, m is the slope and b is the y-intercept with the x-intercept.
The amount Maeve currently has = $130
The number of weekends for the summer = 8
The least amount she wants to earn ≥ $1,250
Linear Inequality:130 + 8x ≥ 1,250
8x ≥ 1,250 130
8x ≥ 1,120
x ≥ 140
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is 3lb more or less than 32oz
3lb is more than 32oz
3lb=48oz
Answer:
more
Step-by-step explanation:
There are 16 ounces to a pound
3 pounds would be 48 ounces
so 3 pounds is more than 32 ounces
After selling half their card collections, DeShawn and Stephanie each buy 9 new cards. What is the ratio of the number of cards DeShawn has to the number Stephanie has?
The ratio stay the same in the example because sharing amount is the same.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
After selling half their card collections, DeShawn and Stephanie each buy 9 new cards.
The number of cards that DeShawn and Stephanie have will be 9. Then the ratio is given as,
Ratio = 9 / 9
Ratio = 1
And the ratio of DeShawn and Stephanie togather to the remaining cards is given as,
Ratio = (9 + 9) / [{2 x (9 + 9)} / 2]
Ratio = 18 / (2 x 18 / 2)
Ratio = 18 / 18
Ratio = 1
The ratio stay the same in the example because sharing amount is the same.
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The complete question is given below.
Subtract 4x + 6 from 7 + 2x?
Answer:
1-2x
Step-by-step explanation:
[tex](7+2x)-(4x+6)=7+2x-4x-6=1-2x[/tex]
In a survey of 1,600 people who owned a certain type of car, 880 said they would buy that car again. What percent surveyed were satisfied with the car?
The percent of people satisfied with the survey is 55%
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100.
Given that, in a survey of 1,600 people who owned a certain type of car, 880 said they would buy that type of car again, we need to find what percent of the people surveyed were satisfied with the car,
The percent of people satisfied with the survey = 880 / 1600 × 100
= 55%
Hence, the percent of people satisfied with the survey is 55%
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Jill was given a large jar of jam. She gave one sixth of the jam to Jan. Jill then gave one thirteenth of the remaining jam to Jas. Jill was left with 1 kg of jam. What was the weight, in kg, of the jam in Jill’s jar at the start?
The weight, in kg, of the jam in Jill’s jar at the start is solved to be
15.6 kgHow to find the weight of the jam in Jill's jarLet's call the weight of the jam in the jar at the start "x".
After giving 1/6 of the jam to Jan, Jill had
= x - x/6
amount remaining = 5/6 x
After giving 1/13 of the remaining jam to Jas, Jill had
= 5/6 x - (5/6 x)/13
= 12/13 (5/6 x) left.
amount remaining = 12/13 (5/6 x)
Since Jill was left with 1 kg of jam, 12/13 (5/6 x) = 1.
Solving for x, we have:
12/13 (5/6 x) = 1
5/6 x = 13
x = 13 * 6/5
= 15.6 kg
So the weight of the jam in Jill's jar at the start was 15.6 kg.
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if the average rate of change of f(x) over the interval x=4 to x=8 is 12, and f(4) = 17 find the vaule of f(8).
Answer:
29
Step-by-step explanation:
f(8) - f(4) = 12
f(4) =17
so f(8) = 17+12 =29
The student used the gift card to spend the same amount of money at the coffee shop every day until the remaining value of the card was $0. This function represents f(n), the value, in dollars, of the gift card after n days.f(n) = −2.5n + 75 Based on the function, how much money, in dollars, did the student spend each day at the coffee shop?
The student spent $2.5 each day at the coffee shop.
Step-by-step explanation:The student spent $2.5 each day at the coffee shop because -2.5 is the coefficient of the variable "n" in the function f(n) = -2.5n + 75. The coefficient represents the rate of change or how much the value of the function changes for each unit increase in the variable. In this case, for each increase of 1 day, the value of the gift card decreases by $2.5, meaning the student spent $2.5 each day.
The function is solved and the amount of money the student spent each day on the coffee shop is A = $ 2.50
What is a function rule?The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given data ,
Let the function be represented as A
Now , the value of A is
f ( x ) = -2.5n + 75
We know that the function is f(n) = -2.5n + 75, where n is the number of days.
The coefficient of n (-2.5) represents the rate at which the value of the gift card is decreasing per day.
Hence , the student spent $2.5 each day at the coffee shop
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BCDF is a square with FD=55. Find BD. Round to the nearest tenth, if necessary.
The diagonal BD of the square BCDF will be 55√2 units.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
BCDF is a square with FD = 55.
The diagonal of the square is given by the Pythagoras theorem. Then we have
D² = 55² + 55²
D² = 55²(2)
D = 55 √2 units
The diagonal BD of the square BCDF will be 55√2 units.
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(3a-3/4) times 1/3 if a is 3/8
Answer:
15/24
Step-by-step explanation:
(3a-3/4)
where a is 3/8,
we substitute the value of a;
(3(3/8)-3/4)
(9/8-3/4) =15/8
15/8 times 1/3 =15/24.
q11 in it faaaaaaaaaaaaaaaaaaast
In April of 2015 , a magnetic levitation train in Japan broke the speed record for a train, reaching a top speed of 600 kilometers per hour.
:
Part 1 of 2
(a) How many miles can the train go in an hour? Round to the nearest hundredth, if necessary.
The train can go ___miles per hour.
372.82 miles can the train go in an hour.
What is Unit Conversion?The same attribute is expressed using a unit conversion, but in a different unit of measurement.
For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.
Given:
Speed = 600 Kmph
We know 1 Km= 0.62137119 miles
Now, converting Km to miles
speed = 600 x 0.62137119
= 372.82 miles
Hence, the speed is 372.82 miles.
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