Match each expression on the left with an equivalent expression on the right. Not all of the options on the right will be used.
361,000
1,400
100 x 14
14(10)
361 - 1000
100(361)
36, 100
14,000
3,610
140
On solving the provided question, we can say that on matching the expressions are 100X 14 = 1400 and 14(10) = 140 and 361 . 100 = 36100 and 100(361) = 36100
what is expression ?In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.
so, on matching the expressions are
100X 14 = 1400
14(10) = 140
361 . 100 = 36100
100(361) = 36100
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Estimate the quotient for :
11, 942 ÷ 14
Answer: 853
Step-by-step explanation:
See the attached math problem, please help!
The equations of the rows are
x + 3y - z = 44x - 2y + 7 = 20-3x + y + 5 = 8How to determine the equations of the rowsFrom the question, we have the following parameters that can be used in our computation:
The augmented matrix given as
\(\left[\begin{array}{ccc|c}1&3&-1&4\\4&-2&7&20\\-3&1&5&8\end{array}\right]\)
From the above, we set the columns as follows:
x = first row
y = second row
z = third row
constant = fourth row
Using the above as a guide, we have the following:
x + 3y - z = 4
4x - 2y + 7 = 20
-3x + y + 5 = 8
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Write an expression for the perimeter of the triangle shown below:
A). 5.5x − 9
B). 5.5x + 9
C). 10x − 39
D). 10x − 9
Answer:
Answer B 5.5x + 9
Step-by-step explanation:
Perimeter is the distance around the three sides of the triangle
P = (0.3x + 24) + (5x) + (0.2x - 15)
P = (0.3x + 5x + 0.2x) + (24 - 15)
P = 5.5x + 9
Hannah went to the fair with her friends. She spent $7 to enter the fair and decided to play games until she won a stuffed animal. Each game cost $0.50 to
play. If Hannah spent $19 total at the fair, how many games did she play?
O 12
O 4
O 6
O 26
Answer:
24 games
Step-by-step explanation:
7 to enter
0.5 per game
19 dollars spent
19 = 7 + 0.5x
19 - 7 = 0.5x
12 = 0.5x
x = 12/0.5
x = 24
A family has a $42,000 annual salary. Can they afford an $85,000 house with a $65,000 mortgage requiring payments of $720 per month, including principal, interest, taxes, and insurance?
Yes! they can afford an $85,000 house with a $65,000 mortgage requiring payments of $720 per month.
What is in a mortgage?
Principal, interest, taxes, and insurance make up the majority of mortgage payments. Your outstanding loan balance is reduced by the amount of the principal part. Borrowing money has a cost, which is interest.
Given data:
Annual Salary =$42,000
Cost =$85,000
Mortgage = $65000
Monthly Payment = $720
First Criterian : - Never Spend more than 2.5 times of your Annual Income.
2.5 * 42,000
= 105,000
it can be afforded.
Second Criterian : - Monthly Payment should not exceed Weekly Income
Monthly Payment = 720
Weekly earnings = 42000 / 52 weeks = 807
it can afforded.
Third Criterian : - monthly payment should not exceed 28% of monthly earnings.
Monthly payment = 720
Monthly earnings = 42,000 / 12 = 3500
28% * 3500
= 980
it can be afforded.
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Triangle ABC was created by joining A (3,2), B (4,5), and C (7,3) with line segments. Triangle ABC is reflected over the x – axis and then reflected over the y – axis to form a triangle with side lengths x, y, and z. Match to show which side lengths are equal.
Answer:
z, y, x
Step-by-step explanation:
Match the corresponding sides.
Malcolm needs to buy 7 pizza slices for him and his brother Mitchell, and each cost $3.64. The pizza store is giving customers 20% off each slice. What is the total cost for the pizzas?
Answer: $5.096 or $5.10 (nearest cent)
Step-by-step explanation:
first u find 20%of one slice pizza
which is ²⁰/¹⁰⁰ × 3.64 = 0.728
then u multiply 0.728 by 7 = $5.096
Find the output, y, when the input, x, is -9.
y =
Answer:
when x=-9, y=1
Step-by-step explanation:
the graph shows when the x is at -9, the y is at 1
When 36x^4 + 12x^8 is divided by 12x^4, the result is
The result is 3+x^4.
Do the ratios
15
6
and
20
8
form a proportion?
Answer:
The ratios are equal and form a proportion. Explanation: To find out if 6:9=10:15. 69and1015 ← cross- multiply. 6×15=9×10. 90=90.
Step-by-step explanation:
The ratios are equal and form a proportion. Explanation: To find out if 6:9=10:15. 69and1015 ← cross- multiply. 6×15=9×10. 90=90.
Help please??????????
Answer:
457.25
1636.4
Step-by-step explanation:
To find this you need to figure out what the probability of you needing it is. I believe that you then need to see how much you will pay with that. ex:1050 with only 32% chance that you will need it. So 336. 225 but only 45 %, so 121.25.
1,580 guarantied. 24. 32.4. Add all these together you get 1636.4.
HEY I NEED HELP ASAP!!!!!!!!!!!!!
this is the problem I need help with
n - 25/4 =3
Answer:
n = 37/4
Step-by-step explanation:
that's the answer to you question
Please answer with work given.
a) The case is: Test if the second trial takes less time.
b) The hypothesis are given as follows:
Null: \(H_0: \mu_d \geq 0\).Alternative: \(H_1: \mu_d < 0\).c) The test statistic is: t = -1.59.
d) The rejection region is t < -2.015, and since the test statistic is greater than this, the null hypothesis is not rejected.
What are the hypothesis tested?At the null hypothesis, we test if there is not enough evidence that the second trial takes less time, that is, if the mean of the differences is not negative, hence:
\(H_0: \mu_d \geq 0\).
At the alternative hypothesis, we test if there is enough evidence that the second trial takes less time, hence:
\(H_1: \mu_d < 0\)
Considering a left-tailed test, as we are testing if the mean is less than a value, with 6 - 1 = 5 df and a significance level of 0.05, the critical value is of:
t = -2.015.
Hence the rejection region is:
t < -2.015.
What is the test statistic?The equation to calculate the test statistic is given as follows:
\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)
The parameters are:
\(\overline{x}\) is the sample mean.\(\mu\) is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.The sample of the differences is given by:
-16, 8, 3, -78, -43, -3.
Inserting these values into a calculator, the values of the parameters are given as follows:
\(\overline{x} = -21.5, \mu = 0, s = 33.16, n = 6\)
Hence the test statistic is:
\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)
\(t = \frac{-21.5 - 0}{\frac{33.16}{\sqrt{6}}}\)
t = -1.59.
Greater than the critical value, hence the null hypothesis is not rejected.
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If an investment company pays 6% compounded semiannually, how much will you have 5 years from now if you deposit $900?
How much would you earn if it were simple interest instead of compound interest?
With compound interest of 6% paid semiannually, a deposit of $900 would result in $1,191.02 after 5 years, while simple interest would earn $270, resulting in a total of $1,170.
To calculate the future value of an investment with compound interest, we can use the following formula:
FV =\(PV * (1 + r/n)^{(n*t)}\)
where FV, PV, r, n and t is the future value, present value, annual interest rate, number of compounding periods per year and number of years respectively.
In this case, the present value (PV) is $900, the annual interest rate (r) is 6%, and the interest is compounded semiannually, so there are 2 compounding periods per year (n=2). The period (t) of investment is 5 years.
Using these values, we can calculate the future value (FV) as follows:
FV = \(\$900 * (1 + 0.06/2)^{(2*5)\)
= \(\$900 * (1.03)^{10\)
= $1,191.02
Therefore, the future value of the investment after 5 years with compound interest would be $1,191.02.
If the interest were simple interest instead of compound interest, the calculation would be simpler. Simple interest is calculated as follows:
I = P x r x t
where I is the interest, P is the principal or present value, r is the interest rate, and t is the time period.
In this case, the interest rate is still 6% and the investment period is still 5 years, but the interest is calculated only on the principal amount of $900. Therefore, the interest earned would be:
I = $900 x 0.06 x 5
= $270
Therefore, the total amount after 5 years with simple interest would be the sum of the principal and the interest earned, which is:
Total = $900 + $270
= $1,170
Therefore, if the interest were simple interest instead of compound interest, the total amount after 5 years would be $1,170, and the interest earned would be $270.
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A 3-gallon container of disinfectant costs $36.24. What is the price per quart?
Answer:
10.74666666666667 per quart
Step-by-step explanation3 divided 36.24
Please look at the photo. Thank you!
The equations of the composite functions are (h o h)(x) = (x² + 3)² + 3 and (f o f)(x) = x
How to calculate the composite functionsFrom the question, we have the following equations that can be used in our computation:
h(x) = x² + 3
f(x) = 3/4x
From the above, we have
(h o h)(x) = h(h(x))
So, we have
(h o h)(x) = (x² + 3)² + 3
Also, we have
(f o f)(x) = 3/[4(3/4x)]
Evaluate
(f o f)(x) = x
Hence, the composite functions are (h o h)(x) = (x² + 3)² + 3 and (f o f)(x) = x
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surface area of a cuboid 1cm by 10cm by 3cm
Answer:
2lw + 2lh+2hw
Step-by-step explanation:
Answer:
If Im right you had to multiple 1 by 10 and 3
Step-by-step explanation:
Your answer will be 30 but dont forget to add the centimeter at the end
30cm
Hope this helps (:
If a cube has volume 125cm³, find the height of the cube.
Answer:
height = 5 cm
Step-by-step explanation:
a cube has congruent sides (s)
the volume (V) of a cube is calculated as
V = s³
given V = 125 , then
s³ = 125 ( take cube root of both sides )
\(\sqrt[3]{s^3}\) = \(\sqrt[3]{125}\) = \(\sqrt[3]{5^3}\)
s = 5
then height = 5 cm
What is the surface area of a square prism with sides that measure 8 units?
O254 units²
O 300 units²
0314 units²
0384 units²
Answer:
384 units²
Step-by-step explanation:
The area of one face is (8)(8)=64.
Multiplying this by the six faces, we get 64(6)=384
Use your graph to find estimates of the solutions to the equation x^2-x-6=-2
9514 1404 393
Answer:
x ≈ -1.5 or 2.6
Step-by-step explanation:
It appears as though your graph crosses the line y = -2 at approximately x = -1.5 and also at x = 2.6.
These are estimates of the solutions to the equation.
x ≈ {-1.5, 2.6}
Answer:
-2 and 3
Step-by-step explanation:
From the graph, the solution is the points where the curve cuts the x axis. From the graph, you can see that the equation cuts the x axis at two points that is at x=-2 and 3.
Hence the solutions to the equation is -2 and 3
what is the exponential function property of domain?
Answer:
The domain of exponential functions is all real numbers. The range is all real numbers greater than zero. The line y = 0 is a horizontal asymptote for all exponential functions. When a > 1: as x increases, the exponential function increases, and as x decreases, the function decreases.
There are 7 red marbles, 5 blue marbles, and 11 green marbles in a bag. If John randomly pulls a marble from the bag, what is the probability that he selects a blue marble? Give your answer as a decimal to the nearest hundredth.
Answer:
0.23
Step-by-step explanation:
For which triangle does the Pythagorean Theorem
express the relationship between the lengths of its three
sides?
A
B
C
D
Pythagorean theorem is represented by triangle B.
Which triangle express the relationships according to Pythagorean theorem?
In this question we find four cases of triangle, of which we must determine what triangle can be explained by Pythagorean theorem. This theorem offers a relationship between the three sides of the triangle:
r² = x² + y²
Where:
x, y - Legsr - Hypotenuse.Please notice that hypotenuse is the longest side of the triangle. Graphically speaking, there is a right triangle, that is, a triangle with one right angle. Then, triangle B express the relationship according to Pythagorean theorem.
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Steve travels two times as fast as you. Traveling in opposite directions, they are 120 miles apart after 2.5 hours. Find the rate of travel
PreCalc work, Need help with writing piece wise functions with graphs level 2. Giving branliest.
The piece-wise linear functions can be written as follows:
\(f(x) = -0.5x + 3, x < 5\).\(f(x) = -5, x = 5\)\(f(x) = -x + 9, x > 5\).What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For x less than 5, the y-intercept is of b = 3 and the function also gos through (2,2), hence the slope is:
m = (2 - 3)/(2 - 0) = -0.5.
Hence the rule is:
\(f(x) = -0.5x + 3, x < 5\).
When x = 5, the function is constant at -5, hence:
\(f(x) = -5, x = 5\)
For x less than 5, the function goes through points (6,3) and (7,2), hence the slope is:
m = (2 - 3)/(7 - 6) = -1.
Then:
y = -x + b
When x = 6, y = 3, hence the y-intercept is given as follows:
3 = -6 + b
b = 9.
Hence the rule is:
\(f(x) = -x + 9, x > 5\).
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Q=SYSTEMSClassifying systems of linear equations from graphsFor each system of linear equations shown below, dassify the system as "consistent dependent," "consistent independent," or "inconsistent." Then, choose thebest description of its solution. If the system has exactly one solution, give its solution.System ASystem BSystemLine 1:Line 1: Y:y= -4Line 1: y
To start, let's define consistent and inconsistent systems:
Cosistent Independent:
- Has one solution;
- The lines intercept at 1 point.
Consistent Dependent:
- Has Infinite solutions;
- The lines are the same.
Inconsistent:
- Has no solution;
The lines are parallel.
Now, let's evaluate each system.
System (A):
As we can observe in the graph, the lines are the same.
Also, you can isolate y in both equations to observe that the lines are the same:
Line 1:
\(y=-\frac{1}{4}x-3\)Line 2:
\(x+4y=-12\)To isolate y in line 2, let's subtract x from both sides:
\(\begin{gathered} x+4y-x=-12-x \\ 4y=-x-12 \end{gathered}\)And now divide both sides by 4:
\(\begin{gathered} \frac{4y}{4}=\frac{-x-12}{4} \\ y=-\frac{1}{4}x-3 \end{gathered}\)As can be observed, Line 1 and 2 are the same.
So, the system is consistent dependent.
This means that the system has Infinite solutions.
System (B):
As we can observe in the graph, the lines are parallel.
Also, comparing the equations, observe that they have the same angular coefficient but different intercepts, confirming that the lines are parallel.
So, the system is inconsistent.
This means that the system has no solutions.
System (C):
As we can observe in the graph, the lines intercept at one point.
So, let's find the intercept.
Do y1 = y2:
\(\begin{gathered} y_1=y_2 \\ -\frac{1}{2}x-3=x \end{gathered}\)Now, isolate x by adding 1/2x to both sides.
\(\begin{gathered} -\frac{1}{2}x-3+\frac{1}{2}x=x+\frac{1}{2}x \\ -3=\frac{2x+x}{2} \\ -3=\frac{3}{2}x \end{gathered}\)Now, multiply both sides by 2/3:
\(\begin{gathered} -3\cdot\frac{2}{3}=\frac{3}{2}x\cdot\frac{2}{3} \\ -\frac{6}{3}=\frac{6}{6}x \\ -2=x \end{gathered}\)Knowing x, substitute it in one equation to find y. In Line 2 x = y. Then,
\(\begin{gathered} x=y \\ \text{If x = -2} \\ -2=y \end{gathered}\)Thus, the intercept is (-2, -2).
So, the system is consistent independent.
This means that the system has a unique solution. The solution is (-2, -2).
What is the standard form polynomial representing the volume of this shipping container?
Answer:
Volume = (24x⁵ + 78x⁴ - 147x³ - 624x² - 360x)
Step-by-step explanation:
Container given in the picture is in the shape of a cuboid.
And volume of a cuboid is measured by the expression,
Volume of a cuboid = Length × width × height
Now substitute the measure of the container's dimensions given in the picture
Volume = (4x² + 3x)(x²- 8)(6x + 15)
= [(4x² + 3x)(x²- 8)](6x + 15)
= [4x²(x² - 8) + 3x(x² - 8)](6x + 15)
= (4x⁴ - 32x² + 3x³ - 24x)(6x + 15)
= (4x⁴ + 3x³ - 32x² - 24x)(6x + 15)
= 6x(4x⁴ + 3x³ - 32x² - 24x) + 15(4x⁴ + 3x³ - 32x² - 24x)
= 24x⁵+ 18x⁴ - 192x³ - 144x² + 60x⁴ + 45x³ - 480x² - 360x
= 24x⁵ + 78x⁴ - 147x³ - 624x² - 360x
Answer:
V = 24x⁵+78x⁴-147x³-624x²-360x
Step-by-step explanation:
Help me out please please
Answer:
490000
Step-by-step explanation:
Substituting \(x=40\),
\(I=-425(40)^2 + 45500(40) - 650000=490000\)
I am stuck please help with this graph.
An equation for the function graphed above include the following: g(x) = -1/4|x + 1| - 2.
How to interpret and determine the equation of g(x)?By critically observing the graph of this absolute value function, we can reasonably infer and logically deduce that the parent absolute value function f(x) = |x| was vertically compressed by a factor of 1/4, reflected over the x-axis, followed by a vertical translation 2 units down, and then a horizontal translation to the left by 1 unit, in order to produce the transformed absolute value function as follows;
f(x) = |x|
y = A|x + B| + C
g(x) = -1/4|x + 1| - 2
In conclusion, the value of the variables A, B, and C are -1/4, 1, and 2 respectively.
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