Step-by-step explanation:
x + 2x + 7x
72 = 9x
72 - 9 = x
63 = x
63 ÷ 3 = 21
piece 1 = 21
piece 2 =21+2 = 23
piece 3 =21+7 = 28
21+23+28 = 72 This proves the above is correct.
Clara writes the equation (x – 13)(x 8) = 196 to solve for the missing side length of a rectangle represented by the factor x 8. what is the missing side length represented by x 8 units of the rectangle?
Answer:
28 units
Step-by-step explanation:
First, we are going to solve the equation to find the value ^^
Let's solve the equation step by step
Step 1. Use the distributive property to destroy the parenthesis
Step 2. Subtract 196 to both sides of the equation
Step 3. Factor the expression
Step 4. Set each factor equal to zero and solve
Since we are dealing with lengths here, and lengths cannot be negative, the only valid solution is 28.
Now, we know from our problem that the missing side of the rectangle is given by the expression , so to find the actual length, we just need to replace with 8 in the given expression and simplify!
We can conclude that the missing side length represented by x + 8 units of the rectangle is 28 units.
Can someone solve this?
Answer:
[tex]\frac{5}{6}[/tex], [tex]\frac{5}{6}[/tex], and "Yes"
Step-by-step explanation:
We will do as the instructions say.
-> See attached.
The height of a cone is twice the radius of its base.
2x
X
What expression represents the volume of the cone, in
cubic units?
O 2x³
O 47x³
Answer: O253
Step-by-step explanation:
The correct expression which represents the volume of the cone is,
V = 2x³π/3
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The height of a cone is twice the radius of its base.
Let radius of cone = x
Then, The height of cone = 2x
Hence, The volume of cone is,
V = 1/3πr²h
V = 1/3 × π × x² × 2x
V = 2x³π/3
Thus, The correct expression which represents the volume of the cone is,
V = 2x³π/3
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f(x)=x2 Translate left 2 units Translate down 2 units
A line passes through the points ( p , a ) and ( p , − a ) where p and a are real numbers. If p = 0 , what is the y-intercept? Explain your reasoning.
The y-intercept of the point where the value of x is zero, hence the y-intercept are -a and a
Intercept of a lineGiven the coordinate points on a line as (p , a) and ( p , − a )
Determine the slope
Slope = -a-a/p-p
Slope = infinity
If the value p is zero, hence the coordinate points will become (0, a) and (0, -a)
Since the y-intercept of the point where the value of x is zero, hence the y-intercept are -a and a
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A=[37], B =[²7], C = [= ² =8].
Which matrix represents (A - B) - C?
A study conducted at a certain college shows that 51% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that 5 randomly selected graduates all find jobs in their chosen field within a year of graduating. Round to the nearest thousandth if necessary.
Answer:
0.035
Step-by-step explanation:
Since all of them find a job, the probability is
[tex]51\%\times51\%\times51\%\times51\%\times51\%\\\\=(51\%)^5\\\\=0.035[/tex]
(rounded to the nearest thousandth)
In the formula d = startroot (x 2 minus x 1) squared (y 2 minus y 1) squared endroot, how does each subtraction expression relate to the pythagorean theorem?
Each subtraction expression, in relation with the Pythagoras Theorem, represents the length of one side of a right-angled triangle with a hypotenuse of length d.
What is Pythagoras Theorem?
The Pythagoras Theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the remaining two sides in a right-angled triangle.
The formula for Pythagoras Theorem is given by,
[tex]h^{2}=a^{2} +b^{2}[/tex]
Here, h is the hypotenuse, a and b are the two legs of the right-angled triangle.
Each Subtraction in view of Pythagoras Theorem
It is is given that,
[tex]d =\sqrt{(x_{2} - x_{1} )^{2}+(y_{2} -y_{1} )^{2} }[/tex]
or [tex]d^{2} =(x_{2} - x_{1} )^{2}+(y_{2} -y_{1} )^{2}[/tex]
Therefore, d is the hypotenuse and each subtraction term represents one leg of the right-angled triangle in accordance with the Pythagoras Theorem.
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Can someone help me out on these geometry questions? Its urgent, gotta have answers fast
5) Transitive property of equality
6) Addition property of equality
7) Subtraction property of equality
8) Division property of equality
9) Multiplication property of equality
10) Transitive property of congruence
11) Substitution property of equality
12) Addition property of equality [add XY to both sides then use segment addition postulate]
13) Subtraction property of equality [subtract XY from both sides then use segment subtraction postulate]
14) Angle addition postulate
15) Addition property of equality [add angle 2 to both sides then use angle addition postulate]
16) Transitive property of equality
The area of a circle is 47.39cm2. find the length of the radius rounded to 2 dp.
The length of the radius rounded to 2 decimal points is 3.88cm.
In geometry, the area enclosed by a circle of radius r is pie π[tex]r^2[/tex].
How to round decimals?
Rounding decimals consists of rounding a decimal number to a certain number of decimal places, to save time and help us express really long numbers in shorter terms. There are certain rules to follow when rounding a decimal number. Put simply, if the last digit is less than 5, round the previous digit down. However, if it’s 5 or more than you should round the previous digit up. So, if the number you are about to round is followed by 5, 6, 7, 8, 9 round the number up. And if it is followed by 0, 1, 2, 3, 4 round the number down.
The area of circle is [tex]47.39cm^2[/tex].
Putting it in the formula we get
[tex]47.39cm^2[/tex] = π[tex]r^2[/tex]
[tex]r^2[/tex] = 47.39 / π
r^2 = 15.0847
r = 3.88 cm
Hence the length of the radius rounded to 2 decimal points is 3.88cm.
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What phrases can be
used to describe the line
representing the relationship between the number of
balloons remaining and the number of hats created?
Select three options.
D positive slope
O negative slope
O constant slope
D increasing function
D decreasing function
Use a graphing calculator to find the value of the correlation coefficient r to determine if there is a strong correlation among the data.
(1, 7), (2, 5), (3, -1), (4, 3), (5, -5)
The value for r = - 0.8535 , there is strong correlation between the variables.
What is a correlation coefficient ?Correlation coefficient describes the relationship between the two variables in the data .
The data given is
(1, 7), (2, 5), (3, -1), (4, 3), (5, -5)
Assuming Linear Regression ,
The data is plotted on the graphing calculator
The value for r = - 0.8535
as the value is in the range of - .85 to -1 , therefore there is strong correlation between the variables.
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Simplify the expression completely.
The solution of the given expression [tex]\sqrt{7xy^7}\sqrt{21x^5y^5}[/tex]will be 7x³y⁶√3.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The given expression will be solved as follows:-
E = [tex]\sqrt{7xy^7}\sqrt{21x^5y^5}[/tex]
E = [tex]\sqrt{7\times 7\times 3\times xy^7\times x^5y^5[/tex]
E=[tex]\sqrt{7\times 7\times 3\times x^6y^{12}[/tex]
E = 7x³y⁶√3.
Therefore the solution of the given expression [tex]\sqrt{7xy^7}\sqrt{21x^5y^5}[/tex]will be 7x³y⁶√3.
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A researcher conducted an experiment to investigate the effects of working in crowded versus uncrowded conditions on the job satisfaction of employees in a variety of work settings. In this study, the dependent variable is
In a research of investigating the effects of working in crowded versus uncrowded conditions on the job satisfaction of employees in a variety of work setting , working is a depending variable and crowding is an independent variable.
Given aim of the research is to investigate the effects of working in crowded conditions and uncrowded conditions.
We know that depending variable is a variable whose value is dependent on the other variable. Independent variable is a variable whose value does not dependent on the other variables.
In the given question working may be affected negatively in crowded environment means there will be less work in crowded environment and more work in uncrowded environment.
Hence the depending variable in research is working.
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The school tuck-shop has milk in 700mL and 1L cartons. If there are 60 cartons and 48L of milk in total, how many 700 mL cartons are there?
60 × 48 = 2880 L
2880 ÷ 700 = 4
Answer:
20 1 Liter Cartons
40 700 ml Cartons
Step-by-step explanation:
Let A be the number of 700ml cartons.
Let B be the number of 1 L cartons
We are told that A + B = 60 cartons total
Rearrange to isolate A: A = 60 - B
700ml is 0.700L
Total volume of milk is 48L
Total volume (in liters) of the 700 ml cartons is from (0.70 L)A
Total volume from the 1L cartons is (1 L)B
Total = (0.70)A + 1B = 48 L
Now use the rearranged equation for A in the above espression:
(0.70)A + 1B = 48 L
(0.70)(60-B) + 1B = 48 L
42 - 0.70B + B = 48
0.30B = 6
B = 20
A is 60 - B or 40
=============
CHECK:
B: 20*(1 L) = 20 L
A: 40*(0.70 L) = 28 L
Total = 48 L YES
с
Instructions: Find the value of the trigonometric ratio. Make sure to simplify the fraction
if needed.
Tan A
Check
50
30
A
40
B
Using relations in a right triangle, it is found that:
tan(A) = 3/4 = 0.75.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.In this triangle:
The adjacent side to A has length 40.The opposite side to A has length 30.Hence the tangent of A is:
tan(A) = 30/40 = 3/4 = 0.75.
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A scientist has 50 grams of a radioactive element. The amount of radioactive element remaining after t days can be
determined using the equation f()-50
50 (1) ³ . After two days the scientist receives a second shipment of 50 grams of the
same element. The equation used to represent the amount of shipment 2 remaining after t days is f(t)-50
(1)- 50 (2)
of the following is an equivalent form of the expression for the amount remaining in shipment 2?
•(9²
5
50.
19
t
50-(³
The option that is the equivalent form of the expression for the amount remaining in shipment 2 is the second option: 50 ([tex]\frac{1}{2} ^ \frac{t}{5} / \frac{1}{2} ^ \frac{2}{5}[/tex])
What is the radioactive element about?Note that:
f(t)= 50 (1/2)^ [tex]\frac{t-2}{5}[/tex]
f(t)= 50 (1/2)^ [tex]\frac{\frac{t}{5} } - {\frac{2}{5} }[/tex]
Note also that in indices, [tex]x^{-y}[/tex] = 1/ [tex]x^{y}[/tex]
Then: 50 ([tex]\frac{1}{2} ^ \frac{t}{5} / \frac{1}{2} ^ \frac{2}{5}[/tex])
([tex]50 \frac {1}{2} ^ \frac{t}{5} / \frac{1}{2} ^ \frac{2}{5}[/tex])
= 50 ([tex]\frac{1}{2} ^ \frac{t}{5} / \frac{1}{2} ^ \frac{2}{5}[/tex])
Therefore, The option that is the equivalent form of the expression for the amount remaining in shipment 2 is the second option: 50 ([tex]\frac{1}{2} ^ \frac{t}{5} / \frac{1}{2} ^ \frac{2}{5}[/tex])
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increase the number 1.25 by 8/25 of it
Answer: 1.65
Step-by-step explanation:
First, we must find 8/25 of 1.25. This is using multiplication.
1.25 * 8/25 = 0.4
Now, we can increase 1.25 by 8/25 of it. This is using addition.
1.25 + 0.4 = 1.65
What is the slope of line a? 48 POINTS
Answer:
-3
Step-by-step explanation:
[tex]Slope = \frac{Change in Y}{Change in X}[/tex]
Take two points
(1, -5) and (-1, 1)
Plug in their y and x coordinates
[tex]\frac{-5 - 1}{1-(-1)} =\frac{-6}{2} = -3[/tex]
Answer:
1st answer is correct.
Step-by-step explanation:
First, let us take two coordinates of the line.
( 0 , -2 ) ⇒ ( x₁ , y₁ )
( -1 , 1 ) ⇒ ( x₂ , y₂ )
We have to use the below formula to find the slope of the line.
Slope = m
[tex]m = \frac{y_1-y_2}{x_1-x_2}[/tex]
Let us find it now.
[tex]m = \frac{-2-1}{0-(-1)}\\m = \frac{-3}{1}\\m=-3[/tex]
The FBI wants to determine the effectiveness of their 10 Most Wanted list. To do so, they need to find out the fraction of people who appear on the list that are actually caught. In an earlier study, the population proportion was estimated to be 0.26. How large a sample would be required in order to estimate the fraction of people who are captured after appearing on the 10 Most Wanted list at the 98% confidence level with an error of at most 0.04?
The sample size required to estimate the fraction of people who are captured after appearing on the 10 most wanted list is 228.
Given standard deviation of 0.26 ,margin of error of 0.04, and confidence interval of 98%.
We have to determine the sample size required to estimate the fraction of people who are captured after appearing on the 10 ost wanted list.
We can find the sample size with the help of margin of error.
Margin of error is the difference between the calculated values and real values.
Margin of error=z*σ/[tex]\sqrt{n}[/tex]
where σ is standard deviation,
n is sample size and z is critial z value.
We have to find the z value for 98% confidence level from z table.
z value=2.326.
Put the values in the formula of margin of error.
0.04=2.326*0.26/[tex]\sqrt{n}[/tex]
[tex]\sqrt{n}[/tex]=2.326*0.26/0.04
[tex]\sqrt{n}[/tex]=15.119
squaring both sides we get
n=228.58
By rounding we get
n=228.
Hence the sample size needed is 228.
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Point P is the center of dilation. Triangle S T U is dilated to create triangle S prime T prime U prime. The length of P T is 2. The length of T T prime is 10.
Which statements justify that the dilation of triangle STU is an enlargement increasing its size by the magnitude of the scale factor? Select two options.
The triangle pre-image is closer to the point of dilation than the image.
The triangle image is closer to the point of dilation than the pre-image.
The value of the scale factor, One-sixth, is between 0 and 1.
The value of the scale factor, 6, is greater than 1.
The vertices of the pre-image are collinear with the vertices of the imag
The statements that justify that the dilation of triangle STU is an enlargement increasing its size by the magnitude of the scale factor include:
A. The triangle pre-image is closer to the point of dilation than the image.
D. The value of the scale factor, 6, is greater than1.
What is dilation?It should be noted that dilation refers to the transformation of an object.
In this case, the triangle pre-image is closer to the point of dilation than the image and the value of the scale factor, 6, is greater than1.
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How to find the answer to0.291×0.34
Answer:
0.291×0.34=0.09894
Answer: 0.09894
We are going to use long division:
What is the first step to solve the following system of equations using substitution? 3x+y=15 5x-3y=11Divide the second equation by 3. Multiply the first equation by 3. Solve the first equation for y. Add the two equations together.
Answer:
(4, 3)
Step-by-step explanation:
#1. Isolate x:
3x + y = 15
y = 15 - 3x
Substitute and solve for x:
5x - 3y = 11
5x - 3(15 - 3x) = 11
5x - 45 + 9x = 11
5x + 9x = 11 + 45
14x = 56
x = 4
Substitute and solve for y:
y = 15 - 3x
y = 15 - 3(4)
y = 15 - 12
y = 3
Answer:
C. Solve the first equation for y
===================
Given system3x + y = 155x - 3y = 11If we are looking for substitution, then should solve one of the equations for one of the variables. This will allow us to substitute same into other equation and solve for the other variable.
Let's see what would be easy solution.
Equation 1Solving for x is not straight away (we isolate x and divide all terms by its coefficient) as it has coefficient of 3.
Solving for y is easy, we just need to isolate it:
3x + y = 15 ⇒ y = - 3x + 15Equation 2Both of the variables have coefficients that are not factors of the constant term, so the easiest option is to solve the first equation for y.
This gives us the answer choice C.
Simplify
(13x² +10) - 9x²
math. is 1.096 x 10 ^4 the right answer?
Work Shown:
[tex]1.04 \cdot 10^4 + 5.6 \cdot 10^2\\\\10,400 + 560\\\\10,960\\\\1.096 \cdot 10^4\\\\[/tex]
Note: Something like [tex]5.6 \cdot 10^2[/tex] means we move the decimal point two spots to the right to get to 560. If the exponent was negative, then we move that many spaces to the left.
A rectangle field is ten times as long as it is wide. If the perimeter of the field is 1650 feet, what are the dimensions of the field
Answer:
Below in bold.
Step-by-step explanation:
If the width is x feet then the length is 10x feet, so:
2(x + 10x) = 1650
22x = 1650
x = 75 feet.
So the width is 75 feet and the length is 750 feet,
In the following exercises, multiply the binomials. Use any method.
256. (r + s)(3r + 2s)
Answer:
Hence the expression [tex]$$(4z-y)(z-6)=4z^2-yz-24z+6y$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (4z-y)(z-6).We have to multiply the given expression.Multiply the (4 z-y) by -6, multiply the (4 z-y) by z then add like terms.[tex]$$\begin{matrix}{} & {} & {} & {} & 4z & - & y \\ \times & {} & {} & {} & z & - & 6 \\ \end{matrix}$$[/tex]
________________
[tex]$$\begin{matrix}{} & {} & {} & - & 24z & + & 6y \\ 4{{z}^2} & - & yz & {} & {} & {} & {} \\ \end{matrix}$$[/tex]
______________________
[tex]$$\begin{matrix}4{{z}^2} & - & yz & - & 24z & + & 6y \\ \end{matrix}$$[/tex]
Please answer with everything needed i appreciate everyones help:)0)
Answer:
1/3
Step-by-step explanation:
please mark brainliest if correct
Hurrry help number is chosen at random form 1 to 50 find the probiotic of selecting prime numbers
Answer: [tex]\frac{3}{10}[/tex] or 30%
Step-by-step explanation:
We will divide the wanted outcomes by the possible outcomes.
[tex]\displaystyle \frac{\text{wanted outcomes}}{\text{possible outcomes}} =\frac{\text{number of prime number}}{\text{number of numbers 1 through 50}} =\frac{15}{50}=\frac{3}{10}\;\; \text{or 30\%}[/tex]
The prime numbers from one through fifty are; 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47.
-> This is 15 numbers
How many ink cartridges can you buy with 105 dollars if one cartridge costs 15 dollars ?
Answer:
7
Step-by-step explanation:
105/15=7
7 ink cartridges you can buy with 105 dollars.
What is a linear equation in math?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.One cartridge costs = 15 dollars
No of cartridge we buy in 105 dollars = 105 /15
= 7
Therefore, 7 ink cartridges buy can with 105 dollars.
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