The original fraction has a denominator that is 3 less than the numerator. If we define the numerator as x, then the denominator is x-3, and the fraction can be written as x/(x-3).
If 1 is added both to the numerator and denominator, the resulting fraction is equal to 10/7.
Then, we can write:
[tex]\begin{gathered} \frac{x+1}{(x-3)+1}=\frac{10}{7} \\ \frac{x+1}{x-2}=\frac{10}{7} \\ 7(x+1)=10(x-2) \\ 7x+7=10x-20 \\ 7x-10x=-20-7 \\ -3x=-27 \\ x=\frac{-27}{-3} \\ x=9 \end{gathered}[/tex]With the value of x, we can replace it in the fraction and know the value of it:
[tex]\frac{x}{x-3}=\frac{9}{9-3}=\frac{9}{6}=\frac{3}{2}[/tex]Answer: The fraction is 9/6, that can be simplified to 3/2 or 1.5.
Use the graph of f to describe the transformation that results in the graph of g. Then sketch the graphs of g and f.
EXPLANATION
Since we have the function:
[tex]f(x)=(\frac{1}{3})^x[/tex]Graphing this an the transformation into a graph calculator we have:
We can see that the transformated function is translated 2 units to the right, and that It is also translated 4 units down.
Thus, the transformations are the following:
g(x) is the graph of f(x) translated 2 units to the right and 4 units down.
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The information given in the table on the Value of a Car and the Age of the Car, gives;
First Part;
The dependent variable is; The Value of Car
The independent variable is; The Age of Car
Second part;
The situation is a function given that each Age of Car maps to only one Value of Car.
What is a dependent and a independent variable?A dependent variable is an output variable which is being observed, while an independent variable is the input variable which is known or controlled by the researcher.
First part;
The given information in the table is with regards to how the car's value decreases with time, therefore;
The dependent variable, which is the output variable, or the variable whose value is required is the current Value of the Car (Dollars)The independent variable, which is the input variable, or the variable that determines the value of the output or dependent variable, is the Age of Car (Years)Second part;
A function is a relationship in which each input value has exactly one output.
Given that the Values of the cars are all different, and no two car of a particular age has two values, therefore;
The situation is a functionGiven that the first difference varies depending on the age of the car, the function can be taken as a piecewise function
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Step by step solution thank you much appreciated
Answer:
11.796
Step-by-step explanation:
2nd term
[tex] {1.3}^{2} = 1.3 + \frac{1.3}{ \frac{10}{3} } [/tex]
[tex] {1.3}^{2} = 1.69[/tex]
add first term
[tex]27.8 + 1.69 = 29.49[/tex]
times by 0.4 or ×2/5
[tex]29.49 \times \frac{2}{5} = \frac{58.98}{5} [/tex]
[tex] = 11.796[/tex]
Which expressions represent a quadratic expression in factored form? Select all the correct answers.
x^2 − x − 72
(x + 3)(x − 7)
-8(x + 56)
(x + 1)(x − 2)
(x − 2) + (x + 3)
The expressions that represent a quadratic expression in factored form is (x + 1)(x − 2).
What is quadratic expression?Quadratic expression can be described as the mathematical expression that posses the variable which have highest power of 2.
It should be noted that the quadratic equation is usually expressed in the form ax^2 + bx + c where the abc are the known numbers in the equation that will be used in the calculation of the factors of the equation and in the quadratic equation the number a will not be equal to zero in the equation.
Therefore, option C is correct.
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If 16 is added to a number, the result is 35 less than twice the number. Find the number.
Let us represent the number as x:
16 is added to a number is represented as:
[tex]16+x[/tex]The result been 35 less than twice the number is represented as:
[tex]2x-35[/tex]Combining the above expression together to find the number will be:
[tex]16+x=2x-35[/tex]Simplifying further:
[tex]\begin{gathered} 16+35=2x-x \\ 51=x \\ \end{gathered}[/tex]The number, therefore, is 51
Find the missing quantity with the information given. Round rates to the nearest whole percent and dollar amounts to the nearest cent.Original Price = $6.50$ Markdown = $1.30Reduced Price = ?
Since we have a markdown of $1.30 we just need to substract this amount to the original price, then we have:
[tex]6.50-1.30=5.20[/tex]Therefore the reduced price is $5.20
In the picture shown below, a cube with a side of 5 inches is placed directly on top of a larger cube which has a side of 18 inches. Then, another cube with a side of 3 inches is placed directly to the side of the lower cube. What is the surface area of this assembly? (drawing below is not to scale)
For this problem, we are given three cubes. Cube A is on top of cube B, the cube C is glued to the side of cube B. We need to calculate the surface area for the whole piece.
The surface area of a cube is given by the following:
[tex]A_{\text{surface}}=6\cdot l^2[/tex]Where "l" is the measurement of the length of the side on each cube.
To calculate the whole surface area, we need to calculate each cube individually then sum them. Let's start with cube A, since this cube is on top of Cube b, one of its faces shouldn't count for the surface area, therefore we have:
[tex]\begin{gathered} A_{\text{cubeA}}=5\cdot5^2=125\text{ square inches} \\ \end{gathered}[/tex]Now we need to calculate the surface area for cube C, which is very similar to cube A, as shown below:
[tex]A_{\text{cubeC}}=5\cdot3^2=45\text{ square inches}[/tex]Finally, we need to calculate the area for cube B, this one is different because we need to subtract one face from cube A and one for group C.
[tex]\begin{gathered} A_{\text{cubeB}}=6\cdot18^2-5^2-3^2 \\ A_{\text{cubeB}}=6\cdot324-25-9 \\ A_{\text{cubeB}}=1994-25-9=1910 \end{gathered}[/tex]The total area is the sum of all areas:
[tex]A=1910+45+125=2080[/tex]The total surface area is equal to 2080 square inches.
Can u please help me solve ? I'm reviewing for a final, ty
Part A
we have that
Both students verify the identity properly
student A ----> expand the left side of the identity
student B ----> expand the right side of the identity
but the result is the same
both students proved that the given equation is an identity
Part B
Identities[tex]\begin{gathered} sin^2x+cos^2x=1\text{ ----> identity N 1 in step 3} \\ cos^2x=1-sin^2x \end{gathered}[/tex]and
[tex]cscx=\frac{1}{sinx}\text{ -----> identity N 2 step 5}[/tex]What is the equation of the line that passes through the point (7,6) and has a slope of 0
The equation of the line that passes through the point (7, 6) with slope 0 is y = 6
Given,
The points which the line passes, (x₁, y₁) = (7, 6)
Slope of the line, m = 0
We have to find the equation of the line:
We know that,
y - y₁ = m(x - x₁)
So,
y - 6 = 0(x - 7)
y - 6 = 0
y = 6
That is,
The equation of the line that passes through the point (7, 6) with slope 0 is y = 6
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A Geiger counter counts the number of alpha particles from radioactive material. Over a
long period of time, an average of 16 particles per minute occurs. Assume the arrival of
particles at the counter follows a Poisson distribution. Round your answers to four decimals.
a) Find the probability of exactly 21 particles arrive in a particular one minute period.
0.0426053 O
b) Find the probability of exactly one particle arrives in a particular one second period.
0.20424755689724
a) The probability of exactly 21 particles arrive in a particular one minute period is 0.0426
b) The probability of exactly one particle arrives in a particular one second period is 0.2042
What is probability?Probability is the ratio of the total number of conceivable outcomes to the number of outcomes in an exhaustive set of equally likely alternatives that result in a particular occurrence.
The probability is given by:
P(X=x) = (e⁻ⁿ nˣ)/x!
a) The probability of exactly 21 particles arrive in a particular one minute period is given by :
P(X=21) = (e⁻16 × 16²¹)/21!
P(X=21) = (2.176746853×10¹⁸)/51090942171709440000
P(X=21) = 0.0426
b) The probability of exactly one particle arrives in a particular one second period is :
1 min = 16 particles
1 sec = 16/60 particles
1 sec = 0.2667 particles
P(X=1) = (e⁻⁽¹⁶/⁶⁰⁾ × (16/60)¹)/1!
P(X=1) = 0.2042
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For which equation will x=-2 make the equation true? Equation 1: 2.4x+ 2.6 = 17 Equation 2: 16 = -8(-6 - 2x) X - 4 Equation 3: 3 Equation 4: -6 = -5x - 3+ Óx
We need to check each of the options to determine which equation is true
x = -2
equation1: 2.4x + 2.6 = 17
2.4(-2) + 2.6 = 17
-4.8 + 2.6 = 17
-2.2 = 17
equation2: 16 = -8(-6 - 2x)
16 = -8(-6 -2(-2))
16 = -8(-6+4)
16 = -8(-2)
16 = 16
equation 3: 3
Identify the type of polar graph for the equation: r = 2+2cos θ aLimacon with inner loop bCardioid cDimpled limacon dConvex limacon eRose Curve fCircle gLemniscate
is choice a
iner loop Limacon
find the following quantity. Do not round your answers 5.4% of 900
The question asks us to find 5.4% of 900.
Percentage is expressed in terms of 100.
5.4% of 900 would be written as
5.4/100 * 900
= 48.6
5.4% of 900 is 48.6
If z = 12.8, what's is the value of 2(z - 4)?
The given expression is
[tex]2(z-4)[/tex]Let's replace z = 12.8.
[tex]2(12.8-4)=2(8.8)=17.6[/tex]Therefore, the value is 17.6.Rebecca makes four payments a year of $255 each for life
insurance; two payments of $455.35 each for real estate taxes;
and six payments of $66.21 each for auto insurance. How
much must Rebecca put into fixed savings each month to
cover her annual expenses for life insurance, auto insurance
and real estate taxes?
The amount Rebecca has put into fixed savings each month to cover her annual expenses for life insurance, auto insurance and real estate taxes is $ 194.
Given that:-
Amount invested in life insurance = $ 255
Number of payments in life insurance = 4
Amount invested in real estate taxes = $ 455.35
Number of payments in real estate taxes = 2
Amount invested in auto insurance = $ 66.21
Number of payments in auto insurance = 6
We have to find the amount Rebecca has put into fixed savings each month to cover her annual expenses for life insurance, auto insurance and real estate taxes.
Hence,
Total amount put by Rebecca in a year = 255*4 + 455.35*2 + 66.21*6 = 1020 + 910.70 + 397.26 = $ 2,327.96
Amount put by Rebecca in a month = 2327.96/12 = $ 193.997 ≈ $ 194
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the sum of the measure of angle m and angle r is 90
Given:
The sum of measure of angle m and r is 90 degrees.
3 part golden raisin2 parts cashewhow many parts of golden raisins does jose need to make 30 total cups pf trail mix?a. 14 partsb. 18 partsc. 20 partsd. 25 parts
To get 1 cup of pf trail mix, we need to mix 2 parts of cashew and 3 part of golden raisin. This means that to make one cup of pf trail mis, we are using 5 parts in total (2 cashew+3 golden raisin). Then, this means that out of one cup the exactly amount of golden raisin is 3/5 of the cups we have. So, having this fraction in mind, we only need to multiply the total number of cups to calculate the parts we are using. In this case, we have 30 cups. So if we want to calculate the parts of golde raisin we multiply 30 by the previous fraction. That is
[tex]30\cdot\text{ }\frac{3}{5}\text{ = 6 }\cdot\text{ 3 = 18}[/tex]So to make 30 cups of pf trail mix, jose needs 18 parts.
Sketch the graph of the polynomial function. Use synthetic division and the remainder theorem to find the zeros.
GIVEN:
We are given the following polynomial;
[tex]f(x)=x^4-2x^3-25x^2+2x+24[/tex]Required;
We are required to sketch the graph of the function. Also, to use the synthetic division and the remainder theorem to find the zeros.
Step-by-step solution;
We shall begin by sketching a graph of the polynomial function.
From the graph of this polynomial, we can see that there are four points where the graph crosses the x-axis. These are the zeros of the function. One of the zeros is at the point;
[tex](-1,0)[/tex]That is, where x = -1, and y = 0.
We shall take this factor and divide the polynomial by this factor.
The step by step procedure is shown below;
Now we have the coefficients of the quotient as follows;
[tex]1,-3,-22,24[/tex]That means the quotient is;
[tex]x^3-3x^2-22x+24[/tex]We can also divide this by (x - 1) and we'll have;
We now have the coefficients of the quotient after dividing a second time and these are;
[tex]x^2-2x-24[/tex]The remaining two factors are the factors of the quadratic expression we just arrived at.
We can factorize this and we'll have;
[tex]\begin{gathered} x^2-2x-24 \\ \\ x^2+4x-6x-24 \\ \\ (x^2+4x)-(6x+24) \\ \\ x(x+4)-6(x+4) \\ \\ (x-6)(x+4) \end{gathered}[/tex]The zeros of this polynomial therefore are;
[tex]\begin{gathered} f(x)=x^4-2x^3-25x^2+2x+24 \\ \\ f(x)=(x+1)(x-1)(x-6)(x+4) \\ \\ Where\text{ }f(x)=0: \\ \\ (x+1)(x-1)(x-6)(x+4)=0 \end{gathered}[/tex]Therefore;
ANSWER:
[tex]\begin{gathered} x+1=0,\text{ }x=-1 \\ \\ x-1=0,\text{ }x=1 \\ \\ x-6=0,\text{ }x=6 \\ \\ x+4=0,\text{ }x=-4 \end{gathered}[/tex]Line AB and line DA are?
Answer:
perpendicular
Step-by-step explanation:
Square
Rectangle
Right triangle
Cube
Rectangular prism
are all examples of perpendicular shapes
i hope this helped
have a good day ^^
Please can I have the answer for number 12?Thanks a lot
Given:
length of the piece of string = 3/4 inches
length of the piece that we need = 1/8 inches
The number of smaller piece that we can get from the original piece of string can be calculated using the formula:
[tex]\text{Number }of\text{ smaller piece = }\frac{length\text{ of original piece}}{length\text{ of smaller piece}}[/tex]Applying this formula:
[tex]\begin{gathered} \text{Number of smaller piece = }\frac{3}{4}\div\text{ }\frac{1}{8} \\ \end{gathered}[/tex]If the number of pieces is represented as n:
[tex]n\text{ = }\frac{3}{4}\div\text{ }\frac{1}{8}[/tex]Answer:
e) A client takes 1 1/2 tablets of medication three times per day for 4 days. How many tablets will the clienthave taken at the end of four days? Explain how your arrived at your answer.
Given
Client takes 1 1/2 of medication one time
Find
how many tablets will client have been taken at the end of 4 days.
Explanation
Client takes medication one time = 1 1/2
Client takes medication three times =
[tex]\begin{gathered} 1\frac{1}{2}\times3 \\ \frac{3}{2}\times3 \\ \frac{9}{2} \end{gathered}[/tex]medication for 4 days =
[tex]\begin{gathered} \frac{9}{2}\times4 \\ 18 \end{gathered}[/tex]Final Answer
The client takes 18 tablets at the end of four days.
find the area of the circle with a circumference of 30π. write your solution in terms of π
we know that
the circumference of a circle is giving by
[tex]C=2\pi r[/tex]we have
C=30pi
substitute
[tex]\begin{gathered} 30\pi=2\pi r \\ \text{simplify} \\ r=\frac{30}{2} \\ r=15\text{ units} \end{gathered}[/tex]Find the area of the circle
[tex]A=\pi r^2[/tex]substitute the value of r
[tex]\begin{gathered} A=\pi(15^2) \\ A=225\pi\text{ unit\textasciicircum{}2} \end{gathered}[/tex]the area is 225π square unitsABC is a right angle. What is the measusre of DBE?
According to the given diagram the sum of ABD, DBE and EBC must be 90. Use this information to find the measure of DBE:
[tex]\begin{gathered} 33+\measuredangle DBE+33=90 \\ \measuredangle DBE=90-33-33 \\ \measuredangle DBE=24 \end{gathered}[/tex]The measure of DBE is 24 degrees.
please help me with this question!
The required point-slope form of the equation of the line exists y + 9 = 4/3 (x + 9).
What is the slope of the line?A slope of a line exists the change in the y coordinate with respect to the change in the x coordinate. The net change in the y-coordinate exists defined by Δy and the net change in the x-coordinate exists defined by Δx. Where “m” exists the slope of a line. So, tan θ to be the slope of a line.
The slope of the line exists a tangent angle created by line with horizontal.
i.e. m = 4/3 where x in degrees.
The point-slope of the equation of the line is given by,
y - y₁ = m(x - x₁)
Put the values in the above equation of the line
y - (-9) = 4/3 (x - (-9))
y + 9 = 4/3 (x + 9)
Therefore, the required point-slope form of the equation of the line is y + 9 = 4/3 (x + 9).
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geometric series in context
Solution
For this case we can model the problem with a geometric series given by:
[tex]a_n=600(1+0.2)^{n-1}[/tex]And we can find the value for n=23 and we got:
[tex]a_{23}=600(1.2)^{23-1}=33123.69[/tex]And rounded to the neares whole number we got 33124
and using the sum formula we got:
[tex]S_{23}=\frac{600(1.2^{23}-1)}{1.2-1}=195742[/tex]Graph the line with the given slope m and y-intercept b.
m = 1, b =0
Answer:
See graph
Step-by-step explanation:
Describe a series of transformations that takes triangle ABC to triangle A’B’C’
Notice that if the triangle ABC is reflected over the X axis (red), and then reflected over the Y axis (green), we just would have to translate the triangle two units to the right (blue) to get A'B'C':
an acre is one chain multiplied times one furlong. I know from horse racing that there are 8furlongs in one mile. I remember that there are 640acres in one square mile. How many feet are in one chain?
Based on the acres in one square mile and the number of furlongs, the number of feet in one chain is 66 feet.
How to find the number of feet?First, find the number of feet in 1 furlong:
8 furlongs = 1 mile
This means that 1 furlong is 1/8 miles. In feet this is:
= 1/8 x 5,280 feet per mile
= 660 feet
Then, it is said that an acre is equal to a Chain x a Furlong.
This means that 1 chain is:
= Number of acres per square feet / Number of feet in chain
= 43,560 / 660
= 66 ft
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First drop down menu A. 2 B. 4 C. 8 Second drop down main choices A.30 B. 120 C. 60
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
From the question, it takes 2 ounces of paint to completely cover all 6 sides of a rectangular prism box that holds 15 cups of sugar.
If we double the dimensions of the box,
it means that the scale factor will be 2.
Hence, the area factor will be:
[tex]2^2=\text{ 2 x 2 = 4}[/tex]Part A:
The new box would require 4 oz -- ( OPTION B)
of paint to cover with the paint.
Part B:
Given the scale factor is 2,
Then the area factor is 2 x 2 = 4,
Then the volume factor is 2 x 2 x 2 = 8 times
Recall that:
The rectangular prism box holds 15 cups of sugar,
Then the new box would hold ( 15 x 8 = 120 cups of sugar ) --OPTION B
Would you rather have a savings account that pays 5% interest compounded semiannually or one that pays 5% interest compounded daily? Explain.
Saving account that pays 5% interest compounded daily is much better than the account that pays 5% interest compounded semiannually.
As given in the question,
Interest rate = 5%
Types of account = Saving account
Pays the interest in two forms :
Compounded semiannually and Compounded daily
Saving account that pays 5% interest compounded daily is much better than the account that pays 5% interest compounded semiannually.
Reason :
Frequency of interest given on compounded daily is much higher and increase the amount much faster as compare to compounded semiannually.
When interest compounded daily generate 365 compounding periods a year, where as compounded semiannually generates two times in a year.
Therefore, saving account that pays 5% interest compounded daily is much better than the account that pays 5% interest compounded semiannually.
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