the error in the equation is 3 is not multiplied by 4 which gives wrong value of x .
What is the linear equation ?A linear equation is a first-order (linear) term and a constant in an algebraic equation of the type y=mx+b, where m is the slope and b is the y-intercept. The previous equation, which has the variables y and x, is sometimes referred to as a "linear equation with two variables."
The typical form for linear equations with two variables is Ax+By=C. For instance, the linear equation 2x+3y=5 is in standard form. Finding both the intercepts of an equation in this way is quite easy (x and y).
Calculation3 (x + 4) = 13
3x + 12 = 13 \\the place where the error was occurred in the question\\
3x = 1
x = 1/3
this is correct value of x
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Use synthetic division to find the quotient and remainder when
2x^3-9x² +14x-2 is divided by x-1.
Dividing (2x³ - 9x² + 14x - 2) by (x - 1) with synthetic division method given the remainder 5 and the quotient 2x² - 7x + 7 + (5/x-1).
What is synthetic division?One unique way to divide polynomials is by using the synthetic division method. This approach, where the leading coefficient should be equal to 1, is a special case of multiplying a polynomial expression by a linear factor. In the specific case of dividing by a linear factor, the synthetic division is a shorthand, or shortcut, method of polynomial division. However, the synthetic division is typically used to locate polynomial zeroes (or roots), not to divide out factors.So, 2x³ - 9x² + 14x - 2 ÷ x - 1 by synthetic division as follows:
(Refer to the images attached below for calculations)2x³ - 9x² + 14x - 2 ÷ x - 1:
Remainder: 5Quotient: 2x² - 7x + 7 + (5/x-1)Therefore, dividing (2x³ - 9x² + 14x - 2) by (x - 1) with synthetic division method given the remainder 5 and the quotient 2x² - 7x + 7 + (5/x-1).
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A survey of 600 school employees yielded the following information: 449 were instructors, 325 were full-time faculty, and 260 of the instructors were full-time faculty. How many of the 600 surveyed school employees were instructors or were full-time faculty?
Answer:
260+325 = 585
260 where instructors that were full time and 325 were already full time. this is correct if I am reading your question correctly if not the answer is likely 260
The total body surface area, or BSA, of a human is difficult to calculate. There are various models that estimate BSA based on a person's weight and height. One simpler model is
the height in the first case will be 191 cm and the weight in the second case will be 106 kg.
We are given the function as:
BSA = √( w h / 3600)
where:
h = height
w = weight
BSA = body surface area
1) Now, for w = 68 kg and BSA = 1.9, we get the height as:
1.9 = √( (68) h / 3600)
3.61 = 68 h / 3600
12,996 = 68 h
h = 12996 / 68
h = 191.12 cm
h ≈ 191 cm
2) for h = 165 cm and BSA = 2.2, we get the weight as:
2.2 = √( w (165) / 3600)
4.48 = 165 w / 3600
17424 = 165 w
w = 17424/ 165
w = 105.6 kg.
w ≈ 106 kg
Therefore, we get that, the height in the first case will be 191 cm and the weight in the second case will be 106 kg.
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What is the value of c?
14=-2c-6-3c
Answer:
-4
Step-by-step explanation:
14= -5c-6
+6 +6
________
20 = -5c
÷-5 ÷-5
________
-4 = c
based on the infomation in the table , is the cost of the apples proportional to the weight of apples?
pounds of apples cost of apples
2 3.76
3 5.64
4 7.53
5 9.40
The given table shows that does not show a proportional relationship, as the ratio between the output and the input is not the same for all terms of the table.
What is a direct proportional relationship?A direct proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality k, as defined below.
y = kx
In this problem, we have that:
The input x is the number of pounds of apples.The output y is the cost of the apples.To verify if it shows a proportional relationship, we have to divide the output by the input in each case, hence:
k = 3.76/2 = 1.88.k = 5.64/3 = 1.88.k = 7.53/4 = 1.8825.k = 9.40/5 = 1.88.Due to the different constant for 4 pounds, the table does not show a proportional relationship,
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what is equivalent to (x+7)^2 ?
1. x^2+49
2. (x-7)(x+7)
3. (x+7)(x+7)
4. (7x)(7x)
⇒In this case what is in the brackets is being treated as being the term . so this means that if we are to expand then we expand the whole term in full detail.
⇒In this case we have x+7 as the term of the expression which means when we expand we are going to expand the whole term x+7
[tex]=(x+7)^{2} \\=(x+7)(x+7)[/tex]
The third option is the answer.
GOODLUCK!!
I8. Last night, you spent a total of 51 minutes working on your homework problems for math andbiology. Each math problem takes 5 minutes to complete and each biology problem takes 3minutes to complete. You completed a total of 15 problems. Write a system of equations thatdetermines how many math problems and how many biology problems you completed lastnight.
Let x represent the number of math problems that you completed.
Let y represent the number of biology problems that you completed
From the information given,
You completed a total of 15 problems. This means that
x + y = 15
If each math problem takes 5 minutes to complete, it means that the time to complete x math problems is 5 * x = 5x
If each biology problem takes 3 minutes to complete, it means that the time to complete y biology problems is 3 * y = 3y
If you spent 51 minutes working on your homework problems for math and
biology, it means that
5x + 3y = 51
Thus, the system of equations is
x + y = 15
5x + 3y = 51
[tex]5(\frac{x+5}{9} )-9[/tex]
Answer:
I don't know
Step-by-step explanation:
I don't know
8−8, minus
=-5=−5 AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
Answer:
AAAAAAAAAA
Step-by-step explanation: AAAAAAAAAAAAAAAA
answer this question please
a. Absolute value function the reference beam is g(x) = |8x/5|.
b. g(x) = +8x/5 ; x < 5 and g(x) = -8x/5 > 5.
What is defined as the absolute value function?An absolute value function is one that has an algebraic expression enclosed in absolute value symbols. Remember that a number's absolute value is its distance from 0 just on number line.For the given function;
Part a: The reference beam is passing from the points;
(x₁, y₁) = (5, 8)
(x₂, y₂) = (0, 0)
Then the slope of the line is -
m = (y₂ - y₁)/(x₂ - x₁)
Put the values ;
m = (0 - 8)/(0 - 5)
m = 8/5
The equation of the line is;
y - y₁ = m(x - x₁)
Put the values;
y - 0 = 8/5(x - 0)
y = 8x/5
Or in absolute modulus function for the path of reference beam; y = |8x/5|.
Part b: absolute function in terms of piecewise function;
g(x) = +8x/5 ; x < 5 as the slope is increasing.
and g(x) = -8x/5 > 5.; as the slope is decreasing.
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y varies directly with x, and y = 40in when x = 15in
If y varies directly with x, that means there is going to be a constant that connects both the x and y variable.
[tex]\begin{gathered} \text{When x=15, and y=40, then} \\ k=\frac{y}{x} \\ k=\frac{40}{15} \\ k=\frac{8}{3} \\ \text{Therefore, the equation is going to be;} \\ y=\frac{8}{3}x \end{gathered}[/tex]The appropriate direct variation equation is stated above, and that is;
y = 8/3x
Name all transformations of the following function
Notice that the parent function of y is:
[tex]f(x)=\sqrt{x}.[/tex]Now, recall that a function h(x) translated n units to the left is represented by:
[tex]h(x+n),[/tex]translated m units up :is represented by
[tex]h(x)+m,[/tex]reflected across the x-axis :is represented by
[tex]-h(x),[/tex]vertically compressed by a factor of 1/k :is represented by
[tex]\frac{1}{k}h(x).[/tex]Therefore, y is f(x) translated 3 units to the left, reflected over the x-axis, vertically compressed, and translated 2 units up.
Answer:y is its parent function translated 3 units to the left, reflected over the x-axis, vertically compressed, and translated 2 units up.
Which ratio is equivalent to 9/78.
A: 1/8
B: 3/26
C: 1/3
D: 3/18
Answer:
3/26
Step-by-step explanation:
you simply divide both numbers by there largest lcm which is 3
9/3=3
78/3=26
Together 3/26
10. An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 4 cm long. A second side of the triangle is 7.4 cm long. Find the longest and shortest possible lengths of the third side of the triangle.
Round answers to the nearest tenth of a centimeter.
O 44.4 cm, 11.1 cm
11.1 cm 49 cm
O 24 cm 49 cm
444 cm, 3.2 cm
The longest and shortest possible lengths of the third side of the triangle are 4.9 cm and 11.1 cm.
What does the Angle Bisector Theorem state?It states that the opposite side of a triangle is divided into segments by each angle bisector that are proportional in length to the adjacent sides.
Given:
An angle bisector divides the opposite side of the triangle into segments 6 cm and 4 cm long.
Second side of the triangle is 7.4 cm.
We have to calculate the longest and shortest possible lengths of the third side of the triangle.
By Angle Bisector Theorem we can solve this problem,
In the triangle ABC, AD is the angle that bisects angle A, placing D on side BC.
Now, BD / DC = AB / AC
BC = 6 + 4 = 10 cm
Angle bisector divides BC into 2 segments,
BD = 6 cm
CD = 4 cm
If AB = 7.4 cm,
6/4 = 7.4 / AC
AC = 7.4(4) / 6
AC = 29.6 / 6
AC = 4.94 cm (shortest possible length of the third side of the triangle)
If AC = 7.4 cm
6/4 = AB/7.4
AB = 6(7.4)/4
AB = 44.4/4
AB = 11.1 cm (longest possible length of the third side of the triangle)
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Sort the following into either terminating or non-terminating categories. 2%, 3/4, 105/15, 1/3, 15/7, 81/11
Terminating
Non-Terminating
The terminating category consists of 2%, 3/4, and 105/15.
The non-terminating category consists of 1/3, 15/7, and 81/11.
What are terminating and non-terminating decimals?Decimals with an end digit are said to be terminating decimals. The number of digits in a decimal, which it is, is finite (or terms). Examples include 0.15, 0.86, etc. The decimals without a terminal are known as non-terminating decimals. The number of terms in it is unlimited.Given: 2%, 3/4, 105/15, 1/3, 15/7, 81/11
To determine whether these fractions are terminating or non-terminating decimals,
2% = 2/100 = 0.02
It is a terminating decimal.
3/4 = 0.75
It is a terminating decimal.
105/15 = 7
It is an integer, hence terminating.
1/3 = 0.3333333...
It is a non-terminating decimal.
15/7 = 2.14285714
It is a non-terminating decimal.
81/11 = 7.36363636
It is a non-terminating decimal.
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what is the slope and y intercept of 4x + 7y=18?
Answer:
-4/7, 18/7
Step-by-step explanation:
[tex]4x+7y=18 \\ \\ 7y=-4x+18 \\ \\ y=-\frac{4}{7}x+\frac{18}{7}[/tex]
The table below displays results from experiments with polygraph instruments. Find the positive predictive value for the test. That is, find the probability that the subject lied, given that the test yields a positive result.
_ No_(Did_Not_Lie) Yes_(Lied)
Positive_test_results 10 45
Negative_test_results 34 12
Using it's concept, the probability that the subject lied, given that the test yields a positive result is of 9/11 = 0.8182 = 81.82%.
What is a probability?The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.
In this problem, we want to find the probability that the subject lied, given that the test yields a positive result, hence:
The total outcomes are the tests resulting in a positive.The desired outcomes is the number of tests out of those positive in which the subject lied.From the table, we have that:
There were 10 + 45 = 55 positive test results.In 45 of those tests, the subject lied.Hence the probability is given as follows:
p = 45/55 = 9/11 (simplifying by 5)
p = 9/11 = 0.8182 = 81.82%.
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The recipe for junk crunchies requires a total of 8 cups of sugar and flour together. If the recipe had called for 1/4 cup more sugar, the amount of sugar would be half the amount of flour. How many cups of sugar does the recipe call for?
The recipe of the junk calls for 16/7 cups of sugar
How to determine the number of cups of sugar in the recipe?From the question, the given parameters are:
Total number of cups = 8
Let the number of cups of sugar be x and the number of cups of flour be y
So, we have the following equation
x + y = 8
Also, we have:
The recipe uses 1/4 cup more sugar, so the amount of sugar equals half the amount of flour
This means that
(1 + 1/4) * x = 1/2 * y
Evaluate the sum and the products
So, we have
5/4x = 1/2y
Make y the subject
y = 5/2x
Substitute y = 5/2x in x + y = 8
x + 5/2x = 8
Evaluate the sum
3.5x = 8
Divide by 3.5
x = 16/7
Hence, the cups of sugar is 16/7
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The mean per capita income is $21,604 per annum with the standard deviation of $727 per annum. What is the probability that the sample mean will be less than $21,635 if a sample of 193 persons is randomly selected? Round your answer to four decimal places
Explanation
In the question, we are given that
[tex]\begin{gathered} \mu=21,604 \\ \sigma=$ 727 $ \\ n=193 \end{gathered}[/tex]First, we will get the standard deviation of the sample mean as
[tex]\sigma_x=\frac{\sigma}{\sqrt{n}}=\frac{727}{\sqrt{193}}=52.3306[/tex]Then, we can find the probability that the sample mean will be less than $21,635 for a sample of 193 persons
[tex]\begin{gathered} P(\bar{X}<21635)=P(z<\frac{\bar{X}-\mu}{\sigma_x})=P(z<\frac{21635-21604}{52.3306}) \\ =P(z<0.59238) \end{gathered}[/tex]Therefore, using the z score calculator
[tex]P(z<0.59238)=0.7232[/tex]Answer: 0.7232
Solve each equation mentally.
a. ½ ·x = 1
b.x = 1
c. 1 + 1 = x
A.) [tex]x = 2[/tex]
B.) [tex]x=1[/tex] (Nothing further can be done with this.)
C.) [tex]x=2[/tex]
_____________________________________
Hope this helps! If not, feel free to comment below on the matter and I'll see what else I can do to assist you further. If it did help though, feel free to lmk! Thanks and good luck!
m - a + n + p , for a
The expression m = a + n + p can be written as a = m - n - p after making the subject a.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
The expression is:
m = a + n + p
To solve for a make the subject as a:
a = m - n - p
Thus, the expression m = a + n + p can be written as a = m - n - p after making the subject a.
The question is incomplete.
The complete question is:
Solve for a, if the expression is m = a + n + p.
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Marie is calculating an annuity payment. Her mortgage of $200,000 compounds monthly for 30 years. What is the nt value she will use in her formula?
Based on the annuity payment that Marie will make and the number of years, the nt value that she will use in her formula is 360 months.
How to find the nt value?The nt value is the number of periods that Marie will need to pay her annuity payment. This value can be yearly, monthly, weekly and even daily.
As the mortgage compounds monthly in this instance, the nt value will need to be monthly as well.
To find the nt value, the formula is:
= Number of years x number of compounding periods per year
= 30 x 12 times a year
= 360 months
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Answer:
360
Step-by-step explanation:
i did that and i got it right
how much does $3000 earn in 6 months at in interest rate of 4%, compounded quarterly?
The amount earned by $3000 deposited in the account after 6 months is $60.30
What does quarterly compounding mean?
Quarterly compounding means that the interest is computed and credited to the account every quarter, that is every 3 months, in other words, our future value formula would indicate quarterly interest rate rather than an annual interest rate
FV=PV*(1+r)^N
FV=the amount in the account after 6 months=unknown\
PV=initial amount deposited in the account=$3,000
r=quarterly interest rate=4%/4=0.01
N=number of quarters in 6 months=2
FV=$3000*(1+0.01)^2
FV=$3000*(1.01)^2
FV=$3000*1.0201
FV=$ 3,060.30
amount earned=FV-PV
amount earned=$3060.30-$3000
amount earned=$60.30
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help with this please
Consider the given radical,
[tex]\sqrt[]{128}[/tex]Factorize the number,
[tex]128=2^7[/tex]Consider the following properties,
[tex]\begin{gathered} a^{m+1}=a^m\times a \\ a^{mn}=(a^m)^n \end{gathered}[/tex]Then the radical can be simplified as,
[tex]\sqrt[]{128}=\sqrt[]{2^7}=\sqrt[]{2^6\times2}=\sqrt[]{64\times2}=\sqrt[]{64}\times\sqrt[]{2}[/tex]Thus, the radical is simplified as,
[tex]\sqrt[]{128}=\sqrt[]{64}\times\sqrt[]{2}=8\sqrt[]{2}[/tex]What is the approximate area of the shaded sector of the circle?
The formula for the area(A) of the sector is,
[tex]A=\frac{\theta}{360}\times\pi r^2[/tex]Given:
[tex]\begin{gathered} \theta=139^0 \\ r=4m \end{gathered}[/tex]Therefore,
[tex]A=\frac{139^0}{360^0}\times\pi\times4^2[/tex]Simplify
[tex]\begin{gathered} A=\:19.40806\approx19.41\text{ \lparen2 decimal places\rparen} \\ \therefore A=19.41m^2 \end{gathered}[/tex]Hence,
[tex]A=19.41m^2\text{ \lparen OPTION D\rparen}[/tex]Find the surface area of the ball shown to the right .The ball has a surface of _ cm2(Simplify your answer .Type an exact answer in terms of pie.)
Surface area of a sphere: 4 π r^2
Where:
r = radius = d/2 = 14/2 = 7
Replacing
SA = 4 π 7^2 = 4 π 49 = 196π cm2
find the slope of line passing through each of the following pairs of points and draw the graph of the line. (4,3), (2,2)
The slope of line passing through the pair of points (4,3) and (2,2) is 1/2.
What is the slope of the line with the given coordinates of points?Slope is simply expressed as change in y-values over the change in x-values.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Given the data in the question;
Point 1( 4,3 )
x₁ = 4y₁ = 3Point 2( 2,2 )
x₂ = 2y₂ = 2Slope m = ?
Plug the given coordinates into the slope formula and solve for m.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 2 - 3 )/( 2 - 4 )
Slope m = ( -1 )/(-2 )
Slope m = ( 1 )/( 2 )
Slope m = 1/2
Therefore, the slope of the line segment with the given coordinates is 1/2.
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A figure is dilated by a factor of 3. Which of following statements about the image of the figure is true?
When an image is dilated by a factor of 3, the statement about the image of the figure that is true is Both the area and the perimeter increase.
What happens when a shape is dilated?When a shape is dilated, the effect on the shape is that its dimensions are made to be longer. For instance, a shape dilated by 2 would see all its dimensions increase by 2.
In the case of a figure that is dilated by a factor of 3, it means that the shape would increase by 3 in size.
The effect of this is that the perimeter would increase by 3. The area of the figure would also increase thanks to the increase in dimensions by 3.
Options for this question include:
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Consider the matrices.
What operations are defined for these matrices?
Drag the operation to the boxes to correctly complete the table.
[0]. and Q = []
00
Answer:
Defined: M-N
Not defined: Q+P, M+P, L-N
Step-by-step explanation:
Just took the test
The graph shows the number of states and Washington, DC, within each range of electoral votes for the 2020 presidential election. Which interval contains 11 states? Check all that apply.
0 to 3
3 to 6
6 to 9
9 to 12
12 to 15
15 to 18
18 to 21
Based on the number of states and their electoral votes in the 2020 presidential election, the intervals with 11 states are:
3 to 66 to 9How to find the intervals?The graph on electoral votes by state in 202, gives the number of electoral votes as a range from 0 to 21 but in intervals of 3.
In 0 - 3 electoral votes, the number of states is 16.
In 3 - 6 electoral vote interval, number of states is 11.
In 6 - 9 electoral vote interval, number of states is 11.
In 9 - 12 electoral vote interval, number of states is 3.
In 12 - 15 electoral vote interval, number of states is 3.
In 15 - 18 electoral vote interval, number of states is 3.
In 18 - 21 electoral vote interval, number of states is 4.
The two intervals with 11 states are therefore 3 - 6 and 6 - 9.
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