x Michael uses synthetic division to divide f(x) by g(x), his last line of work 0/3is shown. How would he write his answer of f(x) divided by g(x). *7 0 24 0 07x^2+24Х
We know that the last line of the synthetic division is 7
Person A went to the store and bought some books at $12 each and some DVDs at $15 each. The bill (before tax) was less than $120. Which inequality represents the situation if x=books and y=DVDs?A) 12x+15y = 120B) 12x+15y < 120C) 12x+15y >-D) none of the above
Since the cost of each book is $12, and x is the number of books, the total cost of books will be 12x.,
Similarly, since the cost of each DVD is $15, and y is the number of DVDs, the total cost of DVDs will be 15y.
Thus, the total cost of books and DVDs will be 12x + 15y.
We know that the total cost was less than $120, so this expression should be less than 120.
Thus, the inequality is:
[tex]12x+15y<120[/tex]Which corresponds to alternative B.
To check wether the amount in the alternatives can be purchased, we just need to substitute x and y and check wether the inequality is valid:
A
[tex]\begin{gathered} 12\cdot5+15\cdot5<120(?) \\ 60+75<120(?) \\ 135<120\to invalid \end{gathered}[/tex]B
[tex]\begin{gathered} 12\cdot6+15\cdot2<120(?) \\ 72+30<120(?) \\ 102<120\to valid \end{gathered}[/tex]C
[tex]\begin{gathered} 12\cdot2+15\cdot6<120(?) \\ 24+90<120(?) \\ 114<120\to valid \end{gathered}[/tex]D
[tex]\begin{gathered} 12\cdot0+15\cdot10<120(?) \\ 0+150<120(?) \\ 150<120\to invalid \end{gathered}[/tex]E
[tex]\begin{gathered} 12\cdot8+15\cdot0<120(?) \\ 96+0<120(?) \\ 96<120\to valid \end{gathered}[/tex]Thus, the amounts that could have been purchased are thouse in alternatives B, C and E.
a monument that is 169.4 ft tall is built on a site that is 67.3 Ft below sea level how many feet above sea level is the top of the monument
Answer:
102.1 ft
Explanation:
We can represent the situation as follows:
So, we need to find the value of H. Therefore, H is equal to:
H = 169.4 ft - 67.3 ft
H = 102.1 ft
So, the top of the monument is 102.1 ft above sea level.
Use the followingA test has 28 questions that total 100 points. The test contains multiple choice questions that areworth 3 points each and short answer questions that are worth 5 points each15. Write a system of finear equations to represent the situation16. Write a matrix equation that corresponds to the system in question 15.17. Solve the system using matrices to determine how many multiple choice and short answerquestions are on the test
The equations are:
x + y = 28 ...............................................(1)
3x + 5y = 100 .........................................(2)
Explanation:Parameters:
Total questions = 28
Total points = 100
Mulitple choice questions = 3 points each
Short answer quesitons = 5 points
Let x represent the number of multiple choice question, and y be the number of short answer
x + y = 28 ...............................................(1)
3x + 5y = 100 .........................................(2)
In a matrix form, this is:
[tex]\begin{bmatrix}{1} & {1} \\ {3} & {5}\end{bmatrix}\begin{bmatrix}{x} \\ {y}\end{bmatrix}=\begin{bmatrix}{28} \\ {100}\end{bmatrix}[/tex]Solving the above, we have:
[tex]undefined[/tex]according to a census, there were 66 people per square mile (population density) in a certain country in 1980. By 2000, the # of people per square mile had grown to 76. This information was used to develop a linear equation in slope intercept form, given below, where x is the time in years and y is the population density. Think of 1980 as year zero. what is the population density expected to be in 2018? y = 1/2x + 66
Determine the value of x for taking 1980 as 0.
[tex]\begin{gathered} x=2018-1980 \\ =38 \end{gathered}[/tex]The equation is y = 1/2x + 66.
Substitute the value of x in the equation to determine the population density in 2018.
[tex]\begin{gathered} y=\frac{1}{2}\cdot38+66 \\ =19+66 \\ =85 \end{gathered}[/tex]So population density in year 2018 is 85.
Answer: 85
which figure can we transformee into figure k by a reflection across the x-axis and dilation of 1/2.
The rule for reflecting a point through the x-axis is (x, -y) and to dilation is (1/2x, 1/2y):
Now, let's se what figure can be transformed into figure K:
J
(8, 4), reflecting through x-axis (8, -4), dilation (4, -2) --> This point meets figure K
Let's prove with another point of J:
(4, 4) ---> (4, -4) ---> (2, -2) --> This point also meets figure K
Then we can say that figure J can be transformed into figure K
. Find the value of the variables in the rhombus below. B A 0
As the triangles are congruent and isosceles we get that
[tex]\begin{gathered} B=37=A=D \\ C=180-2\cdot37=106 \\ 24=4x-4 \\ 4x=28\rightarrow x=\frac{28}{4}=6 \end{gathered}[/tex]2. Identify the vertex from the quadratic function y=-5(x-6)^2+8 *2 points(-5, 6)(-6,8)(6,8)(8,6
Answer
2) Option C is correct.
The vertex of the quadratic function is at
x = 6, y = 8.
In coordinate form, the vertex = (6, 8)
4) Option A is correct.
-3 stretches the graph and reflects it about the x-axis.
Explanation
2) We are told to find the vertex of the quadratic function. The vertex of a quadratic function is the point at the base of the curve/graph of the function. It is the point where the value of the quadratic function changes sign.
The x-coordinate of this vertex is given as
x = (-b/2a)
The y-coordinate is then obtained from the value of the x-coordinate.
The quadratic function for the question is
y = -5 (x - 6)² + 8
We first need to put the quadratic function in the general form of
y = ax² + bx + c
So, we first simplify the expression
y = -5 (x - 6)² + 8
= -5 (x² - 12x + 36) + 8
= -5x² + 60x - 180 + 8
y = -5x² + 60x - 172
So,
a = -5
b = 60
c = -172
For the vertex
x = (-b/2a)
= [-60/(2×-5)]
= [-60/-10]
= 6
So, if x = 6.
y = -5x² + 60x - 172
y = -5(6²) + 60(6) - 172
y = -5(36) + 360 - 172
y = -180 + 360 - 172
y = 8
So, the vertex of the quadratic function is at
x = 6, y = 8.
In coordinate form, the vertex = (6, 8)
Option C is correct.
4) y = -3(x²)
The graph of x² is a parabola, but multiplying the function x² by -3 transforms the graph.
The 3, because it is greater than 1, stretches or enlarges the graph.
And the minus sign in front of the 3, ,that is, -3 reflects the graph about the x-axis.
So, altogether, -3 stretches the graph and reflects it about the x-axis.
Option A is correct.
Hope this Helps!!!
if you can make one scarf with 3/5 of a ball of yarn how many can you make with 15 balls of yarn?
Explanation:
To find out how many scarfs you can make with 15 balls of yarn we have to divide 15 by 3/5, because with 3/5 you can make 1 scarf:
[tex]15\colon\frac{3}{5}=\frac{15\cdot5}{3}=\frac{75}{3}=25[/tex]Answer:
WIth 15 balls of yarn you can make 25 scarfs
Given the following exponential function, identify whether the change representsgrowth or decay, and determine the percentage rate of increase or decrease y=5600(1.07)^x
y= 5600 (1.07)^x
Base = 1.07
When the base of an exponential function is greater than one, it represents growth.
We can rewrite the base as:
1.07 = 1+r= 1 +0.07
r=0.07
r= increase rate
Percentage rate of increase = 0.07 x 100 = 7%
1 What is the image of (12,-8) after a dilation by a scale factor of 4 centered at the origin? 12.4) b 18-32) 13,-2)
A dilation of a point by a factor of 4 means that its coordinates will be multiplied by 4, so the image of the point (x,y) after the dilation will be (4x,4y). With this in mind, let's solve the problem:
[tex]H\text{ = }(12\cdot4,-8\cdot4)=(48,-32)[/tex]The answer is (48,-32).
Given f(x)= -3x^3 - 8x^2 - x + 8 andg(x)= 3x^3 - 6x^2 - 8x - 8What would (f-g)(x) and (f-g)(-1) be?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
f(x)= -3x³ - 8x² - x + 8
g(x)= 3x³ - 6x² - 8x - 8
Step 02:
functions:
(f - g)(x):
(f - g)(x) = -3x³ - 8x² - x + 8 - (3x³ - 6x² - 8x - 8)
(f - g)(x) = -3x³ - 8x² - x + 8 - 3x³ + 6x² + 8x + 8
(f - g)(x) = - 6x³ - 2x² + 7x + 16
(f - g)(-1):
(f - g)(-1) = - 6(-1)³ - 2(-1)² + 7(-1) + 16
(f - g)(-1) = - 6(-1) - 2(1) + 7(-1) + 16
(f - g)(-1) = 6 - 2 - 7 + 16
(f - g)(-1) = 13
That is the full solution.
Find the area of the polygon. 17 ft 14 ft 4 ft- 3 ft 4 ft The area of the polygon is (Type a whole number.)
Notice that the polygon can be divided on 3 rectangles, as shown in the following diagram:
The 14 ft side on the original image was split on a segment of 10ft and another of 4ft.
The areas of these rectangles, are:
[tex]\begin{gathered} A_1=(17ft)(10ft)=170ft^2 \\ A_2=(4ft)(3ft)=12ft^2 \\ A_3=(4ft)(4ft)=16ft^2 \end{gathered}[/tex]The total area of the polygon is the sum of the areas of the three rectangles:
[tex]\begin{gathered} A=170ft^2+12ft^2+16ft^2 \\ =198ft^2 \end{gathered}[/tex]Therefore, the area of the polygon is:
[tex]198ft^2[/tex]_________ ____________ allows us to derive new facts quickly from those we know. (spelling counts)
Derived Facts allows us to derive new facts quickly from those we know.
What is a derived fact?
Derived facts are math facts that are derived from known facts. For example, if we know the doubles fact, 3+3=6, then we can derive the answer to 3+4 by using the 3+3 fact and adding 1 to it. So a derived fact strategy is the mental process of deriving a new fact from a known fact.
What is a related fact example?
We say: Two plus One equals Three. We can also use these same three numbers in our math fact: 2, 1, and 3 to make a related fact. This time our math fact will read: 1 + 2 = 3 because we added 1 and then 2 to get a total of 3.
What are the 3 phases of multiplication fact mastery?
Phase 1: Modeling or counting to find the answer.
Phase 2: Deriving answers using reasoning strategies based on known facts.
Phase 3: Efficient production of answers (Mastery).
Hence the answer is Derived Facts allows us to derive new facts quickly from those we know.
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I need a little help understanding this
I'm going to use the letters L and W for the length and the width of the granite rectangle. We know that the length is 3 times the width. With this information we can build the following equation:
[tex]3W=L[/tex]We also know that the perimeter of the section must be less than 320 inches. The perimeter of a rectangle is giving by two times its length plus two times its width. Then we have the equations:
[tex]\begin{gathered} \text{Perimeter}=2L+2W \\ \text{Perimeter}<320 \\ 2L+2W<320 \end{gathered}[/tex]Since we know that L=3W then:
[tex]\begin{gathered} L=3W \\ W=\frac{L}{3} \end{gathered}[/tex]Now that we know that W=L/3 we can substitute L/3 in place of W on the inequality I wrote before:
[tex]\begin{gathered} 2L+2W<320 \\ 2L+2\cdot\frac{L}{3}<320 \\ \frac{8}{3}L<320 \\ L<320\cdot\frac{3}{8} \\ L<120 \end{gathered}[/tex]This means that the length must be less than 120 inches. This is the same as statement D which is the answer for this problem.
Calculate the volume of the figure.*2 pointsCaptionless ImageA) 273 in^3B) 50 in^3C) 260 in^3D) 176 in^3
The volume of a rectangle is:
[tex]\begin{gathered} V=\text{ lenght x width x height} \\ V=\text{ 13 in x 10 in x 2 in} \\ V=\text{ 260 in}^3 \end{gathered}[/tex]The answer is C. 260 in^3
Sketch vector v. Be sure to number your axes. Then find the magnitude of vector v. Show all work.
Step 1
Sketch the vector V.
[tex]v=-2i\text{ +5j}[/tex]Step 2
Find the magnitude of the vector. The magnitude of a vector is given as;
[tex]\begin{gathered} |v|=\sqrt{(i)^2+(j)^2} \\ i=-2 \\ j=5 \\ \left|a+bi\right|\:=\sqrt{\left(a+bi\right)\left(a-bi\right)}=\sqrt{a^2+b^2} \end{gathered}[/tex][tex]\begin{gathered} |v|=\sqrt{(-2)^2+(5)^2} \\ |v|=\sqrt{4+25} \\ |v|=\sqrt{29} \end{gathered}[/tex]Therefore, the magnitude is given as;
[tex]|v|=\sqrt{29}[/tex]Is the line through points P(3, -5) and 2(1, 4) parallel to the line through points R(-1, 1) and S(3,Explain.
As given by the question
There are given that the two-point;
[tex]\begin{gathered} P(3,\text{ -5) and Q(1, 4)} \\ R(-1,\text{ 1) and S(3, -3)} \end{gathered}[/tex]Now,
First, find the slope of both of the lines from the point
Then,
For first line:
[tex]\begin{gathered} PQ(m)=\frac{y_2-y_1}{x_2-x_1} \\ PQ(m)=\frac{4_{}+5_{}}{1_{}-3_{}} \\ PQ(m)=\frac{9}{-2} \\ PQ(m)=-\frac{9}{2} \end{gathered}[/tex]Now,
For the second line:
[tex]\begin{gathered} RS(m)=\frac{y_2-y_1}{x_2-x_1} \\ RS(m)=\frac{-3_{}-1_{}}{3_{}+1_{}} \\ RS(m)=-\frac{4}{4} \\ RS(m)=-1 \end{gathered}[/tex]Since both slopes are different, they are not parallel lines, which means parallel lines have the same slope.
Hence, the correct optio
Someone help how do I find if it’s a function
To know if this is a function, simply perform a vertical line test on it.
If it passed the vertical line test then it is a function but if it fails it then it is not a function
In the graph given, if you draw a vertical point at any point, we woulld not have two points on the vertical line, hence it is a function
write an equation of the line that satisfies the given conditions. give the equation (a) in slope intercept form and (b) in standard form. m=-7/12 ,(-6,12)
Given the slope of the line:
[tex]m=-\frac{7}{12}[/tex]And this point on the line:
[tex](-6,12)[/tex](a) By definition, the Slope-Intercept Form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
In this case, you can substitute the slope and the coordinates of the known point into that equation, and then solve for "b", in order to find the y-intercept:
[tex]12=(-\frac{7}{12})(-6)+b[/tex][tex]12=\frac{42}{12}+b[/tex][tex]\begin{gathered} 12=\frac{42}{12}+b \\ \\ 12=\frac{7}{2}+b \end{gathered}[/tex][tex]\begin{gathered} 12-\frac{7}{2}=b \\ \\ b=\frac{17}{2} \end{gathered}[/tex]Therefore, the equation of this line in Slope-Intercept Form is:
[tex]y=-\frac{7}{12}x+\frac{17}{2}[/tex](b) The Standard Form of the equation of a line is:
[tex]Ax+By=C[/tex]Where A, B, and C are integers, and A is positive.
In this case, you need to add this term to both sides of the equation found in Part (a), in order to rewrite it in Standard Form:
[tex]\frac{7}{12}x[/tex]Then, you get:
[tex]\frac{7}{12}x+y=\frac{17}{2}[/tex]Hence, the answers are:
(a) Slope-Intercept Form:
[tex]y=-\frac{7}{12}x+\frac{17}{2}[/tex](b) Standard Form:
[tex]\frac{7}{12}x+y=\frac{17}{2}[/tex]The probability distribution for arandom variable x is given in the table.Х- 10-505101520Probability.20.15.05.1.25.1.15Find the probability that x = -10
To find the probability of a distribution given in table form we have to look for the x we are searching and see its corresponding probability in the table.
In this case we notice that to x=-10 corresponds the probability .20, therefore:
[tex]P(x=-10)=0.20[/tex]To help pay for culinary school, Susan borrowed money from an online lending company.
She took out a personal, amortized loan for $52,000, at an interest rate of 5.65%, with monthly payments for a term of 15 years.
For each part, do not round any intermediate computations and round your final answers to the nearest cent.
If necessary, refer to the list of financial formulas.
(a) Find Susan's monthly payment.
$0
(b) If Susan pays the monthly payment each month for the full term,
find her total amount to repay the loan.
$0
(c) If Susan pays the monthly payment each month for the full term,
find the total amount of interest she will pay.
$0
Susan's monthly payment is $4578.2, Susan pays the monthly payment each month for the full term, then 54938 is amount to repay the loan and If Susan pays the monthly payment each month for the full term, then 2938 is the total amount of interest she will pay.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
Susan took out a personal, amortized loan for $52,000, at an interest rate of 5.65%, with monthly payments for a term of 15 years.
5.65% of 52000
5.65/100×52000
0.0565×52000
2938
2938+52000=54938
Ina year we will have 12 months.
So let us divide 54938 by 12
54938/12=4578.2
Susan's monthly payment is $4578.2
If Susan pays the monthly payment each month for the full term, then 54938 is amount to repay the loan.
If Susan pays the monthly payment each month for the full term, then 2938 is the total amount of interest she will pay.
Hence Susan's monthly payment is $4578.2, Susan pays the monthly payment each month for the full term, then 54938 is amount to repay the loan and If Susan pays the monthly payment each month for the full term, then 2938 is the total amount of interest she will pay.
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Use the value of x to find the measure of Angle 1.x=25 5x-5 2x+10
Given:
• x = 25
,• ∠1 = 5x - 5
,• ∠2 = 2x + 10
Let's find the measure of angle 1.
To find the measure of angle 1, substitute 25 for x in (5x - 5) and evaluate.
We have:
m∠1 = 5x - 5
m∠1 = 5(25) - 5
m∠1 = 125 - 5
m∠1 = 120
Therefore, the measure of angle 1 is 120 degrees.
ANSWER:
∠1 = 120°
Write 3 equivalent ratios for 5:8
Given data:
The given ratio is a=5:8.
Multiply 2 on numerator and denominator both.
[tex]\begin{gathered} a=\frac{2(5)}{2(8)} \\ =\frac{10}{16} \end{gathered}[/tex]Multiply 3 on numerator and denominator both.
[tex]\begin{gathered} a=\frac{3(5)}{3(8)} \\ =\frac{15}{24} \end{gathered}[/tex][tex]\begin{gathered} a=\frac{4(5)}{4(8)} \\ =\frac{20}{32} \\ \end{gathered}[/tex]When solving the equation 15 = -3x + 3, the first step would be
Answer:
Subtract 3 from both sides
Step-by-step explanation:
When solving a linear equation, you need to get all the constants to one side and all the variable terms to the other side. In the equation 15=-3x+3, there is one constant on the left, and a variable term and a constant on the right. You have to move the constant, in this case 3, to the left side in order to solve. To do this, you perform the opposite operation, so in this case, you would subtract 3 from both sides. The 3 on the right will cancel out with the minus three, so you will have a zero on the right side, which can just be removed. You are left with 12=-3y.
what is 8q= 96 what is it?
To find the value of q, divide both sides of the equation by 8:
[tex]\begin{gathered} 8q=96 \\ \Rightarrow\frac{8q}{8}=\frac{96}{8} \end{gathered}[/tex]Simplify both members of the equation:
[tex]\begin{gathered} \Rightarrow q=\frac{96}{8} \\ \Rightarrow q=12 \end{gathered}[/tex]Therefore:
[tex]q=12[/tex]differentiatey = 3x√x⁴-5
Given:
[tex]y=3x\sqrt{x^4-5}[/tex]Required:
We need to differentiate the given expression.
Explanation:
Consider the given expression.
[tex]y=3x\sqrt{x^4-5}[/tex][tex]y=3x(x^4-5)^{\frac{1}{2}}[/tex]Differentiate the given expression with respect to x.
[tex]Use\text{ }(uv)^{\prime}=uv^{\prime}+vu^{\prime}.\text{ Here u=3x and v=}(x^4-5)^{\frac{1}{2}}.[/tex][tex]y^{\prime}=3x(\frac{1}{2})(x^4-5)^{\frac{1}{2}-1}(4x^3)+(x^4-5)^{\frac{1}{2}}(3)[/tex][tex]y^{\prime}=\frac{3x(4x^3)}{2\left(x^4-5\right)^{\frac{1}{2}}}+3(x^4-5)^{\frac{1}{2}}[/tex][tex]y^{\prime}=\frac{6x^4}{\left(x^4-5\right)^{\frac{1}{2}}}+3(x^4-5)^{\frac{1}{2}}[/tex][tex]y^{\prime}=\frac{6x^4}{\left(x^4-5\right)^{\frac{1}{2}}}+\frac{3(x^4-5)^{\frac{1}{2}}(x^4-5)^{\frac{1}{2}}}{(x^4-5)^{\frac{1}{2}}}[/tex][tex]y^{\prime}=\frac{6x^4}{\left(x^4-5\right)^{\frac{1}{2}}}+\frac{3(x^4-5)}{(x^4-5)^{\frac{1}{2}}}[/tex][tex]y^{\prime}=\frac{6x^4}{\left(x^4-5\right)^{\frac{1}{2}}}+\frac{3x^4-15}{(x^4-5)^{\frac{1}{2}}}[/tex][tex]y^{\prime}=\frac{6x^4+3x^4-15}{\left(x^4-5\right)^{\frac{1}{2}}}[/tex][tex]y^{\prime}=\frac{9x^4-15}{\left(x^4-5\right)^{\frac{1}{2}}}[/tex][tex]y^{\prime}=\frac{3(3x^4-5)}{\left(x^4-5\right)^{\frac{1}{2}}}[/tex][tex]y^{\prime}=\frac{3(3x^4-5)}{\sqrt{x^4-5}}[/tex][tex]y^{\prime}=\frac{3(3x^4-5)}{\sqrt{x^4-5}}\times\frac{\sqrt{x^4-5}}{\sqrt{x^4-5}}[/tex][tex]y^{\prime}=\frac{3(3x^4-5)\sqrt{x^4-5}}{x^4-5}[/tex]Final answer:
[tex]y^{\prime}=\frac{3(3x^4-5)\sqrt{x^4-5}}{x^4-5}[/tex]Caleb is renting a kayak for 14.50 per half hour. how much would it cost Caleb to rent the kayak for 5 minutes
Answer:
It would cost Caleb approximately $2.4 to rent kayak for 5 minutes
Explanation:
Given that Caleb is renting a kayak for $14.40 per half hour.
This means he rents it for 30 minutes, as 30 minutes is half an hour.
In an equation form, we can write as:
$14.40 = 30 minutes
So that:
1 minute = $(14.50/30)
= $0.48
This mean he rents at $0.48 per minute
For 5 minutes, it would cost him:
$0.48 * 5 = $2.4 approximately.
5. In a 45-45-90 right triangle if the hypotenuse have length "x V 2", the leg 2 pointshas length IOхO 2xO x 2XV3
Given data:
In a right angle triangle hypotenues is given that is
[tex]H=x\sqrt[]{2}[/tex]Now, by the Pythagorean theorem we have
[tex]\text{Hypotenues}^2=Perpendicular^2+Base^2[/tex]So, by the hit and trial method
Let , perpendicular = base = x we get
[tex]\begin{gathered} H^{}=\sqrt[]{x^2+x^2} \\ H=\sqrt[]{2x^2} \\ H=x\sqrt[]{2} \end{gathered}[/tex]Thus, the correct option is (1) that is x
Select the expression equivalent to:(4x + 3) + (-2x + 4)A: 2x + 7B: -2x + 12C: -8x + 12D: 6x + 7
(4x + 3) + (-2x + 4)
Eliminating the parentheses:
4x + 3 - 2x + 4
Reordering:
4x -2x + 3 + 4
2x + 7