Given the functions:
[tex]\begin{gathered} f(x)=x^2-7 \\ g(x)=x^2+3x+7 \end{gathered}[/tex]We will find: f(x) • g(x)
So, we will find the product of the functions
We will use the distributive property to get the result of the multiplications
So,
[tex]\begin{gathered} f\mleft(x\mright)•g\mleft(x\mright)=(x^2-7)\cdot(x^2+3x+7) \\ f\mleft(x\mright)•g\mleft(x\mright)=x^2\cdot(x^2+3x+7)-7\cdot(x^2+3x+7) \\ f\mleft(x\mright)•g\mleft(x\mright)=x^4+3x^3+7x^2-7x^2-21x-49 \\ f\mleft(x\mright)•g\mleft(x\mright)=x^4+3x^3-21x-49 \end{gathered}[/tex]so, the answer will be:
[tex]f\mleft(x\mright)•g\mleft(x\mright)=x^4+3x^3-21x-49[/tex]Given the venn diagram below, what is the correct notation?A. ⊘B. (M∩F)′C. (M∪F)′D. none of these
Given
SolutionThe complement of a set using Venn diagram is a subset of U. Let U be the universal set and let A be a set such that A ⊂ U. Then, the complement of A with respect to U is denoted by A' or AC or U – A or ~ A and is defined the set of all those elements of U which are not in AThe shaded region is
[tex](M\cup\text{ F \rparen'}[/tex]The final answerOption C
Find the sum of the arithmetic series given a₁ =A. 650B. 325C. 642D. 1266Reset SelectionPrevious Jixt45, an=85, and n = 5.
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: write the given details
[tex]a_1=45,a_n=85,n=5[/tex]STEP 2: Write the formula for calculating the sum of arithmetic series
STEP 3: Find the sum
By substitution,
[tex]\begin{gathered} S_n=5(\frac{45+85}{2}) \\ S_n=5(\frac{130}{2})=5\times65=325 \end{gathered}[/tex]Hence, the sum of the series is 325
What values of z and y make angle ABC = RPM?
Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.
If triangles ABC and RPM are congruent, it means that:
[tex]\begin{gathered} AB=RP \\ BC=PM \\ AC=RM \\ m\angle A=m\operatorname{\angle}R \\ m\operatorname{\angle}B=m\operatorname{\angle}P \\ m\operatorname{\angle}C=m\operatorname{\angle}M \end{gathered}[/tex]For x, we have that:
[tex]\begin{gathered} BC=PM \\ BC=43 \\ PM=3x-8 \end{gathered}[/tex]Thus, we have that:
[tex]\begin{gathered} 43=3x-8 \\ 3x=43+8=51 \\ x=\frac{51}{3} \\ x=17 \end{gathered}[/tex]For y, we have:
[tex]\begin{gathered} m\operatorname{\angle}B=m\operatorname{\angle}P \\ m\operatorname{\angle}B=12y\degree \\ m\operatorname{\angle}P=62.4\degree \end{gathered}[/tex]Thus, we have that:
[tex]\begin{gathered} 12y=62.4 \\ y=\frac{62.4}{12} \\ y=5.2 \end{gathered}[/tex]Therefore, the answers are:
[tex]x=17,y=5.2[/tex]The LAST OPTION is correct.
Find the future value in dollars of an 18 month investment of $4900 into simple interest rate account that has an annual simple interest rate of 5.5%
Answer:
$5304.25.
Explanation:
The simple interest formula is given by
[tex]A=P(1+rt)[/tex]where
A = future value
P = princple amount
r = interest rate /100
t = time interval.
Now in our case
A = unknown
P = $4900
r = 5.5 / 100
t = 18 / 12 ( we are converting months to years. 18 months = 18 /12 years )
Putting the above values into the simple interest rate formula gives
[tex]A=4900\lbrack1+\frac{5.5}{100}\times(\frac{18}{12})\rbrack[/tex]which simplifies to give
[tex]\boxed{A=\$5304.25.}[/tex]Hence, the future value is $5304.25.
May I please get help with this math problem. I have been trying many times to find all correct answers to each length.
To draw a triangle, you cannot take three random line segments, they have to satisfy the triangle inequality theorems.
0. Triangle Inequality Theorem One: the lengths of any two sides of a triangle must add up to more than the length of the third side.
Procedure:
• Evaluating the first values given: (adding the two smallest values)
[tex]5.2+8.2=13.4[/tex]Now, we have to compare this addition with the bigger value. As 13.4 > 12.8, these can be side lengths of a triangle.
• Evaluating the second values given: (adding the two smallest values)
[tex]5+1=6[/tex]Comparing this addition with the bigger value, we can see that 6 < 10, meaning that these values cannot be side lengths of a triangle.
• Evaluating the third values given: (adding the two smallest values)
[tex]3+3=6[/tex]Comparing, we can see that 6 < 15. Therefore, these cannot be side lengths of a triangle.
• Evaluating the final values given:
[tex]7+5=12[/tex]We can see that 12 < 13, so these cannot be side lengths of a triangle.
Answer:
• 12.8, 5.2, 8.2: ,can be side lengths of a triangle.
,• 5, 10, 1: ,cannot be side lengths of a triangle.
,• 3, 3, 15: ,cannot be side lengths of a triangle.
,• 7, 13, 5: ,cannot be side lengths of a triangle.
2. A bag contains 50 marbles, 28 red ones and 22 blue ones. A marble is picked at random from the bag. What is the probability of picking: a red marble first? a blue marble?
Answer:
28/50
Step-by-step explanation:
If there is 50 marbles and you have 22 blue and 28 red and they want you to find what the chance of picking a red marble out of the bag your chances would be 28/50 hope this helps!
Hurry Will give 75 points
(Score for Question 3: of 4 points)
3. The equation y = 14x describes the amount of money Louis earns, where x is the number of hours he works
and y is the amount of money he earns.
The table shows the amount of money Carl earns for different numbers of hours worked.
Carl's Earnings
Time (h)
Money earned
($)
Hours 3 5 8 10
Money 54 90 144 180
(a) How much money does Carl earn per hour? Show your work.
(b) Who earns more per hour? Justify your answer.
(c) Draw a graph that represents Carl's earnings over time in hours. Remember to label the axes.
Answer:
Carl earns 18 dollars an hour, we can get this by dividing the money earned by time which gets your answer.
Part a: Carl earning per hour is $18.
Part b: More Money is earned by Carl.
Part c: The graph that represents Carl's earnings is drawn.
What is termed as the equation?A mathematical statement consisting of two expressions joined by an equal sign is known as an equation. 3x - 5 = 46 is an example of an equation. We have the value for the variable x as x = 17 after solving this equation.For the given question,
The amount of the money Louis have is defined by the equation.
y = 14xx is the number of hours.y is the amount of money.Carl's Earnings
Time (h) Hours 3 5 8 10
Money earned($) 54 90 144 180
Part a: Carl earning per hour.
For 3 hours Carl earns $54.
For one hour-$54/3 = $ 18.
Part b: More Money is earned by-
For 1 hours Carl earns $8.
For 1 hour Louis earning is y = 14×1 = $14.
Thus, Carl earns more.
Part c: The graph that represents Carl's earnings over time in hours is drawn.
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Enrique takes out a student loan to pay for his college tuition this year. Find the interest on the loan if he borrowed $2500 at an annual interest rate of 6% for 3 years.Simple interest
Answer:
$450
Explanation:
The interest of the loan can be calculated using the following equation:
[tex]I=P\cdot r\cdot t[/tex]Where P is the amount that he borrowed, r is the interest rate and t is the number of years.
So, replacing P by 2500, r by 0.06, and t by 3 years, we get:
[tex]\begin{gathered} I=2500^{}\cdot0.06\cdot3 \\ I=450 \end{gathered}[/tex]Then, the interest of the loan is $450.
At which of the following points do the two equations f(x)=3x^2+5 and g(x)=4x+4 intersect?A. (0,5)B. (1,8)C. (0,4) D. (8,1)
Given the equations:
[tex]\begin{gathered} f(x)=3x^2+5 \\ \\ g(x)=4x+4 \end{gathered}[/tex]Let's find the point where both equations intersect.
To find the point let's first find the value of x by equation both expression:
[tex]3x^2+5=4x+4[/tex]Now, equate to zero:
[tex]\begin{gathered} 3x^2+5-4x-4=0 \\ \\ 3x^2-4x+5-4=0 \\ \\ 3x^2-4x+1=0 \end{gathered}[/tex]Now let's factor by grouping
[tex]\begin{gathered} 3x^2-1x-3x+1=0 \\ (3x^2-1x)(-3x+1)=0 \\ \\ x(3x-1)-1(3x-1)=0 \\ \\ \text{ Now, we have the factors:} \\ (x-1)(3x-1)=0 \end{gathered}[/tex]Solve each factor for x:
[tex]\begin{gathered} x-1=0 \\ Add\text{ 1 to both sides:} \\ x-1+1=0+1 \\ x=1 \\ \\ \\ \\ 3x-1=0 \\ \text{ Add 1 to both sides:} \\ 3x-1+1=0+1 \\ 3x=1 \\ Divide\text{ both sides by 3:} \\ \frac{3x}{3}=\frac{1}{3} \\ x=\frac{1}{3} \end{gathered}[/tex]We can see from the given options, we have a point where the x-coordinate is 1 and the y-coordinate is 8.
Since we have a solution of x = 1.
Let's plug in 1 in both function and check if the result with be 8.
[tex]\begin{gathered} f(1)=3(1)^2+5=8 \\ \\ g(1)=4(1)+4=8 \end{gathered}[/tex]We can see the results are the same.
Therefore, the point where the two equations meet is:
(1, 8)
ANSWER:
B. (1, 8)
A convention center is in the shape of the rectangular pyramid with a height of 444 yd. Its base measures 348 yd by 418 yd. Find the volume of the convention center. If necessary, round your answer to the nearest tenth.
Given:
Length of the base = 418 yd
Width of the base = 348 yd
Height of the pyramid = 444 yd
Find: Volume of the rectangular pyramid
Solution:
The formula to get the volume of the rectangular pyramid is:
[tex]V=\frac{1}{3}\text{Area of the base}\times height[/tex]Since the base is rectangular, we can replace the "area of the base" into "length x width" since that is the formula for the area of a rectangle.
[tex]V=\frac{1}{3}l\times w\times h[/tex]Let's plug in the given data to the formula above.
[tex]V=\frac{1}{3}418yd\times348yd\times444yd[/tex]Then, solve for V or volume.
[tex]\begin{gathered} V=\frac{1}{3}\times64,586,016yd^3 \\ V=21,528,672yd^3 \end{gathered}[/tex]Answer: The volume of the convention is 21, 528, 672 yd³.
The sum of three consecutive integers is −387. Find the three integers.
Answer:
-130, -129, -128
Step-by-step explanation:
consecutive integers are when one integer is greater than the previous one and so on... so assuming the smallest integer which we start with is "x", the next integer is "x+1", and the next integer is "x+1+1".
Adding all these together will give us the sum of three consecutive integers:
[tex]x+(x+1)+(x+1+1)[/tex]
Simplifying inside the parenthesis gives us
[tex]x+(x+1)+(x+2)[/tex]
Simplifying the entire expression gives us the following:
[tex]3x+3[/tex]
This is equal to -387 as stated in the problem, so let's set it equal to -387
[tex]3x+3=-387[/tex]
Subtract 3
[tex]3x=-390[/tex]
Divide by 3
[tex]x=-130[/tex]
Since the consecutive integers are just +1, then +2, we can define the three consecutive integers as
-130, -130 + 1, -130 + 2
which simplifies to
-130, -129, -128
3 1/2 berry and pinaple pies
times 2 rasberry pies
A box of a granola contains 16.8 ounces . It cost $5.19 . What is the cost , to the nearest cent , of the granola per ounce ? A . $0.12 B . $0.31 C . $3.24
The cost per unit ounce is obtained by computing the quotient:
[tex]c=\frac{C}{N}.[/tex]Where:
• c is the cost per unit ounce,
,• C is the cost,
,• N is the number of ounces that you get for C.
In this problem we have:
• C = $5.19,
,• N = 16.8 ounces.
Computing the quotient, we get:
[tex]c=\frac{5.19}{16.8}\cong0.31[/tex]dollars per ounce.
Answer: B. $0.31
Look at this graph: у 10 9 8 7 6 5 3 2 1 0 1 2 3 4 5 6 7 8 9 10 What is the slope?
EXPLANATION
As we can see in the graph, we can calculate the slope with the following equation:
[tex]\text{Slope}=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]Let's consider any ordered pair, as (x1,y1)=(1,7) and (x2,y2)=(5,8), replacing this in the equation will give us:
[tex]\text{Slope}=\frac{(8-7)_{}}{(5-1)}=\frac{1}{4}[/tex]Answer: the slope is equal to 1/4.
Please help me step by step
The value of the function f(x) at x = 0 is found as -1.
What is meant by the term function?A function is described as the connection between such a set of inputs that each have one output. A function is a relationship between inputs in which each input is linked to exactly one output. Every function does have a domain and a codomain, as well as a range. In general, a function is denoted by f(x), where x would be the input. A function's general representation is y = f(x). In mathematics, a function is a special relationship between inputs (the domain) and outputs (the codomain), where each input has precisely one output and the output could be traced all the way back to its input.For the given question,
The graph of the function f(x) = -x² + 4x - 1 is given.
For finding the value of f(x) at x = 0, check the y-coordinate of the graph when x = 0.
Put x = 0 in the given function.
f(0) = -0² + 40 - 1
f(0) = - 1
Thus, the value of the function f(x) at x = 0 is found as -1.
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Which of the binomials below is a factor of this trinomial?x^2 - 13x + 42A. x + 84B. x - 7C. x^2 +12D. x + 7
Given the following trinomial:
[tex]x^2-13x+42[/tex]To factor the trinomial, we need two numbers the product of them = 42
And the sum of them = -13
Two of the numbers of factors of 42 = -6, and -7
So, the factor of the trinomial will be as follows:
[tex]x^2-13x+42=(x-6)(x-7)[/tex]So, the answer will be option B. x - 7
A road sign is in the shape of a regular pentagon. What is the measure of each angle on the sign? Round to the nearest tenth. 540 252 54 Od 108
Internal angles of a polygon
The triangle has n=3 sides, and the sum of its internal angles is 180°
The rectangle has n=4 sides, and the sumo of its internal angles is 360°
There is a general formula to calculate the sum of the internal angles of any polygon of n sides:
Sum = 180° ( n -2 )
For a pentagon (n=5), the sum of angles is:
Sum = 180° ( 5 -2 ) = 180° * 3 = 540°
We are required to find the measure of each internal angle. Since the pentagon is regular, all of its internal angles measure the same, thus:
The measure of each angle = 540° / 5 = 108°
Need help ASAP Which graph shows the asymptotes of the function f(x)= 4x-8 _____ 2x+3
First we will calculate the vertical asymptote, is when the denominator of the function given is equal to zero
[tex]\begin{gathered} 2x+3=0 \\ x=-\frac{3}{2} \end{gathered}[/tex]then we will calculate the horizontal asymptote because the degree of the numerator and the denominator is equal we can calculate the horizontal asymptote with the next operation
[tex]y=\frac{a}{b}[/tex]a= the coefficient of the leading term of the numerator
b=the coefficient of the leading term of the denomintor
in our case
a=4
b=2
[tex]y=\frac{4}{2}=2[/tex][tex]y=2[/tex]As we can see the graph that shown the asymptotes of the function is the graph in the option C.
(1 point) A variable of a population has a mean of I = 250 and a standard deviation of o = 49.
Solution
Question 1a:
- The population mean and sample mean are approximately the same in theory. The only difference is that the distribution of the sample will be wider due to a larger uncertainty caused by having less data to work with.
- Thus, we have:
[tex]\begin{gathered} \text{ Sample Mean:} \\ 250 \\ \\ \text{ Standard Deviation:} \\ \frac{\sigma}{\sqrt{n}}=\frac{49}{\sqrt{49}}=\frac{49}{7}=7 \\ \end{gathered}[/tex]Question 1b:
- The assumption is that the distribution is a normal distribution (OPTION C)
Question 1c:
Yes, the sampling distribution of the sample mean is always normal (OPTION B). This is in accordance with the central limit theorem.
Lindsay is designing a dog pen. The original floor plan is represented by figure PQRS. Lindsay dilates the floor plan by a scale factor of 1/2 with a center of dilation at the origin to form figure P'Q'R'S'. The final figure is P"Q"R"S". What are the coordinates of P'Q'R'S'?
Since we have the original coordinates P(-6, 9), Q(3, 9), R(3, 3) & S(-6, 3) and the scale factor, we multiply each x-component and y-component of each point by 1/2 in order to get P'Q'R'S', that is:
P'(-3, 9/2)
Q'(3/2, 9/2)
R'(3/2, 3/2)
S'(-3, 3/2)
And those are our P'Q'R'S' coordinates after the scaling,
Jamal built a toy box in the shape of a rectangular prism with an open top. The diagram below shows the toy box and a net of the toy box.
Okay, here we have this:
Considering the provided figure, we are going to calculate the requested surface area, so we obtain the following:
So to calculate the surface area we will first calculate the area of the base, the area of the short side and the area of the longest side, then we have:
Base area=6 in * 14 in=84 in^2
Short side area=8 in * 6 in = 48 in^2
Longest side area=8 in * 14 in=112 in^2
Total surface area=Base area+ 2(Short side area) + 2(Longest side area)
Total surface area=84 in^2+ 2(48 in^2) + 2 (112 in^2)
Total surface area=84 in^2+ 96 in^2 + 224 in^2
Total surface area=404 in^2
Finally we obtain that the total surface area in square inches of the toy box is 404 in^2.
Simplify 17(z-4x)+2(x+3z)
Answer:
23z-66x
Step-by-step explanation:
Look at the attachment please :D
Determine the value for which the function f(u)= -9u+8/ -12u+11 in undefined
ANSWER
[tex]\frac{11}{12}[/tex]EXPLANATION
A fraction becomes undefined when its denominator is equal to 0.
Hence, the given function will be undefined when:
[tex]-12u+11=0[/tex]Solve for u:
[tex]\begin{gathered} -12u=-11 \\ u=\frac{-11}{-12} \\ u=\frac{11}{12} \end{gathered}[/tex]That is the value of u for which the function is undefined.
cuales son los dos numeros enteros cuyo producto es 294 y cuyo cociente es 6?
1.- You need two equations
- x*y = 294
- x/y = 6
2.- Solve for x
x = 6y
(6y)y = 294
3.- Simplifying
6y^2 = 294
-Solve for y
y^2 = 294/6
given the function m(a)=27a^2+51a find the appropriate values:
solve m(a)= 56
a=
A function is a relationship between inputs where each input is related to exactly one output.
The value of a when m(a) = 56 is 7/9.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
We have,
m(a) = 27a² + 51a ____(1)
m(a) = 56 ____(2)
From (1) and (2) we get,
56 = 27a² + 51a
27a² + 51a - 56 = 0
This is a quadratic equation so we will factorize using the middle term.
27a² + 51a - 56 = 0
27a² + 71a - 21a - 56 = 0
(9a−7) (3a+8) = 0
9a - 7 = 0
9a = 7
a = 7/9
3a + 8 = 0
3a = -8
a = -8/3
We can not have negative values so,
a = -8/3 is neglected.
Thus,
The value of a when m(a) = 56 is 7/9.
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4y - 6 = 2y + 8how to solve this equation
To solve this equation, we need to collect like terms
To collect like terms, we bring the terms similar to each other to the same side
In this case, the value having y will be brought to same side of the equation
Kindly note that if we are bringing a particular value over the equality sign, then the sign of the value has to change
This means if negative, it becomes positive and if positive, it becomes negative
Proceeding, we have
4y - 2y = 8 + 6
2y = 14
divide both sides by 2
2y/2 = 14/2
y = 7
The value of y in this equation is 7
Find how many years it would take for an investment of $4500 to grow to $7900 at an annual interest rate of 4.7% compounded daily.
To answer this question, we need to use the next formula for compound interest:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]From the formula, we have:
• A is the accrued amount. In this case, A = $7900.
,• P is the principal amount. In this case, $4500.
,• r is the interest rate. In this case, we have 4.7%. We know that this is equivalent to 4.7/100.
,• n is the number of times per year compounded. In this case, we have that n = 365, since the amount is compounded daily.
Now, we can substitute each of the corresponding values into the formula as follows:
[tex]A=P(1+\frac{r}{n})^{nt}\Rightarrow7900=4500(1+\frac{\frac{4.7}{100}}{365})^{365t}[/tex]And we need to solve for t to find the number of years, as follows:
1. Divide both sides by 4500:
[tex]\frac{7900}{4500}=(1+\frac{0.047}{365})^{365t}[/tex]2. Applying natural logarithms to both sides (we can also apply common logarithms):
[tex]\ln \frac{7900}{4500}=\ln (1+\frac{0.047}{365})^{365t}\Rightarrow\ln \frac{7900}{4500}=365t\ln (1+\frac{0.047}{365})[/tex]3. Then, we have:
[tex]\frac{\ln\frac{7900}{4500}}{\ln(1+\frac{0.047}{365})}=365t\Rightarrow4370.84856503=365t[/tex]4. And now, we have to divide both sides by 365:
[tex]\frac{4370.84856503}{365}=t\Rightarrow t=11.9749275754[/tex]If we round the answer to two decimals, we have that t is equal to 11.97 years.
A manufacturing company currently uses 15 workers to load and unload trucks. Each worker can move an average of 15 boxes per minute. A robotics firm has built a robot that can load and unload boxes at the rate of 21 boxes per minute. How many robots will it take to do the same job as the 15 humans?
It will take 11 robots to do the same job as the 15 humans
Explanation:Given:
Workers in use = 15
Each worker can move an average of 15 boxes per minute.
A robot has been built that can move an average of 21 boxes per minute
15 worker would move:
15 * 15 boxes = 225 boxes per minute.
The number of robots it will take to move 225 boxes is:
225/21 = 10.7
It will take 11 robots to do the same job as the 15 humans
Debra will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $50 and costs anadditional $0.15 per mile driven. The second plan has an initial fee of $59 and costs an additional $0.11 per mile driven.for what amount of driving do the two plans cost the same? i need the answer for miles and cost
First plan cost is modeled as:
50 + 0.15x
where x are the miles driven
Second plan cost is modeled as:
59 + 0.11x
If the two plans cost the same, then:
50 + 0.15x = 59 + 0.11x
0.15x - 0.11x = 59 - 50
0.04x = 9
x = 9/0.04
x = 225 miles
which corresponds to a cost of:
50 + 0.15*225 = $83.75
Attached is a photo of my written question, thank you.
Given:
The function is,
[tex]f(x)=-2x^2-x+3[/tex]Explanation:
Determine the function for f(x + h).
[tex]\begin{gathered} f(x+h)=-2(x+h)^2-(x+h)+3 \\ =-2(x^2+h^2+2xh)-x-h+3 \\ =-2x^2-2h^2-4xh-x-h+3 \end{gathered}[/tex]Determine the value of expression.
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{-2x^2-2h^2-4xh-x-h+3-(-2x^2-x+3)}{h} \\ =\frac{-2h^2-4xh-h}{h} \\ =-2h-4x-1 \end{gathered}[/tex]So exprression after simplification is,
-2h - 4x - 1
