The area of the rectangle is 24 ft^2
the width of the rectangle is w = 8 ft
The expression for the area of the rectangle is given as follows.
A = l * w
[tex]\begin{gathered} 24=l\times8 \\ l=\frac{24}{8}=3 \end{gathered}[/tex]The length is l = 3 ft.
[tex]l=\text{ 3 ft}[/tex]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
Alex has a $100 budget to buy food for his birthday
party. Each pizza costs $10 and each soda bottle
costs $3. Alex will buy 7 pizzas.
What is the greatest number of soda bottles Alex can
buy without going over budget?
If Alex has a $100 budget to buy food for his birthday, each pizza cost $10 and each soda bottle cost $3, and Alex bought 7 pizzas, then the greatest number of soda bottles Alex can buy without over budget 10 soda bottles
The total budget = $100
The cost of one pizza = $10
Number of pizza he bought = 7
The total cost of pizza = 7×10 = $70
The remaining money = 100-70
= $30
The cost of one soda bottle = $3
Number of soda bottle can he buy using the remaining money = 30/3
= 10 soda bottles
Hence, if Alex has a $100 budget to buy food for his birthday, each pizza cost $10 and each soda bottle cost $3, and Alex bought 7 pizzas, then the greatest number of soda bottles Alex can buy without over budget 10 soda bottles
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5 Which equations have the same value of x as 6 2 3 -9? Select three options. -9(6) 5x+4=-54 5x+4=-9 5x=-13 5X=-58
The given equation is-
[tex]\frac{5}{6}x+\frac{2}{3}=-9[/tex]If we multiply the equation by 6, we would have the same value for the variable x since we are multiplying the same number on each side. So, the second choice is an equivalent equation to the given one.
Let's multiply by 6.
[tex]\begin{gathered} 6\cdot\frac{5}{6}x+6\cdot\frac{2}{3}=-9\cdot6 \\ 5x+4=-54 \end{gathered}[/tex]So, the third expression is also an equivalent expression.
Then, let's subtract 4 on each side.
[tex]\begin{gathered} 5x+4-4=-54-4 \\ 5x=-58 \end{gathered}[/tex]The last choice is also an equivalent expression.
Therefore, the right choices are 2, 3, and 6.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,
p and q are roots of the equation 5x^2 - 7x +1. find to value of p^2 x q +q^2 x p and (p/q)+(q/p)
1) Let's find the roots of the equation: 5x² -7x +1
5x² -7x +1
2) Calling x_1 =p and x_2= q
Plugging them into the (p/q)+(q/p) expression, dividing the fractions. And then rationalizing it we'll have finally:
[tex]\frac{\frac{7+\sqrt[]{29}}{10}}{\frac{7-\sqrt[]{29}}{10}}+\frac{\frac{7-\sqrt[]{29}}{10}}{\frac{7+\sqrt[]{29}}{10}}=\frac{7+\sqrt[]{29}}{10}\cdot\frac{10}{7-\sqrt[]{29}}\text{ +}\frac{7-\sqrt[]{29}}{10}\cdot\frac{10}{7+\sqrt[]{29}}\text{ =}\frac{39}{5}[/tex]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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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.
Ava graphs the function h(x) = x^2 + 4. Victor graphs the function g(x) = (x + 4)^2. Which statements are true regarding the two graphs? Select three options.Ava’s graph is a vertical translation of f(x) = x^2.Victor’s graph is a vertical translation of f(x) = x^2.Ava’s graph moved 4 units from f(x) = x^2 in a positive direction.Victor’s graph moved 4 units from f(x) = x^2 in a positive direction.Ava’s graph has a y-intercept of 4.
Given,
Ava graphs the function h(x) = x^2 + 4.
Victor graphs the function g(x) = (x + 4)^2.
Required:
Check the correct statement about graph.
The graph of Ava and vector function is:
Here, victor graph was represented by blue curve and ava graph by green curve.
For first statement,
Ava’s graph is a vertical translated by 4 units.
Hence, statement is true.
For second statement,
The graph of victor is not vertically translated.
Hence, statement is false.
For statement three,
The curve of the Ava graph is moved 4 unit up in the positive direction. It is in y axis. Hence, statement is true.
For statement forth,
The curve of the victor graph is moved to negative direction not positive. Hence, statement is false.
For statement fifth,
The graph of Ava has the y intercept at 4. So, statement is correct.
Hence, option A (Ava’s graph is a vertical translation of f(x) = x^2), option C (Ava’s graph moved 4 units from f(x) = x^2 in a positive direction) and option E (Ava’s graph has a y-intercept of 4.) is true.
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.
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.
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.
At the park there is a pool shaped like a circle. A ring-shaped path goes around the pool. Its inner radius is 7 yd and its outer radius is 9 yd.We are going to give a new layer of coating to the path. If one gallon of coating can cover 5v * d ^ 2 how many gallons of coating do we need? Note that coating comes only by the gallon, so the number of gallons must be a whole number. (Use the value 3.14 for pi.)
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
Find the area when length = 5.2
(Equilateral Triangle)
Answer: 3√3 / 4
Step-by-step explanation:
A = 8^2√3 where s √3
A = ( √3)^2 * √3 / 4
A = 3√3/4
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.
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.
(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.
Find the solutions of the following equations in the interval [0, 2π).
In order to solve this equation, we can first do the following steps to simplify it:
how many hours did the plumber work to fix the plumbing
The total cost of the fix is C = $375.
The plumber charges a fixed rate per call of F = $50 and charges a variable rate of v = $25 per hour, if h is the number of hours he worked, we can write:
[tex]\begin{gathered} C=F+v\cdot h \\ 375=50+25\cdot h \end{gathered}[/tex]This equation shows that the total cost is equal to the fixed cost plus the variable cost. The variable cost is equal to the hourly rate times the number of hours of work.
Then, we can calculate h as:
[tex]\begin{gathered} 375=50+25h \\ 375-50=25h \\ 325=25h \\ h=\frac{325}{25} \\ h=13 \end{gathered}[/tex]Answer: he worked 13 hours.
NOTE:
Table of values:
If we need to use a table of values to solve this, we will have two columns: one for the number of hours and the other for the total cost.
We can make the table have more detail and separate the cost column in 3: one for the fixed cost, one for the variable cost and the last one for the total cost.
Then, we would write in each column:
1) Hours: the number of hours, from 0 to the amount we consider.
2) Fixed cost: this column will have the value $50 for all the rows, as it is independent of the number of hours.
3) Variable cost: this column will have values proportional to the hours. This values will be 25 times the number of hours.
4) Total cost: this column will add both the fixed cost and variable cost.
Then, we will obtain the following table.
We can now look for the value $375 in the Total cost column.
We find that this cost correspond to 13 hours:
Graph:
We can now use the data from the table to graph the total cost in function of the number of hours.
A survey was given asking whether they watch movies at home from Netflix, Redbox, or a video store.Use the results to determine how many people use Redbox.60 only use Netflix64 only use Redbox24 only use a video store 8 use only a video store or Redbox38 use only Netflix or Redbox 35 use only a video store or Netflix5 use all three24 use none of these
SOLUTION
We will use a Venn Diagram for this problem.
Let N represent those that use Netflix, R represent those that use Redbox and V represent those that use video store. The Venn Diagram is shown below
From the Venn Diagram above, the number in each part of a circle, represents the information
Now, how many people use Redbox?
The number of those that use Redbox is represented by the circle R, so we add all the numbers in this circle, we have
[tex]n(R)=38+64+5+8=115[/tex]Hence the answer is 115
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.
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.
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
If Allie’s parents are willing to spend $300 for a party, how many people can attend?
At least 20 people can attend the party
A figure is made up of three triangles. Each triangle has a baseof 4.5 feet and a height of 4.5 feet. What is the total area of thefigure?
Area of Compound Figures
A figure is made up of 3 triangles with a base b=4.5 feet and a height h=4.5 feet
The area of a triangle of base b and height h is:
[tex]A=\frac{b\cdot h}{2}[/tex]Substituting the given values:
[tex]A=\frac{4.5ft\cdot4.5ft}{2}=10.125ft^2[/tex]The total area is 3 times the above area, thus:
[tex]A_t=3\cdot10.125ft^2=30.375ft^2[/tex]Answer: a.
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
Use the cross Products Property to solve the proportions.1. 3/4 = v/142. 5/n = 16/32
1) 3/4 = v/14
v = (3 x 14) / 4
v = 42/4
v = 10.5
2) 5/n = 16/32
5(32) = n(16)
n = 5(32) / 16
n = 160/16
n = 10
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!
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
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°
