Use the rectangle at the right to answer the following questions. a. Find the area of the entire rectangle. Show your work. b. Calculate the perimeter of the figure. Show your work.
Answers
Length of the entire rectangle = 12 + 5 = 17
Width of the entire rectangle = 6+4 = 10
Part a
Area of rectangle = Length x width
Area of the entire rectangle = 17 x 10 = 170 square units
Part b
Perimeter of rectangle = 2( length + width )
Perimeter of the entire rectangle = 2(17 + 10 )
=2 (27) = 54
Perimeter of the entire rectangle = 54 units
Length of the entire rectangle = 12 + 5 = 17
Width of the entire rectangle = 6+4 = 10
Part a
Area of rectangle = Length x width
Area of the entire rectangle = 17 x 10 = 170 square units
Part b
Perimeter of rectangle = 2( length + width )
Perimeter of the entire rectangle = 2(17 + 10 )
=2 (27) = 54
Perimeter of the entire rectangle = 54 units
Related Questions
Home Liquidators marks up its merchandise 35% on cost. What is the company’s equivalent markup on selling price?
Answers
Home Liquidators marks up its merchandise 35% on cost, the company's equivalent markup on the selling price is 25.9%.
What is an equivalent value?An equivalent value represents equality.
Equivalent values show that two paired mathematical expressions are equal.
How is the markup on the selling price determined?The markup on the selling price can be derived by equating the markup on cost with the markup on the selling price as follows:
Markup on cost = 35%
Cost = 100%
Selling price = 135%
Markup on selling price = 25.9% (0.35/1.35 x 100)
Thus, we can describe Home Liquidators' markup on the selling price as equivalent to 25.9% or simply 26%.
Learn more about equivalent values at https://brainly.com/question/2972832
#SPJ1
A spherical iron ball is coated with a layer of ice of uniform thickness. If the ice melts at the rate of 8 mL/min, how fast is the outer surface area of ice changing when the outer diameter of the ball with ice on it is 24 cm?
Answers
When the outer diameter of the ball with ice on it is 24 cm then the outer surface area of ice changes at the rate of 1/90cm²/sec.
As given in the question,
Spherical ball is coated with uniform thickness.
Ice melts at the rate of 8ml/min
= (8/60)cm³/sec
Consider r as the radius of given spherical ball
Diameter = 24cm
⇒Radius 'r' =12cm
Volume 'V' = (4/3)πr³
⇒ dV /dt = (4/3)π(3r²r')
⇒-(8/60) = (4/3)π(3 ×12²×r')
⇒r' =-(8/60)×(1/576π)
⇒r' = - 1/ 4320π
Rate at which change in surface area
A =4πr²
⇒A' = 4πrr'
⇒A' = 4π (12) ( - 1/ 4320π)
= -1/90 cm²/sec.
Decrease in surface area = 1/90 cm²/sec.
Therefore, when the outer diameter of the ball with ice on it is 24 cm then the outer surface area of ice changes at the rate of 1/90cm²/sec.
Learn more about surface area here
brainly.com/question/2835293
#SPJ1
Factor the polynomial and use the factored form to find the zeros. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)
P(x) = x3 − 2x2 − 15x
x =
Answers
Answer:
-3, 0, 5
Step-by-step explanation:
You want the zeros of P(x) = x³ − 2x² − 15x using the factored form.
Factored formWe notice right away that x is a factor of every term. Factoring that out gives us a quadratic to factor:
P(x) = x(x² -2x -15)
To factor this, we need two factors of -15 that have a sum of -2. The factors -5 and +3 have those properties. That means our factored form is ...
P(x) = x(x +3)(x -5) . . . . factored form
ZerosThis product will be zero when any of its factors is zero. Considering them one at a time, we find the zeros of P(x) to be ...
x = 0
x +3 = 0 ⇒ x = -3
x -5 = 0 ⇒ x = 5
The zeros of P(x) are -3, 0, 5.
1. There are three car manufacturing factories A, B and C, and they are producing the same type
of cars. They are employing 1000, 2000 and 3000 men and producing 10, 15 and 25 cars per
month respectively. Find the labor productivity of each firm and the production of each firm
per year.
Answers
18)Betsy is collecting data on the amount of time shoppers spend inside of a particular large department store. She stands outside the department store and surveys every 10th shopper who exits. What type of sampling is used? Explain your answer.
Answers
Consider the 5 main types of sampling: Random, Systematic, Convenience, Cluster, and Stratified.
In the case of systematic sampling, every kth element of the data set is taken.
In our case, consider all the shoppers and imagine that they can be ordered in a line; then, Betsy selected the 10th shopper in the line, the 20th one, and so on.
This is analogous to systematic sampling; the answer is systematic sampling.Esmeralda rents a car from a company that rents by the hour. she has to pay an initial fee of $50, and they charge her $8 per hour. she has $150 available to spend on car rental. what is the greatest number of hours for which she can rent the car?A. 18 hoursB. 12.5 hoursC. 12 hoursD. 13 hours
Answers
Let the number of hours be x,
Initial fee is $50,
Amount charged per hour is $8
The charge for a number of x hours is'
[tex]x\times8=8x[/tex]The total amount Esmeralda has is $150,
Therefore,
[tex]8x+5\leq150[/tex]Solving for x to find the greates number of hours,
[tex]\begin{gathered} 8x+50\leq150 \\ \text{Collect like terms,} \\ 8x\leq150-50 \\ 8x\leq100 \\ \text{Divide both sides by 8} \\ \frac{8x}{8}\leq\frac{100}{8} \\ x=12.5\text{ hours} \end{gathered}[/tex]Hence, the greates number of hours is 12.5 hours.
Option B is the right answe
If there are 40 seats per row how many seats are in 90 rows?
Answers
Answer:
3,600 seats
Step-by-step explanation:
If you have 40 seats in a row, and there are 90 rows, you simply take the amount of seats, and multiply that by the amount of rows.
-Hope this helps
Answer:
Step-by-step explanation:
3600
If you were to multiply 40 seats by 90 rows, you would result with 3600 seats!
How many different arrangements of 5 be formed if the first must Work (of allowed?
Answers
ANSWER
There are 913,952 different 5-letter combinations that can be formed.
EXPLANATION
Recall that there are 26 letters in the English Alphabet.
From the question, we are to find the arrangement of 5 letters with the first letter being either W or K, and repetition of letters is allowed.
The possibilities for the 1st letter is 2 since the 1st letter can be either W or K;
More so, the possibilities for the 2nd letter is 26;
The possibilities for the 3rd letter is 26;
The possibilities for the 4th letter is 26, and
The possibilities for the 5th letter is 26;
The possibilities of arranging 5 letters = 2 x 26 x 26 x 26 x 26 = 913,952.
Hence, a total of 913,952 different 5-letter combinations can be formed.
1. Sally uses 312 cups of flour for each batch of cookies.
How many cups does she need to make 4 batches of cookies?
Answers
Ronald purchased a brand new phone for $450.00. Since phones are taxablehe had to pay a sales tax of 45%. much sales tax did Ronald pay for the phone ?
Answers
If the price of gas was on average $2.85 per gallon, and thus was $1.36 cheaper than a year before, what is the percent of decrease in price?
Answers
The price of gas = $2.85 per gallon
It was $1.36 cheaper than a year before.
So, the price before = 2.85 + 1.36 = $4.21
So, the percent of decrease = 1.36/4.21 = 0.323 = 32.3%
Hi can you help me find the correct match to each question?
Answers
GIVEN:
We are given a set of 4 statements as indicated in the attached image.
Required;
Determine whether each statement is TRUE or FALSE.
Solution;
(1) Look at the digit to the right of the digit to which you are rounding to tell whether to round up or leave it the same.
This statement is TRUE
(2) If the digit to the right of the digit to which you are rounding is four or less, you keep the digit the same.
This statement is TRUE.
(3) If the digit to the right of the digit to which you are rounding is five or more, you keep the digit the same.
This statement is FALSE.
(4) Look at the digit to the left of the digit to which you are rounding to tell whether to round down or leave it the same.
This statement is FALSE.
The point P is on the unit circle. If the y-coordinate of P is −3/5, and P is in quadrant IV, then
x = _________
Answers
Answer:
[tex]\frac{4}{5}[/tex]
Step-by-step explanation:
Knowing that [tex]{-\frac{3}{5}}^{2} + {\frac{4}{5}}^{2} = 1, {-\frac{3}{5}}^{2} + {-\frac{4}{5}}^{2} = 1[/tex],
so x can be positive or negative 4/5,
and we know that x coordinate of any point in quadrant IV is positive,
so x = 4/5.
Find the length of the given side for the congruent triangles ABC and A'B'C'.
The length of side AC
The length of side AC is ____.
Answers
ABC and A'B'C' are congruent triangle. The length of the side AC is 5.31cm.
congruent triangle - Congruent triangles are those whose two sides and included angle match those of another triangle's matching sides and angle.
rules -
Each of the three sides is equal.A comparable side and two angles share the same properties.The angle between the two sides is also equal, and there are two equal sides.(given)
AB = 17 cm
BC = 34 cm
Using the trigonometric functions
cos x = B/H
cos(81°) = B/34
B = Cos(81°) x 34
B = 5.31.
ABC and A'B'C' are congruent triangle. The length of the side AC is 5.31cm.
To know more about triangle
https://brainly.com/question/576340
#SPJ1
Finding the intercepts, asymptotes, domain, and range from the graph of a rational function
Answers
From the given graph
The asymptotes are the dotted lines in the graph, then
The vertical asymptote is x = 3
The horizontal asymptote is y = 1
The domain is all values of x that make the function defined
Since x can not equal 3, then
The domain is
[tex]D=(-\infty,3)\cup(3,\infty)[/tex]The range is all values of y corresponding to the values of the domain (x)
Since y can not equal 1, then
The range is
[tex]R=(-\infty,1)\cup(1,\infty)[/tex]The x-intercept is the value of x at the graph intersecting the x-axis
Since the graph intersects the x-axis at the point (6, 0), then
The x-intercept is 6
The answer is the first choice 6
The y-intercept is the value of y at the graph intersection the y-axis
Since the graph intersects the y-axis at point (0, 2_, then
The y-intercept is 2
The answer is the second answer 2
Is my answer correct help me please
Answers
3(-2) + 4
-6 + 4
whichever number has the greater value, that’s the sign you use. In this case it’s 6
6-4=2
Keep the negative
-2 is the answer
Find the weight of the steel rivet shown in the figure (steel weighs 0.0173 pounds per cubic centimeter)Round to the nearest tenth as needed.
Answers
step 1
the volume of the figure is equal to the volume of the frustums of the cone plus the volume of the cylinder
Find out the volume of the cylinder
we have
r=2.8/2=1.4 cm
h=10.7 cm
[tex]V=\pi\cdot r^2\cdot h[/tex]substitute given values
[tex]\begin{gathered} V=\pi\cdot1.4^2\cdot10.7 \\ V=20.972\pi\text{ cm3} \end{gathered}[/tex]Find out the volume of the frustum
the formula to calculate the volume is
[tex]V=\frac{1}{3}\cdot\pi\cdot h\cdot\lbrack R^2+r^2+R\cdot r\rbrack[/tex]we have
R=5.6/2=2.8 cm
r=2.8/2=1.4 cm
h=1.9 cm
substitute given values
[tex]V=\frac{1}{3}\cdot\pi\cdot1.9\cdot\lbrack2.8^2+1.4^2+2.8\cdot1.4\rbrack[/tex][tex]V=8.689\pi\text{ cm3}[/tex]Adds the volumes
V=20.972pi+8.689pi
V=29.661pi cm3
Multiply by the density
29.661pi*0.0173=1.6 lb
therefore
the answer is 1.6 lbCan someone help me with this please and thank you
Answers
The histogram is skewed to the left, the mean is less than the median.
In the picture below, angle 2 = 130 degrees, what is the measurement of angle 1?
Answers
Answer:
50°
Step-by-step explanation:
[tex]\angle 1[/tex] and [tex]\angle 2[/tex] form a linear pair, and are thus supplementary (meaning they add to 180°).
You have a huge review project for English where you have to answer 300 questions. You start on it after school at 5:00. At 6:30, you have answered 55 questions.What time will you finish your assignment if you don't take any breaks?
Answers
Given :
The total questions = 300
Time of starting = 5:00
At 6:30 the number of answered questions = 55
The time spent to answer 55 questions = 6:30 - 5:00 = 1:30 hours
Which is equal to : 1 hour and 30 minutes = 90 minutes
So, the rate of answering the questions =90/55 = 18/11 minute per question
So, for solving the 300 questions, the time will be :
[tex]300\cdot\frac{18}{11}=490\frac{10}{11}\min [/tex]So, 490 10/11 minutes = 8 hours and
Perform the indicated operation of multiplication or division on the rational expression and simplify
Answers
The division of two fractions is the same as multiplying the first by the inverted second fraction:
Then, in this case:
[tex]\frac{24y^2}{5x^2}\div\frac{6y^3}{25x^2}=\frac{24y^2}{5x^2}\times\frac{25x^2}{6y^3}[/tex]Step 2: multiplication of two fractionsWe multiply two fractions by multiplying the numerators and the denominators:
[tex]\frac{24y^2}{5x^2}\times\frac{25x^2}{6y^3}=\frac{24y^2\times25x^2}{5x^2\times6y^3}[/tex]Step 3: simplifying the numbers of the fractionWe know that
[tex]\frac{25}{5}=5\text{ and }\frac{24}{6}=4[/tex]Then, we can use this in our fraction:
[tex]\begin{gathered} \frac{24y^2\times25x^2}{5x^2\times6y^3}=5\cdot4\frac{y^2x^2}{x^2y^3} \\ \downarrow\text{ since 5}\cdot4=20 \\ 5\cdot4\frac{y^2x^2}{x^2y^3}=20\frac{y^2x^2}{x^2y^3} \end{gathered}[/tex]Step 4: exponents of the resultWe know that if we have a division of same base expressions (same letters), the exponent is just a substraction:
[tex]\begin{gathered} \frac{y^2}{y^3}=y^{2-3}=y^{-1} \\ \frac{x^2}{x^2}=x^{2-2}=x^0=1 \end{gathered}[/tex]Then,
[tex]20\frac{y^2x^2}{x^2y^3}=20y^{-1}\cdot1=20y^{-1}[/tex]Since negative exponents correspond to a division, then we can express the answer in two different ways:
[tex]20y^{-1}=\frac{20}{y}[/tex]Answer:[tex]20y^{-1}=\frac{20}{y}[/tex]In a recent survey of dog owners, it was found that 901, or 34%, of the owners take their dogs on vacation with them. Find the number of dog owners in the survey that do NOT take their dog on vacation with them rounded to the nearest whole number
Answers
we have that
34% represents 901 owners that take their dogs on vacation with them
so
the percentage of dog owners in the survey that do NOT take their dog on vacation is equal to
100%-34%=66%
Applying proportion
901/34=x/66
solve for x
x=(901/34)*66
x=1,749 ownersGiven the following linear function sketch the graph of the function and find the domain and range.
F(x)=2/7x-2
pls show how did u solve it
Answers
Linear function f(x) = 2/7x - 2
It has no domain or range restrictions, so both of them include all real numbers.
Doman x ∈ ( - ∞, + ∞),Range y ∈ ( - ∞, + ∞).The graph is attached
help I'm practicing
Answers
We have the next formula to find the volume of a triangular prism-
[tex]V=B\times h[/tex]where
B= area of the base
h= height
in our case
B=18 square inches
H= 5 inches
[tex]V=18\times5=90in^3[/tex]the volume of the triangular prism is 90 cubic inches
Which function is the result of vertically stretching ƒ(x) = x2 by a factor of 2 and translating it 4 units upward?Question 8 options:A) y = –4x2 + 2B) y = 2x2 + 4C) y = 2x2 – 4D) y = 4x2 + 2
Answers
To find the result function,
First stretch it, multiplying it by the factor we want to stretch.
So f(x) = x²
Stretching the function by a factor of 2:
g(x) = 2* f(x)
g(x) = 2* x²
On the other hand, to translate a function 4 units upward, we need to sum it to the function, so the result function is:
g(x) = 2x² + 4
The answer is option B.
In the diagram below, FG is parallel to CD. If the length of CD is the same as the length of FE, CE = 26, and FG = 11, find the length of FE. Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.
Answers
Answer:
The length of FE is √286 units.
Explanation:
Let the length of FE = x
Since FG is parallel to CD, then triangles EFG and ECD are similar triangles.
The ratio of the corresponding sides are:
[tex]\frac{FE}{CE}=\frac{FG}{CD}[/tex]Substitute the given values from the diagram above:
[tex]\frac{x}{26}=\frac{11}{x}[/tex]We then solve the equation for x.
[tex]\begin{gathered} \text{ Cross multiply} \\ x^2=26\times11 \\ \text{ Take the square root of both sides} \\ x=\sqrt{26\times11} \\ x=\sqrt{286} \\ \implies FE=\sqrt{286}\text{ units} \end{gathered}[/tex]The length of FE is √286 units (in simplest radical form).
25, -34, -2, 56, 8,-7 greatest to least
Answers
To arrange this from the greatest to the least
we will first look out for the positive numbers
Among the positive numbers, 56 comes first
then 25 and finally 8
Then we move to the negative numbers
-2 comes first
then -7 and then -34
Hence
56, 25, 8, -2, -7, -34
By hu Background: Given I go to the mobile application as Logged user on the US market with active Brainly Tutor subscription And I type the question And I submit valid subject (e.g: "[mathematics]") And tutor for chosen subject is available in tutor application (e.g: "[mathematics]") Scenario: When I click "[Ask question]" button Then following helping options are presented: | "Ask Tutor" | | "Ask Community" | When I click "[Ask Tutor]" button And I submit "[Ask your question]" button Then there is a redirection to the waiting screen When I am connected with the tutor Then "[We have found one]" screen is presented And the tutor's avatar is presented And privacy policy regulations are presented
Answers
43524
[tex]\frac{d32423657565\mod{43242}}{dx}_{564564}[/tex]4tet
54
write a part to part and a part to whole ratio for each problem situationof the 250 students surveyed 142, prefer carrots and 97 prefer peas
Answers
Here, we want to write ratios in part to part and in part to whole ratio
For the part to part
Writing carrot to peas, we have;
[tex]142\colon97[/tex]For the parts to whole ratio, we have;
[tex]\begin{gathered} \text{Carrot} \\ \frac{142}{250}\text{ = 142:250} \\ \text{Peas} \\ \frac{97}{250}\text{ = 97:250} \end{gathered}[/tex]Jackson bought a Ford Mustang for $40,000 and it depreciates in value 9% per year. Write an equation that
models the value of Jackson's car.
Answers
Answer:
[tex]v = 40000( {.91}^{x} )[/tex]