1) Assuming this is a quadrilateral, then the area is width times length
So
A =10 x 7
A= 70 m²
It's an area of 70 m²
17. Felicia bought 5 pieces of candy for 75 cents. Write a proportion youcould solve to find out how much would 8 pieces cost? *
Given the information on the problem, we can write the 5 pieces of candy for 75 cents like this:
[tex]\frac{75\text{ cents}}{5\text{ pieces}}[/tex]then, for 8 pieces, we would have the following proportion:
[tex]\frac{x\text{ cents}}{8\text{ pieces}}[/tex]then, we can equate both proportions to get the following:
[tex]\begin{gathered} \frac{75\text{ cents}}{5\text{ pieces}}=\frac{x\text{ cents}}{8\text{ pieces}} \\ or \\ \frac{75}{5}=\frac{x}{8} \end{gathered}[/tex]thus, solving for x, we get:
[tex]\begin{gathered} \frac{x}{8}=\frac{75}{5} \\ \Rightarrow x=\frac{75}{5}\cdot8=120 \\ x=120\text{cents} \end{gathered}[/tex]therefore, 8 pieces cost $1.20
Draw the circle ( x − 3 ) 2 + y 2 = 1 .
A drawing of this equation of a circle (x − 3)² + y² = 1 is shown in the image attached below.
What is the equation of a circle?Mathematically, the standard form of the equation of a circle is represented by this mathematical expression;
(x - h)² + (y - k)² = r² ....equation 1.
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.From the information provided, we have the following equation of a circle:
(x − 3)² + y² = 1 .........equation 2.
By comparing equation 1 and equation 2, we can logically deduce the following parameters:
Coordinate at the center, h = 3.Coordinate at the center, k = 0.Radius of circle, r = 1.In conclusion, the given equation of a circle (x − 3)² + y² = 1 was plotted by using an online graphing calculator.
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Complete Question:
Draw the circle (x − 3)² + y² = 1.
2x+y=21;y=-2x+21please hurry I need this straight away use any method
Answer:
(k, -2k+21) where k is any integer
Explanation:
Given the following simultaneous equation;
2x+y=21 ..... 1
y=-2x+21 ..... 2
Subtitute equation 2 into 1:
2x + (-2x+21) = 21
2x -2x+21 = 21
0x = 21-21
0x = 0
x = 0/0
Since the variables cannot be determined, we will subtitute x = k
Substitute x = k into equation 2;
From 2: y = -2x+21
y = -2k+21
Hence the solution to the system of equation is (k, -2k+21) where k is any integer
For each scenario below, choose the graph that gives the best representation.(A) Carlos is driving on the freeway at a constant speed. He then speeds up to pass a truck, After passing the truck, he exits the freeway and slows down.(B) Rachel is delivering a pizza to Mark's house. She drives at a constant speed toward the house until she hits a traffic jam and has to stop for severalminutes. After, she starts up again and drives at a faster speed than before.
Given:
Given the word problem, we can deduce the following information:
a)
1. Carlos is driving on the freeway at a constant speed.
2. He then speeds up, and exits the freeway and slows down.
Based on hte given information, the graph should have a constant or horizontal line at the first part, increases as he speeds up on the second part, and decreases as he slows down.
Thus the graph should be:
b)
1. Rachel is delivering at a constant speed toward the house until she hits a traffic jam and has to stop for several minutes.
2. She starts up again and drives at a faster speed than before.
So based on the given information, the graph should have a horizontal line at the first part since Rachel is driving at a constant speed. Next, the line should be increasing and higher than the horizontal line since Rachel is driving at a faster speed than before.
Therefore, the graph is:
need this asap What is the x-coordinate of the solution to this system of equations: 4x + y = 2 x - y = 3
Given the following system of equations:
[tex]\begin{cases}4x+y=2 \\ x-y=3\end{cases}[/tex]to find the x-cooridnate of the solution, we can solve for 'y' the first equation to get the following:
[tex]\begin{gathered} 4x+y=2 \\ \Rightarrow y=2-4x \end{gathered}[/tex]next, we use this value on the second equation to get the following expression:
[tex]\begin{gathered} x-y=3 \\ \Rightarrow x-(2-4x)=3 \end{gathered}[/tex]simplifying we get the following:
[tex]\begin{gathered} x-(2-4x)=3 \\ \Rightarrow x-2+4x=3 \\ \Rightarrow x+4x=2+3 \\ \Rightarrow5x=5 \\ \Rightarrow x=\frac{5}{5}=1 \\ x=1 \end{gathered}[/tex]therefore, the x-coordinate of the solution to the system of equations is x = 1
To which subset of the real numbers does 22‾√ belong?
Ok
Squared root of 2 is a irrational number because it can not be expressed as a fraction.
So the correct choice is Irrational, the last one.
Use the factor theorem to find all real zeros for the given polynomial and one of it's factors.Polynomial: f(x)=3x^3+x^2-20x+12 Factor: x+3List the zero's from smallest to largest. If a zero is not an integer write it as a fraction.The zeros are Answer , Answer and Answer
the zeros are -3, 2/3, and 2
Explanation:[tex]\begin{gathered} f(x)=3x^3+x^2\text{ - 20x + 12} \\ We\text{ n}eed\text{ to test if x + 3 is a factor} \end{gathered}[/tex]x + 3 = 0
x = -3
We will susbtitute -3 for x in the polynomial:
[tex]\begin{gathered} f(-3)=3(-3)^3+(-3)^2\text{ - 20(-3) + 12} \\ f(-3)=\text{ 3(-27) + 9 + 60 + 12 } \\ f(-3)\text{ = 0} \end{gathered}[/tex]Since the remainder is zero, this means x + 3 is a factor of the polynomial
Using synthetic division to get the remaining factor after factoring (x + 3):
[tex]3x^3+x^2-20x+12=(3x^2\text{ - 8x + 4)(x + 3)}[/tex]Using the factor theorem to find other factors:
[tex]\begin{gathered} f(x)=3x^2\text{- 8x + 4} \\ \text{factors of 4 = }\pm1,\text{ }\pm2,\text{ }\pm4 \\ \text{Let's try x = }1 \\ f(1)\text{ = }3(1)^2\text{- 8(1) + 4 = 3(1) - 8 + 4 = -1} \\ f(2)\text{ = }3(2)^2\text{- 8(2) + 4 = 3(4) - 16 + 4 = 0} \\ \text{Since f(2) = 0} \\ x\text{ = 2} \\ x\text{ - 2 = 0 . As a result, (x - 2) is a factor of the polynomial} \end{gathered}[/tex]Using synthetic division:
[tex]3x^2\text{- 8x + 4 = (x - 2)(3x -2)}[/tex][tex]\begin{gathered} 3x^3+x^2-20x+12=(3x^2\text{ - 8x + 4)(x + 3)} \\ 3x^3+x^2-20x+12=(x-2)(3x-2\text{)(x + 3)} \end{gathered}[/tex][tex]\begin{gathered} \text{x - 2 = 0; x = 2} \\ 3x\text{ - 2; x = 2/3} \\ x\text{ + 3; x = -3} \\ \text{The zeros are 2, 2/3 and -3} \\ \end{gathered}[/tex]From the smallest to the largest, the zeros are -3, 2/3, and 2
A travel agency polled its customers about their favorite kind of vacation. The results of the survey are shown in the given two-way frequency table.
Vacation Preferences
Seaside Mountain Historical Sightseeing Total
Female 38 36 32 17 123
Male 43 52 23 19 137
Total 81 88 55 36 260
What is the marginal relative frequency of customers who prefer sightseeing vacations?
A.
0.47
B.
0.21
C.
0.14
D.
0.89
The marginal relative frequency of customers who prefer sightseeing vacations is (C) 0.14
The ratio of a row total's or column total's frequency to the overall frequency of the data is known as marginal relative frequency. It is frequently used to examine broad trends in a single type of data.
[tex]Marginal relative frequency = \frac{sightseeing(total)}{Total}[/tex]
= 36/260
= 0.1385
≅ 0.14
Hence, marginal relative frequency of customers who prefer sightseeing vacations is 0.14.
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in rst the measure of ∠J=90° the measure of ∠H=69° and Hl=88 feet. find the length of JH to the nearest tenth of a foot
From the information provided, we can construct the following triangle;
The measure of angle J is 90 degrees, the measure of angle H is 69 degrees and line HI measures 88 feet. Therefore to calculate line JH;
[tex]\begin{gathered} \cos \theta=\frac{adj}{hyp} \\ \cos 69=\frac{JH}{88} \\ \text{Cross multiply and you'll have;} \\ 88\times\cos 69=JH \\ 88\times0.35836794\ldots=JH \\ 31.5363\ldots=JH \\ JH\approx31.5ft \end{gathered}[/tex]The answer is 31.5 feet (rounded to the nearest tenth of a foot
A drawer is filled with 2 black shirts, 7 white shirts, and 11 gray shirts.One shirt is chosen at random from the drawer. Find the probability that it is not a black shirt.Write your answer as a fraction. I need help with this math problem
There is a total of 2 + 7 + 11 = 20 shirts
The function f(x)= 4x is one to one Find A and B
Given:
[tex]f(x)=4x[/tex]a)
[tex]\begin{gathered} x=4f^{-1}(x) \\ f^{-1}(x)=\frac{x}{4}\text{ , for all x} \end{gathered}[/tex]Option C is the final answer.
b)
[tex]\begin{gathered} f(f^{-1}(x))=f(\frac{x}{4}) \\ =4(\frac{x}{4}) \\ =x \end{gathered}[/tex][tex]\begin{gathered} f^{-1}(f(x))=f^{-1}(4x) \\ =\frac{4x}{4} \\ =x \end{gathered}[/tex][tex]f(f^{-1}(x))=f^{-1}(f(x))=x[/tex]h e l p please. can't solve. picture explains, and i know the answer, but i cannot figure out how to make the equation to solve
We want to find how many miles Jodi traveled if her ride costed $12.50. We also know that a taxi ride has an initial fee of $3.75 plus $1.25 for every 1/2 mile traveled.
This means that for every mile, the fee will be:
[tex]2(1.25)=2.50[/tex]And the expression for the cost on terms of the miles traveled will be:
[tex]\begin{gathered} 3.75+2.50x \\ \text{where }x\text{ represents the number of miles traveled } \end{gathered}[/tex]As we know that Jodi spent $12.50 on a ride, we equal the value to the above expression:
[tex]3.75+2.50x=12.50[/tex]And we solve for x, as we want to know the number of miles:
[tex]\begin{gathered} 2.50x=12.50-3.75 \\ 2.50x=8.75 \\ x=\frac{8.75}{2.50}=3.5 \end{gathered}[/tex]This means that the number of miles that Jodi traveled was 3 and a half.
if a 3/4 of a cup serving of cereal provides your full daily value of vitamin B6 then what percentage of your daily value of vitamin B6 will you receive in 1/2 of a cup of your cereal
Given
3/4 cup serving of cereal provides 100% of vitamin B6 requirement
The percentage of daily value that would be available in 1/2 of a cup of cereal is:
[tex]\begin{gathered} \text{= }\frac{\frac{1}{2}}{\frac{3}{4}}\text{ }\times\text{ 100 \%} \\ =\text{ }\frac{1}{2}\times\frac{4}{3}\text{ }\times\text{ 100\%} \\ \text{= }\frac{4}{6}\text{ }\times\text{ 100\%} \\ =\text{ 66.67\%} \end{gathered}[/tex]Hence, the percentage of the daily value in 1/2 of a cup is 66.67%
zoo nutritionist orders 5 1/4 tons of apples and 7 2/4 tonsof bananas each year to feed theanimals. She orders 6 times as manytons of herbivore pellets than tons offruit. How many tons of herbivorepellets does the nutritionist order?
From the information provided, the zoo nutritionist orders the following quantity of fruits;
[tex]\begin{gathered} 5\frac{1}{4}\text{ tons of apples} \\ 7\frac{2}{4}\text{ tons of bananas} \\ \text{Total}=5\frac{1}{4}+7\frac{2}{4} \\ \text{Total}=\frac{21}{4}+\frac{30}{4} \\ \text{Total}=\frac{51}{4}\text{ tons} \\ \end{gathered}[/tex]Next, we are told that the nutritionist orders 6 times as many tons of pellets than tons of fruits.
This means for every ton of fruit ordered, there was 6 tons of pellets ordered.
Therefore;
[tex]\begin{gathered} \text{Fruits:Pellets}=1\colon6 \\ \text{When fruits are }\frac{51}{4}tons \\ \text{Pellets}=\frac{51}{4}\times6 \\ \text{Pellets}=\frac{306}{4} \\ \text{Pellets}=76\frac{1}{2}tons \end{gathered}[/tex]ANSWER:
[tex]\text{Pellets ordered}=76\frac{1}{2}tons[/tex]Combine like terms and write each expression in standard form
SOLUTION
From the expression
[tex]x^2-5+2x+x^2[/tex]combining like terms we have to bring the x-squares together, we have
[tex]\begin{gathered} x^2+x^2-5+2x \\ 2x^2-5+2x \end{gathered}[/tex]To write in standard form, the 2x should come before the -5, so we have
[tex]2x^2+2x-5[/tex]Hence the answer is
[tex]2x^2+2x-5[/tex]N. Students wanted to determine theheight of the flagpole. They measuredits shadow as 27 ft and the shadow of a 6ft tall student as 2 ft. How tall is theflagpole? Use the digit in the ones placeof your answer for N.
Given:
Shadow of flagpole = 27 feet
Height of the tall student = 6 feet
Shadow of the tall student = 2 feet
Required:
the height of the pole
Explanation:
Both the triangles are similar so the ratio of their corresponding sides are equal
[tex]\frac{height\text{ }of\text{ }flagpole}{height\text{ }of\text{ }student}=\frac{shadow\text{ }of\text{ }flagpole}{shadow\text{ }of\text{ }student}[/tex]Substituting the given values we get
[tex]\begin{gathered} \frac{height\text{ }of\text{ }flagpole}{6}=\frac{27}{2} \\ \\ height\text{ }of\text{ }flagpole=\frac{27\times6}{2}=27\times3 \\ \\ height\text{ }of\text{ }flagpole=81\text{ }feet \end{gathered}[/tex]Final answer:
The height of the flagpole is 81 feet.
Given that events "A" and "B" are independent, P(A) = 0.80, and P(A and B) = 0.24, what is P(B)?
Answer:
P(B)=0.3
Explanation:
Given two independent events, A and B:
[tex]P(A\cap B)=P(A)\times P(B)[/tex]Substitute the given values:
[tex]\begin{gathered} 0.24=0.8\times P(B) \\ \text{ Divide both sides by 0.8} \\ \frac{0.24}{0.8}=\frac{0.8\times P(B)}{0.8} \\ P(B)=0.3 \end{gathered}[/tex]The probability of event B is 0.3.
35) Use a formula to find the area of the figure.a15 in.7 in.20 in.
Given
height = 7 inches
base = 20 inches
Recall the formula for finding the area of the triangle
[tex]\begin{gathered} A_{\text{triangle}}=\frac{1}{2}bh \\ \text{where} \\ b\text{ is the base} \\ h\text{ is the height} \end{gathered}[/tex]Substitute the given dimensions of the triangle and we have
[tex]\begin{gathered} A=\frac{1}{2}bh \\ A=\frac{1}{2}(20\text{ in})(7\text{ in}) \\ A=\frac{1}{2}\cdot140\text{ in}^2 \\ A=70\text{ in}^2 \\ \\ \text{Therefore, the area of the triangle is }70\text{ in}^2. \end{gathered}[/tex]Give an interval over which the function is increasing. Give an interval over which it is decreasing
one interval where the function is increasing is
(-3;1)
one interval where the function is decreasing is
(1;4)
The salaries of the employees at four companies are summarized below. Answer the question about them.
Given,
Company A: the range of the salaries is $60000 and the mean salary is $22000.
Company B: the range of the salaries is $58000 and the mean salary is $29000.
Company C: the range of the salaries is $67000 and the mean salary is $27000.
Company D: the range of the salaries is $63000 and the mean salary is $28000.
Required
The company have least average salary and least variability.
a) From the given data, it is clearly seen that the company that have the lowest salary is $22000.
Hence, the company that have the lowest salary is Company A.
b)From the given data, it is clearly seen that the company that have the least salary variability is $58000.
Hence, the company that have the least salary variability is Company B.
Karen owns a seafood restaurant. She orders trout from an online retailer.Each pound of trout costs $30, and the company charges a $2 fee forshipping the order. However, if Karen orders 10 or more pounds, the troutcosts only $24 per pound, but the shipping fee is $6.Which piecewise function models the cost of x pounds of trout?○ A. f(x) = {={O B. f(x) ={O c. f(x) = -O D. f(x) =30x + 2, 0< x≤ 1024x+6, x 1024x+6, 0
The piecewise function that models the cost of x pounds of trout is:
[tex]C =\left \{ {{30x + 2}\\ x < 10\atop {24x + 6 x \geq 10}} \right.[/tex]
Let the number of pounds of trout is x and the price is C.
For, x < 10 :
From the question, we have
Each pound of trout costs $30
C = 30x + 2 ....1 )
For, x ≥ 10 :
Each pound of trout costs $24.
C = 24x + 6 ....2 )
Therefore, the piecewise function that models the cost of x pounds of trout is:
[tex]C =\left \{ {{30x + 2}\\ x < 10\atop {24x + 6 x \geq 10}} \right.[/tex]
Piecewise Function :
A function with many parts of curves in its graph is said to be piecewise. It implies that based on the value of the input, it has many definitions. In other words, a piecewise function responds differently to various inputs. A piecewise function, or f(x), is a function with various definitions at various intervals of x. A piecewise function's graph is divided into sections that each correspond to one of its definitions. A very good illustration of a piecewise function is the absolute value function.
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50 points!
What is the value of x?
Enter your answer in the box.
x =
Answer:
x = 3
Hope this helps!
Step-by-step explanation:
ΔABC is a 45°, 45°, 90° triangle. The longest side ( 6[tex]\sqrt{2}[/tex] ) can be [tex]x\sqrt{2}[/tex] while AB and CB are x. Because 6[tex]\sqrt{2}[/tex] is equal to [tex]x\sqrt{2}[/tex], you can see that x is equal to 6. Both AB and CB are equal to 6. ΔBDC ( CDB ) is a right triangle ( 30°, 60°, 90° ) so, BD = x, CB = 2x, and CD = [tex]x\sqrt{3}[/tex]. CB is equal to 6 so 2x = 6, x = 3.
Find the prime factorization and match your result to the correct answer below 231.Select one:a. 21•11b. 2•3•7•11c. 3•7•11d. 3•77
Solution
Hence, the prime factorization of 231 is 3•7•11
Hence, the correct option is C.
I need help on this!Greater than, less than or equal to?number 28
Explanation:
We can draw a number line to see the numbers and check which one is greater:
2.5 is on the left of 3, so it is less than 3.
Answer:
2.5 < 3
I’m not sure how to solve this I just know I have to get 5 with an exponent of 7 I think
this is an addition of powers .
on sunday , Margos dad gives 5c, we will represent it as 5^1
therefore: sunday 5^1
Monday 5^1 x ( 5^1)
because bases are the same , we add exponents
this means that 5^1(5^1) = 5^2
Tuesday 5^2(5^1) = 5^3
wednesday 5^3(5^1) = 5^4
thursday 5^4( 5^1)= 5^5
Friday 5^5(5^1)= 5^6
saturday 5^6 (5^1)= 5^7
On average, there are six pages in every chapter of a Rodriguez Hernandez novel. Each book has Approximately 73 chapters. Rodriguez Hernandez has published 54 books. Approximately how many pages has Rodriguez Hernandez written?
Given:
There are given that 6 pages in every chapter and each book have 73 chapters.
Explanation:
According to the question:
We need to find the pages for 54 books.
So,
First, we need to find that 73 chapters mean one book.
Then,
[tex]\begin{gathered} 1ch\rightarrow6pages \\ 76ch\rightarrow6\times76 \\ =456pages \end{gathered}[/tex]Now,
We need to find the pages for 54 books:
So,
[tex][/tex]Analyze the diagram below and complete the instructions that follow./Find sinA.1/3B.5/14C.4/5D.12/13
As given by the question
There are given that the triangle.
[tex]\begin{gathered} OM^2=3^2+4^2 \\ OM=5 \end{gathered}[/tex][tex]undefined[/tex]How do you solve linear equations in algebra ?-3y>-3-4x
Given linear equations in algebra: -3y >-3-4x
The above is an inequality.
To solve linear equation with two variables we need two equations.
Only one equation is given. The only other explanation is to solve for any of the variables by making it the subject of formula.
Quicy has 1/2 box of cereal to eat over 6 days if he splits the 1/2 box into equal portions how much will he eat each day
ANSWER:
1/12 of the cereal box
STEP-BY-STEP EXPLANATION:
In this case we must divide the amount that we have, that is, half a box of cereal by the number of portions that are desired equal, that is, 6
Therefore, we are left with:
[tex]\frac{\frac{1}{2}}{6}=\frac{1}{2\cdot6}=\frac{1}{12}[/tex]That is, for each day, you will have to eat 1/12 of the cereal box
Without graphing, find the slope of the line that goes through each pair of coordinate points. (0,5) and (8,2 ) [Choose ] (2,-1) and (6, 1) [ Choose ] (-3,-2) and (- 1,-5) [ Choose]
Answers:
(0,5) and (8,2 ) = 2/3
(2,-1) and (6, 1) = 1/2
(-3,-2) and (- 1,-5) = -3/2
Explanation:
The slope of a line that goes through two points (x1, y1) and (x2, y2) can be calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So, the slope of a line that goes through (0,5) and (8,2) is equal to:
[tex]m=\frac{2-0}{8-5}=\frac{2}{3}[/tex]The slope of a line that goes through (2, -1) and (6, 1) is:
[tex]m=\frac{1-(-1)}{6-2}=\frac{1+1}{4}=\frac{2}{4}=\frac{1}{2}[/tex]The slope of a line that goes through (-3, -2) and (-1, -5) is:
[tex]m=\frac{-5-(-2)}{-1-(-3)}=\frac{-5+2}{-1+3}=-\frac{3}{2}[/tex]Therefore, the answers are:
(0,5) and (8,2 ) = 2/3
(2,-1) and (6, 1) = 1/2
(-3,-2) and (- 1,-5) = -3/2