9 Ron's family plans to add a new room to their house. They initially planned the width and the length of the room to be 10 feet and 25 feet. Now they want to add to the width. The amount they want to add to the width is shown by the variable I. 25 101 + Ron thinks that the area of the room will be 250 + 257. Is he correct? Why or why not? Select all that apply. A Yes, because the area of the room is the sum of 25.10 and 25r. No, because the area of the room is the sum of 25 . 10 and I. No, because the area of the room is the product of 25 + 10 and 25.1. D Yes, because the area of the room is the product of 25 and 10+ I.
Answers
The room is a rectangle with dimensions 25 and x + 10. The area of a rectangle is the product of its dimensions, so the area will be:
[tex]25\cdot(x+10)[/tex]We have to add the parenthesis because we first need to add 10 and x and then multiply. Distributing the 25, we have:
[tex]25\cdot(x+10)=25\cdot x+25\cdot10=25x+250=250+25x[/tex]As we can see, this matches what Ron thinks the area will be, so he is correct. Thus, the answer is "Yes". The why can be both because the area is the sum of 25*10 and 25x and because the area is the product of 25 and 10 + x.
So, the correct alternatives are A and D.
Related Questions
Which best describes the relationship between the line that passes through the points (2, 3) and (5,8) and the line that passes through the points (-7, 5) and (-12, 8)?A. same lineB. parallelC. neither perpendicular nor parallelD. perpendicular
Answers
Given the line which passes through the points (2, 3) and (5,8) and the line that passes through the points (-7, 5) and (-12, 8).
To determine the relationship which best describes the line, the first thing we do is find the gradients of the lines.
For point A and B with coordinates:
[tex]A(x_1,y_1),B(x_2,y_2)[/tex][tex]\text{Gradient, m= }\frac{y_2-y_1}{x_2-x_1}[/tex]For points (2, 3) and (5,8)
[tex]\text{Gradient, m= }\frac{8-3}{5-2}=\frac{5}{3}[/tex]For the points (-7, 5) and (-12, 8)
[tex]\text{Gradient, m= }\frac{8-5}{-12-(-7)}=\frac{3}{-5}=-\frac{3}{5}[/tex]• Two lines are said to be ,parallel, ,if their gradients are the same.
,• Two lines are said to be ,perpendicular ,if the ,product of the gradients is -1.
Product of the two gradients
[tex]\begin{gathered} =\frac{5}{3}\times-\frac{3}{5} \\ =-1 \end{gathered}[/tex]Since the product of the gradients is -1, the two lines are said to be perpendicular.
The correct option is D
HELP ME WITH THESE THREE QUESTIONS PLEASE (GIVING BRAINLIEST TO THE BEST ANSWER.) 90 points
The perimeter of the figure is 18 units. Complete the statements to find the side lengths.
1. Find the distance from A to B. Explain how you found this distance.
2. Add the distances of the vertical and horizontal segments. These are the distances from A to B, B to C, and C to D. Show how you found the total.
3. Use the perimeter to find the length of segment AD. This is the distance from A to D. Explain how you found your answer.
Answers
Answer:
1. 6 units
2. 13 units
3. 5 units
Step-by-step explanation:
Granny Smith is making strawberry jelly. She places 6.3 ounces in each jar to give as gifts.granny was able to fill 9.5 jars. How many ounces of strawberry jelly did granny make
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factorise 10y²+21y-10
Answers
Answer:
(2y+5)x(5y-2)
Step-by-step explanation:
For a polynomial of the form ax² - bx + c rewrite the middle term as a sum of two terms whose product is a·c=10·-10 = -100 and whose sum is b= 21.
We factor 21 out of 21y.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{10y^{2}+21(y)-10 } \end{gathered}$}}[/tex]
Rewrite 21 as −4 plus 25.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{10y^{2}+(-4+25)y-10 } \end{gathered}$}}[/tex]
Apply the distributive property.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{10y^{2}-4y+25y-10 } \end{gathered}$}}[/tex]
Factor the highest common denominator of each group. Group the first two terms and the last two.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{(10y^{2}-4y)+25y-10 } \end{gathered}$}}[/tex]
Factor the highest common denominator (GCF) of each group.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{2y(5y-2)+5(5y-2) } \end{gathered}$}}[/tex]
Factor the polynomial by factoring the greatest common denominator, 5y-2.
[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{(5y-2)(2y+5) } \end{gathered}$}}}[/tex]
The answer is: (5y - 2)(2y + 5)After a 35% reduction, you purchase a new bike for $282.75. What was the price of the bike before the reduction?
A) First write an equation you can use to answer this question. Use x as your variable and express any percents in decimal form in the equation.
B) Solve your equation in part [A] to find the original price of the bike.
Answers
The equation to represent this situation is given by 0.65x = 282.75 .
In the various mathematical formulas that are used, the equals sign is used to show that two expressions on either side of the equal sign are equal. The meaning of the word equation and its cognates might vary slightly depending on the language.
Finding the exact values of the unknown variables that result in the given equality is the very first step in the solving of a variable equation. The values of the unknown variables that fulfil the equality are the equation's solutions, also known as the variables for which the equation must be solved. There are two sorts of equations.
Le t the original cost of the bike be x dollars.
After 35% reduction the new cost is x - (35% of x) = 0.65 x
Therefore 0.65 x = 282.75
or, x = 435
Therefore the cost of the bike is $435.
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If you have 10 white slips of paper, 6 red slips of paper, and 4 blue slips of paper, writing the ratio of red slips compared to the total number of slips. How many red slips do you have? How many slips of paper do you have?
Answers
Answer:
6:20 - 2:4 (simplified)
Step-by-step explanation:
20 total slips
6 red slips
Kali just started a new sales floor job to save for college. She earns 15.75 plus a flat fee of 50 . She wants to earn between 200 and 400 . The following inequality represents her earning potential
200 ≤ 15.75x + 50 ≤ 400 Solve the inequality PLEASE HELP ASAP
!!
Answers
Kali needs to work between 10 to 22 hours to earn an income between 200 and 400
Flat fee earned by Kali = 50
Earning per hour of Kali = 15.75
Required income is between 200 and 400
Inequality: Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Inequality represents the equation:
200<=15.75x + 50<=400
200<= 15.75x + 50
150<= 15.75x
x = 9.52
So, she needs to work a minimum of 10 hours
15.75x+50<=400
15.75x <=350
x <= 22.22
So, she can work a maximum of 22 hours
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pls help l need to finish this
Answers
Answer:
y = 3x+3
Step-by-step explanation:
The rate of change, or slope, in this case, is 3, as we can either count the increase in y-values or perform the Δy/Δx (slope equation: [tex]\frac{9-3\\}{2-0}[/tex])to yield three, meaning that the (3x) in this equation would be the slope. Since the y-intercept is the constant in the equation and the y-intercept is always when x=0 (when the graph crosses the y-axis) on the XY plane, we can just subtract 3 from the x=1 coordinate, meaning that the y-intercept/x=0 coordinate would be (0, 3), leaving 3 as the constant.
Therefore,
the equation is y = 3x+3.
3 1/4 - 3 1/6 uhmmm yeahh
Answers
Given the Subtraction:
[tex]3\frac{1}{4}-3\frac{1}{6}[/tex]You can identify that the denominators are different, then, you need to follow these steps in order to find the Difference (the result of the Subtraction):
1. Find the Least Common Denominator (LCD):
- Decompose the denominators into their Prime Factors:
[tex]\begin{gathered} 4=2\cdot2=2^2 \\ 6=2\cdot3 \end{gathered}[/tex]- Multiply the common and non-common factors with the largest exponents:
[tex]LCD=2^2\cdot3=12[/tex]2. Divide the LCD by each original denominator and multiply the Quotient by the corresponding numerator:
[tex]\begin{gathered} =3\frac{1\cdot3}{12}-3\frac{1\cdot2}{12} \\ \\ =3\frac{3}{12}-3\frac{2}{12} \end{gathered}[/tex]3. Subtract the whole number parts and then subtract the fractions. You get:
[tex]\begin{gathered} =0\frac{3-2}{12} \\ \\ =\frac{1}{12} \end{gathered}[/tex]Hence, the answer is:
[tex]=\frac{1}{12}[/tex]Is the sequence described as 3,5,8,12,17...... arithmetic. Explain your answer
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Based on the sequence given of 3,5,8,12,17, it would be incorrect to say that the sequence is arithmetic. The sequence is not arithmetic.
What is an arithmetic sequence?In an arithmetic sequence, one would find that the number that separates each of the figures in the sequence is the same. In other words, the common difference between each figure is the same.
For instance, 2, 5, 8, 11, 14 has the common difference of 3 so this is an arithmetic sequence.
The sequence given of 3,5,8,12,17 is not arithmetic because the difference between each number is not common and instead increases.
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A submarine sandwich shop surveyed a group of 20 prospective customers surveyed would be willing to pay a maximum of $4.01 to $5
A. 20 %
B.30%
C.5%
D.10%
Answers
Answer: 10%
Step-by-step explanation:
2 out of 20 people are willing to pay a maximum of 4.01 to 5 which is 0.10 which equals 10%
Which point shown in the graph below is the image of point P after a counterclockwise rotation of 90° about the origin? Please help me
Answers
We can see that if we rotate P 90° counterclockwise it would be located in the first quadrant. So it can be A or B. But A forms a 90° with the position of point P. So, the answer is A.
Find the exact values of the remaining trigonometric functions of if terminates in Quadrant IV and tan() = −3/4.
Answers
We know that the angle terminates in the fourth quadrant and that the tangent of it is -3/4.
Angles that are on the fourth quadrant have a negative sine and a positive cosine.
We can start with the cot():
[tex]\cot\theta=\frac{1}{\tan\theta}=\frac{1}{-\frac{3}{4}}=-\frac{4}{3}[/tex]We can relate the cosine with the tangent as:
[tex]\begin{gathered} \tan\theta=\frac{\sin\theta}{\cos\theta}=\frac{\sqrt{1-\cos^2\theta}}{\cos\theta} \\ -\frac{3}{4}=\frac{\sqrt{1-\cos^2\theta}}{\cos\theta} \\ -\frac{3}{4}\cos\theta=\sqrt{1-\cos^2\theta} \\ (-\frac{3}{4}\cos\theta)^2=1-\cos^2\theta \\ \frac{9}{16}\cos^2\theta=1-\cos^2\theta \\ (\frac{9}{16}+1)\cos^2\theta=1 \\ \frac{9+16}{16}\cos^2\theta=1 \\ \frac{25}{16}\cos^2\theta=1 \\ \cos^2\theta=\frac{16}{25} \\ \cos\theta=\sqrt{\frac{16}{25}} \\ \cos\theta=\frac{4}{5} \end{gathered}[/tex]We can now calculate the sine of the angle as:
[tex]\begin{gathered} \sin\theta=\tan\theta\cdot\cos\theta \\ \sin\theta=-\frac{3}{4}\cdot\frac{4}{5}=-\frac{3}{5} \end{gathered}[/tex]We can now calculate the sec() and csc() as:
[tex]\begin{gathered} \sec\theta=\frac{1}{\cos\theta}=\frac{5}{4} \\ \\ \csc\theta=\frac{1}{\sin\theta}=-\frac{5}{3} \end{gathered}[/tex]Answer:
sin() = -3/5
cos() = 4/5
cot() = -4/3
sec() = 5/4
csc() = -5/3
A shop has a sale that offers 20% off all prices. On the final day they reduce all the sale prices by 25%. Linz buys a radio on the final day
Work out the overall percentage reduction on the price of the radio.
Answers
The overall percentage reduction in the price of the radio is 40%.
What is the overall decline?Percentage is the fraction of an amount expressed as a number out of hundred. Percentage is a measure of frequency. The sign that is used to represent percentages is %.
Let's assume that that initial price of the radio is 100.
Price of the radio after the 20% decline in price = (1 - 0.2) x 100
0.8 x 100 = 80
Price of the radio after the 25% decline in price = (1 - 0.25) x 80
0.75 x 80 = 60
The percentage decline in price = (initial price / final price) - 1
(60 / 100) - 1 = 0.4 = 40%
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what is a relation function?
Answers
Answer: A relation is just a relationship between x and y-coordinates. It maps inputs to outputs. A function is just a special kind of relation: any input has exactly one output.
Step-by-step explanation:
Help me to answer 1b, solve the problem in detail, thank you
Answers
Hello
we are given a function and asked to find the reminder when it is divided by a binomial
According to the remainder theorem, f(a) would be the remainder from dividing f(x) by x -a
[tex]\begin{gathered} x-a=x-2 \\ a=2 \end{gathered}[/tex]but our f(x) is given as
[tex]\begin{gathered} f(x)=2x^3+7x^2-8x+3 \\ a=2 \\ \end{gathered}[/tex][tex]f(a)=f(2)=2(2)^3+7(2)^2-8(2)+3=31[/tex]From the calculation above, the answer to this question is 31
4.5 un 5.5 6 y 0.5 0.6 0.8 Which is most likely the equation of the line of best fit for the data given in the table? A y = 0.34 x - 09 B y = 0.25x - 0.7 y =0.45x-1 D y = 0.50x -0.6
Answers
The Solution.
The correct answer is y = 0.34x - 0.9 (option A ).
Step 1:
First, we shall determine the slope of the line by picking two coordinates from the table.
I need help identifying the coordinates
Answers
The z-score values for the given quantile are found.
What is defined as the z-score?A Z-Score is a measurable statistic of a score's connection to the mean among a set of scores.A Z-score can tell a trader whether a value is usual for a given data set or atypical.In contrast, the Z-score is the amount of standard deviations a provided data point is from the mean. The Z-score is negative for data points that fall below the mean. 99% of values in most large data sets have a Z-score among -3 and 3, indicating that they are three deviations above and below mean.For the given question;
The given normal quantile plot are-
-1.28, -0.52, 0.00, 0.52, 1.28
The corresponding z-score taken from the positive and negative z table are-
-1.28 = 0.101-0.52 = 0.3050.00 = 0.500.52 = 0.6981.28 = 0.899The z-score values for the given quantile are found.
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If Amy Van swam her recordbreaking 50 m by swimming to one end of the pool, then turning around and swimming back to her starting position, what would her average velocity be
Answers
Answer:
zero
Step-by-step explanation:
You want Amy Van's average velocity when she swims 50 m to the end of the pool and back.
Average velocityAverage velocity is the ratio of the change in position to the amount of time over which that change occurs. When Amy ends up where she started, she has not changed position at all, so her average velocity is ...
Vave = (change in position)/time = 0/time = 0
Her average velocity is zero.
HELP PLEASEEEEE!!!!!!
Answers
One rational number between -0.45 and -0.46 is -0.451, such that:
-0.45 > -0.451 > -0.46
How to find a rational number in the given interval?
So we want to find a rational number between -0.45 and -0.46. Remember that any decimal number with a finite number of digits after the decimal point (like the above numbers) is a rational number.
So:
3.16436
2.21412
1.4
All of these are rational numbers.
Then a rational number on the interval -0.45 and -0.46 could be -0.451, which is smaller than -0.45 and larger than -0.46
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i need help with my homework PLEASE CHECK WORKnumber 4
Answers
ANSWER:
Option c
[tex]h=-\frac{\operatorname{\ln}(0.62)}{0.079}[/tex]STEP-BY-STEP EXPLANATION:
The function given in the statement is the following:
[tex]D(h)=615\cdot\:e^{-0.079h}[/tex]If D(h) = 383, we substitute and solve for h, just like this:
[tex]\begin{gathered} 383=615\cdot \:e^{-0.079h} \\ \\ e^{-0.079h}=\frac{383}{615} \\ \\ \ln(e^{-0.079h})=\ln\left(\frac{383}{615}\right) \\ \\ -0.079h=\ln(0.62) \\ \\ h=-\frac{\ln(0.62)}{0.079} \end{gathered}[/tex]Therefore, the correct answer is option c.
How many solutions does the system of equations have? Explain1. Y = 5x - 4Y = -4 + 5xHow many solutions does the system of equations have? Explain2.Y=2x+3Y=-3x+6How many solutions does the system of equations have? Explain3. Y=-4x+5Y=-4x+5How many solutions does the system of equations have? Explain
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1. it has infinite solutions because since the equations are equal it is a line equation and a line has infinite points
2. It will have only one solutions, because the lines aren't parallel or the same line (we know that because there won't be a number that you can multiply by one of the equations and obtain the other one)
3.it has infinite solutions because since the equations are equal it is a line equation and a line has infinite points
6 in. 4 in 6 in 10 in
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we have that the figure of a rectangle and a triangle. So the area of this figure is:
[tex]A=6\cdot10+\frac{4\cdot4}{2}=60+8=68[/tex]so the answer is 68 in^2
Jose hopes to earn $1400 in interest in 3.4 years times from $56,000
Answers
To solve this problem, we will use the formula for compound interest:
[tex]r=k\cdot((\frac{P_N}{P_0})^{1/(NK)}-1).[/tex]Where:
• Pₙ = principal amount after N years,
,• P₀ = initial principal amount,
,• r = interest ratio in decimals,
,• k = compound periods per year.
From the statement, we know that:
• N = 3.4 years,
• P₀ = $56,000,
• Pₙ = P₀ + interest = $56,000 + $1,400 = $57,400,
,• r = ?,
,• k = 4 (the interest is compounded quarterly.
Replacing these values in the formula above, we get:
[tex]r=4\cdot((\frac{57400}{56000})^{1/(3.4\cdot4)}-1)\cong0.00727=0.73\%.[/tex]AnswerThe annual interest must be 0.73%.
Fine the end behavior and x-value of holeEquation is to the right
Answers
Given the function:
[tex]\: f\mleft(x\mright)=\frac{x+1}{\left(x-3\right)\left(x^2-1\right)}[/tex]The end behaviour of the function f(x) describes the behaviour of the function as x approaches +∞ and -∞.
When x approaches +∞,
[tex]\lim _{x\rightarrow\infty}f(x)=\text{ }\lim _{x\rightarrow\infty}\frac{x+1}{(x-3)(x^2-1)}=0[/tex]Thus, as x approaches +∞, the function f(x) approaches zero.
When x approaches -∞,
[tex]\lim _{x\rightarrow-\infty}f(x)=\text{ }\lim _{x\rightarrow-\infty}\frac{x+1}{(x-3)(x^2-1)}=0[/tex]Thus, as x approaches -∞, the function f(x) approaches zero.
x-value of the hole:
For a rational function f(x) given as
[tex]f(x)=\frac{p(x)}{q(x)}[/tex]Provided that p(x) and q(x) have a common factor (x-a), the function f(x) will have a hole at x=a.
Thus, from the function f(x)
[tex]f(x)=\frac{x+1}{(x-3)(x^2-1)}[/tex]by expansion, we have
[tex]f(x)=\frac{x+1}{(x-3)(x^{}-1)(x+1)}[/tex]The expression (x-1) is a common factor of the numerator and the denominator.
Thus,
[tex]\begin{gathered} x-1=0 \\ \Rightarrow x=1 \end{gathered}[/tex]Hence, the x-value of the hole is 1.
What is a constant rate of change
Answers
Answer:A rate of change is a rate that describes how one quantity changes in relation to another quantity. Constant rate is also called as uniform rate which involves something travelling at fixed and steady pace or else moving at some average speed. For example, A car travels 3 hours.
Step-by-step explanation:
Consider the following system of equations 4x + 6=24 and 2x + 3y=8 How many solutions does this system have? Justify your answer. Part B If we triple each side of the first equation 4x+6y=24, we have 12x+18y=72. Explain why the new system 12x+18y=72 and 2x+3y=8 has the same number of solutions as the original system.
Answers
The solution of the given system of equation will have infinite many solutions.
In the above question, the following equations are given
4x + 6y = 24
2x + 3y = 8
Now, we need to find the number of solutions that this system of equation will have
We know that,
a1 x + b1 y = c1
a2 x + b2 y = c2
is the general system of equation, and
[tex]\frac{a1}{a2} \neq \frac{b1}{b2}[/tex] then unique solution, or
[tex]\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}[/tex] then there will be infinite solutions or,
[tex]\frac{a1}{a2} = \frac{b1}{b2} \neq \frac{c1}{c2}[/tex] then there will be no solution
Now, we'll check for the given system of equations
a1 = 4, b1 = 6 , c1 = 24
a2 = 2, b2 = 3 , c2 = 8
[tex]\frac{a1}{a2} = \frac{b1}{b2} \neq \frac{c1}{c2}[/tex] = 2 = 2 [tex]\neq[/tex] 3
As this condition satisfies the third condition, the solution of the given system of equation will have infinite many solutions.
Now as we multiply the first equation 4x + 6=24 by 3 we get we have 12x+18y=72, the system will still have same solutions as only the equations are multiplied by a constant k = 3 which does not affect the solution.
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Please help me ASAP!! I will not hesitate to give brainliest to the best answer!!
Answers
Answer:
The correct answers are below, if you want a more in depth explanation let me know and I will provide
Step-by-step explanation:
- The Diver surfaced 3 min before the Watcher
- When the noticed was received, the Diver was 20 ft deeper than the watcher
- 3 Min after receiving the notice, the diver and the watcher are at the same depth
Save-A-Lot Bank is advertising a rate of 2.5% interest compounded annually.If $2000 is invested, how much money, to the nearest cent, will be inthe account after 10 years.
Answers
Question on Compound Interest.
The formula below can be used to calculate the compound interest;
[tex]\begin{gathered} A\text{ = p(1+}\frac{r}{100})^n \\ \text{Where A = amount,(\$) (that is, the money that will be in the account)} \\ r=\text{interest rate per annum, (\%)} \\ P=Pr\text{incipal, (\$), ( that is, the money invested)} \\ n=\text{ number of periods, years, } \end{gathered}[/tex]Where A= ? , P =$2000, r =2.5% and n = 10 years
Substituting these values into the formula above, we get
Note that: Amount = Principal + Interest, though not needed in this question.
[tex]\begin{gathered} A=P(1+\frac{r}{100})^n_{} \\ \\ A=2000(1+\frac{2.5}{100})^{10} \\ \\ A=2000(1+0.025)^{10} \\ A=2000(1.025)^{10}\text{ }=\text{ 2560.169 }\approx\text{ \$2560.17} \end{gathered}[/tex]Thus, the correct answer is $2560.17
I need help with this
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[tex] { 3 }^{ - 1} \times {3}^{x + 1} - { 3}^{x - 2} + {3}^{ - 2} \times { 3}^{x + 3} = 35 \\ {3}^{ - 1 + x + 1} - {3}^{x - 2} + {3}^{ - 2 + x + 3} = 35 \\ {3}^{x} - {3}^{x - 2} + { 3}^{ - 2 + 3 + x} = 35 \\ { 3 }^{x} - {3}^{x - 2} + {3}^{x + 1} = 35 \\ {3}^{x} - {3}^{x} \times {3}^{ - 2} + {3}^{x} \times {3}^{1} = 35 \\ {3}^{x} (1 - {3}^{ - 2} + 3) = 35 \\ {3}^{x} (3 + 1 - \frac{1}{9}) = 35 \\ \\ {3}^{x} (4 - \frac{1}{9} ) = 35 \\ {3}^{x} ( \frac{35}{9} ) = 35 \\ \frac{ {3}^{x}( \frac{35}{ 9 } )}{ \frac{35}{9} } = 35 \div ( \frac{35}{9} ) \\ {3}^{x} = 9 \\ {3}^{x} = { 3 }^{2} \\ x = 2[/tex]
ATTACHED IS THE SOLUTION.
I USED THE LAWS OF EXPONENTS.
GOODLUCK.