use the graph of y=-x/3 -1 determine which of the ordered pairs of the solution to the equation select all correct answers
Answers
Given:
[tex]y=-\frac{x}{3}-1[/tex]We have the graph below:
To determine the correct ordered pairs, let's solve for each of them.
a) (x, y) ==> (0, -1)
From the equation, substitute 0 for x and -1 for y:
[tex]\begin{gathered} y=-\frac{x}{3}-1 \\ \\ -1=-\frac{0}{3}-1 \\ \\ -1=0-1 \\ \\ -1=-1 \\ \\ \text{Therefore (0, -1) is a solution} \end{gathered}[/tex]b) (x, y) ==> (3, -2)
Substitute 3 for x and -2 for y:
[tex]\begin{gathered} y=-\frac{x}{3}-1 \\ \\ -2=-\frac{3}{3}-1 \\ \\ -2=-1-1 \\ \\ -2=-2 \\ \\ (3,\text{ -2) is a solution} \end{gathered}[/tex]c) (x, y) ==> (3, -5)
Substitute 3 for x and -5 for y:
[tex]\begin{gathered} y=-\frac{x}{3}-1 \\ \\ -5=-\frac{3}{3}-1 \\ \\ -5=-1-1 \\ \\ -5=-2 \\ \\ (3,\text{ -5) is not a solution} \end{gathered}[/tex]d) (0, -5)
Substitute 0 for x and -5 for y:
[tex]\begin{gathered} y=-\frac{x}{3}-1 \\ \\ -5=-\frac{0}{3}-1 \\ \\ -5=0-1 \\ \\ -5=-1 \\ \\ (0,\text{ -5) is not a solution} \end{gathered}[/tex]e) (x, y) ==> (-3, 0)
Substitute -3 for x and 0 for y:
[tex]\begin{gathered} y=-\frac{x}{3}-1 \\ \\ 0=-\frac{-3}{3}-1 \\ \\ 0=1-1 \\ \\ 0=0 \\ \\ \text{The ordered pair (-3, 0) is a solution} \end{gathered}[/tex]ANSWER:
(0, -1)
(3, -2)
(-3, 0)
Related Questions
Graph the line x=3 .
Answers
According to the given equation, x=3, the line that represents it is a vertical line that passes throught the x axis at x=3.
This is a constant line, which means that for all the values of y, x will always be 3.
The graph of this line is the following:
Hannah bought a total of 5.12 pounds of fruit at the market. she bought 2.5 pounds of pears and she also bought some bananas. how many pounds of bananas did she buy please show work and answer
Answers
Hannah bought pears and bananas only, so let's write the following equation:
[tex]\text{total}=\text{pears}+\text{bananas}[/tex]If the total weight bought is 5.12 and 2.5 pounds are pears, we can calculate the weight of bananas bought:
[tex]\begin{gathered} 5.12=2.5+\text{bananas} \\ \text{bananas}=5.12-2.5 \\ \text{bananas}=2.62 \end{gathered}[/tex]So Hannah bought 2.62 pounds of banana.
x = Round to the nearest hundredth or keep as a s
Answers
x=6.67
1) Examining that figure, we can state that we have two similar triangles with proportional sides and congruent angles.
2) So let's write a proportion so that we can find the measure of x
[tex]\begin{gathered} \frac{hipotenuse}{hipotenuse\text{ 2}}=\frac{\text{Leg}}{\text{leg 2}} \\ \frac{18}{10}=\frac{12}{x} \\ 18x=120 \\ x=\frac{120}{18} \\ x=\frac{20}{3}\text{ }\cong6.66667 \end{gathered}[/tex]3) Since the answer must be rounded to the nearest hundredth we have
the answer as x=6.67
Use f(x)=-x-8 and g(x) = x² + 8x − 15 to answer the following: a) f(1) + g(–3) b) g(−9) − f(–7)
Answers
ANSWER:
a) -37
b) 9
Given:
f(x)=-x-8 and g(x) = x² + 8x − 15
a) f(1) + g(–3)
f(1) = 1 - 8 = -7
g(-3) = -3² + 8(-3) - 15 = 9 - 24 - 15 = -30
f(1) + g(–3) = -7 + (-30)
= -7 - 30
-37
b) g(−9) − f(–7):
g(-9) = -9² + 8(-9) - 15 = 81 - 72 - 15 = -6
f(-7) = -7 - 8 = -15
Thus,
g(−9) − f(–7) = -6 - (-15)
= -6 + 15
= 9
without using a calculator prove whether 1728 is a perfect cube
Answers
Since the prime factors of 1728 can be grouped into triples of equal factors, it is a perfect cube.
Find the area of a circle with a diameter of 15 units round your answer to the nearest whole
Answers
The area of the circle is 177 units^2
Explanation:Given:
diameter of the circle = 15 units
To find:
the area of the circle
The formula for the area of a circle = πr²
let π = 3.14
diameter = 2(radius)
radius = diameter/2
radius = 15/2 = 7.5 units
[tex]\begin{gathered} Area\text{ of the circle = 3.14}\times7.5^2 \\ \\ Area\text{ of the circle = 176.625} \\ \\ To\text{ the nearest whole number, the area of the circle is 177 units}^2 \end{gathered}[/tex]for the function y=1/2-x at what values of x will the rate of change of y with respect to x equal 1/16
Answers
Given:
[tex]y=\frac{1}{2-x}[/tex]To Determine: Using the increament method the rate of change of y with respect to x
[tex]\begin{gathered} y+\Delta y=\frac{1}{2-(x+\Delta x)} \\ \Delta y=\frac{1}{2-(x+\Delta x)}-y \end{gathered}[/tex]Substitute for y
[tex]\begin{gathered} \Delta y=\frac{1}{2-(x+\Delta x)}-\frac{1}{2-x} \\ \Delta y=\frac{2-x-(2-(x+\Delta x)}{(2-(x+\Delta x)(2-x)} \\ \Delta y=\frac{2-x-(2-x-\Delta x)}{(2-(x+\Delta x)(2-x)} \\ \Delta y=\frac{2-x-2+x+\Delta x}{(2-(x+\Delta x)(2-x)} \\ \Delta y=\frac{\Delta x}{(2-(x+\Delta x)(2-x)} \end{gathered}[/tex][tex]\begin{gathered} \text{Divide through by }\Delta x \\ \frac{\Delta y}{\Delta x}=\frac{\Delta x}{(2-(x+\Delta x)(2-x)}\times\frac{1}{\Delta x} \\ \frac{\Delta y}{\Delta x}=\frac{1}{(2-(x+\Delta x)(2-x)} \end{gathered}[/tex][tex]\frac{dy}{dx}=\frac{1}{(2-x)(2-x)}[/tex]Hence, the rate of change of y with respect to x is
[tex]\frac{dy}{dx}=\frac{1}{(2-x)^2}[/tex]A gold bar is similar in shape to a rectangular prism. A gold bar is approximately 7 1 6 in. x2 in. x 1 in. If the value of gold is $1,417 per ounce, about how much 8 2 is one gold bar worth? Use the formula w ~ 11.15n, where w is the weight in ounces and n= volume in cubic inches, to find the weight in ounces. Explain how you found your answer.
Answers
ANSWER and EXPLANATION
We want to find how much the gold bar is worth.
First, we have to find the volume of the gold bar.
The volume of a rectangular prism is:
[tex]\begin{gathered} V=L\cdot W\cdot H \\ L=\text{length;} \\ W=\text{width;} \\ H=\text{height} \end{gathered}[/tex]Therefore, the volume of the gold bar is:
[tex]\begin{gathered} V=6\cdot2\frac{7}{8}\cdot1\frac{1}{2} \\ V=6\cdot\frac{23}{8}\cdot\frac{3}{2} \\ V=25.88\text{ cubic inches} \end{gathered}[/tex]Now, convert the volume to weight y using:
[tex]\begin{gathered} w\approx11.15n \\ \text{where w = weight in ounces; n = volume in cubic inches} \end{gathered}[/tex]Therefore, its weight is:
[tex]\begin{gathered} w\approx11.15\cdot25.88 \\ w\approx288.56\text{ ounces} \end{gathered}[/tex]Finally, multiple the weght by the value of gold:
[tex]\begin{gathered} \text{Worth}=288.56\cdot1417 \\ \text{Worth}=\text{ \$}408,889.52 \end{gathered}[/tex]Therefore, the volume of the gold bar is about 25.88 in³, so the weight is approximately 288.56 ounces. So one gold bar is worth about $408,889.52
Choose all of the options below that are expressions.
5t +1
9+4t
16=t
2-17t
6-t
3t=0
Answers
Answer:
here are the answers
Step-by-step explanation:
5t +1 2-17 3t=0 so yeah those are the answers
I think?
question 1 estimated number of dogs = 6.99 × 107=6.99 • 10,000,000=69,900,000estimated number of cats = 3.61 × 107=3.61 • 10,000,000= 36,100,000estimated number of birds = 8.3 × 106= 8.3 • 1,000,000= 8,300,000-------------------------------------------Question 2The estimated number of dogs is 6.99 x 10⁷The estimated number of cats is 3.61 x 10⁷The estimated number of birds is 8.3 x 10⁶The power of 10 in 8.3 x 10⁶ is 6 which is less than the power of 10 in the other two numbers. To make the calculation simpler, convert this number so the exponents are all the sameMultiply and divide 8.3 x 10⁶ by 10 to increase its exponent by 18.3x 10⁶= 10/10 • 8.3x 10⁶=8.3/10 •10⁶ •10= 0.83 x 10⁷
Answers
SOLUTION
For question 1, we have
[tex]\begin{gathered} 6.99\times10^7=69,900,000 \\ 3.61\times10^7=36,100,000 \\ 8.3\times10^6=8,300,000 \end{gathered}[/tex]Take the sum of the number above, we have
[tex]\begin{gathered} 69,900,000+36,100,000+8,300,000 \\ =114,300,000 \end{gathered}[/tex]For Question 2, we have
We need to add the number without converting to the ordinary form i.e will add the number in thier exponential form.
[tex]6.99\times10^7+3.61\times10^7+0.83\times10^7[/tex]The exponent is the common factor, hence we add the other numbers
[tex]\begin{gathered} (6.99+3.61+0.83)\times10^7 \\ =11.43\times10^7 \end{gathered}[/tex]Changin the result in question 2 to ordinary form, we have
[tex]11.43\times10^7=11.43\times10,000,000=114,300,000[/tex]Hence
Yes the answer in question 1 and question 2 are the same.
We can tell this because the nunbers have the same values(they are the same) but are in different forms(ordinary form and the exponential form). Hence the numbers can be use interchangeably.
Aaron received credit of$48 on a purchase of $960. What percent of$960 is 48%?
Answers
we have
[tex]\begin{gathered} \frac{48}{960}=\frac{x}{100} \\ 100\times\frac{48}{960}=100\times\frac{x}{100} \\ x=5 \end{gathered}[/tex]answer: 5%
Then he drove home at a speed of 5 blocks every 4 minutes. How do I graph that?
Answers
We have to graph the position versus time.
We start by identifying the segments.
1) The initial position (x=0, y=0) is his house.
2) He drove for 4 minutes at a speed of 1 block/min. This means that we have a line with slope m=1 from x=0 to x=4. The value of y when x=4 is also 4.
Then, the final point of this segment is (4,4).
3) He spent 3 minutes in the store. This means that y=4 between x=4 and x=4+3=7.
The final point of this segment is (7,4).
4) He drove at a speed of 2 blocks/minute (slope m=2) for 6 blocks until he got to the bank. Then, the new position is y=7+6=13. If the slope is m=2, then he will spent 6/2=3 minutes to reach the bank. As he already spent 7 minutes, he arrived to the bank at x=7+3=10.
Then, the final position of this segment will be (10,13).
5) Then, he returns at a speed of 5 blocks every 4 minutes. This correspond to a slope m=-5/4. This slope is negative as he is now returning to his house and, then, y is decreasing.
-15-3r=6r+3c Solve for r.
Answers
Answer:
[tex]r=\frac{-c-5}{3}[/tex]Explanation:
We want to solve for r in the equation below;
[tex]-15-3r=6r+3c[/tex]We need to move all terms of r to one side and divide both sides by the coefficient of r.
firstly subtract 6r from both sides;
[tex]\begin{gathered} -15-3r-6r=6r-6r+3c \\ -15-9r=3c \end{gathered}[/tex]then add 15 to both sides;
[tex]\begin{gathered} -15+15-9r=3c+15 \\ -9r=3(c+5) \end{gathered}[/tex]divide both sides by -9;
[tex]\begin{gathered} \frac{-9r}{-9}=\frac{3(c+5)}{-9} \\ r=\frac{-(c+5)}{3} \\ r=\frac{-c-5}{3} \end{gathered}[/tex]Therefore;
[tex]r=\frac{-c-5}{3}[/tex]Mrs worthy estimate the weight of her puppy to be 20 pounds. The actual weight of the puppy is 25.4 pounds. what is the percent error of Mrs worthy estimation?round to the nearest tenth
Answers
Given data:
The estimate weight of the puppy is E=20 pound.
The actual weight is A=25.4 pounds.
The expression for the percentage error is,
[tex]e=\frac{A-E}{A}\times100[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} e=\frac{25.4-20}{25.4}\times100 \\ =\frac{5.4}{25.4}\times100 \\ =21.26 \end{gathered}[/tex]Thus, the percentage error is 21.26%.
Given that every tenth person in line will get a coupon for a free box of popcorn at the movies what is the probability that you don't get a coupon when your in line
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Given that every tenth person in line will get a coupon for a free box of popcorn at the movies.
We are meant to find the probability that you don't get a coupon when you are in the line.
Step 2:
We can see that the probability that the person was in the line and got a coupon is:
[tex]\frac{1}{10}[/tex]Then, the probability that the person did not get a coupon when he was in the line is:
[tex](\text{ 1 -}\frac{1}{10})\text{ = }\frac{9}{10}[/tex]In a box there a total of four prizes: Two of them are worth $4, a single prize worth $26, and a single prize worth $241. A player will reach into the box and draw one of the prizes at random. What is the fair price for this game?
Answers
So,
First of all, the player has a 1/4 chance of drawing any of the 4 prizes.
This means that the probability of drawing a prize of $4 is 1/2 because there are 2 prizes worth of $4. The probability of drawing a prize of $26 is 1/4 and the probability of drawing a prize of $241 is also 1/4.
To find the fair price, we need to find the expected value of this problem:
This can be obtained by multiplying any possible value of a price for the probability of drawing a prize of that value and adding all these Hvalues together.
This is:
[tex]\begin{gathered} 4\cdot\frac{1}{2}+26\cdot\frac{1}{4}+241\cdot\frac{1}{4} \\ \\ =\frac{275}{4}=68.75 \end{gathered}[/tex]Therefore, the fair price of this game is $68.75.
A line cuts the y-axis at (0, -6) and passes through the point (9, -3). Find the equation of the line.
Answers
point 1 (0,-6) and point 2 (9,-3)
the equation is
[tex]y-y1=m(x-x1)[/tex]where m =
[tex]m=\frac{y2-y1}{x2-x1}=\frac{-3-(-6)}{9-0}=\frac{-3+6}{9}=\frac{3}{9}=\frac{1}{3}[/tex]answer: the equation of the line is
[tex]\begin{gathered} y-(-6)=\frac{1}{3}(x-0) \\ y+6=\frac{1}{3}x \\ y+6-6=\frac{1}{3}x-6 \\ y=\frac{1}{3}x-6 \end{gathered}[/tex]Provide reasons for the proofGiven line m is parallel to line nprove angle 1 is supplementary to angle 3
Answers
The first reason is Given.
The second is corresponding angles theorem.
The third one is definition of congruent angles.
The fourth is definition of linear pair.
The fifth is linear pair theorem.
The sixth is definition of supplementary angles.
The seventh is addition property of equality.
The eighth is definition of supplementary angles.
For each scenario, use the tape diagram to help answer the question. Think of different labels to use for the diagram depending on the situation. Mai has picked 1 cup of strawberries for a cake, which is enough for 3/4 of the cake. How many cups does she need for the whole cake?Priya has picked 1 1/2 cups of raspberries. which is enough for 3/4 of a cake. How many cups does she need for the whole cake?
Answers
Answer:
The number of cups of strawberries needed to make a whole cake is;
[tex]\begin{gathered} \frac{4}{3}\text{ cups} \\ or \\ 1\frac{1}{3}\text{ cups} \end{gathered}[/tex]Explanation:
Given that;
[tex]1\text{ cup of strawberries can make }\frac{3}{4}of\text{ a cake}[/tex]To get the number of cups of strawberries needed for a whole cake.
Let us multiply both sides by 4/3;
[tex]\begin{gathered} 1\times\frac{4}{3}\text{ cup of strawberries can make }\frac{3}{4}\times\frac{4}{3}of\text{ a cake} \\ \frac{4}{3}\text{ cup of strawberries can make 1-whole }of\text{ a cake} \end{gathered}[/tex]Therefore, the number of cups of strawberries needed to make a whole cake is;
[tex]\begin{gathered} \frac{4}{3}\text{ cups} \\ or \\ 1\frac{1}{3}\text{ cups} \end{gathered}[/tex]For an arch length s, area of sector A, and central angle θ of a circle of radius r, find the indicated quantity for the given value. r=4.28 ft, θ= 2.79, s=?
Answers
The area of a sector S follows the equation:
[tex]S=\frac{1}{2}r^2\theta[/tex]Where θ is the angle and r the radius.
In this case, we have:
• r = 4.28ft
,• θ = 2.79
We write:
[tex]\begin{gathered} S=\frac{1}{2}(4.28)^2\cdot2.79 \\ S\approx25.554168 \end{gathered}[/tex]Then, the answer, rounded up to two decimal places is
[tex]S=25.55[/tex]y=3sin(1/2 x+pi/6)please find amplitude period and phase shift
Answers
The given function is
[tex]y=3\sin (\frac{1}{2}x+\frac{\pi}{6})[/tex]We have to use the following form
[tex]a\sin (bx-c)+d[/tex]Where the amplitude is a, the period is 2pi/b, and the phase shift is c/b. In the given function a = 3, b = 1/2, and c = pi/6.
[tex]\begin{gathered} a=3 \\ T=\frac{2\pi}{b}=\frac{2\pi}{\frac{1}{2}}=4\pi \\ \theta=\frac{c}{b}=\frac{\frac{\pi}{6}}{\frac{1}{2}}=\frac{2\pi}{6}=\frac{\pi}{3} \end{gathered}[/tex]Therefore, the amplitude is 3, the period is 4pi, and the phase shift is pi/3.a) Rotation, then reflectionb) Translation, then rotationc) Rotation, then translationd) Translation, then reflection
Answers
the answer is the option
d) Translation, then reflection
because
First translation
the rule is
(x,y) -------> (x+6, y-3)
6 units at righ and 3 units down
Second Reflection
the reflection is across the vertical line locate 3 units at left figure 2
see the attached figure to better understand the problem
please wait a minute
Which number is located between 8710and95?
Answers
-8 7/10 and -9 2/10
-8-7/10 = -87/10
-9 - 2/10= -92/10
Answer is -9 1/10 = -91/10
because -91 is between -87 and -92
Answer is OPTION B))
Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth. sin 5° = ____
Answers
we want to calculate the following value
[tex]\sin (5)[/tex]Using a calculator, we have that
[tex]\sin (5)=0.08715574274765817[/tex]so, rounded to the nearest hundredth, we have that
[tex]\sin (5)\approx0.09[/tex]Brad thinks that 2.2.2.2 is represented by 4^2.What is wrong with this answer?
Answers
There is nothing wrong in the answer because
[tex]2\cdot2\cdot2\cdot2=4\cdot4=4^2[/tex]but it should be represented by
[tex]2\cdot2\cdot2\cdot2=2^4[/tex]Solve the equation for t:8t - r = 12t
Answers
ANSWER
[tex]t=-\frac{r}{4}[/tex]EXPLANATION
We want to solve the given equation for t:
[tex]8t-r=12t[/tex]To do this, separate the variables of the equation and simplify it:
[tex]\begin{gathered} 8t-12t=r \\ -4t=r \\ t=\frac{r}{-4} \\ t=-\frac{r}{4} \end{gathered}[/tex]That is the solution to the equation for t.
The function f(x) = =+ 1 has a vertical asymptote atA. I = 0OB. I = 1OC. A=-1OD. f(x) = -1Reset Selection
Answers
The function is given to be:
[tex]f\left(x\right)=\frac{-4}{x}+1[/tex]The vertical asymptote is when the denominator is equal to 0. T
Therefore, we have the vertical asymptote to be at:
[tex]x=0[/tex]OPTION A is the correct option.
Calculate the average (mean) of the data shown, to two decimal placesx8.325.313.423.9129.312.31.4
Answers
Given the set of of data:
x
8.3
25.3
13.4
23.9
12
9.3
12.3
1.4
We are to find the average (mean).
To find the means of a set of data, we first add up the data and divide by the total number of data.
The Formular for mean (m)
Mean (m) = sum of the terms
number of terms
number of terms = 8
Mean (m) = 8.3 + 25.3 + 13.4 + 23.9 + 12 + 9.3 + 12.3 + 1.4
8
Mean (m) = 105.9
8
Mean (m) = 13.2375
Mean (m) = 13.24 ( two decimal places).
[tex]1 + ( - 2)[/tex]what is answer this
Answers
This problem involves the addition of integers. When we add up a positive number and a negative number, it results in subtraction. The final answer will have a sign the same as the higher number.
In this problem, the negative number has a higher value than the positive number, hence, the final answer is a negative number. Doing the operation, we get
[tex]1+(-2)=-1[/tex]Answer: -1
Peter, a cyclist, rides 5.673 kilometers, takes a break, and then rides an additional 4321 meters.a. How many hectometers total did he ride?How many decimeters did he ride?
Answers
Explanation:
a) First Distance = 5.673 kilometers
2nd distance = 4321 meters
Total distance = 1st distance + 2nd distance
Total distance = 5.673 kilometers + 4321 meters
Conversion from kilometers to meters:
1 kilometer = 1000meters
5.673 kilometers = 5673 meters
Total distance in meters = 5673 meters + 4321 meters
Total distance in meters = 9994 meters
Conversion of meters to hectometers:
100 meters = 1 hectometers
9994 meters = x
cross multiply:
100(x) = 9994(1)
100x = 1994
x = 1994/100
x = 19.94 hectometers
Hence, he rode 19.94 in hectometers
b) converting to decimeters:
It is easier to convert from meters to decimeters
0.1 meters = 1 decimeter
9994 meters = y
y(0.1) = 1(9994)
0.1y = 9994
y = 9994/