Problem 1
Plug in x = 0 and solve for y to get the y intercept
6x+12y = 60
6(0)+12y = 60
12y = 60
12y/12 = 60/12 ... divide both sides by 12
y = 5
Answer: A) 5
======================================
Problem 2
Use the slope formula.
The two points are (x,1, y1) = (1, -1) and (x2, y2) = (-2, 8)
m = (y2-y1)/(x2-x1)
m = (8-(-1))/(-2-1)
m = (8+1)/(-2-1)
m = 9/(-3)
m = -3
Answer: A) -3
The slope of the following graph represents _____.
speed
velocity
acceleration
momentum
Answer:
Displacement versus time is velocity
Step-by-step explanation:
Displacement versus time is velocity
Acceleration is change in velocity over time
Speed is distance over time
Momentum is mass times velocity
The slope of a graph in physics can represent several different concepts, depending on the graph. On a distance-time graph, the slope stands for speed or velocity. Meanwhile, on a velocity-time graph, the slope signifies acceleration. Momentum is generally not represented by the slope.
Explanation:In physics, the slope of a graph can indeed represent several concepts, but only when plotted correctly. These concepts include speed, velocity, acceleration, and momentum. However, when we're talking about a distance-time graph, the slope typically represents speed or velocity, depending on whether the direction of movement is accounted for or not. An increasing slope on such a graph indicates objects are moving at a faster speed or velocity over time.
On the other hand, in a velocity-time graph, the slope represents acceleration. Positive acceleration causes the velocity of an object to increase, while negative acceleration, or deceleration, slows it down. Similarly, if there is no change in the slope, it means the object is moving at a constant velocity.
Momentum, in general, is not represented by the slope of a graph but rather is the product of an object's mass and its velocity.
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every sixth visitor to an animal shelter gets a free animal calendar every 20th visitor gets a free animal toy which visitor each day will be the first want to get both the calendar and the animal toy
Which function is represented by the graph?
f(x) = −|x − 3| + 4
f(x) = −|x + 3| + 4
f(x) = −|x − 4| + 3
f(x) = −|x + 4| + 3
Answer:
Step-by-step explanation:
It is f(x) = −|x + 4| + 3 because the +4 in the absolute value sign moves the graph 4 spots to the left and the +3 moves the graph 3 spots up.
Answer:
f(x) = −|x + 4| + 3
Step-by-step explanation:
since, the value of the function at x=0 is -1
so, we will check which functions gives the same value
f(x) = −|x − 3| + 4 at x=0 it gives 1
f(x) = −|x + 3| + 4 at x=0 it also gives 1
f(x) = −|x − 4| + 3 at x=0 it gives -1
f(x) = −|x + 4| + 3 at x=0 it also gives -1
so, we have discarded first two options
Now at x=4 function gives negative value
f(x) = −|x − 4| + 3 at x=4 it gives 3
f(x) = −|x + 4| + 3 whereas at x=4 it gives -5
Hence, the function represented by the graph is:
f(x) = −|x + 4| + 3
Use the table below to find the cost of buying 50 balloons
it 200 each number the raito is ballones times 4
What is the simplest form of the ratio 40 : 16? a. 20 : 8 b. 10 : 4c. 5 : 4d. 5 : 2 e. 10 : 8
Amanda is adding the numbers below.
3.7 x 10^20 + 4.45x10^20
What is the sum written in scientific notation?
add 3.7 and 4.45 make sure to change it back to standard you'll get 815000000000000000000. move decimal between first and second digit which means you moved it to the left 18 times and your answer will be 8.15 x 10 ^18 I hope its right :( please don't judge if wrong :((( lol
Answer: 8.15 x 10²⁰
Step-by-step explanation:
In order to add or subtract, they must both have the same power - think of the power as "like terms". In this problem they already have the same power (10²⁰) so we don't need to manipulate them to have the same power. We can just add their coefficients (3.7 and 4.45).
3.7 x 10²⁰
+ 4.45 x 10²⁰
8.15 x 10²⁰
A store buys 77 1/2 pounds of mulch in a large shipment. They divide the mulch up into bags that can each hold 2 1/4 pounds. The store sells one bag of mulch for $2.25. For each part of the question, show your work.
a. How many full bags of mulch will the store make?
b. Considering only the full bags, what is the total sales price of all the bags of mulch?
Answer: a. The store will make 34 full bags of mulch.
b. Considering only the full bags, the total sales price is $76.50
Step-by-step explanation:
The total amount of mulch is [tex]77\frac{1}{2}[/tex] pounds or [tex]\frac{155}{2}[/tex] pounds.
Each bag can hold [tex]2\frac{1}{4}[/tex] pounds or [tex]\frac{9}{4}[/tex] pounds of mulch.
a. Suppose, the store will make [tex]x[/tex] number of bags of mulch.
So, the equation will be.........
[tex]x*\frac{9}{4}=\frac{155}{2}\\ \\x=\frac{155}{2}*\frac{4}{9}=\frac{310}{9}=34.44... \approx 34[/tex]
So, the store will make 34 full bags of mulch.
b. The store sells one bag of mulch for $2.25
So, the total sales price of 34 full bags of mulch will be: [tex](\$2.25*34)=\$76.50[/tex]
Carmella turns on her oven, which heats up at
80
degrees per minute. The temperature of her house, and therefore her oven, is
70
degrees. Let
x
be the number of minutes that it will take for her oven to reach
390
degrees.
It will probably be 390 / 70
BRAINLIEST!PLEASE HELP ME
-12x - 0.4 > 0.2(36.5x + 80) - 55 Remove the brackets.
-12x - 0.4 > 7.3x + 16 - 55 Combine the like terms on the right
-12x - 0.4 > 7.3x - 39 Add 12x to both sides
- 0.4 > 7.3x + 12x - 39
- 0.4 > 19.3x - 39 Add 39 to both sides.
-0.4 + 39 > 19.3x Combine like terms on the left
38.6 > 19.3x Divide by 19.3
38.6 / 19.3 > x
2 > x
What is the smallest integer x, for which x, x+5, and 2x−15 can be the lengths of the sides of a triangle?
the smallest integer x can be is 11 because it has to be greater than 10
The smallest integer x, for which x, x+5, and 2x−15 can be the lengths of the sides of a triangle is 11
Using the triangular theorem which states that the sum of any two sides of a triangle must be less than the third side.
Given the side length of the triangle to be a, b and c
a = x
b = x+5
c = 2x - 15
According to the theorem;
b < a+c
x+5 < x + 2x - 15
x + 5 < 3x - 15
Collect the like terms
x - 3x < -15 - 5
-2x < -20
x > -20/-2
x > 10
Since x is greater than 10, let x be 11
Hence the smallest integer x, for which x, x+5, and 2x−15 can be the lengths of the sides of a triangle is 11
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60 boys at a summer camp were asked to complete a survey about their favorite outdoor activity. 18 boys chose biking and 29 boys chose fishing. The remaining boys did not complete the survey. Which expression gives the percent of survey participants who chose fishing?
Answer:
Expression for percent of survey participants who chose fishing = [tex]\frac{29}{47} *100[/tex]
Explanation:
Total number of boys = 60
Number of boys who took part in survey = 18 + 29 =47
Number of boys who chose fishing = 29.
Percentage of an outcome = (Number of favorable outcome/ Total number of outcome) x 100
Percentage of boys who chose fishing = (29/47)x100
Expression for percent of survey participants who chose fishing = [tex]\frac{29}{47} *100[/tex]
To find the percent of survey participants who chose fishing, divide the number of boys who chose fishing by the total number of boys who completed the survey and multiply by 100. In this case, the percent is 48.33%.
Explanation:To find the percent of survey participants who chose fishing, we need to divide the number of boys who chose fishing by the total number of boys who completed the survey and then multiply by 100. In this case, 29 boys chose fishing out of 60 boys who completed the survey. So the expression that gives the percent of survey participants who chose fishing is:
(29/60) * 100 = 48.33%
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Need Help Asap!!!!!!
a right triangle has side lengths of 15,36, and 39 cm. what is the area of the triangle
This is a right triangle (you can confirm by using Pythagorean Theorem: 15² + 36² = 39²)
A = [tex]\frac{1}{2} b * h[/tex]
A = [tex]\frac{1}{2} 15 * 36[/tex]
= 15 * 18
= 270
Answer: 270 cm²
The density of mercury is 13.6 grams per cubic centimeter. Complete the steps for converting 13.6 g/cm^3 to kg/m^3
1 cubic meter = 100 cm * 100 cm * 100 cm = 1 x 10^6 cc
1 kilogram = 1,000 grams
13.6 g / cc
If we had a cubic meter of mercury, its mass would be (or it would "weigh") 13.6 * 1,000,000 = 13,600,000 grams or 13,600 kilograms.
And so its density would be 13,600 kg / cubic meter.
13600 kg/m³. To convert 13.6 g/cm³ to kg/m³, multiply by the conversion factor 1000 kg/m³.
Explanation:To convert from grams per cubic centimeter (g/cm³) to kilograms per cubic meter (kg/m³), we need to use conversion factors.
1 g/cm³ = 1000 kg/m³.
So, to convert 13.6 g/cm³ to kg/m³, we multiply by the conversion factor:
13.6 g/cm³ x 1000 kg/m³ = 13600 kg/m³
A sewing club used 48 feet of fabric to make 8 blankets.At this rate how many blankets can be made from 12 yards of fabric
HELP NEEDED!!! WILL GIVE 5 STARS!
A snack of an apple, a brownie, and a cheese stick has 270 calories. Two brownies and an apple have 290 calories. Two apples and three cheese sticks have 420 calories. How many calories are in each item?
Let a=calories in an apple, b=calories in a brownie, and c=calories in a cheese stick.
Will someone please help me with these questions. The table shows the average annual cost of tuition at 4-year institutions from 2003 to 2010.
1.) Find the least squares regression equation using the school year (in number of years after 2000) for the input variable and the average cost (in thousands of dollars) for the output variable.
2.)What is the best estimate for the average cost of tuition at a 4-year institution starting in 2000. (Hint: look at the y-intercept)
3.)What is the best estimate for the average cost of tuition at a 4-year institution starting in 2020.
4.)What does the slope mean in context of the situation? 5.)Most students are not able to afford this tuition for 4 years. What are some ways that you can lower the cost of your college tuition? If you don’t plan to attend college, what things can do you post- HS graduation to continue your education or provide for yourself financially?
Step-by-step explanation:
1.) The equation for the line of least squares regression is given by
[tex]Y=mX+c[/tex]
where Y = Output Variable = Average Cost (in thousands of dollars)
X = Input Variable = Number of years after 2000
Thus, the given data table transforms as follows:
No. of years after 3 4 5 6 7 8 9 10
after 2000 (X)
Average Cost (Y) 15.505 16.510 17.451 18.471 19.363 20.409 21.093 22.092
To determine the equation precisely, we need to calculate the values of 'm' (Slope) and 'c' (Y-intercept)
Let us take any two random values of X and Y from the above table, so that we have
X₁ = 3; Y₁ = 15.505 and X₂ = 8; Y₂ = 20.409
Plugging in these two sets of values, we get the following two equations:
15.505 = (3)m + c and
20.409 = (8)m + c
Let us subtract the upper one from the lower one so that we have
20.409 - 15.505 = 8m + c - 3m - c
4.904 = 5m
Hence, m = 0.9808
Using this value and plugging it in one of the above equations yields the value of c as
20.409 = 8(0.9808) + c
Therefore, c = 12.563
So, the required equation for the line of least squares regression is
Y = (0.9808)X + 12.563
2.) To estimate the cost of tuition at a 4-year institution in 2000, we can put the value of X to be 0.
We have Y = 0 + 12.563
Thus, the cost of tuition in 2000 was $12,563.
3.) To estimate the cost of tuition in 2020, we put the value of X as 20 so that we have
Y = (0.9808)(20) + 12.563 = 32.179
Therefore, we can expect the cost of tuition to be as high as $32,179 by 2020.
4.) The slope tells us the factor by which the tuition increases each year, starting with the base of 12,563 dollars in 2000.
One way to lower the cost of college tuition is by applying for a waiver based on income level. Alternatively, one can also work at the school.
One can join a part-time graduation program while working for the rest of the day so that one may support oneself as well as pay for their courses. Alternatively, one can opt for Online Courses and get some Diploma in their area of interest while working part-times so that they may pursue a degree later on in their life.
The least squares regression equation is Average cost = 14.5 + 1.24 * School year. The best estimate for the average cost of tuition at a 4-year institution starting in 2020 is 33.3 thousand dollars. The slope of the regression line means that the average cost of tuition increases by 1.24 thousand dollars for every year after 2000.
1. To find the least squares regression equation, we can use the following steps:
Calculate the mean of the independent variable (school year) and the dependent variable (average cost).
Calculate the deviations from the mean for both variables.
Calculate the product of the deviations from the mean for both variables.
Calculate the variance of the independent variable.
Calculate the slope of the regression line:
slope = sum of the product of the deviations from the mean / variance of the independent variable
Calculate the y-intercept of the regression line:
y-intercept = mean of the dependent variable - slope * mean of the independent variable
Calculations:
Mean of school year: 5.5
Mean of average cost: 19.0
Deviations from the mean for school year: -1.5, -0.5, 0.5, 1.5, 2.5
Deviations from the mean for average cost: -3.5, -2.5, -1.5, -0.5, 1.5
Product of the deviations from the mean: 5.25, 1.25, -0.75, 0.75, 3.75
Variance of the independent variable: 4.25
Slope of the regression line: 5.25 / 4.25 = 1.24
Y-intercept of the regression line: 19.0 - 1.24 * 5.5 = 14.5
Least squares regression equation:
Average cost = 14.5 + 1.24 * School year
A square has a are of 81 feet what is the length of each side
If the sum of a number and nine is doubled, the result is eight less than the number. Find the number.
Equation
Let the number = x
2*(x + 9) = x - 8
Solve
2(x + 9) = x - 8 Remove the brackets on the left
2x + 18 = x - 8 Subtract x from both sides
2x - x + 18 = - 8 2x and - x will combine
x + 18 = - 8 Subtract 18 from both sides
x = -8 - 18
x = - 26
Check
LHS
2(-26 + 9)
2(-17)
-34
RHS
x - 8
-26 - 8
- 34 and the RHS = LHS and they check
Your number would be -26
Sorry if this is wrong but I'm pretty sure its right
Given e (-2,3) f(-2,-2) g(3,-2) h(3,3) prove efgh is a rhombus
the answer to this question (-2,3)
25x5+15x3-40x2 anyone?
25 * 5 + 15 * 3 - 40 * 2 =
125 + 45 - 80 =
170 - 80 =
90
What number multiplied by itself 2 times equals 49
You're basically looking for the square root of 49. In fact, if a number [tex] x [/tex] gives [tex] y [/tex] when multiplied by itself two times, then you have [tex] x^2 = y [/tex], which also means that [tex] x [/tex] is the square root of [tex] y [/tex], i.e. [tex] x = \sqrt{y} [/tex]
In your case, the answer is 7, because you have
[tex] \sqrt{49}=7 \iff 7^2 = 49 [/tex]
which is indeed true
Answer:
Step-by-step explanation:
You want the square root of 49, which is 7
Given the equation Y -3 equals 1/2 (X +6 )in point slope form identify the equation of the same line in standard form
The standard form of a line:
[tex]Ax+By=C[/tex]
We have the equation of a line in the slope-point form:
[tex]y-3=\dfrac{1}{2}(x+6)[/tex] use distributive property
[tex]y-3=\dfrac{1}{2}x+3[/tex] add 3 to both sides
[tex]y=\dfrac{1}{2}x+6[/tex] multiply both sides by 2
[tex]2y=x+12[/tex] subtract x from both sides
[tex]-x+2y=12[/tex] change the signs
[tex]x-2y=-12[/tex]
Increasing the price of an item decreases the amount of people willing to buy it
Independent....
Dependent ...
In economic theory, the price of a product is considered the independent variable, and the quantity of the product demanded by consumers is considered the dependent variable. As price (independent variable) increases, the quantity demanded (dependent variable) decreases.
Explanation:In the context of economics and specifically, the law of demand, the price of a commodity is the independent variable and the quantity demanded is the dependent variable. This means that the amount of a product that consumers are willing to buy (dependent variable) can change based on the price of the product (independent variable). If a price changes, if all other factors remain constant, the quantity demanded will react accordingly. For example, if the price of an item increases, the quantity demanded decreases because consumers are less willing to buy the item due to its high price. Conversely, if the price decreases, the quantity demanded increases because the product becomes more affordable to consumers.
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Sophia buys a reel of thread for sewing. There are 10m of thread on the reel. She uses 210cm. How much is left on the reel in centimeters?
Answer:
7.9 meters left. or 790 cm
Step-by-step explanation:
HELP PLEASE!
What is the reason for Statement 7 of the two-column proof?
A) Angle Addition Postulate
B) Linear Pair Postulate
C) Ruler Postulate
D) Angle Congruence Postulate
Given: ∠A and ∠B are supplementary. m∠A=90°
Prove: ∠A≅∠B
Statements Reason
1. [tex]\angle A[/tex] and [tex]\angle B[/tex] are supplementary Given
2. [tex]m \angle A + m \angle B = 180^\circ[/tex] Def of supplementary angles
3. [tex]m \angle A = 90^\circ[/tex] Given
4. [tex]90^\circ + m \angle B = 180^\circ[/tex] Substitution property of Equality
5. [tex]m \angle B = 90^\circ[/tex] Subtraction property of Equality
6. [tex]m \angle A = m \angle B[/tex] Substitution property of Equality
7. [tex]\angle A \cong \angle B[/tex] Angle congruence postulate
When the measures of two angles are equal, then the angles are congruent by Angle congruence postulate.
Answer:
1. and are supplementary Given
2. Def of supplementary angles
3. Given
4. Substitution property of Equality
5. Subtraction property of Equality
6. Substitution property of Equality
7. Angle congruence postulate
When the measures of two angles are equal, then the angles are congruent by Angle congruence postulate.
Step-by-step explanation:
200 is 90 more than five times d. Find d.
Let:
Equation:
Solve:
200-90= the answer then find d which is easy
LOTS OF POINTS! PLEASE HELP!
Lena is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.
Company A charges $111 and allows unlimited mileage.
Company B has an initial fee of $75 and charges an additional $0.90 for every mile driven.
For what mileages will Company A charge less than Company B?
Use m for the number of miles driven, and solve your inequality for m.
Company A = 111
Company B = 75 + 0.90m ( 75 plus 0.90 per mile)
Set the 2 to equal and solve for m ( miles)
111 = 75 + 0.90m
Subtract 75 from each side:
36 = 0.90m
Divide both sides by 0.90:
m = 36 / 0.90
m = 40
At 40 miles both Company A and Company B would cost the same.
So for Company A to cost less than Company B, you would have to drive more than 40 miles.
m>40
There are 1000 toothpicks in a regular-sized box. If a jumbo box is made by doubling all the dimensions of the regular-sized box, how many toothpicks will the jumbo box hold?
Hi, here is the solution.
The doubling each dimensions increases the volume by 8. That is (2 * 2* 2)
There 1000 toothpicks in a regular box.
The jumbo box hold 8 *1000 = 8000 toothpicks.
Thank you.
Use synthetic division to find the quotient and remainder. Express your answer as a polynomial.
1. 2x^3-11x^2+13x-21*x-3
2. 3x^3+7x^2-13x+10*x+2
3. 2x^3+13x^2-21x+9*x-1
4. 7x^3-8x+16/x-2
5. 8x^4-14x^3-71x^2-10x+24/x-4
1. 2x³ - 11x² + 13x - 21 ÷ x - 3
x - 3 = 0 ⇒ x = 3
3 | 2 -11 13 -21
| ↓ 6 -15 -6
2 -5 -2 -27
1. Answer: 2x² - 5x - 2 - [tex]\frac{27}{x - 3}[/tex]
*************************************************************
2. 3x³ + 7x² - 13x + 10 ÷ x + 2
x + 2 = 0 ⇒ x = -2
-2 | 3 7 -13 10
| ↓ -6 -2 30
3 1 -15 40
2. Answer: 3x² + x - 15 + [tex]\frac{40}{x + 2}[/tex]
3. 2x³ + 13x² - 21x + 9 ÷ x - 1
x - 1 = 0 ⇒ x = 1
1 | 2 13 -21 9
| ↓ 2 15 -6
2 15 -6 3
3. Answer: 2x² + 15x - 6 + [tex]\frac{3}{x - 1}[/tex]
4. 7x³ + 0x² - 8x + 16 ÷ x - 2
x - 2 = 0 ⇒ x = 2
2 | 7 0 -8 16
| ↓ 14 28 40
7 14 20 56
4. Answer: 7x² + 14x + 20 + [tex]\frac{56}{x - 2}[/tex]
5. 8x⁴ - 14x³ - 71x² - 10x + 24 ÷ x - 4
x - 4 = 0 ⇒ x = 4
4 | 8 -14 -71 -10 24
| ↓ 32 72 4 -24
8 18 1 -6 0
5. Answer: 8x³ + 18x² + x - 6
6. Dawn lingua bought three yards of cloth to make some curtains. The cloth was on sale for $2.25 per yard. How much did dawn pay for the cloth if the sales tax was 5%?
7.25 u need to add 2.25+5=7.25