What is the equation of the line that passes through the point (1, -3) and has a
slope of -3?
The equation of the line is, y = -3x.
What is point slope form of the line?
A line's point slope form equation is y - y1 = m(x – x1). Consequently,
y - 0 = m(x - 0), or y = mx, is the equation of a line passing through the origin with a slope of m.
Let the line passes through the point (1, -3) and having slope of -3.
Consider, the point slope form of the line,
[tex]y-y_1=m(x-x_1)[/tex]
Plug, [tex](x_1, y_1) = (1, -3), m = -3[/tex]
So, the above equation becomes
[tex]y-(-3)=-3(x-1)\\y+3=-3x+3\\y=-3x+3-3\\y=-3x[/tex]
Hence, the equation of line that passes through the point (1, -3) and having slope -3 is y = -3x.
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if f(x) = 2x - 4 find f(a^2)
Answer: [tex]f(a^2)=2a^2-4[/tex]
Step-by-step explanation:
Substituting [tex]a^2[/tex] for [tex]x[/tex], [tex]f(a^2)=2a^2-4[/tex].
1. Which of the following equations exemplifies the Additive Identity Property?
A) 1+(7+8)=(1+7)+8
B) 8+1=1+8
C) 33+0=33
D) 14+3=7+10
2. Which of the following equations exemplifies the Multiplicative Identity Property?
A) 9.5x1=9.5
B) 3x10=2x15
C) 3x0=0x3
D) 9(5x6)=(9x5)6
i got A for 2. but im confused on the first
1. the equation that exemplifies the additive identity property is: C. 33 + 0 = 33.
2. The equation that exemplifies the multiplicative identity property is: A. 9.5 × 1 = 9.5.
What is the Additive Identity Property?The additive identity property states that the sum of adding zero to any number will give you the same number itself.
For example, 4 + 0 = 0.
What is the Multiplicative Identity Property?The multiplicative identity property states that a number multiplied by 1 will always give you a product that is the same number itself.
For example, 4 × 1 = 4.
1. The equation, 33 + 0 = 33, shows the additive identity property, because the sum is the same number itself after 0 is added to it.
2. The equation, 9.5 × 1 = 9.5, also shows the multiplicative identity property.
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let x represent one number and let Y represent another number.
The sum of two numbers is -7.
If one number is subtracted from the other, their difference is 11.
Use the given conditions to write a system of equations.
Solve the system and find the numbers
Answer:
c I got you ok answer c
Step-by-step explanation:
bc I got this correct
Answer:
Its D, x+y=-7;x-y=11. Also Part 2 is 2,-9
Step-by-step explanation:
Just did it Pearson 2022
3-107. Find common denominators and calculate each of the following sums.
b. +3
What is the least common multiple of 8 and 4? Of 5 and 3?
T
d. Explain how finding the least common multiple of two numbers can help
you add fractions.
Answer:
LCM(8,4)=8.LCM(5,3)=15. LCM can be used to create equivilant fractions, meaning you can add fractions with much more efficiency.
Step-by-step explanation:
3. Functions f and g are shown below. Which
best represents
function g?
a. g(x) = f(x) - 3
b. g(x) = -f(x)
c. g(x) = f(x)
d. g(x) = f(x - 2)
Answer:
i think it might be c
Step-by-step explanation:
a triangle has sides with lengths of 10meters, 16 meters and 20meters. is it a right angled triangle
Answer:
It is not a right triangle.
Step-by-step explanation:
If the triangle were a right triangle, then the Pythagorean theorem would apply.
The Pythagorean theorem says: [tex]A^{2} + B^{2} = C^{2}[/tex]
If A = 10, B = 16, and C = 20, then [tex]10^{2} + 16^{2} = 20^{2}[/tex].
[tex]10^{2} + 16^{2} = 100 + 256 = 356[/tex]
[tex]20^{2} = 400[/tex]
In conclusion, [tex]356 \neq 400[/tex], so this triangle is not a right triangle.
Delilah has assets that total $56,326 and liabilities that total $32,129. What is her net worth?
The net worth of Delilah given the assets and liabilities will be $24197.
How to calculate the net worth?From the information given, Delilah has assets that total $56,326 and liabilities that total $32,129.
It should be noted that the formula to calculate the net worth will be:
= Assets - Liabilities
= $56,326 - $32,129
= $24197
The net worth is $24197.
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Swimming pool A holds 215 gallons
213 gallons of water. How many times as many gallons does pool a hold
than pool B? (Example 5)
2B times as many gallons does pool A hold than pool B.
What is gallons?
The gallon is a volumetric unit that is used in both imperial and American customary measurements.
The imperial gallon (imp gal), which is equal to 4.54609 liters and was once used in various Caribbean nations as well as the United Kingdom, Ireland, Canada, Australia, and Australia.
Given:
Swimming pool A has 2^15 gallons of water.
Swimming pool B has 2^13 gallons of water.
We have to find the number of times pool A hold than pool B.
It is obvious that Swimming Pool A holds more water than Swimming Pool B.
Consequently, we must determine how many times as many gallons Pool A holds as Pool B:
2^15 > 2^13.
Therefore,
A = 2^15, B = 2^15
[tex]A = (\frac{2^1^5}{2^1^3}) B = 2B\\ A = 2B[/tex]
Hence the proof.
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A cube-shaped gift box has a volume of 1000 cubic inches. Solve s³ = 1000 to find the lengths of one side of the box.
s=__in.
If 4x+5y=−5 is a true equation, what would be the value of 8+4x+5y?
Answer:
3
Step-by-step explanation:
[tex]4x + 5y = - 5 \\ 8 + 4x + 5y = {?} \\ 8 + - 5 \\ = 3 \\ 8 + 4x + 5y = 3[/tex]
In a recent court case it was found that during a period of 11 years people were selected for grand jury duty and % of them were from the same ethnicity. Among the people eligible for grand jury duty, % were of this ethnicity. Use a significance level to test the claim that the selection process is biased against allowing this ethnicity to sit on the grand jury. Identify the null hypothesis, alternative hypothesis, test statistic, p-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the p-value method and the normal distribution as an approximation to the binomial distribution.
The Null and Alternative hypothesis are
Hₒ: π= 0.79
Hₐ: π > 0.79
Statistic Z = -26.38
P-value = 0
Conclusion : The null hypothesis is
rejected .
Final Conclusion : which implies that population proportion is different from
π= 0.79.. This sample proportion can notbe product of chance.
There is enough evidence to support to the claim that selection of people is biased against allowing this ethnicity to sit on the grand jury.
We have problem of proportion and we have to apply hypothesis testing in it .
We claim that the selection is biased against allowing this ethnicity to sit on the grand jury. This means that proportion of people of enthic selected for jeury in a way below from proportion that eligible for jury .
Null and Alternative hypothesis are
Hₒ: π= 0.79
Hₐ : π> 0.79
The significance level is 0.01
The sample we will use is total of 876 people that were selected for grand jury duty (n= 876). 42% of them were entnicity for which we are testing , so sample proportion is p= 0.42
The standard error is
σₚ= s√ (π(1-π)/n)= √ 0.79 (1-0.79)/ 876 = √0.00019 = 0.0137~ 0.014
Then we can calculate Z – value
Z = (p-π+0.5/n)/ σₚ =( 0.42 – 0.79 + 0.5/876 )/ 0.014 = - 0.03964/0.014 = - 26.387
P-value for this test statistic is 0
P-value (z<-26.38)= 0
P-value = 0 < 0.01
As we see that P-value is less lower then significance level . This sample result is unpredictable. The null hypothesis is rejected which implies that population proportion is different from π= 0.79
This sample proportion can not be product of chance.
There is enough evidence to support to the claim that selection of people is biased against allowing this ethnicity to sit on the grand jury.
#Complete Question:
In a recent court case it was found that during a period of 11 years 876 people were selected for grand jury duty and 42% of them were from the same ethnicity. Among the people eligible for grand jury duty, 79.5% were of this ethnicity. Use a 0.01 significance level to test the claim that the selection process is biased against allowing this ethnicity to sit on the grand jury. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method and the normal distribution as an approximation to the binomial distribution. Which of the following is the hypothesis test to be conducted?
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a bag contains red marbles, white marbles, green marbles, and blue marbles. there are an equal number of red marbles and white marbles, and five times as many green marbles as blue marbles. there is a chance of selecting a red marble first. what is the fewest possible number of green marbles in the bag?
The fewest possible number of green marbles in the bag is 5.
Defined the word probability?Probability is used to describe the chances of an occurrence. We can evaluate the numerical data involved with the likelihood that a distinct event will occur using probability. Probabilities are expressed as percentages, or, in decimal number, as numbers ranged from 0% to 100%.As per the stated question.
Since there is a 35% possibility of obtaining a red, the same percentage must apply to getting a white.
35+35=70%
You have a 100% probability of selecting a marble,
70+30=100
The probability that you will select a blue or green stone must thus be 30%.
And if there are B blue marbles, then there will be 5 green marbles.
B+5B=30%
6B=30%
Blue=5%
Green = 30-5=25%
Thus, the ratio becomes.
Red: White: Green : blue
35 : 35 : 25: 5
Dive each by 5.
7 : 7 : 5 : 1
Thus, the fewest possible number of green marbles in the bag is 5.
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The complete question is-
A bag contains red marbles, white marbles, green marbles, and blue marbles. There are an equal number of red marbles and white marbles, and five times as many green marbles as blue marbles. There is a 35% chance of selecting a red marble first. What is the fewest possible number of green marbles in the bag?
So, anyone wann.a decorate my rrom with me? we could give decorating ideas and what not, just bore.d
Answer: sure:)
Step-by-step explanation:
5. If f(x)=4x - 1 and f(x)=11, find x.
Answer:
x = 3
Step-by-step explanation:
f(x)=4x - 1
f(x)=11, find x.
We want the value of x that would make 4x-1 equal to 11. Use 11 instead of f(x):
f(x)=4x - 1
11=4x - 1
Solve:
12 = 4x
x = 3
If x were 3, 4x-1 would be 4*3-3 or 11
in a sale, prices are reduced by 12%. Hani bought a pair of boots for the sale price of £61.60. what was the original price of the boots?
Answer: $68.99
Step-by-step explanation:
12% of 61.60 is 7.39200, if you simplify the total, you would get 7.39. Then, you add the total with the sale price to get the original price. Which in this case is $68.99.
X+3y+z=-8
2x+y-6z+20
x-2y+z=-13
The solution for the system of equations -
x+3y+z=-8
2x+y-6z=20
x-2y+z=-13
is x = 5.875, y = 1, z = 16.875
What is the general equation of a Straight line?
The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line in point slope form can be also written as-
[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]
We have the following set of equations -
x+3y+z=-8 ..[1]
2x+y-6z=20 ..[2]
x-2y+z=-13 ..[3]
We can write eq [3] as -
z = - 13 - x + 2y
So, eq [1] and [2], will become -
x + 3y + (-13 - x + 2y) = -8
x + 3y - 13 - x + 2y = -8
5y = - 8 + 13
5y = 5
y = 1 ..Eq[4]
AND
2x + y - 6z = 20
2x + y - 6(- 13 - x + 2y) = 20
2x + y + 78 + 6x - 12y = 20
2x + 1 + 78 + 6x - 12 = 20
8x = 47
x = 5.875 ..Eq[5]
Now -
x - 2y + z = -13
5.875 - 2 + z = - 13
z = 16.875
Therefore, the solution for the system of equations -
x+3y+z=-8
2x+y-6z=20
x-2y+z=-13
is x = 5.875, y = 1, z = 16.875.
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An arithmetic sequence a starts 24, 20,... Explain how you would calculate the value
of the 20th term.
Answer:
Step-by-step explanation:
first you need to find the nth term
that would be -4n+28
then you just need to substitute 20 into the position of n
-4*20 = -80
-80+28=-52
What is the end behavior for the liner function?
Lines do not end, so there can not be an end behavior.
What is straight line?
Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.
The equation of the right sideline is y+8 = [tex]\frac{4+8}{2-0}[/tex] (x-0)
y+8 = 6(x -0)
y =6x - 8
Now the endpoint of the line is given so it will not extend indefinitely.
Hence the Lines do not end so there can not be an end behavior.
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A football team has an away game, and the bus breaks down. The coaches decide to drive the players to the game in cars and vans. Four players can ride in each car. Six players can ride in each van. There are 48 players on the team. The equation $4x+6y=48$ models this situation, where $x$ is the number of cars and $y$ is the number of vans
The 4 possible solutions in the context of the problem are (0, 8), (3, 6), (6, 3), and (9, 2)
Given the equation that models the situation expressed as:
4x + 6y = 48
We are to find 4 possible solutions for x and y. Note that the values of x and y must be integers.
If there are no cars i.e. at when x = 0
4(0) + 6y = 48
0 + 6y = 48
6y = 48
y = 48/6
y = 8
One of the solution is (0, 8)
If there are 3 cars, i.e. at when x = 0
4(3) + 6y = 48
12 + 6y = 48
6y = 48 - 12
y = 36/6
y = 6
The second solution will be (3, 6)
If there are 6 cars, i.e. at when x = 6
4(6) + 6y = 48
24 + 6y = 48
6y = 48 - 24
y = 24/6
y = 4
The third solution will be (6, 3)
If there are 9 cars, i.e. at when x = 9
4(9) + 6y = 48
36 + 6y = 48
6y = 48 - 36
y = 12/6
y = 2
The fourth solution will be (9, 2)
Hence the 4 possible solutions in the context of the problem are (0, 8), (3, 6), (6, 3), and (9, 2)
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Study the figure. What is the measure of the missing interior angle?
The value of the missing interior angle is 25°
What is a right-angled triangle?A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle.
given angles of the triangle, 90° and 65°
Let, the unknown angle be x
so that,
x + 90 + 65 = 180 ( sum of angles in a triangle)
x + 155 = 180
x = 180 - 155
x = 25°
In conclusion, the unknown angle is 25°
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Which equation represents a line which is perpendicular to the line y=2x-5y
Answer:
Step-by-step explanation:
y=-3x
I could be wrong, but I hope it helps at
Find g(x), where g(x) is the translation 1 unit left of f(x)=9x–8.
Where g(x) is the translation 1 unit left of f ( x ) = 9x – 8 then g(x) is
g (x ) = 9x + 1What is translation?Translation refers to a type of transformation that involve a straight line movement.
Movements as seen in translation includes
leftrightupdownThe up and down movements are on the vertical direction controlled by the y coordinate.
The left and right movements are on the horizontal direction controlled by the x coordinate.
When translating a graph, adding units moves the graph to the left and removing units moves the graph to the right.
hence we say
f(x) = 9x – 8
g(x) = f(x + 1)
= 9(x+1) – 8
= 9x + 9 - 8
= 9x + 1
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The gradient of a curve C is given by
dy = x² + 6 + 9x-².
dx
The point (3, 20) lies on C. Find an equation for the curve C in the form y = f(x).
Answer:
[tex]y = \frac{1}{3} {x}^{3} + 6x - \frac{9}{x} - 4[/tex]
Step-by-step explanation:
explanation shown in picture ^^
700% of what number is 1,540
If 700% of a number is 1540, then the number is 220
The given percentage = 700%
The percentage of a number is defined as the ratio that can be expressed as the fraction of 100.
Consider the number as x
Here the 700% of the number is 1540
Then the equation will become
x × 700% = 1540
Solve the equation and find the value of x
x × (700/100) = 1540
Divide the terms first
x × 7 = 1540
Move the 7 to the right hand side of the equation
x = 1540/7
Divide the terms
x = 220
Hence, if 700% of a number is 1540, then the number is 220
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How many 8s in 72?
How many 800s in 72,000?
How many 5s in 450,000?
How many 3,000s in 270,000?
How many 90s in 63,000?
3c + bc - 2a if a=6,b=4, and c=10
Answer:58
Step-by-step explanation:
PLS HELP I DONT UNDERSTAND THIS-
Which types of classification does e fall under? Select all the different classifications.
A) Natural numbers
B) Whole numbers
C) Integers
D) Rational numbers
E) Irrational numbers
F) Real numbers
Making a certain shade of paint requires mixing 3 parts silver with 4 parts green. Meg uses this data to start this table of equivalent ratios. A 2-column table has 3 rows. Column 1 is labeled Silver paints (parts) with entries 3, blank, blank. Column 2 is labeled Green paint (parts) with entries 4, blank, blank. Which ratios are equivalent to 3 parts silver paint to 4 parts green paint? Check all that apply. 4:5 6:8 5:6 9:12
The ratios that are equivalent to 3 parts silver paint to 4 parts green paint are: 6:8 and 9:12.
What is a ratio?A ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.
Generally speaking, a proportional relationship can be represented by the following mathematical expression:
x = ky
Where:
x represents the silver paints (parts).y represents the green paint (parts).k represents the constant of proportionality.In this context, the constant of proportionality or ratio of the quantity of silver paint (parts) to green paints (parts) can be calculated as follows:
Constant of proportionality (k) = x/y
Constant of proportionality (k) = 3/4
Now, we can determine the equivalent ratios as follows:
Equivalent ratio = 4/5 ≠ 3/4
Equivalent ratio = 6/8 = 3/4 (divide by 2)
Equivalent ratio = 5/6 ≠ 3/4
Equivalent ratio = 9/12 = 3/4 (divide by 3).
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the answer is 6:8 and 9:12
Step-by-step explanation: hope this helped ;D
Zach took a science test. He answered 42 questions correctly and 8 questions incorrectly.
What percentage of the questions did Zach answer correctly?
Answer:
84%
Step-by-step explanation:
correct answers = 42
incorrect answers =8
total mark=50
% of the correct =
[tex] \frac{42}{50} \times 100 = 84[/tex]answer is 84%
