The equation of the straight line is 2y + 21x = 10. The correct option is (D).
How to represent a straight line on a graph?To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.
The given points are (-4, 47) and (2, -16) respectively.
The equation of the straight line passing through them can be written as,
(y - 47)/(x - (-4)) = (-16 - 47)/(2 - (-4))
=> (y - 47)/(x + 4) = -63/6
=> (y - 47)/(x + 4) = -21/2
=> 2(y - 47) = -21(x + 4)
=> 2y - 94 = -21x - 84
=> 2y + 21x = -84 + 94
=> 2y + 21x = 10
Hence, the standard form of the straight line passing through given points is 2y + 21x = 10.
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A fair dice i rolled once, what i the probability of getting a factor of 4 or a multiple of 3
Lets Recall the formula of Probability, where we know that;
P = Favourable outcomes / possible outcome
Given that , after rolling a die once we get the chances of probability
So , the total possible outcomes are 6 because are only 6 highest outcome possible
The factors of 4 are the numbers 1 , 2 and 4 which means its 3 outcomes
And the multiple of 3 are the numbers 3 and 6 which means it has 2 outcome
So, the chances of the outcome on the dice are = 1,2,3,4,6
Thus,
Probability = (1,2,4,3,6) / 6
There are 5 favourable outcomes on the numerator ,
Thus,
P=5/6
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Please help me solve!!
The percentage of population between 130 and 102 is 68%.
What is Normal Distribution?The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.
Given that the mean is 116 and the standard deviation is 14. Therefore, the approximate population between the given range of 102 to 130 is,
P(102 ≤ X ≤ 130) = P(X ≤ 130) - P(102 ≤ X)
[tex]= P(z \leq \dfrac{130-116}{14})- P(z \leq \dfrac{102-116}{14})[/tex]
= P(z ≤ 1) - P(z ≤ -1)
= 0.8413 - 0.1587
= 0.6826
Hence, the percentage is 68%.
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S, P, T.
S, P, Y.
TP,x
TxY
Answer:
S , P , T
Step-by-step explanation:
collinear points are points that lie on the same line.
S , P , T lie on the same line and are therefore collinear
Answer:
SPT
Step-by-step explanation:
You also have XPY but that isn't a choice in your list. SPT goes in a straight line making it collinear
To gather information about the elk population, scientists marked 30 elk. Later, they flew over the area and counted 150 elk, 18 of which
were marked.
To the nearest whole number, what is the best estimate of the elk population?
O 198
O 200
O250
O 280
Answer:
250
Step-by-step explanation:
We can approximate that the scientists counted [tex]\frac{18}{30}=\frac{3}{5}[/tex] of the elk.
So, the best estimate of the elk population is [tex]150(5/3)=250[/tex].
Answer:1,250
Step-by-step explanation:
A pair of shoes is priced at $35.99 but is on sale for 20% off. What is the sale price of the shoes?
Answer:
The shoes are on sale for $28.79
Step-by-step explanation:
First, you find the 20% of 35.99 which is 7.198.
Then, i rounded that number to 7.20.
Then do $35.99 - 7.20.
Your final answer is $28.79!
Hope this helps and good luck!
Help me plssssssssssssssssssss
Answer:
(2,0)
Step-by-step explanation:
5x + 9y = 10
4x -3y = 8 If I multiple this second equation all the way through by 3, then the y's would cancel out when I add the equations together.
12x -9y = 24 multiplied the second equation through by 3
5x + 9y = 10 Add the 2 equations together
17x = 34 Divide both sides by 14
x = 2
Plug 2 in for x for either of the two original equations and solve for y
5x + 9y = 10
5(2) + 9y = 10
10 + 9y = 10 Subtract 10 from both sides
9y = 0 Divide both sides by 0
y = 0
(2,0)
39 is 0.3% of what number? Use pencil and paper. Would you expect the answer to be a lot less than 39, slightly less than 39, slightly greater than 39, or a lot greater than 39? Explain.
39 is 0.3% of 13,000.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let the number be x
So, 0.3% of x= 39
0.3/ 100 x= 39
0.3 x = 3900
x= 3900/ 0.3
x= 13000
Hence, 39 is 0.3% of 13,000.
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Add [tex]\frac{1}{3}[/tex]+4.1 Write your answer as a mixed number in simplest form.
Answer: It will be 4.433333333 as a decimal and 4 13/30 as a mixed number in simplest form
ƒ”(x)=6x, f'(-3)=20, ƒ(-3)=-5
f(x)=?
Answer:
f(x) = x^3 - 7x + 1
Step-by-step explanation:
ƒ”(x)=6x ==> ƒ”(x)=6 * (x^1)
f'(x)=6/(1+1) * x^(1+1) + C ==> C is a constant that doesn't affect the derivative
f'(x)=6/2 * x^2 + C ==> simplify the first derivative
f'(x)=3 * x^2 + C ==> f'(x)=3(x^2) + C
f'(-3)=3((-3)^2) + C ==> plug in -3 into the derivative equation
f'(-3)=3(9) + C ==> simplify
20=3(9) + C ==> plug in 20 for f'(-3)
20=27+C
20-27=27-27+C ==> solve for C
C=-7
f'(x)=3(x^2) + (-7) ==> plug in -7 for C
f'(x)=3(x^2) - 7 ==> simplify
f(x) = 3/(2+1) * x^(2+1) - 7x + C
f(x) = 3/3 * x^3 - 7x + C
f(x) = x^3 - 7x + C
f(-3) = (-3)^3 - 7(-3) + C ==> plug in -3 into f(x)
f(-3) = -27 - (-21) + C
f(-3) = -27 + 21 + C ==> simplify
f(-3) = -6 + C
-5 = -6 + C ==> plug in -5 for f(-3)
-5 + 6 = -6 + 6 + C ==> solve for C
C = 1 ==> simplify
f(x) = x^3 - 7x + 1
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What is the largest possible product of two positive integers whose sum is 9?
Answer:
The largest possible product of two positive integers whose sum is 9 is achieved when the two integers are as far apart as possible, which occurs when one integer is the largest possible integer and the other is the smallest possible integer. The largest possible integer is the one that is closest to but less than 9, which is 8, and the smallest possible integer is 1. The product of 8 and 1 is 8, so the largest possible product of two positive integers whose sum is 9 is 8.
what is y in the solution for the system of equations x+5y=17 and 6x-5y=-3
The answer for the equation is x = 1 , y = 3.
Solve the following system: using elimination:
x + 5 y = 17 | (equation 1)
6 x - 5 y = -3 | (equation 2)
Swap equation 1 with equation 2:
6 x - 5 y = -3 (equation 1)
x + 5 y = 17 (equation 2)
Subtract 1/3 × (equation 1) from equation 2:
6 x - 5 y = -3 (equation 1)
0 x+(20 y)/3 = 20 (equation 2)
Multiply equation 2 by 3/20:
{6 x - 5 y = -9 | (equation 1)
{0 x+y = 3 | (equation 2)
Add 5 × (equation 2) to equation 1:
6 x+0 y = 6 (equation 1)
0 x+y = 3 | (equation 2)
Divide equation 1 by 6:
x+0 y = 1 | (equation 1)
0 x+y = 3 | (equation 2)
Collect results:
Answer: x = 1 , y = 3
What is equation?There are numerous ways in which one may define an equation. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an ‘equal’ sign. The most basic and simple algebraic equations consist of one or more variables in math. A linear equation may have more than one variable. A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.To learn more about linear equation refer to:
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20) In 28
A) 3.915
C) 4.295
B) 2.153
D) 3.332
Answer:
D
Step-by-step explanation:
Use a calculator to approximate [tex]\ln 28[/tex] to the nearest thousandth.
If 2x-18=-5 then what if x?
find the 12th term of the geometric sequence
5,-25,125....
The 12th term of the geometric sequence is a₁₂ = -244140625.
Define Geometric Progression
A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value. Its general term is,
aₙ = a₁ · rⁿ⁻¹.
The geometric sequence,
5, -25, 125 ....
from here,we know
a₁ = 5
Calculate the ratios of all the adjacent terms ,
r = aₙ₊₁ / aₙ
r = -25/5 = -5
r = 125/-25 = -5
We know, the formula for geometric sequence is
aₙ = a₁ · rⁿ⁻¹
Where, a₁ = initial term
r = common ratio
Now, we need to find 12th term so for that n = 12
Now, plug in the values
aₙ = a₁ · rⁿ⁻¹
a₁₂ = 5 * (-5) ¹²⁻¹
= 5 * -5¹¹
After calculation we get,
a₁₂ = -244140625
Hence, the 12th term of the geometric sequence is a₁₂ = -244140625.
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is 40 miles in 3 hours faster then 50 miles in 4 hours
Answer:
Step-by-step explanation:
To find which one is faster, it would be distance/speed.
40m/3 = 13.33 repeating
50m/4 = 12.5
You would be traveling faster at 40 miles in 3 hours since you are going at 13.33 miles per hour
20. A pair of standard dice are rolled. What is
the probability that at least one die is a 5,
given that the sum of the numbers on the
dice is at least 8?
The probability that at least one die is a 5, given that the sum of the numbers on the dice is at least 8 = 2/5
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
The outcomes when the sum dice is 8 are
S = { (2,6), (3,5), (4,4), (5,3) , (6,2)}
Total outcomes = 5
Number of outcomes when there is at least one die is a 5,
given that the sum of the numbers on the dice is at least 8 = 2
Probability = (Number of possible outcomes)/(Total number of outcomes)
So, the probability that at least one die is a 5, given that the sum of the numbers on the dice is at least 8 = 2/5
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If ABC is an equilateral triangle, then the mA =60
A. If the mA = 60, then ABC is an equilateral triangle.
B. If ABC is not an equilateral triangle, then the mA does not equal 60.
C. If the mA does not equal 60, then ABC is not an equilateral triangle.
Answer is C!
The true statement from the given options is C. If the mA does not equal 60, then ABC is not an equilateral triangle.
Equilateral triangle:An equilateral triangle is one in which the angles and all three sides are equal. An equilateral triangle is also called an equiangular triangle since each of its angles has a value of 60 degrees.
The equal angle in an Equilateral triangle = 60°
Here we have 3 options
A. If the mA = 60, then ABC is an equilateral triangle.
B. If ABC is not an equilateral triangle, then the mA does not equal 60.
C. If the mA does not equal 60, then ABC is not an equilateral triangle.
Here we need to justify which of the given point will be true in the case of Equilateral Triangles.
Given
Option A: If the mA = 60, then ABC is an equilateral triangle.
With the measurement of A = 60°, here we can't conclude that ABC is an equilateral triangle because there is a possibility that the remaining angles are not equal to 60°
Option B: If ABC is not an equilateral triangle, then the mA does not equal 60.
Any type of triangle can have an angle that is equal to 60° so the given statement is wrong.
Option C. If the mA does not equal 60, then ABC is not an equilateral triangle.
As we know each angle of an equilateral triangle is 60°, So it is true that If the mA does not equal 60, then ABC is not an equilateral triangle.
Therefore,
The true statement from the given options is C. If the mA does not equal 60, then ABC is not an equilateral triangle.
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Solve the following matrix equations .
with full explanations and working please
The matrix equations are solved as
a) The value of matrix X is [tex]X = \begin{pmatrix}-2&0&4\end{pmatrix}[/tex]
b) The value of matrix X is [tex]X=\begin{pmatrix}-5&1\end{pmatrix}[/tex]
What is multiplication of matrices?
The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. The first matrix must have the same number of columns as the second matrix has rows. The number of rows of the resulting matrix equals the number of rows of the first matrix, and the number of columns of the resulting matrix equals the number of columns of the second matrix
Given data ,
a)
Let the value of the matrix be X
Now , the equation is
[tex]2X = \begin{pmatrix}-4&0&8\end{pmatrix}[/tex]
Now , on simplifying the equation , we get
Divide by 2 on both sides of the equation , we get
[tex]X = \begin{pmatrix}-4&0&8\end{pmatrix} / 2[/tex]
Now , the value of matrix X is
[tex]X = \begin{pmatrix}-2&0&4\end{pmatrix}[/tex]
Therefore , the value of matrix X is [tex]X = \begin{pmatrix}-2&0&4\end{pmatrix}[/tex]
b)
Let the value of the matrix be X
Now , the equation is
[tex]3X\:-\:\begin{pmatrix}1&7\end{pmatrix}=\begin{pmatrix}-16&-4\end{pmatrix}[/tex]
On simplifying the equation , we get
Adding [tex]\begin{pmatrix}1&7\end{pmatrix}[/tex] on both sides of the equation , we get
[tex]3X=\begin{pmatrix}-16&-4\end{pmatrix}+\begin{pmatrix}1&7\end{pmatrix}[/tex]
Now , the value for 3X can be calculated as adding the 2 matrices
[tex]3X=\begin{pmatrix}-15&3\end{pmatrix}[/tex]
Divide by 3 on both sides of the equation , we get
[tex]X=\frac{1}{3}\begin{pmatrix}-15&3\end{pmatrix}[/tex]
So , [tex]X=\begin{pmatrix}-5&1\end{pmatrix}[/tex]
Therefore , the value of matrix X is [tex]X=\begin{pmatrix}-5&1\end{pmatrix}[/tex]
Hence , the matrix equations are solved as
a) The value of matrix X is [tex]X = \begin{pmatrix}-2&0&4\end{pmatrix}[/tex]
b) The value of matrix X is [tex]X=\begin{pmatrix}-5&1\end{pmatrix}[/tex]
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Bro someone help me with this math pls fast
Answer:
Step-by-step explanation:
Can You Please Send Me A Clearer Picture I Can Help
sum of -7x² - 1 and x² - x - 5
Answer:
-6x²-x-6
Step-by-step explanation:
-7x²-1+x²-x-5
-6x²-1-x-5
-6x²-x-6
Please complete this Pythagorean Theorem page 50 points And I will give brainiest and thanks and invites.
Applying the Pythagorean theorem, the missing side of each of the right triangle are:
i. c = 15.8 m
ii. s = 24.1 cm
iii. a = 12.8 feet
iv. t = 4.6 inches
Pythagorean Theorem.Pythagorean theorem is one that can be used to determine the third unknown side of a right angled triangle. It is given by:
/Hyp/^2 = /Adj/^2 + /Opp/^2
The missing side of each of the right triangle can be determined as:
1. Let the value of unknown hypotenuse side by represented by c, so that:
/Hyp/^2 = /Adj/^2 + /Opp/^2
c^2 = /13/^2 + /9/^2
= 169 + 81
= 250
c = [tex]\sqrt{250}[/tex]
= 15.8
c = 15.8 m
2. Let the value of unknown hypotenuse side be represented by s, so that;
/Hyp/^2 = /Adj/^2 + /Opp/^2
s^2 = /16/^2 + /18/^2
= 256 + 324
= 580
s = [tex]\sqrt{580}[/tex]
= 24.1
s = 24.1 cm
3. Let the value of unknown adjacent side be represented by a,
/Hyp/^2 = /Adj/^2 + /Opp/^2
19^2 = a^2 + /14/^2
361 = a^2 + 196
a^2 = 361 - 196
= 165
a = [tex]\sqrt{165}[/tex]
= 12.8
a = 12.8 ft
4. Let the unknown adjacent side be represented by a,
/Hyp/^2 = /Adj/^2 + /Opp/^2
/11/^2 = t^2 + /10/^2
121 = t^2 + 100
t^2 = 121 - 100
= 21
t = [tex]\sqrt{21}[/tex]
= 4.6
t = 4.6 in
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What is the measure of ∠Y 40° 80° 90° 100°?(please help me)
The measure of <Y: 40⁰,80⁰90⁰100⁰ are the complementary angles and their supplementary angles respectively which are 50⁰,10⁰,0⁰ and 70⁰ respectively
How to calculate measurement of angles?The measure of angles is defined as the complementary or or supplementary angle of the given angle.
Complementary angles add up to 90⁰
supplementary angles add up to 180⁰
The given angles are: 40⁰, 80⁰, 90⁰ and 100⁰
The measure of 40⁰
x+40=90⁰
x=90-40
x=50⁰
The measure of 80⁰ is
x+80=90
x=90-80
x=10⁰
The measure of 90⁰ is
x+90=90
x=90-90
x=0⁰
The measure of 100⁰ is
x+100=180
Since 100⁰ is an obtuse angle
x=180-100
x=80⁰
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Colleen and Kara were ordering at Mc D's. Colleen ordered 4
hamburgers and 2 fries, paying $11. Kara ordered 4 hamburgers and 4
fries. She paid $14. What is the cost of one hamburger and what is the
cost of one order of fries?
Express Colleen's Order in terms of H and F.
1.
Express Kara's Order in terms of H and F.
Solve for H and F using the elimination method.
Answer: Fries = $1.50 Hamburger = $2
Step-by-step explanation:
so since the first person payed 11 for 4 burgers and 2 fries and the second person got 2 more fries than the first person and spent 14 and there is a 3 dollar difference which 3 divided by 2 is 1.5 which means that the fires a 1 dollar and 50 cents. so 3 dollars subtracted from 11 equals 8 and 8 divided by 4 is 2 dollars leaving you with hamburgers being 2 dollars and fries being 1 dollar and 50 cents
to compute the minimum sample size for an interval estimate of μ when the population standard deviation is known, we must first determine all of the following except _____.
To compute the minimum sample size for an interval estimate of μ when the population standard deviation is known, we must first determine all of the following except The Degrees of Freedom.
Given,
To compute the minimum sample size for an interval estimate of μ when the population standard deviation is known, we must first determine all of the following except _____.
Now, According to the question:
Let's know:
The Degrees of Freedom:
Degrees of freedom refers to the maximum number of logically independent values, which are values that have the freedom to vary, in the data sample. Degrees of freedom is calculated by subtracting one from the number of items within the data sample.
Hence, To compute the minimum sample size for an interval estimate of μ when the population standard deviation is known, we must first determine all of the following except The Degrees of Freedom.
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Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Ashley's hair grew 1 and 1/2 inches in 2 and 3/4 of a month. At what
Rate did ashley's hair grow per month?
Ashley's hair grew at a rate of approximately 0.545 inches per month.
What is the rate of change?
Rate of change problems can generally be approached using the formula R = D/T, or rate of change equals the distance traveled divided by the time it takes to do so.
To find the rate at which Ashley's hair grew per month, we need to divide the total amount of hair growth by the number of months.
First, let's convert the units to a common denominator. 1 and 1/2 inches is the same as 3/2 inches, and 2 and 3/4 months is the same as 11/4 months.
Now we can divide the total amount of hair growth (3/2 inches) by the number of months (11/4 months) to get the rate at which Ashley's hair grew per month:
(3/2 inches) / (11/4 months) = (3/2) * (4/11) inches/month
= 6/11 inches/month
= approximately 0.545 inches/month
Therefore, Ashley's hair grew at a rate of approximately 0.545 inches per month.
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Simplify 6(4x-3)-9x
Answer:
(24x-18)-9x
hope this helps, tell me if you need to simplify it further
pls help due now!!!!!!!!!
The correct option for the given linear equation condition is D. i.e. Liza will pass Ralph after 5 hours, and they each will have travelled 325 miles.
What is a linear equation?
When the parameter in the equation has a degree of 1, the system is said to be linear. One, two, or even more variables could be present.
The collection of two or more linear equations involving the same variables is known as a system of linear equations.
From the question,
The situation is given as:
y = 60x + 25
y = 65x
The time after Liza leaves, she passes Ralph will be
or, 65x = 60x + 25
or, 5x = 25
or, x = 5 hours
Then the distance covered by both of them, then after 5 hours will be
y = 65 (5)
y = 325 miles
Hence, the correct option is D.
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The distance traveled at speed s for time t is st. Keith rode on a train traveling at 60 miles per hour for 2.5 hours.
How far did the train travel?
Answer:
150 miles
Step-by-step explanation:
60*2.5=150
Find the 200th term in the sequence below.
a₁ = 8
d=12
The 200th term in the sequence is 2,396.
To find the 200th term in the sequence we have the formula:
an=a1+(n-1)d --------(1)
Given that values of a1 and d are 8,12
"a1" is called the first value of the sequence.
"d" is called the difference between two numbers.
Assume that n is 200 because we have to find the 200th term.
Now, we will substitute all the values in the above equation(1)
an=a1+(n-1)d
a200=8+(200-1)12
a200=8+(199)12
a200=8+2,388
a200=2,398.
So, the 200th term in the sequence is:2,398
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