Answers
Answer:
slope = - \(\frac{4}{3}\) , point on line = (4, - 3 )
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
y + 3 = - \(\frac{4}{3}\) (x - 4) ← is in point- slope form
with slope m = - \(\frac{4}{3}\) and point on line (a, b ) = (4, - 3 )
Related Questions
Please help me I will mark BRAINLIEST THANK YOUUUUU
Answers
Answer:
33%
Step-by-step explanation:
The multiples of 3 are 3,6,9,12
Sum is 6+14+12+1 = 33
The total is 3+6+8+11+14+16+15+12+9+5+1=100
The experimental probability is number of multiples of 3 over the total
33/100 = 33%
A baseball is covered with 42.3 cm2 of leather. Another larger baseball is to be constructed so that the ratio of the volume of the larger baseball to that of the smaller baseball is 16 over 3. What will be the surface area of the new baseball? Round your answer to the nearest tenth
Answers
We are told that the volumes between two spheres is 16/3, this means that:
\(\frac{V_1}{V_2}=\frac{16}{3}\)Now the formula for the volume of a sphere is:
\(V=\frac{4\pi r^3}{3}\)Replacing in the previous formula:
\(\frac{\frac{4\pi r^3_1}{3}}{\frac{4\pi r^2_2}{3}}=\frac{16}{3}\)Simplifying:
\(\frac{r^3_1}{r^3_2}=\frac{16}{3}\)Now we solve for the first radius which is the radius of the bigger sphere:
\(r^3_1=\frac{16}{3}r^3_2\)Now we determine the radius of the smallest ball using the formula for the surface area of a sphere:
\(A_S=4\pi r^2_2\)Now we replace the value of the surface area:
\(42.3=4\pi r^2_2\)Now we solve for the radius:
\(\frac{42.3}{4\pi}=r^2_2\)Taking square root on both sides:
\(\sqrt[]{\frac{42.3}{4\pi}}=r_2\)Solving the operation:
\(1.83\operatorname{cm}=r_2\)Now we replace the value of the radius in the proportion:
\(r^3_1=\frac{16}{3}(1.83\operatorname{cm})^3\)Solving the operations:
\(r^3_1=32.7\operatorname{cm}^3\)Taking cubic root to both sides:
\(r_1=\sqrt[3]{32.7\operatorname{cm}^3}\)Solving the operation:
\(r_1=3.19\operatorname{cm}\)Now we use the formula for the surface area using the new radius:
\(A_S=4\pi r^2_1\)Replacing the radius:
\(A_S=4\pi(3.19cm)^2\)Solving the operation:
\(A_S=127.9\operatorname{cm}^2\)Therefore, the surface area of the new ball is 127.9 square centimeters.
According to the graph, what is the factorization of x - 5x + 6? y=x2.5x + 6 5 A. (x - 3)(x-2) B. (x+3)(x - 2) C. (x-3)(x + 2) O D. (x + 3)(+ 2) E PREVIOUS
Answers
Given:
To find the factorization of the graph,
\(x^2-5x+6\)By factorization, we get
\(\begin{gathered} x^2-2x-3x+6 \\ x(x-2)-3(x-2) \\ (x-3)(x-2) \end{gathered}\)Hence option a) is the correct answer.
3 6 9 12 15 18 21 24 27 30 is odd or even numbers?
Answers
Answer: Half of them are even and half of them are odd.
Step-by-step explanation:
The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.
The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.
Therefore, out of the given numbers, half of them are even and half of them are odd.
________________________________________________________
2n²×5 work out 6th term of this sequence
Answers
The 6th term of this sequence is 360
How to determine the 6th term of this sequenceFrom the question, we have the following parameters that can be used in our computation:
Sequence representation = 2n² × 5
This means that
nth term = 2n² × 5
So, we have
f(n) = 2n² × 5
For the 6th term, the value of n is 6
i.e. n = 6
Substitute the known values in the above equation, so, we have the following representation
f(6) = 2(6)² × 5
Evaluate
f(6) = 360
Hence, the 6th term s 360
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PLZ HELP THIS IS DUE TODAY AND PLZ NO LINKS.
Answers
Answer:
a - they should be large and sturdy
Step-by-step explanation:
The article states that artificial reefs can be made from materials such as concrete, or large pieces of waste such as subway cars, takes, and aircraft carriers. All of these items are large and sturdy.
Hope this helps, have a wonderful day :))
Which of the following is the correct graph of the solution to the inequality −8 ≥ −5x + 2 > −38?
number line with an open dot at 2 with shading to the left and another open dot at 8 with shading to the right
number line with an open dot at 8 and at 2 with shading in between
number line with a closed dot on 2 and an open dot on 8 and shading in between
number line with closed dots at 2 and 8 with shading between the 2 and the 8
Answers
We want to see which would be the correct graph of a given inequality.
We will see that the correct option is the third one:
"number line with a closed dot on 2 and an open dot on 8 and shading in between"
Here the inequality is:
-8 ≥ −5x + 2 > −38
Let's simplify this, first we can subtract 2 in the 3 parts of the inequality:
-8 - 2 ≥ −5x + 2 - 2 > −38 - 2
-10 ≥ −5x > −40
Now we can divide the 3 parts by -5, notice that as it has a negative sign, the direction of the symbols must change:
-10/-5 ≤ −5x/-5 < −40/-5
2 ≤ x < 8
Then the graph will be a solid dot at x = 2 (because x = 2 is a valid solution) that extends to the right unitl it hits an open dot at x = 8 (because x = 8 is not a solution).
Thus the correct option is the third one:
"number line with a closed dot on 2 and an open dot on 8 and shading in between"
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what is da rate to question
Answers
The calculated value of the rate of the graph is 0.8
How to determine the rate of the graphfrom the question, we have the following parameters that can be used in our computation:
The graph
Where, we have
(0, -16) and (20, 0)
The rate of the graph is calculated as
Rate = Change in y/x
using the above as a guide, we have the following:
Rate = (0 + 16)/(20 - 0)
Evaluate
Rate = 0.8
Hence, the rate is 0.8
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Which shows a rational number plotted correctly on a number line?
Answers
A triangle LMN with ln = 12 cm,Nm= x cm, Nk = 6cm and Km 8cm
Calculate the value of
(i) x
(ii) o
Answers
The value of x is 9 cm, and angle O is 0 degrees.
To solve the triangle LMN and find the values of x and angle O, we can use the Law of Cosines and the Law of Sines. Let's go step by step:
(i) To find the value of x, we can use the Law of Cosines. According to the Law of Cosines, in a triangle with sides a, b, and c, and angle C opposite to side c, the following equation holds:
c^2 = a^2 + b^2 - 2ab * cos(C)
In our case, we want to find side NM (x), which is opposite to angle N. The given sides and angles are:
LN = 12 cm
NK = 6 cm
KM = 8 cm
Let's denote angle N as angle C, side LN as side a, side NK as side b, and side KM as side c.
Using the Law of Cosines, we can write the equation for side NM (x):
x^2 = 12^2 + 6^2 - 2 * 12 * 6 * cos(N)
We don't know the value of angle N yet, so we need to find it using the Law of Sines.
(ii) To find angle O, we can use the Law of Sines. According to the Law of Sines, in a triangle with sides a, b, and c, and angles A, B, and C, the following equation holds:
sin(A) / a = sin(B) / b = sin(C) / c
In our case, we know angle N and side NK, and we want to find angle O. Let's denote angle O as angle A and side KM as side b.
We can write the equation for angle O:
sin(O) / 8 = sin(N) / 6
Now, let's solve these equations step by step to find the values of x and angle O.
To find angle N, we can use the Law of Sines:
sin(N) / 12 = sin(180 - N - O) / x
Since we know that the angles in a triangle add up to 180 degrees, we can rewrite the equation:
sin(N) / 12 = sin(O) / x
Now, we can substitute the equation for sin(O) from the Law of Sines into the equation for sin(N):
sin(N) / 12 = (6 / 8) * sin(N) / x
Now, we can solve this equation for x:
x = (12 * 6) / 8 = 9 cm
So, the value of x is 9 cm.
To find angle O, we can substitute the value of x into the equation for sin(O) from the Law of Sines:
sin(O) / 8 = sin(N) / 6
sin(O) / 8 = sin(O) / 9
9 * sin(O) = 8 * sin(O)
sin(O) = 0
This implies that angle O is 0 degrees.
Therefore, the value of x is 9 cm, and angle O is 0 degrees.
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The figure for the given question is provided here :
Which of the following is an equation of a curve that intersects at right angles every curve of the family y=(1/x)+k (where k takes all real values)?a. y=-xb. y=-x^2c. y=(-1/3)x^3d. y= (1/3)x^3e. y=lnx
Answers
The equation of the curve that intersects at right angles to every curve of the family y=(1/x)+k is y=lnx
y=-x+k is the equation of a curve that meets at right angles every curve in the family y=(1/x)+k (where k can take any real value). This is known as the 'orthogonal curve' of the y=(1/x)+k family. It is calculated by obtaining the reciprocal of the original equation and then removing k from the y-axis.
A straight line with a negative slope is given by the equation y=-x+k. Every point on the line has an x-value that is the inverse of its y-value. At the point where x=1/k and y=k, the equation will always meet the curve of the family y=(1/x)+k at a right angle. This point is the same for all values of k and is known as the 'origin' of the function.
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A bag has eight balls labeled A, B C D, E, F. G, and H. One ball will be randomly picked, and its letter will be recorded as the outcome. Give the sample space describing all possible outcomes. Then give all of the outcomes for the event of choosing a letter from A to D. If there is more than one element in the set, separate them with commas. Sample space: l 00 X 5 Event of choosing a letter from 4 to D
Answers
The Event of choosing a letter from F to D is
n(A) = 4
What is an Event?A series of possible results from an experiment that have been given a probability is called an event. Separate events in an experiment may not be equally probable, since they may involve vastly dissimilar sets of outcomes, and a single result may be a component of many different events.
Given that a bag contains eight different balls, each of which is labeled from A to H. Given that a ball is selected at random, and the letter it lands on is written down as the result. Given that there is an equal chance of drawing any one of the balls, the sample space for drawing one ball is
Generally, the equation for S is mathematically given as
S = {A,B,C,D,E,F,G,H} and n(S) = 8
Therefore
G = The event of choosing a label from D to F
Where
F= {A,B,C,D}
Sample size
n(A) = 4
In conclusion,
n(A) = 4
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5. You buy a boat for $35,000 that * 10 points
depreciates in value at about 17%
per year. How much will it be worth
in 3 years?
Your answer
Answers
Answer:
9000
Step-by-step explanation:
Match the following. Match the items in the left column to the items in the right column. 1. domain the first element of a relation or function; also known as the input value. 2. output a relation in which every input value has exactly one output value. 3. input the x-value of a function. 4. relation any set of ordered pairs (x, y) that are able to be graphed on a coordinate plane. 5. function the y-value of a function. 6. range the second element of a relation or function; also known as the output value.
Answers
The matching of items and their corresponding descriptions are 1. Domain, 2.Output, 3. Input, 4. Relation, 5. Function, and 6. Range.
What is the appropriate matching of the following items?1. Domain - the first element of a relation or function; also known as the input value.
3. Input - the x-value of a function.
6. Range - the second element of a relation or function; also known as the output value.
4. Relation - any set of ordered pairs (x, y) that are able to be graphed on a coordinate plane.
2. Output - a relation in which every input value has exactly one output value.
5. Function - the y-value of a function.
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Give me one example of an item where you would need to find the area of a square. Also, Give me one example of an item where you would need to find the area of a rectangle.
Answers
An example of an item where you would need to find the area of a square is a square table.
An example of an item where you would need to find the area of a rectangle is a phone that has a rectangular shape.
How to calculate the area?It's important to note that the area of a square is the multiplication of its sides by itself. For example, if the side is 4cm, the area will be:
= 4²
= 4 × 4.
= 16cm²
The area of a rectangle will be:
= Length × Width
Assuming length and width are 5cm and 2cm. This will be:
= 5 × 2
= 10cm²
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how do I find X thanks
Answers
Answer:
x = 60
Step-by-step explanation:
By applying mean ratio theorem in the given right triangles ΔABC and ΔBDC,
\(\frac{AD}{BD}=\frac{BD}{DC}\)
BD² = AD × DC
BD² = 36 × 64
BD = \(\sqrt{36\times 64}\)
BD = 48
By applying Pythagoras theorem in right triangle ΔADB,
AB² = AD² + BD²
x² = (48)² + (36)²
x² = 3600
x = 60
Solve the equation 6(2x + 4)2 = (2x + 4) + 2.
Answers
Answer:
6
2x+4
=3
3x
⋅2
x+8
⇒6
4
⋅3
2x
⋅2
2x
=3
3x
⋅2
x+8
⇒6
4
=3
x
⋅2
8−x
⇒3
4
⋅2
4
=3
x
⋅2
8−x
∴x=4.
Answer:
x=-21/11 .
Step-by-step explanation:
The expression (3 - 7i)2 is equivalent to
Answers
Answer:
Step-by-step explanation:
Triangle XYZ is rotated 90° counterclockwise about the origin to produce X'Y'Z'. What are the coordinates of X'Y'Z'?
Answers
Answer:
59
Step-by-step explanation:
6 plus 4 equals 8 plus 9
Identify the coordinates of each vertex of triangle XYZ.
Apply the 90° counterclockwise rotation rule, which states that when rotating a point 90° counterclockwise about the origin, the new coordinates of the point will be (-y, x).
Substitute the coordinates of each vertex into the rotation rule to find the coordinates of the corresponding vertex in X'Y'Z'.
For example, let's say that the coordinates of triangle XYZ are:
X = (2, 3)
Y = (-1, 4)
Z = (0, -2)
To find the coordinates of X'Y'Z', we can apply the rotation rule to each vertex as follows:
X' = (-3, 2)
Y' = (-4, -1)
Z' = (2, 0)
Therefore, the coordinates of X'Y'Z' after rotating triangle XYZ 90° counterclockwise about the origin are:
X' = (-3, 2)
Y' = (-4, -1)
Z' = (2, 0)
Note that the order of the vertices may change after the rotation, but the coordinates of each vertex will correspond to the same vertex in the original triangle.
In 2010, the population of a city was 144,000. From 2010 to 2015, the population grew by 8%. From 2015 to 2020, it fell by 7%. How much did the population decrease from 2015 to 2020, to the nearest 100 people?
Answers
Answer:
144600
Step-by-step explanation:
In 2010, pop'n 144,000.
From 2010 to 2015, the population grew by 8%.
so by 2015 = 144000*1.08 = 155520
From 2015 to 2020, it fell by 7%.
so 155520 * (1-7%) = 155520 * 0.93 = 144634
round to the nearest 100 = 144600
write an equivalent expression (2+5)(x+3)=?
Answers
Answer:
7x+21
Step-by-step explanation:
(2+5)(x+3)
= (7)(x+3)
=7x+21
Suppose you had a population of fish whose lengths were normally distributed with a mean of 50 centimeters and a standard deviation of 5 centimeters. You draw a simple random sample of size 10, record the length of each fish, and calculate the mean of the sample lengths. What do you think your sample mean would most likely be
Answers
Answer:
The sample mean would most likely be 50 centimeters.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)
In this question:
The mean of the population is 50 centimers.
So, by the Central Limit Theorem, the sample mean would most likely be also 50 centimeters.
An investor wants to save money to purchase real estate. She buys an annuity with yearly payments that earn 5.3% interest compounded annually payments will be made at the end of each year find the total value of the annuity in 16 years if each yearly payment is 693.
Answers
The total value of the annuity in 16 years, with yearly payments of $693 and an interest rate of 5.3% compounded annually, is approximately $12,739.62.
To calculate the total value of the annuity in 16 years, we can use the formula for the future value of an annuity:
FV = P * ((1 + r)^n - 1) / r
Where:
FV is the future value of the annuity,
P is the yearly payment,
r is the interest rate per compounding period, and
n is the number of compounding periods.
In this case, the yearly payment (P) is $693, the interest rate (r) is 5.3% or 0.053, and the number of compounding periods (n) is 16.
Let's substitute these values into the formula and calculate the total value of the annuity:
FV = 693 * ((1 + 0.053)^16 - 1) / 0.053
FV = 693 * (1.053^16 - 1) / 0.053
Using a calculator, we can evaluate the expression inside the parentheses:
1.053^16 ≈ 1.9738
Substituting this value back into the formula:
FV = 693 * (1.9738 - 1) / 0.053
FV = 693 * 0.9738 / 0.053
FV ≈ 12739.62
Therefore, the total value of the annuity in 16 years, with yearly payments of $693 and an interest rate of 5.3% compounded annually, is approximately $12,739.62.
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Given the point and slope, write the equation of the line. (-8,6); slope = 1/4
Answers
Answer:
\(y=\frac{1}{4}x+8\)Explanation:
Given the properties of a line.
• Point, (x1, y1) = (-8, 6)
,• Slope, m = 1/4
It is required that we find the equation of the line.
Since we are given a point on the line and its slope, to find the equation of the line, we make use of the slope-point formula for a line.
\(y-y_1=m(x-x_1)\)Substitute the given values.
\(\begin{gathered} y-6=\frac{1}{4}\lbrack x-(-8)\rbrack \\ y-6=\frac{1}{4}\lbrack x+8\rbrack \\ \text{Add 6 to both sides} \\ y-6+6=\frac{1}{4}\lbrack x+8\rbrack+6 \\ y=\frac{1}{4}\lbrack x+8\rbrack+6 \\ \text{Open the bracket} \\ y=\frac{1}{4}x+\frac{1}{4}(8)+6 \\ y=\frac{1}{4}x+2+6 \\ y=\frac{1}{4}x+8 \end{gathered}\)The equation of the line is:
\(y=\frac{1}{4}x+8\)
The triangles at the top are similar. What is the area of the large triangle
Answers
Solution
Step 1
find the value of x on the bigger triangle using the ratio of similar sides since both triangles are similar.
\(\begin{gathered} \frac{base\text{ of small triangle}}{base\text{ of big triangle }}=\frac{height\text{ of small}}{height\text{ of big triangle}} \\ \frac{5}{7.5}=\frac{8}{x} \\ 5x\text{ = 8 }\times7.5 \\ x\text{ = }\frac{60}{5} \\ x\text{ =12cm} \end{gathered}\)Step 2
Use the expression for the area of a triangle to find the area of the big triangle
\(\begin{gathered} \text{The area of a triangle =}\frac{1}{2}\times base\text{ of big triangle}\times height\text{ of big triangle} \\ A=\text{ }\frac{1}{2}\times7.5\times12 \\ A=45cm^2 \\ \end{gathered}\)Hence the area of the big triangle is 45 cm squaredT. Option D is right
DeMarkus says that a store overcharged him on the price of the video game he bought. He thought that the price
of the original price, but it was really off the original price. He misread the advertisement. If the
original price of the game was $48, what is the difference between the price that De Markus thought he should pay
and the price that the store charged him?
was marked
11
10
Answers
The difference between the price that DeMarkus thought he should pay and the price that the store charged him is $24
The question provided is incomplete. Here is the complete question : DeMarkus says that a store overcharged him on the price of the video game he bought. He thought the price was marked 1/4 of the original price, but it was really 1/4 off the original price. He misread the advertisement. If the original price of the game was $48 , what is the difference between the price that DeMarkus thought he should pay and the price that the store charged him? A. $28.50B. $36.00C. $42.50D. $24.00
The first step is to determine the price DeMarkus thought the price of the videogame was = 1/4 of the original price
1/4 x $48 = $12
The second step is to determine the actual discounted price.
Actual discounted price = original price = (1/4 of the price)
48 - (1/4 x $48 = $12)
$48 - $12 = $36
The third step is to determine the difference in the prices
$36 - $12 = $24
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Please list all of the fractions that are greater than 7/12
Answers
Answer:
5/9, 9/12, 6/7, 6/9 are the ones I believe so far
Step-by-step explanation:
BASE
Which angle has a positive measure?
Answers
Answer:
An angle with a positive measure will have rotated counterclockwise, or doesn't cross over itself at the start of the rotation. As you can see, the only graph that initially turns counterclockwise is the first graph.
Step-by-step explanation:
Complete the input-output table for the function y = 3x.
Input-Output table
Answers
Answer:
Y: 0, x:0
Y:1, x: 3
Y: 2, x: 6
Y: 3, x:9
Step-by-step explanation:
Plug in the x to get the y
here are the 2 questions in the 2 pics separated lol
Answers
Answer:
60 and 87
Step-by-step explanation:
Question 1: The chance of losing would be 100% - 40% = 60%.
Question 2: Again, we just have to do 100% - 13% = 87%.
Answer:
Below
Step-by-step explanation:
First question:
Jade has a 40% chance of winnig wich could be expressed as 2/5
The chance of losing is the remainning pourcentage from 100%
●100-40 =60%
60% is the chance of losing wich could be expressed as 3/5
The sum of 3/5 and 2/5 is 1 so it's true.
■■■■■■■■■■■■■■■■■■■■■■■■■
Same method for the 2nd question:
The person has a 13 % chance of winning.
The chance of losing is 87%
● 100-13 =87