Answers
Step by step
Finding the constant of proportionality is the same as finding rate of change, or slope.
Here we have the given point of (1, 4)
y /x = 4 /1 or 4
We can see another possible point on the graph, (2, 8)
y /x = 8 /2 or 4
Related Questions
Arthur found that for every 200 peasants only 10 had seen a Dane. If there were 150,000 peasants in the kingdom how many had never seen a Dane?
Answers
We can solve this problem by applying the rule of 3.
If 10 out of 200 peasants had seen a Dane, x out of 150,000 had seen a Dane.
We can calculate x as:
[tex]\begin{gathered} 200\text{ peasants}\longrightarrow10\text{ seen Dane} \\ 150,000\text{ peasants}\longrightarrow x=\frac{10}{200}\cdot150,000=0.05\cdot150,000=7,500 \end{gathered}[/tex]Out of 150,000, 7,500 had seen a Dane. Then 150,000-7,500=142,500 peasants had never seen a Dane.
Answer: 142,500 peasants had never seen a Dane.
Jim has a total of 77 red and Blue marbles. The number of blue marbles is five more than twice the number of red marbles.A. Write a pair of linear equations to represent the information. Be sure to state what the variables represent.B. Explain the substitution method of solving this pair of equations. Solve the equations to find the number of red marbles.
Answers
A.
Jim has a total of red and blue marbles.
Let "r" represent the number of red marbles and "b" represent the number of blue marbles, to determine the total number of marbles he has, you have to add both, so that:
[tex]r+b=77[/tex]You know that the number of blue marbles "b" is five more than twice the number of red marbles "r"
Twice the number of red marbles means that r is multiplied by 2, you can express it as "2r", and he has five more than twice the number of red marbles, then you have to add 5 to 2r. You can express the number of blue marbles as follows:
[tex]b=2r+5[/tex]B.
Using both equations you can calculate the values of b and r using the substitution method.
We know that b=2r+5, and that r+b=77, the substitution method allows us to replace the known value of b, which is "2r+5" into the equation "r+b=77", this way we will determine one equation with only one variable "r":
[tex]\begin{gathered} r+b=77\to\text{if b=2r+5} \\ r+(2r+5)=77 \end{gathered}[/tex]From this expression, you can determine the value of r, first erase the parentheses, and simplify the like terms:
[tex]\begin{gathered} r+2r+5=77 \\ 3r+5=77 \end{gathered}[/tex]Second, pass 5 to the other side of the expression by applying the opposite operation to both sides of the equal sign:
[tex]\begin{gathered} 3r+5-5=77-5 \\ 3r=72 \end{gathered}[/tex]Third, divide both sides by 3 to reach the value of r:
[tex]\begin{gathered} \frac{3r}{3}=\frac{72}{3} \\ r=24 \end{gathered}[/tex]He has 24 red marbles
name the place value for each digit in the number 1,675,892
Answers
29.95 per gallon * 12.25 gallons long division
Answers
First, we can multiply each number by 100 to eliminate the decimal part:
29.95 * 100 = 2995
12.25 * 100 = 1225
We can do it because 100/100 = 1 and the division is not altered.
Then, we have the following division:
1. Find a value that you can multiply by 1225 that is near or exactly 2995. After this, multiply the value by 1225 and subtract the result from 2995 (dividend).
Try with 2:
Then 2 x 1225 = 2450
_2____
1225 | 2995
- 2450
----------
545
Now the rest 545 is less than the divisor (1225). We can also see that we do not have more numbers besides the last digit of the dividend (2995). In this case, we can add a zero beside 545 to get the decimal part of the division.
We can also have to add a dot at the quotient.
That is:
_2.____
1225 | 2995
- 2450
----------
5450
We need, again, to find a number that multip
f(x)=x^2-2x+ 3; d(x) = X-4
Answers
Answer: A1:F-IF.A.1. A1:F-IF.A.2. A1:F-IF.A.3. A1:F-IF.B.4. A1:F-IF.B.5 ... Find all the zeros of the polynomial y = x 3 - 2x 2 - 3x. A. -3, 1.
Step-by-step explanation:
Express your answer as a polynomial in standard form.f(x) = x² - 7x + 14 g(x) = 4x - 9 Find: (gof)(x)
Answers
On a coordinate plane, how are the locations of the points (-3, 7) and (-3,-7) related?
Answers
The two points / coordinates are (-3, 7) and (-3 , -7).
The relationship that exists between two points.
it is a reflection across x-axis.
Solution:Reflection over x-axis: A reflection or flip over the x-axis in which the x-axis is the line of reflection. The formula is: (x , y) → (x,−y) ( x , y ) → ( x , − y ) .Simply multiply the output variable by -1 to represent an equation on the x-axis: y = f(x) → y = −f(x) y = f ( x ) → y = − f ( x ).When a point is reflected across the y-axis, the y-coordinate remains unchanged, but the x-coordinate is assumed to be the additive inverse.Simply multiply the input variable by -1 to reflect an equation over the y-axis: y=f(x)→y=f(−x) y = f ( x ) → y = f ( − x ) .Given 2 coordinates, (-3, 7) and (-3,-7)
It is clear from the given points (-3, 7) and (-3, -7), that the x-coordinates are the same but the sign of the y-coordinates is opposite.If we reflect a figure across the x-axis, we change the sign of the y-coordinate while keeping the x-coordinates the same, i.e.,So the given points (-3, 7) and (-3,-7) has a relation that is it is reflection about x-axis.
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An object falls from an airplane
that is flying at an altitude of
6400 ft. How many seconds later
will the object hit the ground? Use
the equation 16t2 = d, where d is
the distance in feet and f is the
time in seconds.
Answers
Answer:
t = 20 seconds
Step-by-step explanation:
The force of gravity upon an object results in that object accelerating at 16ft/s². By substituting 6400ft in the equation 16t² = d you get:
16t² = 6400
Next, isolate t by dividing both sides by 16
t² = 400
Now, solve for t by taking the square root of both sides
[tex]\sqrt{t^2} = \sqrt{400}[/tex]
t = 20
I need help please!!!!!!!!!!!,,,,,,,,,,,,,,
Answers
Answer:
Step-by-step explanation:
all work is in the pics below
the check understanding question is there also
Find the surface area of the prism. 10 m Not drawn to scale b 600 m2 150 m2 280 m2 d 42 m2
Answers
Here, we have a rectangular prism.
Given:
Length, L = 10 m
Width, w = 6 m
Height, h = 5 m
Let's find the surface area of the rectangular prism.
To find the surface area of the rectangular prism, apply the formula below:
[tex]SA=2(wl+hl+hw)[/tex]Input values into the formula:
[tex]\begin{gathered} SA=2(6\ast10+5\ast10+5\ast6) \\ \\ SA=2(60+50+30) \\ \\ SA=2(140) \\ \\ SA=280 \\ \\ SA=280m^2 \end{gathered}[/tex]Therefore, the Surface Area of the rectangular prism is 280 square meters
ANSWER:
c. 280 m²
What is the solution to the equation below? A = 16 B. X2 CE 04
Answers
Here, we want to get the value of x
The first thing we have to do here is to isolate the root
We have this as;
[tex]\begin{gathered} \sqrt[]{x}\text{ = 12-8} \\ \sqrt[]{x}\text{ = 4} \\ (\sqrt[]{x})^2=4^2 \\ x\text{ = 16} \end{gathered}[/tex]please help ill try to give brainiest
Answers
Answer:
4 cups of sugar require 14 cups of sugar
Step-by-step explanation:
Given 7/8 cup flour= 1/4 cup sugar
Required determine the cups of flour for 4 cups of sugar
Determine the cups of flour for 4 cups of sugar
First, we need to determine the unit rate for 1 cup of sugar.
This is done by multiplying both sides by 4
Next, we determine cup of flour for 4 cups of sugar.
This is done by multiplying both sides by 4
Hence;4 cups of sugar require 14 cups of sugar
I hope this helps! if it doesn't if you tell me what the options are I can try to help more.
Solve for x by "Factoring". You MUST show every level of work (like you saw in the lesson) in order to receive full credit.
x^2-x-42
=(x^2+6)+(-7x-42)
=x(x+6)-7(x+6)
=(x+6)(x-7)
keep going to solve for x
Answers
The factorization of the quadratic expression 25x² - 4 gives us (x + 6)(x - 7) where; x = -6 or 7
How to factorize a quadratic equation?We are given the quadratic equation as;
x² - x - 42
Now, this quadratic equation can be written as;
x² + 6x - 7x - 42
We can group this using algebra properties to get;
(x² + 6x) - (7x + 42)
Collecting like terms gives us;
x(x + 6) - 7(x + 6)
Thus, the factorization is;
(x + 6)(x - 7)
Thus, the values of x would be;
x + 6 = 0
x = -6
x - 7 = 0
x = 7
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The measure of <1 is greater than 97° and at most 115°. Graph the possible values of x.
Answers
Answer:
The possible values of x are 10, 11, and 12
Step-by-step explanation:
9(10) + 7 = 97
9(11) + 7 = 106
9(12) + 7 = 115
The Hoffmans are planning their next family night. They always have dinner out somewhere and then do something fun together. There are 2 adults and 7 children in the family. Each family member is allowed 4 meal suggestions, and each child is allowed 4 activity suggestions. Assuming no family members choose the same thing, how many different family night possibilities are there?
Answers
Explanation
Number of children = 7
Number of adults = 2
Meal Suggestion per family member=4
Activity Suggestion per child = 4
Total number of family member = (7 + 2) = 9
Therefore, total meal suggestion
[tex]9\times4\text{ =36}[/tex]Total activity suggestions
[tex]7\times4=28[/tex]Hence the number of different possibilities
[tex]36+28=64[/tex]Answer
[tex]64[/tex]if g(x)=(x + 1), for what value of x will g(x)=3?A) 1B) 2C) 3D) 4
Answers
Given
[tex]g(x)=x+1[/tex]You need to calculate the value of x for g(x)=3, replace it in the equation as follows:
[tex]3=x+1[/tex]And calculate for x, to do so, you can pass the "+1" to the other side of the equal sign by performin the oposite operation "-1" to both sides:
[tex]\begin{gathered} 3-1=x+1-1 \\ 2=x \end{gathered}[/tex]For x=2 g(x)=3
a bag of the same size small balls contains 6 blue balls, 5 red balls, 5 yellow balls, and 4 green balls. What is the probability of selecting a blue or green ball on the first draw?
Answers
Explanation: We first need to add up all of the balls in the bag to get our denominator.
6 + 5 + 5 + 4 = 20
We then need to determine how many blue and green balls there are in total for our numerator.
6 blue balls + 4 green balls = 10.
So our answer is 10/20. Now we need to simplify. We need to get the greatest common multiple of 10 and 20. 10 is the greatest common multiple. We now need to divide each side by 10 to get our simplest form. 10/10 is 1 and 20/10 is 2.
Our final answer because of this is 1/2. I have converted it to a percent and a decimal. You may probably know that 1/2 is 50% and that 50% is .5 so I’ll spare you the explanation for that. Hope this helps!
Tommy wishes to retire at the age of 67 with $95,000 in savings. Determine the monthly payment into an IRA if the APR is 6.8% and he begins making payments at:Step 1: 25 years oldThe next part is finding the answer for 35 years old
Answers
Step 1
State the annuity formula
[tex]A=\frac{P[(1+\frac{r}{n})^{nt}-1]}{\frac{r}{n}}[/tex]where;
[tex]\begin{gathered} P=? \\ r=6.8\text{\%=}\frac{6.8}{100}=0.068 \\ n=12 \\ t=67-25=42 \\ A=\text{ \$95000} \end{gathered}[/tex]Step 2
Find the monthly payment from 25 years old
[tex]95000=\frac{P[(1+\frac{0.068}{12})^{42\times12}-1]}{\frac{0.068}{12}}[/tex][tex]\begin{gathered} \frac{0.068P\left[\left(1+\frac{0.068}{12}\right)^{42\times \:12}-1\right]}{\frac{0.068}{12}}=95000\times \:0.068 \\ 195.02614P=6460 \\ \frac{195.02614P}{195.02614}=\frac{6460}{195.02614} \\ P=33.1237639 \\ P\approx\text{ \$}33.12 \end{gathered}[/tex]Step 3
Find the monthly payment from 35 years old
[tex]\begin{gathered} 95000=\frac{P[(1+\frac{0.068}{12})^{32\times12}-1]}{\frac{0.068}{12}} \\ n=67-35=32 \\ \frac{P\left[\left(1+\frac{0.068}{12}\right)^{32\times \:12}-1\right]}{\frac{0.068}{12}}=95000 \\ \frac{0.068P\left[\left(1+\frac{0.068}{12}\right)^{32\times \:12}-1\right]}{\frac{0.068}{12}}=95000\times \:0.068 \\ 93.08447P=6460 \\ P=69.39933 \\ P=\text{\$69.40} \end{gathered}[/tex]Answer;
[tex]\text{ \$69.40}[/tex]Please help me solve
Whoever answers correctly gets brainliest
For those who can't see the paper:
π²/♾️=9
Answers
Answer:
I think the answer will be the infinity sign=1 whole, 1/9
A solid has volume 2 cubic units and surface area 10 square units. The solid is dilated, and the image has volume 128 cubic units. What is the surface area of the new solid?
Answers
In this type of problem. You need to determine first the unit dimension..
The dimension of the volume is in cubic so the unit dimension will be the cube root the volume:
Let u = unit dimension
[tex]u=\sqrt[3]{V}[/tex]So we now have the unit dimension, dilating it with a scale factor of k will give as a new volume. Since it is a unit dimension, you need to take the cube of it so you will arrive with the new volume.
So the new volume will be :
[tex]V_{\text{new}}=(uk)^3[/tex]or just simply :
[tex]V_{\text{new}}=(k\sqrt[^{}3]{V})^3[/tex][tex]k=\frac{\sqrt[3]{V_{\text{new}}}}{\sqrt[3]{V}}=\sqrt[3]{\frac{V_{new}}{V}}[/tex]Solving for the scale factor k :
[tex]k=\sqrt[3]{\frac{128}{2}}=\sqrt[3]{64}=4[/tex]So now we have the scale factor of k = 4
Now for the Surface Area , the dimension of it is in square units, so the unit dimension will be the square root of the surface area :
It has almost the same formula for k, but the difference is only the cube root or the square root.
So we can state that the New surface area will be :
[tex]SA_{\text{new}}=(k\sqrt[]{SA})^2[/tex]Solving for the New surface area :
[tex]SA_{\text{new}}=(4\sqrt[]{10})^2=160[/tex]So the answer is 160 square units.
The measure of the larger angle of an isosceles triangle is sixteen times the measure of each of the other two angles. Find the measure of the larger angle.
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The sum of two numbers is 12 4 times the smaller number is 1 less than 3 times the larger number
Answers
Answer: 5 and 7
Step-by-step explanation:
Let x be the smaller number and y be the larger number.
x + y = 12
4x = 3y - 1
I will solve for y by substituting for x from the first equation. (There are different ways to solve this, but for simplicity I am using the substitution method.)
x = 12 - y
4(12 - y) = 3y - 1
48 - 4y = 3y - 1
49 = 7y
y = 7
Now that I have found the larger number y, I will now plug it into the first equation and solve for x.
x + y = 12
x + 7 = 12
x = 5
there is a stack of cards, each given a different number 1-10, suppose we select a card randomly from the stack, replace it, then randomly select a card. what is the probability that the 1st card is an ODD number and the second card is Less then 5?
Answers
Given that:
- A stack of different cards numbered from 1 to 10.
- A card is randomly selected and then replaced. Then another card is randomly selected.
• You need to find the probability that the first card is an odd number.
By definition, Odd Numbers are those numbers that cannot be divided by 2. In this case, these are:
[tex]1,3,5,7,9[/tex]Knowing that the total number of cars is:
[tex]10[/tex]You can set up:
[tex]P(X=ODD)=\frac{5}{10}[/tex]Then:
[tex]P(X=ODD)=\frac{1}{2}[/tex]• You need to find the probability that the second card is less than 5.
Notice that the numbers cards from the stack that are less than 5 are:
[tex]1,2,3,4[/tex]Therefore, you can set up that:
[tex]\begin{gathered} P(X<5)=\frac{4}{10} \\ \\ P(X<5)=\frac{2}{5} \end{gathered}[/tex]• Now you can set up:
[tex]P=\frac{1}{2}\cdot\frac{2}{5}[/tex]Solving the Multiplication, you get:
[tex]\begin{gathered} P=\frac{1\cdot2}{2\cdot5} \\ \\ P=\frac{2}{10} \\ \\ P=\frac{1}{5} \end{gathered}[/tex]Hence, the answer is:
[tex]P=\frac{1}{5}[/tex]In the expression 5^2, the 2 represents the _________________.
A: product
B :sum
C: base
D: exponent
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In the expression 5^2, the 2 represents the D. exponent.
What is exponent?Exponentiation is a mathematical process that involves the base b and the exponent or power n. An exponent is the result of multiplying a certain number or variable (such as x, y, or z) by itself.
The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself. For instance, the number 6⁴ is multiplied by itself four times,
In this case, 5² will be 5 × 5 = 25.
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If the average of 12, 7, 9, a, and b is 12, thenwhat is the average of a + b?
Answers
If the average of 12, 7, 9, a, and b is 12, then
what is the average of a + b?
we know that
the average is equal to
(12+7+9+a+b)/5=12
simplify
(28+a+b)/5=12
Multiply both sides by 5
28+a+b=60
isolate (a+b)
a+b=60-28
a+b=32average a+ba+b/2=32/2=16answer is 16A restraurant Buys 56 Pounds of Beef at $1.12/ Pound and 24 quarts of Milk at $.90 quart. how Much Money was spent?
Answers
Answer:
Step-by-step explanation:
1.12 * 56 = 62.72
.90 * 24 = 21.60
62.72 + 21.60 = $84.32
Estimate 93+ 31 by first rounding each number to the nearest ten.
Answers
Answer:
To estimate 93+31 by first rounding number to the nearest ten.
Solving 93+31, we get
[tex]93+31=124[/tex]Explanation:
Simply put, when you have a number and you want to round to the nearest tens, this means that you will need to find which 10 they are nearest to. For example, if you think about the number 53, you can easily say that it is near 50 than it is near 60. So the rounded number of 53 nearest to ten is 50.
Here, the number is 124
Rounding the number to the nearest ten.
[tex]124\approx120[/tex]Answer is: 120.
Hey help me out pls I would love if you did
Answers
Firstly, we would find the fractional part of the circle and then express it as a percentage.
The circle has 4 sub-divisions and a part of it is shaded. Thus, the fractional part of the shaded area is:
[tex]\frac{1}{4}[/tex]Expressing this as percentage, we have:
[tex]\frac{1}{4}\times100=25\text{\%}[/tex]Hence, the percentage represented by the shaded area is 25%
A rocket is launched straight up. What is its velocity at the top of its flight?
Answers
If a rocket is launched straight up, then the velocity at the top of its flight will be zero.
Given that the rocket is launched straight up.
We are required to find the velocity which will the be at the top of its flight.
Velocity is basically the directional speed of a object in motion as an indication of its rate of change in position as observed from a particular frame of reference and measured by a particular standard of time.
At the top of flight its velocity becomes zero but not the acceleration because it is under the effect of gravitational acceleration.
Hence if a rocket is launched straight up, then the velocity at the top of its flight will be zero.
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which of the following statements have the same result? explain each step in solving each one. 1. f(3) when f(x)=2x+32. f^-1(3) when f(x)=2x-9/33. 5y+13=4y+4(10 points)
Answers
Let's find the inverse function:
1. replace f(x) with y
[tex]y=\frac{2x-9}{3}[/tex]2. Replace every x with a y and every y with an x:
[tex]x=\frac{2y-9}{3}[/tex]3. solve for y:
[tex]y=\frac{3x+9}{2}[/tex]4. replace y with f^-1(x)
[tex]f^{-1}(x)=\frac{3x+9}{2}[/tex]Now:
[tex]f^{-1}(3)=\frac{3(3)+9}{2}=\frac{9+9}{2}=\frac{18}{2}=9[/tex]since the functions are equal for x = 3 we can conclude that they have the same result
[tex]f(3)=f^{-1}(3)[/tex]