The equation of the line is y=-1/5x+4/5.
Calculating m, the slope we subtract two of the points,
(-1, 1)
(4, 0)
This equals 0-1/4+1, which simplifies to -1/5
The slope is -1/5 and we can put that into the slope-intercept form along with a point to get b, the y-intercept.
So, y=-1/5x+b
Substituting x and y with a point.
1=-1/5(-1)+b
1=1/5+b
b=4/5
So, the equation is y=-1/5x+4/5.
What is the Equation of a Line?The equation of a line is a single illustration of numerous points on the line. the general form of the equation of a line is of the form ax + via + c = zero and any factor on the road satisfies this equation. these two minimal requirements to shape the equation of a line are the slope of the road and a factor on the line.
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What is 0.7(repeating) as a fraction in simplest form? show work
Answer:
0.7=7/10
this is the fraction in the simplest form
Step-by-step explanation:
A softball pitcher has a 0.42 probability of throwing a strike for each pitch. If the softball pitcher throws 20 pitches, what is the probability that exactly 7 of them are strikes?
Round your answer to three decimal places.
Answer: 0.15
Step-by-step explanation:
7 (0.42)/ 20
How many digits are in a phone number including the area code
Answer:
11 digits
Step-by-step explanation:
x-xxx-xxx-xxxx
Counting these x's they would be 11. (if living in U.S.A)
The area code has 3 numbers. The first section has 3. Last section has 4. 6+4=10
There are 10 digits in a phone number.
1. What are the solutions (coordinate points) to the system of equations?
y=x^2+5x+6 and y=3x+6
2. Prove algebraically what type of function this is (even, odd, or neither).
f(x)=x^6-x^4
3. Given the function f(x)=x^2+3x-2
What is the average rate of change for the function from 2 to 6? Show your work.
Question 1
The given system of equations is:
[tex]y = {x}^{2} + 5x + 6 \\ y = 3x + 6[/tex]
Equate the two equations:
[tex] {x}^{2} + 5x + 6 = 3x + 6[/tex]
Rewrite in standard form:
[tex] {x}^{2} + 5x - 3x + 6 - 6 = 0[/tex]
[tex] {x}^{2} + 2x = 0[/tex]
[tex]x(x + 2) = 0[/tex]
[tex]x = 0 \: or \: x = - 2[/tex]
When we put x=0, in y=3x +6, we get:
[tex]y = 3(0) + 6 = 6[/tex]
One solution is (0,6)
When we put x=-2, into y=3x+6, we get:
[tex]y = 3( - 2) + 6 = 0[/tex]
Another solution is (-2,0)
The solutions are; (0,6) and (-2,0)
Question 2:
The function is
[tex]f(x) = {x}^{6} - {x}^{4} [/tex]
Let us put x=-x,
[tex]f( - x) = {( - x)}^{6} - {( - x)}^{4} [/tex]
This gives:
[tex]f( - x) = {x}^{6} - {x}^{4} [/tex]
We can observe that:
[tex]f(x) = f( - x)[/tex]
This is the property of an even function.
Question 3:
The given function is
[tex]f(x) = {x}^{2} + 3x - 2[/tex]
The average rate of change of f(x) from x=a to x=b is given as:
[tex] \frac{f(b) - f(a)}{b - a} [/tex]
This is the slope of the secant line connecting the two points on f(x)
From x=2 to x=6, the average rate of change
[tex] = \frac{f(6) - f(2)}{6 - 2} \\ = \frac{ {6}^{2} + 3 \times 6 - 2 - {2}^{2} - 3 \times 2 + 2 }{4} \\ = \frac{36 + 18 - 4 - 6}{4} \\ = \frac{44}{4} \\ = 11[/tex]
The average rate of change is 11
How many times larger is 6•10^8 than 1•10^5
Answer:
6 * [tex]10^{3}[/tex] larger
Step-by-step explanation:
divide [tex]\frac{6*10^{8}}{1*10^{5} }[/tex]
[tex]\frac{6*10^{8}}{1*10^{5} }[/tex] = 6 * [tex]10^{3}[/tex]
Answer:
6000
Step-by-step explanation:
aka 6*10^3
What is the volume of this?
Answer:
Step-by-step explanation: 288
Marvin Martian, Aly Alien, and Hank Human are all looking for a hidden spaceship. Their probabilities of
finding the spaceship first are as follows:
P(Marvin wins) = 30%
P(Aly wins) = 0.2
P(Hank wins)
Put the following events in order from least to most likely.
Aly wins
Hank wins
Marvin wins
Answer: Aly , Marvin, Hank
Step-by-step explanation:
Aly has the lowest with 20, Marvin has 30, and hank has 50. it says least to mostly likely to win
The question pertains to probabilities. It has been determined that the most probable event is either Hank winning or Marvin winning, and it's least likely for Aly to win.
Explanation:The question is regarding the probability of three individuals, Marvin Martian, Aly Alien, and Hank Human, finding a hidden spaceship first. We know the probabilities of Marvin and Aly finding it first but the probability of Hank finding it is not given.
However, from the properties of probability, we know that the sum of the probabilities for all possible outcomes is 1. Therefore, if we add the probabilities of Marvin and Aly finding the spaceship first, we get 0.30(30%) + 0.2(20%) = 0.5(50%). We then subtract this from 1 to get Hank's probability, which is, therefore, 1 - 0.5 = 0.5(50%).
So, in order from least to most likely: Aly wins (0.2 or 20%), then Hank and Marvin are equally likely to win (0.5 or 50% each).
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The lengths of sides of a right triangle are 16 meters, 30 meters, and 34 meters. The triangle is dilated by a scale factor of 4,5. How many meters long is the hypotenuse of the new triangle?
Answer:
16mt + 30 mt
Step-by-step explanation:
your welcome!
If (6,39) and (-5,-49) are two anchor pint find the equation of the line
Answer:
[tex]y =8x+9[/tex]
Step-by-step explanation:
The points are (6,39) and (-5,-49)
We need to find the equation of this line.
The slope is given by:
[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]
[tex]m = \frac{ - 49 - 39}{ - 5 - 6} [/tex]
[tex]m = \frac{ - 88}{ - 11} [/tex]
[tex]m = 8[/tex]
We use the formula:
[tex]y-y_1=m(x-x_1)[/tex]
We substitute the point (6,39) and m=8 to get:
[tex]y - 39 = 8(x - 6)[/tex]
We expand to obtain:
[tex]y - 39=8x-48[/tex]
[tex]y =8x-48 + 39[/tex]
[tex]y =8x + 9[/tex]
To find the equation of the line passing through two points, we can use the point-slope form of a linear equation:
[tex]\[y - y_1 = m(x - x_1)\][/tex]
Where:
- [tex]\( (x_1, y_1) \)[/tex] is one point on the line.
- [tex]\( m \)[/tex] is the slope of the line.
First, let's find the slope (\(m\)) using the two given points:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Given points:
[tex]\( (x_1, y_1) = (6, 39) \)\( (x_2, y_2) = (-5, -49) \)\[ m = \frac{-49 - 39}{-5 - 6} \]\[ m = \frac{-88}{-11} \]\[ m = 8 \][/tex]
Now, we have the slope (\(m\)). We can choose either of the two given points and plug them into the point-slope form. Let's use \( (6, 39) \):
[tex]\[ y - 39 = 8(x - 6) \][/tex]
Now, we can simplify this equation to get it into slope-intercept form (\(y = mx + b\)):
[tex]\[ y - 39 = 8x - 48 \]\[ y = 8x - 48 + 39 \]\[ y = 8x - 9 \][/tex]
So, the equation of the line passing through the points (6, 39) and (-5, -49) is [tex]\( y = 8x - 9 \).[/tex]
Rational Numbers
Every integer is a
number
A.
rational
B. whole
C. natural
D.
negative
Reset
Submit
Answer:
a. Every integer is a __________ number.
A.
rational < this onee
B.
whole
C.
natural
D.
negative
Step-by-step explanation:
Can u help me with my homework please it is a little bit harder then I thought
The distance around the pool is 43.96 m.
Solution:
The distance across the circle is diameter.
The distance around the circle is circumference.
The value of π = 3.14
Diameter of the circle = 14 m
Circumference of the circle = πd
= 3.14 × 14 m
Circumference of the circle = 43.96 m
The distance around the pool is 43.96 m.
Francisco uses 12 ounces of milk for every 18 ounces of fruit in his smoothie recipe, Nia uses 8 ounces of milk for every 12 ounces of fruit in her smoothie recipe. Who would use more milk if they each use 6 ounces of fruit?
Answer: there both equal
Step-by-step explanation: first we have to find the unit rate of both. Francisco unit rate for his recipe is 12/18=6/9=2/3 so the unit rate is 2/3
Nia uses 8/12=4/6=2/3 so the both will have the same if they use 6 ounces
Final answer:
Both Francisco and Nia use a proportional amount of milk in their smoothies; thus, they would both use 4 ounces of milk for 6 ounces of fruit.
Explanation:
To determine who would use more milk if they each use 6 ounces of fruit, we need to compare Francisco's and Nia's milk-to-fruit ratios. Francisco uses 12 ounces of milk for every 18 ounces of fruit, and Nia uses 8 ounces of milk for every 12 ounces of fruit. To find how much milk they would use for 6 ounces of fruit, we can set up a proportion for each and solve for the amount of milk.
For Francisco:
12 ounces of milk / 18 ounces of fruit = x ounces of milk / 6 ounces of fruit.
Using cross-multiplication, we get:
18x = 12 × 6.
Dividing both sides by 18 gives us:
x = (12 × 6) / 18 = 4 ounces of milk.
For Nia:
8 ounces of milk / 12 ounces of fruit = y ounces of milk / 6 ounces of fruit.
Using cross-multiplication, we get:
12y = 8 × 6.
Dividing both sides by 12 gives us:
y = (8 × 6) / 12 = 4 ounces of milk.
Therefore, both Francisco and Nia would use 4 ounces of milk for 6 ounces of fruit in their smoothie recipes.
In which set does −173 belong?
Answer:
Step-by-step explanation:
rational number
6yd 7yd 3yd Find the volume of this rectangular pyramid.
Answer: The volume is 126 yards
Step-by-step explanation:
Answer:
the answer is 128
Step-by-step explanation:
first, i did 6x7 and got 42
then, i muutiplied 42 and 3 and got 128
thank me
Solve the expression :
-6x + 5 – 4x < 45
Answer:
x>-4
Step-by-step explanation:
-6x + 5 – 4x < 45
Combine like terms
-10x + 5 < 45
Subtract 5 from each side
-10x + 5 – 5 < 45-5
-10x< 40
Divide each side by -10, remembering to flip the inequality
-10x/-10 >40/-10
x >-4
Solve The Expression :
-6x + 5 – 4x < 45
Answer:
x > -4
Step-by-step explanation:
Step 1: To combine like terms means to add the same variable numbers together.
-6x + 5 - 4x < 45
-10x + 5 < 45
Step 2: Subtract 5 from both sides
-10x + 5 - 5 < 45 - 5
-10x < 40
Step 3: Divide both sides by -10
-10x / -10 < 40 / -10
Since you divided by a negative, you need to reverse/flip the sign.
x > -4
Answer: x > -4
Steps to solve:
-6x + 5 – 4x < 45
~Combine Like Terms
(-6x - 4x) + 5 < 45
~Simplify
-10x + 5 < 45
~Subtract 5 to both sides
-10x + 5 - 5 < 45 - 5
~Simplify
-10x < 40
~Divide -10 to both sides and switch the symbol since we're dividing a negative number
-10x/-10 > 40 / -10
~Simplify
x > -4
Best of Luck!
Use the Distributive Property to find 3(13+5) written as an equivalent expression.
Answer:
54 or as an expression (3 * 13) + (3 * 5)
Step-by-step explanation:
Step 1: Distribute
To distribute means to break the parenthesis apart. To make two different combinations.
3(13 + 5)
(3 * 13) + (3 * 5)
Step 2: Multiply it out
(3 * 13) + (3 * 5)
39 + 15
54
Answer: 54 or as an expression (3 * 13) + (3 * 5)
Answer: 39 + 15
Step-by-step explanation: 3(13 + 5) can be simplified by distributing the 3 through both terms that are inside the parentheses.
So we have 3(13) + 3(5) which simplifies to 39 + 15 or 54.
So 3(13) + 3(5) is an equivalent.
1 hundeedth+3 tenths= ? hunderdth
Answer:
0.31
Step-by-step explanation:
one hundredth is 0.01 and 3 tenths would be 0.3 so just add those two together :)
How do you write 11/3 as a whole number?
Answer: 11/3 is a fraction that cannot be written as a whole number
Step-by-step explanation:
11/3 is a fraction that can only be reduced to 3 2/3
whats the mean in 4, 8, 3, 9, 5
Answer:
The mean/average is 5.8
Step-by-step explanation:
The mean is the average
Step 1: Find the average
4 + 8 + 3 + 9 + 5
29 / 5
5.8
Answer: The mean/average is 5.8
The fraction bar represents which equation?
Answer: The last option
Step-by-step explanation:
3/4÷1/8=6
This is the answer because this is the only equation that gives a true answer all the others give an incorrect answer.
The two sets of shipping containers shown have the same total volume.
Complete the equation and expression below about the volume of the containers.
WHATS THE Volume for the red container in set 2
Plz answer ASAP!!!
Answer:
Set 1: 43 ft3 + 21 ft3 = 64ft3
Red prism in set 2: 16ft3
Step-by-step explanation:
When you add the first one together you get 64. So what plus 48 = 64? Your answer is 16.
. If you pick one card at random from a standard deck of cards, what is the probability it
will be a Diamond?
Answer:
13/52
Step-by-step explanation:
i think that because in one deck of cards there are 52 cards in total and you divide 52 ÷ 4 it will give you 13 and you divide by four because there are 4 suits in total.
30% of number A is 10 more than 20% of number B. 30% of number B is 35 more than 20% of number A. Find the numbers A and B.
PLEASE PLEASE DUE TODAY!!!
Final answer:
To solve for A and B, we translated the word problem into two algebraic equations and then solved the system of equations step-by-step to find that A equals 200 and B equals 250.
Explanation:
We are given two equations based on the relationship between 30% of number A and 20% of number B, and vice versa. Let's translate the words into algebraic expressions where A and B represent the numbers we need to find:
0.30A = 0.20B + 10 (Equation 1)
0.30B = 0.20A + 35 (Equation 2)
Now let's solve this system of equations step-by-step:
Multiply both sides of Equation 1 by 10 to clear out decimals: 3A = 2B + 100.
Multiply both sides of Equation 2 by 10 as well: 3B = 2A + 350.
Rearrange Equation 1 to get A on its own: A = (2B + 100) / 3.
Substitute the expression for A from step 3 into Equation 2: 3B = 2((2B + 100) / 3) + 350.
Multiply through by 3 to clear the fraction: 9B = 4B + 200 + 1050.
Simplify to find B: 5B = 1250, so B = 250.
Substitute B back into the equation from step 3 to find A: A = (2(250) + 100) / 3, so A = 200.
Therefore, the numbers we are looking for are A = 200 and B = 250.
Which algebraic expression represents the phrase "seven more than half of a number"?
Answer:
7 + q/2
Step-by-step explanation:
"seven more than half of a number"?
There are two sides to the phrase
1) let the number be "q"
2) Seven (7) more: Adding seven (7 +)
3) Half of a number: dividing the number by '2'
Equation = 7 + q/2
On a winters day, the average temperature during the daytime is 40°F. At night the temperature falls to 24°F. What is the percentage decrease?
Answer:
40%
Step-by-step explanation:
so first we can calculate what percentage of 40 24 is
we can do that with 24/40 which equals 0.6, or 60 percent
100-60
that means that there was a 40 percent decrease.
two friends bought a $14 pizza. Each person bought their own drink. The total cost of the food can be represented by the expression $2x + $14. What expression represents the cost of food for one person
The expression representing the cost of food for one person is $x + $7.
For the expression that represents the cost of food for one person if two friends bought a $14 pizza, and each person bought their own drink at $2x (where x is the number of drinks).
To find the cost for one person, we start with the total cost expression $2x + $14. Since there are two friends, we divide this total cost by 2. The expression for the cost of food for one person is $x + $7. This represents the individual cost of one person's drink at $2x, divided by 2, plus half of the pizza cost, which is $14 divided by 2, resulting in $7.
Identify the angle relationships in the table.
Answer:
4 & 8 = Corresponding Angles | 6 & 7 = Linear Pair | 1 & 3 = Vertical Angles | 2 & 8 = Alternate Interior Angles
Step-by-step explanation:
Draw a picture that shows 1/4*3 explain in words your picture with connections to the expression
Answer:
look at pic
Step-by-step explanation:
Calculate the M.A.D 13, 17, 19, 27
Answer:
4
Step-by-step explanation:
Sample size: 4
Mean: 19
MAD: 4