A line intersects the points (0,-4)and (1,2). What is the slope-intercept equation for this line?
Answer:
y = 6x - 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, - 4) and (x₂, y₂ ) = (1, 2)
m = [tex]\frac{2+4}{1-0}[/tex] = 6
note the line crosses the y- axis at (0, - 4) ⇒ c = - 4
y = 6x - 4 ← in slope- intercept form
Simplify (ignore my garbage camera quality ....)
Answer:
C. 3
Step-by-step explanation:
Given expression is:
[tex]({3^{\frac{1}{7}})^7[/tex]
We know that the rules of exponents are used to solve these kind of questions.
When there is exponent on exponent like in this question 1/7 has an exponent of 7 , the exponents are multiplied.
So,
[tex]=3^{(7*\frac{1}{7} )}[/tex]
The 7's will be cancelled out and remaining power will be 1
[tex]=3^1\\=3[/tex]
Hence, option C is correct ..
Answer:
The correct answer is option C
3
Step-by-step explanation:
Points to remember
Identities
(xᵃ)ᵇ = xᵃᵇ
(x¹/ᵃ)ᵇ = xᵃ/ᵇ
To find the correct answer
It is given that, (3¹/⁷)⁷
By using above identities we can write,
(3¹/⁷)⁷ = 3⁽¹/⁷ *⁷⁾
= 3¹
= 3
Therefore the simplified form of (3¹/⁷)⁷ = 3
The correct answer is option C
(3¹/⁷)⁷ = 3
What is the difference of the two polynomials?
(9x2 + 8x) - (2x2 + 3x)
Answer:
7x^2+5x
Step-by-step explanation:
Given
Polynomial 1: 9x^2+8x
Polynomial 2: 2x^2+3x
We have to find subtraction of both
So,
9x^2+8x - (2x^2+3x)
First of all the brackets will be eliminated by multilying the minus sign
9x^2+8x-2x^2-3x
The terms with same power of variable will be written together
9x^2-2x^2+8x-3x
=7x^2+5x ..
Answer:
7x^2 + 5x.
Step-by-step explanation:
I just took the test and got a 100%. :)
Let f(x) = 5x-6 and g(x) = 3x-2. Find f(x)+g(x)
Answer:
8x-8
Step-by-step explanation:
Since you are adding the two functions: f(x)+g(x), substitute what they equal into this expression:
5x-6+3x-2
Combine like terms:
5x+3x-6-2
Simplifying gives:
8x-8
Hope this helps!
A fruit salad recipe calls for 2 cups of strawberries for every cup of grapes,
and will serve 4 people. If Anthony wants to serve 6 people, how much of
each ingredient will he need?
Answer:
3 cups of strawberries, 1 1/2 cups of grapes
Step-by-step explanation:
Basically you need 1 C of strawberries and 1/2 C of grapes for 2 people. Multiply those amounts by 3, for 6 people
What is the volume of the prism shown?
1,386 ft^ 3
1,260 ft^ 3
1,540 ft^ 3
1,512 ft^ 3
Answer:
1386 ft^3.
Step-by-step explanation:
Volume = width * length * height
= 9 * 11 * 14
= 1386 ft^3.
Can someone pleaseee help me out
Answer:
both answers are inside
Step-by-step explanation:
70 is greater then 23 which explains why it's hotter. Absolute value is the distance from a number to 0. being 70 slots away from 0 is greater than 23 slots.
What is the length of the apothem, rounded to the nearest inch? Recall that in a regular hexagon, the length of the radius is equal to the length of each side of the hexagon.
4 in.
5 in.
9 in.
11 in.
Answer:
The third option, or 9, is the answer.
Step-by-step explanation:
The length of the apothem can be found using the pythagorean theorem. Since the length of each side of the hexagon is 10, the base of the triangle is 5, since 10/2=5. Plugging these two values into the pythagorean equation leaves 25+b^2=100.
B^2 = 75, so the length of the apothem is sqrt(75)
this is approximately 8.66, so the answer is 9.
The length of the apothem is 9 inch.
What is ApothemThe apothem of a regular polygon is a line segment from the center to the midpoint of one of its sides.
Using the pythagoras theorem.
As, the length of each side of the hexagon is 10.
so, the base of the triangle is 10/2=5.
Now using two values we get
25+b²=100.
B² = 75
Hence, so the length of the apothem is √75 = 8.66 = 9 (approx)
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Use the distance formula to find the distance between (-3,5) and (3,1)
Answer:
√52
Step-by-step explanation:
D=√(3+3)²+(1-5)²
=√36+16
=√52
Answer:
52
Step-by-step explanation:
A scatter plot is made to model the amount of money left to pay on a car loan. The data used for the scatter plot are shown in the table:
Answer:
"the original amount of the loan"
Step-by-step explanation:
x value would be the time in months and y value would be the loan amount that is left.
The y-intercept is basically the point where x is 0. So, we can say the y-intercept would be when time is 0.
That's basically when the loan started and the y-value represents the full loan amount., which is $22,000.
The correct answer is third option -- "the original amount of the loan".
Answer:
The correct option is C.
Step-by-step explanation:
It is given that a scatter plot is made to model the amount of money left to pay on a car loan.
From the given table we can conclude that the number or months represented by variable x and the amount of money owed is represented by variable y.
At y-intercept the value of x is 0. It means the y-intercept represents the amount of money owed when the number of months is 0.
In other words, the y-intercept of the model represents the original amount of loan.
Therefore the correct option is C.
Explain how the Quotient of Powers was used to simplify this expression.
this expression is factored what is it's trinomal form?
(5x+2)(x-3)
Answer:
5x² - 13x - 6
Step-by-step explanation:
Each term in the second factor is multiplied by each term in the first factor, that is
5x(x - 3) + 2(x - 3) ← distribute both parenthesis
= 5x² - 15x + 2x - 6 ← collect like terms
= 5x² - 13x - 6
What is the probability of drawing three queens from a standard deck of cards, given that the first card drawn was a queen? Assume that the cards are not replaced.
Answer:
The probability of drawing three queens is 1/425
Step-by-step explanation:
* lets talk about the deck cards
- The deck cards has 52 cards
- It has four symbols (heart , diamond , clubs , spades)
- Each symbol has 16 cards (from 1 to 10 and king , queen , princess)
* Lets solve the problem
- We will drawing three cards
- The cards are not replaced
- That means the total of the card will reduce by 1 after each drawing
- The cards will drawing are queens
- The first card drawn will be a queen
∵ The first card drawn is queen
∴ The number of cards for the second drawn is 52 - 1 = 51
∵ There are 4 queens in the deck cards we took one for the first choice
∴ The number of queen for the second choice is 4 - 1 = 3
∴ The probability of second choice is 3/51
- Now there are 2 queens and 50 cards after the second choice
∴ The number of the queen is 3 - 1 = 2
∴ The number of the deck cards is 51 - 1 = 50
∴ The probability of third choice is 2/50
- The probability of the three cards is the product of the two fractions
∴ The probability of drawing three queens = 3/51 × 2/50 = 6/2550
- Simplify the fraction
* The probability of drawing three queens = 1/425
Which number line shows the solution to -4 -(-1)?
Answer:
D
Step-by-step explanation:
The Line goes from 0 to -4 and then -(-1) makes +1 so -4 goes to -3
Answer:
D. I did an pre-exam with this question and got it right
If the radius of a cylinder is doubled and the height is tripled, what happens to the volume?
A)
It is multiplied by 6.
B)
It is multiplied by 12.
It is multiplied by 18.
D)
It is multiplied by 32
Answer:
B
Step-by-step explanation:
Original volume = pi * r^2 * h
New r = 2*r
New h = 3*h
New Volume = pi * (2r)^2 *3*h
New Volume = pi * 4r^2 * 3 *h
New Volume = 4*3 * pi * r^2 + h
Conclusion
The New Volume = 12* the original volume
Solve for x. 9x - 1 = -11 x = -1 x = -1 x = 1 x = 1
Answer:
x=-1
Step-by-step explanation:
Add by 1 from both sides of equation.
9x-1+1=-11+1
Simplify.
-11+1=-10
9x=-10
Divide by 9 from both sides of equation.
9x/9=-10/9
Simplify, to find the answer.
x=-10/9
x=-1 is the correct answer.
I hope this helps you, and have a wonderful day!
Answer:
x = -1.11111111111111(repeating)
Step-by-step explanation:
9x - 1 = -11
Add 1 to each side
9x - 1+1 = -11+1
9x = -10
Divide each side by 9
9x/9 = -10/9
x = -10/9
x = -1.11111111111111(repeating)
If 0.75:n: 5:8 then n is equal to
Final answer:
To solve the proportion 0.75:n = 5:8, set the two ratios equal to each other and solve for n.
Explanation:
To solve the proportion 0.75:n = 5:8, we can set the two ratios equal to each other:
0.75/n = 5/8
Next, we can cross-multiply to solve for n:
0.75 * 8 = 5 * n
6 = 5n
Lastly, we can divide both sides of the equation by 5 to find the value of n:
n = 6/5
Therefore, n is equal to 1.2.
Help plz ..I don’t get this
Answer:
Number of cakes decorated = 1.4 in a minute
Step-by-step explanation:
A baker decorates 42 cupcakes in 30 minutes. If she decorates cupcakes at the constant rate then we have to find the number of cakes the baker can decorate in 1 minute.
We should always use the unitary method to calculate the outcome.
∵ A baker can decorate in 30 minutes = 42 cakes
∴ baker can decorate in 1 minute = [tex]\frac{42}{30}=1.4[/tex] cupcakes.
Therefore, 1.4 cakes per minute will be the answer.
After one month, Devon finds that his 10 friends slept an average of 0.5 hour more each night when they drank milk before bed. Based on this, Devon concludes that drinking milk makes teenagers sleepy. what is one reason why Devon's conclusion is most likely invalid?
Answer:
He did not test it against anyone who did not drink milk before bed and he tested it on a relatively small number of people. In order to have more accurate results he should include more people in the study and should test it against the same number of people who haven't drank milk before bed. He should also take into account the amount of milk that they drank before going to bed.
Answer:
No comparision and repeatibility
Step-by-step explanation:
Firstly, this total number of hours each friend sleeps is not specified and therefore can vary each night. What is constant is that they drank milk before they slept and for one month the analysis was made. Secondly, he never made a comparison between milk drinkers and non-milk drinkers and therefore the analysis is just one sided and open to other effects such as exercise, eating habits etc. Furthermore, no repeatability was conducted to determine if the same results would be obtained. Lastly, the ages of the friends are unknown so making a conclusion of teenagers is inaccurate.
A tractor drags a 300 lb. concrete block 80 ft. in 120 seconds. Determine the power output of the tractor.
2400 ft-lb/sec
300 ft-lb/sec
200 ft-lb/sec
120 ft-lb/sec
For this case we have that by definition, the mechanical power is given by:
[tex]P = \frac {W} {t}[/tex]
Where:
W: It is the work done
t: It's time
For its part:
[tex]W = F * d[/tex]
Where:
F: It is the applied force
d: It is the distance traveled
According to the data we have that the drag force of the tractor is [tex]F = 300lb[/tex], while the distance traveled is [tex]d = 80ft.[/tex]
Substituting:
[tex]P = \frac {300 * 80} {120}\\P = \frac {24000} {120}\\P = 200[/tex]
Finally, the power is:
[tex]\frac {200lb-ft} {s}[/tex]
Answer:
Option C
The correct option is 200 ft-lb/sec. The power output is 200 ft-lb/sec.
Determining the Power Output of a Tractor
To find the power output of the tractor dragging a 300 lb. concrete block over a distance of 80 ft. in 120 seconds, we need to use the formula for power:
Power = Work / Time
Step-by-step explanation:
1. Calculate the Work Done: Work is calculated as the force applied times the distance moved by the force. Here, the force is the weight of the block (300 lb), and the distance is 80 ft.
Work = Force x Distance
Work = 300 lb x 80 ft = 24,000 ft-lb.
2. Calculate the Time: The time given is 120 seconds.
3. Calculate the Power: Power is the rate at which work is done, given by dividing the work by the time.
Power = Work / Time
Power = 24,000 ft-lb / 120 sec = 200 ft-lb/sec.
Therefore, the power output of the tractor is 200 ft-lb/sec.
Which point-slope form equation represents a line that passes through (3,-2) with a slope of -4/5
Answer:
y + 2 = - [tex]\frac{4}{5}[/tex](x - 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
here m = - [tex]\frac{4}{5}[/tex] and (a, b) = (3, - 2), hence
y - (- 2) = - [tex]\frac{4}{5}[/tex](x - 3), that is
y + 2 = - [tex]\frac{4}{5}[/tex](x - 3)
Can someone plz help me
Answer:
One point greater than the last grade
Step-by-step explanation:
1. First off, N is the variable, so that means it can be any number, and when it uses the word greater, it means to ADD another number, which means one point greater.
Hello There!
n+1 could represent one point greater than the last test grade.
In this case, n could be the last grade so if we put this in words, the last test grade + 1 point so 1 would represent adding from the previous test.
for f(x)=3x+1 and get g(x) =x2-6, find (f-g)(x)
Answer:
(f - g)(x) = (3x + 1) - (x2 - 6) = 3x + 1 - x2 + 6 = -x2 + 3x + 7
i hope this helps.
For this case we have the following functions:
[tex]f (x) = 3x + 1\\g (x) = x ^ 2-6[/tex]
We must find[tex](f-g) (x).[/tex]
By definition we have to:
[tex](f-g) (x) = f (x) -g (x)[/tex]
So:
[tex](f-g) (x) = 3x + 1- (x ^ 2-6)\\(f-g) (x) = 3x + 1-x ^ 2 + 6\\(f-g) (x) = - x ^ 2 + 3x + 6 + 1\\(f-g) (x) = - x ^ 2 + 3x + 7[/tex]
Answer:
[tex](f-g) (x) = - x ^ 2 + 3x + 7[/tex]
Can someone please help me
Your answer would be 48.
Just multiply.
2 x 8 = 16
16 x 3 = 48
Hope helps!-Aparri
What is the slope-intercept equation of the line that includes (0,7) and (3,10)?
[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{10}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{10-7}{3-0}\implies \cfrac{3}{3}\implies 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-7=1(x-0)\implies y-7=x\implies y=x+7[/tex]
Answer: y= x + 7
Step-by-step explanation:
boom
Which two numbers does 128 lie in between on a number line
Answer:
it's 11.3 and 11.4
Step-by-step explanation:
11.3 = 127.69
11.4 = 129.96
Evaluate x - 7 for x = 14.
Answer:
x=21
Step-by-step explanation:
x-7=14
add 7 to both sides
x=21
The expression x - 7 for x = 14 is equal to 7.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To evaluate x - 7 for x = 14,
We substitute 14 for x and simplify:
x - 7 = 14 - 7 = 7
Therefore,
The expression x - 7 for x = 14 is equal to 7.
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The length of a rectangle is 8cm greater than twice its width. Find the dimensions if the area
is 42cm
Answer:
Length [tex]14\ cm[/tex]
Width [tex]3\ cm[/tex]
Step-by-step explanation:
Let
x-----> the length of rectangle
y ----> the width of rectangle
we know that
The area of rectangle is equal to
[tex]A=xy[/tex]
[tex]A=42\ cm^{2}[/tex]
so
[tex]42=xy[/tex] ----> equation A
[tex]x=2y+8[/tex] ---> equation B
substitute equation B in equation A and solve for y
[tex]42=(2y+8)y\\ \\2y^{2}+8y-42=0[/tex]
Solve the quadratic equation by graphing
The solution is [tex]y=3\ cm[/tex]
see the attached figure
Find the value of x
[tex]x=2(3)+8=14\ cm[/tex]
therefore
Length [tex]14\ cm[/tex]
Width [tex]3\ cm[/tex]
The dimensions of the rectangle are: Width ( W = 3 ) cm and Length ( L = 14 ) cm
We are given that the length L is 8 cm greater than twice its width W. This can be expressed as:
[tex]\[ L = 2W + 8 \][/tex]
The area of the rectangle is given by the formula:
[tex]\[ A = L \times W \][/tex]
Given that the area is 42 cm², we can write:
[tex]\[ 42 = (2W + 8) \times W \][/tex]
Expanding the equation:
[tex]\[ 42 = 2W^2 + 8W \][/tex]
Rearranging the equation in standard quadratic form:
[tex]\[ 2W^2 + 8W - 42 = 0 \][/tex]
Now, let's solve this quadratic equation for ( W ). We can use the quadratic formula:
[tex]\[ W = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \][/tex]
Where:
- a = 2
- b = 8
- c = -42
Now, let's substitute the values into the quadratic formula:
[tex]\[ W = \frac{{-8 \pm \sqrt{{8^2 - 4 \times 2 \times (-42)}}}}{{2 \times 2}} \]\[ W = \frac{{-8 \pm \sqrt{{64 + 336}}}}{{4}} \]\[ W = \frac{{-8 \pm \sqrt{{400}}}}{{4}} \]\[ W = \frac{{-8 \pm 20}}{{4}} \][/tex]
Now, we have two possible values for \( W \):
[tex]\[ W_1 = \frac{{-8 + 20}}{{4}} = \frac{{12}}{{4}} = 3 \]\[ W_2 = \frac{{-8 - 20}}{{4}} = \frac{{-28}}{{4}} = -7 \][/tex]
Since the width cannot be negative, we discard [tex]\( W_2 = -7 \)[/tex]. Thus, the width of the rectangle is ( W = 3 ) cm.
Now, let's find the length using the equation ( L = 2W + 8 ):
[tex]\[ L = 2 \times 3 + 8 \]\[ L = 6 + 8 \]\[ L = 14 \][/tex]
Pittsburgh, Pennsylvania and State College, Pennsylvania are 9.8 inches apart on a map that has as inches equal to 15 miles.
a) Set up a proportion to show the relationship between the distance in miles and the size of the map
b) How far apart are the cities in real life?
We can set up and solve a proportion to determine the actual distance between two cities using a scale of distance on a map. The setup would be 1/15 = 9.8/x and by solving this proportion we find the two cities are 147 miles apart.
Explanation:The topic at hand involves understanding a proportion, an important part of mathematical concepts. More specifically, we are dealing with a proportion that involves distances on a map and the equivalent distances in real life.
For part a) of your question, the proportion can be expressed as '1 inch on the map is to 15 miles in real life as 9.8 inches on the map is to x miles in real life'. In mathematical terms, this can be written as:
1/15 = 9.8/x
For part b) of your question, we can determine the actual distance between Pittsburgh, Pennsylvania and State College, Pennsylvania by solving the proportion for x:
To do this, you can cross multiply (1 * x = 15 * 9.8), getting you x = 147 miles. This means Pittsburgh and State College are 147 miles apart in real life.
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In mathematics, you can use proportions to solve map reading and scale problems. The relationship between the map distance and real distance is given as a proportion 1/15 = 9.8/x. Using cross-multiplication, we find that Pittsburgh and State College are 147 miles apart in real life.
Explanation:The relationship between the distance on the map and the actual distance can be represented as a proportion. This is a Mathematical concept often used in map reading and scale problems.
Given in the problem, we know that 1 inch on the map is equivalent to 15 miles in real life. Thus, a) the proportion can be set up like this: 1/15 = 9.8/x. Here x represents the actual distance between Pittsburgh and State College in miles.
To find the actual distance (b), we cross-multiply and solve for x: x = 9.8 * 15, which equals 147 miles. Therefore, Pittsburgh and State College are 147 miles apart in real life.
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-0.00483 as a fraction
Answer:
I think this is right 483/100000
Sorry if i'm wrong