y = - 5
substitute the value of x = 4 into the equation and solve for y
- 12 + 9y = - 57 ( add 12 to both sides )
9y = - 45 ( divide both sides by 9 )
y = [tex]\frac{-45}{9}[/tex] = - 5
-3(-4)+9y=-57
12+9y=-57
9y=-57-12
9y=-69
9y/9=69/9
y=-23/3
Calculate the slope of the line that passes through the labeled points on the graph.
m=(Y2-Y1)/(X2-X1)
(1.) m=(2-(-1))/(-2-3) = 3/-5 = -3/5
(2.) m=(-2-1)/(-3-2) = -3/-5 = 3/5
(3.) m=Infinity (equation: x=-2)
The slopes of the lines passing through the given points are: 1. [tex]\((-2,2)\)[/tex] and [tex]\((3,-1)\)[/tex]: [tex]\(m = -\frac{3}{5}\)[/tex]. 2. [tex]\((-3,-2)\)[/tex] and [tex]\((2,1)\)[/tex]: [tex]\(m = \frac{3}{5}\)[/tex]. 3. [tex]\((-2,-2)\)[/tex] and [tex]\((-2,3)\)[/tex]: The slope is undefined (vertical line).
To calculate the slope m of a line given two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], you can use the formula:
[tex]\[m = \frac{y_2 - y_1}{x_2 - x_1}\][/tex]
Let's apply this formula to the given points:
1. For points (-2,2) and (3,-1):
[tex]\[m = \frac{-1 - 2}{3 - (-2)} = \frac{-3}{5}\][/tex]
2. For points (-3,-2) and (2,1):
[tex]\[m = \frac{1 - (-2)}{2 - (-3)} = \frac{3}{5}\][/tex]
3. For points (-2,-2) and (-2,3):
[tex]\[m = \frac{3 - (-2)}{(-2) - (-2)} = \frac{5}{0}\][/tex]
The slope for the third set of points is undefined because the denominator becomes zero, indicating a vertical line. The first two sets of points have slopes of [tex]\(-\frac{3}{5}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex] respectively.
I need help ASAP how ever gets the right answer first I wil mark Brainliest!!!
Answer:
The area of this tabletop is
6 ft. × 2 ft. = 12 ft.²
It's quite easy and simple, but I need help with it.
Least to greatest ordering integers
Answer:
5, 19, 24, 46, 77, 98
Step-by-step explanation:
Just write the numbers in order (I am assuming from least to greatest). You can use a number line if necessary.
what is the answer to 2x-3y=11 2x+y=9
Show work plz
Tina bought two pairs of regular socks and one pair of long fleece socks .The fleece socks cost $12.If the final price ,including 5% sales tax ,was $30.45,what was the price of each pair of regular socks?
Trisha spins a spinner. the pointer lands on three prime numbers .she says the sum is less than 12.which could be the number
The sum of the first three prime numbers less than 12 is 2, 3, and 5.
What is a Prime number?A prime number is a positive integer having exactly two factors that are 1 and number itself. Any number that does not follow this is termed a composite number.
Given
Trisha spins a spinner. the pointer lands on three prime numbers.
She says the sum is less than 12.
How to find the prime number?The prime numbers are as follows,
2, 3, 5, 7, 11..so on
So the sum of the first three prime numbers will be
2 + 3 + 5 = 10
Hence, the sum of the first three prime numbers less than 12 is 2, 3, and 5.
More about the prime number link is given below.
https://brainly.com/question/4184435
which is the focus of a parabola with equation y^2=4x
The focus is (1,0)
Hope this helps!
Answer:
focus is (1,0)
Step-by-step explanation:
the focus of a parabola with equation [tex]y^2=4x[/tex]
Focus point lies inside the parabola
To find the focus of a parabola we need to find the vertex
the distance between the focus and vertex is the value of p.
Focus point is (h+p,k)
Where (h,k) is the vertex
Given equation is in the form of [tex](y-k)^2=4p(x-h)[/tex]
Given equation can be written as [tex](y-0)^2=4(x-0)[/tex]
So the vertex is (0,0)
Now we find the value of p
[tex]4p = 4[/tex]
So [tex]p=1[/tex]
Focus is (h+p,k) that is (1,0)
The graph of y= -4x+7 is:
A. a line that shows the set of all solutions to the equation
B.A point that shows the y-intercept
C.A point that shows only one solution to the equation
D.A point that shows one solution to the equation
Answer:
A is the answer
Step-by-step explanation:
The graph of the equation y = -4x+7 is a line that shows the set of all solutions of the equation.
What is equation of the line ?"The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system. The numerous points which together form a line in the coordinate axis are represented as a set of variables x, y to form an algebraic equation, which is referred to as an equation of a line. Using the equation of any line, we can find whether a given point lies on the line or not.
The equation of line is a linear equation with a degree of one"
"The equation of a line can be formed with the help of the slope of the line and a point on the line."
Here is the equation of the line is given,
y = -4x + 7
since, it is the equation of a line, it contains all the solutions on the graph.
Hence, option A is the correct option.
To know more about equation of motion here
https://brainly.in/question/16516318
#SPJ2
Bradley solved the following equation 4(5x - 6) = 2(8x + 10)
Hello! I'm guessing you need someone to solve this equation!
4(5x-6)=2(8x+10)
20x-24=16x+20
Add 24 on both sides!
20x=16x+44
Subtract 16x on both sides!
4x=44
Divide 4 by 44
x=11
An engineer designing a ramp in a football stadium was told to keep the slope to a ratio of 1:10. The ramp height is 25 ft. What is the Ideal Mechanical Advantage of the ramp? (Its 10.05, but how do I solve it?)
we know that
To calculate the ideal mechanical advantage for an inclined plane, divide the length of the incline by the height of the incline
Step 1
Find the horizontal distance of the ramp
we know that
the ramp has a slope of [tex]1:10[/tex]
so
by proportion
[tex]\frac{1}{10} \frac{height}{long} =\frac{25}{x} \frac{height}{long} \\ \\x=25*10 \\ \\ x=250\ ft[/tex]
Step 2
Find the length of the incline of the ramp
Applying the Pythagorean Theorem
[tex]incline^{2}=height^{2}+horizontal^{2}[/tex]
substitute the values
[tex]incline^{2}=25^{2}+250^{2}[/tex]
[tex]incline^{2}=63,125[/tex]
[tex]incline=251.25\ ft[/tex]
Step 3
Find the ideal mechanical advantage
[tex]Ideal\ Mechanical\ Advantage=\frac{incline}{height}[/tex]
substitute the values
[tex]Ideal\ Mechanical\ Advantage=\frac{251.25}{25}=10.05[/tex]
therefore
the answer is
the Ideal Mechanical Advantage of the ramp is [tex]10.05[/tex]
pepper jackie decides her map of the youth center is too small. She draws a new map of the youth center that is 3 times larger. What is the scale of the map?
Solution:
Let starting map of youth center has Dimension (Preimage)
1 unit of y= k units
1 unit of x = t units
The new map of youth center which is 3 times larger than original(Image)
1 unit of y= 3 k units
1 unit of x = 3 t units
Image = 3 × Pre- image
The image is larger than Pre- image.
So, Scale of the new map = 3 × The original dimension of map.
Answer:
the answer is 1 in: 4 ft
Step-by-step explanation:
i took the test and hopefully i’ve helped you luv
At 8:00 a.m. the temperature outside in Juneau, Alaska was -16.5 . By noon the temperature had increased by 15.25 . What is the temperature at noon?
It would be -1.25 degrees at noon.
stans cookie recipe makes 24 cookies and calls for exactly 384 sprinkles. he is wondering how many sprinkles (p) he will need to make 60 cookies. he assumes each cookie will have the same number of sprinkles. how many sprinkles does stan need to make 60 cookies
Answer:
960 sprinkles
Step-by-step explanation:
If 24 cookies call for EXACTLY 384 sprinkles, then 16 sprinkles fit on each cookie. 384/24 = 16
If 16 sprinkles fit on each cookie, 16 cookies on 60 cookies would be 960.
60 x 16 = 960
Answer:
Its 960
Step-by-step explanation:
I did it on khan academy, and got it right!
A local hamburger shop sold a combined total of 237 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold
The square root of 5 is between which two integers
[tex]2<\sqrt5<3\\\\\text{because}\\\\2^2=4\\(\sqrt5)^2=5\\3^2=9\\\\2^2=4<(\sqrt5)^2=5<3^2=9[/tex]
Integers are positive and negative numbers without decimal points.
The square root of 5 is between 2 and 3
The number is given as:
[tex]\mathbf{n = \sqrt{5}}[/tex]
Evaluate the square root
[tex]\mathbf{n = 2.2361}[/tex]
The above number is greater than 2 but less than 3.
So, we can say that:
2.2361 is between 2 and 3
Hence, the square root of 5 is between 2 and 3
Read more about integers at:
https://brainly.com/question/11337513
Find the measure of z.
A. 80°
B. 83 °
C. 70 °
D. 87 °
Given that 1 kilogram weighs approximately 22 pounds, rewrite 10 pounds as an equivalent number of kilograms
Answer:
0.4545 kgs.
Step-by-step explanation:
Given that 1 kg weighs approximately 22 pounds.
i.e. 1kg= 22 lbs.
We can use this to convert lbs into kg.
22 lbs = 1 kg
Hence 1 lb = 1/22 = 0.04545 kg
Now to find out the equivalent weight for 10lbs,
we have conversion factor as 1 lb= 0.04545 kg
Hence 10 lbs = 10(0.04545) = 0.4545 kgs
Hence 10 pounds written in equivalent kgs would be0.4545 kgs.
John earns $437 a week after a 15% pay rise. What was his pay initially? Round your answer to the nearest dollar. Do not include the dollar sign in your answer. For example, if your answer is $200.10, enter 200.
The answer to this question is 380
Answer:
380 dollar.
Step-by-step explanation:
John earns $437 a week after a 15% pay rise.
Let the initially pay of John be x
x + (15% of x) = 437
x + 0.15x = 437
1.15x = 437
x = [tex]\frac{437}{1.15}[/tex]
x = 380
Initially his pay was 380 dollar.
a man is 76 inches tall. the length from his head to his shoulders is 14 inches, and the length from his waist to his shoulders is 30 inches. what is the length from his feet to his waist
use inequality symbol to compare -3 + 7--------10 - 2
[tex]-3+7=4[/tex]
[tex]-10-2=-12[/tex]
[tex]4>-12[/tex]
A cube has a length, width and height of 6 feet. What is the volume in cubic INCHES?
Volume of cube = ( side)^3
Side = 6 feet = 6×12 = 72 inches ( 1ft =12 inch)
Vol. = (72)^3 = 72×72×72= 373248 cubic inches
Answer:
6
Step-by-step explanation:
Change the number 43,456 to its word name.
A. Four hundred thirty-four hundred and fifty six
B. Forty-three thousand, four hundred fifty six
C. Four hundred three thousand, four hundred fifty six
D. Forty-three thousand, four fifty six
Answer:
B
Step-by-step explanation:
Ramona is a saleswoman whose base pay plus commissions amounted to $52561 last year. If her base pay was $23690 and she made $77,300 in sales last year, what is her rate of commission
A) 68%
B) 37%
C) 31%
D) 46%
Answer:
B) 37%
Step-by-step explanation:
Given,
The total base pay and commission = $ 52561,
While, base pay = $ 23690,
So, the amount of commision = Total base pay and commission - base pay = $ 52561- $ 23690 = $ 28871,
Also, total sale = $77,300,
Hence, the rate of the commission( in percentage )
[tex]=\frac{Commission}{Sale}\times 100[/tex]
[tex]=\frac{28871}{77300}\times 100[/tex]
[tex]=\frac{2887100}{77300}[/tex]
[tex]=37.3492884864\%[/tex]
[tex]\approx 37\%[/tex]
Option 'B' is correct.
How many different 10 digit phone numbers are possible if numbers can be repeated
It was would numbers 000-000-0000 through 999-999-9999. So that would be 9,999,999,999 + 1 = 10 billion different 10-digit phone numbers.
Nita wants to buy a new keyboard for her computer. She will buy the keyboard when it is on sale for under $50 Write an inequality that describes k, the price in dollars at which Nita will buy the keyboard
This would be k < 50.
This inequality states that k, the price at which Nita wants to buy the new keyboard, is less than 50 dollars.
Answer:
0 ≤ k ≤ 50
Step-by-step explanation:
Here k represents the price of the keyboard ( in dollars ),
Given,
Nita will buy the keyboard,
If the price of the keyboard is under $ 50,
That is, [tex]k \leq 50[/tex]
Also, the price can not be negative,
⇒ [tex]0 \leq k[/tex]
Hence, the required inequality is,
[tex]0 \leq k \leq 50[/tex]
Mariana wears her winter coat when the temperature is colder than − 4 C . Write an inequality that is true only for temperatures ( t ) at which Mariana wears her winter coat.
t<-4
Mariana only wears her coat when it is colder than -4 so t must be less than -4.
Answer: t < -4
Step-by-step explanation:
We want to represent temperatures colder than -4 C
In mathematical terms, we want to represent temperatures less than -4 C
t < -4
Suppose the size of each cube is doubled and the size of the large box is doubled. How many of these new cubes will fit in that new large box?
Insert either < or > between the pair of numbers to make a true statement.
the square root of 2 is 1.4
So √2 < 1.9
2b+4=-18-9b ; solving equations with variables on both sides
To solve this, first add -9b on both sides of the equation to get the variable on only one side of the equation.
2b+4=-18-9b
2b+9b+4=-18-9b+9b
11b+4=-18
Then subtract 4 from both sides of the equation.
11b+4=-18
11b+4-4=-18-4
11b=-22
Divide 11 on both sides of the equation to find the values of b.
[tex]\frac{11b}{11}[/tex]=[tex]\frac{-22}{11}[/tex]
b=-2