Which is the correct slope-intercept equation for a line that passes through the points (1,-3) and (-3,17)
Answer:
[tex]y=-5x+2[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0)1) Determine the slope (m)
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where two points that the line passes through are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (1,-3) and (-3,17)
[tex]=\frac{17-(-3)}{-3-1}\\=\frac{17+3}{-3-1}\\=\frac{20}{-4}\\=-5[/tex]
Therefore the slope of the line is -5. Plug this into [tex]y=mx+b[/tex]:
[tex]y=-5x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=-5x+b[/tex]
Plug in one of the given points and solve for b
[tex]-3=-5(1)+b\\-3=-5+b[/tex]
Add 5 to both sides of the equation to isolate b
[tex]-3+5=-5+b+5\\2=b[/tex]
Therefore, the y-intercept of the equation is 2. Plug this back into [tex]y=-5x+b[/tex]:
[tex]y=-5x+2[/tex]
I hope this helps!
Evaluate the following expression at x = -4
-5x-1
Determine the number of solutions for the equation shown below.
X = X-9
A. 1
B. 2
C. 0
D. Infinitely many
Answer:
The equation has 0 solutions (answer C).
Step-by-step explanation:
Starting with x = x - 9, we subtract x from both sides. This leaves us with:
0 = -9,
which is never true.
The equation has 0 solutions (answer C).
find the height x of the tree
Answer:
19.8 m
Step-by-step explanation:
To find the height of the tree, we can use the trig ratio tangent:
θ = angle, h = height
tan θ [tex]= \frac{opposite}{adjacent}[/tex]
tan 33° = h / 30.5
h = (tan 33°)(30.5)
h = (0.6494)(30.5)
h = 19.8 m
hi i need help with this algebra vocabulary please
Answer:
slope
Step-by-step explanation:
The slope is the rise divided by the run
Answer: The slope.
Step-by-step explanation: That's what I think.
A car was bought for D750,000 and was sold for D775,000 calculate the percentage profit
the trapezium is drawn on a centimetre grid
Answer:
21 cm²
Step-by-step explanation:
Applying,
A = (a+b)h/2............. Equation 1
Where A = area of the trapezium, a = length of the first parallel side, b = length of the second parallel side, h = height.
From the diagram
Given: a = 5 cm (5 grids), b = 9 cm (9 grids), h = 3 cm (3 grids)
Substitute these values into equation 1
A = 3(5+9)/2
A = 3(14)/2
A = 3×7
A = 21 cm²
Evaluate the expression below when x = 7 and y = 8.
5x2−3y
Answer:
221
Step-by-step explanation:
Substitute x = 7 and y = 8 into the expression
5(7)² - 3(8)
= 5(49) - 24
= 245 - 24
= 221
The graph represents the piecewise function:
f(x)= { __, if -1 ≤ x ≤ 1; __, if 3 ≤ x ≤ 5 }
Answer:
4, x-1
Step-by-step explanation:
The first piece of this function goes from -1 to 1. Since that part of the function is a horizontal line at y=4, and has no slope, this first part is just 4.
The second piece of this function goes from 3 to 5. This piece does have a slope that you can either solve or just from reading the graph will give you a slope of 1. Since one of the points is (3, 2), we can figure out that the y-intercept is -1. (You can also just extend the line across the y-axis). When putting this equation together we get x-1 being the second part.
The solution is:
The graph represents the piecewise function:
f(x)= { 4, if -1 ≤ x ≤ 1;
(x - 1), if 3 ≤ x ≤ 5 }
What is graph?In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.
here, we have,
The first piece of this function goes from -1 to 1.
Since that part of the function is a horizontal line at y=4, and has no slope, this first part is just 4.
so, we have,
The second piece of this function goes from 3 to 5.
This piece does have a slope that you can either solve or just from reading the graph will give you a slope of 1.
Since one of the points is (3, 2), we can figure out that the y-intercept is -1. (You can also just extend the line across the y-axis).
When putting this equation together we get x-1 being the second part.
Hence, The solution is:
The graph represents the piecewise function:
f(x)= { 4, if -1 ≤ x ≤ 1;
(x - 1), if 3 ≤ x ≤ 5 }
To learn more on graph click:
brainly.com/question/17267403
#SPJ7
6
b
160°
45°
Find a, b, and c.
A. a = 12,6 = 673,c=316
B. a = 12,6 = 1213,c=31/6
C. a = 6/3,6 = 12,C= 612
D. a=6x3,6 = 12-/3,c=ba/2
Answer:
C. a = 6√3, b = 12, c = 6√2
Step-by-step explanation:
First let's find b using the cos. The cos is the adjacent side if the angle divided by the hypotenuse. We know the value of the adjacent side and we know that cos(60°) = 1/2 = 0.5:
cos(60°) = 6/b
0.5 = 6/b
b = 6/0.5
b = 12
Now we can find a using the Pythagorean theorem:
b² = 6² + a²
12² = 6² + a²
144 = 36 + a²
a² = 144 - 36
a² = 108
a = √108
a = 6√3
And now we can find c using cos again:
cos(45°) = c/b
√2/2 = c/12
c = 12•√2/2
c = 6√2
please answer quickly easy 10 points but please answer quick
Answer:
He traveled 520 miles
Step-by-step explanation:
8 x 65 = 520
Answer: 520 miles
Step-by-step explanation:
Data: Juan drove 8 hours
Drove at an average Speed of 65 mph
Miles driven=x
Only step: Multiply 65 by 8 which is 520
Explanation: Since Juan drove at an average speed of 65 miles per hour, that means he drove 65 mile for every hour he drove. So since he drove for 8 hours, you multiply 8 hours by 65 miles so that you get get the total amount of hours driven by him.
Don't forget to add "Miles" to the end of your answer because most math teachers tend to want that in an answer like this.
I hope this helps(Mark brainiest if you want to, thanks)
Dan, Harry and Regan sell cars.
Dan sells x cars.
Harry sells 5 more cars than Dan.
Regan sells twice as many cars as Dan.
Write an expression, in terms of x, for the mean number of cars Dan, Harry and Regan sell.
Answer:
4X+5
Step-by-step explanation:
Dan : X
Harry: X+5
Regan: 2X
X+X+5+2X
Answer:
[tex]Mean = \frac{4x + 5}{3}[/tex]
Step-by-step explanation:
Given:
Dan sold = x
Harry sold 5 more than Dan, that is = x + 5
Regan sold twice as Dan = 2x
[tex]Mean = \frac{ Total \ cars \ sold}{number\ of \ them \ sold \ it }\\\\Mean = \frac{x + ( x+ 5) +2x }{3} = \frac{4x + 5}{3}[/tex]
The dolphin is 20 feet below the serface of the ocean.
Answer: we wont be able to answer if there is no fill out box
Step-by-step explanation:
Answer:
Can you complete the sentence?
plz help me with this
Answer:
27.7
Step-by-step explanation:
Pythagorean Theorem
[tex]88.3^{2}[/tex] - [tex]10.7^{2}[/tex] = [tex]x^{2}[/tex] (10.7 comes from half of the 21.4 side)
[tex]x^{2}[/tex] = height
Write an equation for the line that contains (-15, -8) and is parallel to the
graph -3x + 5y = -8
Answer:
y=3/5x+1
Step-by-step explanation:
Hi there!
We are given the equation -3x+5y=-8 and we want to find the equation of the line that is parallel to -3x+5y=-8 and contains the point (-15,-8)
parallel lines have the same slopes, but different y intercepts.
So let's first find the slope of -3x+5y=-8
We can do this by converting the equation from standard form (ax+by=c where a, b, and c are free coefficients (numbers)) to slope-intercept form (y=mx+b, where m is the slope and b is the y intercept)
add 3x to both sides
5y=3x-8
divide by 5 on both sides
y=3/5x-8/5
3/5 is in the place of where m is, so that means that 3/5 is the slope of the line
we can write the equation of the new line in slope-intercept form.
Here it is so far:
y=3/5x+b
we need to find b
Because the line will pass through the point (-15,-8), we can use it to solve for b
substitute -15 as x and -8 as y
-8=3/5(-15)+b
multiply
-8=-9+b
add 9 to both sides
1=b
substitute 1 as b into the equation
y=3/5x+1
There's the equation of the line :)
Hope this helps!
I am timed. Please answer this.
Answer:
9
Step-by-step explanation:
because volume of a prism is area × length
so area of triangle is 4*4/2=8 so 72÷8=9.
hope this helps:)
A sample of a radioactive isotope had an initial mass of 120 mg in the year
2010 and decays exponentially over time. A measurement in the year 2015
found that the sample's mass had decayed to 50 mg, What would be the
expected mass of the sample in the year 2018, to the nearest whole number?
Answer:
2015-2010=5
50÷5=10
120-50=70
2017-2015=2
2*10=20
70-20=50mg
2018=50mg
can someone help please!!
find the maximum value of function f(x) = -1.1x^2 - 3.6x + 1
Step-by-step explanation:
everything can be found in the picture
Solve 2x + 6 > 20. OLA X> 18 B. X>7 O c. x
someone help por favor
Answer:
2x+6>20
2x>20-6
2x/2>14/2
x>7
So your answer would be B
(write and solve an algebraic equation to find the measure of each angle based on the given description.)
***11. Two angles form a linear pair. The measure of one angle is 24° more than the
measure of the other angle.
Answer:
The angles are 78° and 102°.
Step-by-step explanation:
Let the one angle is y and the other number if y + 24.
The sum of the angles of the linear pair is 180°.
So, according to the question
y + y + 24 = 180
2 y = 180 - 24
2 y = 156
y = 78°
So, one angle is 78° and the other is 78° + 24° = 102°.
Originally a rectangle has dimensions 12in by 8in. if the same amount increases on both sides, the area is doubled find the new dimensions
Step-by-step explanation:
Let the increase in the size of the length and breath be 'x'.
The area of the rectangle = 12in × 8in
=96 in²
From the question,
(12+x)(8+x)=96×2 in²
or, 96+12x+8x+x²= 192
or, x²+20x+96-192=0
or, x²+20x-96=0
or, x²+24x-4x-96=0
or, x(x+24)-4(x+24)=0
or, (x-4)(x+24)=0
Either, Or,
x-4=0 x+24=0
Therefore, or, x= –24 (Which is impossible)
x=4
So the new dimensions are 12+4=16 inch and 8+4=12 inch.
pretty simple just fill in the blank from the drop down menu please !
Answer:
vertical hope this helps
Answer:
vertical, goodluck
Step-by-step explanation:
I took this
The school is having a bake sale. It costs $6 to make a cake. The school wants to make a 25% profit on each cake. How much should the school charge for each cake?
Answer:
$1.50
Step-by-step explanation:
25% of 6 is basically just 6/4, which is 1.5.
This is money we're talking about, so the answer is $1.50
Length of radius r ?
Answer: 10
We know that the radius of a circle is always perpendicular to the tangent. And so apply the Pythagoras theorem.
Answer:
The answer would be 10.
Step-by-step explanation:
We're doing C^2 - B^2 = A^2 since we know the hypotenus. 26 x 26 is 676 and 24 x 24 is 576. Subtract the two products to get 100. The square root of 100 is 10.
Kiran's father is 65 years old. He is 8 years older than three
times Kiran's age. Find Kiran's age?
Answer:
let kiran's age be x
kiran's father's age is 65
acc.to ques
kiran's father is 8 years older than 3 times kiran's age ....which gives us the equation as follows
8+3x =65
therefore
3x =65-8
3x =57
x =57/3
x= 19 ans
so kiran's age is 19 years.
Answer:
kiran is 19 years old.
Step-by-step explanation:
kiran's father age = 65
let kiran's age be x
kiran's father is 8 years older than three times kiran's age means 8 + 3x
so according to the question equation is
65 = 8 + 3x
65 - 8 = 3x
57/3 = x
19 = x
therefore kiran's age is 19 years.
One floor is randomly taken from a
vase containing 5 red flowers,
2 white flowers, and 3 pink flowers.
Find the probability of taking a red
or a pink flower.
What pattern can you use to find other terms of the sequence given below? 14, 6, -2, -10, -18, … Add _________ to the previous term to find the next term
Answer:
Add -8
Step-by-step explanation:
Take the second term and subtract the first term
6-14 = -8
Check with the third and second terms
-2 -6 = -8
We are subtracting 8 from each side
(or adding -8)
Step-by-step explanation:
14, 6, -2, -10 , -18
ok so if you are starting at 14 then you would be add -8
14-8=6
6-8=-2
so on and so on..
But if you are starting from -18 then you would add 8
-18, -10,-2, 6, 14
-18+8=-10
-10+8=-2 so on and so on
so either one of those depending on which number your starting with
can someone pls help for brainlest
Answer:
6.28km
Step-by-step explanation:
Hey,
We know that the circumfrence is the perimetert of a full circle. If we want to find the perimeter of a semicircle all we have to do is find the circumfrence and then divide it by 2 since we want to know the perimeter of half the circle.
Circumfrence is equal to 2πr. Where r is the radius and since we know the radius we an solve for the circumfrence.
2(π)(1km)=2kmπ.
The problem tells us to use 3.14 for pi so let's multiply 2 by 3.14.
6.28km is the answer!
give four pairs of prime numbers whose difference is 2
Answer:
(3, 1) (5, 3) (7, 5) (13, 11)
Step-by-step explanation:
There are only three of them that I know of:
(7, 5) (13, 11) (19,17)
(6x-4) (3x+4)º find the value of x.
Answer:
x = 20
Step-by-step explanation:
The angles form a straight line so they add to 180 degrees
6x-4 + 3x+4 = 180
Combine like terms
9x=180
Divide by 9
9x/9 = 180/9
x= 20
20
Hope this helps! :)
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