Linear equations are commonly organized in slope-intercept form:
[tex]y=mx+b[/tex]
m = slopeb = the y-intercept (the value of y when x=0)To find the equation of a line given two points:
Determine the slope of the line using the slope formulaPlug the slope into [tex]y=mx+b[/tex]Determine the y-intercept by solving for bPlug the y-intercept back into the equationSolving the QuestionWe're given:
The line passes through the points (8,-45) and (2,-9)First, determine the slope using the following formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex] where the given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
⇒ Plug in the given points (8,-45) and (2,-9):
[tex]m=\dfrac{-45-(-9)}{8-2}\\\\m=\dfrac{-45+9}{8-2}\\\\m=\dfrac{-36}{6}\\\\m=-6[/tex]
Therefore, the slope of the line is -6. Plug this into [tex]y=mx+b[/tex] as m:
[tex]y=-6x+b[/tex]
Now, determine the y-intercept:
[tex]y=-6x+b[/tex]
⇒ Plug in one of the given points as (x,y) and solve for b:
[tex]-9=-6(2)+b\\-9=-12+b\\3=b[/tex]
Therefore the y-intercept of the line is 3. Plug this back into [tex]y=-6x+b[/tex]:
[tex]y=-6x+3[/tex]
Answer[tex]y=-6x+3[/tex]
A b c d or e what one will give brainlest
Evaluate the following expression
(10 + 2) = 6 + 53
Answer:12=59
Step-by-step explanation:
write 12/root2 + root18 in the form broot2 where b is an interger
[tex]\dfrac{12}{\sqrt 2} + \sqrt{18}\\\\\\=\dfrac{12 + \sqrt{18 \times 2}}{\sqrt 2}\\\\\\=\dfrac{12+\sqrt{9 \times 4}}{\sqrt 2}\\\\\\=\dfrac{12+3 \times 2}{\sqrt 2}\\\\\\=\dfrac{18}{\sqrt 2}\\\\\\=\dfrac{18\sqrt 2}{\left(\sqrt 2\right)^2}\\\\\\=\dfrac{18\sqrt 2}2\\\\\\=9\sqrt 2[/tex]
Given the 4 points below,
identify what shape is
formed and how you
found your answer.
A(-1,0), B(0, 2), C(4,0), and
D(3,-2)
basically it's a quadrilateral
hope it really helps..!!
Find
a
and
d
for an arithmetic sequence where the 5th term is 10 and the 6th term is 8.
Answer:
Step-by-step explanation:
Arithmetic sequence:
[tex]\boxed{a_n =a + (n-1)*d)}[/tex]
a₅ = 10 a + 4d = 10
a₆ = 8 a + 5d = 8
Multiply the equation (I) by (-1) and then add. 'a' will be eliminated and we can find the value of 'd'
(I)*(-1) -a - 4d = -10
(II) a + 5d = 8 {Now add}
d = -2
Substitute d = -2 in equation (I)
a + 4*(-2) = 10
a - 8 = 10
a = 10 + 8
a = 18
a = 18 , d = -2
Sequence: 18 ,16 , 14 , 12 , 10 , ......
Solve the following quadratic by
completing the square.
f(x) = x2 + 10x - 1
Answer:
x = -5 plus/minus sqrt( 26 )
Step-by-step explanation:
Let's remember the binomial square formula
A^2 + 2AB + B^2 = (A + B)^2
We have:
x^2 + 2*5x -1
Hence, if we replace
A = x
B = 5
we get a perfect square: x^2 + 2*5x + 25 = (x + 5)^2. [++]
Based on this reasoning, let's set f(x) = 0
x^2 +10x -1 = 0
Let's add 26 on both terms:
x^2 +10x +25 = 26
Based on [++]: (x + 5)^2 = 26
Square root on both sides
(x + 5) = plus/minus sqrt (26)
x = -5 plus/minus sqrt (26)
6=sqrt x^2+3-x
steps included please
Answer:
-3/2
Step-by-step explanation:
6=|x|+3-x
move the terms
-|x|+x=3-6
-|x|+x=-3
-x+x=-3 , x > 0 (put a line under >)
-(-x)+x=-3 , x < 0
-3/2 , x < 0 find the intersection
x= -3/2
if you dont want it as a fraction you can do -1.5 in decimal form
Gavin needs to fill the fish tank below with water. The directions state that the water level
should be 2 inches below the top of the tank. Write an expression to show the volume of water
Gavin needs to fill the tank according to the directions.
(2x-6) inches
00
x inches
2x inches
Answer:
the volume is 300cubic inches
the expression is l x w x (h-2)
Megan wants to buy a designer handbag and plans to earn the money from babysitting. Suppose the interest rate is 8% and she is willing to wait one year to purchase the bag. How much babysitting money will she need to earn today to buy the bag for $400 one year from now? (Enter just the number in dollars without the $ sign or a comma and round off decimals to the closest integer, i.e., rounding $30.49 down to $30 and rounding $30.50 up to $31.)
Answer:
370
Step-by-step explanation:
FV = PV ( 1 + i) i = interst in decimal
400 = PV ( 1.08)
PV = 400 / 1.08 =
Find the greatest common factor of 34 and 36.
Answer:
2
Step-by-step explanation:
Factors of 34 include : 1,2,17 and 34
Factors of 36 are : 1,2,3,4,6,9,12,18,36
The only two common are 1 and 2
2 is greater tha one
So the gcf is 2.
Brainliest would be appreciated
Answer:
The greatest common factor is 2.
Step-by-step explanation:
You need to find the greatest common factor between 34 and 36.
Factors of 34: 1, 2, 17, and 34.
1*34=34
2*17=34
17*2=34
34*1=34
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Therefore, the greatest common factor of 34 and 36 is 2, which is our answer.I hope this helps! Let me know if you have any questions.
Can someone help me please?
Answer:
Wow that's a lot of questions. The answers are 2, 3/4, 4, 6, 10, 5, 48500, 48000, and 50000
Step-by-step explanation:
Hope this helped
1. How many degrees are in this angle, which is one-fourth of the circle?
Answer: 90 degrees
Step-by-step explanation: A circle is 360 degrees so since that is 1/4 you can divide
360/4 = 90 (: hope this helps
Answer:
90* x 4 = 360*
360* / 4 = 90*
Step-by-step explanation:
A circle has 360* all around.
In the angle that was drawn, it is 90*
The degrees for the space outside of 90* is x
x = ? 360* - 90* = 280* x = 280*
hope this helped
Jason opened the triangular pyramid-shaped box to cover it with wrapping paper. How much wrapping paper will he need?
Answer:
How might the situation lead to bullying?
Step-by-step explanation:
How might the situation lead to bullying?
the answer B
PLEASE HELP ME ON THIS
Answer:
About 154 Square
Explanation:
To find an area of a circle you multiply pi by the radius squared so 7² = 49 and 49 x 3.14 = 153.86 which is the closest to 154.
where do the graphs of f(x)=cos(x/2) and g(x)= sqrt2 - cos(x/2) intersect on the interval [0,360)?
(See image below for clear question and answer choices)
Answer:
(a) 90°
Step-by-step explanation:
A graph can help you answer the question about where the graphs of the two functions intersect. It shows the one angle of intersection to be 90°.
__
You can also determine this analytically.
f(x) = g(x)
cos(x/2) = √2 -cos(x/2)
2cos(x/2) = √2 . . . . . . . . . . add cos(x/2)
cos(x/2) = √2/2 . . . . . . . . divide by 2
x/2 = ±45° +360°×n . . . . . for an integer n
x = ±90 +720°×n . . . . multiply by 2
x = 90° is the only solution in the desired range.
It takes Kim 7 hours to proof a chapter of Hawkes Learning Systems' Introductory Algebra book and it takes Harding 2 hours. How long would it take them working together? (Round your answer to two decimal places.)
Directions: Match each image of a ray with the correct way to write it.
Answer:
1 + G = Push in p To Much P
Step-by-step explanation:
g= gunnaaa 1+gunnaaa = push ing P
Can someone help me please?
A cat eats 2/3 of a tin of cat food every day. How many tins of cat food will she eat in 1 week?
First, how many days are in a week?
7 days are in a weekSo 7x 2/3First, Convert any mixed numbers to fractions.
Then your initial equation becomes:
2/3×7/1
Applying the fractions formula for multiplication,
=2×7 x 3×1
=14/3
Simplifying 14/3, the answer is
4 and 2/3
Therefor, your answer is 4 2/3
1
Maurice drove 48 miles north and then 36 miles west. Find the
shortest distance from the point where he ended up to his starting
point.
Answer: 60 miles
Step-by-step explanation: If you draw it out you get a triangle with side lengths 48 and 36 and you need to find the hypotenuse.
Use pythagorean's theorem a^2+b^2=c^2 or 48^2+36^2=c^2 and you get that the hypotenuse=60
what's the estimate of 6.48 + 9.34 and what's the estimate 15.71 + 12.2
Answer:
Your Estimated Equations and Answers: 6+9= 15 ; 16+12 = 28
Step-by-step explanation:
Estimating can be equivalent to rounding. This is because you're trying to find an approximate number or sum.
6.48 + 9.34 is your first question.
You should round it to the nearest whole number.
6.48 ~ 6 and 9.34 ~ 9
*Rounding rules applied here*
(~ this sign is the approximate or rounded to symbol)
Now, do 6+9 =
6+9= 15
______________________________________________
15.71 + 12.2 is your next question.
Same as last, round to the nearest whole number.
15.71 ~ 16 and 12.2 ~ 12
Now, do 16+12
16+12 = 28
Which pieces of information may be found on a person's credit report?
Select each correct answer.
past due bills
social security number
marital status
medical history
criminal record
mortgage payment
Answer:
Past due bills
social security number
mortgage payment
Question
The dimensions of a cereal box are shown below.
32 cm
9 cm
21 cm
What is the volume of the box?
Answer:
6048 cm2Step-by-step explanation:
32*9*21
Finding volume is simple as pie for a cube.
Length*Height*width
find the sum of the fractions below. 5/8 + 1/n = 7/8 A. 3 B. 3 5/12 C. 3 4/9 D. 4
Answer:
D. 4
Step-by-step explanation:
1) Subtract 5/8 from both sides.
1/n = 7/8 - 5/8
2) Simplify 7/8 - 5/8 to 1/4.
1/n = 1/4
3) Multiply both sides by n.
1 = 1/4n
4) Simplify 1/4n to n/4.
1 = n/4
5) Multiply both sides by 4.
1 * 4 = n
6) Simplify 1 * 4 to 4.
4 = n
7) Switch sides.
n = 4
Check Answer:
5/8 + 1/n = 7/8
1) Let n = 4.
5/8 + 1/4 = 7/8
2) Simplify 5/8 + 1/4 to 7/8.
7/8 = 7/8
Dr. Weinstein took 50 ounces of a 20% silver
alloy and mixed it with a 40% silver alloy to get
a 30% silver alloy. How many ounces of the 40%
silver alloy did he use?
Answer:
I think it is 100
Answer:
Step-by-step explanation:
The answer is 50 ounces
Because 30% silver is right in between 20% silver and 40% silver, it would have to be the same amount to be 30%
When you multiply a whole number by 10 to the 5th power , will there always be the same number of
zeros before the decimal point as in your answer to Part A? Explain your reasoning.
Answer:
Answer:
Step-by-step explanation:
a whole number can be ANY counting number
10 to the 5th power = × 10 × 10 × 10 × 10 × 10
when you multiply by any positive power of ten, you are making it really big
23 × 10 × 10 × 10 × 10 × 10 = 2,300,000
30 × 10 × 10 × 10 × 10 × 10 = 3,000,000
100 × 10 × 10 × 10 × 10 × 10 = 10,000,000
the pattern is the whole number followed by 5 zeros that show 5 place values
Order from least to greatest the given numbers.
-5,13,4,-10,-1
A)
-5,-1,-10,4,13
B)
-10, 4, 13,-1,-5
C)
-10,-5, -1, 4, 13
D)
-5, -10,-1, 13,4
Answer:
Option C) is correct......
The table shows the results of a survey on the preferred flavor of ice cream. Based on this survey, what is the probability that an adult prefers chocolate ice cream?
A) 55/52
B) 55/54
C) 55/107
D) 55/119
Answer:
d
Step-by-step explanation:
cause this means that it is rise over run
find the binomial factor s^2+10s+25
[tex]s^2+10s+25\\\\=s^2+2\cdot 5 \cdot s +5^2\\\\=(s+5)^2\\\\=(s+5)(s+5)[/tex]
Gabe is designing a flashlight that uses a parabolic reflecting mirror and a light source. The shape of the mirror can be modeled by a parabola that opens upward with a diameter of 4 in. and a depth of 1 in. The vertex of the parabola is at the the origin. Where should Gabe place the bulb to ensure a perfect beam of light?
(0,1)
(0,4)
(1,0)
(4,0)
Answer:
C. (1,0)
Step-by-step explanation:
If we make use of a parabolic reflecting mirror and a light source.
Given thar the equation of parabolic mirror is Y2 = 4ax
The given data in the problem is x = 1 and y = 2
So subject value is y2 = 4ax
4 = 4 a (1)
a = 1
So x = 1
thus focus is at (x, y) = (1,0)
Therefore, option C is correct answer.