Answer:
[tex]\displaystyle y =\frac{1}{2}x+5[/tex]
Step-by-step explanation:
Equation of the line
The slope-intercept form of a line is given by:
[tex]y=mx+b[/tex]
Being:
m = the slope of the line
b = the y-intercept
We can also use the point-slope form of the line:
[tex]y - k=m(x-h)[/tex]
Being:
(h,k) = A point that belongs to the line
Two lines of slopes m1 and m2 are perpendicular if:
[tex]m_1.m_2=-1[/tex]
We are given the line:
[tex]y=-2x+5[/tex]
Whose slope is m1=-2
Thus, the perpendicular line has a slope of:
[tex]\displaystyle m_2=-\frac{1}{m_1}[/tex]
[tex]\displaystyle m_2=-\frac{1}{-2}[/tex]
[tex]\displaystyle m_2=\frac{1}{2}[/tex]
The required line contains the point (-8,1), thus the equation is:
[tex]\displaystyle y - 1=\frac{1}{2}(x+8)[/tex]
Removing the parentheses:
[tex]\displaystyle y - 1=\frac{1}{2}x+\frac{1}{2}\cdot 8[/tex]
Adding 1:
[tex]\displaystyle y =\frac{1}{2}x+\frac{1}{2}\cdot 8+1[/tex]
Operating:
[tex]\displaystyle y =\frac{1}{2}x+4+1[/tex]
[tex]\mathbf{\displaystyle y =\frac{1}{2}x+5}[/tex]
If y = x is compressed by a factor of 1/2 and translated up one unit, the new Function would be:
What are the solutions of the equation X4-9x2 + 8 = 0? Use u substitution to solve.
O x = 1 and x = 2.13
O x=+1 and x=+22
O x= ti and X=
O x = ti and X=25
=+21/2
Answer: the answer is B
Step-by-step explanation:
The solutions of the equation X⁴-9x² + 8 = 0 is ±2√2 and ±1
How to solve equation using substitutionX⁴-9x² + 8 = 0
Let x² = y
Then the equation becomes y² - 9y + 8 = 0
This is in the form ax² + bx + c = 0
We can solve by using quadratic formula for finding roots
x = {-b ± √(b² - 4ac)} / 2a
where,
a = 1, b = -9, c = 8= {-(-9) ± √((-9)2 - 4(1)(8))} / 2(1)
= {9 ± √(81 - 32)} / 2
= {9 ± √49} / 2
= {9 ± 7}/2
= 16/2, 2/2
= 8, 1
y = 8,1
x = ±2√2, ±1
Learn more about equation:
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What is an equation of the line that passes through the points (3,4) and (−4,−3)? Put your answer in fully reduced form
Answer:
The equation of the line is y = x + 1
Step-by-step explanation:
The equation of the line is y = m x + b, where
m is the slope of the lineb is the y-interceptThe rule of the slope of the line is m = [tex]\frac{y2-y1}{x2-x1}[/tex] , where
(x1, y1) and (x2, y2) are two points on the line∵ The line passes through points (3, 4) and (-4, -3)
∴ x1 = 3 and y1 = 4
∴ x2 = -4 and y = -3
→ Substitute them in the rule of the slope above to find it
∵ m = [tex]\frac{-3-4}{-4-3}[/tex] = [tex]\frac{-7}{-7}[/tex] = 1
∴ m = 1
→ Substitute it in the form of the equation above
∴ y = 1(x) + b
∴ y = x + b
→ To find b substitute x by 3 and y by 4 in the equation
∵ 4 = 3 + b
→ Subtract 3 from both sides
∵ 4 - 3 = 3 - 3 + b
∴ 1 = b
→ Substitute it in the equation
∴ y = x + 1
∴ The equation of the line is y = x + 1
Jessica and her father are comparing their ages. At the current time, Jessica's father is 24 years older than her l. Three years from now, Jessica father will be five times her age at the point
Answer:
Jessica is currently 3 years old and her father is 27 years old.
Step-by-step explanation:
System of Equations
Let's call:
x = Jessica's age
y = Jessica's father's age.
There are two conditions:
1: Jessica's father is 24 years older than her or, equivalently:
y = x + 24
2: Three years from now, he will have five times her age.
Three years from now, Jessica will have x+3 years, and her father will have y+3 years, thus:
y + 3 = 5( x + 3 )
Substituting the first condition into the second:
x + 24 + 3 = 5( x + 3 )
Operating:
x + 27 = 5x + 15
Subtracting x and 15:
27 - 15 = 5x - x
12 = 4x
Solving:
x = 12 / 4 = 3
x = 3
y = 3 + 24 = 27
y = 27
Jessica is currently 3 years old and her father is 27 years old.
If X=4, is each statement true or false? plsssss helpp me it due today
A. x/4=1
B. -8=2x
C. x exponent 2 = ( -16)
D. -12 = x times (-3)
E. 12=x+ x+ x
F. x + 4 = -8
Answer:
A.True
B.False
C.False
D.True
E.True
F.False
Step-by-step explanation:
A. It's true because 4/4 is 1
B. It's false because 2×4 is 8 not -8
C. x exponent 2, 4 exponent 2 is 16 not -16
D. 4×(-3) is -12 so it's true
E. ×+×+×, 4+4+4 is 12 so again it's true
F. ×+4, 4+4=8 not -8
I think the answers are this!
What is angle A and B??
Answer:
A=45 b=110
Step-by-step explanation:
I used a calc
Answer:
A=135 b=200
Step-by-step explanation:
135+200+25=360
X+(x+65) +25=360
Subtract 25 from both sides
X+ (x+65)=335
Combine like terms
2x +65=335
Subtract 65 from both sides
2x =270
Divide by 2
X=135
To get b you just do 135+65=200
What is the vertex of the function x^2+x-5
Answer:
y=(x+1/2)^2-21/4
Step-by-step explanation:
Kevin can complete 45 multiplication problems in 2 minutes. What is the unit rate?
Answer: 22.5
Step-by-step explanation: 45/2
Answer:
0.04 4 is repeated
Step-by-step explanation:
If the prime factors of a number are all the prime numbers less than 10 and no factor is repeated, what is the number?
Answer:
210Step-by-step explanation:
Prime less than 10:
2, 3, 5, 7The number is:
2*3*5*7 = 210What expressions are equivalent to 3(4x+3)?
Answer: B, D, E
Step-by-step explanation: Its very easy to check, For B, you notice that it is the same, only the numbers are swapped. In multiplication, this is perfectly fine. For D, I just knew that the answer was 12x+9. And in D, there are 3 4x and 3 threes', so that one was correct. And for E, all you have to do is to multiply accordingly to the distributive property
Some algae contains up to 50% oil by weight. How much oil is in a 7.3-ounce sample of this type of algae?
Answer:
3.65
Step-by-step explanation:
this is the same as saying
50%of 7.3
which is 3.65
A total of 60 children signed up for hockey there were 3 boys for every 1 girl that signed up how many of the children who signed up for hockey where girls
45 boys and 15 girls
given f(x)=2x^2 and g(x)=4x-5, the composition f(g(x)) is equal to 32x^2-80 x+53 now find an expression for g(f(x))
Answer:
the answers you'd put in the box are 8 and 7.
when the drop down question pops up, the answer i commutative.
Step-by-step explanation:
i got it right lol
When Jeremiah looked at his cell phone bill for the month, he saw that he had spent 2/5 of his minutes talking to his mother and 1/5 of his minutes talking to his best friend. What fraction of the minutes did Jeremiah spend talking to either his mom or his best friend?
Answer:
that would be 3/5 minutes
Step-by-step explanation:
Describe what the graph of the sounds at a rock concert look like.
Answer:
The graph would be similar to a Sin or Cos graph with a vertical shift. As the music gets louder the graph will go up and as the music and crowd become quieter, the graph will go down. Going up and down until the end of the concert where it will be 0.
Step-by-step explanation:
This is because the concert music would be loud, causing the sound on the graph to have a steady line.
Hope this helped! :)
A rectangular patio is 9 yd 2 ft long and 5 yd 2 ft wide. What is the perimeter of the patio in yards?
Answer:
Step-by-step explanation:
perimeter = 2(length + width)
= 2(9 yd 2 ft + 5 yd 2 ft)
= 2(14 yd 4 ft)
= 28 yd 8 ft
I’m so confused may sb help please
Answer:
Line L has a slope of 1 and Line k has a slope of 2.
Step-by-step explanation: You can figure this out by using the rise (up) over run (left/right) method. Line l had 1/1 which equals 1 and line K was 2/1 which equals 2!
Answer: it is D
Step-by-step explanation:
line L hits a new point every 1 point. Line
K hits a new point at every 2 points.
what is (9+8)/(88+77)
Answer:
Exact form: 17/165
Decimal form: 0.103
Step-by-step explanation:
hope this helps :)
Answer:
0.1
Step-by-step explanation:
(9+8)/(88+77)
(17)/(165)
17/165
0.1030303030
0.10
The city park is 9 2/5 miles from Roland Elementary School. The city library is 3 3/10 miles from the same school. How much farther from the school is the park than the library?
Answer:
6 1/10
Step-by-step explanation:
just need to find out the difference in the distances
9 2/5 - 3 3/10 = 6 2/5 - 3/10 = 6 1/10
If you would like to venture further, you can check out my Instagram page (learntionary) where I post notes and mathematics tips. Thanks!
Just subtract 3_3/10 from 9_2/5.
Let 3_3/10 be 33/10.
Let 9_2/5 be 47/5.
47/3 - 33/10 =
LCD is 30.
30 ÷ 3 = 10.
10 x 47 = 470
30 ÷ 10 = 3
3 x 33 = 99
We now have (470 - 99)/30.
This becomes (371/30) miles.
You can express (371/30) miles as a mixed number answer if needed.
Factor 20w - 15.
please someone help!
Answer:
5( 4w -3)
Step-by-step explanation:
just pulled out a 5
Answer:
[tex]\huge\boxed{\sf 5(4w-3)}[/tex]
Step-by-step explanation:
[tex]\sf 20w-15\\\\Highest\ Common\ Factor= 5\\\\Take \ 5 \ common\\\\5(4w-3)\\\\This \ is \ the \ required\ factorized \ form\\\\\rule[225]{225}{2}[/tex]
Hope this helped!
~AnonymousHelper1807Jada completed four out of 10 assignments. What is the ratio of completed to end complete assignments in simplest form?
Answer:
48
Step-by-step explanation:
dddd
5x +7y =19, -5x - 3y = 11
Whats the best method to solve this equation?
- Elimination
- substitution
- these equations are unsolved
-
629 divided by the number c equals 17 what is c answer fast WILL MARK BRAINLY!!
Answer:
c=37
Step-by-step explanation:
The answer c is 37.
What is Division?Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number
Here is is given that,
629 divided by the number c equals 17.
Here 629 is the dividend, c is the divisor and 17 is the quotient.
We have to find the value of the divisor.
Mathematically the given statement can be written as,
629 / c = 17
Multiplying both sides of the equation with c, we get,
629 = 17 c
Dividing both sides by 17,
c = 629 / 17
c = 37
Hence the value of c is 37.
To learn more about Division, click on the link given below :
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Math:hey everyone I have a quick question, Ps the picture is there!
Answer:
3/8 < 7/16 < 11/20 < 5/6
Step-by-step explanation:
⚠️⚠️What should I change ? And why ? ⚠️⚠️
⚠️look at the photo for mor detailed instructions⚠️
DON’T TROLL and if you don’t know don’t answer
Answer/Step-by-step explanation:
Change the 3rd and 4th input. ALL the input values must be different even if they have the same output values in order to be a function. NONE of the input values should be the same, it just has to be something completely different for it to be correct. It may not be linear, but It will be correct.
If ∆ABC congruent ∆DEF, which of the following can you NOT conclude as being true?
A. AC congruent DF
B. ‹B congruent ‹E
C. AB congruent EF
D. ‹C congruent ‹F
Answer:
I believe the answer would be C (sorry i messed uo the first time)
Answer:
C
Step-by-step explanation:
Please help and give an explanation. I’m struggling
Answer:
y = 1/3x -4
Step-by-step explanation:
The y intercept is -4 as you can see in the graph. To find the slope look at the graph and find where it perfectly intercepts. It goes up one block and to the right three. So the slope is 1/3 . Since the line is going up to the top right it’s a positive slope.
When you flip a shape over the x-axis and then thy- axis is it the same as rotating 180 degrees counterclockwise?
Answer:
yes
Step-by-step explanation:
Dina invests £450 in a savings account with annual compound interest.
After five years, there is £534.46 in the account.
What interest rate has she been receiving?
Answer:
3.3%
Step-by-step explanation:
compound interest: A = Pe^(rt)
A = 534.46
P = 450
t = 5
534.46/450 = e^(5r)
e^(5r) = 1.18
lne^(5r) = ln 1.18
(5r)lne = ln1.18
ln1.18 = 5r
5r = 0.165
r = 0.033
or 3.3%
Work out the area of this trapezium.
15m
6m
10m
Answer:
105m²
Step-by-step explanation:
15+6=21
21÷2=10.5
10.5x10=105