Answer:
[tex]\boxed {\boxed {\sf y-5= 2(x+2)}}[/tex]
Step-by-step explanation:
We are asked to find the equation of a line in point-slope form.
As the name of the form describes, we need both a point and the slope. We are given a point, but we have to find the slope.
1. SlopeThe line is parallel to the line with the equation of 4x-2y= -5. Parallel lines have the same slope, so once we find the slope of the line with the given equation, we have the slope of the other line whose equation we are finding.
[tex]4x-2y= -5[/tex]
We can find the slope by putting the equation into slope-intercept form, or y=mx+b (where m is the slope and b is the y-intercept). We must isolate the variable y. 4x is being added to -2y. The inverse of addition is subtraction, so subtract 4x from both sides.
[tex]4x-4x-2y= -5-4x[/tex]
[tex]-2y= -5-4x[/tex]
y is being multiplied by -2. The inverse of multiplication is division, so divide both sides by -2.
[tex]-2y/-2=(-5-4x)/-2\\ y= \frac{-5}{-2} + \frac{-4x}{-2} \\ y= \frac{5}{2}+2x[/tex]
The coefficient of x is the slope, so the slope of the line is 2. Any line that is parallel also has a slope of 2.
2. Point- Slope EquationNow we have a point and a slope, so we can use the point-slope formula:
[tex]y-y_1=m(x-x_1)[/tex]
Where m is the slope and (x₁, y₁) is the point.
We know the slope is 2 and the point is (-2,5).
m=2 x₁ = -2 y₁= 5[tex]y-5=2(x- -2 ) \\\bold {y-5= 2(x+2)}[/tex]
The equation of the line in point-slope form is y-5= 2(x+2)
Can someone help me with this math homework please!
Answer: f(t) = 1.5t + 5
invested $8200 at the rate of 4.5% p.a. It earned $738 simple interest. The
period of investment was
Answer:
2 yrs
Step-by-step explanation:
SI =PTR/100
738=8200 x T x 4.5 /100
738 x 100 / 8200 x 4.5 = T
T =2
Evaluate 0.0096 * 4.2 over 0.6 * 0.48 leaving the answer in standard form
the answer for the question is 14*10raise the power -6
4|x+3|<8 i need help asap
Answer:
-5 <x<-1
Step-by-step explanation:
4|x+3|<8
Divide by 4
4|x+3| /4<8/4
|x+3|<2
There are two solutions one positive and one negative, remember to flip the inequality for the negative
x+3 <2 and x+3 >-2
Subtract 3 from each side
x+3-3 <2-3 and x+3-3 >-2-3
x<-1 and x>-5
-5 <x<-1
(x² - 3x)√(2x² - 3x - 2)≥0
Answer:
(-infinity, -1/2] and [3, infinity] Let e know if anything didn't make sense.
Step-by-step explanation:
A good way to think about it is a graph is either at 0, greater than 0 or less than 0. If you can find all of the zeroes then you can test each zero by checking points before and after. the graph will either cross and change signs, or stay the same.
So we want to find the zeroes.
Much like the factored form of a quadratic (x - a)(x - b) this inequality has two expressions being multiplied together, so if you can find when they are 0 you will have all the zeros. We shoudl also check when they do not exist just to be safe.
(x^2 - 3x) itself is a quadratic. so lets find its zeroes.
x^2 - 3x
x(x - 3)
So the zeroes are 0 and 3. lets find the zeroes of the other expression before checking signs.
sqrt(2x^2-3x-2) will be at 0 when the quadratic inside is at 0, and will not exist if the quadrati is negative, so let's look for both. first the 0s. I am going to complete the square
2x^2 - 3x - 2 = 0
2(x^2 - (3/2)x - 1) = 0
2[(x - 3/4)^2 - 25/16] = 0
2(x - 3/4)^2 - 25/8 = 0
2(x - 3/4)^2 = 25/8
(x - 3/4)^2 = 25/16
x - 3/4 = +/- 5/4
x = +/-5/4 + 3/4
x = -2/4 or 8/4
x = -1/2 or 2
Let me know if you couldn't follow that. Anyway, using those zeroes we can tell 2x^2 - 3x - 2 is negative between the two zeroes, since it is a parabola that opens upwards and crosses the x axis at those zeroes. this means sqrt(2x^2 - 3x - 2) does not exist from x=-1/2 and x=2. This means for the other zero above at x=0, the iequality will not exist. So now we have 3 points to look at.
-1/2 for its first 0 and where it then stops existing up to 2, which is also a 0. Finally 3 is the last 0.
at x=-1/2 all values before it are positive
x=2 has values immediately after it negative
x=3 then it switches so all values after that are positive since it is the last 0
Now we know that (x^2 - 3x) * sqrt(2x^2 - 3x - 2)is positive or equal to 0 along the intervals, (-infinity, -1/2] and [3, infinity]
Which equation is the inverse of y = 2x2 – 8?
y = plus-or-minus StartRoot StartFraction x + 8 Over 2 EndFraction EndRoot
y = StartFraction plus-or-minus StartRoot x + 8 EndRoot Over 2 EndFraction
y = plus-or-minus StartRoot StartFraction x Over 2 EndFraction + 8 EndRoot
y = StartFraction plus-or-minus StartRoot x EndRoot Over 2 EndFraction + 4
Answer:
y = (√x/2) ± 2
Step-by-step explanation:
Here, we want to get the inverse of the given function
y = 2x^2 - 8
make x the subject of the formula
y + 8 = 2x^2
Divide through by 2
y/2 + 4 = x^2
x = √y/2 ± 2
Now switch place for x and y
y = (√x/2) ± 2
Answer:
d
Step-by-step explanation:
Find BD , given that line AB is the angle bisector of < CAD
Answer:
23
Step-by-step explanation:
The answer is 23 by the definition of angle bisector.
What is the solution to this equation 1/2n^2+18=0
Answer:
n = ±6 .
Step-by-step explanation:
A quadratic equation is given to us and we need to find out the solution of the given equation . The given equation is ,
[tex]\rm\implies -\dfrac{1}{2}n^2+18=0 [/tex]
Subtracting 18 both sides ,
[tex]\rm\implies -\dfrac{1}{2}n^2 = -18 [/tex]
Multiplying both sides by -2 ,
[tex]\rm\implies -2\times\dfrac{1}{2}n^2 = -2\times -18 [/tex]
On simplyfing , we get ,
[tex]\rm\implies n^2= 36 [/tex]
Putting squareroot both sides ,
[tex]\rm\implies n= \sqrt{36} [/tex]
This equals to ,
[tex]\rm\implies \boxed{\quad\blue{\rm n =\pm 6 }} [/tex]
Hence the value of n is ±6 .
$4.20 × $ 5.00=
A. $12.50
B. $21.00
C. $21
Answer:
C. $21 (as well as B)
Step-by-step explanation:
→ $4.20 × $ 5.00 = ?
→ 4.20 × 5.00
→ 4.2 × 5.0
→ 21 {final answer}
Hence, option (C) is answer.
Use an algebraic equation to find the measures of the two angles described below. Begin by letting x represent the degree measure of the angle's complement.
The measure of the angle is 64 degrees greater than its complement.
What is the measure of the complement?
Answer:
13 degrees
Step-by-step explanation:
Let x be the degree measure of the angle's complement
Then we have the other angle is x + 64
Because the 2 angles complement each other so the sum of the 2 angles is 90
So we have the equation: 2x + 64 = 90
<=> 2x = 26
<=> x = 13
Which proportion would you use to find what percent 6 is of 40?
Answer:
6/100 = x/40
Step-by-step explanation:
6% is represented by 6/100, x is the variable in the proportion, and 40 is the whole you are finding the percentage of
One year josh had the lowest ERA (earned-run average, mean number of runs yielded per nine innings pitched) of any male pitcher at his school, with an ERA of 2.89. Also,alice had the lowest ERA of any female pitcher at the school with an ERA of 3.31 . For the males, the mean ERA was 5.083 and the standard deviation was 0.672. For the females, the mean ERA was 4.032 and the standard deviation was 0.649. Find their respective z-scores. Which player had the better year relative to their peers, josh or alice ? (Note: In general, the lower the ERA, the better the pitcher.)
Answer:
Josh's ERA had a z-score of -3.26.
Alice's ERA had a z-score of -1.11.
Due to the lower z-score(ERA is a stat that the lower the better), Josh had a better year relative to his peers.
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Josh:
ERA of 2.89, mean of 5.083, standard deviation of 0.672. So
[tex]X = 2.89, \mu = 5.083, \sigma = 0.672[/tex], and the z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.89 - 5.083}{0.672}[/tex]
[tex]Z = -3.26[/tex]
Josh's ERA had a z-score of -3.26.
Alice:
ERA of 3.31, mean of 4.032, standard deviation of 0.649. So
[tex]X = 3.31, \mu = 4.032, \sigma = 0.649[/tex], and the z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3.31 - 4.032}{0.649}[/tex]
[tex]Z = -1.11[/tex]
Alice's ERA had a z-score of -1.11.
Which player had the better year relative to their peers, josh or alice ?
Due to the lower z-score(ERA is a stat that the lower the better), Josh had a better year relative to his peers.
If the area of a rectangle is x^2 + 10x + 21 and the
width is x + 7, then what is the perimeter?
a) 4x + 20
b) 2x + 14
c) 2x + 10
4x+20
OPTION A is the correct answer.
angelA and angelB are complementary angles. If m angel = ( x-23)° and m angel B = (2x + 29°) then find the measure of angle B.
Answer:
The measure of angle B is 29°.
translate into an algebraic expression: “a increased by b%”
Given:
The given statement is: [tex]a[/tex] increased by [tex]b\%[/tex].
To find:
The algebraic expression for the given statement.
Solution:
We know that "+" sign is used when a value increased.
It is given that [tex]a[/tex] increased by [tex]b\%[/tex]. So, it can be written as:
[tex]a[/tex] increased by [tex]b\%[/tex][tex]=a+b\%\text{ of }a[/tex]
[tex]=a+\dfrac{b}{100}\times a[/tex]
[tex]=a+\dfrac{ab}{100}[/tex]
Therefore, the required algebraic expression is [tex]a+\dfrac{ab}{100}[/tex].
Triangle ABC is shown below.
What is the length of line segment AC?
А
ОООО
2х
3х – 7
14
18
В
4х – 10
С
Answer:
hey mate i don't think your question is complete anyways here is what i found and i hope it is useful .
Step-by-step explanation:
(if the below is the diagram then this might help.)
In the given triangle ABC shown in the figure ∠ABC = ∠ACB
Since angles are equal so opposite sides of equal angles will be equal.
Now mAB = mAC
By putting values in terms of x
2x = 3x - 7
x = 7
Now mAC = 3x - 7
By putting value of x = 7
mAC = 3×7 - 7 = 21 - 7 = 14
Therefore length of line segment AC is 14 units.
I hope this helps !!!!!!!!!!!!!!!!!!!
Can someone help me with this math homework please!
Answer:
3.5
Step-by-step explanation:
From the graph,
x1 = 0
x2 = 4
y1 = 0
y2 = 14
Formula : -
Slope = ( y2 - y1 ) / ( x2 - x1 )
Slope
= ( 14 - 0 ) / ( 4 - 0 )
= 14 / 4
= 7 / 2
= 3.5
Answer:
7/2
Step-by-step explanation:
the slope of a line is the ratio of y/x.
it describes how many units y changes, when x changes a defined number of units.
an increase is indicated by "+", and a decrease by "-".
the point with full integer/natural numbers as coordinates is (4, 14).
that means that when coming from point 0 (0, 0) x increases by 4 units, and y increases by 14 units.
so, the slope of line is 14/4 = 7/2
help me with this please
Answer:
q.4 's answer is d. miles
q.5 's answer is 3
q.6 's answer is 6
can you tell what the dot means i can tell you the other two's too
If a person is randomly selected, find the probability that his or her birthday is NOT in May. Ignore leap years.
Answer:
1/334
Step-by-step explanation:
There are 31 days in May, subtract that from 365 days and you get 334, and there is an equal chance that she is born in any one of those 334 days, thus 1/334.
Pls give step by step explanation
Answer:
6. A 5c + 3e + 2
7. A w = P/2 - 125
8. D point S
Step-by-step explanation:
6.
3 triangles + 5 hexagons + 2 squares =
= 3e + 5c + 2(1)
= 5c + 3e + 2
7.
perimeter = P
length = 250 m
width = w
P = 2L + 2W
P = 2(250) + 2w
2w = P - 500
w = (1/2)(P - 500)
w = (P - 500)/2
w = P/2 - 250
Incorrect expression: w = P/2 - 125
8.
X = 5
Y = -25
X - Y = 5 - (-25) = 5 + 25 = 30
S = 30
Which one is it please help meee
the first option would be the answer
[tex]\boxed{3x - 7=3x-2}[/tex]
Solve for 'x'. Thank you.
Hi there!
»»————- ★ ————-««
I believe your answer is:
There are no solutions to the equation.
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Solving for 'x':}}\\\\3x-7=3x-2\\-----------\\\rightarrow 3x - 7 + 7 = 3x - 2 + 7\\\\\rightarrow 3x = 3x + 5\\\\\rightarrow 3x - 3x = 3x - 3x + 5\\\\\rightarrow \boxed{0 = 5}\\\\-----------\\\text{The answer boxed is a \textbf{contradiction. }}\text{Therefore, there is no solution.}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
3x-7=3x-23x-3x=-2+70=5it has no solution
please help me solve
5w^2(2w+4w^7)
Answer:
10w^3+20w^9
Step-by-step explanation:
5w^2(2w+4w^7)
distribute
5w^2 * 2w + 5w^2 (4w^7)
10w^3+20w^9
Answer:
10w^3+20w^9
Step-by-step explanation:
25. The Jones family is designing their new garage and workshop. The workshop will be a
smaller square attached to the larger square garage. The sides of the garage are 4 times as
long as the sides of the workshop, and the sum of the areas of the two squares is 612 square
feet. How long are the sides of the workshop and the garage?
Answer:
Step-by-step explanation:
each side of workshop = x
area of workshop = x²
each side of garage = 4x
area of garage = (4x)² = 16x²
total area = x² + 16x² = 17x²
17x² = 612
x² = 36
x = √36 = 6 ft
each side of workshop = 6ft
each side of garage = 24ft
Can someone help me please hurry
Using the data in the table, which statement is true?
Answer: Choice C. mean > median
================================================
Explanation:
Multiply each measure with their corresponding frequency.
8*1 = 810*3 = 3014*2 = 28Add up those products: 8+30+28 = 66
Then divide by the total frequency n = 1+3+2 = 6 to get 66/6 = 11 as the mean.
mean = 11
----------------
Since we have n = 6 values in this list, this means the median is between slot n/2 = 6/2 = 3 and slot 4.
Note how that places us in the middle row because 1+3 = 4 encapsulates both of those slots mentioned. So the median is 10.
Or you could list out the values in roster notation {8, 10, 10, 10, 14, 14} to see that {10,10} occupy the middle most slots. So the median is (10+10)/2 = 20/2 = 10.
median = 10
-----------------
The mode is simply the most frequent value. The table shows that mode = 10 since it occurs 3 times, compared to 8 showing up 1 time and 14 showing up twice.
-----------------
We have the following summary
mean = 11median = 10mode = 10With that in mind, let's go through the answer choices.
We can see that mean < mode is false, since it should be mean > median, so cross choice A off the list.mean = median is also false, so choice B is crossed off as well.mean > median is true since 11 > 10 is true. Choice C is the answer. Note how this being true directly contradicts choice B, which is another reason to see why choice B is false.median > mode is false because 10 > 10 is false. It should be median = mode. Choice D is crossed off the list.What is the solution to -4(8-3x)>6x-8?
O x > -4/3
O x < -4/3
O x > 4
O x < 4
Answer:
x [tex]\geq[/tex] 4
Step-by-step explanation:
-4(8-3x)[tex]\geq[/tex]6x-8 multiply inside the parenthesis with -4
12x - 32 [tex]\geq[/tex] 6x - 8 export like terms to the same side of the inequality
12x - 6x [tex]\geq[/tex] 32 - 8
6x [tex]\geq[/tex] 24 divide both sides by 6
x [tex]\geq[/tex] 4
What is the solution to -4(8 - 3x) ≥ 6x - 8 ?
Solution :Assume this ≥ sign as = sign
- 4(8 - 3x) ≥ 6x - 8By simplifying the left hand side we get
- 32 + 12x ≥ 6x - 8Transposing them to the other side
12x - 6x ≥ 32 - 8 6x ≥ 24 x ≥ 24/6 x ≥ 4Hence, the correct answer is the third option i.e. x ≥ 4
x^2(y-z)+y^2(z-x)+z^2(x-y)
Jika 2x-3/x=5, maka nilai dari 4x^2 - 9/x^2 adalah
Answer:
=2x-3 / x=5
=2(5)-3
=10-3
=7
What is the equation of the line shown in the graph?
Drag and drop the expressions to write the equation of the line in slope-intercept form.
X, 2x, -X, -2x, 1, -1, -2 -4
Y=( )+( )
Answer:
y = -x -2
Step-by-step explanation:
-1 is the slope
-2 is the y-intercept
slope = [tex]\frac{-4-1}{2-(-3)}[/tex] = [tex]\frac{-5}{5}[/tex] = [tex]\frac{-1}{1}[/tex] = -1
