of a line in point slope form

Answer:

f(-2) = 2

f(0) = 4

f(4) = -1

Step-by-step explanation:

Given the graph of a piecewise function:

[tex]\displaystyle\mathsf{f(x) = \left \{ {{x\:+\:4\quad if\:\:x\leq \:0} \atop {-\frac{1}{2}x\:+\:1\quad if\:\:x\: >\:0}} \right.}\\[/tex]

Side note:

I used the method of finding the linear equations in slope-intercept form to establish the piecewise function. First, I solved for the slope by choosing two points in each defined interval. Then, I plugged in the y-intercepts of each interval, for f(x) = x + 4: the y-intercept is (0, 4) where b = 4; for f(x) = -½x + 1, the y-intercept is (0, 1) where b = 1.

There are two methods for determining the range values of the given domain values.  

Method 1: The first method is using the graph to find the corresponding range values of the given domain {-2, 0, 4}.  

Method 2: Alternatively, we could use the rules provided by the piecewise function in evaluating the following domain values.  This post will use the second method (using the piecewise function) to evaluate the input values.

Regardless of the method used, the results will remain the same.

Since the input value is x = -2, then we must use the function, f(x) = x + 4:

f(x) = x + 4

f(-2) = -2 + 4

f(-2) = 2

Therefore, the range value given the domain, x = -2 is 2, or simply: f(-2) = 2.

Given the input value is x = 0, then we must also use the function, f(x) = x + 4:

f(x) = x + 4

f(0) = 0 + 4

f(0) = 4

Therefore, the range value given the domain, x = 0 is 4, or  f(0) = 4.

Since the input value is x = 4, then we must use the function, f(x) = -½x + 1:

f(x) = -½x + 1

f(4) = -½(4) + 1

f(4) = -2 + 1

f(4) = -1

Therefore, the range value given the domain, x = 4 is -1, or  f(4) = -1.

Step-by-step explanation:

3x-28=2x-9

3x-2x=28-9

x=19°

For angle FGH = 2x-9° = 38°-9° = 29°.

For angle HGI = 3x-28° = 57°-28° = 29°.

For angle FGI = 29°+29° = 58°.

hope this helps you.

Answer:

In order to write the equation of a circle, we need two things their centre as well as the radius. so….diameter always intersect each other at the centre of the circle, hence after solving the equation of diameter, we get the intersecting point(x, y)=(3,2). now, we have already given one point…and as per the question circle passing through that point itself. so by applying distance formula, we can obtain the value of radius. thus we get radius 2√2. now we have required things to get the equation of a circle. we know the standard equation of circle having centre =(x1,y1) and radius = r is (x-x1)²+(y-y1)²=r² hence we can find the equation of circle by putting the coordinate (x1,y1)=(3,2) and radius =2√2 in the above mentioned standard equation.

Step-by-step explanation:

:3

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

roots of the quadratic equation ~

discriminant ~

nature of roots ~

sum of the roots ~

product of the roots ~

[tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]

Let's solve he given quadratic equation using quadratic formula ~

Let's consider the following values ~

According to quadratic formula, the roots are ~

where, ( b² - 4ac ) is known as it's discriminant ~

that is equal to ~

Hence, Discriminant = 144

And since discriminant is positive, then the roots of the quadratic polynomial are real .

Let's find the roots now ~

So, the two roots are ~

and

Sum of roots ~

product of roots ~

Answer:

the answer is b

Step-by-step explanation:

Answer:

Percentage change should be 25%

Step-by-step explanation:

25 - 20

---------- x 100%

20

5

---- x 100% = 25% increase

20

25 percent increase

Answer:

Step-by-step explanation:

-5+3 + (-1/6)+ 5/6

-2 - 1/6 + 5/6

-2 + 4/6 (do this boring math)

Answer:

[tex]-1\frac{1}{3}[/tex] aka [tex]\frac{-4}{3}[/tex]

Step-by-step explanation:

-5+3+(-1/6)+ 5/6

Ok soo -5+3 is -2 So then

-2-[tex]\frac{1}{6}[/tex]+[tex]\frac{5}{6}[/tex]

-2+(-[tex]\frac{1}{6}[/tex]+[tex]\frac{5}{6}[/tex])

-[tex]\frac{1}{6}[/tex]+[tex]\frac{5}{6}[/tex]=[tex]\frac{4}{6}[/tex] or [tex]\frac{2}{3}[/tex]

-2+[tex]\frac{2}{3}[/tex]=-1[tex]\frac{1}{3}[/tex]

Answer:

Write a ratio.

70 : 5

x : 1

To solve for x, cross multiply.

70 : 5x

Divide both sides by 5.

14 = x

So, NoClue can rap 14 syllables per second.

:)

Answer:

Rational numbers can be depicted on the number line. The centre of the number line is called Origin (O). Positive rational numbers are illustrated on the right side of zero (called origin), and negative on left side of origin. The representation of rational numbers on the number line depends on the type of fraction.

Step-by-step explanation:

The numbers on the number line increase as one moves from left to right and decrease on moving from right to left. Here, fractions and decimals have been represented on the number line. A number line can also be used to represent both positive and negative integers as well.

ANSWER:

The ANSWER IS 2. if two solutions are allowed then 2. AND 3. and if your rounding, then 2. 3. and 4.

Step-by-step explanation:

For the first one it is: 0.27... or 3/11

For the second one it is: 6

For the third one it is: 1 or 6, meaning it has two solutions

For the fourth one it is: 6.285714, or 44/7

for the first one: 15-x=54x -> add x to both sides: 15=55x -> then divide both sides by 55: x=3/11

for the second one: 8+3x=6x-10 -> subtract 6x from both sides: 8-3x=-10 -> subtract 8 from both sides: -3x=-18 -> divide both sides by -3: x=6

I'm actually supposed to be doing school, so I don't have time to explain the last two, but I wanted to help, so please give 4 stars or brainliest. and thanks for waiting patiently.

The equation 8+3x=6x−10 has {6} as its solution set. Option B is correct.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

The equations that have {6} as its solution set is,

We have to solve the equation in order to find the value of x,

Equation 1,

15−x=54x

54x+x=15

55x=15

x=0.27

Equation 2,

8+3x=6x−10

6x-3x=-10+8

3x=18

x=6

Equation 3,

x²+2=7x−4

x²-7x+6=0

x²+6x+x+6=0

x(x+6)+1(x+6)=0

(x+1)=0 , x=-1

(x+6)=0, x=-6

Equation 4,

43−4x=3x−1

4x+3x=43+1

7x=44

x=44/7

x=6.285

Thus, the equation 8+3x=6x−10 has {6} as its solution set. Option B is correct.

Learn more about the equation here,

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Answer:

0.85

Step-by-step explanation:

total samples cases = 20

chances that are even or odd prime are 17 chances

2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20

probability = 17/20

= 0.85

Answer:

5 more treats

Step-by-step explanation:

The total number of treats if she gives each person 4 treats is

. 37 people * 4 treats = 148 treats

Subtract 143 (number of treats she has) from 148 (total number of treats to give out)

. 148 treats - 143 treats = 5 treats

143 treats

37 patients

how many treats will she need to make in order for each patient to receive 4 treats.

[tex]4 \times 37[/tex]

[tex] = 148[/tex]

[tex] = 148 - 143[/tex]

[tex] = 5[/tex]

therefore, she'll have to make 5 treats more in order for each patient to receive 4 treats

answer= option D

Answer:

D 22ilsjjssiksksksksksksks

Step-by-step explanation:

212

Answer:

105.6 km

Step-by-step explanation:

Use: King Henery Doesn't Usually drink chocolate milk

K in king stands for kelo

H in Henery stands for hecto

D in Doesn't stands for deka

U in Usually stands for Meters, Liters, and Grams

d in drink stands for Deci

c in chocolate stands for Centi

And m in milk stands for milli

Answer:

y2-y1 over x2-x1, typically the second or set of the higher numbers would be #2 so im taking 0,11 as #2

Step-by-step explanation:

7 i believe

Answer:

y2-y1/x2-x1

11-4/1-0

7/1

slope = 7

Answer:

12 and 16

Step-by-step explanation:

Turn it into algebra.

Make one of the pieces x. So x+4 is the piece that is 4 feet longer and x is the piece that it is 4 feet longer than.

So x+4+x=28, which is the total length, and if you simplify it, it makes 2x+4=28.

Then you just solve it, so do 28-4=24, and then divide that by 2, which gets 12.

Then you substitute 12 where x has been substituted for the pieces.

One piece is x feet, so that just stays 12, and another piece is x+4, so 12+4 which is 16.

To make sure it's correct, you can check it by doing 16-12=4 and add 12 and 16 together which gets the correct total of 28.

Answer:

A or C

Step-by-step explanation:

Answer:

the answer is 20% increase I used a calculator but you should be able to do that math by taking 40 dividing by five where that ends up being 8 that is 20 percent of 40 so adding that back to the original amount is a 20 percent increase hope this helps

Step-by-step explanation:

Step-by-step explanation:

2/3 cups white paint mix with 2 2/3 cups = 8/3 cups blue paint.

so, 2/3 / 8/3 = 2×3 / 3×8 = 6/24 = 1/4.

therefore, the mix ratio white/blue paint is 1/4 (1 part white, 4 parts blue).

so, for 3 cups of white paint we need 3×4 = 12 cups of blue paint.

Answer: 7.00x10^2

Step-by-step explanation:

Are you asking for the quotient of (1.155 x 10^5)/(1.65 x 10^2)?

If so, divide (1.155/1.65) = 0.7000.

Then subtract 2 (the bottom exponent from [tex]10^{2}[/tex]) from the top exponent:  [tex]10^{5}[/tex] becomes [tex]10^{3}[/tex].

Combine the two:  0.7000x10^3

Move the decimal point to the right by one:  7.00x10^2 (to 3 sig figs).

7 x 10² is the quotient of 1.155 x 10⁵ and 1.65 x 10² expressed in scientific

notation.

To find the quotient of these two numbers in scientific notation, you divide the two significant figures and then subtract the exponents of 10. The calculation would be as follows:

(1.155 x 10⁵) / (1.65 x 10²)

Dividing the significant figures:

1.155 / 1.65

= 0.7

Subtracting the exponents:

5 - 2 = 3

So, the quotient in scientific notation is approximately:

0.7 x 10³

Which can also be written as:

7 x 10²

Hence, the quotient of 1.155 x 10⁵ and 1.65 x 10² expressed in scientific

notation is 7 x 10².

To learn more on Number system click:

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Answer:

15

Step-by-step explanation:

speed is distance over time so its 30 devided by 2

We can't get the answer if there's no problem?

Answer:

it will take 3 hours For them to cover 60 miles and meet

Step-by-step explanation:

In pic

(Hope this helps can I pls have brainlist (crown)☺️)

Answer:

D) QR≅ST

The answer follows from basic AAS congruences

Answer:

line PQ≅line SU

Step-by-step explanation:

∆PQR       ∆UST

P corresponds to U

Q corresponds to S

R corresponds to T

line PQ to line US

line QR to line ST

line PR to line UT