Answers
Answer:
The function is f(x) = 2x + 3 for x ≥ - 2 and f(x) = - 2x - 5 for, x < - 2.
The vertex of the function is (-2,-1)
Domain of the function is (-∞, +∞)
Range of the function is [-1, +∞).
Step-by-step explanation:
The function has a graph in two parts.
The right side part passes through the points (-2,-1) and (0,3).
So, the equation of this part will be
[tex]\frac{y - 3}{3 - (- 1)} = \frac{x - 0}{0 - (- 2)}[/tex]
⇒ y - 3 = 2x
⇒ y = 2x + 3
Again, the left side part of the graph passes through the points (-2,-1) and (-4,3).
Therefore, the equation of this part will be
[tex]\frac{y - 3}{3 - (- 1)} = \frac{x - (- 4)}{- 4 - (- 2)}[/tex]
⇒ y - 3 = - 2(x + 4)
⇒ y - 3 = - 2x - 8
⇒ y = - 2x - 5
Therefore, the function is f(x) = 2x + 3 for x ≥ - 2 and f(x) = - 2x - 5 for, x < - 2. (Answer)
The vertex of the function is (-2,-1) (Answer)
Domain of the function is (-∞, +∞) (Answer)
Range of the function is [-1, +∞). (Answer)
Related Questions
9. Using the diagram below, if < 2 = 107*. find each missing angle:
M24 =
m26 =
mZ8 =
m25 =
m27 =
Answers
Answer:
24
Step-by-step explanation:
The daughter is 36 years younger than her mother. How many years ago was the mother 5 times the daughters age, if she is 50 years old now?
Answers
Answer:
The answer is 5 years ago.
Step-by-step explanation:
5 years ago the age of the mother was 5 times the daughter's age.
How to form an equation?
Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Suppose the current age of the daughter is D while the mother is M.
As per the given, The daughter is 36 years younger than her mother.
D = M - 36
And , M = 50
D = 50 - 36 = 14
Let's say x year age the mother was 5 times the daughter's age.
(M - x) = 5(D - x)
(50 - x) = 5(14 - x)
50 - x = 70 - 5x
-x + 5x = 70 - 50
4x = 20
x = 5
Hence "5 years ago the age of the mother was 5 times the daughter's age".
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cross product property
Answers
Using the cross product property on this proportion gives us the following equation:
20 (2x - 9) = 10 (9)
Use the distributive property and multiply
40x - 180 = 90
Add 180 to both sides
40x = 270
Divide 40 from both sides
x = 270/40
Simplify fraction
x = 27/4
This should be your answer. Let me know if you need any clarifications, thanks!
The cross product is a type of multiplication between vectors that results in a vector product. It has the distributive property and is anticommutative.
Explanation:The cross product is a type of multiplication between vectors that results in a vector product. It is denoted by the symbol A x B and is also known as the vector product.
The cross product has the distributive property, which allows us to distribute a vector across the sum of two other vectors. For example, A x (B + C) = (A x B) + (A x C).
The cross product is anticommutative, meaning that the order in which we multiply two vectors matters. A x B = -B x A.
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suppose your sat score is 2040 a college with an average sat score for admitted students of which of these would most likely be your best opinion
a. 1640
b. 2060
c. 1220
d. 1480
Answers
Answer:
1640.
Step-by-step explanation:
1640 would be your best option. As you are much higher than average. 2060 would not be a better option as you are below average in this case.
Answer:2060
Step-by-step explanation: your closest to 2060
Determine the sign of cos pi divided by seven
Answers
Answer:
As π/7 is in first quadrant and all trig functions are positive there,
so, cos pi/7 is positive.
Step-by-step explanation:
In 1st quadrant, all trigonometric functions are positive. Measure of Angle Ф is from 0 to π/2, and measure of reference angle is Ф.In 2nd quadrant, sinФ and cosecФ are positive. Measure of Angle Ф is from π/2 to π, and measure of reference angle is π - Ф.In 3rd quadrant, tanФ and cotФ are positive. Measure of Angle Ф is from π to 3π/2, and measure of reference angle is Ф - π.In 4th quadrant, cosФ and secФ are positive. Measure of Angle Ф is from 3π/2 to 2π, and measure of reference angle is 2π - Ф.Please check the attached figure a.
As π/7 is in first quadrant and all trig functions are positive there,
so, cos pi/7 is positive.
Keywords: trigonometric function, cos π
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I candy store sells 100 types of candy. Out of these 100 types, 2/5 contain chocolate. How many contain chocolate?
Answers
Answer:
Step-by-step explanation:
so 2/5 of 100 contain chocolate...
2/5 * 100 = 200/5 = 40 <== contain chocolate
How do you do this equation: 9|5x+8|=54
Answers
Answer (2 answers):
x = -2/5, x = -14/5
Step-by-step explanation:
First step is to try and get the absolute value by itself on one side and everything else that's not inside the absolute value on the other side.
9|5x+8|=54
|5x+8| = 54/9
|5x+8| = 6
Remember how absolute values turn everything positive? For example
|-4|=4, but |4|=4 as well. So we must do the same to our problem by splitting up the absolute equation into two parts.
|5x+8| = 6 and |-(5x+8)| = 6
now solve the first equation.
(Just remove the absolute value sign and solve it normally)
5x+8 = 6
5x = -2
x = -2/5
Now solve the other equation
-(5x+8) = 6
-5x - 8 = 6
-5x = 14
x = -14/5
A 3 cm by 3 cm rectangle sits inside a circle with radius of 4 cm
Answers
Answer:
41.24 cm²
Step-by-step explanation:
Here is the complete question: A 3 cm by 3 cm rectangle sits inside a circle with radius of 4 cm. What is the area of the shaded region?
Given: measurement of rectangle is [tex]3\ cm\times 3\ cm[/tex]
Radius of circle is 4 cm.
We can find the area of shaded region by subtracting area of rectangle from area of circle.
First, lets find the area of rectangle
Formula; Area of rectangle= [tex]length\times width[/tex]
Area of rectangle= [tex]3\ cm\times 3\ cm= 9\ cm^{2}[/tex]
∴ Area of rectangle= 9 cm²
Now, finding the area of circle.
Formula: Area of circle= [tex]\pi r^{2}[/tex] (∵ r is radius)
Area of circle= [tex]3.14\times 4^{2} = 3.14\times 16[/tex]
∴ Area of circle= 50.24 cm²
Next solving to find area of shaded region.
Area of shared region= [tex]\textrm{Area of the circle} - \textrm{Area of the rectangle}[/tex]
Area of shaded region= [tex]50.24\ cm^{2} - 9\ cm^{2} = 41.24\ cm^{2}[/tex]
∴ Area of shaded region= 41.24 cm²
1. 112 in 8 hours
2.150 miles in 6 gallons
Answers
Answer:
first step divide 112 by 8 which is going to give you 14 per hours. second step 150 by 6 is going to give you 25 per hours
I'm assuming that you want to find the unit rate of both scenarios.
I'm going to assume that you meant 112 miles in 8 hours.
Divide to find the unit rate: 112 / 8 = 14 miles per hour.
150 miles in 6 gallons
Divide to find the unit rate: 150 / 6 = 25 miles per gallon.
Best of Luck!
8➗2(2+2)????????????
Answers
Answer:
16
Step-by-step explanation:
So according to PEMDAS we need to do the work in the parentheses first. 2 plus 2 is 4 so we will put 4 in the parentheses to replace 2 plus 2. Now we will divide 8 by 2 which is 4. since 4 is right next to the parentheses, we need to multiply the 4 by the 4 in the parentheses. 4 times 4 is 16.
To describe a specific arithmetic sequence, Elijah wrote the recursive formula:
Write a linear equation that models this sequence using the sketchpad below.
Answers
Answer:
[tex]t_{n} = 30 + 7n[/tex], where, n = 0, 1, 2, 3, 4, .........
Step-by-step explanation:
Given the arithmetic sequence in recursive formula.
f(0) = 30 and f(n + 1) = f(n) + 7 ......... (1)
Therefore, putting n = 0 in equation (1) we get f(1) = f(0) + 7 = 30 + 7 = 37 {Since, f(0) is given to be 30}
Again, putting n = 1 in equation (1) we get f(2) = f(1) + 7 = 37 + 7 = 44
And, putting n = 2 in equation (1) we get f(3) = f(2) + 7 = 44 + 7 = 51
and so on.
Therefore, the arithmetic sequence is 30, 37, 44, 51, .......
Therefore, the linear equation of this sequence is given by [tex]t_{n} = 30 + 7n[/tex], where, n = 0, 1, 2, 3, 4, .........
(Answer)
Two points are located at (2,3) and (8,-5) complete the equations below to show how you can use the pythagorean theorem to find the distance between these two points
Answers
Answer:
3
Step-by-step explanation:
please help !!!!!!!!
Answers
Answer:
x = 65
Step-by-step explanation:
The triangle has 2 congruent sides and is therefore isosceles.
The base angles are congruent, both 25°
Subtract the sum of the base angles from 180° for vertex angle
vertex angle = 180° - (25 + 25)° = 180° - 50° = 130°
Hence x = 130° ÷ 2 = 65
The ratio of girls to boys at a movie is 3:8. If there are 32 boys, how many girls are at the movie
Answers
Answer: 12 girls
Step-by-step explanation: Our first step in this problem is to write down the unit ratio that is involved. In this case, it's girls/boys.
Next, we set up our proportion. We know that at a movie there are 3 girls for every 8 boys so we have 3/8 and we are asked how many girls are at the movie if 32 boys are the movie so that's x/32.
Now we have the proportion 3/8 = x/32.
Notice that the 32 boys must go on the bottom of the second ratio because our unit ratio tells us that we put girls/boys.
Solving from here, we use the means-extremes property to get 3 times 32 to get 96 = 8 times x or 8x. So we have 96 = 8x.
Dividing both sides by 8, we find that 12 = x.
This means that 12 girls are at the movie when 32 boys are at the movie.
20 points and I will mark you as brainliest
Answers
Answer:
Rock phosphate, insoluble phosphates in bone deposits, and dissolved phosphates available to plants
Lana is trying to find an equation for a line that passes through (5, 2) and is parallel to 3x + 2y = 15. Explain the steps that Lana could take to determine the equation. A) Write 3x + 2y = 15 in slope-intercept form. Then, substitute the slope of that line and the point (5, 2) into the point-slope formula. B) Write 3x + 2y = 15 in slope-intercept form. Then, substitute the reciprocal of the slope of that line and the point (5, 2) into the point-slope formula. C) Write 3x + 2y = 15 in slope-intercept form. Then, substitute the opposite reciprocal of the slope of that line and the point (5, 2) into the point-slope formula. D) Write 3x + 2y = 15 in slope-intercept form. Then, substitute the opposite reciprocal of the slope of that line and the point (0, 0) into the point-slope formula.
Answers
Answer:
A
Step-by-step explanation:
3x+2y=15
-3x
2y=15-3x
divide by 2
y=-3/2x+7.5
Parallel Line = Same Slope
y=-3/2x+b
substitute (5,2)
2=-3/2(5)+b
2=-7.5+b
+7.5
9.5=b
Final Equation: y=-3/2x+9.5
Lana needs to first convert the equation to slope-intercept form, and then use the parallel line's slope with the provided point in the point-slope formula to find her line's equation.
Explanation:The correct option for Lana to find an equation for a line that passes through the point (5, 2) and is parallel to the given equation 3x + 2y = 15, is option A.
First, Lana needs to write the given equation in slope-intercept form which is y = mx + b, where m is the slope and b is the y-intercept. To do this, she needs to rearrange the equation by subtracting 3x from both sides and dividing by 2, which gives y = -1.5x + 7.5.
Parallel lines have the same slope, so the slope, m, of Lana's line is -1.5. Now, she uses the point-slope form of a linear equation which is y - y1 = m(x - x1), where (x1, y1) is the point the line passes through. Substituting the point (5, 2) and slope -1.5 into this equation, Lana gets y - 2 = -1.5x + 7.5.
She rearranges this to get her final equation.
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Evaluate 18 - (2 + 6h), if h= 2
Answers
Good morning,
Answer:
if h= 2 ⇒ 18 - (2 + 6h) = 4.
Step-by-step explanation:
if h= 2 Then 18 - (2 + 6h) = 18 -(2+6×2) = 18 - 14 = 4.
:)
96
97
98
99 100
This number line
shows the numbers
between
95 and 101
85 and 96
O97 and 102
Answers
Answer:
This number line
shows the numbers
between 95 and 101.
Step-by-step explanation:
96, 97, 98, 99, and 100 all fall between 95 and 101.
97, 98, 99, and 100 are all greater than 96, so option 2 is incorrect.
96 is less than 97, so option 3 is incorrect.
Sybil grows and sells watermelons. The function C = 4n + 15 represents her cost, in
dollars, for producing n watermelons. Her revenue, or the amount she receives for
selling n watermelons, can be represented by the function R = 6n. Which function
represents Sybil's profit, P, for selling n watermelons?
Answers
Sybil's profit for selling n watermelons is represented by the function P = 2n - 15, which is the result of subtracting her cost function from her revenue function.
Explanation:The function that represents Sybil's profit, P, for selling n watermelons is found by calculating the difference between her revenue and her costs. The profit function, therefore, is the revenue function R = 6n minus the cost function C = 4n + 15. Executing the subtraction, we get:
P = R - C
P = 6n - (4n + 15)
P = 6n - 4n - 15
P = 2n - 15
This function represents the profit made on selling n watermelons.
Final answer:
The function representing Sybil's profit for selling n watermelons is P = 2n - 15.
Explanation:
Profit can be calculated by subtracting the total cost from the total revenue. In this case, the total revenue function is R = 6n and the total cost function is C = 4n + 15. To find the profit function, we subtract the total cost function from the total revenue function:
P = R - C
P = 6n - (4n + 15)
P = 2n - 15
Therefore, the function representing Sybil's profit for selling n watermelons is P = 2n - 15.
In the 6,492.709 which number is in the 10th place?
Answers
I believe that the answer is 7 because it is in the tens place.
Sorry misunderstood the Question the other user is correct
originally had a 2
Answer:
7 because it is in the 0.1 (1/10 or tenth) place of the number
Can anyone answer this? I will give brainliest to whoever answers the fastest and correctly!
Answers
Answer:
-1
Step-by-step explanation:
The answer is minus one. The third quadrant only has all negative numbers therefore the answer is -1. All the other answers in the selection is positive.
Answer:
A. -1
Step-by-step explanation:
In the third quadrant, the x-coordinate and the y-coordinate are negative.
The x-coordinate must be a negative number.
Answer: A. -1
2/2 - 1/4 show answer subtracting fractions
Answers
Answer:
3/4
Step-by-step explanation:
2/2=1
1-1/4=4/4-1/4=3/4
Answer:
3/4
Step-by-step explanation:
1. Cancel 2.
1 - 1/4.
2. Get the same dominators.
1 X 1/4 X 4/4
3. Simplify.
4/4 - 1/4.
4-1/4
3/4
Every year Aiden uses income from his job to pay for 75% of his college tuition. Next year’s tuition will be $720 more than this year’s, and Aiden will pay $2400. How much is this year’s tuition?
Answers
Answer:
$2,480
Step-by-step explanation:
Let $x be next year tuition. Aiden will pay $2,400, that is 75% of $x.
$x - 100%
$2,400 - 75%
Write a proportion:
[tex]\dfrac{x}{2,400}=\dfrac{100}{75}\\ \\75x=2,400\cdot 100\\ \\75x=240,000\\ \\x=3,200[/tex]
Next year’s tuition will be $720 more than this year’s, then this year tuition is
[tex]\$3,200-\$720=\$2,480[/tex]
Factorization of 45r+63s+63
Answers
Answer:
9(5r+7s+7)
Step-by-step explanation:
Answer:
9(5r+7s+7)
Step-by-step explanation:
Rewrite 63 as 7*9
Rewrite 63 as 7*9
Rewrite 45 as 5*9
=5 * 9r+ 7 * 9s + 7 * 9
Factor out common term: 9
= 9(5r+7s+7)
EXTRA POINTS IF ANSWERED FAST: Kevin recorded the distances he ran last week. The total number of miles he ran on Monday through Wednesday is the same as the total number of miles he ran on Thursday and Friday. How many miles did Kevin run on Wednesday? PLZZZZ ANSSWWWEEERRR
Answers
Answer:
[tex]5\frac{2}{3}[/tex] miles.
Step-by-step explanation:
Kevin recorded the distances he ran last week in the table attached to this question.
Now, the total number of miles he ran on Monday through Wednesday is the same as the total number of miles he ran on Thursday and Friday.
Hence, {x + (x + 9) + (x + 4)} = {2x + (4x - 2)}
⇒ 3x + 13 = 6x - 2
⇒ 9x = 15
⇒ [tex]x = \frac{15}{9} = \frac{5}{3}[/tex]
Therefore, he ran on Wednesday = x + 4 = [tex]\frac{5}{3} + 4 = \frac{17}{3} = 5\frac{2}{3}[/tex] miles. (Answer)
Answer: 9 miles
Step-by-step explanation:
x + x + 9 + x +4 = 2x + 4x-2
Collecting like terms
x + x + x +9 + 4 = 2x + 4x -2
Collect like terms
3x +13 = 6x -2
3x - 6x = -2 -13
-3x = -15
Divide both side by -3
x = 5
Therefore ; total number he ran on Wednesday
x + 4
If x = 5
Therefore total number he ran on Wednesday = 5+4
= 9
which is a slope intercept form of an equation for the line containing (0,5) slope -3
Answers
Answer:
y=-3x+5
Step-by-step explanation:
y-y1=m(x-x1)
y-5=-3(x-0)
y-5=-3(x)
y-5=-3x
y=-3x+5
A company's stock was selling at
$16 a share. A month later, it was
selling at $20 a share. What is
the percent increase?
[?]%
Answers
old: $16
new: $20
percent increase
-> formula: (new-old / old) x 100
(20-16 / 16) x 100
4/16 x 100
0.25 x 100
answer: 25% increase
According to the question,
Old selling price,
$16New selling price,
$20We know the formula,
→ [tex]Percent \ increase = \frac{New \ selling \ price- Old \ selling \ price}{Old \ selling \ price}\times 100[/tex]
By putting the values,
[tex]= \frac{20-16}{16}\times 100[/tex]
[tex]= \frac{4}{16}\times 100[/tex]
[tex]= 0.25\times 100[/tex]
[tex]= 25[/tex] (%)
Thus the above approach is appropriate.
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Take a factor out of the square root: 4sqrt450
Put a positive factor back into the square root:-5sqrt0.6
please help
Answers
Answer:
4[tex]\sqrt{450}[/tex] = 4[tex]\sqrt{25 * 18}[/tex]
= 4 × 5 [tex]\sqrt{18}[/tex]
= 20 [tex]\sqrt{18}[/tex]
= 20 [tex]\sqrt{9 * 2}[/tex]
= 20 × 3 [tex]\sqrt{2}[/tex]
= 60 [tex]\sqrt{2}[/tex]
-5 [tex]\sqrt{0.6}[/tex] = -5 [tex]\sqrt{0.6}[/tex]
= - [tex]\sqrt{25 * 0.6}[/tex]
= - [tex]\sqrt{25 * \frac{3}{5}[/tex]
= - [tex]\sqrt{15}[/tex]
Steps Explanation:
simplify 450 to 25 * 18now we can take the square root of 25 to give 5, which is factored out.follow this step to the end till it is completely simplifiedFor the second part, factor in 5 by squaring it to give 25 and simplify to the endWill give brainliest! 20 Points!
Hi! Some help with these problems would be great thank you!
Answers
Answer:
Question 1:
Draw a line that crosses the largest number of dots. Then use the line to check the best prediction of the number of baseballs that will be used if 275 pitches are thrown.
Question 2:
A). y = 1.2x - 6
Question 3:
J). y = [tex]\frac{9}{4}x - 81[/tex]
Question 4:
F). f(n) = -3n + 24 *Although it doesn't work when f(n) = 6 and n = 6*
Step-by-step explanation:
Question 2:
The line passes throught point (5, 0) and is parallel to the line whose equation is y = 1.2x + 3.8
For parallel lines, their values of slope is the same.
So our line, that passes through point (5, 0), also has a slope of 1.2
Taking another point (x, y) on our line;
Slope = change in y ÷ change in x
1.2 = [tex]\frac{y - 0}{x - 5}[/tex]
y = 1.2x - 1.2(5)
y = 1.2x - 6
Question 3:
The line passes x-axis at point (36, 0)
The line is perpendicular to another line whose equation is y = -[tex]\frac{4}{9}x[/tex] + 5
For perpendicular lines, the product of their slopes = -1
Let's say the slope of our unknown line is a ;
Given: The slope of our second line is -4/9
So,
a × -4/9 = -1
a = -1 × -9/4 = 9/4
Taking another point (x, y) on our unknown line;
Slope = change in y ÷ change in x
9/4 = [tex]\frac{y - 0}{x - 36}[/tex]
Cross-multiplying that you get;
y = [tex]\frac{9}{4}x - 81[/tex]
Question 4:
The function that model that situation is f(n) = -3n + 24 though it doesn't work when f(n) = 6 and n = 6
mathematics help plz
Answers
Answer: 4, 6,7,10
Step-by-step explanation: since X is greater than 3, then X can assume all numbers great than 3.
Answer:
4, 6, 7, 10Step-by-step explanation:
x > 3 - we read: all numbers greater than number 3
Therefore:
#1: NOT, because -1 < 3 and -2 < 3
#2: NOT, because all numbers are less than 3
#3: NOT, because 3 is not greater than 3
#4: YES, because all numbers are greater than 3.