For the function f(x) = −2(x + 3)2 − 1, identify the vertex, domain, and range.
Answers
Answer:
Vertex: (-3, -1)
Domain: All real numbers or (-∞, ∞)
Range: (-∞, -1]
Step-by-step explanation:
Quadratic Function: f(x) = a(bx - h)² + k
(h, k) is vertex
Step 1: Find vertex
f(x) = -2(x + 3)² - 1
h = -3
k = 1
Vertex = (-3, 1)
Step 2: Graph
When we graph, we should see our domain and range.
Domain is all x-values that can be inputted into the function.
Range is all y-values that can be outputted from the function.
Related Questions
russell bought a CD player that costs $120 before it went on sale for 15% discount. If he paid 5% sales tax on the sale price, how much did russell pay for the cd player?
Answers
Answer:
$107.10
Step-by-step explanation:
The original price of the CD player is $120 and we need to take 15% off.
We can find how much we need to subtract by multiplying 120 by .15, which equals 18. Then we can subtract that from 120, to get a sales price of $102.
A shortcut is subtracting 15 from 100 to get 85, and then doing 120*.85 = 102.
From the sales price of 102, there's a 5% tax to add on. 102 * .05 = 5.1
102+5.1 = 107.1
Answer:
$107.10
Step-by-step explanation:
First, find the discount.
Multiply the discount rate, 15% by the price of the CD player, $120
discount rate * price
15% * $120
Convert 15% to a decimal. Divide 15 by 100 or move the decimal place two spots to the left.
15/100= 0.15 or 15.0 --> 1.5 --> 0.15
0.15 * $120
$18
Since it is a discount, subtract $18 from the regular price of $120.
$120-$18
$102
Next, find the tax.
Multiply the tax rate, 5% by the price of the discounted CD player, $102
tax rate * discounted price
5% * $102
Convert 5% to a decimal. Divide 5by 100 or move the decimal place two spots to the left.
5/100= 0.05 or 5.0 --> 0.5 --> 0.05
0.05* $102
$5.10
Since it is tax, add $5.10 to the discounted price of $102.
$102 + $5.10
$107.10
Russell will pay $107.10 for the CD Player after a discount and tax.
AB formed by (-8, -1) and (-4, 2)
CD formed by (0, -3) and (12, 6)
Answers
The lines AB and CD are parallel lines.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The slope of line AB is m=2+1/-4+8
m=3/4
The slope of line CD is m=9/12=3/4
Both the lines AB and CD having the same slopes.
In parallel lines the slope will be same.
Hence, the lines AB and CD are parallel lines.
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En una clase de 25 alumnos hay 15 cajas de lápices de colores. Cada caja contiene 20 lápices. Queremos que todos los alumnos tengan el mismo número de lápices. ¿Cuántos lápices tendrá cada alumno?
Answers
Answer: Each student will have 12 pencils.
Step-by-step explanation:
Given: Total students= 25
Total colored boxes = 15
Total pencils in 1 box =20
Then total pencils in all 15 boxes = 20 × 15 = 300
Now, the number of pencils each students will get = (Number of pencils in all 15 boxes) ÷ (Total students)
= 300÷ 25
= 12
Therefore, Each student will have 12 pencils.
A sound system originally priced at $480 is on sale for 20 percent off. The tax on the purchase after the discount id 7.5 percent. What id the total cost of the sound system including tax?
Answers
Answer:
$412.80
Step-by-step explanation:
480 x 0.20(20%)=96
480-96=384
384 x .075(7.5%)=28.8
384+28.80=412.80
Which equation shows the inverse property of multiplication? 4 + (-4) = 0 -8 + (-3) = -3 + (-8) 2 times one-half = 1 Eight-fifths + 0 = Eight-fifths
Answers
Answer:
2 times one-half = 1
Step-by-step explanation:
In order to show a property of multiplication, the equation must involve multiplication. There is only one choice that does.
2 times one-half = 1
__
The multiplicative inverse of a number, multiplied by the number, results in 1, the multiplicative identity element.
Equation C,2 times one-half = 1 shows the inverse property of multiplication. Option C is correct.
What is multiplicative inverse?A multiplicative inverse is a number whose value is equal to 1 when multiplied by the original number.
The left-hand side of the equation is;
LHS = 2 times one-half
LHS = 2×(1/2)
LHS = 2
The right-hand side of the equation is;
RHS =1
If both LHS and RHS are equal and the RHS value is equal to 1 the RHS is the multiplicative inverse of LHS.
Equation C,2 times one-half = 1 shows the inverse property of multiplication.
Hence, option C is correct.
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0.2 reapiting into fracting
Answers
Answer:
the answer would be 2/9
Step-by-step explanation:
0.22222222... =
2/9
Answer:
1/5
Step-by-step explanation:
2.
[tex] \sqrt{9} [/tex]
find each square root
Answers
Answer:
√3x3
The answer is 3......
A commercial jetliner hits an air pocket and drops 264 feet. After climbing 151 feet, it drops another 103 feet. What is its overall vertical change?
Answers
Answer:
If we take the drops as negatives, and the climbs as positives (the answer will be the absolute value of these) we get:
-221 +174 -156.
When you add these together, you get -203. So the overall vertical change is the absolute value of this, or 203 ft.
Nick's class did an experiment. They put the same amount of water into four paper cups. To start the temperature was the each cup They put the cups in four different places They left them for thirty minutes, Next they used a thermometer to find the temperature of each cup of water. Predict which location should have the highest temperate
Answers
Answer: in a sunny spot of the classroom and im guessing 95?
Step-by-step explanation:
Using Accuracy and Precision
-vani is building a rectangular play area. The length of
me play area is 75 meters. The width of the play area is
- 3 meters. If she wants to cover the area in foam, how
much foam does she need to buy?
Due to the accuracy of the tape measure Avani used
the amount of foam needed to cover the play area is
38.9 square meters
Answers
Answer:
a little bit confusing
Rewrite the expression in the form x
Answers
Answer:
See below (I hope this helps!)
Step-by-step explanation:
When dividing exponential terms of the same base, we can simply subtract the exponents, therefore:
[tex]\frac{x^{6} }{x^{8} } = x^{(6-8)} = x^{-2}[/tex]
After school activities activity number student Spanish club 19 baseball 24 drama 15 homework help 17 soccer 20 which ratio compares the numbers of students to Spanish clubs in the the total number of students
Answers
Answer:
19:95
Step-by-step explanation:
Spanish club have 19 students
Baseball have 24 students
Drama have 15 students
Home work help have 17 students
Soccer have 20 students
The first step is to calculate the total number of students
= 19 + 24 + 15 + 17 + 20
= 95 students
Since the Spanish club have 19 students and the total number of students is 95 then, the ratio which compares the number of students in Spanish club to the total number of students is 19:95
Answer: 19:95, 19 to 95, or 19/95. They all equal the same so it depends which one is your option. ORDER OF RATIO MATTERS!!
Explanation: The students in the Spanish club are 19 and to find the total number of students, you add 19 + 24 + 15 + 17 + 20 which equals 95. Then you put 19 first then 95. This is because it asked to compare the number of students in the Spanish clubs (so this is first) to the the total number of students (so this is second).
What is the slope of the line that passes through the points (8, 7) and (4, 5)
Answers
Answer:
[tex] \huge{ \boxed{ \sf{ \frac{1}{2} }}}[/tex]
Step-by-step explanation:
[tex] \star{ \text{ \: Let the points be A and B}}[/tex]
[tex] \star{ \text{ \: Let A( 8 , 7 ) be ( x1 , y 1) and B ( 4 , 5 ) be ( x2 \: , y2 )}}[/tex]
[tex] \boxed{ \sf{ \: Slope = \frac{y2 - y1}{x2 - x1} }}[/tex]
[tex] \mapsto{ \sf{Slope = \frac{5 - 7}{4 - 8} }}[/tex]
[tex] \underline{ \text{Remember!}} : [/tex]The negative and positive integers are always subtracted but posses the sign of the bigger integer
[tex] \mapsto{ \sf{Slope = \frac{ - 2}{ - 4}}} [/tex]
[tex] \mapsto{ \sf{Slope = \frac{1}{2} }}[/tex]
[tex] \text{Hope \: I \: helped!}[/tex]
[tex] \text{Best \: wishes!}[/tex]
~[tex] \text{TheAnimeGirl}[/tex]
Use the order of operations to solve the problem. 7 x 8 + 4 +1
Answers
Answer:
7x8 is 56 plus four plus one equals 61
Step-by-step explanation:
The diagonal of a square is 10m long. What is the length of the side of the square?(Give your answer to the nearest cm)
Answers
Explanation:
Form: d = a sqrt(2)
Where d = diagonal = 10m and a = side length
10 = a sqrt(2)
10/sqrt(2) = a
Rationalize the denominator:
10/sqrt(2) x sqrt(2)/sqrt(2)
= 10 sqrt(2)/2
= 5 sqrt(2)
Thus, a = 5 sqrt(2)m
Change to cm:
5 sqrt(2) x 100cm = 500 sqrt(2)cm
the side length of a square measures 2 x+1 and the side lengths of a triangle are 2x, 2x, and 3x+10.The square and triangle have the same perimeter. Find the perimeter
Answers
Answer:
perimeter = 52
Step-by-step explanation:
side of square = 2x + 1
so first lets find the perimeter of squarep = 4 × s (side)
p = 4(2x +1)............. from the given
p = 8x + 4...... we will come back for this equation
side of trianles = 2x,2x,3x + 10
second lets find the perimeter of trianglep = s + s + s ( all the three sides)
p = 2x + 2x + 3x + 10
p = 7x + 10........we got another equation we will use it later
The question says the perimeter of square and the perimeter of triangle are equal so8x + 4(the perimeter of square we solved before) = 7x + 10(the perimeter of triangle we solved before)8x + 4 = 7x + 10
8x - 7x = 10 - 4
x = 6 ... now lets substitute x
8x + 4
8 × 6 +4
48 + 4
52
the same thing will happen if we substitute for the perimeter of triangle too.
hope u like it ❤️❤️❤️
for any question comment me
How many solutions does the equation 3(4h−1)=−4(3h−5) have?
Answers
Answer:
Step-by-step explanation:
I don’t want more question
I need help no more stress????
i need help please idk what to do
Answers
Answer:
(X - 10, y - 5)
Step-by-step explanation:
Just like walking
The earth experiences 50.000 earthquakes per year. Assuming it is a year with 365 days,find the number of earthquakes per hour
Answers
Answer:
0.00570776255
Step-by-step explanation:
there are 8760 hours in a year
divide 50 by 8760
0.00570776255
The number of earth quakes per hour is 5.7077.
What is Unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
In one year = 50,000 occurs
In one year = 365 days
In 1 day = 24 hour
In 365 days= 8760 hours
So, number of earthquakes occurred in one hour
=50000/8760
=5.7077
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In integers what is -11 -6
Answers
Answer:
-17
Step-by-step explanation:
Anyone know it’s middle school work
Answers
Answer:
B
Step-by-step explanation:
Using the conversion
1 Kg = 1000 g , then
3745 ÷ 1000 = 3.745 Kg
What is the measure of each angle?
Answers
2x+x+3-6=180
3x=183
x=61
(All measure in degree)
Hope this can help.
Is
Below
Step by step
Lindsay is playing a video game. She begins with an initial score of
500 points but loses 280 point throughout the game. She represents
her score using the expression shown.
500 - 280
Which of the following expressions also represents Lindsay's video
game score?
O A. 280 - 500
O B. 280 + 500
O C. 500 - (-280)
O D. 500 + (-280)
Answers
The expressions also represent Lindsay's video game score is 500 + (-280). The correct option is D.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Lindsay is playing a video game. She begins with an initial score of 500 points but loses 280 points throughout the game.
The expression will be written as below:-
E = 500 + (-280)
Therefore, the expressions also represent Lindsay's video game score is 500 + (-280). The correct option is D.
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??????????????????????????????????????????????
Answers
the second one is 2x^2-2x-2
the third one is 6h+6k
I'm on a 10 minute time limit. Please Answer!!!!! Show Work.
Answers
Answer:
623.64
Step-by-step explanation:
Really?!? Just use a calculator. I think thats right haven't done this in a while
this is true or false?
Answers
Answer:
The multiplication yes don't know about the addition
Step-by-step explanation:
10b + 18 < 2(4b+2)
Need held
Answers
Answer:
Step-by-step explanation:
10b +18 <2(4b +2)
10b +18 <8b +4
10 b - 8b <4 - 18
2b <-16
b <-16:2
b <-8
Which of the following units is incommensurable with miles? Select the two correct answers. (1 point)
acres
inches
meters
yards
grams
Answers
Answer:
grams
Step-by-step explanation:
Miles measures distance
Looking through the given options; acres, inches, metres and yards are also units of length.
So, we can conclude that they are commensurable with miles.
However, grams measures weights.
Hence,
From the list of given options; grams is incommensurable with miles because they measure different entities.
Answer:
acres and grams
Step-by-step explanation:
Miles is a measure of distance. Acres is a measure of area, and grams is a measure of mass. Knowing this you should know that these two are the answer. Your welcome!
PLEASE HELP TIMED SO PLEASE HURRY
Answers
Answer:
U got this
Step-by-step explanation:
THIS IS CHEATING
Simplify the expression 2k+10k-(2k+3)+13