Answers
Answer:
(a) 1
(b) 1 3/4
(c) [-2, 4]
(d) [-1/4, 2]
Step-by-step explanation:
Apparently, the vertex of the graph is (1, 2) and it goes through points (-1, 1) and (3, 1). In vertex form, the equation for this is ...
y = a(x -1)^2 +2
We can find the value of 'a' from the point (3, 1):
1 = a(3 -1)^2 +2 = 4a +2 . . . . substitute for x and y, and simplify
-1 = 4a . . . . . . . subtract 2
-1/4 = a . . . . . . divide by 4
So, ...
f(x) = -1/4(x -1)^2 +2
__
(a)Above, we assumed point (-1, 1) was on the graph:
f(-1) = 1
__
(b)Using the equation we found, ...
f(2) = -1/4(2 -1)^2 +2 = -1/4 +2
f(2) = 1 3/4
__
(c)The domain is the horizontal extent of the graph, apparently from x = -2 to x = 4.
domain: [-2, 4] or -2 ≤ x ≤ 4
__
(d)The range is the vertical extent of the graph. The minimum can be found at the end of the domain:
f(4) = -1/4(4 -1)^2 +2 = -9/4 +2 = -1/4
The maximum has already been established as the vertex at y=2.
range: [-1/4, 2] or -1/4 ≤ y ≤ 2
Related Questions
Please help me I need it please
Answers
Answer:
42.6%
Step-by-step explanation:
The percent increase is calculated as
percent increase = [tex]\frac{increase}{original}[/tex] × 100%
increase = $3.55 - $2.49 = $1.06
% increase = [tex]\frac{1.06}{2.49}[/tex] × 100% ≈ 42.6% (to the nearest tenth )
i need help on this
Answers
Answer:
The answer is B.
3x + 5y = 24
4x + 3y = 21
Step-by-step explanation:
x = cost of a chocolate chip cookie
y = cost of an oatmeal cookie
3x + 5y = 24
4x + 3y = 21
Lets solve:
-3(3x + 5y = 24) ==> -9x - 15y = -72
5(4x + 3y = 21) ==> 20x + 15y = 105
Let's add our new equations:
-9x - 15y = -72
20x + 15y = 105
11x = 33
/11 /11
x = $3.00 (the cost of each chocolate chip cookie)
Now lets find the cost of each oatmeal cookie using one of our original equations: 3x + 5y = 24
3(3) + 5y = 24
9 + 5y = 24
-9 -9
5y = 15
/5 /5
y = $3 (the cost of each oatmeal cookie)
Each type of cookie (chocolate chip and oatmeal), costs $3.00
Hope that helps!
A tree is 4 ft 2 in. Tall. To find the height of a tower, the shadow of the tree and the shadow of the tower were measured. What is the height h of the tower?.
Answers
Answer:
20 ft
Step-by-step explanation:
Convert all measurements to a single unit, inches, using the fact that 1 foot is equal to 12 inches.
ZY=(24⋅12) in.
Simplify.
ZY=288 in.
RH=(4⋅12) in.+2 in.
Simplify.
RH=50 in.
RQ=(5⋅12) in.
Simplify.
RQ=60 in.
ZX¯¯¯¯¯ and QH¯¯¯¯¯¯ are parallel because the rays of the Sun that form them are parallel. Therefore, the angles they form with the ground
are congruent: ∠Z≅∠Q.
∠Y≅∠R by the Right Angle Congruence Theorem.
Therefore, by the Angle-Angle Similarity △ZXY~△QHR.
Find XY. Set up a proportion with the lengths of the known sides and the unknown length (height of the tower).
ZYQR=XYHR
Substitute the values.
28860=h50
Cross multiply.
60h=50(288)
Simplify.
60h=14400
Divide both sides by 60.
h=240
The height of the tower is 240 in., or 20 ft.
can someone pls help me on this question i’ve literally been stuck on it all day
Answers
From a sample tray, 4 out of the last 10 cake samples chosen were strawberry. based on past data, of the next 20 samples taken, how many you should expect to be pieces of strawberry cake?
Answers
Answer:
8 pieces
Step-by-step explanation:
What is the volume of this figure
Answers
Answer :
22 Cubic Units Enjoy.
◊ YusuCr ◊
Write the equation in standard form. Identity the center and radius.
x² + y2 + 8x-4y-7=0
Answers
Answer:
See belowStep-by-step explanation:
Given equation:
x² + y² + 8x - 4y - 7 = 0Convert this to standard form by completing the square:
(x - h)² + (y - k)² = r², where (h, k) - center, r - radiusx² + 2*4x + 4² + y² - 2*2y + 2² - 16 - 4 - 7 = 0(x + 4)² + (y - 2)² - 27 = 0(x + 4)² + (y - 2)² = 27 (x + 4)² + (y - 2)² = (√27)²The center is (- 4, 2) and the radius is √27
Which word phrase describes the algebraic expression x - 16. 5? 16. 5 decreased by x x less 16. 5 x more than 16. 5 16. 5 minus x.
Answers
The expression "x -16.5" is expressed as "x less 16.5". Option B shows the correct expression.
What is the expression?The expression is defined as a set of terms combined using the operations addition, subtraction, multiplication, or division.
The given expression is [tex]x - 16.5[/tex].
The expression shows that 16.5 is subtracted from x. The resulting value is 16.5 less than x.
If the expression is expressed in words, it would be "x minus 16.5" or "x is reduced by 16.5"
Hence we can conclude that the expression "x -16.5" is expressed as "x less 16.5". Option B shows the correct expression.
To know more about the expression, follow the link given below.
brainly.com/question/13947055.
state weather (-2)3 will be positive or negative
Answers
Answer:
negative.
Step-by-step explanation:
rules of multiplying intergers;
- * - = +
+ * + = +
- * + = - (-2) x 3 follows this rule)
+ * - = -
James is riding in a 102-mile bike race.
When he stops for his first water break,
he is told that the second part of the
course is twice as long as the first part.
How long is the first part of the course?
Answers
Answer:
The first part of the course is 34 miles
Step-by-step explanation:
If you get 34 miles into a 102 miles bike race, you still have 68 miles left, which is double 34
Answer:
34
Step-by-step explanation:
34 + 68 =102
34×2 =102 so 34 is the answer.
A large cheese pizza cost $7.40. Diego has $40 to spend on pizzas. How many large cheese pizzas can he affors?
Answers
Answer:
If 7.40 is the price of a pizza, we have to make sure that he spends less than $40 on large pizzas. if Diego buy 5 pizzas he would spend $37 and would not have enough to afford another large pizza, meaning that he can buy 5 large pizzas
Pls help. It is due in 20 mins
Answers
100%-20%=80%
0.8(80/100)x200= 160
200-160=40
-1 < x < 4
x is an integer.
Write down the possible values of x.
Answers
Answer:
0, 1, 2, 3
Step-by-step explanation:
-1 < x < 4 means that x has to be an integer (whole number aka no fractions) between -1 and 4. Note that the < and > means that x cannot be -1 or 4 since it has to be greater than -1, or smaller than 4.
Write an equation in slope-intercept form for the line with slope - 3/5 and y-intercept -1. Then graph the line.
Answers
See the attached image
Write the equation in standard form. 4y−5x=3(4x−2y+1)
Answers
Answer:
-17x+10y=3
Step-by-step explanation:
Standard form is:
Ax+By=C
Let's start by simplifying the equation:
4y-5x=3(4x-2y+1)
Distribute the 3:
4y-5x=3(4x)+3(-2y)+3(1)
4y-5x=12x-6y+3
Subtract 12x from both sides
4y-17x=-6y+3
Add 6y to both sides
10y-17x=3
-17x+10y=3
Solve Tangent (x minus pi) minus cosine (x minus StartFraction 3 pi Over 2 EndFraction) = 0, x is an element of left-brace 0, 2 pi).
Answers
Answer:
x ∈ {0, π, 2π}
Step-by-step explanation:
The expression can be simplified, which facilitates an answer.
tan(x -π) -cos(x -3π/2) = 0
The tangent function has a period of π, so tan(x-π) = tan(x). The cosine function shifted right by 3π/2 is equivalent to the opposite of the sine function.
tan(x) +sin(x) = 0 . . . . substitute simpler equivalents
sin(x)/cos(x) +sin(x) = 0 . . . . use equivalent for tan(x)
sin(x)(1/cos(x) +1) = 0 . . . . factor out sin(x)
sin(x)(cos(x)+1)/cos(x) . . . . . combine terms to a single fraction
This has solutions where sin(x) = 0 and where cos(x) = -1. Those solutions are integer multiples of π.
x ∈ {0, π, 2π}
Answer:
B
Step-by-step explanation:
Evaluate the function
Answers
Answer:
[tex]f(10) \: is \: \: - 183[/tex]
Step-by-step explanation:
[tex]f(x) = { - 2x}^{2} + 17[/tex]
Question :Find f(10) ?
Solution :[tex]f(x) = { - 2x}^{2} + 17[/tex]
Substitute x = 10
[tex]f(10) = - 2 {(10)}^{2} + 17[/tex]
[tex] f(10) = - 2(100) + 17[/tex]
[tex]f(10) = - 200 + 17[/tex]
[tex] \boxed{f(10) = - 183}[/tex]
The following table shows the working populations, average salaries, and income tax rates of France and Germany. Country Workforce Average Salary (€) Income Tax Rate France 31,491,232 29,766 69. 3% Germany 38,844,017 32,104 45. 2% Based on the information in the table, how do the annual tax revenues of Germany and France compare to one another? a. The French government gathers €85,930,190,677 more than the German government. B. The French government gathers €543,141,128,984 more than the German government. C. The German government gathers €309,680,310,056 more than the French government. D. The German government gathers €223,750,119,378 more than the French government.
Answers
Percentage is a way to describe a part of a whole. French government gathers €85,930,190,677 more than the German government.
What is Percentage?A percentage is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
We know that the number of people who are working in France is 31,491,232 and their average salary is €29,766 while the amount of tax they pay from their salary is 69.3%. therefore, the total amount of tax that France will gather,
[tex]Tax_{France} = 31,491,232 \times 29,766 \times 69. 3\%[/tex]
[tex]= 31,491,232 \times 29,766 \times \dfrac{69. 3}{100}\\\\= 31,491,232 \times 29,766 \times 0.693\\\\=6.49596\times 10^{11}[/tex]
Now, the population that is working in Germany is 38,844,017 while the average earning of the population is €32,104 and they pay 45.2% of their salary as tax. therefore,
[tex]Tax_{Germany} = 38,844,017 \times 32,104 \times 45.2\%[/tex]
[tex]= 38,844,017 \times 32,104 \times 45.2\%\\\\= 38,844,017 \times 32,104 \times \dfrac{45.2}{100}\\\\= 38,844,017 \times 32,104 \times 0.452\\\\=5.63666 \times 10^{11}[/tex]
Further, the difference between the tax of the two countries can be written as,
[tex]\text{Differene in the tax}= Tax_{France} - Tax_{Germany} = 85,930,190,677[/tex]
hence, the French government gathers €85,930,190,677 more than the German government.
Learn more about Percentage:
https://brainly.com/question/6972121
Answer:
Based on the information in the table, how do the annual tax revenues of Germany and France compare to one another?
a. } The French government gathers €85,930,190,677 more than the German government.b. } The French government gathers €543,141,128,984 more than the German government.
c. } The German government gathers €309,680,310,056 more than the French government.
d.} The German government gathers €223,750,119,378 more than the French government.
Step-by-step explanation:
Correct on Edge 2022
If f(x) = 9/4x, what is the value of f(-10)
Answers
Step-by-step explanation:
Substitute f(-10) into the function:
[tex]f(-10)=\frac{9}{4(-10)}[/tex]
Multiply:
[tex]f(-10)=\frac{9}{(-40)}[/tex]
Simplify:
[tex]f(-10)=-0.225[/tex]
At the Flyer Factory, the assembly line produces 102 computers
in a batch. The computers are packaged in boxes with 25 each.
if 10 batches are made in one day, how many computers will be
leftover at the end of it?
Answers
20
Step-by-step explanation:
1 batch = 4 boxes (of 25)& 2 left over
10 batch in a day = 40 boxes & 20 left over
Please help! It's homework!
Answers
Can’t see clearly
The number of points scored by the bears, eagles, and cowboys last weekend was three consecutive odd numbers. the bears scored the least number of points and the cowboys scored the most. if the product of the points scored by the bears and cowboys was 37 more than the 8 times the sum of the points scored by the eagles and cowboys, how many points did the eagles score?
A) 13 points
B) 15 points
C) 17 points
D) 19 points
E) 21 points
Please show solution
Answers
Answer: The Philadelphia Eagles tried to blow a 19-point lead to the Chicago Bears, but managed to hold on for a 22-14 victory in a rematch of the NFC Wild Card Game to move to 5-4 on the year. Philadelphia allowed the Bears to score 14 unanswered points after taking a 19-0 lead in the third quarter, but put together one of their most impressive drives of the season in taking 8:14 off the clock in the fourth quarter, converting four consecutive third downs in the most critical junction of the game.
Chicago never got the ball back after Jake Elliott hit a 38-yard field goal with 26 seconds left to make it 22-14. Bears tight end Adam Shaheen muffed the catch on the kickoff and the Eagles recovered to deny Chicago a last ditch effort for a Hail Mary and an attempt to tie the game with a two-point conversion.
Jordan Howard scored a touchdown in his first game against his former team, finishing with 19 carries for 82 yards and a touchdown. Zach Ertz had his best game of the season as the Eagles tight end had nine catches for 103 yards and a touchdown, a 25-yard catch for his second score of 2019.
The Bears had just nine total yards in the first half, but rallied back in this game with two scoring drives in three possessions between the third and fourth quarter. Chicago's offense had no turnovers, but finished with just 164 yards of offense. Mitchell Trubisky went 10 of 21 for 125 yards with no touchdowns and a 66.6 passer rating. The Bears have lost their fourth consecutive game after a 3-1 start to the season, falling to 3-5 and remaining in last place in the NFC North.
Step-by-step explanation:
The number of points scored by the eagles is 19 points.
Suppose the points scored by the bears, eagles, and cowboys are x, x+2, x+4 respectively.
It is given the product of the points scored by the bears and cowboys was 37 more than the 8 times the sum of the points scored by the eagles and cowboys.
This means, x(x+4) =37+8(x+2+x+4)
x(x+4) =37+8(2x+6)
[tex]x^{2} +4x = 37+16x+48[/tex]
[tex]x^{2} -12x-85=0[/tex], which is a quadratic equation.
What is a quadratic equation?Any equation in the form [tex]ax^{2} +bx+c=0[/tex] is called a quadratic equation where [tex]a\neq 0[/tex].
[tex]x^{2} -17x+5x-85=0[/tex]
[tex]x(x-17)+5(x-17)=0[/tex]
[tex](x-17)(x+5)=0[/tex]
[tex]x=17[/tex]
So, eagles scored x+2 = 17+2 =19 points.
Therefore, The number of points scored by the eagles is 19 points.
To get more about quadratic equations visit:
https://brainly.com/question/1214333
heeeeelppppp please heeelpppp omg 25 points
Answers
Answer:
The fraction, or the one on the right is larger by just a few decimals.
Step-by-step explanation:
Have an amazing day :D
What is the volume of a right circular cylinder with a base diameter of 6 m and a height of 5 m? Enter your answer in the box. Express your answer using π. M³ $\text{Basic}$.
Answers
The volume of the cylinder depends on its radius and height. The volume of the cylinder is 141.3 m3.
What is the volume of the cylinder?The volume of the cylinder is defined as the density of the cylinder which measures the amount of material contained by the cylinder.
Given that the height h of the cylinder is 5m and the diameter d of the base of the cylinder is 6m.
The radius of the cylinder is given below.
[tex]r = \dfrac {d}{2}[/tex]
[tex]r= \dfrac {6}{2}[/tex]
[tex]r = 3\;\rm m[/tex]
The volume of the cylinder is calculated as given below.
[tex]V = \pi r^2 h[/tex]
[tex]V = 3.14 \times 3^2 \times 5[/tex]
[tex]V = 141.3 \;\rm m^3[/tex]
Hence we can conclude that the volume of the cylinder is 141.3 m3.
To know more about the volume of the cylinder, follow the link given below.
brainly.com/question/12748872.
5. Solve for x:
1/x-1/3=-1/3x
Answers
Answer:
(x-3)/9
Step-by-step explanation:
STEP
1
:
-x
Simplify ——
3
Equation at the end of step
1
:
(3 - x) -x
——————— • ——
3x 3
STEP
2
:
3 - x
Simplify —————
3x
Equation at the end of step
2
:
(3 - x) -x
——————— • ——
3x 3
STEP
3
:
Canceling Out :
3.1 Canceling out x as it appears on both sides of the fraction line
Final result :
x - 3
—————
9
hope this helps!!
please help me find total surface area
Answers
Answer:
190mm2
Step-by-step explanation:
8x6=48
8x7=56
8x7=56
6x5/2=15
6x5/2=15
48+56+56+15+15=190
What is the solution to the proportion? (1 point)
Answers
Answer:
Your answer would be 25.
What is the length of the hypotenuse, c? Round your answer to the nearest hundredth.
Answers
Answer:
Step-by-step explanation:
By using the Pythagorean theorem:
b^2+3^2=5^2
b^2+9=25
b=sqrt (25-9)
b=sqrt(16)
b=4
=> 4^2+7^2=c^2
16+49=c^2
65=c^2
=>c=sqrt(65)
c = (approximately) 8
I'm very confused, can someone explain this to me?
Answers
Answer: 118 degrees
Step-by-step explanation:
By the exterior angle theorem.
3x + 12 + 2x + 16 = 6x + 10
5x + 28 = 6x + 10
x = 18
So measure of angle 3 = 6(18) + 10 = 118 degrees
Evaluate the expression 3. 14(a2 ab) when a = 4 and b = 2. (Input decimals only, such as 12. 71, as the answer. ) Answer for Blank 1:.
Answers
Answer:
1792
Step-by-step explanation:
14(a^2 ab)
a=4 b=2
=14(4^2*4*2)
=14(16*8)
=14*128
1792