Answer: Factor the numerator and denominator and cancel the common factors.
7x/6+5/6
Step-by-step explanation:
What are the vertes, the axis of symmetry, the maximum or minimum value,
the domain, and the range of each function?
5. f(x)=2(x-4)^2+3
Answer:
vertex: (4,3)
axis of symmetry: x=4
Domain (interval notation) : ( − ∞ , ∞ )
Domain (set-builder notation): { x | x ∈ R }
Range (interval notation): Range: [ 3 , ∞ )
Range (set-builder notation): { y | y ≥3 }
Maximum/minimum value: (4,3)
Step-by-step explanation:
Savvas Texas Algebra II
Topic 1 Performance Task
Topic 1 Performance Task
Filling Balloons
You are planning a surprise birthday party, and you would like to decorate with some
helium-filled balloons. You plan to use two different sizes of balloons. You will need to
purchase balloons and helium based on your party plans. The volume and cost of balloons
and helium tanks are listed below:
• The volume of each small balloon is 300 in."
3
• The volume of each large balloon is 1000 in.'.
• One package of 50 small balloons costs $2.59.
• One package of 24 large balloons costs $1.99.
• One small tank of pressurized helium can fill 20 ft of balloons. It costs $10.49.
You would like to fill at least 30 of each size of balloon for your party, but you would like to
use all of the helium you purchase. In addition, you would like to spend the least money
possible for balloons.
Task Description
Use functions to determine the number of balloons you need and how much your
supplies will cost.
Answer:
The number of small balloons = 46
The number of large balloons = 159
The number of bottles of helium gas = 5
The total cost of the supplies = $68.97
Step-by-step explanation:
The volume of each small balloon = 300 in.³
The volume of each large balloon = 1000 in.³
The cost of one package of 50 small balloons = $2.59
The cost of one package of 24 large balloons = $1.99
The volume of one small tank of pressurized helium = 20 ft³
The volume cost of one small tank of pressurized helium = $10.49
By conversion
20 ft³ = 34,560 in.³
The volume of 30 small balloons = 30 × 300 in.³ = 9,000 in.³
The volume of 30 large balloons = 30 × 1000 in.³ = 30,000 in.³
The volume taken by 24 large balloons = 24,000 in.³,
24 large balloons cost = $1.99
The volume taken by 50 small balloons = 15,000 in.³
50 small balloons cost = $2.59
Therefore, we buy more large balloons
We have;
A×300 + B×1000 = C×34,560
Given that all the helium will be used, the volume of helium will be a multiple of 300, therefore, when 5 bottles of helium is used, we have;
A×300 + B×1000 = 5×34,560 = 172,800 in.³
Given that there will be at least 30 of each balloon, gives;
We remove the minimum possible quantity (more than 30) of small balloons from 172,800 in.³ leaving multiples of 1,000s as follows;
Using Excel, the quantities of 36 and 46 small balloons give the same cost
For 46 small balloons
The volume of 46 small balloons = 13,800 in.³
Therefore, 172,800 in.³ - 13,800 in.³ = 159,000 in.³ = The volume of the large balloons
The quantity of the large balloons = 159,000 in.³/(1,000 in.³/balloon) = 159 balloons
Therefore, we have 46 small balloons, and 159 large balloons, with 5 small bottles of helium gas
The number of package of large balloons is 159/24 = 6.625 ≈ 7 packages
The cost of the 7 packages of large balloons = 7 × $1.99 = $13.93
The number of package of small balloons is 46/50= 0.92 ≈ 1 package
The cost of the 1 packages of small balloons = 1 × $2.59 = $2.59
The cost of the five bottles of helium = 5 × $10.49 = $52.45
$68.97
The number of small balloons = 46
The number of large balloons = 159
The number of bottles of helium gas = 5
The total cost of the supplies = $68.97
At the same cost, we can also have;
The number of small balloons = 36
The number of large balloons = 162
The number of bottles of helium gas = 5
The total cost of the supplies = $68.97
Therefore, we can have 36 or 46 small balloons and 162 or 159 large balloons along with 5 bottles of helium gas with a total cost of $13.93 + $2.59 + $52.45 = $68.97.
Simplify the expression where possible.(-4 x^2 )^2
Answer:
[tex]16x^{4}[/tex]
Step-by-step explanation:
[tex](a^{m})^{n}=a^{m*n} \\\\\\[/tex] and [tex](a*b)^{m}= a^{m}*b^{m}[/tex]
[tex](-4x^{2})^{2} = (-4)^{2} *(x^{2})^{2}\\\\\\=16 * x^{2*2}\\\\=16x^{4}[/tex]
a. 5x10 to the third power
Answer:
5000
Step-by-step explanation:
the answer is 5000 because the third power to ten is 1000 and since 5x10= 50 you just have to make it a thousand so, 5000
Answer:5000
Step-by-step explanation: take notes
The graph of quadratic function f(x) = px²-5x+q, where p and q are constants, has a maximum point. The possible value of p is
(A) -1
(B) 0
(C) 1
(D) 2
How do i do this. Im mad lost
Answer:
x-int: (8/3, 0)
y-int: (0, -32/3)
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
x-intercept is the x-value when y = 0
y-intercept is the y-value when x = 0
Step 1: Write equation
2x - 1/3 = 1/2y + 5
Step 2: Subtract 5 on both sides
2x - 16/3 = 1/2y
Step 3: Multiply 2 on both sides
4x - 32/3 = y
Step 4: Rewrite
y = 4x - 32/3
Step 5: Find x-int
0 = 4x - 32/3
32/3 = 4x
x = 8/3
(8/3, 0)
Step 6: Find y-int
y = 4(0) - 32/3
y = 0 - 32/3
y = -32/3
(0, -32/3)
do yall have online school or can you go to school
Answer:
i am doing online school
Step-by-step explanation:
Answer:
I've got online school full time for at least my first quarter but I think we'll be in online for more than half the year.
Diego says a quadrilateral with four congruent sides is always a regular polygon. Mai says it never is one. Do you agree with either of them?
Help please!!!
Answer:
mai is correct
Step-by-step explanation:
a quadrilateral with four congruent sides is never a regular polygon it is a rhombus. hope this helps!
A regular polygon has four congruent sides and four congruent angles.
I do not agree with any of them, because both arguments are incorrect
For a polygon to be a regular polygon, the following conditions must be met
All four sides must be congruentAll four angles must be congruent (90 degrees)Some quadrilaterals with four congruent sides are:
Rhombus, Kite, Square, etc.
A rhombus has four congruent sides, but all four angles are not congruent.
This means that Diego's argument is incorrect
All sides and angles of a square are congruent.
Because Mai says such polygons can never be a regular polygon, then Mai's argument is also wrong.
Hence, I do not agree with any of them.
Read more about polygons at:
https://brainly.com/question/15941789
Solve the equation. Simplify your answer if possible. 4m-3=-27
Answer:
-6
Step-by-step explanation:
multiplicative inverse of 21/49
Answer:
49/21
Step-by-step explanation:
You just have to switch the numerator and denominator so you can cancel out the number from one side of the equation in a normal problem
In a recent year, the top-selling cookie in America was Nabiscos Chips Ahoy, with sales of $294.6
million. The total cookie sales for that year were $3,124 milion. What percent of the total cookie sales
was due to Chips Ahoy?
Answer:
9.43%
Step-by-step explanation:
Divide the Chips Ahoy sales by the total sales, then multiply by 100
(294.6/3,124) x 100
= 9.43%
So, 9.43% of the total cookie sales were from Chips Ahoy
From the set 12345 which values make the inequality n+1>4true?
18 divided by (1+5)(4-2)
Answer:
= 3/2
[tex] = \frac{18}{(1 + 5)(4 - 2)} [/tex]
[tex] = \frac{18}{(6)(2)} [/tex]
[tex] = \frac{18}{12} [/tex]
Simplify the fraction.
[tex] = \frac{3}{2} [/tex]
Answer:
1/2 or 0.5
Step-by-step explanation:
PEMDAS (parentheses, exponents,multiplication, division, addition, subtraction)
Parentheses: 1+5=6, 4-2=2
Multiply: 6•2=12
Division: 18 divided by 12= 3/2 or 1.5
3x + 7 - x + 2 A.2x + 9 B.2x + 5 C.4x + 9 D.4x - 5
Answer:
A
Step-by-step explanation:
3x + 7 - x + 2 combine like terms
3x - x + 7 + 2
2x + 9
Option A
If someone could actually help me you will be so nice of you please I don’t understand this
Answer:
So, the function is increasing over: [tex](4,\infty)[/tex]
And it's decreasing over: [tex](-\infty,4)[/tex]
Step-by-step explanation:
So first, let's graph the function. Please refer to the attached graph.
The function is increasing when the function is going upwards, and the function is decreasing when the function is going downwards.
From the graph, we can see that the function is going upwards after x=4. Therefore, the function is increasing for all values to the right of 4. In interval notation, this is:
[tex](4,\infty)[/tex]
Also, we can see that the function is going downwards all the way from the left until x=4. Thus, the function is decreasing from for all values to the left of 4. In interval notation, this is:
[tex](-\infty,4)[/tex]
So, the function is increasing over: [tex](4,\infty)[/tex]
And it's decreasing over: [tex](-\infty,4)[/tex]
And those are our answers :)
Important Notes:
Note that we do not use brackets with the 4. This is because the function is only increasing to the right of 4 and decreasing to the left of 4. At exactly 4, the function is still; it is neither increasing nor decreasing. Thus, x equals exactly 4 will be in neither of our intervals.
solve by factoring y²-4=3y
Answer:
(y + 1) • (y - 4)
Step-by-step explanation:
Trying to factor by splitting the middle term
1.1 Factoring y2-3y-4
The first term is, y2 its coefficient is 1 .
The middle term is, -3y its coefficient is -3 .
The last term, "the constant", is -4
Step-1 : Multiply the coefficient of the first term by the constant 1 • -4 = -4
Step-2 : Find two factors of -4 whose sum equals the coefficient of the middle term, which is -3 .
-4 + 1 = -3 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 1
y2 - 4y + 1y - 4
Step-4 : Add up the first 2 terms, pulling out like factors :
y • (y-4)
Add up the last 2 terms, pulling out common factors :
1 • (y-4)
Step-5 : Add up the four terms of step 4 :
(y+1) • (y-4)
Which is the desired factorization
Final result :
(y + 1) • (y - 4)
Answer:
y =-1y=4Step-by-step explanation:
[tex]y^2-4=3y\\\mathrm{Subtract\:}3y\mathrm{\:from\:both\:sides}\\y^2-4-3y=3y-3y\\\\\mathrm{Simplify}\\y^2-3y-4=0\\\\\mathrm{Solve\:by\:factoring}\\\mathrm{Factor\:}y^2-3y-4:\quad \left(y+1\right)\left(y-4\right)\\\\\mathrm{Solve\:}\:y+1=0:\quad y=-1\\\mathrm{Solve\:}\:y-4=0:\quad y=4\\\\y=-1,\:y=4[/tex]
Use the figure to the right to find the value of PT. T is the midpoint of PQ.
PT = 3x + 9 and TQ = 5x -5
PT=(Simplify your answer.)
Answer:
PT=30 units
Step-by-step explanation:
Given that:
Line PQ which has a mid point at T.
[tex]PT = 3x + 9[/tex] and
[tex]TQ = 5x -5[/tex]
To find:
PT = ? in simplified terms.
Solution:
First of all, let us recall that mid point on a line segment is a point that divides the line in two equal parts.
In other words:
If a point B is the mid point of line segment AC, then AB = BC.
Here, the point T is the midpoint of PQ.
i.e. PT = TQ
[tex]3x+9=5x-5\\\Rightarrow 3x-5x=-5-9\\\Rightarrow -2x=-14\\\Rightarrow x=7[/tex]
Putting value of [tex]x[/tex] in PT above:
[tex]PT = 3x+9 = 3 \times 7 +9 \\\Rightarrow \bold{PT=30\ units}[/tex]
Answer:
32
Step-by-step explanation:
did it, and i was wrong. it gave the right answer that is it. credit to me.
The school band sold 200 tickets to their concert. If 90 adult tickets were sold , What percent of the tickets sold were adult tickets?
Answer:
45%
Step-by-step explanation:
What is the opposite of 49?
Answer:
-49 is the answer for the question
Frank has completed 34 deliveries so far this week. He needs to make 85 deliveries for the week. What percentage of his deliveries has Frank completed?
Answer: 40 percentage of his deliveries has Frank completed
Step-by-step explanation:
Given : Deliveries completed by Frank = 34
Total deliveries = 85
Percentage of deliveries has Frank completed = [tex]\frac{\text {Deliveries completed by Frank}}{\text {Total deliveries}}\times 100[/tex]
Putting in the values:
Percentage of deliveries has Frank completed = [tex]\frac{34}{85}\times 100=40\%[/tex]
Thus 40 percentage of his deliveries has Frank completed
Explain why angle is considered a defined term in geometry.
Answer:
An angle is considered a defined term in geometry because defined terms are terms that have a formal definition and can be defined using other geometrical terms.
Angle: Two rays that share the same endpoint, however, the rays take off in different directions. The area in the middle of the two rays is the angle measure.
Where do students go to school? Although 80.4% of first‑time first‑year students attended college in the state in which they lived, this percent varied considerably over the states. A stemplot of the percent of first‑year students in each of the 50 states who were from the state where they enrolled is provided. The stems are 10s and the leaves are 1s. The stems have been split in the plot.
Answer:
Step-by-step explanation:
it always depends of what school you are in
What is the area of the enlarged rectangle?
O 48 square units
O 168 square units
O 336 square units
O 588 square units
Answer: B
Step-by-step explanation:
It’s 168 because to solve problems for the area of a reduced or enlarged figure, first square the scale factor. Then use the given dimensions to find the area of the original figure. Multiply the square of the scale factor by the area of the original to get the reduced or enlarged figure.
Answer:
D 558
Step-by-step explanation:
May I get some help?
Answer:
4 and the correct answer is 34
Step-by-step explanation:
choice c or 4; correct solution is 34 :)
hope this helps :)
Help me out with this one please
Answer:
5) x = -1
6) x = 2
Step-by-step explanation:
5) 5 + 2x + 6 = x + 10
2x + 11 = x + 10
2x + 1 = x
1 = -x
-1 = x
6) (9x + 7) + (-3x + 20) = 39
6x + 27 = 39
6x = 12
x = 2
Answer:
For question 5, x= -1
Step-by-step explanation:
Segment Addition Postulate = ab+bc=ac
For Question 5,
(a) + (b) = (c)
5+2x + 6 = x+10
5+2x+6=x+10
To solve that,
5+2x+6=x+10
Add 5+6
11+2x=x+10
Subtract 11 from both sides
2x= x-1
x-1=2x
Factors that are composite to 60
Answer:
60 is a composite number. 60 = 1 x 60, 2 x 30, 3 x 20, 4 x 15, 5 x 12, or 6 x 10. Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. Prime factorization: 60 = 2 x 2 x 3 x 5, which can also be written 60 = 2² x 3 x 5.
Answer:
[See Below]
Step-by-step explanation:
✦ The composite factors of 60 are:
✧ 1 , 2 , 3 , 4 , 5 , 6 , 10 , 12 , 15 , 20 , 30, 60
~Hope this helps Mate. If you need anything feel free to message me.
(I've included some pictures that should help you out if you don't understand still.)
Express an integer: a debt of $50
What’sThe answer
Answer:
-50
Step-by-step explanation:
A debt is something you owe so it is a negative number
-50
Answer:
-50
Step-by-step explanation:
Please help me out with these questions.
Answer:
here's the answers to your questions
Solve for m: 18d − 2m + 9k < 5k + 10
[tex]18d-2m+9k[/tex] < [tex]5k+10[/tex]
[tex]18d-2m[/tex] < [tex]-4k +10[/tex]
[tex]-2m[/tex] < [tex]-4k +10 -18d[/tex]
[tex]m[/tex] > [tex]\frac{-4k+10-18d}{-2}[/tex] (flipped the sign because we're dividing by a negative)
[tex]m[/tex] > [tex]2k+5+9d[/tex]
Answer:
m > 2k + 9d- 5
Solve x+2=1/2x-1 Please hurry!
Answer:
X = - 6Step-by-step explanation:
x + 2 = 1/2x - 1[tex]2 + 1 = \frac{1}{2}x - x[/tex]
[tex]3 = - \frac{1}{2}x[/tex]
[tex]x = \frac{ - 3}{ \frac{1}{2} } \\ x = \frac{ - 6}{1} \\ x = - 6[/tex]
Hope this helps :)
A construction company is setting up signs on 2 miles of road. If the company places a sign every 1 4 mile, how many signs will it use?
Every 1/4 mile it places a sign.
So we need to find out how many 1/4 mile there is in the total 2 miles.
To know that: We carry out 2 divide 1/4
2 / (1/4)
2 * 4/1
= 8
So there are eight (8), 1/4 miles on the 2 miles of road.
8
Hope this explains it.
Answer:
the answer is 8 signs ;)