Expand the polynomial:
(5a+1/5 b)^2
To write f(x) = 2x2 – 44x + 185, factor out from the first two terms. Next, form a perfect square trinomial keeping the value of the function equivalent: f(x) = 2(x2 – 22x + 121) + 185 – 242 The function written in vertex form is f(x) = (x – )2 + .
Answer:
f(x) = 2(x-11)^2 - 57
Step-by-step explanation:
To write f(x) = 2x^2 – 44x + 185, factor out from the first two terms.
Next, form a perfect square tri nomial keeping the value of the function equivalent: f(x) = 2(x^2 – 22x + 121) + 185 – 242
To get vertex form we factor x^2 -22x+121
product is 121 and sum is -22
-11*-11= 121 and sum -11+(-11)= -22
x^2 -22x+121
(x-11)(x-11)
f(x) = 2(x^2 – 22x + 121) + 185 – 242
f(x) = 2(x-11)(x-11)+ 185 – 242
f(x) = 2(x-11)^2 - 57
(80z) to the 3/4 power
Graph the line with slope -2/3 passing through the point (2,1)
To graph a line with a given slope passing through a point, use the point-slope form of a linear equation. Convert the equation to slope-intercept form, [tex]y = mx+b[/tex]. Plot the line on a graph using the y-intercept and the slope to find additional points.
Explanation:To graph a line with a given slope and passing through a point, we can use the point-slope form of a linear equation, y - y1 = m(x - x1). In this case, the point-slope form would be y - 1 = (-2/3)(x - 2). We can simplify this equation into slope-intercept form, y = mx + b, by distributing the slope and rearranging the terms. After simplifying, the equation becomes y = (-2/3)x + 7/3. Finally, we can plot the line on a graph using the slope-intercept form equation by identifying the y-intercept at (0, 7/3) and using the slope to find additional points on the line.
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Help please! 10 points!
10: Gavin builds furniture for a living. he Sells chairs for $45 and tables for $70 each. It takes Gavin 4 hours and $10 worth of supplies to build each chair. A table requires 10 hours and $15 worth of supplies to make. Gavin wants to work for no more than 40 hours per week and spend no more than $80 on materials. Write a system of inequalities and state 3 possible combos.
Let's assume
number of chairs =x
number of tables =y
we are given
Gavin builds furniture for a living. he Sells chairs for $45 and tables for $70 each
So, we can find objective function as
[tex] Z=45x+70y [/tex]
now, we can find inequalities
A table requires 10 hours and $15 worth of supplies to make
so, total hours to make table =10y
amount spent on table =15y
It takes Gavin 4 hours and $10 worth of supplies to build each chair
so, total hours to make chair =4x
amount spent on chair =10x
total number of hours to make chair and table =4x+10y
Gavin wants to work for no more than 40 hours per week
so, we get
[tex] 4x+10y\leq 40 [/tex]
spend no more than $80 on materials
so, we get
[tex] 10x+15y\leq 80 [/tex]
so,
objective function:
[tex] Z=45x+70y [/tex]
Constraints:
[tex] 4x+10y\leq 40 [/tex]
[tex] 10x+15y\leq 80 [/tex]
The following data show the weight, in ounces, of 10 different bags of candy:
10 3 7 3 4 21 6 10 1 2 4
After removing the outlier, what does the mean absolute deviation of this data set represent?
A. On average, the weight of a bag of candy varies 3.2 ounces from the mean of 4 ounces.
B. On average, the weight of a bag of candy varies 2.6 ounces from the mean of 5 ounces.
C.On average, the weight of a bag of candy varies 3.2 ounces from the mean of 5 ounces.
D.On average, the weight of a bag of candy varies 2.6 ounces from the mean of 4 ounces.
PLZ HELP ME NEEDDDDDDDD HELP PLZZZZZZZZZ!!!!!!!!!!!! I DON'T GET IT! HELPPPPP
Think this belongs to math, I'm not sure though, anyway, what is the width and length of a wooden plank if the dimension is 12,5 x 8,5cm?
You can infer from this problem that the shape of the wooden plank is a rectangle based on the dimensions given. The length of a rectangle is usually the longest side of the rectangle so you can conclude that the length of the rectangle is 12.5 cm. Therefore, the width is 8.5 cm.
6. How could you change the simulation to generate data for three pets? Result Frequency Heads, Heads 9 Heads, Tails 14 Tails, Heads 18 Tails, Tails 9 Total 50
PLEASE HELP WILL GIVE BRAINLYEST
Answer: what i did was put "change one of the tails, heads or heads, tails to add the data for the 3 pets" because you couldn't tell if it was heads tails or tails heads
Final answer:
To generate data for three pets in a simulation, expand the outcome possibilities to include all combinations of Heads and Tails for three entities, and then record the frequency of each outcome to analyze probabilities or patterns.
Explanation:
To determine how to change a simulation to generate data for three pets when you currently have data for two, you need to expand the number of possible outcomes to account for the additional pet. For the current two-pet scenario, there are four outcomes: Heads-Heads, Heads-Tails, Tails-Heads, and Tails-Tails. When adding a third pet, each of these outcomes would branch into two further outcomes, representing the two possibilities for the third pet (let's call it Pet C).
The possible outcomes would be:
Heads-Heads-HeadsHeads-Heads-TailsHeads-Tails-HeadsHeads-Tails-TailsTails-Heads-HeadsTails-Heads-TailsTails-Tails-HeadsTails-Tails-TailsFor each outcome, you would simulate or record the frequency as you did with the two-pet scenario, totaling the number of trials to ensure you have complete data for analysis. You would then use this data to analyze the probabilities or patterns of outcomes involving three pets.
Which describes a parameter of a population?
A) all the golf balls produced last Monday by the Acme Company
B) 63% of Rains County agree with the latest U.S. foreign policy
C) 88% of students at Emory High School have been to a football game
D) 45% of Jacksonville, Florida residents have been to the beach last summer
Answer:
A) all the golf balls produced by the Acme Company
Step-by-step explanation:
Which situations accurately describe a ratio of ? Select all that apply
A ratio compares two quantities and can form a proportion when two ratios are equivalent. A unit rate is a ratio with one quantity of one, while a unit scale compares actual object dimensions to a model or drawing. These concepts are used in various fields, including health sciences and when working with scale models or maps.
Explanation:A ratio is a comparison between two different quantities. When we express ratios, we can use a fraction format, a colon, or the word 'to'. Examples include 2/3, 2:3, and '2 to 3'. In certain situations, this comparison can lead to the formation of a proportion, which occurs when two ratios are equivalent, like 1/2 = 3/6. Proportions are especially useful when we deal with scale distances or dimensions, such as in map reading or model building.
A unit rate is a type of ratio in which one of the quantities is one. An example would be 55 miles per hour or 55 miles/1 hour. This is often used when discussing speed or cost per unit.
Similar to a unit rate is a unit scale, which compares the actual dimensions of an object to the dimensions of a model or drawing of the object. An example of a unit scale is 1 inch = 100 feet, which can be written as a ratio of 1 inch/100 ft.
In sectors like the health sciences, ratios are used to describe solutions and are given in terms of proportions, for example, 1:1000. In making comparisons or constructing models, we might set ratios equal to the unit scale to form proportions for various dimensions like length and width.
Four different situations accurately describe ratios.
Certainly! Let's evaluate each situation to see if it accurately describes a ratio.
Sally found five green fruit loops in her cereal bowl, out of every thirteen pieces.
This situation does describe a ratio: 5 green fruit loops to 13 total pieces. The ratio is 5:13.
Tobias picked five daisies and eight roses.
This situation does describe a ratio: 5 daisies to 8 roses. The ratio is 5:8.
Aly painted eight trees for every three birds.
This situation does describe a ratio: 8 trees to 3 birds. The ratio is 8:3.
For every eight shots, Micah made five baskets.
This situation also describes a ratio: 5 baskets to 8 shots. The ratio is 5:8.
So, all four situations accurately describe ratios.
The complete question is:
Which situations accurately describe a ratio of? Select all that apply.
Sally found five green fruit loops in her cereal bowl, out of every thirteen pieces.
Tobias picked five daisies and eight roses.
Aly painted eight trees for every three birds.
For every eight shots, Micah made five baskets.
in a first aid kit the ratio of large bandages to small bandages is 5 to 2. Based on this ratio, how many large bandages are in the kit if there are total of 60 bandages?
What is the length of the diagonal of a 10cm by 15com rectangle
a2 + b2 = c2
102 + 152 = c2
100 + 225 = c2
√325 = c
5√13 = c
The diagonal measures 5√13 cm.
Write a real-world problem that can be represented by a rule and a table using division
The rent for an office space is $674.30 per month. The office is 306 1/2 square feet in area.What is the monthly cost per square foot to rent the office
A:$22.48
B:$2:20
C:$0.46
D:$0.22
Would (j^-13)(j^4)(j^6) equal to j^-312?
The equation b=540−30m gives the balance b (in dollars) that you owe on a drum set after m monthly payments. What is the balance after 9 monthly payments?
nicole has a board that is 88 in. long. She nees to cut it to fit a space 80 3/8 in. long. how much should she cut off the board
jocelyn estimates that a piece of wood measures 5.5 cm. If it actually measures 5.62 cm, what is the percent error of Jocelyn’s estimate?
The distance between Rosa’s house and her school is 3/4 mile. She ran 1/4 mile.What fraction of the way to school did she run?
Samuel needs $29 to download some songs and movies on his MP3 player. His mother agrees to pay him $6 an hour for raking leaves in addition to his $5 weekly allowance. What is the minimum number of hours Samuel must work in one week?
Trent is fishing from a pier. ●The tip of his fishing rod is 53 ¾ feet above the surface of the water. ●The hook on the end of the fishing line is directly below the tip of the fishing rod 12 ⅔ feet below the surface of the water. Trent estimates that the distance between the tip of his fishing rod and the hook is less than 65 feet. Is Trent’s estimate reasonable? Explain your answer. HELP Please
800 hm = _____ cm
8
0.08
8,000,000
80,000
Answer:
Exactly what they said (the answer is i bold at the bottom)
Step-by-step explanation:
I need help with my assignments on these two questions
a. Using properties of exponents, the value of the expression is 10⁰
b. The equation has no solution
What are properties of exponents?a. Properties of exponents are mathematical rules that allow us to simplify and manipulate expressions involving exponents. These properties help us perform operations such as multiplication, division, and raising to a power more efficiently.
In the given problem, we have to solve and simplify using properties of exponents.
Given that; [tex]\frac{10^-^3}{10^-^3}[/tex];
we can apply quotient rule when dividing exponents here;
[tex]\frac{10^-^3}{10^-^3} = 10^-^3 ^+^3 = 10^0[/tex]
The answer is 10⁰
b. To simply the equation, we just need to use basic mathematical operation to find the value of x.
3x - 2x + 4 = 5x - 4x - 8
Simplify;
x + 4 = x - 8
Collect like terms
x - x = -8 - 4
0 = -12
No solution
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HELP WILL MARK BRAINLIEST!!!!!!!!!!!Cindy has to write an 18-page report. If she has written 1/3 of a report so far, how many pages has she written?
A. 4 pages
B. 6 pages
C. 8 pages
D. 9 pages
Prove it is rational by writing it as a quotient of two integers. Please answer these problems, I need to check my answers. Ignore the blank ones, I was able to check them. Thank you!
1. 2.4
2. 74
3. 17.3333333…
4. π
5.
6. –18
7.
8. 87.125
9. –30
10. –8.3
11. 58.25
12. 121
13. 4.5
14.
The top of the Washington Monument is a triangular pyramid with a triangle base. Each triangular face is 58 feet tall and 34 feet wide and covered with white marble. About how many square feet of marble cover the faces of the pyramid?
Answer:
[tex]3,944ft^{2}[/tex] of marble is needed.
Step-by-step explanation:
The picture below represents the top of the Washington Monument, with 4 triangles, one on the base and the other 3 forming the monument.
First of all whe have to find the area of one pyramid:
[tex]A=\frac{height*width}{2}[/tex]
Replacing the values, we have:
[tex]A=\frac{58ft*34ft}{2}[/tex]
[tex]A=986ft^{2}[/tex]
As we have 4 triangles forming the top of the Monument, we have to multiply by 4 to find the quantity of marble to use:
Quantity of marble=Area of each triangle * quantity of triangles
Quantity of marble=[tex]986ft^{2}*4[/tex]
Quantity of marble=[tex]3,944ft^{2}[/tex]
To find the area of marble covering the Washington Monument's pyramid faces, calculate the area of one triangular face (985 square feet) and then multiply by 3, resulting in approximately 2955 square feet.
The Washington Monument's pyramid at the top has triangular faces that are covered with white marble. Each face is 58 feet tall and 34 feet wide. To find the total area covered by marble, we need to calculate the area of one triangular face and then multiply by the number of faces.
Calculate the area of one triangular face using the formula for the area of a triangle: Area = 1/2 * base * height.Substitute the given measurements: Area = 1/2 * 34 feet * 58 feet = 985 square feet.Each triangular pyramid has three faces. So, multiply the area of one face by 3: Total Area = 3 * 985 square feet = 2955 square feet.Therefore, approximately 2955 square feet of marble cover the faces of the pyramid.
what is the circumference of a circle with a diameter of of 8.4 cm?
What value of k makes the equation true?
a.2
b.3
c.4
d.8
Its C. 4
Correct on edge :D
Help! How do i find a solution set? (I have a texas ti graphing calculator if that helps) An example is
(x - a)(x + b) = 0
How would I find the solution set for this?
Please explain to me in an easy to understand, step by step way.
If you know how to use a texas TI calculator, you can also explain to me how to do it on the calculator, but that is not required
Answer:
The solution set is given by {a, -b}.
Step-by-step explanation:
We have the equation,
[tex](x - a)(x + b) = 0[/tex]
Equating the factors to 0 gives,
[tex](x - a)=0[/tex] and [tex](x + b)=0[/tex]
i.e. x = a and x = -b
So, the solutions of the equation [tex](x - a)(x + b) = 0[/tex] are x= a and x= -b.
Thus, the solution set is given by {a, -b}.
find two consecutive odd integers such that 36 more than the lesser is three times the greater
Final answer:
To find two consecutive odd integers such that 36 more than the lesser is three times the greater, set up an equation and solve for the variable x. The two consecutive odd integers are 15 and 17.
Explanation:
To find two consecutive odd integers such that 36 more than the lesser is three times the greater, we can set up an equation:
x + 36 = 3(x + 2)
Simplifying this equation, we get:
x + 36 = 3x + 6
Subtracting x from both sides, we get:
36 = 2x + 6
Subtracting 6 from both sides, we get:
30 = 2x
Dividing both sides by 2, we get:
15 = x
Therefore, the two consecutive odd integers are 15 and 17.