Find the vertex of this parabola:
y = -4x2 + 8x - 13
Answer:
Below in bold.
Step-by-step explanation:
y = -4x2 + 8x - 13
Divide first 2 terms by -4:-
y = -4(x^2 - 2x) - 13
Convert to vertex form by completing the square:
y = -4[(x - 1)^2 - 1] - 13
y = -4(x - 1)^2 + 4 - 13
y = -4(x - 1)^2 - 9 <---------- Vertex form
y = a(x - j)^2 + k <---------- General form with vertex = (j, k).
So comparing, we see that the vertex is (1, -9).
i will give you both my kidneys for this answer!!!! Select the correct answer.
Consider functions fand g.
f(x) = 3x+1.what is the value of (f(g(1))
Answer:
1
Step-by-step explanation:
when x is 1 g(1) is 0
so
(f(g(1)) is f(0)
f(0) is 3√0 + 1 which is
1
sorry it looks like its not one of the answer choices
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The composition of functions f ( g ( 1 ) ) = 1
What is Composition of functions?Evaluation of a function at the value of another function is known as Composition of function. A function composition is a process in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.
Given data ,
Let the first function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = 3√x + 1
Let the second function be represented as g ( x )
Now , the value of g ( x ) is
g ( 1 ) = 0
g ( 2 ) = 1
g ( 3 ) = 4
g ( 4 ) = 9
Now , the composition of function is given by f ( g ( 1 )
The value of g ( 1 ) = 0
And , f ( x ) = 3√x + 1
when x = 0
So , the value of f ( 0 ) = 3√0 + 1
The function is f ( 0 ) = 1
Hence , the value of the function f ( g ( 1 ) = 1
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Suppose a = 16 and b = 20. what is c
Allen was making trail mix, but he only wanted to make of the recipe. If the whole recipe called for of a cup of peanuts, how many cups will he need to make of the recipe? Choose the model that matches the situation.
It can be inferred that the amount of nuts that Allen requires depends on the amount of the recipe that he wants to make.
How many cups of nuts does Allen require to make the recipe?According to the information provided, one serving of the recipe calls for one cup of nuts. According to this, it can be inferred that to make a smaller or larger portion of the recipe, this amount must be divided or multiplied.
For example, if Allen calls for making two servings of the recipe, he would use two cups of nuts, while if he calls for making a half serving, he would use half a cup of nuts.
Note: The question is missing because there is some missing information. However I can answer it based on my general prior knowledge.
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Answer:
1/6
Step-by-step explanation:
A box, with rectangular sides, base and top is to have a volume of 2 cubic feet. It has a square base. Express the
surface area A of the box in terms of the width w of the base. If the material for the base and top costs 10 dollars/ft2
and that for the sides costs 20 dollars/ft express the total cost C as a function of the width.
The total surface area is 2w² + 8/w, while the total cost is $(20w² + 160/w)
What is volume?Volume is the amount of space occupied by a three dimensional shape or object.
Let w represent the width of the base and h represent the height. Hence:
w²h = 2
h = 2/w²
The surface area = 2w² + 4(hw) = 2w² + 4(2/w² * w) = 2w² + 8/w
The total cost = 2w² * $10 + (8/w) * $20 = $(20w² + 160/w)
The total surface area is 2w² + 8/w, while the total cost is $(20w² + 160/w)
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One of the legs of a right triangle measures 2 cm and the other leg measures 17 cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answer:
17.1
Step-by-step explanation
a^2+b^2=c^2
2^2 + 17^2 = c^2
4 + 289 = c^2
293 = c^2
square root of 293 or 17.1
In the figure below, triangle QRT, triangle RSQ, and triangle QST are scalene triangles.
If mQRS = 37° and mTQS = 34°, what is mTQR?
A.
87°
B.
90°
C.
93°
D.
109°
mTQR = 87°
HOPE IT HELPS...!!!
Answer:
[tex] \sf m \angle TQR = 87 \degree[/tex]
Step-by-step explanation:
Given:
∆QRT, ∆RSQ and ∆ QST are scalene traingle.
[tex]m \angle QRS = 37 \degree \\ m \angle TQS = 34 \degree \\ m \angle QST = 90 \degree[/tex]
To find:
[tex]m \angle TQR = ?[/tex]
Solution:
In ∆ QTS,
[tex] \sf \: m \angle TQS + m \angle QTS +m \angle QST = 180 \degree \: \\ \sf (properties \: of \: triangle)[/tex]
[tex] \sf \: 34 + m \angle QTS +90 = 180 \degree \: \\ \sf m \angle QTS = 180 - 90 - 34 \\ \sf \: m \angle QTS = 180 - 124 \\ \sf \: m \angle QTS = 56 \degree[/tex]
Now in ∆QTR,
[tex] \sf \: m \angle QTR + m \angle TQR + m \angle TRQ \: = 180 \degree \\ \sf (properties \: of \: triangle)[/tex]
[tex] \sf \: 56 + m \angle TQR + 37 \: = 180 \degree \\ \sf m \angle TQR = 180 - 56 - 37 \\ \sf m \angle TQR = 87 \degree[/tex]
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4) A circle has a circumference of 219.8 yd. What is the diameter of the circle?
a) 35 yd
b) 70 yd
c) 30 yd
Answer:
70
Step-by-step explanation:
Circumference = pi × diameter
219.8 = pi × diameter
219.8/pi = diameter
Diameter = 69.96....
= 70yd
Exercise: 6.68 'Cat Owners': According to the American Veterinary Medical Association, 30% of Americans own a cat. Find the probability that exactly 2 out of 8 randomly selected Americans own a cat. In a random sample of 8 Americans, find the probability that more than 3 own a cat.
Using the binomial distribution, it is found that there is a:
0.2965 = 29.65% probability that exactly 2 out of 8 randomly selected Americans own a cat.0.4482 = 44.82% probability that more than 3 own a cat.What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem, we have that:
30% of Americans own a cat, hence p = 0.3.A sample of 8 Americans is taken, hence n = 8.The probability that exactly 2 out of 8 randomly selected Americans own a cat is P(X = 2), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{8,2}.(0.3)^{2}.(0.7)^{6} = 0.2965[/tex]
0.2965 = 29.65% probability that exactly 2 out of 8 randomly selected Americans own a cat.
The probability that more than 3 own a cat is given by:
[tex]P(X > 3) = 1 - P(X \leq 2)[/tex]
In which:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
Hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{8,0}.(0.3)^{0}.(0.7)^{8} = 0.0576[/tex]
[tex]P(X = 1) = C_{8,1}.(0.3)^{1}.(0.7)^{7} = 0.1977[/tex]
[tex]P(X = 2) = C_{8,2}.(0.3)^{2}.(0.7)^{6} = 0.2965[/tex]
Then:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0576 + 0.1977 + 0.2965 = 0.5518[/tex]
[tex]P(X > 3) = 1 - P(X \leq 2) = 1 - 0.5518 = 0.4482[/tex]
0.4482 = 44.82% probability that more than 3 own a cat.
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3
Select all the correct answers.
Which three statements are true as they relate to supply and demand?
As supply rises, prices generally decrease.
o As demand decreases, costs generally increase.
As supply decreases, prices increase.
The average rate of change describes how much a quantity changes as price increases.
o As demand rises, the price of the product decreases.
Answer:
A, C, and D
Step-by-step explanation:
Let's analyze each option:
A) As supply rises, prices generally decrease. This is true as supply and demand have an inverse relationship. The supply curve has a positive slope, showing that as the quantity supplied increases, the price increases. So, shifting the curve to the right does decrease the equilibrium price (assuming the demand curve doesn't fluctuate).
B) As demand decreases, costs generally increase. This is false because a demand curve shows that as the quantity of demand increases, the price decreases for the product. So, shifting the curve to the left only decreases the equilibrium price (assuming the supply curve doesn't fluctuate).
C) As supply decreases, prices increase. This is true because the supply curve has a positive slope, showing that as the quantity supplied increases, the price increases. So, shifting the curve to the left does increase the equilibrium price (assuming the demand curve doesn't fluctuate).
D) The average rate of change describes how much a quantity changes as price increases. This is true because the supply curve measures how much the quantity supplied increases as the price increases, while the demand curve measures how much the quantity demanded increases as the price decreases.
E) As demand rises, the price of the product decreases. This is false because a demand curve shows that as the quantity of demand increases, the price decreases for the product. So, shifting the curve to the right only increases the equilibrium price (assuming the supply curve doesn't fluctuate).
I've attached an example graph to help you visualize all of these factors.
Gabrielle used 7 1/5 inches each of 6 different colors of embroidery floss to make one friendship bracelet. Each package of floss contains 12 feet. How many friendship bracelets can Gabrielle make if she has one package of each color?
The number of friendship bracelets Gabrielle can make is 20 bracelet
Conversion of feet to inches1 feet = 12 inches
12 feet = 144 inches
Number of colors of floss = 6
Quantity of each floss = 12 feet = 144 inches
Total quantity of floss = 6 × 144
= 864 inches
Quantity of each floss used for bracelet = 7 1/5 inches
Total floss used for each bracelet = 6 × 7 1/5
= 6 × 7.2
= 43.2 inches
Number of bracelet Gabrielle can make = Total quantity of floss ÷ Total floss used for each bracelet
= 864 ÷ 43.2
= 20 bracelet
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Jose bought a magazine for $10 and some erasers for $2 per eraser. He spent a total of $25. How many erasers did he buy? Answer using two step equations with X as the variable
Answer:
He bought 7 erasers take 10 dollars and keep adding 2
1. Raphael bought eight pens and nine erasers from a shop and paid GHC 33. His friend, Yao bought five similar pens and six erasers from the same shop and paid GHC 21. Calculate the price of the pen and the erasers respectively.
The price of the pen and the erasers Raphael and his friend bought are GHC 3 and GHC 1 respectively.
How to solve equation simultaneouslylet
x = price of pen
y = price of erasers
The equation
8x + 9y = 33
5x + 6y = 21
multiply (1) by 6 and (2) by 948x + 54y = 198
45x + 54y = 189
subtract to eliminate y48x - 45x = 198 - 189
3x = 9
x = 9/3
x = 3
substitute into (1)
8x + 9y = 33
8(3) + 9y = 33
24 + 9y = 33
9y = 33 - 24
9y = 9
y = 9/9
y = 1
How to solve simultaneous equation:
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Please write no more than two paragraphs. Assignment is worth 25 points We have been talking about variables and how they are measured. For this assignment, I have assigned a paper for you to study on the potential impacts of a paleolithic diet on cardiovascular markers in patients with diabetes.
The impact of a paleolithic diet on cardiovascular markers in patients with diabetes is that it increases the concentration of certain fats in the blood.
What is diabetes?It should be noted that diabetes simply means a condition when the blood glucose is too high.
In this case, the impact of a paleolithic diet on cardiovascular markers in patients with diabetes is that it increases the concentration of certain fats in the blood. It's simply a risk factor for heart diseases.
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The round temperature dial on a thermostat has a diameter of 26 millimeters. What is the dial's circumference?
C = 2 x pi x r = pi x d
so
C = 3,14 x 26 = 81,64 mm
I need help with number one and thank you for your help
Answer: B
Step-by-step explanation: The first X was 1. If you add 1 too the 1/2 in the equation, its 1 & 1/2. theres only one graph that has 1 & 1/2, and its B
A triangular window has an area 240 square feet and height 16 feet. What is its base?
Answer:
30 feet
Step-by-step explanation:
Area of a triangle = bh/2
A = bh/2
240 = b(16)/2
480 = (16)b
30 = b
Base = 30 feet
I hope this helps!
Answer:
30 ft
Step-by-step explanation:
Formula to find the area of a triangle is :
Area = [tex]\frac{1}{2}[/tex] × base × height
Given that,
Area of the triangle = 240 ft²
Height = 16 ft
Base = ??
Let us find now.
Area = [tex]\frac{1}{2}[/tex] × base × height
240 = = [tex]\frac{1}{2}[/tex] × b × 16
240 × 2 = 16b
480 = 16b
Divide both sides by 16.
30 ft ⇒ base
image Consider the graph of g(x) = x2 – 8x + 12. Identify the y-intercept, the vertex, and the zeros of the function.
Answer:
Below in bold.
Step-by-step explanation:
g(x) = x^2 – 8x + 12
Convert to vertex form:
g(x) = (x - 4)^2 - 16 + 12
g(x) = (x - 4)^2 - 4.
So the vertex is at (4, -4).
y-intercept (when x = 0) is ((0-4)^2 - 4 = 16 - 4
- that is (0, 12).
Zeros:
(x - 4)^2 - 4 = 0
(x - 4)^2 = 4
x - 4 = +/- 2
x = 2 + 4 = 6 or x = -2 + 4 = 2.
= 2, 6.
Select Statistical or Not statistical to classify each question.
How many sisters do you have?
How many inches are in 2 feet?
How many pets do you have?
Answer:
1: statistical
2: not statistical
3: statistical
Step-by-step explanation:
The first and third statements can be answered by many people.
How many sisters do you have?
- Not statistical
How many inches are in 2 feet?
- Not statistical
How many pets do you have?
- Not statistical
What are statistical data?Statistical data are numerical or categorical information that has been collected through a systematic process and analyzed using statistical methods.
These data can be used to describe, summarize, compare, and draw conclusions about a population or a sample.
We have,
How many sisters do you have?
- Not statistical
How many inches are in 2 feet?
- Not statistical
How many pets do you have?
- Not statistical
None of these questions involve collecting, analyzing, or interpreting data, which are key characteristics of statistical questions.
They are simply asking for a count or a conversion of units, and do not involve any variability or uncertainty.
Thus,
All the given questions are not statistical.
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how do you solve 7/8+(4/8-2/4)
Two companies provide home Internet services.
The first company charges a one-time fee of $55 for the equipment, plus $30 per month for the service.
The second company charges a one-time fee of $25 for the equipment, plus $45 per month for the service.
In how many months will the services of the two companies cost the same?
Answer:
2 months
Step-by-step explanation:
55+30x=25+45x
55-25=45x-30x
30=15x
x=2
What is 45% of 69/3???
Answer:
10.35
Step-by-step explanation:
69/3 = 23
45% of 23 = 10.35
A map of a highway has A scale of 2 inches= 27 miles. The length of the highway on the map is 9 inches. There are 7 rest stops equally spaced on the highway, including one at each end. You’re making a new map with a scale of 1 inch= 30 miles. How far apart are the rest stops on the new map?
Answer:
From what i've researched, your answer might be "5 miles apart." or possilby "25.7 miles apart."
Step-by-step explanation
Im sorry if none of these answers are correct.
It is a widely held belief that a typical piece of printer paper with a thickness of 0.1 mm can go through at most 7 folds. When folding a piece of paper in half, the number of layers doubles with each fold, which also doubles the thickness. Sylvia is testing this theory and employing a hydraulic press in order to ensure each fold is as tight as possible. If Sylvia is successful in folding the paper completely, determine the thickness of her piece of printer paper after being folded in half 7 times.
12.8mm
Step-by-step explanation:[tex]0.1\times2^7\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left\{2^7\right.=2\times2\times2\times2\times2\times2\times2\\ =0.1\times128\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =\left.\ 128\right\}\\ =12.8mm[/tex]
I hope this helps you
:)
Question 7 (3 points)
A right rectangular prism is shown. Find the surface area of this prism. Refer to your
STAAR 8th Grade Math Reference Sheet for the appropriate formula.
Answer:
196 square feet
Step-by-step explanation:
(learn it before u submit. im here to help not cheat;w;
-ur fellow classmate)
S=ph+2b
s=(p=l+l+w+w) (h)+ (2) (b=lxw)
s=(8+8+10+10) (1) + (2) (8x10)
s=( 36x1 )+ (2x80)
s= 36+160
s=196
God bless ya:)
The area of this prism is 196 square feet.
What is the area of the prism?The prism's area can be calculated by adding its lateral area to the base areas. The process of calculating these areas ends up being facilitated because the two bases of a prism are the same, therefore, it is enough to calculate the area of a base and multiply the result by 2
The formula for the area of the prism is given by:
[tex]S=ph+2b[/tex]
Where:
p=l+l+w+wb=lxwSo we have that:
[tex]s=(p=l+l+w+w) (h)+ (2) (b=lxw)\\s=(8+8+10+10) (1) + (2) (8*10)\\s=( 36*1 )+ (2*80)\\s= 36+160\\s=196[/tex]
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Three DVDs and four CDs cost $92. Two DVDs and three CDs cost
$65. Find the cost of each tape and CD.
Answer:
DVD: $16
CD: $11
Step-by-step explanation:
These two linear equations can represent the system of equations where x equals the cost of a DVD and y equals the cost of a CD:
3x+4y=92
2x+3y=65
When graphed, the solution is at (16,11).
Therefore, one DVD costs $16 and one CD costs $11.
I need help with this question can someone help??
Question is in photo :p
Answer:
The answer to this question is 0.6
Step-by-step explanation:
the quotient of the product of 32 and 15 and the difference of 17 and 9 as a numerical expression?
Answer:
(32×15)/(17 -9)
Step-by-step explanation:
The term "quotient" refers to the result of division. The term "product" refers to the result of multiplication. The term "difference" refers to the result of subtraction.
__
Here, we want the quotient of a product and a difference. This means the product will be divided by the difference. The product is the product of 32 and 15, so its value is (32×15). The difference is the difference of 17 and 9, so its value is (17 -9).
Then the desired numerical expression is ...
[tex]\boxed{\dfrac{32\times15}{17-9}}[/tex]
______
Additional comment
The result of evaluating this expression is ...
(32×15)/(17 -9) = 480/8 = 60
__
For quotients and differences, the order of the operands matters. Our convention is that "the quotient of A and B" means "A/B", and "the difference of A and B" means "A-B".
In general English usage (not specific to a formal math problem), the term "difference" often is used to mean "the positive difference." That is, the wording "the difference between 3 and 4" would generally refer to the value 1 (not -1).
How is the graph of log (x + 3) translated from the graph of log x?
shifted down 3 units
shifted left 3 units
shifted up 3 units
shifted right 3 units
shifted left 3 units
Graphed Below:
red line: log (x + 3)blue line: log (x)Emma made 3/4 of a pound of trail mix. If she puts 1/8 of a pound into each bag, how many bags can Emma fill?