Answers
Given the following equation:
[tex]y=(x-1)^2+2[/tex]We will sketch the graph and identify the axis of symmetry.
the given function is a quadratic function with a vertex at (1, 2)
the graph of the function will be as follows:
As shown, the graph of the function has an axis of symmetry at x = 1
So, the answer will be option 3) x = 1
Related Questions
A rectangular room is 1.5 times as long as it is wide, and its perimeter is 26 meters. Find the dimension of the room.The length is :The width is :
Answers
The rectangular room is 1.5times as long as it is wide and its perimeter is 26m. Let "x" represent the room's width, then the length of the room can be expressed as "1.5x"
The perimeter of a rectangle is equal to the sum of twice the width and twice the length following the formula:
[tex]P=2w+2l[/tex]We know that:
P=26m
w=x
l=1.5x
Then, replace the measurements on the formula:
[tex]\begin{gathered} 26=2x+2\cdot1.5x \\ 26=2x+3x \end{gathered}[/tex]From this expression, you can calculate x, first, add the like terms:
[tex]26=5x[/tex]Second, divide both sides by 5 to determine the value of x:
[tex]\begin{gathered} \frac{26}{5}=\frac{5x}{5} \\ 5.2=x \end{gathered}[/tex]The width is x= 5.2m
The length is 1.5x= 1.5*5.2= 7.8m
solve the following system of equations-5x-3y=-16-3x+2y=-21x=y=
Answers
-5x - 3y = -16
-3x + 2y = -21
Solving for y the first equation:
-5x + 16 = 3y
y = (-5/3)x + (16/3)
Using this value of y into the second equation:
-3x + 2(-5/3)x + 2(16/3) = -21
-3x - (10/3)x + 32/3 = -21
Multiplying all by 3:
-9x - 10x + 32 = -63
-19x = -63 - 32 = -95
x = 95/19
Using this value of x into the y we found with the first equation:
y = (-5/3)x + 16/3
y = (-5/3)(95/19) + 16/3 = -475/57+ 304/57 = -171/57
y = -171/57
x = -31/19 = -1.6315
y = -171/57 = -3
Answer:
x = -1.6315
y = -3
Find all solutions in[0, 2pi): 2sin(x) – sin (2x) = 0
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Based on the answer choices, replace the pair of given values and verify the equation, as follow:
For x = π/4, π/6
[tex]2\sin (\frac{\pi}{4})-\sin (\frac{2\pi}{4})=2\frac{\sqrt[]{2}}{2}-1\ne0[/tex]the previous result means that the given values of x are not solution. The answer must be equal to zero.
Next, for x = 0, π
[tex]\begin{gathered} 2\sin (\pi)-\sin (2\pi)=0-0=0 \\ 2\sin (0)-\sin (0)=0-0=0 \end{gathered}[/tex]For both values of x the question is verified.
The rest of the options include π/4 and π/3 as argument, you have already shown that these values of x are not solution.
Hence, the solutions for the given equation are x = 0 and π
A house has increased in value by 35% since it was purchased. If the current value is S432,000, what was the value when it was purchased?
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The value of the house when it was purchased = $32000
Explanation:The original percentage value = 100%
The current percentage value = 100% + 35% = 135%
Current value = $432000
Original value = x
[tex]\begin{gathered} The\text{ current value =}\frac{135}{100}\times The\text{ original value} \\ \\ 432000=1.35\times x \\ \\ x=\frac{432000}{1.35} \\ \\ x=$ 320000 $ \end{gathered}[/tex]The value of the house when it was purchased = $32000
A baby cows growth. About how many pounds does the baby cow gain each week?
Answers
Growth per week = 124 - 122 = 126 - 124 = 2
. = 2 pounds + 1 pound additional
. = 3
Then answer is
OPTION B) 3 pounds
Find an expression equivalent to the one shown below.913 x 9-6OA. 79OB.919OC. 97OD. 9-78
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Answer:
C. 9⁷
Explanation:
We will use the following property of the exponents:
[tex]x^a\times x^b=x^{a+b}[/tex]It means that when we have the same base, we can simplify the expression by adding the exponents. So, in this case, the equivalent expression is:
[tex]9^{13}\times9^{-6}=9^{13-6}=9^7[/tex]Therefore, the answer is C. 9⁷
A polynomial function is given.
Q(x) = −x2(x2 − 9)
(a) Describe the end behavior of the polynomial function.
End behavior: y → as x → ∞
y → as x → −∞
Answers
The end behavior of the polynomial is:
y → −∞ as x → ∞
y → −∞ as x → −∞
How is the end behavior?Here we have the polynomial:
Q(x) = -x²*(x² - 9)
Remember that polynomials with even degrees have the same behavior for the negative values of x than for the positive, in this case if we expand the polynomial we get:
Q(x) = -x⁴ + 9x²
The leading coefficient is negative, then the end behavior will tend to negative infinity in both ends, then we get:
y → −∞ as x → ∞
y → −∞ as x → −∞
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The length of a rectangular pool is 6 meters less than twice the width. If the pools perimeter is 84 meters, what is the width? A) Write Equation to model the problem (Use X to represent the width of the pool) B) Solve the equation to find the width of the pool (include the units)
Answers
I have a problem with the perimeter of a pool expressed in an unknown which corresponds to "x"
The first thing to do is to pose the corresponding equation, this corresponds to section A of the question
For the length, we have a representation of twice the width minus 6, i.e. 2x-6
For the width we simply have x
Remember that the sum of all the sides is equal to the perimeter which is 84, However, we must remember that in a rectangle we have 4 sides where there are two pairs of parallel sides, so we must multiply the length and width by 2
Now we can represent this as an equation
[tex]2(2x-6)+2x=84[/tex]This is the answer A
Now let's solve the equation for part B.
[tex]\begin{gathered} 2(2x-6)+2x=84 \\ 4x-12+2x=84 \\ 6x=84+12 \\ x=\frac{96}{6} \end{gathered}[/tex][tex]x=16[/tex]In conclusion, the width of the pool is 16
Use Vocabulary in Writing 9. Explain how you can find the product 4 X 2 and the product 8 X 2 Use at least 3 terms from the Word List in your explanation.
Answers
Okay, here we have this:
Date: t rates to determine the better buy? b. Stop and Shop: 6 packages of Oreos cost $15.00 Key Food: 5 packages of Oreos cost $13.25
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To determine the better buy you have to calculate how much one package costs in each shop.
1) 6 packages cost $15.00
If you use cross multiplication you can determine how much 1 package costs:
6 packs ______$15.00
1 pack _______$x
[tex]\begin{gathered} \frac{15.00}{6}=\frac{x}{1} \\ x=\frac{15}{6}=\frac{5}{2}=2.5 \end{gathered}[/tex]Each package costs $2.5
2) 5 packages cost $13.25
5packs_____$13.25
1 pack______$x
[tex]\begin{gathered} \frac{13.25}{5}=\frac{x}{1} \\ x=\frac{13.25}{5}=2.65 \end{gathered}[/tex]Each package costs $2.65
For the second purchase each package cost $0.15 more than in the first purchase.
Is best to buy the 6 packages at $15.00
Solve the equation.k²=47ks.(Round to the nearest tenth as needed. Use a comma to separate answers as needed.
Answers
The initial equation is:
[tex]k^2=47[/tex]Then, we can solve it calculating the square root on both sides:
[tex]\begin{gathered} \sqrt[]{k^2}=\sqrt[]{47} \\ k=6.9 \\ or \\ k=-6.9 \end{gathered}[/tex]Therefore, k is equal to 6.9 or equal to -6.9
Answer: k = 6.9 or k = -6.9
Write an expression to determine the surface area of a cube-shaped box, S A , in terms of its side length, s (in inches).
Answers
The cube consists of 6 equal faces thus the surface area of the cube in terms of its side length s is 6s².
What is a cube?A three-dimensional object with six equal square faces is called a cube. The cube's six square faces all have the same dimensions.
A cube is become by joining 6 squares such that the angle between any two adjacent lines should be 90 degrees.
A cube is a symmetric 3 dimension figure in which all sides must be the same.
The cube has six equal squares.
It is known that the surface area of a square = side²
Therefore, the surface area of the given cube is 6 side².
Given cube has side length = s
So,
Surface area = 6s²
Hence the cube consists of 6 equal faces thus the surface area of the cube in terms of its side length s is 6s².
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find the simple interest earned, to the nearest cent, for each principal interest rate, and time.
Answers
Answer:
$8.40
Explanation:
From the given statement:
Principal = $840
Time = 6 Months
Rate = 2%
Note that Time must be in Years, therefore:
Time = 6 Months = 6/12 = 0.5 Years
[tex]\begin{gathered} \text{Simple Interest }=P\times R\times T \\ =840\times2\%\times0.5 \\ =840\times0.02\times0.5 \\ =\$8.40 \end{gathered}[/tex]The simple interest earned is $8.40
Use the slope and y-intercept to graph the line whose equation is given. 2 y = -x + 5x+1
Answers
ok
y = -2/5 + 1
This is the graph
if [tex] \sqrt{ \times } [/tex]is equal to the coordinate of point D in the diagram above, then X is equal to:
Answers
11)
The number line is divided into 5 equal intervals. if the fourth segment is 7, then we would find the distance between each segment
The distance between the fourth segment and the first segment is 7 - - 1 = 8
Since we are considering the distance between segment 1 and segment 4, the distance between each segment would be
8/4 = 2
Thus,
point D = 7 + 2 = 9
If
[tex]\begin{gathered} \sqrt[]{x\text{ }}\text{ = D, then} \\ \sqrt[]{x}\text{ = 9} \\ \text{Squaring both sides of the equation, we have} \\ x=9^2 \\ x\text{ = 81} \end{gathered}[/tex]Option E is correct
Write an equation of the line that passes through (4, 3) and is parallel to the line defined by 5x-2y-3. Write the answer in slope-intercept form (if possible)
and in standard form (Ax+By-C) with smallest integer coefficients. Use the "Cannot be written" button, if applicable.
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The final answer to the question is highlighted in the box
Suppose that the distribution for total amounts spent by students vacationing for a week in Florida is normally distributed with a mean of 650 and a standard deviation of 120. Suppose you take a simple random sample (SRS) of 35 students from this distribution.
What is the probability that an SRS of 35 students will spend an average o between 600 and 700 dollars? Round to five decimal places
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The probability that an SRS of 35 students will spend an average o between 600 and 700 dollars is 98.61%
Given,
The mean of the normal distribution, μ = 650
Standard deviation of the distribution, σ = 120
n = 35
By using central limit theorem, standard deviation for SRS of n, δ = σ/√n = 120/√35
The z score = (x - μ) / σ
By using central limit theorem,
z score = (x - μ) / δ
Here,
We have to find the probability that an SRS of 35 students will spend an average o between 600 and 700 dollars:
(p value of z score of x = 700) - (p value of z score of x = 600)
z score of x = 700
z = (x - μ) / δ = (700 - 650) /( 120/√35) = (50 × √35) / 120 = 2.46
p value of z score 2.46 is 0.99305
z score of x = 600
z = (x - μ) / δ = (600 - 650) /( 120/√35) = (-50 × √35) / 120 = -2.46
p value of z score -2.46 is 0.0069469
Now,
0.99305 - 0.0069469 = 0.9861031 = 98.61%
That is, the probability that an SRS of 35 students will spend an average o between 600 and 700 dollars is 98.61%
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Finding an output of a function from its graphThe graph of a function fis shown below.Find f (0).543-2f(0) =I need help with this math problem.
Answers
Given:
Given a graph of the function.
Required:
To find the value of f(0), by using graph.
Explanation:
From the given graph
[tex]f(0)=-4[/tex]Final Answer:
[tex]f(0)=-4[/tex]need help. first correct answer gets brainliest plus 15 pts
Answers
We are given that lines V and 0 and lines C and E are parallel.
We are asked to prove that ∠15 and ∠3 are congruent (equal)
In the given figure, angles ∠3 and ∠7 are "corresponding angles" and they are equal.
[tex]\angle3=\angle7[/tex]In the given figure, angles ∠7 and ∠6 are "Vertically opposite angles" and they are equal.
[tex]\angle7=\angle6[/tex]Angles ∠6 and ∠14 are "corresponding angles" and they are equal.
[tex]\angle6=\angle14[/tex]Angles ∠14 and ∠15 are "Vertically opposite angles" and they are equal.
[tex]\angle14=\angle15[/tex]Therefore, the angles ∠15 and ∠3 are equal.
[tex]\angle3=\angle7=\angle6=\angle14=\angle15[/tex]Josslyn placed $4,400 in a savings account which earns 3.2% interest, compounded annually. How much will she have in the account after 12 years?Round your answer to the nearest dollar.
Answers
The equation for the total amount after compounded interest is as follows:
[tex]A=P(1+\frac{r}{n})^{nt}^{}[/tex]Where A is the final amount, P is the initial amount, r is the annual interest, n is how many times per year the interest is compounded and t is the time in years.
Since the interest is compounded annually, it is compounded only once per year, so
[tex]n=1[/tex]The other values are:
[tex]\begin{gathered} P=4400 \\ r=3.2\%=0.032 \\ t=12 \end{gathered}[/tex]So, substituteing these into the equation, we have:
[tex]\begin{gathered} A=4400(1+\frac{0.032}{1})^{1\cdot12} \\ A=4400(1+0.032)^{12} \\ A=4400(1.032)^{12} \\ A=4400\cdot1.4593\ldots \\ A=6421.0942\ldots\approx6421 \end{gathered}[/tex]So, she will have approximately $6421.
School: Practice & Problem Solving 7.1.PS-18 Question Help A rectangle and a parallelogram have the same base and the same height. How are their areas related? Provide an example to justify your answer The areas equal. A rectangle has dimensions 5 m by 7 m, so its area is m² A parallelogram with a base of 5 m and a height of 7 m has an area of (Type whole numbers.)
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The image shown below shows the relationship between areas of rectangle and parallelogram
It can be seen that the areas are equal when they have the same sides or dimension
A rectangle has dimensions 5 m by 7 m, so its area is 5m x 7m = 35m²
A parallelogram with a base of 5 m and a height of 7 m has an area of 5m x 7m = 35m²
A game fair requires that you draw a queen from a deck of 52 ards to win. The cards are put back into the deck after each draw, and the deck is shuffled. That is the probability that it takes you less than four turns to win?
Answers
The probability (P) is winning in less than four turns can be decomposed as the following sum:
The probability of winning in one turn is
[tex]P(\text{Winning in turn 1})=\frac{\#Queens}{\#Cards}=\frac{4}{52}.[/tex]The probability of winning in the second turn is
[tex]\begin{gathered} P(\text{ Winning in the second turn})=P(\text{ Lossing (in turn 1)})\cdot P(\text{ Winning (in turn 2)}), \\ \\ P(\text{ Winning in the second turn})=\frac{\#NoQueens}{\#Cards}\cdot\frac{\#Queens}{\#Cards}, \\ \\ P(\text{ Winning in the second turn})=\frac{48}{52}\cdot\frac{4}{52}\text{.} \end{gathered}[/tex]The probability of winning in the third turn is
[tex]\begin{gathered} P(\text{ Winning in the third turn})=P(\text{ Lossing (in turn 1)})\cdot P(\text{ Lossing (in turn 2)})\cdot P(\text{ winning (in turn 3)}), \\ \\ P(\text{ Winning in the third turn})=\frac{\#NoQueens}{\#Cards}\cdot\frac{\#NoQueens}{\#Cards}\cdot\frac{\#Queens}{\#Cards}, \\ \\ P(\text{ Winning in the third turn})=\frac{48}{52}\cdot\frac{48}{52}\cdot\frac{4}{52}\text{.} \end{gathered}[/tex]Adding all together, we get
[tex]\begin{gathered} P(\text{ Winning in less than four turns})=\frac{4}{52}+\frac{48}{52}\cdot\frac{4}{52}+\frac{48}{52}\cdot\frac{48}{52}\cdot\frac{4}{52}, \\ \\ P(\text{ Winning in less than four turns})=\frac{469}{2197}, \\ \\ P(\text{ Winning in less than four turns})\approx0.2135, \\ \\ P(\text{ Winning in less than four turns})\approx21.35\% \end{gathered}[/tex]AnswerThe probability of winning in less than four turns is (approximately) 21.35%.
do you think you'd be able to help me with this
Answers
x = wz/y
Explanation:[tex]\frac{w}{x}=\frac{y}{z}[/tex]To solve for x, first we need to cross multiply:
[tex]w\times z\text{ = x }\times y[/tex]Now we make x the subject of the formula:
[tex]\begin{gathered} To\text{ make x stand alone, we n}ed\text{ to remove any other variable around x} \\ \text{divide both sides by y}\colon \\ \frac{w\times z}{y}\text{ =}\frac{\text{ x }\times y}{y} \end{gathered}[/tex][tex]x\text{ = }\frac{wz}{y}[/tex]Find the coordinates of the other endpoint of a segment with the given endpoint and Midpoint M.T(-8,-1)M(0,3)
Answers
If we have 2 endpoints (x1, y1) and (x2, y2), the coordinates of the midpoint will be:
[tex]\begin{gathered} x=\frac{x_1+x_2}{2} \\ y=\frac{y_1+y_2}{2} \end{gathered}[/tex]Now, we know the coordinates of one endpoint (x1, y1) equal to (-8, -1) and the midpoint (x, y) equal to (0,3), so we can replace those values and solve for x2 and y2.
Then, for the x-coordinate, we get:
[tex]\begin{gathered} 0=\frac{-8+x_2}{2} \\ 0\cdot2=-8+x_2 \\ 0=-8+x_2 \\ 0+8=-8+x_2+8 \\ 8=x_2 \end{gathered}[/tex]At the same way, for the y-coordinate, we get:
[tex]\begin{gathered} 3=\frac{-1+y_2}{2} \\ 3\cdot2=-1+y_2 \\ 6=-1+y_2 \\ 6+1=-1+y_2+1 \\ 7=y_2 \end{gathered}[/tex]Therefore, the coordinates of the other endpoint are (8, 7)
Answer: (8, 7)
A stock is worth $28,775 and drops 33% in one day. What percent does the stock have to grow the next day to get back to $28,775
Answers
ANSWER:
49.254%
STEP-BY-STEP EXPLANATION:
The first thing is to calculate the value after it has drops by 33%, like this:
[tex]\begin{gathered} 28775-28775\cdot33\% \\ \\ 28775-28775\cdot0.33 \\ \\ 28775-9495.75=19279.25 \end{gathered}[/tex]Now, we calculate what should grow by the following equation:
[tex]\begin{gathered} 19279.25+19279.25\cdot \:x=28775\: \\ \\ x=\frac{28775\:-19279.25}{19279.25} \\ \\ x=\frac{9495.75}{19279.25} \\ \\ x=0.49254\cong49.254\% \end{gathered}[/tex]The percent that should grow is 49.254%
2. What is the greatestcommon factor of12. 18, and 36?
Answers
The Solution:
Given the numbers below:
12, 18 and 36.
We are asked to find the greatest common factor of the above numbers.
Note:
Greatest Common Factor means Highest Common Factor (HCF).
Recall:
The Greatest common factor of 12, 18 and 36 is the highest number that can divide 12, 18 and 36 without any remainder.
Thus, the correct answer is 6.
(Algebra 1 Equivalent equations)
In a family, the middle child is 5 years older than the youngest child.
Tyler thinks the relationship between the ages of the ages of the children can be described with 2m-2y=10, where m is the age of the middle child and y is the age of the youngest.
Explain why Tyler is right.
Answers
Let the middle child is m and youngest is y.
The middle child is 5 years older than the youngest child, it can be shown as:
m - y = 5Tyler's equation is equivalent to ours since it can be obtained by multiplying both sides of our equation by 2:
2(m - y) = 2*52m - 2y = 10 ⇔ m - y = 5So Tyler is right.
69=2g-24 I NEED TO FIND G
Answers
Add 24 to 69 to get 93. Then divide 93 by 2 to get G
Which inequality is equivalent to this one?y-83-2O y-8+82-2-8O y 8+82-248o y 8+22-248o Y8+ 25-242
Answers
Given the inequality:
[tex]y-8\le-2[/tex]If we add 2 on both sides, the inequality remains the same and we get:
[tex]y-8+2\le-2+2[/tex]The cost to mail a package is 5.00. Noah has postcard stamps that are worth 0.34 and first-class stamps that are worth 0.49 each. An equation that represents this is 0.49f + 0.34p = 5.00Solve for f and p.If Noah puts 7 first-class stamps, how many postcard stamps will he need?
Answers
ANSWER
[tex]\begin{gathered} f=\frac{5.00-0.34p}{0.49} \\ p=\frac{5.00-0.49f}{0.34} \\ p=4.618\approx5\text{ postcard stamps} \end{gathered}[/tex]EXPLANATION
The equation that represents the situation is:
[tex]0.49f+0.34p=5.00[/tex]To solve for f, make f the subject of the formula from the equation:
[tex]\begin{gathered} 0.49f=5.00-0.34p \\ \Rightarrow f=\frac{5.00-0.34p}{0.49} \end{gathered}[/tex]To solve for p, make p the subject of the formula from the equation:
[tex]\begin{gathered} 0.34p=5.00-0.49f \\ \Rightarrow p=\frac{5.00-0.49f}{0.34} \end{gathered}[/tex]To find how many postcard stamps Noah will need if he puts 7 first-class stamps, solve for p when f is equal to 7.
That is:
[tex]\begin{gathered} p=\frac{5.00-(0.49\cdot7)}{0.34} \\ p=\frac{5.00-3.43}{0.34}=\frac{1.57}{0.34} \\ p=4.618\approx5\text{ postcard stamps} \end{gathered}[/tex]