When the function f(x)=25[tex]x^2[/tex]−2 is vertically stretched by a factor of 2 to create the function g(x), the resulting equation is g(x) = 50[tex]x^2[/tex]−4.
Explanation:The equation of g(x) can be found by vertically stretching f(x) by a factor of 2. Since f(x) = 25[tex]x^2[/tex] - 2, we can multiply the function by 2 to get g(x) the equation:
The function g(x) is described as a vertical stretch of the function f(x) by a factor of 2. If f(x)=25[tex]x^2[/tex]−2, a vertical stretch implies that we multiply all y-coordinates by the given factor, which is 2 in this case. Therefore, g(x) will be 2*f(x).
This gives us:
g(x) = 2*(25[tex]x^2[/tex] −2)
Expand this:
g(x) = 50[tex]x^2[/tex]−4
So, the equation of g(x) after the vertical stretch of f(x) by a factor of 2 is g(x) = 50[tex]x^2[/tex] −4.
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The equation of g(x), which is a vertical stretch of f(x) = 25x² - 2 by a factor of 2, is g(x) = 50x² - 4.
To solve this, we need to apply a vertical stretch to the function f(x).
A vertical stretch by a factor of 2 means multiplying the entire function f(x) by 2.
Given :
f(x) = 25x² - 2
we multiply it by 2:
g(x) = 2 * (25x² - 2)
g(x) = 50x² - 4
So, the equation of g(x) is g(x) = 50x² - 4.
IF Mary had 500.004 in the bank and earns an annual interest rate of 2%, how much will she earn in one year?
Two consecutive odd numbers are such that seven times the smaller, subtracted from nine times the bigger, gives 144. Find the numbers.
The smaller odd number is 63, and the next consecutive odd number is 65.
To find the consecutive odd numbers, an algebraic equation is set up and solved, yielding the smaller odd number as 63 and the next consecutive odd number as 65.
To find two consecutive odd numbers meeting the stipulated condition, we will set up an algebraic equation. Let the smaller odd number be represented by n, then the next consecutive odd number is n + 2. The given condition is that seven times the smaller odd number subtracted from nine times the bigger odd number equals 144. This can be expressed as the equation 9(n + 2) - 7n = 144.
Solving the equation:
Expand the equation: 9n + 18 - 7n = 144Combine like terms: 2n + 18 = 144Subtract 18 from both sides: 2n = 126Divide both sides by 2: n = 63Therefore, the smaller odd number is 63, and the next consecutive odd number is 65.
Let f(x)=81+3e−0.7x .
What is the value of f(−3) ?
Round the answer to the nearest hundredth.
Answer:
[tex]f(-3)=91.25[/tex]
Step-by-step explanation:
Given :f(x)=81+3e−0.7x
To Find: Value of f(−3)
Solution:
[tex]f(x)=81+3e−0.7x[/tex]
Putting x = -3
[tex]f(-3)=81+3e−0.7*(-3)[/tex]
[tex]f(-3)=81+3e+2.1[/tex]
[tex]f(-3)=83.1+3e[/tex]
Since the defined value of e = 2.718
⇒[tex]f(-3)=83.1+3*(2.718)[/tex]
⇒[tex]f(-3)=83.1+8.154[/tex]
⇒[tex]f(-3)=91.25[/tex]
Thus the value of [tex]f(-3)=91.25[/tex]
Answer:
5.85
Step-by-step explanation:
what are alternate interior angles??
Sam owns a small business. There was a loss of $16 on Thursday and a loss of $9 on Friday. On Saturday there was a loss of $5, and on Sunday there was a profit of $27. Find the total profit or loss for the 4 days.
The table shows the membership of two scout troops.
a. What is the percent of change in membership from 2010 to 2011 for Troop A? Round to the nearest tenth of a percent, if necessary.
b. What is the percent of change in membership from 2010 to 2011 for Troop B? Round to the nearest tenth of a percent, if necessary.
c. Which troop has the better record in terms of the number of new members?
d. Which troop has the better record in terms of the percent of change in membership?
Answer:
a. What is the percent of change in membership from 2010 to 2011 for Troop A?
[tex]\frac{16-14}{14}*100[/tex] = 14.28%
b. What is the percent of change in membership from 2010 to 2011 for Troop B?
[tex]\frac{24-21}{21}*100[/tex] = 14.28%
c. Which troop has the better record in terms of the number of new members?
Troop B.
d. Which troop has the better record in terms of the percent of change in membership?
Both have the same percentage change.
Consider a 15-year mortgage at an interest rate of 8% compounded monthly. The amount to be mortgaged is $130,000. After the first month's payment, what is the new outstanding principal?
To find the new outstanding principal after the first month's payment on a 15-year mortgage at an 8% interest rate compounded monthly, we calculate the monthly interest and subtract it from the original principal.
Explanation:To find the new outstanding principal after the first month's payment, we need to calculate the monthly interest and subtract it from the original principal. Here are the steps:
Convert the annual interest rate to a monthly rate by dividing it by 12: 8% / 12 = 0.67%.Convert the mortgage amount to a decimal: $130,000Calculate the interest for one month: $130,000 × 0.67% = $871.67Subtract the interest from the original principal: $130,000 - $871.67 = $129,128.33Therefore, the new outstanding principal after the first month's payment is $129,128.33.
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classify the scatter plot as having a negative or no correlation. HOMEWORK DUE TOMORROW
4/7x = 64
Answer for x
x = 112
This is because
4/7x = 647/4 x 4/7 = 64/1 x 7/4
1x= 448/4
x = 1124w^3−8w+12
factor the polynomial
5t^2+20t+50
factor the polynomial
Lines a and b are parallel. What is the measure of angle b? Enter your answer in the box. b = ∘ Two horizontal lines the top line labeled a and the bottom labeled b with an angled line intersecting both making eight angles, top right angle labeled seventy nine degrees and the bottom right angle labeled X degrees
Answer:
It's 79 I took the test
Stay Alive ~ T∅P I-/
Step-by-step explanation:
Answer:
The measure of [tex]m{\angle}b[/tex] is [tex]79^{\circ}[/tex].
Step-by-step explanation:
Given: Lines a and b are parallel to each other.
To find: The measure of the angle b.
Solution: It is given that Lines a and b are parallel to each other, thus using the parallel lines properties, we have
[tex]m{\angle}a=79^{\circ}[/tex] (Vertically opposite angles)
Now, [tex]m{\angle}a[/tex] and [tex]m{\angle}b[/tex] forms the corresponding angle pair, thus they are congruent.
Hence, [tex]m{\angle}a[/tex]=[tex]m{\angle}b[/tex]=[tex]79^{\circ}[/tex].
Therefore, the measure of [tex]m{\angle}b[/tex] is [tex]79^{\circ}[/tex].
Use a strategy to solve this problem. (Note: I seriously need help and this is due on Sunday!!)
Ian is given some red licorice that is wrapped in a coil. Upon flattening the licorice, Ian discovers that the total length is 60 cm. He then cuts the licorice into two pieces so that the ratio of the lengths of the two pieces is 7:3. Each piece is then bent to form a square. What is the total area of the two squares?
can someone help me with this
Find the product of (3x + 7y)2. 9x2 − 42xy + 49y2 9x2 − 49y2 9x2 + 49y2 9x2 + 42xy + 49y2
Answer:
[tex]9x^{2}+42xy+49y^{2}[/tex]
Step-by-step explanation:
we know that
[tex](a+b)^{2}=a^{2}+2ab+b^{2}[/tex]
In this problem we have
[tex](3x+7y)^{2}[/tex]
so
[tex]a=3x[/tex]
[tex]b=7y[/tex]
substitute
[tex](3x+7y)^{2}=(3x)^{2}+2(3x)(7y)+(7y)^{2}[/tex]
[tex]=9x^{2}+42xy+49y^{2}[/tex]
which of the following sets of numbers will form a right triangle A. 12,13,14 B. 15,16,18 C. 5,6,9 D.5,12,13
The equation d=60t gives the distance d (in miles) a car travels after t hours. Identify the independent and dependent variables.
The required d is the dependent variable and t is the independent variable.
What is equation?In mathematics, an equation is a statement that asserts the equality of two expressions. It typically contains one or more variables, which represent unknown values.
In the equation, d=60t, t is the independent variable and d is the dependent variable. The value of d depends on the value of t, which is the amount of time the car travels, and hence is the independent variable.
Thus, d is the dependent variable and t is the independent variable.
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find the area of the trapezoid with a base of 19 inches, height 12.6 inches and base 29.2 inches
a line inintersects at triangle at least once, but not at any of its vertices. What is the maximum number of sides that a line can intersect a triangle? similarly, a square? a convex quadrilateral? A quadrilateral , in general?
convert 35/8 to a decimal using long division
Barry’s mountain bike weighs 6 pounds more than andy’s. Their bike weigh 42 pound together . Write an equation that represent the sum of weigh altogether.
please help me
The perimeter of a rectangle is 141 feet, and the length is twice the width. What are the dimensions of the rectangle?
What's the width of the rectangle and what's the length?
To find the width and length of the rectangle, we used the perimeter formula and the given relationship between length and width. The width of the rectangle is 23.5 feet and the length is 47 feet, which are found by dividing the perimeter by the sum of the multipliers of width and then multiplying the width by 2 to find the length.
Explanation:The student asked for help with finding the dimensions of a rectangle given its perimeter and a relationship between its length and width. To find the dimensions of the rectangle, we can use algebra.
Firstly, we know the formula for the perimeter (P) of a rectangle is P = 2l + 2w, where l is the length and w is the width. Since we are given that the perimeter is 141 feet and the length is twice the width (l = 2w), we can set up the following equation:
141 = 2(2w) + 2w
Simplifying the equation, we get:
141 = 4w + 2w
141 = 6w
w = 141 / 6
w = 23.5 feet
Since the length is twice the width, the length (l) is:
l = 2 × 23.5 feet
l = 47 feet
Therefore, the dimensions of the rectangle are a width of 23.5 feet and a length of 47 feet.
Order the sides or angles of the triangle from least to greatest
Which expressions are equivalent to 3(x + 3y + 2x − y )?
3(3x + 2y) and 9x + 6y
3(3x + 4y) and 9x + 12y
3(x + 4y) and 3x + 12y
3(x + 2y) and 3x + 6y
HELP ASAP
Hello,
The correct answer is A) 3(3x + 2y) and 9x + 6y
Hope this helps!!!! (:
the diagram shows the shape of the green of a miniature golf hole. what is the area of the green?
The area of green of golf course can be found by summing the area of pieces like that given rectangles and triangles.
The resultant area of the green of the golf course is given by:
100 sq. feet
Composing the area:You have to calculate the area of those smaller pieces to find the total area of the green of the golf course.
Total area = sum of area of trapezoid and parallelogram.The trapezoid in left of figure has height of 4 feet and parallel sides of 8 feet and 12 feet respectively.
Thus:
Area of trapezoid = [tex]\dfrac{1}{2}.\text{sum of parallel sides} \times height[/tex]
Area of trapezoid = [tex]\dfrac{1}{2}.4.(12+8) = 40 \: \rm feet^2[/tex]
The parallelogram on left has height 4 feet and base is of 15 feet.
Thus:
Area of parallelogram = [tex]\text{base} \times \text{height}[/tex] = [tex]4 \times 15 = 60 \: \rm feet^2[/tex]
Thus,
Total area = 40 + 60 = 100 sq. feet.
The resultant area of the green of the golf course is given by:
100 sq. feet
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Expand. Your answer should be a polynomial in standard form. 3h(−h 2 +2h−1)
Answer: -18h^2+85h-18
Step-by-step explanation:
Members at a yoda school pay $11 per class plus a one-time $96 membership fee. Non members pay $14 per class. How many classes would a member have to take to save money compared to taking classes as a non-member?
2. Jamie is the starting pitcher for his baseball team. The coach recorded the number of pitches he threw in one game. Each pitch is either a ball, strike or hit. The coach recorded that 54 pitches, or 60%, were strikes. What is the total number of pitches that Jaime threw in this game?
Answer:
90
Step-by-step explanation:
:)
Shaquira is baking cookies to put in packages for a fundraiser. Shaquira has made
86 chocolate chip cookies and
42 sugar cookies.
Shaquira wants to create identical packages of cookies to sell, and she must use all of the cookies.
What is the greatest number of identical packages that Shaquira can make?
Answer:
2
Step-by-step explanation:
To be able to find the greatest number of identical packages that Shaquira will be able to make, we first need to find the prime factors of the Chocolate Chip Cookies and Sugar Cookies.
86 Chocolate Chip Cookies
42 Sugar Cookies
Let's take the 86 Chocolate Chip Cookies first.
[tex]86 \left \{ {{2} \atop {43}} \right.[/tex] or 86 = 2 x 43
Now let's take the Sugar Cookies.
[tex]42 \left \{ {{2} \atop {21\left \{ {{3} \atop {7}} \right. }} \right.[/tex] or
42 = 2 x 3 x 7
Now that we have the prime factors, we then look for the Greatest Common Factor between the sets of prime factors.
2 x 3 x 7 = 42
2 x 43 = 86
2 = Total number of identical packages.
Answer:
2
Step-by-step explanation:
does the orders pair (2,14) lie on the graph of y=12x?
If a scientist knows the relative age of a fossil, he can also know A. the type of climate from which it came. B. the relative age of the rock where it was found. C. how it became extinct. D. how long the organism was alive.
its science but it made me pick math
Answer:
the relative age of the rock where it was found.
Explanation:
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