We conclude that the image after the dilation is:
y = -6 + (21/8)*x
How to write the dilation?For a function y = f(x), a dilation of scale factor k is written as:
g(x) = k*f(x)
In this case, our function is given by:
-7x + 8y = -16
Solving for y we get:
y = (-16/8) + (7/8)*x
y = -2 + (7/8)*x
Now we apply a scale factor k = 3, so we get the dilated line:
y = 3*( -2 + (7/8)*x) = -6 + (21/8)*x
So we conclude that the image after the dilation is:
y = -6 + (21/8)*x
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A semi-circle sits on top of a rectangle to form the figure below. Find its area and perimeter. Use 3.14 for pi , and round your answer to the nearest tenth.
The area and the perimeter of the figure will be 38.13 in² and 23.42 inches respectively.
How to calculate the area?The area will be:
= Area of semi circle + Area of rectangle
= (1/2 × 3.14 × 3²) + (6 × 4)
= 14.13 + 24
= 38.13 inches²
The perimeter will be:
= (3.14 × 3) + (4 + 6 + 4 + 9.42)
= 23.42 inches
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27 Which describes how the data for word 2 should be plotted on a coordinate grid? From the origin, go 2 units to the right and 9 units up. From the origin, go 2 units to the right and 12 units up. From the origin, go 9 units to the right and 12 units up. From the origin, go 12 units to the right and 9 units up.
The statement which describes how the data should be plotted on a coordinate grid is: C. from the origin, go 9 units to the right and 12 units up.
What is a coordinate grid?A coordinate grid can be defined as a two-dimensional plane which comprises a horizontal line (x-axis) and a vertical line (y-axis) that are perpendicular to one another.
For this coordinate grid, the number of letters in the data for word 2 should be plotted on the x-axis and the percentage of students who spelled the word correctly on the y-axis.
Based on the table, the number of letters for word 2 is equal to 9 while the percentage of students who spelt it correctly is 12.
In conclusion, to plot the data on a coordinate grid, from the origin, go 9 units to the right and 12 units up.
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Complete Question:
The table of values below shows data for a five-word spelling test. Number of Letters vs. Percentage who Spelled Correctly Word Number of letters in the word Percentage of students who spelled the word correctly. Which describes how the data for word 2 should be plotted on a coordinate grid?
Find the remainder when x4 - 5x3 + x2 - 10x - 5 is divided by x + 3.
Use the remainder theorem: we can decompose the given polynomial in terms of quotient and remainder polynomials [tex]q(x)[/tex] and [tex]r(x)[/tex], respectively, such that
[tex]x^4 - 5x^3 + x^2 - 10x - 5 = (x + 3) q(x) + r(x)[/tex]
Then letting x = -3 makes the quotient term vanish, and we're left with a remainder of
[tex]r(-3) = (-3)^4 - 5\times(-3)^4 + (-3)^2 - 10\times(-3) - 5 = \boxed{250}[/tex]
Fill in the blank (check all that apply).
2y and ____ are like terms.
Answer:
y,3y,4y,5y,6y,7y,8y,9y,10y ----------
Step-by-step explanation:
because if the variable is similar with y it is like term of 2y
Answer:
y,3y,4y,5y,6y,7y,8y,9y,10y ----------
Step-by-step explanation:
because if the variable is similar with y it is like term of 2y
3. Find the measures of the angles in the figure.
Answer:
60° , 60° , 120° , 120°Step-by-step explanation:
NOTE :
the sum of the 4 interior angles of a quadrilateral is 360°.
…………………………………………
Then
h + h + 2h + 2h = 360
Then
6h = 360
Then
h = 360 ÷ 6 = 60
Then
2h = 2 × 60 = 120
what is a variable in mathematics?
Answer:
variable, In algebra, a symbol (usually a letter) standing in for an unknown numerical value in an equation. Commonly used variables include x and y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s (arc length).
Answer:
variable, In algebra, a symbol (usually a letter) standing in for an unknown numerical value in an equation. Commonly used variables include x and y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s (arc length).
Step-by-step explanation:
In Maths, a variable is an alphabet or term that represents an unknown number or unknown value or unknown quantity. The variables are specially used in the case of algebraic expression or algebra. For example, x+9=4 is a linear equation where x is a variable, where 9 and 4 are constants.
19% of what number is $6.46?
Answer:
here's the answer
Step-by-step explanation:
19/100*x=6.46
x=$34
Question 1 Justify whether P(x) 5x+0.3x4 √3x + 4x² x3 is a polynomial or not.
Answer:
square root = not polynomial
0.2(7 + 2t) = 0.4t + 1.4
Answer:
all real numbers
Step-by-step explanation:
When you factor in the .2 on the left side you are left with 1.4 + .4t which is equal to the other side. And so, no matter what value for t you plug in, they will always be equal to eachother.
the diagram below shows the use of diverging lens for correction of
Answer:
E
Step-by-step explanation:
The diagram below shows the correct use of diverging lens for correction of myopia.
help me omg omg omg omg omg
Answer:
= -1.2 + 3.28d
Step-by-step explanation:
0.4 * -3 + 0.4 * 8.2d
= -1.2 + 3.28d
Type the correct answer in the box. Rewrite the quadratic function in the form that best reveals the zeros of the function. f(x)=2(2x2+4x)+3
Try this suggested option:
Step-by-step explanation:
f(x)=2(2x²+4x)+3; ⇔
f(x)=4(x²+2x)+3; ⇔
f(x)=4(x²+2x+1)+3-4; ⇔
f(x)=4(x+1)²-1; ⇔
f(x)=(2x+1)(2x+3).
Then the roots are:
[tex]\left[\begin{array}{ccc}x=-1.5\\x=-0.5\end{array}.[/tex]
Factor by grouping
5y^3(y-2)-15y(y-2)
5y³(y-2)-15y(y-2)
= (y-2)×(5y³-15y)
Q.3 If a multiple-choice test consists of 5 questions, each with 4 possible answers of which only 1 is correct, (a) in how many different ways can a student check off one answer to each question? (b) in how many ways can a student check off one answer to each question and get all the answers wrong?
The number of ways to check off one answer to each question is; 20ways.
The number of ways to check off one answer to each question and get it wrong is; 15ways.
In how many number of ways can a student check off one answer to each question?a) Since each question has four possible answers, it therefore follows that the student can choose any of 4 options in each question and consequently, the number of different ways is; 4 × 5 = 20.
b) Since only one option is correct, it follows that there are 3 wrong choices in each question case and hence, the number of ways to pick one wrong answer is; 3 × 5 = 15.
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5
The photograph shows identical red books and identical black books.
All pages have the same thickness.
Which pile has the greater
mean number of pages per book?
Pile W
Pile Y
Explain how you know.
Pile Y has the greater mean number of pages per book because it is 5 books less than pile W.
How to calculate greater mean number of pages?From the complete information, we can deduce that the number of each pile of book is given as follows:
For pile W;
Red books = 10 × 5 = 50 red books.
Blue books = 5 × 5 = 25 blue books.
Therefore, total books in pile W = 50 + 25 = 75 books.
Mathematically, the mean for each pile can be calculated by using the following formula:
Mean = [F(x)]/n
Mean = 75/10
Mean = 7.5.
For pile Y;
Red books = 10 × 5 = 50 red books.
Mean = [F(x)]/n
Mean = 50/5
Mean = 10.
In conclusion, pile Y has the greater mean number of pages per book because it is 5 books less than pile W.
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George and Maria decided to create a garden in their backyard. George works on the garden every third day and Maria works on the garden every fourth day.
If they worked on the garden today, the number of days until they work on the same day again would be.
I need help this is due tomorrow
The stem-leaf plot shows student’s scores on the last math test.
Answer:
1) 8
2) the median of the scores is 81
3) So, 8 students scored in the 70s, and the median score is 81
Step-by-step explanation:
1) the number of numbers listed is how many numbers there are
EX: 4| 1, 2, 5, 6 (where 4|1 equals 41) there are four numbers listed: 41, 42, 45, 462) the median is the middle number! when you list all of the numbers, the one in the middle is the median!
EX: 2, 4, 5, 8, 10the median would be 5! why? because it's in the middle!let me know if any of this is confusing and i'll try to explain it further :)
st: Two- and Three-Dimensional Geometry
A solid machine part is to be manufactured as shown in the figure. The part is made by cutting a small cone off the top of a larger cone. The
small cone has a base radius of 3 inches and a height of 5 inches. The larger cone has a base radius of 9 inches and had a height of 15 inches
prior to being cut. What is the volume of the resulting part illustrated in the figure?
2. If the parent function is y= 4*, which is the function of the graph?
2
4
y=-2(4)*
y=2(4)*
y=3(4)*
A function assigns the values. The function of the given graph is y=3(4)ˣ, thus, the correct option is C.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The complete question is:
If the parent function is y = 4ˣ, which is the function of the graph?
y = −2(4)ˣ
y = −3(4)ˣ
y = 3(4)ˣ
y = 2(4)ˣ
Since the graph intersect the y-axis at 3, and the parent function of the function is y=4ˣ, therefore, we can write,
y = A(4)ˣ
3 = A(4)⁰
3 = A × 1
A = 3
Hence, the function of the given graph is y=3(4)ˣ, thus, the correct option is C.
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Which function is the inverse of f Superscript negative 1 Baseline (x) = negative one-half x minus three-halves?
f Superscript negative 1 Baseline (x) = one-half x minus three-halves
A function assigns the value of each element of one set to the other specific element of another set. The inverse of the function g(x)=-2x -3.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Two function are inverse of each other if,
f(g(x))=x
g(f(x)) = x
Since the function is inverse, therefore, we can write,
g(f(x)) = a(-1x/2 - 3/2) + b
x = -ax/2 - 3x/2 + b
-a/2 = 1
a = -2
-3a/2 + b = 0
b= -3
Thus, the inverse of the function g(x)=-2x -3.
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Answer:
the inverse of the function g(x)=-2x +3 .
Step-by-step explanation:
There is a rack of 11 billiards balls, numbered from 1 to 11. If one ball is selected at random, determine the odds in favor of it being at an even-number ball.
Answer:
5/11 odds / 45.45% chance of being even-numbered
Step-by-step explanation:
There are 5 even-numbered balls (2, 4, 6, 8, 10) and 6 odd-numbered balls (1, 3, 5, 7, 9, 11). So, 5 / 11 balls are even-numbered
if a ball is selected, it has a chance of 5/11 for being even-numbered
5/11 also = 45.45 % [rounded] chance of being even-numbered
What is the Reciprocal of 5 1/2
Answer:
2/11
Step-by-step explanation:
A reciprocal is a number or fraction flipped. So, 5 1/2=11/2. 11/2 flipped is 2/11.
An icicle drips at a rate that can be represented by the function f(x) = −x2 + 8x − 7, where 0 ≤ x ≤ 10 and x is the number of hours after the sun has risen. When f(x) is a negative number, the icicle is not dripping. Determine the values when the icicle starts and stops dripping.
Find when f(x) = 0. By factorizing, we have
-x² + 8x - 7 = - (x - 7) (x - 1) = 0
so either x - 7 = 0 or x - 1 = 0, or simply x = 1 or x = 7.
Split the domain into three intervals, and check the sign of f(x) over each interval at some test point in the interval. The sign will tell you when the icicle is dripping (positive) or not (negative).
• [0, 1) : at x = 0, we have f(0) = -7 < 0
• (1, 7) : at x = 2, we have f(2) = 5 > 0
• (7, 10] : at x = 8, we have f(8) = -7 < 0
This tells us that the icicle is not dripping when 0 ≤ x < 1, begins to drip when x = 1, drips for the duration of 1 < x < 7, stops dripping when x = 7, and keeps on not dripping when 7 < x ≤ 10.
Which value of w makes this equation true?
[tex]\frac{5w + 4 }{3} = \frac{3w}{2}
Answer: -8
Step-by-step explanation:
[tex]\frac{5w+4}{3}=\frac{3w}{2}[/tex]
Cross-multiplying,
[tex]2(5w+4)=9w\\10w+8=9w\\w+8=0\\w=\boxed{-8}[/tex]
At Amy's candy store, small boxes (s) of chocolates contain 12 pieces, and large boxes (L) of chocolates
contain 45 pieces. A customer buys 8 boxes of chocolate containing a combined total of 195 pieces. Which
system of equations models this situation?
Step-by-step explanation:
x = number of small boxes
y = number of large boxes
these equations model the situation :
x + y = 8
12x + 45y = 195
FYI - the solution :
from the first equation we get
x = 8 - y
we use that in the second equation
12(8 - y) + 45y = 195
96 - 12y + 45y = 195
33y = 99
y = 3
x = 8 - y = 8 - 3 = 5
Which algebraic expression is a polynomial?
The algebraic expression that is a polynomial is -6x³ + x² - √5
How to know a polynomial?Polynomials are algebraic expressions that consist of variables and coefficients.
In a simpler term a polynomial can have constants, variables and exponents, but never division by a variable.
Therefore, the polynomial among the options is as follows:
-6x³ + x² - √5
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The monthly rents for five apartments advertised in a newspaper were $650, $650, $800, $1900, and $820. Use the mean, median, and mode of the rents to answer the question. Which value best describes the monthly rents?
Answer:
The Median Best Describes The Monthly Rents
the mean is add up all the numbers and then divide by the amount of numbers so it is 4820 then divide by 5 = 964 so the mean of all of then is 964
the median you have to put it in slamets to biggest so 650 650 800 820 1900 and then you have to put the one(s) in the middle witch is 800 so the median is 800
the mode is the most common numbers that show up and there is 2 650 and one of everything else so the mode is 650
Hope This Helped
y is directly proportional to x 2 . If y = 12 when x = 2 find x when y = 300
Solve: XIV – VI. Show your answer as a Roman Numeral.
A. XIV
B. XII
C. X
D. VIII
Answer:
XIV - VI = VIII
Step-by-step explanation:
14 - 6 = 8
Hope this helps
check whether the system of equations is consistent or inconsistent 7/2x-2/3y+9=0; 2x-3y-8=0
Answer:
hi,
Step-by-step explanation:
A consistent system of equations has at least one solution, and an inconsistent system has no solution.
Here the system has one solution.