To describe the transformation, dilation by a scale factor of 4 with center of dilation at origin the rule is (x,y)→(4x,4y) and , the coordinates of rectangle Q'R'S'T will be Q'(-32,20) , R'(-32,28) , S'(-20,28) , T'(-20,20) .
In the question ,
the coordinates of the rectangle QRST are given as Q(-8,5), R(-8,7), S(-5,7), and T(-5,5) .
we have to to dilate the rectangle by a scale factor of 4 with center of dilation at the origin.
So , to dilate the rectangle by a scale factor of 4 with center of dilation at the origin we multiply coordinates of the original shape with the dilation factor .
So , the rule of transformation becomes
(x,y)→(4x,4y)
Using the above rule to find the coordinates of the rectangle Q'R'S'T' .
given Q = (-8,5)
So, Q' = (4*(-8),4*5)
Q' = (-32,20)
Given R = (-8,7)
So, R' = (4*(-8),4*7)
R' = (-32,28)
Given S = (-5,7)
So, S' = (4*(-5),4*7)
S' = (-20,28)
Given T= (-5,5)
So, T' = (4*(-5),4*5)
T' = (-20,20)
hence , the rectangle Q'R'S'T' coordinates are Q' = (-32,20) , R' = (-32,28) , S' = (-20,28) , T' = (-20,20) .
Therefore , to describe the transformation, dilation by a scale factor of 4 with center of dilation at origin the rule is (x,y)→(4x,4y) and , the coordinates of rectangle Q'R'S'T will be Q'(-32,20) , R'(-32,28) , S'(-20,28) , T'(-20,20) .
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How many 1 3/5-inch-thick books can fit on a 1 4/12-inch-long bookshelf?
You can fit ? books on the bookshelf.
Using division we can calculate that 8 books can fit in the 14 inch long bookshelf .
Division is one of the four basic arithmetic operations, or the process by which two numbers are added together to produce a new number. Multiplication, addition, and subtraction make up the remaining operations.
One way to understand the division of two natural numbers is to tally the occasions in which one number is included within another. This number doesn't have to be an integer. For instance, each individual will receive 5 apples if 20 apples are spread evenly among 4 people.Both types of division are applied to various algebraic structures, or means of describing mathematical structure. These contain polynomial rings in a single indeterminate and are known as Euclidean domains. These are the cases where a defined Euclidean division (with remainder) exists.length of book shelf = 14 inch
length of each book = 1 3/5 inch = 1.6 inches
Number of books = 14 ÷ 1.6 = 8.75 books
Hence by division we get that 8 book can be put in the bookshelf.
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A school wants to create a census to identify the favorite subject of students. Which description describes who they should ask?
all students their favorite subject in school
all sophomores their favorite subject in school
all staff their favorite subject in school
all male students their favorite subject in school
Answer:
all students their favorite subject in school
This morning, the owner of Sam's Spaghetti House withdrew $180 from the restaurant's bank account to pay for an oven repair. This afternoon, he deposited $430 from lunch sales.
What is the total change in the restaurant's bank account relative to where it started
Answer:
The restaurant is at a profit of $250
The graph of the function f(x) = –(x + 3)(x – 1) is shown below.
On a coordinate plane, a parabola opens down. It goes through (negative 3, 0), has a vertex at (negative 1, 4), and goes through (1, 0).
Which statement about the function is true?
The function is positive for all real values of x where
x < –1.
The function is negative for all real values of x where
x < –3 and where x > 1.
The function is positive for all real values of x where
x > 0.
The function is negative for all real values of x where
x < –3 or x > –1.
The true statement about the function are;
⇒ The function is positive for all real values of x, where x < –1.
What is Function?
A relation between a set of inputs having one output each is called a function.
Given that;
The graph of the function;
f(x) = –(x + 3)(x – 1)
Now,
Graph of the function is shown in attached image.
Which is a parabola, It goes through (- 3, 0), has a vertex at (- 1, 4), and goes through (1, 0).
Clearly, When x < -1
Take x = 0 < -1
The value of function;
f(x) = –(x + 3)(x – 1)
= - (0 + 3) (0 -1)
= -3 x -1
= 3
The function is positive.
Thus, The true statement about the function are;
⇒ The function is positive for all real values of x, where x < –1.
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Fill in: -5^2=____-5^2
The complete expression that fills the blank is -5^2 = 0 - 5^2
What are mathematical expressions?These are any statements that use variables, operators and coefficients as its representation
How to completely fill the blanks?The expression is given as
-5^2 = __-5^2
Represent the blank with x
So, we have the following expression
-5^2 = x - 5^2
Add 5^2 to both sides of the equation
So, we have
x = 5^2 - 5^2
Evaluate the difference
x = 0
This implies that -5^2 = __-5^2 gives -5^2 = 0 - 5^2
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Amol drives his truck at an average speed of 50 km/h. He leaves at 07 00 and arrives at 11 15. Calculate the distance he drives.
Answer:
209km/h
Step-by-step explanation:
4hrs 15mins was the time.
4hrs x 50km/h = 200km/h
15 percent of 60: how many minutes is in an hour, is 9.
Hence, The answer would be 209km/h.
A conditional has a(n)? of true or false.
Answer:
The correct option is (b) truth value. If we are given two statements, the first statement is called the hypothesis and the second is its conclusion.
←++
2. The 7th grade class plans to collect at least 600 pairs of socks for people in need. So far, 135
pairs have been collected. How many pairs of socks does the class need to collect over the
next 5 days?
A wall in Marcus's bedroom is 8 feet high and 18 feet long. If he paints of the wall blue, how many square feet will be
blue?
O 77
O 72 1/15
O 154
O 144 1/15
The blue portion of the wall in Marcus's bedroom is discovered to be 144(1/15) or 9.6 square feet in size.
How do you calculate the area of a wall?Use the standard formula of Length x Width = Area to calculate the area of a wall.
What is the area of a wall measured in square meters?Because square feet is the most commonly used measurement in the world when it comes to wall sizes, the measurement unit will have an impact on how you calculate square footage.
It is given that a wall in Marcus's bedroom is 8 feet high and 18 feet long.
So, the area of a wall = 8 × 18
= 144
Further, 1/15 portion is painted with blue color.
So, the portion that is painted with blue = 144 × 1/15
= 9.6
Therefore, the area of the wall in Marcus's bedroom that is painted with blue color is found to be 144(1/15) or 9.6 square feet.
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a whole number is more than 50. if this number is divided by 3, the remainder is 2. if it divided by 4, the remainder is 3. what is the smallest such whole number
The smallest such whole number is 11 which is, Which is divided by 3, the remainder is 2, f it, divided by 4, the remainder is 3
Let the number be x
Here we have to find the whole number which is Divided by 3,4 the remainder is 2,3 respectively,
x+(3–2)= x +1 is multiple of 3
Div by 4 remainder is
3x+(4–3) = x+1 is multiple of 4
So LCM of 3,4 is 3×4 = 12
Hence,x=12 –1 =11
The smallest such whole number is 11 which is divided by 3, the remainder is 2, if it divided by 4, the remainder is 3.
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How would you solve this problem?
The mass of Earth is 5.97 X 10^24 kilograms while the mass of Jupiter is 1.9 x 10^27 kilograms. Approximately how many times greater is the mass of Jupiter compared to Earth? Give your answer in scientific notation.
Provided the figures we have that describe the mass of Earth and the mass of Jupiter, we can conclude that Jupiter is 318 times greater than the mass of Earth.
How do we arrive at the planet with the greater mass?From the figures we have, we can see that the mass of Jupiter is greater than the mass of Earth because it has more zeros.
So, we have to divide the value of the mass of Jupiter by the mass of the earth as follows:
1.9 x 10^27
5.97 X 10^24
=1. 9 ÷ 5.97 × 10^27 - 10^24
= 0.318... ×10³
= 318
Do note that when we have to divide figures that are raised to some figures, the rule will be to subtract the figures as we find in the fact that 27 - 24 is equal to 3. And when we multiply, we arrive at the stated figure.
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A ticket for the train costs $6.23. If Barbara has $32, does she have enough money to buy 5 tickets? Explain your reasoning.
Please help, I’ve been trying to do this for a couple of hours now but I can’t seem to figure it out.
The tables show a Linear function that represents your earnings y in dollars after x working hours
(Picture below)
What is the totals earnings for the 6th hour?
$
What is your hourly wage?
$
Answer:
total earnings at 6th hour: 111
hourly wage (slope): 18.5
Step-by-step explanation:
A linear function has a linear relationship, which essentially states as x increases by one, the y-value increases by some constant amount yielding a straight line.
The slope, or how much the y-value changes as x changes by 1 is generally written as: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We can choose any two points and this should yield the slope of the function, but it's a lot easier to choose y-values that are only separated by an x-value of one.
Let's say: [tex](x_1, y_1)=(4,\ 74)\text{ and }(x_2,y_2)=(5,\ 92.50)[/tex]
If we plug the values into the slope formula we just get: [tex]\frac{92.50-74}{5-4}=\frac{92.50-74}{1}=92.50-74[/tex]
And this makes sense, since by definition of a slope, it's just the change in y over change in x. This is equivalent to how much the y-value changes as x increases by one, so if we select two values with a difference of one in their x-values, the slope just turns out to be the difference between the two numbers.
Simplifying our expression we get: [tex]92.50-74=18.5[/tex]
This slope in this context represents how earnings increases as the hour increases, or in other words the hourly wage.
To calculate the earnings of the 6th hour we can just use the definition of a slope. From the x-value 5 to the x-value 6, the y-value should simply increase 18.5
So adding 18.5 to the y-value at x=5 we get: [tex]92.5+18.5=111[/tex]
Using the figure below, Maggie used the definition of vertical angles to help her solve for x. Since vertical angles are congruent, she set the two given expressions equal to each other. After solving for x, her teacher said she got the wrong value for x. Explain where Maggie made her mistake when solving for x.
Maggie's mistake on the solution of the expression for x was when she subtracted 7x to both sides, the result should have been -3x and not 3x.
What is the solution for the equation?The equation is given as follows, as the angles are congruent, that is, they have the same measure:
4x + 2 = 7x - 25.
First, we isolate x on the left side of the equality, subtracting 7x from both sides, hence:
4x + 2 - 7x = 7x - 25 - 7x
Then the correct expression is:
-3x + 2 = -25
Which is where Maggie's mistake happened, on the subtraction of 4x and 7x.
Then, isolating x, we subtract 2 from both sides of the equality, to remove the +2 term on the left side of the equality.
-3x = -27
3x = 27
x = 27/3
x = 9.
The correct solution is x = 9.
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I need help ASAP 15 points
The value of x is 9 and the mistake that Maggie made is that she did use the proper operation sign when rearranging the numbers.
How to find vertical opposite angles?When any two straight lines intersect each other, then four angles are formed. The angles that are directly opposite to each other are known as opposite angles. They are also called vertical angles or vertically opposite angles.
Now, from the image attached, we see that the two given angles are opposite angles and as such they are congruent. Thus, we have;
4x + 2 = 7x - 25
Rearrange to collect like terms on same side to get;
7x - 4x = 25 + 2
3x = 27
x = 27/3
x = 9
The mistake that Maggie made is that she did use the proper operation sign when rearranging the numbers.
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Find a function of the form y=Asin(kx)+C or y=Acos(kx)+C whose graph matches the function shown below:
The sinusoidal function that matches the graph given is:
g(x) = 4cos((π/7)x) - 2.
What is the cosine function?The cosine function is defined as follows:
g(x) = acos(bx)+d.
The coefficients have these following roles:
a: amplitude.b: The period is of 2π/b.d: vertical shift.For this problem, we use a cosine function because the function is not zero at the origin, while for the sine it is.
From the graph of this function, the maximum value is of 2, while the minimum value is of -6, hence the amplitude is found as follows:
2a = 8 (difference between these values).
a = 4.
Then:
g(x) = 4cos(bx) + d.
A function with amplitude of 4 should oscillate between -4 and 4, while this one oscillates between -6 and 2, meaning that it was shifted 2 units down, hence d = -2 and:
g(x) = 4cos(bx) - 2.
The period is of 14 units, hence:
2π/b = 14
14b = 2π
b = π/7
Hence the function is:
g(x) = 4cos((π/7)x) - 2.
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Solve the following inequality:
3r-13>14
could I have a demonstration of how it worked out
Answer:
r>9
Step-by-step explanation:
3r-13+13>14+13
3r>27
3r/3>27/3
r>9
Answer:
r > 9
Step-by-step explanation:
Hello!
Treat inequality as an equal sign. The only rule is that when you divide or multiply by a negative number, flip the sign.
Solve for r3r - 13 > 143r > 27r > 9The solution is true for any value of r greater than 9.
Three-fourths of students in your classroom like chocolate chip cookie dough ice cream. One-half of these same students also like mint-flavored ice cream. What fraction of students in your classroom like both flavors?
ANSWER FOR 100 POINTS
The fraction of the students in the classroom that like both flavors is 1/4.
How to calculate the fraction?From the information, three-fourths of students in the classroom like chocolate chip cookie dough ice cream and one-half of these same students also like mint-flavored ice cream.
The fraction of the students in the classroom that like both flavors will be the addition of both flavors subtracted from 1. This will be illustrated as:
= (3/4 + 1/2) - 1
= 3/4 + 2/4 - 1
= 5/4 - 1
= 1/4
The fraction is 1/4.
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Giving anyone that gets it right 100 points!
Six cantaloupes are cut up and served into thirty-two equal portions for a catering event. Which of the following shows the amount of cantaloupe in each portion?
A. 0.1875
_
B. 0.1875
C. 0.533
_
D. 0.53
Answer: pretty sure its B
hope this helps :)
Simplify the expression.
3(−6+2 ÷ 4) - 72²
Enter the inverse function of f(x) = 15x - 14.
replace 'x' with 'y'
15y - 14 = x; solve for y
15y = x + 14
y = (x+14)/15
Factor x2 – 3x – 28.
An x-method chart shows the product a c at the top of x and b at the bottom of x. Above the chart is the expression a x squared + b x + c.
Identify the values that should be written to complete the X diagram.
On the top:
On the bottom:
On the sides:
–7 and 4
Rewrite the expression using the numbers on the sides of the X diagram.
Use double grouping to factor the four terms.
x2 – 3x – 28 =
Values needed to complete the X diagram are:
On top -28, On the bottom: -3 and On the sides: -7 and 4.
What do you mean by factorization?An algebraic expression is factorised when it is written as the product of its factors.
The given equation is :
F(x) = x²-3x-28
finding factors,
= x²-7x+4x-28
= x(x-7) +4(x-7)
= (x-7)(x+4)
Given general equation is ax²+bx+c,
on comparing with x²-3x-28
a = 1
b = -3
c = -28
ac = 1*(-28) = -28
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A graph (not shown) of the selling prices of homes in a certain city for the month of April reveals that the distribution is skewed to the left. Which of the following statements is the most reasonable conclusion about the selling prices based on the graph?
Responses
The mean is greater than the median.
The mean is greater than the median.
The median is the average of the first quartile and the third quartile.
The median is the average of the first quartile and the third quartile.
There are fewer selling prices between the first quartile and the median than there are between the median and the third quartile.
There are fewer selling prices between the first quartile and the median than there are between the median and the third quartile.
There are more selling prices that are less than the mean than selling prices that are greater than the mean.
There are more selling prices that are less than the mean than selling prices that are greater than the mean.
The value of maximum minus third quartile is less than the value of first quartile minus minimum.
The statement which is the most reasonable conclusion about the selling prices based on the graph is that: E. the value of maximum minus third quartile is less than the value of first quartile minus minimum.
What is a box and whisker plot?A box and whisker plot is also referred to as boxplot and it can be defined as a type of graph that can be used to graphically represent the five-number summary of a data set with respect to locality, skewness, and spread. Also, the five-number summary include the following:
Minimum (Min).First quartile (Q₁) or lower quartile.Median (Med).Third quartile (Q₃) or upper quartile.Maximum (Max).In Mathematics, the value of maximum minus third quartile (Max - Q₃) is generally less than value of first quartile minus minimum (Q₁ - Min). Mathematically, this can be represented by this expression:
Data value = (Max - Q₃) < (Q₁ - Min)
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for the following exercises, find the lengths of the missing sides if side a is opposite angle a, side b is opposite angle b, and side c is the hypotenuse.
Using relations in a right triangle and the Pythagorean Theorem, it is found that the missing side lengths are as follows:
a = 14.4.c = 15.24.What are the relations in a right triangle?There are three relations in a right triangle, given as follows:
The sine of an angle of the triangle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle of the triangle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle of the triangle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.For this problem, we have that:
tan(A) = b/a.
Hence:
5/12 = 6/a
Applying cross multiplication, the side a is found as follows:
5a = 72
a = 72/5
a = 14.4.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
Hence the hypotenuse c is given as follows:
c² = 5² + 14.4²
c = sqrt(5² + 14.4²)
c = 15.24.
What is the missing information?For the triangle, we have that:
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34 = -w/7 solve for w
Answer: w = -238
Step-by-step explanation:
[tex]34=\frac{-w}{7}[/tex]
Switch sides
[tex]\frac{-w}{7} =34[/tex]
Multiply both sides by 7
[tex]\frac{7\left(-w\right)}{7} =34\cdot \:7[/tex]
Simplify
-w = 238
Divide both sides by -1
[tex]\frac{-w}{-1}=\frac{238}{-1}[/tex]
Simplify
w = -238
If I made any mistakes, please let me know!
I hope this helped :)
If Roni and Allie work together to mow the field, what part of the field would Roni mow?
about 0.52 of the field
about 0.64 of the field
about 0.71 of the field
about 0.87 of the field
If Roni has a riding lawn mower and can mow the field in 30 minutes and Allie is pushing a lawn mower and can mow the field in 75 minutes. If Roni and Allie work together to mow the field, about 0.71 of the field will Roni mow.
Time taken by Roni to mow the field = 30 minutes
Time taken by Allie to mow the field = 75 minutes
Work done by the Roni = x/30
Word done by Allie = x/75
Then they are working together
x/30 + x/70 = 1
Solve the equation
[tex]\frac{70x+30x}{2100}=1[/tex]
70x+30x = 2100
100x = 2100
x = 2100/100
x = 21
Then, the work done by Roni = x/30
= 21/30
= 0.70
Hence, if Roni has a riding lawn mower and can mow the field in 30 minutes and Allie is pushing a lawn mower and can mow the field in 75 minutes. If Roni and Allie work together to mow the field, about 0.71 of the field will Roni mow.
The complete question is
Roni and Allie are mowing the grass at the soccer field. Roni has a riding lawn mower and can mow the field in 30 minutes. Allie is pushing a lawn mower and can mow the field in 75 minutes. If Roni and Allie work together to mow the field, what part of the field would Roni mow?
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What are precise definitions of perpendicular and parallel lines
Answer:
Perpendicular lines: Are lines that intersect at right angles (90°)
Parallel lines: Are lines which have no point of intersection.
Step-by-step explanation:
[tex]{}[/tex]
Does(3, 1)make the inequality 3x + 10y ≥ 20 true?
Answer:
See below
Step-by-step explanation:
Plug in x = 3 And y = 1 to see
3(3) + 10(1) >= 20 ?
9 + 10 >= 20?
19 >= 20 Not true ....the point does not make the inequality true
The Mississippi river flows at a rate of 1 7⁄8 miles per hour. If
Marco floats down the river in a boat for 5 1⁄6 hours, how far will
he float?
I don't know how to do this :(
465/48
Step-by-step explanation:
1 ⅞ miles × 5⅙ = 465/48
________ _______
1 hour × 5⅙ = 5⅙ hours
PLEASE HELP!!!
A system of linear inequalities is graphed below.
What are the linear inequalities for the system? Show your work, or explain your answer.
Answer:
System of linear inequalities is x - y + 1 < 0 and x + 2y +6 < 0
Step-by-step explanation:
Given:
The dotted line has two points as (-1,0) and (0,1).The solid line also has two points as (-6,0) and (0,-3).To Find:
Linear inequality for the system.Formula used:
Equation of a line passing through point (x1, y1) and (x2, y2) is given by (y-y1) = (y2-y1)/(x2-x1) * (x-x1)According to question, we have
Inequality for dotted line :
(y-1) > (0-1)/(-1-0) * (x-0)
y - 1 > x
x - y + 1 < 0...(1)
Inequality for solid line:
(y-(-3)) < (0-(-3))/(-6-0) * (x-0)
y + 3 < -x/2
x + 2y +6 < 0...(2)
Using (1) and (2), we get
System of linear inequalities is x - y + 1 < 0 and x + 2y +6 < 0.