Gregory has 2/3 of a pizza and gives 1/4 of an entire pizza to Marlene. By converting the fractions to a common denominator, we find that he gives away 3/8 of his portion of the pizza to Marlene.
Explanation:Understanding fractions can sometimes be as easy as picturing how you would slice a pie and share it with friends.
Gregory has 2/3 of an entire pizza and decides to give 1/4 of an entire pizza to his friend Marlene.
To solve how much of his portion Gregory gives to Marlene, we need to figure out what fraction 1/4 represents out of the 2/3 that Gregory has.
If we think of the pizza being cut into 12 slices (since 12 is a common multiple of both 3 and 4), Gregory's 2/3 is equivalent to 8/12 of the pizza because (2/3) × (12/1) = 8/12.
Similarly, 1/4 of the pizza is equivalent to 3/12 of the pizza because (1/4) × (12/1) = 3/12.
Now we know that Gregory aims to give away 3/12 of the pizza, but we want to express this as a part of his original 8/12.
To find out what fraction of his part he gives away, we then calculate (3/12) ÷ (8/12).
When we divide these fractions, we can multiply by the reciprocal of the second fraction:
(3/12) × (12/8), which simplifies to 3/8.
Therefore, Gregory gives away 3/8 of his 2/3 of the pizza to Marlene.
Use the properties of exponents to rewrite the expression.
(-5uv)(-5uv)(-5uv)(-5uv)
The expression can be simplified to [tex]625 \times (uv)^4.[/tex]
To rewrite the expression (-5uv)(-5uv)(-5uv)(-5uv) using the properties of exponents, you can consolidate it using the exponent rule that states when you multiply numbers with the same base, you add the exponents. In this case, the base is -5uv, and you are multiplying it four times, so the exponent is 4:
[tex](-5uv)(-5uv)(-5uv)(-5uv) = (-5uv)^4[/tex]
Now, you can simplify further by applying the rule for raising a power to a power, which states that when you raise an exponentiated term to another exponent, you multiply the exponents:
[tex](-5uv)^4 = -5^4 \times (uv)^4[/tex]
-5^4 means -5 multiplied by itself four times:
[tex]-5^4 = -5 \times -5 \times -5 \times -5 = 625[/tex]
So, the expression can be simplified to:
[tex]625 \times (uv)^4[/tex]
This is the expression rewritten using the properties of exponents.
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Points that lie on the same line are sold to be
collinear
Horizontal
ordered
Answer: b,c,e or 2,3,5
Step-by-step explanation:
What constant term should be used to complete the square?
x 2 - 9x + _____ = 6
-81/4
81/36
-9/2
81/4
Final answer:
To complete the square for the equation x² - 9x + _____ = 6, the constant term should be (81/4). This is obtained by dividing the coefficient of x by 2 and then squaring it.
Explanation:
The constant term required to complete the square for the equation x² - 9x + _____ = 6 can be found using a specific algebraic method. To complete the square, the coefficient of the x term should be divided by 2 and then squared. Therefore, for the equation provided, we take (-9/2) and square it, which results in (81/4). The complete equation after adding the constant term will be x² - 9x + 81/4 = 6 which, after completing the square, can be written as (x - 9/2)² = 6 + 81/4.
simplify the expression below. 4^5 x 4^3
Answer:
4^8
Step-by-step explanation:
Because both expressions have the same base, we can add the exponents to simplify the expression:
[tex]4^5*4^3 = 4^{5+3} = 4^8[/tex]
Answer: 4^8 or 65,536
Step-by-step explanation:
The exponent "product rule" tells us that, when multiplying two powers that have the same base, you can add the exponents.
A walking path across a park is represented by the equation y=-2x+5. A
new path will be built perpendicular to this path. The paths will intersect at
the point (-2,9). Identify the equation that represents the new path.
A. y= {x+10
B. y= -2x - 5
C. y= 2x+13
D. y -- 1x+8
Answer:
[tex]y = \frac{1}{2}x+10[/tex]
Step-by-step explanation:
The given path is:
y = -2x+5
Comparing with the standard form of equation:
y = mx+b
So,
m = -2
We know that product of slopes of two perpendicular lines is -1
Let m1 be the slope of the perpendicular line
m*m1=-1
-2*m1 = -1
m1 = -1/-2
m1 = 1/2
So the slope of perpendicular path is 1/2.
Since the new path passes through (-2,9)
[tex]9 = \frac{1}{2}(-2) +b\\9 = -1 +b\\b = 10[/tex]
Putting the values of m and b in standard form
[tex]y = \frac{1}{2}x+10[/tex]
Hence the equation of new path is:
[tex]y = \frac{1}{2}x+10[/tex] ..
which of the following is the best approximation to a solution of the equation e^x=4x+1
Which is the point-slope form of an equation for the line that passes through (0, –5) with slope 2?
Question 3 options:
a)
y = 2x – 5
b)
y – 5 = x – 2
c)
y + 5 = 2x
d)
y = 2(x + 5)
Answer:
c) y + 5 = 2x
Step-by-step explanation:
Insert the coordinates into the formula with their CORRECT signs. Remember, in the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE term of what they really are.
What is .5x5 equal???
Answer:
The answer is 25
Step-by-step explanation:
Aaron bought a new television that has a 92 in. 76 in. screen. It has a feature that splits the screen to allow him to watch 4 channels at once. What is the scale factor and size for each channel when this feature is turned on? (SHOW WORK)
Answer:
The scale factor is equal to 1/2
The dimensions of each channel when splits the screen is 46 in x 38 in
Step-by-step explanation:
we know that
The dimensions of the new television is 92 in x 76 in
Remember that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
A1 -----> the area of the new television
A2 ----> the area of each channel when splits the screen
z-----> the scale factor
[tex]z^{2} =\frac{A2}{A1}[/tex]
we have that
The area of the new television is 4 times the area of each channel
[tex]A1=4A2[/tex]
[tex](A2/A1)=1/4[/tex]
[tex]z^{2} =\frac{1}{4}[/tex]
[tex]z=\frac{1}{2}[/tex] -----> the scale factor
so
When splits the screen, the dimension of each channel is equal to
92/2 in x 76/2 in
so
46 in x 38 in
Remember, if two figures are similar then the scale factor is equal to the ratio of their corresponding sides
Verify the value of the scale factor
92/46=1/2
or
76/38=1/2
Triangle QRS is dilated according to the rule DO,2 (x,y).
What is true about the image △Q'R'S'? Check all that apply.
DO,2 (x,y) = (2x, 2y)
Side Q'S' lies on a line with a slope of -1.
QR is longer than Q'R'.
The vertices of the image are closer to the origin than those of the pre-image.
The distance from Q' to the origin is twice the distance from Q to the origin.
Answer:
True options:
[tex]D_{O,2} (x,y) = (2x, 2y)[/tex]
Side Q'S' lies on a line with a slope of -1.
The distance from Q' to the origin is twice the distance from Q to the origin.
Step-by-step explanation:
Triangle QRS is dilated according to the rule [tex]D_{O,2} (x,y).[/tex] This dilation has the rule
[tex](x,y)\rightarrow (2x,2y)[/tex]
So,
[tex]S(-1,1)\rightarrow S'(-2,2)\\ \\Q(-3,3)\rightarrow Q'(-6,6)\\ \\R(2,4)\rightarrow R'(4,8)[/tex]
True options:
[tex]D_{O,2} (x,y) = (2x, 2y)[/tex]
Side Q'S' lies on a line with a slope of -1.
The distance from Q' to the origin is twice the distance from Q to the origin.
False options:
QR is longer than Q'R', because QR is twice shorter than Q'R'.
The vertices of the image are closer to the origin than those of the pre-image, because the vertices of the per-image are closer to the origin than those of the image (see attached diagram).
Answer:
1, 2, 5 on Ed
Step-by-step explanation:
7x2 +11x-6/7x2 - 10x + 3
Answer:
Final result :
x + 2
—————
x - 1
Step-by-step explanation:
Step-1 : Multiply the coefficient of the first term by the constant 7 • 3 = 21
Step-2 : Find two factors of 21 whose sum equals the coefficient of the middle term, which is -10 .
-21 + -1 = -22
-7 + -3 = -10 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and -3
7x2 - 7x - 3x - 3
Step-4 : Add up the first 2 terms, pulling out like factors :
7x • (x-1)
Add up the last 2 terms, pulling out common factors :
3 • (x-1)
Step-5 : Add up the four terms of step 4 :
(7x-3) • (x-1)
Which is the desired factorization
Please mark brainliest and have a great day!
Answer:
Here's what I get.
Step-by-step explanation:
[tex]\dfrac{ 7x^{2} + 11x - 6}{ 7x^{2} - 10x + 3}[/tex]
One way is to factor the numerator and the denominator
[tex]\dfrac{ 7x^{2} + 11x - 6}{ 7x^{2} - 10x + 3} = \dfrac{(7x - 3)(x + 2)}{ (7x - 3)(x - 1)} = \dfrac{x+2}{x-1}\\\\\text{Except when } x = \dfrac{3}{7}[/tex]
If f(x) = 5x^3 and g(x) = x+1, find (f•g)(x).
A. 5x^4+1
B. 5x^3+1
C. 5x^4+5x^3
D. 6x^3
If f(x) = 5x^3 and g(x) = x+1, find (f•g)(x).
Note: (f•g)(x) means f(x) times g(x).
(f•g)(x) = (5x^3)(x + 1)
(f•g)(x) = 5x^4 + 5x^3
Answer: Choice C
Which of the following is the equation of a line parallel to the line y = 3x + 2,
passing through the point (10.1)?
A. -3x - y = 29
B. 3x - y = 29
C -3x + y = 29
D. 3x + y = 29
Answer:
B
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x + 2 is in this form with slope m = 3
• Parallel lines have equal slopes, hence
y = 3x + c ← is the partial equation of the parallel line
To find c substitute (10, 1) into the partial equation
1 = 30 + c ⇒ c = 1 - 30 = - 29
y = 3x - 29 ← in slope- intercept form
Subtract y from both sides
0 = 3x - y - 29 ( add 29 to both sides )
29 = 3x - y, thus
3x - y = 29 ← in standard form → B
Answer:
B
Step-by-step explanation:
Which angles form a linear pair?
Answer:
Step-by-step explanation:
The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.
Answer:
Adjacent angles formed by two intersecting lines form a linear pair.
Step-by-step explanation:
A linear pair of angles is formed when two lines intersect. A linear pair of angles must add up to 180 degrees.
If two angles are adjacent angles that are formed by two intersecting lines, then they are called linear.
Given fx) = 3x - 1 and g(x) = 2X-3, for which value of does g(x) = f(2)?
A)x=3/2
B)x=2
C)5/2
D)x=4
Answer:
D. x =4
Step-by-step explanation:
problem solved on picture
Lines a and b are parallel and lines e and f are parallel.
What is the value of x?
The angles circled in red below are same side exterior. This means that the sum of them is 180 degrees. You can make a formula like so that you will solve for x...
98 + x = 180
98 - 98 + x = 180 - 98
0 + x = 82
x = 82
Another way to solve:
The angles circled in pink below are opposite side exterior. This means that they must equal each other...
82 = x
x = 82
Hope this helped!
~Just a girl in love with Shawn Mendes
What is the volume if this rectangular prism: 5/2 cm by 3/4 cm by 1/3 cm
Answer:
5/8 cm
Step-by-step explanation:
5/2*3/4=15/8
15/8*1/3=15/24=5/8
Answer:
V = 5/8 cm^3
Step-by-step explanation:
V = l*w*h
V = 5/2 * 3/4 * 1/3
The 3's cancel
V = 5/2 * 1/4 * 1/1
V = 5/8 cm^3
what the length of the hypotenuse of an isosceles right triangle whose legs are 1 unit in length.
Answer: ≈ 1.414
Step-by-step explanation:
You can use the pythagorean theorem, a^2 + b^2 = c^2
a^2 and b^2 are the legs and c^2 is the hypotenuse.
1^2 + 1^2 = c^2
1 + 1 = c^2
2 = c^2
√ 2 = √ c^2
c = ≈ 1.414
What are the slope and the y-intercept of the linear function that is represented by the table?
Answer:
slope rise 3 run 2 1/2
Step-by-step explanation:
if you start from the bottom and if you start from the top it's -3 and -2 1/2
Answer: The slope is 3 and the y-intercept is 3/2
Step-by-step explanation:
The slope of a linear function can be calculated as:
s = (y2 - y1)/(x2 - x1)
Where y2 = f(x2) and y1 = f(x1) and f(x) is the linear function.
So here we can use any two pairs of the set of data, for example, the first two.
(-1 , -3/2) and (-1/2,0)
s = (0 -(-3/2))/(-1/2 - (-1)) = (3/2)/(1/2) =(3/2)*(2/1) = 3
So the slope is equal to 3.
the y-intercept is the value of y when x = 0, in the table we can see that when x = 0. the value of y = 3/2
So the function is: y = 3*x + 3/2
and the correct option is the fourth one.
PLEASE HELP!
Complete the following steps to help find the standard deviation of the data set by hand.
1, 3, 5, 15, 2, 11, 12, 7
a) Find the mean value. (I have already done this, it is 7.)
b) Complete the table to find the deviations and the squared deviations. (I NEED HELP ON THIS THE MOST! Screenshot of table is attached.)
c) Find the sum of the squared deviations. SHOW YOUR WORK.
d) Find the standard deviation. Round your answer to the nearest tenth. SHOW YOUR WORK.
Answer:
See Step-by-step
Step-by-step explanation:
b)Table:
x x-Mean (x-Mean)^2
1 1-7=-6 36
3 3-7=-4 16
5 5-7=-2 4
15 15-7=8 64
2 2-7=-5 25
11 11-7=4 16
12 12-7=5 25
7 7-7=0 0
c)Find the sum of the squared deviations:
(36+16+4+64+25+16+25+0)/8=23.25
d)Find the standard deviation by finding the square root of 23.25
The answer is 4.8
ASAP help
The length of a rectangle is 3 inches more than twice its width, and its area is 65 square inches. What is the width? If w = the width of the rectangle, which of the following expressions represents the length of the rectangle?
A. 2w + 3
B. 2(w + 3)
C. 3(2w)
Answer:
2W+3 I am really sorry if that's wrong, I don't think it is though GOODLUCK
Step-by-step explanation:
Answer:
The correct answer is option A. 2w + 3
w = 5 inches
Step-by-step explanation:
It is given that, the length of a rectangle is 3 inches more than twice its width, and its area is 65 square inches.
To find the correct option
If 'w' is the width of rectangle, then length = 3 inches more than the twice the width
length = 2w + 3
The correct answer is option A. 2w + 3
To find the width
We have area = 65 square inches
Length * Width = 65
(2w + 3) * W = 65
2w² + 3w - 65 = 0
Solving we get ,
w = 5 and -6.5
Therefore w = 5 inches
Rectangle ABCD is dilated by a scale factor of 3 with the center dilation at (0,0). What is the area, in square units, of resulting dilated rectangle A’B’C’D’
Answer:
216
Step-by-step explanation:
The area dilation ratio is the square of the length dilation ratio
The area of the original rectangle is 6*4=24
the length dilation ratio is 1:3
the area dilation ratio would be 1:3² which is 1:9
The resulted area=24*9
=216
Which of the following ratios is proportional to 8 adults: 6 children?
4 adults:3 children
3 adults:4 children
10 adults:5 children
12 adults:10 children
Answer:
12 adults:10 children
Step-by-step explanation:
i don't know how i got it i just know it because i had this exact same question before and i guessed and this was the correct answer :|
Answer:
12 Adults 10 Children
is correct
Find the greatest common factor of the
following monomials:
15x4y6 6x5y?
12x3, 4
1. The monomials are:
[tex]15 {x}^{4} {y}^{6} = 3 \times 5 {x}^{4} {y}^{6} [/tex]
and
[tex]6 {x}^{5} {y} = 2 \times 3 {x}^{5} y[/tex]
The highest common factor is the product of the least powers of the common factors.
The HCF is
[tex]3 {x}^{4} y[/tex]
2. The monomials are:
[tex]12 {x}^{3} = {2}^{2} \times 3 {x}^{3}[/tex]
[tex]4 = {2}^{2} [/tex]
The HCF is
[tex]{2}^{2} = 4[/tex]
145 is what percent of 620
Hello There!
145 is 23.39% of 620
HOW TO SOLVE
Equation: Y = P% * X
We need to solve our equation for "P"
P% = Y/X
P% = 145/620
p = 0.2339
Convert decimal to percent:
Percent = 0.2339 * 100 = 23.39%
Write the first five terms of the arithmetic sequence whose first term is 5 and whose common difference is 6.
Answer:
5, 11,17,23,29
Step-by-step explanation:
To obtain the term in the sequence add the common difference to the previous term, that is
a(1) = 5
a(2) = 5 + 6 = 11
a(3) = 11 + 6 = 17
a(4) = 17 + 6 = 23
a(5) = 23 + 6 = 29
The first five terms of an arithmetic sequence starting with 5 and a common difference of 6 are 5, 11, 17, 23, and 29.
The first five terms of the arithmetic sequence with the first term 5 and a common difference of 6 can be found by successively adding the common difference to the previous term.
Third term (a3) = a2 + 6 = 11 + 6 = 17
Fifth term (a5) = a4 + 6 = 23 + 6 = 29
Therefore, the first five terms of the arithmetic sequence are 5, 11, 17, 23, and 29.
A quilt is designed using a square pattern. Each square contains two rectangles. Each rectangle contains a shaded rhombus.
What is the value of x?
50
55
125
145
Answer:
The value of x is 55 ⇒ 2nd answer
Step-by-step explanation:
* Lets revise the properties of the rhombus
- It has 4 equal sides
- Every two opposite sides are parallel
- Every two opposite angles are equal
- Every two adjacent angles are supplementary (their sum is 180°)
* Now lets solve the problem
- A square divided into two rectangles
- Each rectangle contains a shaded rhombus
- The shaded rhombus has two adjacent angles their measures are
(2x + 20)° and 50°
∵ Every two adjacent angles in the rhombus are supplementary
∵ The sum of the supplementary angles = 180°
∴ The sum of the measures of the angles (2x + 20)° and 50° is 180°
- lets put the equation and solve it to find x
∴ (2x + 20)° + 50° = 180° ⇒ add the like terms
∴ 2x + 70° = 180° ⇒ subtract 70° from both sides
∴ 2x = 110° ⇒ divide both sides by 2
∴ x = 55°
* The value of x is 55
The sum of a number and three more than twice that number is 27. What is the smaller number?
Answer:
7
Step-by-step explanation:
27 + 27 = 54
54 + 3
57
Smaller number is: 7
Describe the symmetry of the plane figure shown below.
A.horizontal line symmetry
B.vertical line symmetry
C.rotational symmetry
D.diagonal line symmetry
Answer:B. vertical line symmetry
Step-by-step explanation:
Answer:
D. diagonal line symmetry
Step-by-step explanation:
What is the rate of change of y with respect to x for this function?
bearing in mind that the average rate of change = slope, and for that we can simply use two points off the table.
[tex]\bf \begin{array}{|cc|ll} \cline{1-2} x&y\\ \cline{1-2} -2&12\\ 0&3\\ 3&-10.5\\ 7&-28.5\\ \cline{1-2} \end{array}\qquad \qquad \begin{array}{llll} (\stackrel{x_1}{-2}~,~\stackrel{y_1}{12})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-10.5}) \\\\\\ slope \implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-10.5-12}{3-(-2)} \\\\\\ \cfrac{-10.5-12}{3+2}\implies \cfrac{-22.5}{5}\implies -\cfrac{4.5}{1}\implies -4.5 \end{array}[/tex]
The rate of change of y with respect to x for the given function with coordinates expressed in the table is; dy/dx = -9/2
The rate of change of y with respect to x for a given linear function is simply the slope expressed as;
dy/dx = (y2 - y1)/(x2 - x1)
Let us take the first 2 coordinates which are;
(-2, 12) and (0, 3)
Thus;
dy/dx = (3 - 12)/(0 - (-2))
dy/dx = -9/2
Or dy/dx = -4.5
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