Answer:
d) 1/6 + (-3/8) + 1/2
Step-by-step explanation:
For equivalence, the sign of each term must match the original. Here's how the answer choices stack up:
a) wrong sign for -3/8
b) wrong sign for -3/8 and for 1/2
c) wrong sign for 1/2
d) correct choice
Final answer:
Option (c) 1/6 + (-3/8) + (-1/2) is equivalent to the original expression 1/6 - 3/8 + 1/2 because it accurately reflects the original values and operations without any alterations.
Explanation:
The student's question asks to find an expression equivalent to the arithmetic operation 1/6 - 3/8 + 1/2. To find the equivalent expression, we should look for an option that represents the same operation without any alteration to the values or their signs.
Upon review, option (c) 1/6 + (-3/8) + (-1/2) is the correct equivalent expression because it maintains the original values and their associated signs. The negative signs in front of the fractions in this option simply denote subtraction, which matches the original expression given.
The use of parentheses in the alternative expression is typical in algebra to emphasize operations, but it does not change the value of the expression. Thus, the correct option is c.
Use a matrix to solve the system.
8.
2x + 6y = 38
(5x - y = 15
Answer:
x=4 and y=5
Step-by-step explanation:
The given system of equations are
[tex]2x+6y=38[/tex]
[tex]5x-y=15[/tex]
The matrix form is
[tex]\begin{bmatrix}2&6\\ \:5&-1\end{bmatrix}\begin{bmatrix}x\\ \:y\end{bmatrix}=\begin{bmatrix}38\\ \:15\end{bmatrix}[/tex]
Let as assume
[tex]A=\begin{bmatrix}2&6\\ \:5&-1\end{bmatrix}[/tex]
[tex]X=\begin{bmatrix}x\\ \:y\end{bmatrix}[/tex]
[tex]B=\begin{bmatrix}38\\ \:15\end{bmatrix}[/tex]
then,
[tex]AX=B[/tex]
[tex]X=A^{-1}B[/tex]
We know that,
[tex]\begin{bmatrix}a\:&\:b\:\\ c\:&\:d\:\end{bmatrix}^{-1}=\frac{1}{\det \begin{bmatrix}a\:&\:b\:\\ c\:&\:d\:\end{bmatrix}}\begin{bmatrix}d\:&\:-b\:\\ -c\:&\:a\:\end{bmatrix}[/tex]
[tex]A^{-1}=\frac{1}{\det \begin{bmatrix}2&6\\ 5&-1\end{bmatrix}}\begin{bmatrix}-1&-6\\ -5&2\end{bmatrix}[/tex]
[tex]A^{-1}=\frac{1}{-32}\begin{bmatrix}-1&-6\\ -5&2\end{bmatrix}[/tex]
[tex]X=\frac{1}{-32}\begin{bmatrix}-1&-6\\ -5&2\end{bmatrix}\begin{bmatrix}38\\ \:15\end{bmatrix}[/tex]
[tex]X=\frac{1}{-32}\begin{bmatrix}\left(-1\right)\cdot \:38+\left(-6\right)\cdot \:15\\ \left(-5\right)\cdot \:38+2\cdot \:15\end{bmatrix}[/tex]
[tex]X=\frac{1}{-32}\begin{bmatrix}-128\\ -160\end{bmatrix}[/tex]
[tex]\begin{bmatrix}x\\ \:y\end{bmatrix}=\begin{bmatrix}4\\ 5\end{bmatrix}[/tex]
Therefore, the value of x is 4 and value of y is 5.
You have a cake that is 10 inches in diameter. You expect 12 people to share it, so you cut it into 12
equal slices. What is the area of each slice of cake? (Hint: the entire cake is 360°)
Answer:
The area of each slice of cake is [tex]\frac{25}{12}\pi\ in^2[/tex]
Step-by-step explanation:
step 1
Find the area of the complete cake
The area of the circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=10/2=5\ in[/tex] ----> the radius is half the diameter
substitute
[tex]A=\pi (5)^{2}[/tex]
[tex]A=25\pi\ in^2[/tex]
step 2
Find the area of each slice of cake
Remember that the area of complete circle subtends a central angle of 360 degrees
If you cut the cake into 12 equal slices
then
the central angle of each slice is equal to [tex]\frac{360^o}{12}=30^o[/tex]
so
Using proportion
Find out the area of each slice for a central angle of 30 degrees
[tex]\frac{25\pi}{360^o}=\frac{x}{30^o} \\\\x= \frac{25\pi}{360^o}(30^o)\\\\x=\frac{25}{12}\pi\ in^2[/tex]
Note This problem could be solved by directly dividing the area of the circle by 12, however, proportions and concepts of central angle were applied for didactic purposes
Each slice of the 10-inch diameter cake, cut into 12 equal slices, has an area of approximately 6.54 square inches.
To find the area of each slice of the cake, we need to calculate the area of the entire cake first and then divide it by 12 since the cake is divided into 12 equal slices.
The formula for the area of a circle is: Area = πr².
Given the diameter of the cake is 10 inches, we first need to find the radius: radius = diameter / 2 = 10 / 2 = 5 inches.
Now, calculate the area of the entire cake:
Area of the full cake = π × (5 inches)² = 25π square inches.
Since the cake is cut into 12 equal slices, the area of each slice is:
Area of each slice = (25π) / 12 = 25π / 12 ≈ 6.54 square inches.
Therefore, each slice of cake has an area of approximately 6.54 square inches.
if logx=-5 what is x
Answer :The value of x when log(x) = -5 is 0.00001.
Step-by-step explanation:
all uses the expression 4.2 * 12.3 * 14.6 to determine the cost of tile in the Floor of a room that measures 12.3 ft by 14.6 feet each square foot of tile cost 4.20 dollars how many decimal places will be in Polish final answer
one
three
five
eight
Answer:
There are three decimal places in the final answer.
Step-by-step explanation:
We have to calculate the expression 4.2 × 12.3 × 14.6, in which the floor dimensions are 12.3 ft by 14.6 ft. which I have to cover with tiles and each square foot of tile costs $4.20.
So, the area of the floor is (12.3 × 14.6) sq. ft. = 179.58 square feet.
Now, the cost of covering the floor with tiles will be = $(179.58 × 4.2) = $754.236.
Therefore, there are three decimal places in the final answer. (Answer)
PLZZZ HURRYYYY ITS TIMEDDDDD
Daniel expanded the expression as shown. What errors did he make? Select three options.
-2(-8x-4y+3/4)=-10x-8y-1 1/4
A. The first term should be positive.
B. The second term should be positive.
C.The last term should be -1 1/2, not -1 1/4.
D. He divided -8 by -2 instead of multiplying -8 by -2.
E. He did not simplify the expression completely.
Answer:
Step-by-step explanation:
-2(-8x - 4y + 3/4) =
16x + 8y - 3/2 ....(-3/2 is the same as - 1 1/2)
errors.....
A. the first term should be positive
B. the second term should be positive
C. the last term should be - 1 1/2
Daniel expanded the expression . The errors made by Daniel are
A. The first term should be positive.
B. The second term should be positive.
C. The last term should be -1 1/2, not -1 1/4.
Given :
Daniel expanded the expression as shown
[tex]-2(-8x-4y+3/4)\\-10x-8y-1 1/4[/tex]
Lets multiply -2 inside the parenthesis and see what happens
[tex]-2(-8x-4y+3/4) \\-2 (-8x)-2(-4y)-2(\frac{3}{4} )[/tex]
we know that negative times negative is positive
Also to simplify the fraction ,we can cancel out 2 and 4
[tex]-2 (-8x)-2(-4y)-2(\frac{3}{4} )\\+16x+8y-\frac{3}{2} \\+16x+8y-1\frac{1}{2} \\[/tex]
So the first and second terms are positive
Also the constant term is -1 1/2
So the errors he make are
A. The first term should be positive.
B. The second term should be positive.
C.The last term should be -1 1/2, not -1 1/4.
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on average, Shawnte drinks 1/2 of a 6 ounce glass of water in 2/3 hour. How much water does she drink in an hour?
Answer:
3 ounces every 40 minutes
60 divided by 40= 1.5
3x1.5= 4.5 ounces
What is the first step to solve this equation 11 minus 3x equals 44
Answer:
x=-11
Step-by-step explanation:
11-3x=44
3x=11-44
3x=-33
x=-33/3
x=-11
15-0 = 0-15. True or False. Justify your statement.
Answer:
False
Step-by-step explanation:
15-0=0
0-15=-15
Graph a line with a slope of
that contains the point (6,3).
The similarity ratio of two similar polygons is 2:3. Compare
the smaller polygon to the larger polygon. Find the ratio
of their areas.
Answer:
The ratio of their areas is 4:9
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
z ---> the scale factor
x ---> the area of the smaller polygon
y ---> the area of the larger polygon
[tex]z^2=\frac{x}{y}[/tex]
we have
[tex]z=\frac{2}{3}[/tex] ---> the scale factor is given
substitute
[tex](\frac{2}{3})^2=\frac{x}{y}[/tex]
[tex]\frac{4}{9}=\frac{x}{y}[/tex]
Rewrite
[tex]\frac{x}{y}=\frac{4}{9}[/tex]
therefore
The ratio of their areas is 4:9
Use natural logarithms to solve the equation. Round to the nearest thousandth.
3e^2x+2=28
A. 1.0797
B. 0.4689
C. 0.9261
D. 2.1595
Answer:
A. 1.0797
Step-by-step explanation:
Given the equation,
3e^2x+2=28
To solve for x, first we move 2 to the other side of the equation.
3e^2x = 28-2
3e^2x = 26
Dividing both sides by 3
e^2x = 26/3
e^2x = 8.67
Taking the natural logarithm if both sides
ln(e^2x) = ln8.67
2x = ln8.667
2x = 2.1595
x = 2.1595/2
x = 1.0797
A line passes through point A(10,15). A second point on the line has an x-value that is 125% of the x-value of point A and a y-value that is 75% of the y-value of point A. Use point A to write an equation of the line in point-slope form.
An equation is y− = (x− )
The equation of the line in the point-slope form is y - 15 = [tex]-\frac{3}{2}[/tex] (x - 10)
Step-by-step explanation:
The point-slope form of a linear equation is [tex]y-y_{1}=m(x-x_{1})[/tex] , where
m is the slope of the line, where [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] , [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] are two points on the line[tex](x_{1},y_{1})[/tex] is a point on the line∵ Point A = (10 , 15)
∵ The x-coordinate of the second point is 125% of x-coordinate
of point A
∴ x-coordinate of second point = [tex]\frac{125}{100}[/tex] × 10
∴ x-coordinate of second point = 12.5
∵ The y-coordinate of the second point is 75% of y-coordinate
of point A
∴ y-coordinate of second point = [tex]\frac{75}{100}[/tex] × 15
∴ y-coordinate of second point = 11.25
∴ The coordinates of the second point are (12.5 , 11.25)
Let us find the slope of the line by using the rule of it above
∵ [tex](x_{1},y_{1})[/tex] = (10 , 15)
∵ [tex](x_{2},y_{2})[/tex] = (12.5 , 11.25)
∴ [tex]m=\frac{11.25-15}{12.5-10}=\frac{-3.75}{2.5}=-\frac{3}{2}[/tex]
Now we can write the equation
∵ The point-slope form is [tex]y-y_{1}=m(x-x_{1})[/tex]
∵ [tex]m=-\frac{3}{2}[/tex]
∵ [tex](x_{1},y_{1})[/tex] = (10 , 15)
- Substitute these values in the form of the equation
∴ y - 15 = [tex]-\frac{3}{2}[/tex] (x - 10)
The equation of the line in the point-slope form is y - 15 = [tex]-\frac{3}{2}[/tex] (x - 10)
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Use the following figure to answer the question
∠ 1 and ∠ 2 are verical angles.
True
False
Answer:
False
Step-by-step explanation:
The only vertical angles shown are 1 and 3. The other pair is 2 and 4
What is the equation for the line?
Answer:
y=4x
Step-by-step explanation:
The line goes through the points (0, 0) and (2, 8).
You can plug these in to the slope formula, and the slope is 4
Since the line intersects the y-axis at 0, the y-intersect is 0.
Using these two pieces of information, you now know that the equation is
y=4x+0, or y=4x.
Hope this helps!
Answer:
Y = mx + c
Step-by-step explanation:
Where
m = gradient or slope
c = intercept (value of y when x=0)
Y = how far up
x = how far along
Guy wants to swim 500 meters. After 75 meters, he takes a break. What percent of his goal has he already met?
Answer:
15%
Step-by-step explanation:
75/500=0.15=15%
Answer:
15%
Step-by-step explanation:
divide 75/500 by 25/25= 3/20
3/20 x 5/5= 15/100
Find the coordinates of the center of the given circle
(x - 5)2 + (y + 3)2 = 25
(5,-3)
(5.3)
(-5,3)
Answer:
The coordinates are (5.3)
Step-by-step explanation:
the temperature is -4 it increases to 8 how many degrees did the temperature increase
Answer:
12 degrees.
Step-by-step explanation:
8 - (-4) = 12. So, the temperature increased by 12 degrees.
The temperature increased by 12 degrees from -4 to 8.
Explanation:The question is asking for the temperature change from -4 to 8 degrees. To find the increase in temperature, you subtract the initial temperature from the final temperature. In this case, 8 (final temperature) minus (-4) (initial temperature), equals 12°C. Hence, the temperature increased by 12 degrees.
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Oceanside bike rental charges 11 dollars plus 8 hours for renting. Tom paid 51 dollars to rent a bike . How many hrs did he pay to have the bike checked out
Answer:
Tom paid $51 renting the bike for 5 hours
Step-by-step explanation:
Given:
Oceanside bike rental charges $11 plus $8 per hour for renting.
Tom paid $51 to rent a bike.
To find the number of hours Tom rented the bike for.
Solution:
Let Tom rent the bike for =[tex]x[/tex] hours.
Hourly rate of renting = $8 per hour
Using unitary method find cost of renting for [tex]x[/tex] hours.
If renting for 1 hour costs = $8
Then for [tex]x[/tex] hours, the cost in dollars will be = [tex]8x[/tex]
Fixed charges = $11
∴ Total cost of renting a bike in dollars for [tex]x[/tex] hours will be given as:
[tex]8x+11[/tex]
Tom paid a total charge of = $51.
So, we have:
[tex]8x+11=51[/tex]
Subtracting both sides by 11.
[tex]8x+11-11=51-11[/tex]
[tex]8x=40[/tex]
Dividing both sides by 8.
[tex]\frac{8x}{8}=\frac{40}{8}[/tex]
∴ [tex]x=5[/tex]
Thus, Tom rents the bike for 5 hours.
x+ 1/8 =1.375 what is the anser
Answer:
1.25
Step-by-step explanation:
x+1/8=1.375
x=1.375-0.125
x=1.25
Answer: 1.25
Move all terms not containing x to the right side of the equation.
Exact Form:
x = 54
Decimal Form:
x = 1.25
Mixed Number Form:
x = 1 1/4
Hope this helps
The area of a triangle is 80in^2. The ratio of the length of its base to its height is 5:2. What are the base and height of the triangle? ..... show work
Answer: base = 20 inches , height = 8 inches
Step-by-step explanation:
The formula fro calculating the area of a triangle , given the base and the height is given as ;
A = [tex]\frac{1}{2}[/tex]bh
The ratio of its base to the height is given as 5: 2 , this means that
2b = 5h , that is
b = [tex]\frac{5h}{2}[/tex]
Substitute this into the formula for finding area , that is
80 = [tex]\frac{1}{2}[/tex] X [tex]\frac{5h}{2}[/tex] X h
80 = [tex]\frac{5h^{2}}{4}[/tex]
Therefore :
[tex]5h^{2}[/tex] = 80 x 4
[tex]5h^{2}[/tex] = 320
[tex]h^{2}[/tex] = 320 / 5
[tex]5h^{2}[/tex] = 64
h = 8 inches
Substitute h = 8 into b = [tex]\frac{5h}{2}[/tex] , then
b = 20 inches
Therefore , the base of the triangle is 20 inches and the height is 8 inches
is (2,4), (-5,2), (7,1), (-6,2) a relation or function
Answer: Function
Step-by-step explanation: A function is a special type of relation and for a relation to be a function, each x-term must correspond with exactly 1 y-term.
The easiest way to determine whether a relation is a function is to look at the x-coordinate of each ordered pair. If any of our ordered pairs have the same x-coordinate with a different y-coordinate, then our relation is no a function.
Since none of our x-terms repeat with different y-terms, this is a function.
Johnny sold crafts at a show. His prices included .07 sales tax. Johnny grossed $1236.00. What was johnny's taxable amount?
The taxable amount was $80.86
Step-by-step explanation:
Given,
Sales tax = .07
Total grossed = $1236.00
Let,
x be the price before sales tax, therefore,
Amount of sales tax = 0.07x
Price before sales tax + Sales tax = Total amount grossed
x+0.07x = 1236
1.07x=1236
Dividing both sides by 1.07
[tex]\frac{1.07x}{1.07}=\frac{1236}{1.07}\\x=1155.14[/tex]
Taxable amount = Total amount grossed - Price before tax
Taxable amount = 1236 - 1155.14 = $80.86
The taxable amount was $80.86
Keywords: subtraction, addition
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Answer:
$80.86 was taxed
Step-by-step explanation:
Find the midpoint of the segment with the endpoints (9,8) and (3,5)
Answer:
The midpoints are ( 6, 6.5 ).
Step-by-step explanation:
Given that the endpoints are A ( 9, 8) and B (3,5)-
As we know that-
If a line segment AB is with endpoints ([tex]x_{1}, y_{1}[/tex]) and ([tex]x_{2}, y_{2}[/tex] then the mid points C are-
C = ([tex]\frac{x_{1} + x_{2} }{2}[/tex] , [tex]\frac{y_{1} + y_{2} }{2}[/tex] )
Here,
A ( [tex]x_{1} = 9, y_{1} = 8[/tex] and B ( [tex]x_{2} = 3, y_{2} =5[/tex]
then the midpoints C are-
C = ( [tex]\frac{9 + 3 }{2}[/tex], [tex]\frac{8 + 5 }{2}[/tex]
C= ( 12/2 , 13/2 )
C = ( 6, 6.5 )
Hence the midpoints are (6, 6.5).
change the subject of the formula to w help
[tex]d = w - r { }^{2} [/tex]
Answer:
w = d + r²
Step-by-step explanation:
Given
d = w - r² ( isolate w by adding r² to both sides )
d + r² = w
which equation is the slope intercept form of this equation?
y-4=-2(x-5)
A) y=-2x+14
B)2x+y=6
C)y-4=-2x+10
D)x=-1/2y+3
Please help me!!!!!!!!!!! ☆I will give brainliest if right☆
Answer:
A) y = -2x + 14Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the equation i point-slope form.
Convert to the slope-intercept form:
[tex]y-4=-2(x-5)[/tex] use the distributive property
[tex]y-4=-2x+(-2)(-5)[/tex]
[tex]y-4=-2x+10[/tex] add 4 t oboth sides
[tex]y-4+4=-2x+10+4\\\\y=-2x+14[/tex]
A construction crew has just finished building a road. The road is 10 5/6 kilometers long. If the crew worked for 5 days, how many kilometers of road did they build each day? (Assume they built the same amount each day.)
Write your answer as a mixed number in simplest form.
Answer:
Step-by-step explanation:
10 5/6 km...in 5 days
(10 5/6) / 5 =
(65/6) / 5 =
65/6 * 1/5 =
65/30 =
2 1/6 kilometers per day <===
is it possible for one body to be at rest and moving at the same time? Why is that?
Answer:
yes
Step-by-step explanation:
it is possible that a body can be moving and at rest at the Same time. this is relative motion. an object that seem to be in motion for one subject can be stationary for another.
For example, A passenger in a bus. he/she is moving for a person walking on the pathway. but for the passenger next to him/her, they are at rest.
Answer:
Yes
Step-by-step explanation:
It is possible if you take into account different points of reference.
If you are in a car, sitting on a seat, while the car is moving, you are not moving with respect with the car. Since the car is moving with respect to the ground, you are moving with respect to the ground.
If you think bigger, you are always in motion. You may be standing in a position not moving at all with respect to the ground, but since the Earth is moving around the sun, you are moving with respect to the sun.
What is the Square root of -1
Answer:
the square root of -1 is i
Step-by-step explanation:
Answer:
[tex]\large\boxed{\sqrt{-1}=i}[/tex]
Step-by-step explanation:
[tex]\sqrt{-1}=i\\\\i-\text{immaginary unit}\ \left(i^2=-1\right)\\\\\text{It's a complex number.}[/tex]
If every 3 hours John walked 8 miles. How many miles did John walk in 1 hour
8 ÷ 3 = 2 2/3 miles
yeeeeeeeee
Answer:
2.66 miles every hour
Step-by-step explanation:
8/3
has a y-intercept of 21 and slope of -5.
Answer:
Step-by-step explanation:
Intercept c = 21 and slope m = -5
y = mx + c
y = -5x + 21