The values of a and b are 8 and 54 respectively
How to find the values of a and b such that WX is perpendicular to YZ?The given parameters are:
WVY= 4a + 58
XVY = 2b - 18
From the question, we understand that WX is perpendicular to YZ
This means that
WVY= 90
XVY = 90
So, we have
4a + 58 = 90
2b - 18 = 90
Solve for a in 4a + 58 = 90
4a = 90 - 58
Evaluate
4a = 32
Divide by 4
a = 8
Solve for b in 2b - 18 = 90
2b = 90 + 18
Evaluate
2b = 108
Divide by 2
b = 54
Hence, the values of a and b are 8 and 54 respectively
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What are the coordinates of G after it is ROTATED 90 DEGREES CLOCKWISE?
The coordinates of G after it is rotated by 90 degrees will be ( 3, 4 ).
What is a translation?
The process of changing the location of the image on the coordinate system will be known as the translation.
Our point A(x,y) becomes A' when a point is rotated 90 degrees counterclockwise about the origin (-y,x). To put it another way, flip x and y, and make y-negative.
Given that point, G is translated to 90 degrees. The translated coordinates of point G will be calculated as:-
( -x, y ) = ( y, x )
( -4 , 3 ) = ( 3 , 4)
Therefore, the coordinates of G after it is rotated by 90 degrees will be ( 3, 4 ).
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What is the equation of the linear function in slope intercept form described by this table?
The equation of the linear function in slope intercept form is given as y = -2x + 1
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
From the table, the linear function contains the points (0, 1) and (2, -3), hence:
y - 1 = [(-3 - 1)/(2 - 0)](x - 0)
y = -2x + 1
The equation of the linear function in slope intercept form is given as y = -2x + 1
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In the morning, there were 260 cars in a parking lot. In the evening, the number of cars decreased by 35%. How many cars remained in the parking lot?
169 cars are remaining in the parking lot
How to calculate the number of cars left in the parking lot ?There are 260 cars in the parking lot
This number decreased by 35%
100% - 35%
= 65%
65/100
= 0.65
The number of cars left can be calculated as follows
= 260 × 0.65
= 169
Hence there are 169 cars left in the parking lot
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On a long hike Lucy drank 6 pints of water. How much is this in quarts?
On a long hike Lucy drank 6 pints of water, which is equal to 3 quarts.
What is quarts?An English measurement of volume equal to one-quarter gallon is the quart. There are now three different types of quarts in use: the liquid quart, dry quart, and imperial quart of the British imperial system. One liter is roughly equivalent to each. It is divided into four cups or two pints (in the US). The precise dimensions of the quart have historically changed in line with shifting values of gallons over time and in relation to various commodities.
A measure of liquid capacity that is equal to two pints or a quarter of a gallon, or roughly 0.94 liter in the US and 1.13 liter in the UK.
Since, 1 quart = 2 pints
Therefore by unitary method we can say,
2pint= 1 quart
6pint= 3quarts
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The following trial balance of Reese Corp. at December 31, 2014 has been properly adjusted except for the income tax expense adjustment. Reese Corp. Trial Balance December 31, 2014 Dr. Cr. Cash $ 775,000 Accounts receivable (net) 2,695,000 Inventory 2,085,000 Property, plant, and equipment (net) 7,566,000 Accounts payable and accrued liabilities $ 1,701,000 Income taxes payable 654,000 Deferred income tax liability 85,000 Common stock 2,350,000 Additional paid-in capital 3,680,000 Retained earnings, 1/1/14 3,450,000 Net sales and other revenues 13,560,000 Costs and expenses 11,180,000 Income tax expenses 1,179,000 $25,480,000 $25,480,000 07. The current assets total is: A. $6,080,000 C. $5,405,000 B. $5,555,000 D. $4,955,000
The current assets total for Reese Corp. on December 31, 2014, is B. $5,555,000.
What are the current assets?The current assets are Cash and Cash Equivalents (Marketable Securities), Accounts Receivable, Inventory, and Prepaid Liabilities (Expenses).
The current assets are the short-term portion of the total assets.
The current assets show Reese Corp.'s short-term liquidity and the company's ability to meet its short-term obligations (current liabilities), especially to suppliers, vendors, and other short-term creditors.
Data and Calculations:Reese Corp.
Trial Balance
December 31, 2014
Dr. Cr.
Cash $ 775,000
Accounts receivable (net) 2,695,000
Inventory 2,085,000
Property, plant, and equipment (net) 7,566,000
Accounts payable and accrued liabilities $ 1,701,000
Income taxes payable 654,000
Deferred income tax liability 85,000
Common stock 2,350,000
Additional paid-in capital 3,680,000
Retained earnings, 1/1/14 3,450,000
Net sales and other revenues 13,560,000
Costs and expenses 11,180,000
Income tax expenses 1,179,000
$25,480,000 $25,480,000
Current Assets:Cash $ 775,000
Accounts receivable (net) 2,695,000
Inventory 2,085,000
Total current assets = $5,555,000
Thus, the current assets total for Reese Corp. on December 31, 2014, is B. $5,555,000.
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Solve for y.
6x - 4y = 11
Answer:
y = 3/2x -11/4
Step-by-step explanation:
6x - 4y = 11
Solve for y
Subtract 6x from each side
6x-6x - 4y =-6x+ 11
- 4y =-6x +11
Divide each side by -4
-4y/-4 = -6x/-4 + 11/-4
y = 3/2x -11/4
Answer:
[tex] \sf \: y = \frac{(11 - 6x)}{ - 4} \\ [/tex]
Step-by-step explanation:
[tex] \sf \: First, \: take \: 6x \: to \: right \: side.[/tex]
[tex] \sf \: - 4y = 11 - 6x[/tex]
[tex] \sf \: Now \: divide \: both \: sides \: by \: -4 \: to \: make \: y \: the \: subject. [/tex]
[tex] \sf \: \frac{ - 4y}{ - 4} = \frac{(11 - 6x)}{ - 4} \\ \sf \: y = \frac{(11 - 6x)}{ - 4} [/tex]
Translate to an equation. Then solve the equation.
Seven times the difference of some number and 2 amounts to the quotient of 112 and 8.
Answer: 7(x-2(112/8))= 7(x-28)= 7x - 28*7
7x = 28*7
x=28
Y varies jointly with X y=16 when x=4 and z= 1/2 find y when x= 2 and z= 1/4
The value of y when x= 2 and z= 1/4 is y = 4
In this question, we have been given y varies jointly with x and z.
This means y is directly proportional to x and z.
y = 16 when x = 4 and z = 1/2
We need to find the value of y when x= 2 and z= 1/4
From y = 16 when x = 4 and z = 1/2 we can compute the equation as,
y = 8xz
16 = 8(4)(1/2)
16 = 8 × 2
16 = 16
So, the equation is y = 8xz
Now for x= 2 and z= 1/4,
y = 8xz
y = 8 × 2 × (1/4)
y = 2 × 2
y = 4
Therefore, the value of y when x= 2 and z= 1/4 is y = 4
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Gavin and Jim are marking exam
papers.
Each set takes Gavin 41
minutes and Jim 1 hour. Express the
times Gavin and Jim take as a ratio in its
simplest form.
Answer:
41:60
Step-by-step explanation:
Time taken by Gavin takes = 41 minutes
Time taken by Jim takes = 1 hour
We know that 1 hour = 60 minutes
So, the ratio of times that Gavin and Jim take as a ratio would be
Gavin:Jim
41:60
Can someone please help
Answer: 40
Step-by-step explanation:
when x=0, y=0
when x=2.5, y=100
(y2-y1)/(x2-x1)=
(100-0)/(2.5-0)=
100/2.5=40
Answer:
40
Step-by-step explanation:
the point on the graph is (1,40). The ordered pair is in the form (x,y) The constant of proportionality is the y/x or 40/1 which equals 40.
WORTH 75 POINTS Find an equation of the perpendicular bisector of the segment "AB" which has end points points A(1, –2.5) and B(5, 5.5).
Answer:
Step-by-step explanation:
Suppose we have a bottomless bag of 3 different kinds of balls: blue, green, and red. How many possibilities are there to choose 3 balls and arrange them in a line.
The number of possibilities that are there to choose 3 balls is 6.
How to illustrate the information?From the information, we have a bottomless bag of 3 different kinds of balls: blue, green, and red.
The number of possibilities that are there to choose 3 balls will be:
= 3!
= 3 × 2 × 1
= 6 possibilities.
Therefore, the number of possibilities that are there to choose 3 balls is 6.
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if x/x+3 = 0.625, what is
the value of x-4/x-1
Solving the first equation we can find that the value of x is x = 5, then we can replace that in the other expression and we can see that the value of the expression is 1/4.
What is the value of x-4/x-1?First, we need to find the value of x.
We know that:
x/(x + 3) = 0.625
Solving that equation we will get:
x = 0.625*(x + 3)
x - 0.625*x = 3*0.625
x*(1 - 0.625) = 3*0.625
x = 3*0.625/(1 - 0.625) = 5
So the value of x is 5 (and it will be in both expressions)
Now we can replace that value in the given expression (just replace the variable x by the number 5)
(x - 4)/(x - 1) = (5 - 4)/(5 - 1) = 1/4
The value of the expression is 1/4.
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A researcher wants to study the effects of sleep deprivation on motor skills. Nine people volunteer for the experiment: Amanda, Brian, Christine, David, Emily, Fred, George, Heather, and Ivan. Use the row of digits in the random number table below to select a simple random sample of three subjects (ignore zeros). The other six subjects will go into the control group. If the subjects are numbered 1 through 9 alphabetically, what are the numbers of the three subjects selected? List the subjects that will go in the treatment group.
The numbers of the three subjects selected are 6,3 and 9.
The subjects that will go in the treatment group Fred, Christine and Ivan
What is data?A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
Given:
Nine people volunteer for the experiment: Amanda, Brian, Christine, David, Emily, Fred, George, Heather, and Ivan.
line/column (1) (2) (3) (4)
1 22663 42156 60419 98022
1 16901 87295 56738 04619
1 63949 92781 15658 58219
So, the numbers of the three subjects selected are 6,3 and 9.
and, Fred, Christine and Ivan are the three subjects.
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If you ask Megan how many dogs she has, she answers with a riddle: "Four-sevenths of my dogs plus 9." How many dogs does she have?
Step-by-step explanation:
This is a simple system of equations problem, with our equation being:
[tex]\frac{4}{7}x+9=x[/tex]
We know this as her dogs (x) is equal to 4/7 of her dogs (x) plus 9. Now all we must do is solve for x:
[tex]\frac{4}{7}x+9=x\\\\\frac{4}{7}x=x-9\\\\\frac{4}{7}x=\frac{7}{7}x-9\\\\\frac{-3}{7}x=-9\\\\x=21[/tex]
Please help me I’ll mark brainly
Answer: -3
Step-by-step explanation:
Part F
Complete the table to find the rule for the reflection, the coordinates of triangle ABC, and the coordinates of the reflected Image, triangle A'B'C'.
Original Coordinates New Coordinates
(.)
AT.)
B(,)
((.)
(x,y)
A(.)
B(.)
((.)
Answer:
A
Step-by-step explanation:
Do the following calculation according to correct significant figures:
2.9/1.3 +4.0=
Answer: 6.2
Step-by-step explanation:
2.9/1.3 +4.0=
2.23 + 4.0=
2.2 + 4.0=6.2
The given information is,
→ (2.9/1.3) + 4.0
Let's solve the problem,
→ (2.9/1.3) + 4.0
→ 2.23 + 4 = 6.23
Thus, the answer is 6.23.
a 12-foot piece of string is cut into two pieces so that the longer piece is 3 feet longer than twice the shorter piece. if the shorter piece is x feet long, find the lengths of both pieces.
Answer:
3 ft and 9 ft
Step-by-step explanation:
what is the answer to
8-(4*2)/2=
7. After testing for COVID-19 at Mulago Hospital, the ratio of positive to negative to asymptomatic cases was 4:5:7 respectively. If the total number of negative and positive cases was 63, (a) find the number of negative cases tested at the hospital. (03 Marks)
Answer:
7. After testing for COVID-19 at Mulago Hospital, the ratio of positive to negative to asymptomatic cases was 4:5:7
Step-by-step explanation:
ve and positive cases was 63, (a) find the number of negative cases tested at the hospital. (03 Marks)
Alex makes $20 an hour as a dental assistant. She works 8 hours per day, and 80 hours on each paycheck. How much does Alex make, before
taxes, on each paycheck?
Answer:
give the amount of tax please
Answer: 160
Step-by-step explanation:
20 per hour 8h a day
160 per day
20x8
A barista is mixing a house blend of coffee that is 25% light roast. If there are 8 pounds of the light roast available, how much of the blend can the barista make?
The amount of blend that the barista can make is 2
What is percentage?Percentage can be defined as the ratio of a number to 100.
It is represented using the symbol; '%'
From the information given, we have;
We have 25% of light roastThere are also 8 pound of light roastTo get the amount of blend, we have;
= 25% of 8 pound
This is expressed as;
= 25/ 100 × 8
= 0. 25 × 8
= 2 blends
Thus, the amount of blend that the barista can make is 2
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Ling is a camp counselor at a local summer camp. She is in charge of the weekly craft activity
for 40 campers. She plans to make fabric-covered frames that each require 1/6 yard of fabric.
The camp director gave her 6 2/3 yards of fabric remnants for this project. Does Ling have
enough fabric for her craft activity?
She has the exact amount of fabric that she needs for this project.
Does Ling have enough fabric for her craft activity?
We know that she is in charge of 40 campers, and she wants to make fabric-covered frames, such that each one needs 1/6 yards of fabric.
We know that he has a total of 6 + 2/3 yards to do this, and we need to see if that is enough.
Now, for each one of the 40 campers she needs 1/6 yards, so the total amount she needs is given by the product:
T = 40*(1/6 yards) = 40/6 yards = (36 + 4)/6 yards = (6 + 4/6) yards
T = (6 + 2/3) yards
So she has the exact amount of fabric that she needs for this project.
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−2(3n+ 8) = −6(n − 2)
Answer:
Step-by-step explanation:
0
Graph the line y=kx+1 given that the point M belongs to the line. M (1, 3)
The graph of the equation of the line y = k · x + 1 is shown in the image attached below.
How to derive and graph the equation of a line
In this problem we know that a function represents a line and that a point belongs to it. The equation of the line is of the form:
y = k · x + 1
Where k is the slope of the line equation.
If we know that (x, y) = (1, 3), then the equation of the line is:
3 = k + 1
k = 2
Then, the equation of the line is y = 2 · x + 1 and we proceed to graph the equation by means of a graphing tool. The result is presented in the image attached below.
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Which of the following sets does the number 0.1453 belong to
Answer: The number 0.1453 belong to rational numbers and real numbers.
Step-by-step explanation:
The whole numbers are 0,1,2,3,..., so 0.1453¯¯¯¯¯ (repeat bar on 53)does not belong to the set of whole numbers. The integers are the whole numbers and their opposites, so 0.1453¯¯¯¯¯(repeat bar on 53) does not belong to the set of integers. Rational numbers include decimals that repeat or stop.The integers are the whole numbers and their opposites, so 0.1453¯¯¯¯¯(repeat bar on 53) does not belong to the set of integers.Rational numbers include decimals that repeat or stop. Because 0.1453¯¯¯¯¯(repeat bar on 53) is a repeating decimal number, it belongs to the set of rational numbers. Because 0.1453¯¯¯¯¯(repeat bar on 53) is a rational number, it does not belong to the set of irrational numbers.Because 0.1453¯¯¯¯¯(repeat bar on 53) is a rational number, it does not belong to the set of irrational numbers.All rational numbers are real numbers, so 0.1453¯¯¯¯¯ (repeat bar on 53) belongs to the set of real numbers. In summary, 0.1453¯¯¯¯¯(repeat bar on 53) belongs to the following sets: rational numbers and real numbers.Therefore,
The number 0.1453 belong to rational numbers and real numbers.
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2 + 3 * 5 – 1 + (3 – 5)
Answer:
14
Step-by-step explanation:
PEMDAS
parathesis first
3-5=-2
2+3*5-1-2
next multiply
3*5=15
2+15-1-2
go in order of subtracting and adding
2+15=17
17-1-2
17-1=16
16-2
14
In the expression 5+2+ 5 x + 2 x + x , you can combine
In the expression 5 + 2 + 5x + 2x + x we can combine the like terms to get the simplified form of the expression as 7 +8x.
What are like terms?If two words have the same variable portion, we refer to them as "like terms." When comparing algebraic terms to locate similar terms, we first disregard the coefficients and merely check to see if the variables and exponents are the same. The terms that meet this requirement are known as like terms.
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given expression 5 + 2 + 5x + 2x + x
Combine the like terms
5 + 2+ 5x + 2x +x
=(5+2) + (5+2+1)x
= 7+ 8x
This is the simplified form of the given expression.
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SOMEONE HELP PLS ILL MARK BRAINLIEST
Based on the linear pair postulate, the value of x is proven to be 11.
See proof below.
What is a Linear pair?A linear pair is formed by two adjacent angles that lie on a straight line, thus, they have a sum that is equal to 180 degrees.
We know that angle 1 and angle 2 are a linear pair, the complete proof would be stated as follows:
Statement Reason
1. Angle 1 and angle 2 are a linear pair 1. Given
2. Angle 1 and angle 2 are supplementary 2. Linear pair postulate
3. m<1 + m<2 = 180° 3. Supplementary angles
4. 11x - 6 + 4x + 21 = 180 4. substitution
5. 15x + 15 = 180 5. Combine like terms
6. 15x = 165 6. Subtraction property
7. x = 11 7. Division property
Thus, based on the linear pair postulate, the value of x is proven to be 11.
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