Answer:
Step-by-step explanation: Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.
During a race, all members of a rowing team should keep the oars parallel to produce maximum speed. Let m∠1 = 6x + 18 and m∠2 = 9x +12, and x = 10.
What type of angle pair are angles 1 and 2? (3 points)
Find the measure of angles 1 and 2. Show your steps. (4 points)
Are the oars parallel? Which theorem would be used to prove that the oars are parallel? (3 points)
∠ 1 and ∠ 2 are consecutive angles, the measures are 78° and 102° respectively and converse of consecutive angles theorem will prove the oars parallel.
What are consecutive angles?A pair of angles formed on each side of the transversal when it interacts with two parallel lines are known as consecutive angles. The angles in the same region (either interior or exterior) on each of the parallel lines form consecutive angles pairs and are supplementary.
Given that, in a race, all members of a rowing team should keep the oars parallel to produce maximum speed, and m∠1 = 6x + 18 and
m∠2 = 9x+12, and x = 10.
Putting the value of x, we get,
m∠1 = 6x + 18 = 6*10 + 18 = 78°
m∠2 = 9x+12 = 9*10 + 12 = 102°
m∠1 + m∠2 = 180°
Therefore, ∠1 and ∠2 are consecutive angles pairs.
We can prove that oars are parallel by converse of consecutive angles theorem.
Hence, ∠ 1 and ∠ 2 are consecutive angles, the measures are 78° and 102° respectively and converse of consecutive angles theorem will prove the oars parallel
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Determine which integers in the set S:{-24, -6, 12, 24) will make the inequality (m-3) s(m-12) false. OS:{-24, 24} OS:{-24, -6} OS:{-6, 12} OS:{12, 24}
The integers in the set S:{-24, -6, 12, 24) that will make the inequality 1/3(m - 3) ≤ 1/6(m - 12) false are: S:{12, 24}.
How to determine the integers?In order to determine which integers are true and false with respect to a solution of the given inequality, we would have to test the given integers by substituting their values into the inequality as follows;
For integers (-24, 24), we have:
1/3(m - 3) ≤ 1/6(m - 12)
1/3(-24 - 3) ≤ 1/6(-24 - 12)
1/3(-27) ≤ 1/6(-36)
-9 ≤ -6 (True).
For integers (-24, 24), we have:
1/3(m - 3) ≤ 1/6(m - 12)
1/3(24 - 3) ≤ 1/6(24 - 12)
1/3(27) ≤ 1/6(36)
9 ≤ 6 (False).
For integers (-24, -6), we have:
1/3(m - 3) ≤ 1/6(m - 12)
1/3(-6 - 3) ≤ 1/6(-6 - 12)
1/3(-9) ≤ 1/6(-18)
-3 ≤ -3 (True).
For integers (-6, 12), we have:
1/3(m - 3) ≤ 1/6(m - 12)
1/3(12 - 3) ≤ 1/6(12 - 12)
1/3(9) ≤ 1/6(0)
3 ≤ 0 (False).
For integers (12, 24), we have:
1/3(m - 3) ≤ 1/6(m - 12)
1/3(12 - 3) ≤ 1/6(12 - 12)
1/3(9) ≤ 1/6(0)
3 ≤ 0 (False).
1/3(m - 3) ≤ 1/6(m - 12)
1/3(24 - 3) ≤ 1/6(24 - 12)
1/3(27) ≤ 1/6(36)
9 ≤ 6 (False).
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The purchase price of an iPad is $610. If the sales tax rate is 6.5%, what is the amount of sales tax?
Answer:
Step-by-step explanation:
$603.5
Answer:39.65
Step-by-step explanation:
turn 6.5% to 0.065
610 x 0.065=39.65
If you buy an AED 50 meal with a 5% tax.
The tax amount to be paid is AED
Answer:
2.5 dhs
Step-by-step explanation:
5% of AED50
50x5/100=250/100
=AED2.5
The regular price of swimming lessons is $20 per hour. The sale price for new students is 75% of the regula
price. What is the sales price?
A train travels at 80 miles per hour. An equation can be written that compared that the time(t) with the distance(d). What is the domaine and range?
The equation that compares the time (t) with the distance (d) would be; 80 (t) = d
What is an equation?
An expression that depicts the relationship between two or more numbers and variables is called an equation. Two or more equations that can be solved to get a singular result are referred to as a system of equations. The equation's power must be in one degree.
Given that A train travels at 80 miles per hour. We need to find the equation that compares the time (t) with the distance (d)
where t means time so if the train travels 2 hours then it will travel;
80 × 2 = 160 miles
Therefore, the equation that compares the time (t) with the distance (d) would be; d = 80t.
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Alexa has $4.75 worth of dimes and quarters. She has 2 more dimes than quarters. Determine the number of dimes and the number of quarters that Alexa has.
Answer:
Alexa has 13 quarters and 15 dimes.
Step-by-step explanation:
First, we should set up a system of equations using the given information. We can use q to represent the number of quarters and d to represent the number of dimes.
Since quarters are $0.25, dimes are $0.10, and the total is $4.75 we know 0.25q + 0.1d = 4.75
The problem tells us that there are 2 more dimes than quarters, so d = q + 2
To solve for the number of quarters, we can substitute the second equation into the first equation.
0.25q + 0.1 (q + 2) = 4.75
0.25q + 0.1q + 0.2 = 4.75
0.35q = 4.55
q = 13
Then, to solve for the number of dimes, we can substitute q into the second equation.
d = q + 2
d = 13 + 2
d = 15
Question 10(Multiple Choice Worth 2 points)
(Adding and Subtracting with Scientific Notation MC)
Simplify (3.7 x 10-9) - (8.2 x 10-8). Write the final answer in scientific notation.
O-7.83 x 10-8
-7.83 x 10-9
O-4.5 x 10¹
O-4.5 x 10-¹
The simplified value of (3.7 x 10^-9) - (8.2 x 10^-8) in scientific notation is - 7.83 x 10^-8. Option A is correct.
We will solve the given expression using laws of exponents.
Some laws of exponents are:
(a²) · (a³) = a²⁺³ = a⁵(a²)³ = a²ˣ³ = a⁶(a²) ÷ (a³) = a²⁻³ = a⁻¹a⁻¹ = 1 / aWe are given:
(3.7 x 10^-9) - (8.2 x 10^-8)
= (3.7 x 10^(-1 -9)) - (8.2 x 10^-8)
= (3.7 x 10^-1 x 10^-8) - (8.2 x 10^-8)
= (0.37 x 10^-8) - (8.2 x 10^-8)
= (0.37 - 8.2) x 10^-8
= - 7.83 x 10^-8
So, the simplified value of (3.7 x 10^-9) - (8.2 x 10^-8) is - 7.83 x 10^-8.
Thus, the simplified value of (3.7 x 10^-9) - (8.2 x 10^-8) in scientific notation is - 7.83 x 10^-8. Option A is correct.
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Daya contributes a set percentage of her gross pay towards a 401k account and will have a total of $172,486.00 by retirement. Daya's employer also contributes a set percentage, which will increase her total by $161,531.00. What is the percent increase between the total without Daya's employer contribution and the total with? Round to the nearest whole percent.
94%
79%
52%
48%
The percent increase between the total without Daya's employer contribution and the total with is A. 94%.
How to calculate the percentage?From the information, Daya contributes a set percentage of her gross pay towards a 401k account and will have a total of $172,486.00 by retirement and her employer also contributes a set percentage, which will increase her total by $161,531.00.
Therefore, the percentage increase will be:
= Increase in amount / Original amount × 100
= 161,531/172486 × 100
= 94%
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A Bunch of Systems
Solve each system of equations without graphing and show your reasoning. Then, check
your solutions.
2x + 3y = 7
-2x + 4y = 14
Answer:
(- 1, 3 )
Step-by-step explanation:
2x + 3y = 7 → (1)
- 2x + 4y = 14 → (2)
add (1) and (2) term by term to eliminate x
(2x - 2x) + (3y + 4y) = (7 + 14)
0 + 7y = 21
7y = 21 ( divide both sides by 7 )
y = 3
substitute y = 3 into either of the 2 equations and solve for x
substituting into (1)
2x + 3(3) = 7
2x + 9 = 7 ( subtract 9 from both sides )
2x = - 2 ( divide both sides by 2 )
x = - 1
As a check
substitute the values of x and y into the left side of both equations and if equal to the right side in both equations then the values of x and y are true.
(1) 2(- 1) + 3(3) = - 2 + 9 = 7 ← true
(2) - 2(- 1) + 4(3) = 2 + 12 = 14 ← true
then (- 1, 3 ) is the solution to the system
Answer:(- 1, 3 )
Step-by-step explanation:
Evaluate the expression when a = -6 and y=4. y-9a
(can someone help? I'm not used to how this is formatted.)
Answer: 58
Step-by-step explanation:
First you substitute the values, so
4-9*-6
Then you solve using order of operations
Answer:
58
Step-by-step explanation:
y-9a
Let a = -6 and y=4
Substitute the values in
4 -9(-6)
Multiply first
4 + 54
Add
58
PLEASE HELP. I need both the x and y and the length of DF
The value of x is 17, y is 2 and length of DF is 20.
Basic Proportionality Theorem (can be abbreviated as BPT) states that, if a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.
For x
DG = GE ( Given )
DG + GE = DE
DE = 2(DG)
DG/DE = 1/2
hence GH/EF = 1/2
By Basic Proportionality Theorem ( BPT )
(x – 3) / 28 = 1/2
after cross multiplication
2(x – 3) = 28
2x – 6 = 28
2x = 34
x = 17
For y
By Basic Proportionality Theorem (BPT) to side DF
DF = 2(DH)
DH/DF = 1/2
(y + 8) / (y + 8 + x – 7) = 1/2
after cross multiplication
2(y + 8) = y + 8 + x – 7
put x = 17
2(y + 8) = y + 8 + 17 – 7
2(y + 8) = y + 18
2y + 16 = y + 18
2y = y + 2
2y – y = 2
y = 2
DF = 2(2+8)
= 2(10)
= 20
Hence, x is 17, y is 2 and DF is 20.
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Factor -1/2 out of 1/2x+6
Answer:
-x-12
Step-by-step explanation:
1/2x+6
first divide by -1/2 or multiply by -2(its the reciprocal)
-2(1/2x+6)
-2*1/2x+6*-2
-x-12
If h(x) = -2x + 10, what is the value of x when h(x) = 2
Answer:
-6
Step-by-step explanation:
to solve you need to substitute the value of x in the equation which is given as 2so if you rewrite the equation it will be
-2(2)+10
=(-2*2)+10
=-4+10
=6
Evaluate n(x) = -1 - x + 4 when x = -2,0, and 5
x = -2, n(-2) = -1 - (-2) + 4 = 5
x = 0, n(0) = -1 - 0 + 4 = 3
x = 5, n(5) = -1 - 5 + 4 = -2
If there are 20 boxes of bicycles/tricycles total and 48 wheels total how many tricycles were ordered?
write and graph a system of linear equations to model the situation
The system of equations is:
x + y = 20
2x + 3y = 48
And its graph can be seen in the image at the end.
How to write and solve the system of equations?Let's define the variables:
x = number of boxes with a bicycley = number of boxes with a tricycle.Each bicycle has 2 wheels, each tricycle has 3 weels, and we know that there are 20 boxes and 48 wheels, then the system of equations is:
x + y = 20
2x + 3y = 48
To solve the system graphically we just need to graph both lines on the same coordinate axis and see at which point do the lines intersect, the graph is below.
The solution is x = 12, y = 8.
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In the picture, you see 1 paper cup and 5 paper cups that are stacked together. The table shows the heights of stacks with different numbers of cups.
Which function rule gives the height of a stack of cups in terms of the number of cups in a stack?
The function rule that gives the height of a stack of cups is h(c) = 8+ 2(c)
How to determine the function rule that gives the height of a stack of cups?
Looking at the image, 1 paper cup has a body height of 8cm (total height = 10cm) and the height of the cups increases by 2cm for each cup added.
If you add three cups, for example, the height increases by 6cm (3 x 2cm). If you add n cups the height will increase by 2n and the total height will be 8+2n
Number of cups, c >>>>> Process >>>>> Height of stack, h(cm)
c 8+ 2(c) h
h(c) = 8+ 2(c)
Note: It is h(c) because c is the input and h is the output
Therefore, the function rule that gives the height of a stack of cups in terms of the number of cups in a stack is h(c) = 8+ 2(c)
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Adding two negatives makes a bigger number? Is this true or false? Explain.
Answer: False, adding two negatives does not make a bigger number. I know this because when adding the two negatives, the absolute value will get bigger. However, the value of the number gets smaller.
Look at the chart below. There are several places marked *
out with a blue box. Figure out what place goes in each
box. Then, type the second letter of each missing place in
order from greatest place value to least place value in
ALL CAPITALS.
Answer:
no chart
Step-by-step explanation:
show chart let us see what to use
Find the exact value of the expression. Do not use a calculator.
sin 79°-cos 11°
I got 0. I'm not sure if that's right.
Answer:
sin(79°) - cos(11°) = 0
Step-by-step explanation:
Based on the rule sin(90-x) = cos(x), we can transform the expression. See the attached for more details
Please solve both blanks and round to the nearest tenth please<3
The inequality will be 3.70x ≤ 145 and the number of items that you can by is x ≤ 39
Total budget that you have = $145
The price of each item = $3.70
Consider the number of items = x
The inequality will be
3.70x ≤ 145
We have to solve the inequality to find the number of items
3.70x ≤ 145
Divide 3.70 on the both side of the inequality
3.70x / 3.70 ≤ 145 / 3.70
x ≤ 39.18
x ≤ 39
The number of items that you can buy is x ≤ 39
Hence, the inequality will be 3.70x ≤ 145 and the number of items that you can by is x ≤ 39
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Which of the following is the solution of
the system of equations shown?
A. (2, 2)
B. (-2, 2)
C. (2,-2)
D. (-2,-2)
(The answer isn’t B. I already tried that)
PLEASE HELP WILL GIVE 100 POINTS AND BRAINLEST ANSWER BOTH QUESTIONS TWO ANSWERS FOR EACH!!
Circumcenter is equidistant from the vertices, perpendicular bisectors will cross. Incentre is equidistant from the sides. Where the angle bisector cross incenter
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
We have to choose the properties of circumcenter.
Circumcenter is equidistant from the vertices.
It is equidistant from the three vertices of the triangle, and thus you can construct a circle centered at the circumcenter and circumscribing the triangle.
and perpendicular bisectors will cross.
We have to choose the properties of incenter.
Incentre is equidistant from the sides.
Where the angle bisector cross incenter
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10 A factory produces lemon-scented widgets. Each widget is cheaper, the more that are produced, but costs will go up if too many widgets are produced, due to storage requirements. The accountant for the factory says that the costs for producing x thousands of units a day can be approximated by the formula C = 0.04x2 - 8.504x + 25302. Find the daily production level that will minimize the costs. Be sure to show your work and include units of measurement.
The daily production level that will minimize the costs is 106300 units.
How to calculate the production level?From the information, the function is given as C = 0.04x² - 8.504x + 25302.
c = cost
From the function, the following can be deduced:
a = 0.04
b = 8.504
c = 25302
Then, -b/(2a) will be:
= -8.504 / (2 × 0.04)
= 106.300
Note that production level will minimize the cost in thousands.
The production level will now be:
= 106.300 × 1000
= 106300 units
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I need help with this please.
(50 POINTS)
Answer: ( -2, -3 )
Step-by-step explanation:
the normal model n(58,21) describes the distribution of weights of chicken eggs in grams. suppose that the weight of a randomly selected chicken egg has a z-score of -1.41. what is the weight of this egg in grams? round to the nearest hundredth of a gram.
By using normal distribution, it is obtained that weight of a randomly selected chicken egg is 28.39 grams
What is normal distribution?
Normal distribution is a continuous type probability distribution whose probability density function is
[tex]\frac{1}{\sigma \sqrt{2\pi}}e^{-\frac{z^2}{2}[/tex]
where, z = [tex]\frac{x - \mu}{\sigma}[/tex]
[tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation
In case of normal distribution
Formula for z = [tex]\frac{x - \mu}{\sigma}[/tex]
[tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation
Let the weight of the egg be x grams
Here, z = -1.41, [tex]\mu[/tex] = 58 and [tex]\sigma[/tex] = 21
[tex]-1.41 = \frac{x - 58}{21}\\[/tex]
x = -1.41 [tex]\times[/tex] 21 + 58
x = 28.39 grams
Weight of a randomly selected chicken egg is 28.39 grams
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Select the correct answer.
Which number best represents the slope of the graphed line?
A. -5
B.-1/5
C. 1/5
D.5
Answer:
A. -5
Step-by-step explanation:
You want the slope of a graphed line that crosses grid points (0, 2) and (1, -3).
SlopeThe sign of the slope is positive if the line goes up to the right. This line goes down to the right, so the sign of its slope is negative. (Eliminates choices C and D)
The magnitude of the slope is the ratio of vertical distance to horizontal distance between two points. This line drops 5 vertical squares for each square to the right, so its slope is ...
rise/run = -5/1 = -5
The slope is best represented by -5.
__
Additional comment
From a point on the line that is a crossing of grid lines, if the line crosses the next vertical grid line before it crosses the next horizontal grid line, the magnitude of its slope is less than 1.
Here, the line crosses several horizontal grid lines before it crosses another vertical grid line, so its slope has a magnitude greater than 1. When the choice is between -5 and -1/5, the larger magnitude number is -5.
From two points on the line, you can find the slope using the formula ...
m = (y2 -y1)/(x2 -x1)
m = (-3 -2)/(1 -0) = -5/1 = -5 . . . . . . using points (0, 2) and (1, -3)
A farmer estimates that he will harvest 7250 bushels of wheat. The weather is perfect during the growing season, so he harvests 1 more bushels of wheat than expected. How many bushels of wheat does the farmer harvest?
The number of bushels of wheat does the farmer harvest is 7251 bushels of wheat
The farmer's estimated number of bushels of wheat in the harvest = 7250 bushels
The weather is perfect during the growing season
The number of additional bushels of wheats harvested = 1 bushels
The number of bushels of wheat does the farmer harvest = The farmer's estimated number of bushels of wheat in the harvest + The number of additional bushels of wheats harvested
Substitute the values in the equation
The number of bushels of wheat does the farmer harvest = 7250 + 1
Here we haver to use the addition
Add the terms
= 7251 bushels of wheat
Hence, the number of bushels of wheat does the farmer harvest is 7251 bushels of wheat
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what is the probability of picking a blue marble randomly out of a bag of 6 blue marbles, 3 black marbles, and 8 orange marbles while rolling a 3 on a 6-sided dice at the same time?
Using the concepts of probability, we got that 0.063 is the probability of picking a blue marble randomly out of a bag of 6 blue marbles, 3 black marbles, and 8 orange marbles while rolling a 3 on a 6-sided dice at the same time
We know very well that probability is defined as the fraction of number of favorable outcomes to the total number of outcomes.
Here, we are rolling a 6-faced dice.
Getting 3 on the top face of dice is same as the any number getting from 1 to 6 on the top face of the dice.
So, every number has equal probability to come on the top face, therefore the probability of getting 3 on the top face of dice is (1/6)
Now, similarly total number of marbles in the bag=6 blue +3 black+8 orange marble=17 marbles.
Now, picking one marble from 17 marble is can be done in [tex]^1^7C_1[/tex] ways, similarly choosing 1 blue marble from 6 marble can be done in [tex]^6C_1[/tex] ways.
So, probability of picking 1 blue marble randomly=6/17
Now, the probability of picking 1 blue marble from 17 marbles along with rolling dice probability is given by =(6/17)×(1/6)=(1/17)=0.063
Hence, the probability of picking a blue marble randomly out of a bag of 6 blue marbles, 3 black marbles, and 8 orange marbles while rolling a 3 on a 6-sided dice at the same time is 0.063
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Question 12
<
>
Cost of Bottled water. A water bottling company charges $8 per month for their water dispenser and
$4 for each gallon of water delivered. If you have g gallons of water delivered in a month, then the
expression 8 + 4g gives the amount of your bill for that month. Find the monthly bill for 20 gallons.
The monthly bill for 20 gallons of water is $88.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
A water bottling company charges $8 per month for their water dispenser and $4 for each gallon of water delivered.
If you have g gallons of water delivered in a month.
Then, the equation to represent the amount of your bill for that month.
8+ 4g
Now, for g=20 the amount of bill would be
= 8 +4(20)
= 8+ 80
= $88
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