Explanation:
To add mixed fractions we have to follow these steps:
[tex]1\frac{1}{14}+3\frac{1}{14}=[/tex]1. Add the whole numbers together
[tex]1+3=4[/tex]2. Add the fractions
[tex]\frac{1}{14}+\frac{1}{14}=\frac{2}{14}=\frac{1}{7}[/tex]3. If the sum of the fractions is an improper fraction then we change it to a mixed number and add the whole part to the whole number we got in step 1.
In this case the sum of the fractions results in a proper fraction, so we can skip this step.
Answer:
The result is:
[tex]4\frac{1}{7}[/tex]
Consider the following functions. Find the domain. Express your answer in interval notation.
Explanation:
[tex]\begin{gathered} f(x)\text{ = - }\sqrt[]{6-x} \\ g(x)\text{ = 4 - x} \\ (g\text{ - f)(x) = g(x) - f(x)} \end{gathered}[/tex][tex]\begin{gathered} (g\text{ -f)(x) = }4-\text{ x - (-}\sqrt[]{6\text{ - x}}) \\ (g\text{ -f)(x) = 4 - x + }\sqrt[]{6-x} \end{gathered}[/tex][tex]undefined[/tex]Solve the system of two linear inequalities graphically.Graph the solution set of the second linear inequality?
According to the second inequality, y is greater than or equal to -2, which means that the graph will have a solid line, the first step is to pick solid choice.
The boundary line is y=2, we know this by replacing the inequality sign by an equal sign. Two points one this line are (-1,2) and (2,2). We know it because it is an horizontal line that represents a constant function, it means that all the values of y will be 2 (boundary line).
As the equal sign is greater than or equal to, the region that must be shaded is the one above the boundary line.
given which of the following describes the boundary line and shading for the second inequality in the system
Answer:
Solid Line, Shade Above
Explanation:
Given:
[tex]\left\{\begin{array}{l} y<-2 x+3 \\ y \geq x-4 \end{array}\right.[/tex]The second inequality in the system is:
[tex]y\geq x-4[/tex]The intercepts of the boundary line (y=x-4) are (0, -4) and (4,0).
Since the inequality has an equal to sign attached, we use a solid line.
At (0,0)
[tex]\begin{gathered} y\geq x-4 \\ 0\geq-4 \end{gathered}[/tex]Since the inequality 0≥-4 is true, shade the side that contains (0, 0) as shown in the graph below:
So, we use a solid line and shade above the boundary line.
Answer this, please
Zachariah and Khai collect stamps. Zachariah has 7 American stamps out of 12 stamps. Khai has 15 American stamps out of 24 stamps. Which statement is correct?
Zachariah has a higher ratio of American stamps than Khai because 7 over 12 is greater than 15 over 24.
Khai has a higher ratio of American stamps than Zachariah because 7 over 12 is less than 15 over 24.
Zachariah has a higher ratio of American stamps than Khai because 7 over 12 is less than 15 over 24.
Zachariah and Khai have the same ratio of American stamps.
The last statement would be true, because you would convert 7/12 into a fraction and 15/24 into a fraction. From their fraction eyes to State you would turn them into decimals and then percentiles.
Answer:
D: They are both the same
Step-by-step explanation:
I took the test
please help me with this question
The amount should be charged to each attendee to cover the cost of the event is (300 + 45x) / x
Given,
The cost of a convention center to host an event = $300 + $45 per person attending
Number of attendees = x
We have to find a rational expression that represents how much you would need to charge each attendee in order to cover the cost of hosting the event.
Here,
Total cost for the event = Fixed cost + cost per person attending x number of person
Total cost = 300 + 45 × x
Total cost = 300 + 45x
Now,
The amount should be charged to each attendee to cover the cost of the event = (300 + 45x) / x
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parallelogram pqrs has diagonals PR in SQ that intersect at T given s p equals 2 a + 5 + r q equals 5 a - 1 St equals 3 b - 3 + SQ equals 7 b - 9 what are the values of RQ and TQ
SP = 2a+5
RQ= 5a-1
ST = 3b-3
SQ = 7b-9
RQ=?
TQ=?
SP = RQ
2a+5 = 5a-1
Solve for a
5+1 = 5a-2a
6 = 3a
6/3 = a
2=a
RQ= 5a-1 = 5(2)-1 = 10-1 = 9
RQ= 9
ST + TQ = SQ
ST= TQ
TQ= 3b-3
3b-3+3b-3= 7b-9
Solve for b
6b-6 = 7b-9
-6+9 = 7b-6b
3=b
TQ = 3b-3= 3(3)-3= 9-3 =6
TQ= 6
Identify the property of equality that justifies the missing step to solve the given equation.Equation3x + (1 - 8) = 124r-I8 = 12StepsOriginal equationAssociative property of addition4r= 20r=5Division property of equalitya. subtraction property of equalityb. addition property of equalityc. division property of equalityd. multiplication property of equality
From the attached image;
[tex]4x-8=12[/tex]The next step is to add 8 to both sides of the equation to remove -8.
[tex]\begin{gathered} 4x-8+8=12+8 \\ 4x=20 \end{gathered}[/tex]Since we added to the equation.
The step is an addition property of equality
the sugar sweet company is going to transport its sugar to market. it will cost 7500 to rent trucks,and it will cost an additional 225 for each ton of sugar transportlet C represent the total cost (in dollars) and let s represent the amount of sugar ( in tons ) transported. write an equation relating C to S. then use this equation to find the total cost to transport 18 tons of suger.
Given that a sugar sweet company costs to transport its sugar, 7500 to rent truck and additional 225 for each ton.
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octavius wants to write the equation of a line perpendicular to y=-4x + 5 that passes through the point (8,-3). Describe the mistake octavius made and write the correct equation of the line.
The equation of line perpendicular to 4y = x-8 passing through (4,-1) is:
[tex]y = \frac{1}{4} x-5[/tex].
What is a equation of line?These lines are written in the form y = mx + b, where m is the slope and b is the y-intercept. We know from the question that our slope is 3 and our y-intercept is –5, so plugging these values in we get the equation of our line to be y = 3x – 5.
Given equation of line is:
y=-4x + 5
Let [tex]m_{1}[/tex] be the slope of given line
Then,
[tex]m_{1}[/tex] = -4
Let [tex]m_{2}[/tex] be the slope of line perpendicular to given line
As we know that product of slopes of two perpendicular lines is -1.
[tex]m_{1}*m_{2} = -1\\- 4*m_{2}=-1\\ m_{2} = \frac{1}{4}[/tex]
The slope intercept form of line is given by
[tex]y = m_{2}x+c[/tex]
[tex]y = \frac{1}{4} x+c[/tex]
to find the value of c, putting (4,-1) in equation
[tex]-3= \frac{1}{4} *8+c\\-3-2 = c\\c = -5[/tex]
Putting the value of c in the equation
[tex]y=\frac{1}{4} x-5[/tex]
Hence, The equation of line perpendicular to 4y = x-8 passing through (4,-1) is [tex]y=\frac{1}{4} x-5[/tex].
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Form a polynomial whose zeros and degree are given.Zeros: -4, multiplicity 2; -3, multiplicity 1; degree 3O x3 + 8x2 + 40x + 48O x3 - 11x2 + 24x - 48O x3 + 11x2 + 40x + 48O x3 - 11x2 + 40% - 48
can you explain this to me what you are supposed to do this
Solution
If we see the two tirangles given BAC and A'B'C' we can conclude that we have the following congruent angles
< CAB = < C'A'B'
< BCA = < B'C'A'
< ABC = < A'B'C'
Can someone do it for me please
Step-by-step explanation:
13.
a/7 + 5/7 = 2/7
a/7 = 2/7 - 5/7 = -3/7
a = -3
14.
6v - 5/8 = 7/8
6v = 7/8 + 5/8 = 12/8
v = 12/8 / 6 = 2/8 = 1/4
15.
j/6 - 9 = 5/6
j - 54 = 5
j = 5 + 54 = 59
16.
0.52y + 2.5 = 5.1
0.52y = 5.1 - 2.5 = 2.6
y = 2.6/0.52 = 5
17.
4n + 0.24 = 15.76
4n = 15.76 - 0.24 = 15.52
n = 15.52/4 = 3.88
18.
2.45 - 3.1t = 21.05
-3.1t = 21.05 - 2.45 = 18.6
t = 18.6/-3.1 = -6
Which number is not a solution to3(x+4)−2≥7?-2-12 1
The inequality is:
[tex]3(x+4)-2\ge7[/tex]now we solve the inequality for x
[tex]\begin{gathered} 3(x+4)\ge7+2 \\ 3(x+4)\ge9 \\ x+4\ge\frac{9}{3} \\ x+4\ge3 \\ x\ge3-4 \\ x\ge-1 \end{gathered}[/tex]This means that all the number, from -1 to infinit are solution of the inequality, and the only option that is not a solution is a) -2
55mL of hardener to each container of resin. How much hardener should be added to 14 containers of resin?Write your answer in liters.
The amount of hardener added to 1 container of resin = 55mL.
The amount of hardener added to 14 containers is calculated as,
[tex]\begin{gathered} \text{Amount of hardener = 55 }\times\text{ 14 } \\ \text{Amount of hardener = 770 mL} \\ \text{Amount of hardener = 0.770 L} \end{gathered}[/tex]Thus 0.770 litres of hardener must be added to 14 containers of resin.
please when I send u this math explain it for me I'm only 12 and stuff is kinda hard to comprehend
First, we have to get rid of the parenthesis, to do that, we just multiply signs to get
[tex]-14-42[/tex]Now, we sum these numbers since they have the same signs
[tex]-14-42=-56[/tex]Therefore, the answer to (a) is -56.
The second operation is [tex]34+(-24)[/tex]We get rid of the parenthesis
[tex]34-24[/tex]Then, we subtract these numbers since they have different signs
[tex]34-24=10[/tex]Therefore, the answer to (b) is 10.
The third operation is[tex]-7+10[/tex]We just subtract these numbers since they have different signs
[tex]-7+10=3[/tex]Therefore, the answer to (c) is 3.
The fourth operation is[tex]-50+45[/tex]We just subtract
[tex]-50+45=-5[/tex]Therefore, the answer to (d) is -5.
The last operation is[tex]8+88[/tex]We just sum
[tex]8+88=96[/tex]Therefore, the answer to (e) is 96.
Cecilia is making a punch that uses 3 quarts of fruit juice for every quart of citrus soda. How many quarts of each does she need to make 16 quarts of punch?
The number of quarts of each constituent she needs to produce 16 quarts of punch is; 12 quarts of fruit juice and 4 quarts of citrus soda.
What quantity of each constituent is needed to produce 16 quarts of punch?It follows from the task content that the quantity of each constituent that is required to make 16 quarts of punch are to be determined.
Since it follows that 3 quarts of fruit juice are required to mix with every quart of citrus soda, it follows that the amount of punch made in this scenario is; 4 quarts of punch.
Hence, since there are 4 partitions of 4 quarts punch is 16 quarts punch, the amount of.each constituent needed by proportion are as follows;
3 quarts of fruit juice × 4 = 12 quarts of fruit juice.1 quarts of fruit juice × 4 = 4 quarts of citrus soda.Read more on proportion;
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Help I’ll give extra points!10. Camilla is saving to purchase a new pair of bowling shoes that will cost at least $39. She hasalready saved $19. What is the least amount of money she needs to save for the shoes?11. Suppose you earn $20 per hour working part time at a tax office. You want to earn at least$1,800 this month, before taxes. How many hours must you work?For problem 12, translate the phrase intoalgebraic inequality.12. A tour bus can seat 55 passengers. A minimum of 15 people must register for the tour to bookthe bus.
the least amount of money she needs to save is 20
the number of hours you must work is at least 90hours
Explanation:
10) The pair of shoes cost at least $39
at least $39 means: the cost is ≥ 39
≥ means greater than or equal to
Amount saved = $19
Let the least amount of money = x
x + 19 ≥ 39
x ≥ 39-19
x ≥ 20
This means the least amount of money she needs to save is 20
11) Let the number of hours worked = x
Amount earned per hour = $20
Amount to be earned this month is at least $1,800
This means amount to be earned this month ≥ 1800
[tex]\begin{gathered} 20\times x\text{ }\ge\text{ 1800} \\ 20x\text{ }\ge\text{ 1800} \\ \text{Divide through by 20} \\ x\text{ }\ge\text{ }\frac{1800}{20} \\ x\text{ }\ge\text{ 90} \end{gathered}[/tex]This means the number of hours you must work is at least 90hours
Identify the side lengths that form a right triangle.a. 12, 13, 16b. 15, 20, 21c. 9, 40, 42d. 10, 24, 26Identify the side lengths that form a right triangle.a. 3, 4, 8b. 30, 40, 45c. 5, 12, 13d. 6, 12, 133. do the side lengths of 8, 10, and 13 form a right triangle? 4. Determine if ▼ABC is a right triangle if AB=36, AC=48 and BC=60
Answer:
d. 10, 24, 26
Explanation:
To identify the side lengths that form a right triangle, we check if it satisfies the Pythagorean theorem.
By the theorem:
[tex]\begin{gathered} a^2=b^2+c^2 \\ a\text{ is the hypotenuse, the longest side.} \end{gathered}[/tex]a. 12, 13, 16
[tex]\begin{gathered} 16^2=12^2+13^2 \\ 256=144+169 \\ 256\neq313 \end{gathered}[/tex]These side lengths do not form a right triangle.
b. 15, 20, 21
[tex]\begin{gathered} 21^2=15^2+20^2 \\ 441=225+400 \\ 441\neq625 \end{gathered}[/tex]These side lengths do not form a right triangle.
c. 9,40,42
[tex]\begin{gathered} 42^2=9^2+40^2 \\ 1764=81+1600 \\ 1764\neq1681 \end{gathered}[/tex]These side lengths do not form a right triangle.
d. 10, 24, 26
[tex]\begin{gathered} 26^2=10^2+24^2 \\ 676=100+576 \\ 676=676 \end{gathered}[/tex]These side lengths form a right triangle since both sides of the equation are the same.
The Oldest rocks on Earth are about 4 x 10^9 years old. For which of these ages could this be an approximation?
A. 3,862,100,000 years
B. 3.849999999x10^9 years
C. 0.000000004 years
D.4,149,000,000 years
E.3.45x10^9 years
A student worked 51 hr during a week one summer. The student earned $5. 10 per hour for the first 40 hr and $7.65 per hour for overtime. How much did the student earn during the week?
We will determine the earnings for the week as follows:
[tex]W=40(5.10)+11(7.65)\Rightarrow W=288.15[/tex]So, the student earned $288.15 that week.
explain two ways to evulate 32(16-6)
There are two ways to evaluate the expression:
32(16 - 6)
WAY 1
Evaluate the expression in the bracket first, then multiply the result by the content outside the bracket.
32(10)
= 320
WAY 2
Remove the bracket straight, without simplifying the content inside the bracket by multiplying 32 by each element in the bracket.
32*16 - 32*6
= 512 - 192
= 320
And those are the two ways.
3. In one linear function, when you subtracteach y-coordinate from the x-coordinate,the difference is 3. If the x-coordinate isnot greater than 10 and the y-coordinateis a positive whole number, how manyordered pairs are there?
Problem
3. In one linear function, when you subtract each y-coordinate from the x-coordinate, the difference is 3. If the x-coordinate is not greater than 10 and the y-coordinate is a positive whole number, how many ordered pairs are there?
Solution
Here are the conditions
x- y= 3
x <10
y >0
And then we have these as possible answers:
4-1 =3
5-2= 3
6-3=3
7-4=3
8-5=3
9-6=3
Then the total possible pairs are: 6
if 2 angles from a line
If two angles form a linear pair, then they form a straight line, and the sum of their measures is 180 degrees.
This illustrated below;
In the illustration above, angle measure 1 and 2 both equal to 180 degrees. Angle 1 and angle 2 are refered to as a linear pair.
exponent hw.simplify
Answer:
4
Explanation:
Given the below;
[tex]4m^0[/tex]To simplify the above, we have to note that any number or variable raised to the power of 0 is 1.
So, we'll have;
[tex]4m^0=4\times1=4[/tex]What kind of transformation converts the graph of f(x)=(5x+6)^2 into the graph of g(x)=-(5x+6)^2
In order to get from
[tex]f(x)=(5x+6)^2[/tex]To
[tex]f(x)=-(5x+6)^2[/tex]You have to reflect across the x-axis.
Remember that the x-axis is the line with equation
[tex]y=0[/tex]Answer: Option A
A shoe salesman earns a commission of 30%
of all shoe sales made.
Yesterday he sold 3 pairs of shoes for $70 each and 2 pairs of shoes for $80
each. How much did he earn in commission yesterday?
Answer: $111 is earn by shoe salesman as commission .
Step-by-step explanation:
As given the statement in the question be as follow.
Shoes salesman sold 3 pairs of shoes for $70 each and 2 pairs of shoes for $80 each.
Total cost of the pair of shoes = 3 × 70 + 2 × 80
= 210 + 160
= $ 370
As given
shoe salesman earns a commission of 30% of all shoe sales made.
30% is written is decimal form
= 0.30
Commission earns = 0.30 × Total cost of the pair of shoes .
= 0.30 × 370
= $ 111
Therefore $111 is earn by shoe salesman as commission .
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BRAINLIEST!!!!! AND 100 POINTS!!!!!
Answer:
True.
area of green square + area of purple square = area of red square
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
There are 12 freshman 6 sophomores 12 juniors and 16 seniors. What percentage of club members are sophomores
Answer:
13% (rounded)Step-by-step explanation:
12 + 6 + 12 + 16 = 46
46 total students
out of those 46 students, 6 are sophomores
so put that into a fraction it becomes
[tex]\frac{6}{46}[/tex]
which equals
0.130434783
which in percentage is
13.0434783%
or 13% rounded
Graph the inequality. Then write the solution set in interval notation.
Representing intervals as we are doing for your question means we will represent all the possible values of x. To do that we will colour in blue all possible values of x but there is a detail we must to consider. The limits of the interval. for that we have two symbols, [ that means "closed on the value" and ( that means "opened on the value". So if there is a [ on a number it means that number makes part of the interval, but if there is a ( it means that number is not in the interval.
Now, for our inequality we have
Once x can be equal or superior to 2 it means 2 is part of the interval because x can be this value, but x is inferior to 8 but it can not be 8 so 8 is not on the interval. Once we know that, know we can represent our interval as follows:
And that is our final answer.
For an interval notation we can write [2,8).
Mrs. Smith has 12 times as many markers as colored pencils. The total number of markers and colored pencils is 78. How many markers does Mrs. Smith have?ok...answers given so far are not helpful in explaining process.
Let:
x = Colored markers
y =
