The sum of 3 and r can be represented by "3 + r"
If this sum is less than 7, we can use the symbol "lesser than" (<) to compare the sum with the number 7, so our number sentence is:
[tex]3+r<7[/tex]Which statements are true?Select all that apply.A.The slope of AC is equal to the slope of BC.B.The slope of AC is equal to the slope of BD.C.The slope of AC is equal to the slope of line t.D.ECThe slope of line t is equal toAEE.FBThe slope of line t is equal toFDF.The slope of line t is equal to AB
Line t, segments AC, BC and BD are colinear, that is, all of them are in the same line. Then, the true statements are
A, B, and C
Domingo had 250 baseball cards, andJennifer had 82 baseball cards. At thefirst meeting of the Card Club and atevery meeting thereafter, Domingo sold12 cards to Jennifer. After which meetingdid the two have the same numberof cards?
Data:
Domingo: D
Jennifer: J
Initial number of cards:
D=250
J=82
After each meeting(m):
D=250-12m
J=82+12m
After the first meeting: m=1
[tex]D=250-12(1)=238[/tex][tex]J=82+12(1)=94[/tex]You increase in 1 the m after each meeting and get the next table:
Then, they have the same number of cards after 7th meetingf(x) varies inversely with x and f(x)=−10 when x = 20. What is the inverse variation equation? Responses f(x)=−2x f ( x ) = − 2 x f(x)=−5x f ( x ) = − 5 x f(x)=−200x f ( x ) = − 200 x f(x)=−0.5x f ( x ) = − 0.5 x
The equation representing the constant of proportionality is k = xf(x) and the constant of proportionality k = -200
What is proportionality?In mathematics, proportionality indicates that two quantities or variables are related in a linear manner. If one quantity doubles in size, so do the other; if one of the variables diminishes to 1/10 of its former value, so does the other.
Likewise, if the variables are inversely proportional to one another, as one quantity increases, the other quantity decreases by the same proportion or quantity.
We can proceed to substitute the values into the equation above.
k = xf(x)
k = 20 * (-10)
k = -200
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1. Input, X 9753 1 Output, y 1 2 2 3 4 Function - Yes or no
before we can dtermone whether it is a function, there must be a relationship between X and y i.e they must have a constannt of proportionality as shown:
From the table:
when x = 9, y = 1
when x = 7, y = 2
when x = 5, y = 2
when x = 3, y = 3
when x = 1, y = 4
let us determine the constant of proportionality from the given values as shown:
k = y2-y1/x2-x1
when x = 9, y = 1
when x = 7, y = 2
k = 2-1/7-9
k = 1/-2
k = -1/2
Also
when x = 5, y = 2
when x = 3, y = 3
k = 3-2/3-5
k = 1/-2
k = -1/2
Also;
when x = 5, y = 2
when x = 3, y = 3
k = 3-2/3-5
k = 1/-2
k = -1/2
Since all the constant of proportionality are the same;
Hence y = kx
y = -1/2 x
This shows that the tabke is a function and X is directly proportional to y. hence the answer is YES, it is function
8) What is the mass of the teddy bear if the toy car has a mass of 375 grams? 10 .S 0 4kg 3kg 1kg 2kg 000
The mass of the teddy is 1,225 grams
Here, we want to get the mass of the teddybear given the mass of the toy car
Since boith are on the scale, then it means they contribute to the mass on the scale
By reading the scale, we can see that the mass on the scale is 1.6 kg
As we know, 1000 g is 1 kg
It means 1.6 kg in g will be 1.6 * 1000 = 1,600 g
So, we can now subtract the mass of the toy car from this total to get the mass of the teddy
Mathematically, we have this as;
[tex]1600\text{ g - 375 g =1,225 g}[/tex]Find the component form of the sum of u and v with direction angles u and v.
We will have the following:
[tex]\begin{gathered} U_x=14cos(45) \\ \\ U_y=14sin(45) \\ \\ V_x=80cos(180) \\ \\ V_y=80sin(180) \end{gathered}[/tex]Then:
[tex]\begin{gathered} \sum_x=\frac{14\sqrt{2}}{2}+(-80)\Rightarrow\sum=7\sqrt{2}-80 \\ \\ \sum_y=\frac{14\sqrt{2}}{2}+(0)\Rightarrow\sum=7\sqrt{2} \end{gathered}[/tex]So, the component form for the sum of the vectors will be:
[tex]u+v=(7\sqrt{2}-80)i+(7\sqrt{2})j[/tex]If A is the image of A(3, 4) after a dilation with scale factor 7 about the origin, what is the distance between A and A? Hint: Use the distance formula: d = √√(x₂ − x₂)² + (Y₂ − 3₂)² .
0 7 units
○28 units
O 30 units
O 35 units
Answer:
Step-by-step explanation:
you can view this,its similar just the numbers are switched.
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Answer:
35
Step-by-step explanation:
sorry if im wrong sorry
explain why there are two zeros in the product of 5 x 40
EXPLANATION
There are two zeros in the product of 5x40 because multiplying the number 40 5 times give us the number 200 wich is a hundred type number.
Sports Authority marks up New Balance sneakers $30 and sells them for $109. Markup is on cost. What are the cost and percent markup?
If Sports Authority marks up New Balance sneakers for $30 and sells them for $109, then the cost will be $79 while the percent markup will be 37.97%.
What is the cost and percent markup?The original cost of the product can be obtained by subtracting the markup price from the selling price as seen below.
Cost = selling price - markup
Cost = $109 - $30
Cost = $79
Thus, we arrive at the result that the cost of the product by Sports Authority is $79.
Next, we calculate the percent markup with the formula below:
Percent markup = Markup/cost × 100
Percent markup = 30/79 × 100
= 37.97%
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The equation y + 2 = 5(x – 4) represents a linear function. What is the y-intercept of the equation?
Answer:
-22
Step-by-step explanation:
Hello!
We can convert it into Slope-Intercept form: [tex]y = mx + b[/tex]
m = slopeb = y-interceptConverty + 2 = 5(x - 4)y + 2 = 5x - 20y = 5x - 22The y-intercept is -22.
An angle bisector is a ray that divides an angle into two angles with equal measures. If OX bisects ZAOB and mZAOB 142, what is the measure of each of the
angles formed? (Note: Round your answer to one decimal place).
Measure of each of the angles formed between ZAOB is 71° using angle bisector theorem.
What is the angle bisector?In geometry, an angle bisector is a line that divides an angle into two equal angles. The term "bisector" refers to a device that divides an object or a shape into two equal halves. An angle bisector is a ray that divides an angle into two identical segments of the same length.
m(ZAOB)=142°
OX will bisect ZAOB in equal angel both side.
So m(ZAOX) is 71°
And also, m(ZAOB) is 71°
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Which expression demonstrates how the Distributive Property could be used to find the product of 5 and 48?
A. 50 − 5 (2)
B. 5 (50) − 2
C. 5 (50) + 5 (2)
D. 5 (50 − 2) + 5 (2)
E. None of these
Answer:
Step-by-step explanation:
C
University DataReceiving Not ReceivingFinancial Aid Financial AidTotalUndergraduates422238988120Graduates18797312610Total6101462910730If a student is selected at random, what is theprobability that the student receives aid and is agraduate (rounded to the nearest percent)? [? ]%
Need help asap !!!!!
The practical domain is 1 ≤ x ≤ 20 and the practical range is 13.61 ≤ C(x) ≤ 127.61
How to determine the practical domain?From the question, the given parameters are:
Charges = $7.61Reservation = $6Maximum number of windows = 20Total cost = CThe domain is dependent on the number of windows washed
Using the maximum as a guide, the minimum number of windows could be
Minimum = 1
The domain is then represented as
Minimum ≤ x ≤ Maximum
So, we have
1 ≤ x ≤ 20
How to determine the practical range?Using the given parameters in (a), we have
Total cost, C = Charges * Number of windows + Reservation
So, we have
C(x) = 7.61 + 6x
Where x is the number of windows
When x = 0, we have
C(1) = 7.61 + 6(1)
C(1) = 13.61
When x = 20, we have
C(20) = 7.61 + 6(20)
C(20) = 127.61
So, we have the range to be 13.61 ≤ C(x) ≤ 127.61
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Canvas that costs 3/4 cents/in squared is used to make golf bags. Find the cost (in dollars) of 200 rectangular pieces of canvas, each 6.0 in. by 4.0 in.
The cost of 200 rectangular pieces of canvas given its dimensions is $36.
What is the cost?The first step is to determine the area of one of the rectangular pieces. A rectangle is a two-dimensional quadrilateral with four right angles.
Area of a rectangle = length x width
6 X 4 = 24 in²
The next step is to determine the area of the 200 rectangular pieces.
Area of the 200 rectangular pieces = 200 x 24in² = 4,800 in²
The last step is to determine the cost of the 200 rectangular pieces.
Total cost = total area x cost per squared inches
3 / 4 x 4800 = 3600 cents = $36
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Write the first six terms of each arithmetic sequence,Please see the photo
Answer: - 9, - 3, 3, 9, 15, 21
Explanation:
The given formula is
an = a(n - 1) + 6
a1 = - 9
where
n, n - 1 and 1 are subscripts
This is a recursive formula. Each term is defined with respect to the term before it.
From the information given,
first term = a1 = - 9
Second term = a2 = a(2 - 1) + 6 = a1 + 6 = - 9 + 6
a2 = - 3
Third term = a3 = a(3 - 1) + 6 = a2 + 6 = - 3 + 6
a3 = 3
Fourth term = a4 = a(4 - 1) + 6 = a3 + 6 = 3 + 6
a4 = 9
Fifth term = a5 = a(5 - 1) + 6 = a4 + 6 = 9 + 6
a5 = 15
Sixth term = a6 = a(6 - 1) + 6 = a5 + 6 = 15 + 6
a6 = 21
Thus, the first six terms are
- 9, - 3, 3, 9, 15, 21
#3b. Two bicyclists ride in the same direction. The first bicyclist rides at a speed of 8 mph.One hour later, the second bicyclist leaves and rides at a speed of 12 mph. How long will thesecond bicyclist have traveled when they catch up to the first bicyclist?I’m
Answer:
2 hours
Explanation:
[tex]\text{Speed}=\frac{Dis\tan ce}{Time}[/tex]The first bicyclist rides at a speed of 8 mph. Therefore:
[tex]\begin{gathered} 8=\frac{d}{t} \\ \implies d=8t \end{gathered}[/tex]One hour later, the second bicyclist leaves and rides at a speed of 12 mph.
Therefore, the time of the second bicyclist = (t-1) hours.
Therefore:
[tex]\begin{gathered} 12=\frac{d}{t-1} \\ \implies d=12(t-1) \end{gathered}[/tex]Since the second bicyclist will catch up to the first bicyclist, the distance traveled will be the same.
So:
[tex]\begin{gathered} 8t=12(t-1) \\ 8t=12t-12 \\ 8t-12t=-12 \\ -4t=-12 \\ \frac{-4t}{-4}=\frac{-12}{-4} \\ t=3\text{ hours} \end{gathered}[/tex]Therefore, the second bicyclist will have traveled for:
(t-1) = (3-1) =2 hours.
(Please show your work for question 18.)
It is given that AB = CB from this information we conclude that <A=<C by reason :angles opposite equal sides.
<A+<B+<C=180°(Sum of angles in a triangle)
[tex](4x - 13) + (5x - 2) + (4x - 13) = 180 \\ 4x + 5x + 4x - 13 - 2 - 13 = 180 \\ 13x - 28 = 180 \\ 13x = 180 + 28 \\ 13x = 208 \\ \frac{13x}{13} = \frac{208}{13} \\ x = 16[/tex]
x=6°
ATTACHED IS THE SOLUTION
GOODLUCK
Graph the set {x|x2-3} on the number line.Then, write the set using interval notation.
Given,
The expression is,
[tex]\lbrace x|x\ge-3\rbrace[/tex]Required:
The graph of the line.
The interval notation is [-3, infinity).
The line of the inequality is,
Hence, the graph of the line is obtained.
8 Solve: 2 3= 4x + 2 - O- O 1 2 AP 4 ( ) 1 4. O 1 2
We will have the following:
[tex]3=4x+2\Rightarrow1=4x[/tex][tex]\Rightarrow x=\frac{1}{4}[/tex][Third option]
Samuel's family members are choosing numbers to see in what order they will choose gifts. The numbers 1 through 10 are written on pieces of paper. All numbers are equally likely to be chosen. What is the probability that the first person chooses a number less than 3? O A. 10 3 B. 10 2 C. 2 10 O D. 3 10
Answer:
[tex]\text{Probability}=\frac{2}{10}[/tex]Step-by-step explanation:
Probability is represented by the following expression:
[tex]=\frac{\text{Number of ways it can occur}}{Total\text{ number of outcomes}}[/tex]Then, since there are 2 numbers less than 3:
[tex]\text{Probability}=\frac{2}{10}[/tex]How do you solve this?
Answer: B
Step-by-step explanation:
Answer: The answer is B
Step-by-step explanation:
In the figure, what set of angles are corresponding angles?angle 6 and angle 7angle 5 and angle 7angle 1 and angle 7angle 4 and angle 7
Step 1
In geometry, corresponding angles are formed where a line known as an intersecting transversal, crosses through a pair of straight lines. Corresponding angles are the pairs of angles that are found in the same relative position on different intersections.
Step 2
Find the set of corresponding angles
[tex]\text{Angle 4 and angle 7}[/tex]Hence, the set of corresponding angles is; angle 4 and angle 7
One cubic foot holds 7.48 gallons of water, and 1 gallon ofwater weighs 8.33 pounds. How much does 6 cubic feet ofwater weigh in pounds? In tons?
We know that
• 1 cubic foot holds 7.48 gallons of water.
,• 1 gallon of water weighs 8.33 pounds.
The given information is about ratios that we must use to find the answer. Remember that a ratio is a quotient between two magnitudes, that means each statement above represents a fraction which must multiply "6 cubic feet" in order to get the answer. As follows
[tex]6ft^3\cdot\frac{7.48gallons}{1ft^3}\cdot\frac{8.33lb}{1gallon}=\frac{6\cdot7.48\cdot8.33}{1}lb=373\text{.}85lb[/tex]Therefore, 6 cubic feet weighs 373.85 pounds.
On the other hand, 1 ton is equivalent to 2000 pounds. Knowing this, we calculate
[tex]373.85lb\cdot\frac{1ton}{2000lb}\approx0.19ton[/tex]Therefore, 6 cubic feet weighs about 0.19 tons.
The product 8 and the square of a number decreased by 5 is 67. Find the number.
Answer:
3 or -3
Explanation:
Let's call the unknown number x. The square of this number is x². The product of 8 and the square of this number is 8x². Finally, it is decreased by 5, so 8x² - 5 and it is equal to 67, then the equation that represents the statement is:
8x² - 5 = 67
Now, we can solve the equation for x. Add 5 to both sides
8x² - 5 + 5 = 67 + 5
8x² = 72
Divide both sides by 8
8x²/8 = 72/8
x² = 9
Find the square root of both sides
x = √9
x = 3 or x = -3
Therefore, the number is 3 or -3
Question 10 of 11 Step 1 of 1CorrectThcorrectOne group (A) contains 390 people. Three fifths of the people in group A will be selected to win $100 fuel cards. There is another group (B) in a nearby town that willreceive the same number of fuel cards, but there are 553 people in that group. What will be the ratio of nonwinners in group Ato nonwinners in group B after theselections are made? Express your ratio as a fraction or with a colon.AnswerkeypadRestore Your Guth2019 Hawkes Learning
Given : Two groups
Group A: contains 390 people.
Three fifths of the people in group A will be selected to win $100 fuel cards.
So, the number of people who will win = 3/5 * 390 = 234
Group B : contains 553 people
the group will receive the same number of fuel cards
so, the group will receive 234 cards
The non-winners of group A = 390 - 234 = 156
The non-winners of group B = 553 - 234 = 319
The ratio between them = 156 : 319
Graph the line... running through: (1,3) with m=3
First, you have to locate the point (1,3)
Next, from that point, you have to locate the next one. To do that, you need the slope, which in this case is 3. So, from (1,3) you have to move 1 unit to the right and 3 units up, reaching the point (2, 6). Finally, you draw the line that passes through these two points
I’m not sure how to figure this out.What is 8% of 4000?
8% of 4000 express as;
[tex]\begin{gathered} \text{ 8\% of 4000=}\frac{8\times4000}{100} \\ \text{8\% of 4000=320} \end{gathered}[/tex]Thus, 8% of 4000 is 320
Answer : 320
...
subtract 7 1/4 - 4 3/4 simplify the answer and write as a mixed number .122 1/21/43 1/2
Answer
The simplified fraction is 2 1/2
Step-by-step explanation:
[tex]\begin{gathered} \text{Substract 7}\frac{1}{4}\text{ - 4}\frac{3}{4} \\ \text{Step 1: convert the mixed fraction into an improper fraction} \\ 7\frac{1}{4}\text{ = }\frac{(7\text{ x 4) + 1}}{4} \\ 7\frac{1}{4}\text{ = }\frac{29}{4} \\ \\ 4\frac{3}{4}\text{ = }\frac{(4\cdot4)+3}{4} \\ 4\frac{3}{4}\text{ = }\frac{19}{4} \\ We\text{ have} \\ \frac{29}{4}\text{ - }\frac{19}{4} \\ \text{ Find the common denominator} \\ \text{The common denominator is 4} \\ \frac{29\text{ - 19}}{4} \\ =\text{ }\frac{10}{4} \\ =\text{ }\frac{5}{2} \\ =\text{ 2}\frac{1}{2} \\ \text{Hence, the answer is 2}\frac{1}{2} \end{gathered}[/tex]Solve: 5|4x+5|−2≤33 Give your answer as an interval. If no solutions exists - enter No solutions.
The expression given is,
[tex]5|x-3|+3>7[/tex]Subtract 3 from both sides
[tex]\begin{gathered} 5|x-3|+3-3>7-3 \\ 5|x-3|>4 \end{gathered}[/tex]Divide both sides by 5
[tex]\begin{gathered} \frac{5|x-3|}{5}>\frac{4}{5} \\ |x-3|>\frac{4}{5} \end{gathered}[/tex]Apply absolute rule:
[tex]\begin{gathered} x-3<-\frac{4}{5}\text{ or x-3>}\frac{4}{5} \\ \end{gathered}[/tex]Add 3 to both sides
[tex]\begin{gathered} x-3+3<-\frac{4}{5}+3\text{ or x-3+3>}\frac{4}{5}+3 \\ x<\frac{11}{5}\text{ or x>}\frac{19}{5} \end{gathered}[/tex]Therefore, the answer has the form:
[tex](-\infty,A)\cup(B,\infty)[/tex]Hence, the solution using interval notation is
[tex](-\infty,\frac{11}{5})\cup(\frac{19}{5},\infty)[/tex]