In order to a set o points define a function, a value of x can't have two different values of y.
Looking at every option, we have in the option C that the value of x = 0 has two different values of y (1 and -1), therefore this set of points do not define a function.
So the answer is C.
Sal earns $480 per week. Lidia earns $300 per week. Are their salaries proportional if Sal works 40 hours per week and Lidia works 25 hours per week?
True or false?
The given statement "Sal earns $480 per week. Lidia earns $300 per week. Are their salaries proportional if Sal works 40 hours per week and Lidia works 25 hours per week" is true.
As given in the question,
If one amount is proportional to another, the two amounts increase and decrease at the same rate so there is always the same relationship between them
a:b = c:d
a ÷b = c ÷d
ad = bc
let Sal earns $480 per week and he works 40hours per week
480÷40 = 12
Lidia earn $300 per week and she works 25 hours per week
300÷25 = 12
Cross product of their salaries is
480×25=1200
300×40=1200
The ratio of their salaries and their product are equal.
Hence, The given statement "Sal earns $480 per week. Lidia earns $300 per week. Are their salaries proportional if Sal works 40 hours per week and Lidia works 25 hours per week" is true
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-12/7 = 6y solve for y and simplify your answer as much as possible
Answer:
[tex]\displaystyle y = \frac{-2}{7}[/tex]
Step-by-step explanation:
To solve, we will isolate the variable.
Given:
-12/7 = 6y
Divide:
[tex]\displaystyle \frac{\frac{-12}{7} }{6} =\frac{6y}{6}[/tex]
Simplify the right side:
[tex]\displaystyle \frac{\frac{-12}{7} }{6} =y[/tex]
"Keep, change, flip" on the left side:
[tex]\displaystyle \frac{-12}{7} *\frac{1}{6} = y[/tex]
Multiply:
[tex]\displaystyle \frac{-12*1}{7*6}= y[/tex]
[tex]\displaystyle \frac{-12}{42}= y[/tex]
Simplify and reflexive property:
[tex]\displaystyle y = \frac{-2}{7}[/tex]
Hello,Can you help me with question #56 in the photo?Thank you,
In order to calculate the total spending in the town each year, first, multiply by the 70% that is spent within the town,
[tex]\begin{gathered} \text{\$}4,000,000\times70\% \\ \text{\$}4,000,000\times0.70 \\ =\text{\$}2,800,000 \end{gathered}[/tex]Also, multiply by 70% of the amount people will spend after they receive it in town,
[tex]\begin{gathered} \text{ \$}2,800,000\times70\% \\ \text{ \$}2,800,000\times0.70 \\ =1,960,000 \end{gathered}[/tex]Answer:
The total spending in the town each year is $1,960,000
At 6:00 A.M. the temperature was 5°F below zero. At noon the temperature was 2°F above zero. At 6:00 P.M. the temperature was 7°F above zero. Which equation shows the change in temperature from 6:00 A.M. to 6:00 P.M.?
A. |5 – 7| = |–2| = 2°F
B. |2 – 7| = |–5| = 5°F
C. |–5 – 2| = |–7| = 7°F
D. |–5 – 7| = |–12| = 12°F
Based on the temperature at 6:00 am and the temperature at 6:00pm, the change in temperature can be shown by the formula D. |–5 – 7| = |–12| = 12°F.
How to find the change in temperature?To find the change in temperature, you need to subtract the temperature at 6: 00 pm from the temperature at 6: 00 am.
The change in temperature is therefore:
= | temperature at 6 am - temperature at 6pm |
= | -5 - 7 |
= | - 12 °F|
The absolute value of - 12 °F is 12 °F which was therefore the change in temperature.
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If the cost of an 800 number is $29.95 per month plus 28 cents per minute, then the monthly cost varies directly as the number of minutes.TrueFalse
We have the monthly cost is fixed: $29.95.
The cost varies directly as the number of minutes since the total cost per month will be:
[tex]29.95+\frac{28}{100}x[/tex]If we make a call and spend 30 minutes. We need to add this cost to the payment:
[tex]undefined[/tex]PLEASE HELP WILL MARK BRAINLIEST AND 20 POINTS !!
Write the system of equations for the matrix.
[0. 2. 3. / 4
[8 -1 -2 / 5
[2. 0. 1 /9
The three equations that will emerge from the given matrix will be:
2y + 3z = 48x - 1y - 2z = 52x + z = 9What are equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. Like 3x + 5 = 15, for example. There are many different types of equations, including linear, quadratic, cubic, and others. In a mathematical equation, the equals sign is used to express that two expressions are equal.So, the equations for the given matrix will be:
[0. 2. 3. / 4]
[8 -1 -2 / 5 |
[2. 0. 1 / 9 ]
Now, the equation will be:
2y + 3z = 48x - 1y - 2z = 52x + z = 9Therefore, the three equations that will emerge from the given matrix will be:
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All of the triangles are dilations of Triangle D. The dilations use the same center P, but different scale factors. 1) What do Triangles A, B, and C have in common? 2) What do Triangles E, F, and G have in common? 3) What does this tell us about the different scale factors used?
Triangles A, B, and C have a scale factor less than 1 in common
Triangles E, F, and G have a scale factor greater than 1 in commonDifferent scale factors would give different sizes after dilationWhat Triangles A, B, and C have in commonThe figure that completes the question is added as an attachment
From the figure, we can see that triangles A, B, and C are smaller than the original triangle i.e. the triangle D
This means that triangle D is dilated by a scale factor less than 1 to form each of these triangles
What Triangles E, F, and G have in commonThis has just a slight difference to (a)
From the figure, we can see that triangles E, F, and G are bigger than the original triangle i.e. the triangle D
This means that triangle D is dilated by a scale factor greater than 1 to form each of these triangles
What this tell us about the scale factorsThe conclusion about the scale factors is that
Scale factor less than 1 would provide a smaller shapeScale factor greater than 1 would provide a bigger shapeRead more about dilation at
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write the slope intercept form:through: (4, -5), perp. to x= -4
The line should be perpendicular to x = -4
x= -4 is a vertical line crossing the x axis at x= -4
The slope is undefined in x =-4
For an equation in slope intercept form, the general form is ;
y= mx + b where m is the slope and b is the y-intercept
So for any y value, x is always -4
Thus the slope for line x = -4 is not defined
A line perpendicular to x = -4 will thus be a horizontal line with slope 0
For the equation of this line
0= y--5/x-4
0 = y+5 /x-4
0{x-4} = y +5
0 = y+5
y= - 5
Hi, does anyone know the solution to this question?
Hello, in this question we will use the "Sinus Theorem".
The general formula of the Sine Theorem is as follows;
[tex]A=\frac{1}{2}.a.b.sin(C)[/tex]We are given the length of the two sides and the sine value of the angle of the unknown side. We also know the area of the triangle. Let's substitute the required values in this formula to get the result.
[tex]A=\frac{1}{2} (x+2)(2x-3)(sin45^o)[/tex][tex]4\sqrt{2}=\frac{1}{2}(x+2)(2x-3)(\frac{1}{\sqrt{2} } )[/tex][tex]16=(x+2)(2x-3)[/tex][tex]16=2x^2+x-6[/tex][tex]0=2x^2+x-22[/tex]In the last step, we are left with a quadratic equation with one unknown. To solve this equation, we need to calculate the discriminant value.
[tex]Discriminant=b^2-4ac[/tex]There are only two roots of a quadratic equation with one unknown.
[tex]x_{1}=\frac{-b-\sqrt{Discriminant} }{2a}[/tex][tex]x_{2}=\frac{-b+\sqrt{Discriminant} }{2a}[/tex]Thus our x values;
[tex]x_{1}=\frac{-1-\sqrt{177} }{4}[/tex][tex]x_{2}=\frac{-1+\sqrt{177} }{4}[/tex]We cannot accept the first root [tex]x_1[/tex]. Because length cannot be a negative value.
Ans = [tex]x_{2}=\frac{-1+\sqrt{177} }{4}=3.076[/tex]
What percentage of the numbers from 1 to 20 contain the digit 2?
if charlene brewster has times of 8.4, 8.6, 8.3, 8.5, 8.7, and 8.5 and a performance rating of 110%, what is the normal time for this operation? is she faster or slower than normal? [px]
Normal time taken for operation = 7.7
Charlene's work performance is faster than normal time.
Need to define Charlene's average time:
8.4 + 8.6 + 8.3 + 8.5 + 8.7 + 8.5)/6
Avg time taken= 8.5.
Performance rating = 110/100 = 1.1
normal time taken: 8.5/1.1
normal time taken= 7.7
hence, 8.5 [tex]\geq[/tex] 7.7
Charlene is faster than normal time.
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Please help me on this question.
When Madison left her house this morning, her cell phone was 80% charged and itthen started to lose 8% charge for each hour thereafter. Write an equation for B, interms of t, representing the charge remaining in Madison's battery, as a percentage, thours after Madison left her house.
Given:
Initially, the cell phone was 80% charged.
Then started to lose 8% charge for each hour thereafter.
To find:
The equation for B in terms t
working together, it takes two different sized hoses minutes to fill a small swimming pool. if it takes minutes for the larger hose to fill the swimming pool by itself, how long will it take the smaller hose to fill the pool on its own?
Time taken by the smaller hose to fill the pool on its own = 75 minutes
Time taken to fill the swimming pool by the larger hose and smaller hose working together = 30 minutes
Time taken by the larger hose to fill up the swimming pool = 50 minutes
Let 'x' be the time taken by the smaller hose to fill the swimming pool on its own.
In 30 minutes, the larger and smaller hoses together can fill the swimming pool. So in 1 minute, it can fill up 1/30 of the swimming pool.
In 50 minutes, the larger hose can fill up the swimming pool on its own. So the larger hose can fill up 1/50 of the pool in 1 minute.
It takes 'x' minutes for the smaller hose to fill up the pool on its own. So in 1 minute, the smaller hose alone can fill up 1/x of the pool.
Hence 1/30 = 1/x +1/50
⇒ 1/30 = (50+x)/50x
⇒ 30 = 50x/(50+x)
⇒ 30 (50 + x) = 50x
⇒ 1500 + 30x = 50x
⇒ 20x = 1500
⇒ x = 1500/20
⇒ x = 75 minutes.
Thus the smaller hose alone takes 75 minutes to fill up the pool.
The question is incomplete. Find the complete question below:
Working together, it takes two different sized hoses 30 minutes to fill a small swimming pool. If it takes 50 minutes for the larger hose to fill the swimming pool by itself, how long will it take the smaller hose to fill the pool on its own?
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The Sticker Company shipped 5,693,123,456 stickers last month. This month the company shipped 6,966,632,877 stickers. About how many more stickers were shipped this month than last month? A.11,000,000,000B.10,000,000,000C.3,000,000,000D.1,000,000,000
SOLUTION
To get how many more stickers were shipped last month than this month, we simply subtract this month's shipment from last month's shipment.
This becomes
[tex]\begin{gathered} 6,966,632,877-5,693,123,456 \\ =1,273,509,421 \end{gathered}[/tex]Therefore, the we have 1,000,000,000 to the nearest billion.
Option D is the correct answer
Find the equivalent ratio to the ratio 9 to 27 by simplifying the ratio. 3 to 1 , 1 to 3, 1 to 27 ,9 to 3
Given data:
The given ratio is 9:27.
The given ratio can be written as,
[tex]\begin{gathered} 9\colon27=\frac{9}{27} \\ =\frac{1}{3} \\ =1\colon3 \end{gathered}[/tex]Thus, the given ratio can be written as 1:3 so, second option is correct.
Leanne has a bag only containing blue beads and purple beads. (2)/(9) of the beads are blue.
If there are 6 blue beads in the bag, how many beads are purple?
Proportionately, if there are 6 blue beads in the bag, and blue beards are 6 or 2/9 of the total beads, the number of purple beads in the bag is 21.
What is proportion?Proportion refers to the numerical ratio of a value to another.
Proportion shows the quantity of a value contained in another variable.
Since proportions are fractional values, like ratios, they are represented using decimals, fractions, and percentages.
The ratio of blue beards to purple beads = 2:7 or 2/9
The number of blue beads in the bag = 6
The total number of beads in the bag = 27 (6/2 x 9)
The number of purple beads in the bag = 21 (27 x 7/9)
Thus, based on the given proportional ratio of the blue beads to the purple beads, there are 21 purple beads in the bag.
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The expressions (x²-ax-b) and (2x² + b) have a common factor (x + c),
where a, b and c #0
(i) Show that b=2ac/3
(ii) Given that a = -b = -3c, find the common factors.
Given (x+ c) is a common factor of (x^2- ax- b )and (2x^2+b)
x= -c is a root of x^2- ax- b= 0 and x^2+ b= 0
Concept used
Quadratic equationQuadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.
Quadratic Formula-b±√b²-4ac/2a
i) 1- 2a+b= 0
ii) 4+ b^b- 2a= 0
4- 2a+b=0,4+ b- 2a= 0
2a+b= 2c+d
2(c−a)= b−d
(c−a)/ (b−d)= 2
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Which of the following values make the inequality x≤16.3 truea 18.5b 8c 1/4d 32e -3f 16.3
SOLUTION
We want to find which of the following values make the inequality
x ≤ 16.3 to be true.
This inequality means that x is equal to 16.3 or less than 16.3. So the numbers that fall under this are numbers smaller than 16.3 and also 16.3.
The numbers that fall under here are 8, 1/4, -3 and 16.3
Hence the answer b, c, e and f
5. Paetyn is going rock climbing. She starts at 12-yards
above sea level. She ascends 38-yards before lunch. She
descends 15-yards after lunch. What is Paetyn's final height
relative to sea level?
Answer:
35 yards above sea level
Step-by-step explanation:
12 + 38 - 15
50 - 15
35
find the solution of the system of equations
9x+y=28
3x+3y=-12
Answer:
(4, - 8 )
Step-by-step explanation:
9x + y = 28 ( subtract 9x from both sides )
y = 28 - 9x → (1)
3x + 3y = - 12
substitute y = 28 - 9x into (2)
3x + 3(28 - 9x) = - 12 ← distribute parenthesis on left side and substitute
3x + 84 - 27x = - 12
- 24x + 84 = - 12 ( subtract 84 from both sides )
- 24x = - 96 ( divide both sides by - 24 )
x = 4
substitute x = 4 into (1)
y = 28 - 9(4) = 28 - 36 = - 8
solution is (4, - 8 )
What is the slope of the line through the points (6,5) and (4, 10)?
m=
The slope of the line through the points (6,5) and (4, 10) exists -5/2.
What is meant by the slope of a line?A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively. where "m" represents a line's slope. So, the slope of a line is tan.
Determine the coordinates of two points along the line that you choose. Find the difference between these two points' y-coordinates (rise). Find the difference between these two points' x-coordinates (run). Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates.
Let the two points are (6, 5) and (4, 10)
(x1, y1) = (6, 5) and (x2, y2) = (4, 10)
The equation of slope of the line through the points (x1, y1) and (x2, y2) = y2 - y1 / x2 - x1
substitute the values in the above equation, and we get
= 10 - 5 / 4 - 6
= 5 / -2
Therefore, the slope of the line through the points (6,5) and (4, 10) exists -5/2.
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21 A forklift has a maximum carrying capacity of 960 pounds. Each cargo box weighs 60 pounds.
a. Write and solve an inequality that represents the maximum number of cargo boxes the
forklift can carry.
b.
A 120-pound carrying case is used to hold the cargo boxes. What is the maximum number
of cargo boxes the forklift can carry when the carrying case is used? Show that your answer
is correct by showing that one more than your answer would exceed the forklift's capacity
Using the concept of inequality, it can be concluded that;
a) Maximum number of cargo boxes the forklift can carry is 16.
b) Maximum number of cargo boxes the forklift can carry when the carrying case is used is 14.
What is the inequality in mathematics?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to contrast two numbers on the number line based on their sizes.
Let the no. of cargo box be x.
So the equation is 60x≤960
x≤960/60
x≤16
Now the 120 pound additional weight is needed so the equation is:
120 + 60x≤960
60x≤840
x≤14
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If point A, havingcoordinates (p, 3) andpoint B, with coordinates(6, p) lie on a line havinga slope of 2, what is thevalue of p?
Take into account that the slope of a line is given by the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1,y1) and (x2,y2) are two points on the line.
In this case:
(x1,y1) = (p,3)
(x2,y2) = (6,p)
By replacing the previous values into the formula for m, we get:
[tex]m=\frac{p-3}{6-p}[/tex]Now, by making m = 2 and solving for p, we obtain:
[tex]\begin{gathered} \frac{p-3}{6-p}=2 \\ p-3=2(6-p) \\ p-3=12-2p \\ p+2p=12+3 \\ 3p=15 \\ p=\frac{15}{3}=5 \end{gathered}[/tex]Hence, the value of p is p = 5
what do the factoring of special products have in common?
We know that specific products multiply specific kinds of binomials, so these binomials will be the product's factors.
Example:
2 × 3 = 6Factors of 6: 2 × 3What are special products?Simply put, special products are just special cases of multiplying together specific types of binomials. We offer three unique products: (a + b)(a + b) (a - b)(a - b)So, we know that special products are multiplying special types of binomials which means that these binomials will be the factors of the product.
For example:
2 × 3 = 6Factors of 6: 2 × 3Therefore, we know that specific products multiply specific kinds of binomials, so these binomials will be the product's factors.
Example:
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Ken wants to install a row of ceramic tiles on a wall that is 21 3/8 inches wide each tile is 4 1/2 inches wide how many whole dose he need
the width of the wall is 21 3/8 = 171/8
the width of a tile is 4 1/2 = 9/2
so the number of tiles is
(171/8) / (9/2) = 171x2 / (9 x8) = 4.75
so the no of tiles needed is 5.
Two office supply stores sell their brand of copy paper by the pound. One company offers a flat rateshipping charge and the other offers free shipping.Use the graph provided to construct a linear system to model this situation. Solve the system todetermine the amount of copy paper for which the cost is the same at both stores. Use the graph to verifythat your answer is reasonable.220200(450,202.51180160(400,156)1401Cost ($)1201008060(0.56)4020(0,0)Amount of copy paper (lb)-1 (x)-9 (X)50100150200250300350150 00The y-intercept, b, of f(x) isand the slope, m, offix) is
Given the graph in the attached image.
The red line represents f(x) and the blue line represents g(x);
From the graph;
The intercept, b, of f(x) is
[tex]b=56[/tex]and the slope, m, of f(x) is;
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1}=\frac{156-56}{400-0} \\ m=\frac{100}{400} \\ m=\frac{1}{4} \\ m=0.25 \end{gathered}[/tex]So, f(x) is;
[tex]\begin{gathered} f(x)=mx+b \\ f\mleft(x\mright)=0.25x+56 \end{gathered}[/tex]For g(x)
The y-intercept, b, of g(x) is;
[tex]b=0[/tex]and the slope, m, of g(x) is;
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1}=\frac{202.5-0}{450-0} \\ m=\frac{202.5}{450} \\ m=0.45 \end{gathered}[/tex]So, g(x) is;
[tex]\begin{gathered} g(x)=mx+b \\ g(x)=0.45x+0 \\ g(x)=0.45x \end{gathered}[/tex]To derive the solution, let us equate the two equations;
[tex]undefined[/tex]What is the first step in evaluating the expression shown below? (12.9-3.1) x 6.2-2 + 43 00:00 Multiply 3.1 and 6.2. 00:00 Add 2 and 43 Subtract 3.1 from 12.9. Subtract 2 from 6.2.
We have to indicate the steps to follow in order to evaluate:
(12.9-3.1) x 6.2-2 + 43
So FIRST: we solve for the operation indicated inside the parenthesis
12.9 - 3.1 = 9.8 (we subtract 3.1 from 12.9)
This is the answer you need to select.
8. A jewelry artist is selling necklaces at an art fair. It costs $170 to rent a booth at the fair. The cost of
materials for each necklace is $3.50. The artist is selling the necklaces at $12 each. The inequality
12n> 170 +3.50n represents the situation in which the artist makes a profit.
a. Will the artist make a profit if he sells 15 necklaces? Show how you know.
b. Solve the inequality and explain what the solution means in regards to the jewelry artist.
By solving inequality, we can conclude that the artist will not make a profit if he sells 15 necklaces.
What is inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. In mathematics, larger than symbol (>), less than symbol (<), less than or equal to a symbol (<), greater than or equal to a symbol (≥), less than or equal to a symbol (≤), and not equal to a symbol (≠).So, is the artist in profit if he sells 15 necklaces:
The cost to rent a booth is $170.The cost of making a necklace is $3.50.The selling price is $12.Inequality is 12n ≥ 170 +3.50n: (let n = 15)
12n ≤ 170 +3.50n12(15) ≤ 170 +3.50(15)180 ≤ 170 + 52.5180 < 222.5Therefore, by solving inequality, we can conclude that the artist will not make a profit if he sells 15 necklaces.
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The correct question is given below:
A jewelry artist is selling necklaces at an art fair. It costs $170 to rent a booth at the fair. The cost of materials for each necklace is $3.50. The artist is selling the necklaces at $12 each. The inequality 12n> 170 +3.50n represents the situation in which the artist makes a profit. Will the artist make a profit if he sells 15 necklaces? Show how you know.
Point (2,11.9),(4,10.5)
(2,8) , (4,7.5)
(2,6) , (4,1.5)
(2,0.5) , (4.-1)
(2,-1) , (4,-1)
(-2.8,-5.0) , (-3.6,-5.9)
rise over run so what's the answer
Answer: The slope is -0.7, the rise is -1.4, and the run is 2
