- What is the y-intercept of 6x + 12y = 60? A. 5 B. 10 C .60 - What is the slope of the line that contains the points (1, −1) and (−2, 8)? A. −3 B. 7 over 3 negative C. 1 over 3 negative
The y-intercept of the equation 6x + 12y = 60 is 5, and the slope of the line through points (1, -1) and (-2, 8) is -3. Therefore the correct option is A.
Finding the Y-Intercept of a Linear Equation
To find the y-intercept of the linear equation 6x + 12y = 60, we need to set x to 0. If x=0, the equation simplifies to 12y = 60. Dividing both sides by 12 gives us the y-intercept: y = 5. Therefore, the correct answer is A: 5.
Calculating the Slope between Two Points
The slope of a line containing the points (1, -1) and (-2, 8) can be found by using the formula (y2 - y1) / (x2 - x1). Substituting the given points into the formula results in: (8 - (-1)) / (-2 - 1) = 9 / -3 = -3.
A child has 48 quarters and 80 dimes. The child wishes to stack the coins so that each stack has the same number of coins, and each stack contains only one kind of coin. What is the
largest number of coins that the child can place in each stack?
Since the greatest common factor for 48 and 80 is 16 then we conclude the largest number of stack is 16
The largest number of coins that the child can place in each stack is 16, which is the greatest common divisor of the number of quarters (48) and dimes (80) they have.
Explanation:In this problem, we're looking for the greatest number of coins that can evenly divide both the total number of quarters and the total number of dimes the child has. This can be solved by finding the greatest common divisor (GCD) of the numbers, 48 and 80.
The GCD of 48 and 80 is 16. Therefore, the child can create stacks of 16 coins each (either quarters or dimes), ensuring that each stack has the same number of coins and that all coins are used.
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Last week you worked the following hours: Monday, 5½ Wednesday, 6¾ Friday, 4½ How many hours did you work in all last week? A. 16¾ B. 17½ C. 17¾ D. 18½
Answer:
A. 16¾
Step-by-step explanation:
We will convert all the mixed fractions to improper fractions.
Monday, 5½ = [tex]\frac{11}{2}[/tex]
Wednesday, 6¾ = [tex]\frac{27}{4}[/tex]
Friday, 4½ = [tex]\frac{9}{2}[/tex]
Now, we will add all these fractions by taking the LCM of denominator.
The LCM of 2,4 and 2 is 4.
We get the following result after addition.
[tex]\frac{11}{2} +\frac{27}{4} +\frac{9}{2}[/tex]
= [tex]\frac{22+27+18}{4}[/tex]
= [tex]\frac{67}{4}[/tex] hours
In mixed fraction it becomes 16¾ hours.
On a number line, the distance from zero to -7 is 7 units.
Which equation demonstrates this concept?
A.
|-7| = 7
B.
|-7| = -7
C.
72 = 49
D.
0 + 7 = 7
Answer: Option A. |-7| = 7
Solution:
The distance is a positive value, then we must not take in account the sign, and using:
|a| =-a if a<0
with a=-7
|-7| = -(-7)
|-7| = 7
Which of the following angles is an angle of depression?
we know that
The Angle of Depression. is the angle below the horizontal that an observer must look to see an object that is lower than the observer
in this problem
the angle below the horizontal is the angle C
therefore
the answer is
The angle of depression is the angle C
A triangular window has a base of 8 feet and a height of 6 feet. What is its area?
Answer:
24 feet^2
Step-by-step explanation:
Area = 1/2 × base × height
Base = 8 feet
Height = 6 feet
Area = 1/2 × 8 feet × 6 feet = 24 feet²
Answer:
Area = 24 square feet.
Step-by-step explanation:
Given : A triangular window has a base of 8 feet and a height of 6 feet.
To find :What is its area?
Solution : We have given
Base of triangular window = 8 feet.
Height of triangular window = 6 feet.
Area = [tex]\frac{1}{2} * base*height[/tex].
Plugging the values.
Area = [tex]\frac{1}{2} *8* 6[/tex].
Area = 24 square feet.
Therefore, Area = 24 square feet.
Random cell phone calls sent out to a sample size of 850 people is what type of sampling method? (I.e. simple random, etc.)?
Answer: Simple Random Sampling (SRS)
The people chosen are basically picked out of a hat at random, though likely they are chosen by a computer.
Answer:
Random cell phone calls sent out to a sample size of 850 people would typically be considered a form of random sampling. However, the specific type of random sampling can vary. It could be simple random sampling if each person in the population has an equal chance of being called, and the selection is done entirely by chance, such as using a random number generator to select phone numbers.
Alternatively, it could be stratified random sampling if the population is divided into different groups or strata (e.g., age groups, geographic regions), and then random samples are taken from each stratum in proportion to its size.
The exact method used depends on the sampling strategy and goals of the study, but as long as the selection of individuals is based on randomness and each person has an equal chance of being included, it falls under the broad category of random sampling.
Step-by-step explanation:
$2500 was invested for 3 years and earned $450 in intrest. Fine the rate of intrest
Answer:
Step-by-step explanation:
130
In which measurement situations would the most appropriate unit of measurement be meters?
Choose exactly two answers that are correct.
A.
width of a finger
B.
height of a tree
C.
depth of a well
D.
distance from the earth to the sun
Yellow to red 50 yellow and 45 red what it the ratio
50 : 45
10 : 9 (10 yellow : 9 red)
50 yellow and 45 red
The ratio of yellow to red = 50/45 = 10/9
Answer
The ratio of yellow to red is 10/9 or 10:9
Mark bought 12 cookies for $2.70 at this rate how much would it cost him to buy 20 cookies
For Mark to buy 20 cookies, it'll cost him about $4.40
The cost of 20 cookies if 12 cookies cost $2.70 is $4.50.
How much would it cost him to buy 20 cookies?12 cookies cost $2.70
Then,
20 cookies cost $x
Set up the ratio
12 : 2.70 = 20 : x
12/2.70 = 20/x
cross product
12 × x = 2.70 × 20
12x = 54
Divide both sides by 12
x = 54/12
x = $4.50
Therefore, 20 cookies cost $4.50
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Ethan burns 650 calories when he runs for 1 hour suppose he ran 5 hours in a week
How many degrees is one sixth of a circle or 1/6 of a full turn
At the end of the summer, Caitlin had saved $120 from her summer job. This was her initial deposit into a new savings account at the bank. As the school year starts, Caitlin is going to deposit another $5 each week from her allowance. Is her account balance proportional to the number of weeks of deposits? Explain your reasoning.
Let X be the number of weeks she deposits money.
The equation to solve for the account balance would be 120 + 5x ( She started with 120 dollars and is adding 5 dollars per week)
week 1: balance = 120 +5(1) = $125
week 2: balance = 120 +5(2) = $130
week 3: balance = 120 + 5(3) = $135
week 4: balance = 120 +5(4) = $140
Now to see if it proportional divide each total by the number of weeks:
week 1: 125 / 1 = 125
week 2: 130 / 2 = 65
week 3: 135 / 3 = 45
week 4: 140 / 4 = 35
Find the difference between the weeks:
Week 1 & 2 : 125 - 65 = 60
Week 2 & 3: 65 -45 - 20
Week 3 & 4: 45 -35 = 10
Since the 3 differences are not the same, the balance is not proportional to the number of weeks.
What are the x- and y-intercepts of the graph of y = x2 + 3x − 10? x-intercepts: (−2, 0) and (5, 0) y-intercept: (0, 10) x-intercepts: (−2, 0) and (−5, 0) y-intercept: (0, 10) x-intercepts: (−2, 0) and (5, 0) y-intercept: (0, −10) x-intercepts: (2, 0) and (−5, 0) y-intercept: (0, −10)
We have the following function:
[tex]f(x)=x^2+3x-10[/tex]
So, we need to find the x- and y-intercepts of the graph of that function, therefore:
1. x-intercepts
x-intercepts can be found when [tex]y=0[/tex], so:
[tex]0=x^2+3x-10 \\ \\ Using \ Quadratic \ Formula \\ \\ x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ Where: \\ \\ a=1, b=3, c=-10 \\ \\ x=\frac{-3 \pm \sqrt{3^2-4(1)(-10)}}{2(1)} \\ \\ Two \ values: \\ \\ x=2 \ and \ x=-5[/tex]
So, the x-intercepts are:
[tex]\boxed{(2,0) \ and \ (-5, 0)}[/tex]
2. y-intercepts
x-intercepts can be found when [tex]x=0[/tex], so:
[tex]y=(0)^2+3(0)-10 \\ \\ \therefore y=-10[/tex]
So, the y-intercept is:
[tex]\boxed{(0,-10)}[/tex]
_______________________________________
Therefore the right answer is:
x-intercepts: (2, 0) and (−5, 0) y-intercept: (0, −10)
This is indicated in the Figure bellow.
Answer:
2, 0) and (−5, 0)
Step-by-step explanation:
PLEASE HELP THIS IS URGENT!
The engine torque y (in foot-pounds) of one model of car is given by y=−3.75x^2+23.2x+38.8, where x is the speed (in thousands of revolutions per minute) of the engine.
a. To the nearest ten, what is the engine speed that maximizes torque? ------____ revolutions per minute
To the nearest hundredth, what is the maximum torque?
____ ft-lbs
Question 2
b. Explain what happens to the engine torque as the speed of the engine increases.
As the engine speed increases, the torque _____ until the engine speed reaches
_____ thousand revolutions per minute and then the torque ______
Answer-
a. The engine speed that maximizes torque is 3.1 thousand revolutions per minute and the maximum torque is 74.68 ft-lbs
b. As the engine speed increases, the torque increases until the engine speed reaches 3.1 thousand revolutions per minute and then the torque decreases.
Solution-
The given equation is,
[tex]y=-3.75x^2+23.2x+38.8[/tex]
Where x = the speed of the engine (in thousands of revolutions per minute)
y = the engine torque y (in foot-pounds)
a.
In order to calculate the max torque and when it is max, we have to take the help of maxima and minima concepts from application of derivatives.
[tex]\Rightarrow y=-3.75x^2+23.2x+38.8[/tex]
[tex]\Rightarrow {y}'=-7.5x+23.2[/tex]
[tex]\Rightarrow {y}''=-7.5[/tex]
Equating the first derivative to 0, in order to find critical points,
[tex]\Rightarrow {y}'=0[/tex]
[tex]\Rightarrow -7.5x+23.2=0[/tex]
[tex]\Rightarrow x=\frac{-23.2}{-7.5} = 3.093 \approx 3.1[/tex]
As the value of second derivative is negative, hence the value of the function at x=3.1 will be maximum.
The value of max torque is,
[tex]y(3.1)=-3.75(3.1)^2+23.2(3.1)+38.8=74.682 \approx 74.68[/tex]
b.
Calculating the roots of the function,
[tex]\Rightarrow y=0[/tex]
[tex]\Rightarrow -3.75x^2+23.2x+38.8=0[/tex]
[tex]x=-1.369,7.556[/tex]
As these are the roots or x-intercept, the value of the function at these points is zero.
As shown in the graph, the function increases from x=0 to x=3.1 (as the speed can not be negative, so neglecting negative values) and after x=3.1 it decreases.
At about 3093 revolutions per minute, the engine torque reaches its maximum of 44.97 ft-lbs. Prior to this, the torque increases with engine speed, but starts to decrease once the speed surpasses this point.
Explanation:The equation given is that of a downward opening parabola, which means it has a maximum point. The vertex (h, k) of a parabola given by the equation y = a(x-h)^2 + k is at x = -b/2a. For the given equation, a = -3.75 and b = 23.2.
Substituting these values, we get x = -23.2/(2*-3.75) = 3.093 to the nearest thousand, which translates to 3093 revolutions per minute. Substituting this value of x in the equation gives the maximum torque y = -3.75*(3.093)^2 + 23.2*3.093 + 38.8 = 44.97 ft-lbs to the nearest hundredth.
As the engine speed increases, the torque increases until the engine speed reaches about 3093 revolutions per minute. After this, "the torque then starts to decrease".
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2 different pairs of decimals whose sum are 8.69 one pair should involve regrouping
please help asap 25 pts
2y - 3 > -1 |add 3 to both sides
2y > 2 |divide both sides by 2
y > 1
-----------------------------
5 - y > 4 |subtract 5 from both sides
-y > -1 |change the signs
y < 1
y > 1 or y < 1
Therefore your answer is d.Use the place value chart to write 9,000+800+50
The answer is 9,850 if you are adding the numbers together.
Answer:
9,000 + 800 + 50 = 9,850
Step-by-step explanation:
Hope it helped!
Which ordered pair is a solution to this equation?
2x - 9y = 38
(7, 5)
(4, -1)
(3, -3)
(1, -4)
Let's test each alternative :
2 x - 9 y = 38 ( 7,5 ) :
( 2 * 7 ) - ( 9 * 5 ) = 38
14 - 45 = 38
-31 ≠ 38 ( wrong )
( 4 , - 1 ) :
( 2 * 4 ) - ( 9 * ( - 1 ) = 38
8 + 9 = 38
17 ≠ 38 ( wrong )
( 3 , - 3 ) :
2 * ( 3 ) - ( 9 * ( - 3 ) = 38
6 + 27 = 38
33 ≠ 38 ( wrong )
( 1 , - 4 ) :
2* ( 1 ) - 9 * ( - 4 ) = 38
2 + 36 = 38
38 = 38 ( Correct alternative )
( 1 , - 4 ) is correct alternative
What is the value of m inthe figure below? In this diagram, ABD~BCD
Answer:
C. sqrt(95)
Step-by-step explanation:
The three triangles are similar, so you can use the right triangle altitude theorem.
(14 + 5)/m = m/5
19/m = m/5
m^2 = 19 * 5
m^2 = 95
m = sqrt(95)
Answer: C. sqrt(95)
please help asap 23 pts
Solve for r by simplifying both sides of the equation, then isolating the variable.
Your answer is A.
If 200 gems cost $5, how much is each gem?
Help plsss!!
Solve the inequality
8(1/2x - 1/4)> 12 - 2x
a.x > 7
b.x > 7/3
c.x > 5/3
d.x > 5/3
The solution to the inequality 8(1/2x - 1/4) > 12 - 2x is x > 7/3.
Explanation:To solve the given inequality 8(1/2x - 1/4) > 12 - 2x, first you should distribute the 8 to both terms in the parentheses. This gives you 4x - 2 > 12 - 2x. Next, we need to group like terms, so let's add 2x to both sides of the inequality to obtain 6x - 2 > 12. Afterwards, add 2 to both sides, resulting in 6x > 14. Finally, divide each side by 6 to isolate x, which gives x > 7/3. So, the solution is x > 7/3.
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What is an equivalent expression to q(2a+1)
You can distribute the q to both terms to get
[tex] q(2a+1) = q\cdot 2a + q\cdot 1 = 2aq+q [/tex]
Answer:
2aq +q is an equivalent expression for q(2a+1)
Step-by-step explanation:
an equivalent expression to q(2a+1)
To get equivalent expression we need to multiply q inside the parenthesis
q times 2a = 2aq
q times 1 is q
Now we combine both term
q(2a+1)= 2aq + q
So 2aq +q is an equivalent expression for q(2a+1)
Is .98 less than greater than or equal to .980
Answer:
iit =
Step-by-step explanation:
Suzanne can read 1 page in 4 minutes. How many pages can she read in 5 hours?
Answer:
75 pages
Step-by-step explanation:
Look at the following sequence. 128, 320, 800, 2000, . . . If it is a geometric sequence, choose the common ratio. If it is not a geometric sequence, choose “not geometric.” 4 not geometric 2.5 1200
Answer:
It is a geometric sequence en the common ratio is: [tex]r=\frac{5}{2}[/tex].
Step-by-step explanation:
1. By definition, a geometric sequence is a sequence in which you obtain a term by multiplying the previous one by a common ratio.
2. The common ratio is obtained by dividing a term by its preceding term.
3. Keeping this on mind, you have:
[tex]\frac{320}{128}=\frac{5}{2}\\[/tex]
[tex]\frac{800}{320}=\frac{5}{2}[/tex]
[tex]\frac{2000}{800}=\frac{5}{2}[/tex]
4. As you can see, the common ratio is [tex]\frac{5}{2}[/tex]
Answer:
2.5!!
Step-by-step explanation:
100% correct
Erika is ordering cupcakes for a party one cupcake costs $3 there will be 20 guests at the party and she wants each guest to get one cupcake how much will she spend on cupcakes
Erika will spend $60 on cupcakes for the 20 guests at her party by purchasing one $3 cupcake for each guest.
To calculate how much Erika will spend on cupcakes for the party, we need to multiply the number of guests by the cost of each cupcake. Each guest will get one cupcake, and since there are 20 guests, we need 20 cupcakes. The cost of one cupcake is $3.
To find the total cost, we perform the following calculation:
Total cost = Number of cupcakes x Cost per cupcakeTotal cost = 20 x $3Total cost = $60Therefore, Erika will spend $60 on cupcakes for the party.
The number of seconds in a 40-hour work week can be calculated as follows:
First we can calculate how many seconds there are in an hour:
Since 1 hour has 60 minutes and each minute has 60 seconds.
Then 1 hour = 60 minutes * 60 seconds/1minute = 3,600 seconds.
Now we have to multiply x 40 to calculate how many seconds there are in 40 hours.
In a 40-hour work week = 40 hours * 3,600 seconds/1hour = 144,000 seconds
Answer : 144,000 seconds there are in a 40-hour work week
Hope this helps!
[tex]\textit{\textbf{Spymore}}[/tex]
The correct formula to calculate the number of seconds in a 40-hour work week is 40 hours * 60 minutes/hour * 60 seconds/minute (option a). This method accurately converts hours to minutes and then minutes to seconds.
The correct formula for calculating the number of seconds in a 40-hour work week is as follows:
a. 40 hours * 60 minutes/hour * 60 seconds/minute
Here's the breakdown:
1. Start with the number of hours, which is 40 hours.
2. Convert hours to minutes using the conversion factor of 60 minutes per hour.
3. Convert minutes to seconds using the conversion factor of 60 seconds per minute.
By multiplying these three factors together, you obtain the total number of seconds in a 40-hour work week.
The other options (b, c, d) do not correctly set up the conversion factors and units, leading to incorrect results.
So, the correct answer is (a), as it correctly converts 40 hours into seconds using the appropriate conversion factors.
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