[tex]\bf \begin{array}{ccll} \stackrel{x}{weeks}&\stackrel{y}{songs}\\ \cline{1-2} 1&80000\\ 4&300000 \end{array}~\hspace{10em} (\stackrel{x_1}{1}~,~\stackrel{y_1}{80000})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{300000}) \\\\\\ \stackrel{\textit{average rate of change}}{slope = m\implies} \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{300000-80000}{4-1}\implies \cfrac{220000}{3}\quad \approx \quad 73333[/tex]
Fluffy's tail was 1/3 of a meter long. Fireballs tail is 1/4 of a meter long . How much longer is fluffy's than Fireballs tail?
Answer:1/12
Step-by-step explanation:1/3-1/4=1/12
A store manager ordered 28 crates of mangoes.There were 36 mangoes in each crate.WHEN the mangoes were delivered, he sold the ripe mangoes and repacked the rest equally into 73 boxes.There were 12 mangoes in each box.How many ripe mangoes were sold?
Answer:
Number of ripe mangoes were sold as 132
Step-by-step explanation:
Let's assume number of rip mangoes were sold as 'x'
A store manager ordered 28 crates of mangoes
Number of crates =28
There were 36 mangoes in each crate
Number of mangoes in each crate=36
Total number of mangoes=( Number of crates)*(Number of mangoes in each crate)
Total number of mangoes is
[tex]=28\times 36[/tex]
[tex]=1008[/tex]
WHEN the mangoes were delivered
he sold the ripe mangoes and repacked the rest equally into 73 boxes
There were 12 mangoes in each box
Total number of mangoes is
[tex]=73\times 12+x[/tex]
[tex]=876+x[/tex]
now, we can set them equal
[tex]1008=876+x[/tex]
[tex]x=132[/tex]
To find the number of ripe mangoes sold, multiply the number of crates by the number of mangoes in each crate. Then, multiply the number of boxes by the number of mangoes in each box. Finally, subtract the number of mangoes repacked into boxes from the total number of mangoes delivered.
To find the number of ripe mangoes sold, we need to determine the total number of mangoes delivered and then subtract the number of mangoes repacked into boxes.
First, we find the total number of mangoes delivered by multiplying the number of crates (28) by the number of mangoes in each crate (36): 28 crates * 36 mangoes/crate = 1008 mangoes
Next, we find the number of mangoes repacked into boxes by multiplying the number of boxes (73) by the number of mangoes in each box (12): 73 boxes * 12 mangoes/box = 876 mangoes
Finally, we subtract the number of mangoes repacked into boxes from the total number of mangoes delivered to find the number of ripe mangoes sold: 1008 mangoes - 876 mangoes = 132 ripe mangoes
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What is the distance between the points (–6, –10) and (2, 5)?
Answer:
17
Step-by-step explanation:
To find the distance between two points, we use the formula
d =sqrt( (x2-x1)^2 + (y2-y1)^2)
d= sqrt((2--6)^2+(5--10)^2 )
d= sqrt((2+6)^2+(5+10)^2 )
d = sqrt(8^2 + 15^2)
d = sqrt(64+225)
d =sqrt(289)
d =17
You jog 2 kilometers in 12 minutes ,at this rate how much will it take you to complete a 5 kilometers race
Calculate your speed per kilometer, by dividing the known time by the distance already ran:
12 minutes / 2 kilometers = 6 minutes per kilometer.
Now multiply the time for 1 by the total distance:
6 minutes per kilometer x 5 kilometers = 30 minutes total.
Pls help me with this Trig question!
Answer:
s = 65/3 pi
Step-by-step explanation:
The length of the intercepted arc is given by the formula
s =r*theta when theta is given in radians
r = 13
theta = 5 pi/3
Substituting what we know
s = 13 * 5 pi/3
s = 65/3 pi
Since we want an exact answer, we have to leave it in terms of pi and as a fraction
∆ABC is transformed with the center of dilation at the origin.
Pre-image: ∆ABC with vertices A(2, 5), B(6, 10), C(9, −1)
Image: ∆A'B'C' with vertices A' (0.5, 1.25), B' (1.5, 2.5), C' (2.25, −0.25)
What is the scale factor of the dilation that maps the pre-image to the image?
Answer:
1/4
Step-by-step explanation:
We are to find the scale factor of the dilation that maps the pre-image of triangle ABC with vertices A(2, 5), B(6, 10) and C(9, −1) to the image triangle A'B'C' with vertices A' (0.5, 1.25), B' (1.5, 2.5), C' (2.25, −0.25).
Center of dilation is at the origin.
To find the scale factor, we will divide the corresponding vertices of the image and pre-image.
A(2, 5) ---> A' (0.5, 1.25) = [tex]\frac{0.5}{2} , \frac{1.25}{5}=(\frac{1}{4} , \frac{1}{4})[/tex]
B(6, 10) ---> B' (1.5, 2.5) = [tex]\frac{1.5}{6} , \frac{2.5}{10}=(\frac{1}{4} , \frac{1}{4})[/tex]
C(9, −1) ---> C' (2.25, −0.25) = [tex]\frac{2.25}{9} , \frac{-0.25}{-1}=(\frac{1}{4} , \frac{1}{4})[/tex]
Therefore, the scale factor of the dilation is 1/4.
The scale factor of the dilation that maps triangle ABC to triangle A'B'C' is determined by calculating the ratio of the coordinates of corresponding vertices. The scale factor for this transformation is 0.25.
The student is asking how to find the scale factor of a dilation when given the coordinates of the vertices of a triangle before and after the transformation. To determine the scale factor, you need to compare the corresponding sides or coordinates of the pre-image and the image. Below is the step-by-step explanation:
Identify corresponding vertices between the pre-imageTherefore, the scale factor for the dilation that maps the pre-image to the image is 0.25.
The sum of the measures of the interior angles of the polygon below is 1800°
Answer:
False
Step-by-step explanation:
The sum of the interior angles of a regular polygon is (n – 2)180 where n is the number of sides. Since this is a 10 sided figure,
the sum of the interior angles is (10-2)* 180 =1440
Line m contains (6,8) and (-1,2). Line n contains (-1,5) and (5,y). What is the value of y if line m is perpendicular to line n
Answer:
y=-37
Step-by-step explanation:
A perpendicular line has a negative reciprocal slope to the original line. We will use the slope formula to find the slope of line m, then take the negative reciprocal for the slope of line n which will reveal the value of y.
Slope:[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We substitute [tex]x_1=6\\y_1=8[/tex] and [tex]x_2=-1\\y_2=2[/tex]
[tex]m=\frac{2-8}{-1-6}[/tex]
[tex]m=\frac{2-8}{-1-6}=\frac{-6}{-7} =\frac{6}{7}[/tex]
[tex]m\neq \frac{6}{7}[/tex] for line n because it is perpendicular to it. This means we will need to change it into its negative reciprocal which is [tex]m=-\frac{7}{6}[/tex].
We will substitute [tex]m=-\frac{7}{6}[/tex] into the slope formula to find line n's coordinate value y. We will also substitute [tex]x_1=-1\\y_1=5[/tex] and [tex]x_2=5\\y_2=y[/tex] .
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]-\frac{7}{6}=\frac{y-5}{5-(-1)}[/tex]
[tex]-\frac{7}{6}=\frac{y-5}{6)}[/tex]
[tex]6(-\frac{7}{6})=y-5[/tex]
[tex]-42+5=y-5+5[/tex]
[tex]-37=y[/tex]
The value of y that makes Line n perpendicular to Line m is 59/6. This is found by first calculating the slope of Line m and then finding the negative reciprocal (since perpendicular lines have negative reciprocal slopes), and using this new slope to solve for y in Line n.
Explanation:To solve this problem, we first need to understand that the slopes of two perpendicular lines are negative reciprocals of each other. This means that if Line m has a slope of a, then Line n will have a slope of -1/a.
First, let's find the slope of line m which contains the points (6,8) and (-1,2). The formula for slope is (y2-y1)/(x2-x1). This gives us (2-8)/(-1-6) = -6/-7 = 6/7.
Because line n is perpendicular to line m, its slope will be the negative reciprocal of 6/7, which is -7/6. We can then use this slope and the point (-1,5) to find the value of y when x=5 on line n. We use the equation y-y1 = m(x-x1), and substitute the values in: y - 5 = -7/6 * (5 - (-1)), which simplifies to y = -7 + 5 + 35/6 = 29/6 + 30/6 = 59/6.
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The equation yˆ=−5.9x2+39x+2.2 approximates the average number of cars that pass through an intersection x hours after 3:00 p.m. What is the best estimate for the average number of cars that pass through the intersection at 4:30 p.m.?
Answer: 74
Step-by-step explanation:
x = 4:30 - 3:00
= 1:30
= 1.5 hours
y = -5.9x² + 39x + 2.2
= -5.9(1.5)² + 39(1.5) + 2.2
= -5.9(2.25) + 58.5 + 2.2
= 13.275 + 60.7
= 73.975
Answer: 47
Step-by-step explanation:
x = 4:30 - 3:00
= 1:30
= 1.5 hours
y = -5.9x² + 39x + 2.2
= -5.9(1.5)² + 39(1.5) + 2.2
= -5.9(2.25) + 58.5 + 2.2
= -13.275 + 60.7
= 47.425
If A varies inversely as the square of B, what is the effect on B if A is multiplied by 3? Please explain.
Answer:
If A is multiplied by 3, B will be reduced by a factor [tex]\frac{1}{\sqrt{3}}[/tex]
Step-by-step explanation:
Writing the inverse proportionality relationship and expressing the dependence of B on A leads to the following:
[tex]A = \frac{1}{B^2}\implies |B| = \frac{1}{\sqrt{A}}\\B'=\frac{1}{\sqrt{3A}}= \frac{1}{\sqrt{3}}\frac{1}{\sqrt{A}}=\frac{1}{\sqrt{3}}|B|[/tex]
In words, if A triples, B will decrease by a factor [tex]\frac{1}{\sqrt{3}}[/tex], or, in other words, the square of B will decrease to one third of its previous value.
What does the fundamental theorem of algebra state about the equation 2x^2-4x+16=0?
Answer: (A) degree of 2; 1 ± i√7
Step-by-step explanation:
Degree of the polynomial designates the number of roots.
x² - 2x + 8
a=1 b=-2 c=8
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]=\dfrac{-(-2)\pm\sqrt{(-2)^2-4(1)(8)}}{2(1)}[/tex]
[tex]=\dfrac{2\pm\sqrt{4-32}}{2}[/tex]
[tex]=\dfrac{2\pm\sqrt{-28}}{2}[/tex]
[tex]=\dfrac{2\pm2i\sqrt{7}}{2}[/tex]
[tex]=\dfrac{2(1\pm\\i\sqrt7)}{2}[/tex]
= 1 ± i√7
Given the equation y − 3 = fraction 1 over 2 (x + 6) in point-slope form, identify the equation of the same line in standard form.
Answer: x - 2y = -12
Step-by-step explanation:
[tex]y - 3 = \dfrac{1}{2} (x+6)\\2(y - 3) = (2)\dfrac{1}{2}(x + 6)\\2y - 6 = x + 6\\\underline{-x +6}\quad\underline{-x + 6}\\-x + 2y = 12\\-1(-x + 2y = 12)\\x - 2y = -12[/tex]
ANSWER:
-1/2x + y = 6
ABOUT POINT SLOPE FORM:
y - Y1 = m (x - X1)Y1 & X1 is a point on the linem represents the slopeThis form allows you to identify the slope & the point on the lineABOUT STANDARD FORM:
Ax + By = CA & B & C are integersA &B are both non - zeroThis form is good to use when wanting to find the x & y intercepts of a liney - 3 = 1/2 (x + 6)
y - 3 = 1/2x + 3
+ 3 + 3
y = 1/2x + 6
-1/2x -1/2x
-1/2x + y = 6
I'm not sure if my answer is correct... But please tell me if it's correct or incorrect! Thank you! :)
Sweet t purchased a new pair of jeans to wear at the battle of the bands on sale at 40% off.He saved $20 what was his regular price of the jeans
Write the quadratic equation whose roots are 6 and 3, and whose leading coefficient is 4
(Use the letter x to represent the variable)
If α and β are the Roots of a Quadratic Equation ax² + bx + c then :
✿ Sum of the Roots : α + β [tex]\mathsf{= \frac{-b}{a}}[/tex]
✿ Product of the Roots : αβ [tex]\mathsf{= \frac{c}{a}}[/tex]
Let the Quadratic Equation we need to find be : ax² + bx + c = 0
Given : The Roots of a Quadratic Equation are 6 and 3
⇒ α = 6 and β = 3
Given : The Leading Coefficient of the Quadratic Equation is 4
Leading Coefficient is the Coefficient written beside the Variable with Highest Degree. In a Quadratic Equation, Highest Degree is 2
Leading Coefficient of our Quadratic Equation is (a)
⇒ a = 4
⇒ Sum of the Roots [tex]\mathsf{: (6 + 3) = \frac{-b}{4}}[/tex]
⇒ -b = 9(4)
⇒ b = -36
⇒ Product of the Roots [tex]\mathsf{: (6 \times 3) = \frac{c}{4}}[/tex]
⇒ c = 18 × 4
⇒ c = 72
⇒ The Quadratic Equation is 4x² - 36x + 72 = 0
Jenson had 558 game cards. He lost 92 of them in a game and gave 105 game cards to his brother. How many game cards had he left ?
Answer:
After giving 197 cards away, Jenson is left with 361 cards
Step-by-step explanation:
A company produces accessories for smart phones and tablets. The profit on each smart phone case is $2, and the profit on each tablet case is $3. The company made a profit of $1,200 on the cases last month. The equation 2x + 3y = 1,200 represents the company's profit from cases last month, where x is the number of smart phone cases sold and y is the number of tablet cases sold.
1. Change the equation into slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all of your work.
2. Describe how you would graph this line using the slope-intercept method. Be sure to write in complete sentences.
3. Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences.
4. Graph the function. On the graph, make sure to label the intercepts. o You may graph your equation by hand on a piece of paper and scan your work.
5. Suppose in the next month, the total profit on smart phone cases and tablet cases is $1,500. The profit amounts are the same, $2 for smart phone case and $3 for the tablet case. In a paragraph of at least three sentences, explain how the graphs of the functions for the two months are the same and how they are different. Be sure to use complete sentences.
6. Below is a graph that represents the total profits for a third month. Write the equation of the line that represents this graph.
Answer:
y= -2/3x(m) +400(b)
Step-by-step explanation:
1.2x + 3y = 1200
3y = -2x + 1200
y = (-2x/3)x + 1200/3
the slope is -2/3x the y intercept is 400
2.I would plot the ordered pair (0, 400) on the coordinate plane. Then to find the other ordered pair you would use the slope (-2, 3). You should go two spaces to the right of (0, 400) and then three spaces down. After this your slope look like (-2, 397)
3.the function t(x) gives the number of tablets, given that x smart-phones have been sold/produced
t(x) = (-2/3)x + 400
Suppose in the next month, the total profit on smart phone cases and tablet cases is $1,500. The profit amounts are the same, $2 for smart phone case and $3 for the tablet case. In a paragraph of at least three sentences, explain how the graphs of the functions for the two months are the same and how they are different. Be sure to use complete sentences.
They would be similar because the slope would stay the same. The slope would stay the same, because the prices remain the same. They would be different because their y intercept would change
4.F (x) = mx + b
F (x) = mx + 300
F (x) = 6/9x + 300
F (x) = 2/3x + 300
i dont really have clue about how to do next
Solve the system of equations using elimination.
8x + 7y = -16
10x + 7y = -6
A)
(3, 6)
B)
(8, 5)
C)
(7, 10)
D)
(5, -8)
Answer: D.(5, -8)
Step-by-step explanation:
(Multiply by -1)-8x-7y=16
10x+7y=-6
2x=10
X=5
(Subsitite 5 into one) 10(5)+7y=-6
50+7y=-6
7y=-56
Y=-8
Final answer:
To solve the system using elimination, subtract the first equation from the second to find x=5, then substitute x back into one of the original equations to find y=-8. The solution is (5, -8).
Explanation:
To solve the system of equations using elimination, we look at the given pairs:
8x + 7y = -1610x + 7y = -6We can eliminate the y-variable by subtracting the first equation from the second
(10x + 7y) - (8x + 7y) = -6 - (-16)10x - 8x + 7y - 7y = -6 + 162x = 10Divide both sides by 2:
x = 5Now that we have x, we can substitute it back into either of the original equations to find y. Let's use the first equation:
8(5) + 7y = -1640 + 7y = -167y = -16 - 407y = -56Divide both sides by 7:
y = -8Therefore, the solution to the system of equations is (5, -8), which corresponds with answer choice D.
MATH HELP WILL UPVOTE!!!
The function d(h)=50+45h represents the distance a family traveled, in miles, h hours after they stopped for lunch. What does the value 45 represent in this situation?
The family drove 45 miles after they stopped for lunch.
Before lunch, the family traveled at a speed of 45 mph.
After lunch, the family traveled at a speed of 45 mph.
The family drove 45 miles before they stopped for lunch.
Answer:
After lunch, the family traveled at a speed of 45 mph is the only solution that makes sense when simplifying d(h)=50+45H
Step-by-step explanation:
Answer: After lunch the family drove 45 miles per hr. HOPE THIS HELPS!
Solve for x 13x-7 11x+11
Answer:
answer 7.3
13x-7+11x+11=180
Step-by-step explanation:
Joe gets paid 4 pounds to walk a dog. He wants to save 11 pound? How many times does he need to walk the dog.
Answer:
He needs to walk the dog 3 times as 3 times 4 = $12
Step-by-step explanation:
HELP PLEASE!! which of the following represents a function?
please explain too i don’t understand this.
Answer:
A is a function because if draw a line right down the middle no other dots will intercept
Step-by-step explanation:
A function is where one input has only one out put
As you can tell in the table(c) -3 is repeated that's what makes it not a function.same for B since there are more than one inputs it's not a function
Hope this helps!
If you break up the number under the radical in the square root of 36 into two factors that are perfect squares, what are the two factors?
Answer:
6
Step-by-step explanation:
sqrt (36)
Lets break this into parts
sqrt(4 * 9)
sqrt(4) * sqrt(9)
2 * 3
6
A collection of 36 shirts and 42 jackets contains 842 buttons. A collection of 66 shirts and 77 jackets contains 137 buttons. Each shirt has the same number of buttons, and each jacket has the same number of buttons. How many buttons are there in a Fiona's Fashion shirt, and how many buttons are there in a jacket?
Answer:
Step-by-step explanation:
Let x represent the number of buttons on shirts and y represent the number of buttons on jackets.
If 36 shirts and 42 jackets contain 842 buttons. This implies:
36x + 42y = 842 (1)
If 66 shirts and 77 jackets contain 137 buttons. This implies:
66x + 77y = 137 (2)
If you take the first equation: 36x + 42y = 842 and isolate the x, then you will have x = (842 - 42y) / 36
If you substitute x into the second equation:
66((842-42y)/36) + 77y = 137
→ 11(842-42y)/6 + 77y = 137
→ 11(842-42y) + 6(77y) = 137(6)
→ 9262 - 462y + 462y = 822
→ 9262 = 822 which reveals that the equations do not have a solution
Determine the equation of the hyperbola.
Answer:
A) x²/9 -y²/4 = 1
Step-by-step explanation:
The distance from center to one vertex is half the difference of the distances from a point to either focus. That is, the distance from center to the vertex is 3 on the x-axis, so the x-term is (x/3)² = x²/9.
In the picture, ...
... c² = a² + b²
The problem statement tells us c = √13, so we know c² = 13. Then ...
... b² = c² - a² = 13 -9 = 4
and the y-term is y²/4.
Thus, the equation is ...
... x²/9 - y²/4 = 1
_____
You knew that was the correct choice as soon as you knew the x-term.
Daryl earns $8 per hour working after school. He needs at least $352 for a stereo system. Write and solve an inequality to find the number of hours h Daryl must work to reach his goal.
Answer:
Step-by-step explanation:
First you need to divide by the amount he needs by the amount he gets, 352 divided by 8. That equals 44, so he will need to work 44 hours to reach his goal.
Dan paid $34.30 for a sweater the price included a 40% markup what is the cost of the sweater before the markup
Answer:
$24.5
Step-by-step explanation:
Let x be the cost of sweater before markup.
We are told that Dan paid $34.30 for a sweater the price included a 40% markup. This means x plus 40% of x equals 34.30.
We can represent this information as:
[tex]x+\frac{40}{100}x=34.30[/tex]
[tex]x+0.40x=34.30[/tex]
[tex]1.40x=34.30[/tex]
[tex]x=\frac{34.30}{1.40}[/tex]
[tex]x=24.5[/tex]
Therefore, the cost of sweater before the markup was $24.5.
The mean and standard deviation for number of robberies in the U.S. from 2000 to 2015 are x̄ = 354,718 and sx = 28,803. The mean and standard deviation for number of assaults in the U.S. for the same time period are ȳ = 774,140 and sy = 44,910. The correlation coefficient is r = 0.84. Find the equation for the least-squares regression line for number of assaults compared with number of robberies. ŷ = 309,552.15 + 1.31x ŷ = 1.31 + 309,552.15x ŷ = 546,641.84 + 0.64x ŷ = 0.64 + 546,641.84x Unable to determine the equation
Answer:
[tex]\hat{y}=309,552.15 + 1.31x[/tex]
Step-by-step explanation:
The equation for the least-squares regression is,
[tex]\hat{y}=a+bx[/tex]
where b is the slope and a is the intercept.
They can be found out by,
[tex]b=r\cdot \dfrac{SD_y}{SD_x},\\\\a=\overline{y}-b\overline{x}[/tex]
where,
r = correlation coefficient = 0.84
[tex]SD_y[/tex] = standard deviation of y = 44,910
[tex]SD_x[/tex] = standard deviation of x = 28,803
[tex]\overline{y}[/tex] = mean of y = 774,140
[tex]\overline{x}[/tex] = mean of x = 354,718
Putting the values,
[tex]b=0.84\cdot \dfrac{44910}{28803}=1.309\approx 1.31[/tex]
[tex]a=774140-(1.31\times 354718)\approx 309,552.15[/tex]
Therefore the equation is,
[tex]\hat{y}=309,552.15 + 1.31x[/tex]
An electric heater uses 3/5 watts power each hour. How man watts power will the heater use in a 1/2 hour
Answer: 3/10 watts
Step-by-step explanation:
3/5 converts to 6/10
6/10 / 2 = 3/10
Answer:
3/10
Step-by-step explanation:
3/5 converts to 6/10
6/10 / 2 = 3/10
What is the solution to the system of equations?
-3x-4y+z=-1
2x+y-z=-8
x+8y-z=23
A. (-3,4,6)
B. (4,-3,-1)
C. (-3,4,8)
D. (3,-4,-6)
Answer:
The answer is A (-3,4,6).
Step-by-step explanation:
1 Solve for z in -3x-4y+z=-1
z=3x-1+4y
2 Substitute z=3x-1+4y into 2x+y-z=-8
-x-3y+1=-8
3 Substitute z=3x-1+4y into x+8y-z=23
-2x+4y+1=23
4 Solve for x in -x-3y+1=-8
x=-3y+9
5 Substitute x=-3y+9 into z=3x-1+4y
z=-5y+26
6 Substitute x=-3y+9 into -2x+4y+1=23
10y-17=23
7 Solve for y in 10y-17=23
y=4
8 Substitute y=4 into z=-5y+26
z=6
9 Substitute y=4 into x=-3y+9
x=-3
10 Therefore,
x=-3
y=4
z=6
A rotation in the origin is shown. The angle of rotation appears to be A) 30°. B) 45°. C) 60°. D) 90°.
It looks like a 90º rotation
Answer:
90 egress
Step-by-step explanation: