Given,
Total distance [tex]=2\frac{1}{2}[/tex] miles
You run 1/3 of that distance on a hill.
Distance on a hill[tex]=\frac{1}{3} * 2\frac{1}{2}[/tex] miles
You run down a slope for the last 1/2 of the hill=[tex]\frac{1}{3} * 2\frac{1}{2}*\frac{1}{2}[/tex] miles[tex]=\frac{5}{12}[/tex] miles
Distance you run down the slope [tex]=\frac{5}{12}[/tex] miles
Write an equation in slope- intercept form for the line that passes through (-8,-7) and is perpendicular to the graph y= -x-8
Answer: y=-1/8x
Step-by-step explanation:
Choose a point that the perpendicular line will pass through.
(0,0)
Use the slope-intercept form to find the slope.
m=8
The equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.
perpendicular
m= −1/8
Find the equation of the perpendicular line using the point-slope formula.
y+0=−1/8⋅(x+0)
Write in
y=mx+b
form.
y=−1/8x
Hope this helps
Struggling with this… please help
B = 47°
a = 10.9
b = 11.7
How are the angles and sides of the right triangle calculated?
a) Finding B
We know that ,the sum of every angles of a triangle = 180°
So, B + 90° +43° = 180°
B+ 133° = 180°
B = 180° - 133°
=47°
b) Finding a
We know,
[tex]sin\theta =\frac{opposite}{hypotenuse} \\\\sin 43^{\circ} =\frac{a}{16} \\\\a= 16(sin 43^{\circ})\\\\a = 16 (0.681)\\\\a=10.9[/tex]
c) Finding b
We know,
[tex]cos\theta = \frac{adjacent}{hypotenuse} \\\\cos 43^{\circ} =\frac{b}{16} \\\\b = (cos 43^{\circ})16\\\\b= (0.731) 16\\\\b= 11.7[/tex]
What is a right triangle?
A triangle with a right angle or two perpendicular sides is referred to as a right triangle, right-angled triangle, or orthogonal triangle . Trigonometry's foundation is the relationship between the right triangle's sides and other angles. A right triangle's hypotenuse is always the side that faces away from the right angle. It is the right triangle's longest side. From a particular angle, the opposite side is across. The non-hypotenuse side next to a specific angle is referred to as the adjacent side.To learn more about right triangle, refer:
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|-7| and |7|
what does the | mean?
find the value of the variable
Answer:
Step-by-step explanation:
Set 3y+53 equal to 7y-55
3y+53=7y-55 //subtract 3y
53=4y-55 //add 55
108=4y //divide by 4
y=27
Of the sum of the 3rd and 4th term of an AP is -2 and it's 2nd term is 2. Find the common difference of the AP.
⇒Logically we know that to find the [tex]3^{rd}[/tex] term we use [tex]T_{3} =a+2d[/tex]
⇒From
[tex]T_{3} =a+(3-1)d\\T_{3}=a+2d[/tex]
⇒And the [tex]4^{th}[/tex] is equal [tex]T_{4} =a+3d[/tex] from the same method I used above from the general equation of finding the [tex]n^{th}[/tex] term.
⇒It is said the sum of [tex]T_{3}[/tex] and [tex]T_{4}[/tex] is -2 meaning
[tex]T_{3} +T_{4} =(a+2d)+(a+3d)\\-2=a+2d+a+3d\\-2=a+a+2d+3d\\-2=2a+5d[/tex]
⇒It is also said that [tex]T_{2}[/tex] is 2 and we know at this point that
[tex]T_{2} =a+d\\2=a+d[/tex]
⇒Then we can use the simultaneous equations technique to find the value of d.
I will use the substitution method by deriving the third equation from the second equation 2=a+d
a=2-d is the [tex]3^{rd}[/tex] equation that I will substitute in the equation
In the place of a it means I will plug in 2-d in the place of a.
[tex]-2=2a+5d\\-2=2(2-d)+5d\\-2=2(2)+2(-d)+5d\\-2=4-2d+5d\\-2-4=3d\\\\3d=-6\\\\[/tex]
[tex]\frac{3d}{3} =\frac{-6}{3} \\d=-2[/tex]
NOTE if you were also asked to find the value of a you can use the equations above to find the value of a which is the first term. the difference represented by letter d is -2.
GOODLUCK!!
Which equation represents a line that passes through the point (6,−3) and is parallel to the graph of y=3x+1? A y=3x−21 B y=3x+15 C y=−13x−1 D y=−13x+5
Answer:
Choice A
Step-by-step explanation:
The line we need to find has the same slope as the slope of the given line which is 3.
Which of the following are possible
side lengths for a triangle?
A. 18, 12, 6
B. 9, 15,4
C. 5, 18, 14
Answer:
C
Step-by-step explanation:
when u take the 2 shortest sides and add them up, they must be greater than the longest length.
. A bag of potato chips weighs 154 grams. How much does this bag weigh in ounces? 1oz = 28g
Answer:
5.5 oz
Step-by-step explanation:
154÷28
a manufacturer can produce 2970 cell phones when x dollars is spent on labor and y dollars is spent on capital. the equation that relates x and y is 55 x 3 4 y 1 4
The formula in terms of x and y for dy/dx is -3y/x
The value of dy/dx at the point (81,16) is -0.5926
The question is incomplete, the full question is given below:
A manufacturer can produce 2970 cell phones when x dollars is spent on labor and y dollars is spent on capital. the equation that relates x and y is [tex]55x^{\frac{3}{4} } y^{\frac{1}{4} } =2970[/tex]
a. Find a formula in terms of x and y for [tex]\frac{dy}{dx}[/tex]
b. Find the value of dy/dx at the point (81,16). Round your answer to 4 decimal places
Part a
A formula in terms of x and y for [tex]\frac{dy}{dx}[/tex]
We differentiate equation that relates x and y with respect to x by implicit differentiation:
=[tex]\frac{d}{dx} (55x^{\frac{3}{4} } y^{\frac{1}{4} } )=\frac{d}{dx} (2970)[/tex]
=[tex]55(x^{\frac{3}{4} } \frac{d}{dx} (y^{\frac{1}{4} } )+y^{\frac{1}{4} } ((x^{\frac{3}{4} } ))=0[/tex]
=[tex]x^{\frac{3}{4} } y^{\frac{-3}{4} } \frac{dy}{dx} =3y^{\frac{1}{4} } x^{\frac{-1}{4} }[/tex]
= [tex]\frac{dy}{dx} =\frac{-3y^{0.5}x^{-0.5} }{x^{0.75}y^{-0.75} }[/tex]
[tex]=\frac{-3y}{x}[/tex]
=-3y/x
Part b
Value of dy/dx at the point (81,16)
dy/dx at (81,16), x=81, y=16
dy/dx=-3y/x
dy/dx=-3*16/81
dy/dx=-48/81
dy/dx=-16/27
=-0.5926
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Please give me answer to this question!
Answer:
W
Step-by-step explanation:
9 + 7 = 16 and P is the 16th letter of the English Alphabet
4 + 1 = 5 and E is the 5th letter of the English Alphabet
15 + 8 = 23 and W is the 20th letter of the English Alphabet
PLEASE help ( What's the slope of a line that passes through points C (1,3) and B (4,7)
Answer:
slope = [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = C (1, 3 ) and (x₂, y₂ ) = B (4, 7 )
m = [tex]\frac{7-3}{4-1}[/tex] = [tex]\frac{4}{3}[/tex]
Question 7 Mai and Tyler are selling items to earn money for their elementary school. The school earns w dollars for every wreath sold and p dollars for every potted plant sold. Mai sells 14 wreaths and 3 potted plants and the school earns $70.50. Tyler sells 10 wreaths and 7 potted plants and the school earns $62.50. This situation is represented by this system of equations: { 14 w + 3 p = 70 . 50 10 w + 7 p = 62 . 50 Which statements are true in explaining why it makes sense that the solution of this system is also a solution to 4 w + ( − 4 p ) = 8 . 00 ? Select all that apply. (Lesson 2-15) Multiple select question. A) Because 10 w + 7 p is equal to 62.50, subtracting 10 w + 7 p from the left side of 14 w + 3 p = 70 . 50 and subtracting 62.50 from its right side keep the two sides equal. B) The equation 4 w + ( − 4 p ) = 8 . 00 is the result of adding the two equations in the system and then dividing the result by 6. C) The equation 4 w + ( − 4 p ) = 8 . 00 is the result of subtracting the second equation in the system from the first equation. D) The equation 4 w + ( − 4 p ) = 8 . 00 represents the difference between Mai's sales and Tyler's sales, or the result of subtracting Tyler's sales from Mai's. E) The left side of the equation 4 w + ( − 4 p ) = 8 . 00 shows the difference in terms of the items sold. The right side shows the difference in dollars. The cost per wreath, w, and the cost per potted plant, p, haven't changed.
Option (C) is correct which is the equation 4 w + ( − 4 p ) = 8 . 00 is the result of subtracting the second equation in the system from the first equation.
Mai and Tyler are selling items to earn money for their elementary school.
Mai sells 14 wreaths and 3 potted plants and the school earns $70.50. Mathematically we can write,
14 w + 3 p = 70.50 equation 1
Tyler sells 10 wreaths and 7 potted plants and the school earns $62.50. Mathematically we can write,
10 w + 7 p = 62.50 equation2
equation 1 - equation 2 , we get
4 w + ( - 4 p ) = 8.00
which is the required equation.
We can conclude that the equation 4 w + ( − 4 p ) = 8 . 00 is the result of subtracting the second equation in the system from the first equation
So, option (C) is correct.
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You decide to go to a basketball game. The tickets cost $37 each and you paid for you and your cousin to get in.
How much did 2 basketball tickets cost?
Answer:
$74.00
Step-by-step explanation:
Two tickets at $37 apiece, we cal calculate a total by adding 37 + 37,
OR by multiplying
2×37
Either way, the total works out to be $74
Solve: 2(7-4k) > 12 or 5 < 0.2(15k + 10)
The solution the inequality expression given as 2(7-4k) > 12 or 5 < 0.2(15k + 10) is 0.25 > k > -0.4
What are inequality expressions?Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal
How to solve the inequality expression?The inequality expression is given as
2(7-4k) > 12 or 5 < 0.2(15k + 10)
Open the brackets
So, we have
14 - 8k > 12 or 5 < 7.5k + 2
Collect the like terms
So, we have
- 8k > 12 - 14 or 5 - 2 < 7.5k
Evaluate the like terms
So, we have
- 8k > -2 or -3 < 7.5k
Divide both sides by the coefficient of k
So, we have
k < 0.25 or -0.4 < k
Rewrite as
0.25 > k or k > -0.4
Combine
0.25 > k > -0.4
Hence, the solution is 0.25 > k > -0.4
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Mamadou and Brianna work at a dry cleaners ironing shirts. Mamadou can iron 15 shirts per hour, and Brianna can iron 25 shirts per hour. Mamadou worked 2 more hours than Brianna and they ironed 230 shirts between them. Write a system of equations that could be used to determine the number of hours Mamadou worked and the number of hours Brianna worked. Define the variables that you use to write the system.
15x + 25 y = 230 and x - y = 2 is a system of equations that could be used to calculate the number of hours Mamadou worked and Brianna worked.
What exactly is an equation system?A system of equations is a collection of two or more equations that have the same variables. A solution to a system of equations is a set of variable values that satisfy all of the equations at the same time.Given:
Mamadou can iron 15 shirts in one hour, whereas Brianna can do 25. Mamadou put in two more hours of work than Brianna, and the two of them combined to iron 230 shirts.
Let y be the number of hours Brianna, works, and x be the number of hours Mamadou works.
In y hours, Brianna would iron 25y shirts.
In x hours, Mamadou would iron 15x shirts.
Combining total number of shirts,
15x + 25 y = 230
Since, Mamadou put in two more hours of work than Brianna.
x = y +2
x - y = 2
Therefore, for the number of hours Mamadou and Brianna worked, a system of equations 15x + 25 y = 230 and x - y = 2 could be utilised.
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Answer:
15x + 25 y = 230 and x - y = 2
Step-by-step explanation:
Decide whether each table could represent a proportional relationship what dose k =
Table A doesn't represent the constant of proportionality.
Table B doesn't represent the proportional relationship.
How to explain the constant?Treat the values in table as (x,y) values. The result is a linear function
For A, 85/5 = 17 while 79 / 10 = 7.9. This doesn't illustrate a constant.
For B, 1.49/16 and 1.59/20 have different values. In this case, 1.49/16 = 0.093 and 1.59/20 = 0.0795.
Therefore. they don't have a constant of proportionality. This was because the values that were gotten for both A and B aren't equal.
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Decide whether each table could represent a proportional relationship. If the relationship could be proportional, what would the constant of proportionality be?
1. How loud a sound is depending on how far away you are
5 85
10 79
20 73
40 67
b. The fountain drinks at hot dog hut.
16 1.49$
20 1.59$
30 1.89$
At one store Roberto bought 10 packages of batteries. Each package had 24 batteries. At another store, he bought 10 packages of batteries, but each package only had 15 batteries. How many batteries did Roberto buy in all?
Write the equation that is parallel to y = -3x + 7 and passes through the point (2, -1). Write your answer in slope intercept form.
y =
The equation that is parallel to y = -3x + 7 and passes through the point (2, -1) is y=-3x+5.
What is slope Intercept form?The slope intercept form in math is one of the forms used to calculate the equation of a straight line, given the slope of the line and intercept it forms with the y-axis.
y=mx+b
where m is the slope of the line and b is the y intercept.
The slope of the given equation,
y=-3x+7 is -3.
So, to write an equation parallel to the given equation and set of points, use point slope form and the slope of -3
y-y₁=m(x-x₁)
where (2,-1) are x₁, y₁
y-(-1)=-3(x-2)
y+1=-3(x-2)
Multiply with 3 on RHS side
y+1=-3x+6
We have to write in slope intercept form, so shift 1 to RHS.
y=-3x+6-1
y=-3x+5
As you can see, the slope of this line is -3
, which means that the two equations are parallel to each other.
Hence y=-3x+5 is the equation that is parallel to y = -3x + 7 and passes through the point (2, -1).
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Dilate a square with vertices $\left(0,\ 0\right)$(0, 0) , $\left(0,\ 4\right)$(0, 4) , $\left(4,\ 4\right)$(4, 4) , and $\left(4,\ 0\right)$(4, 0) using the scale factor $k=0.5$k=0.5 . What is the value of the ratio (new to original) of the perimeters? the areas?
The ratio (new to original) of the perimeters is equal to 1/2 or 0.5. Also, the ratio (new to original) of the areas is equal to 1/4 or 0.25.
How to determine the value of the ratio (new to original)?In Mathematics, the ratio of the perimeters of two (2) geometric figures would be equal to the scale factor when the two (2) geometric figures are similar;
Let z represent the scale factor.Let y represent the perimeter of the original square.Let x represent the perimeter of the new square.Mathematically, the scale factor of a geometric figure can be calculated by using this formula:
Scale factor, z = Dimension of image/Dimension of original figure = y/x
Scale factor, z = 1/2 or 0.5.
In Geometry, the ratio of the areas of two (2) geometric figures would be equal to the square of scale factor when the two (2) geometric figures are similar.
Scale factor, z = (y/x)²
Scale factor, z = (1/2)²
Scale factor, z = 1/4 or 0.25.
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Complete Question:
Dilate a square with vertices (0, 0). (0, 4). (4, 4), and (4, 0) using the scale factor k = 0.5. What is the value of the ratio (new to original) of the perimeters? the areas?
The ratio of the perimeters is
The ratio of the areas is
Write the equation of the ellipse that has its center at the origin with focus at (0,4) and vertex (0,7).
1) Notice that, in this case, the center is at (0,0) the focus at (0,4) and the Vertex is at (0,7)
2) Since the focus is at the y-axis, and the center is at the origin we can start from the following formula:
[tex]undefined[/tex]Lily solved the equation 3x − 10 = -3x + 8. The explanation of her process is shown. Select the text that shows an error in her process or justification of steps, if one exists. 1. I used the addition property of equality to achieve 6x − 10 = 8. 2. I used the addition property of equality to achieve 6x = 18. 3. I used the subtraction property of equality to achieve the solution of x = 3. There is no error in Lily’s process or justification of steps.
Answer: 3x - 10 = -3x + 8 Add 3x to both sides 6x - 10 = 8 Add 10 to both sides 6x = 18 Divide both sides by 6x = 3
Step-by-step explanation:
If sinØ=4/5 in quadrant ll, what is cosØ?
Answer: cosφ=-3/5
Step-by-step explanation:
[tex]\displaystyle\\sin\phi=\frac{4}{5} \ \ \ \ \ 90^0 < \phi < 180^0\\\\sin^2\phi+cos^2\phi=1\\\\\cos^2\phi=1-sin^2\phi\\\\cos^2\phi=1-(\frac{4}{5})^2\\\\ cos^2\phi=1-\frac{16}{25} \\\\cos^2\phi=\frac{1(25)-16}{25}\\\\ cos^2\phi=\frac{25-16}{25} \\\\cos^2\phi=\frac{9}{25} \\\\cos\phi=б\sqrt{\frac{9}{25} } \\\\cos\phi=б\sqrt{\frac{3^2}{5^2} }\\\\cos\phi=б\sqrt{(\frac{3}{5})^2} \\\\cos\phi=б\frac{3}{5} \\\\90^0 < \phi < 180^0\\\\Hence,\ \\\\cos\phi=-\frac{3}{5}[/tex]
does anyone know what to put on these boxes
Answer:
You should ask your teacher what the heck that means!
Step-by-step explanation:
But still, -7+10=3
which numbers are prime numbers
Answer:
1,3,5,7,17,23
Step-by-step explanation:
An engineer created a scale drawing of a building using a scale in which 0.25 inch represents 2 feet. The length of the actual building is 250 feet.
What is the length in inches of the building in the scale drawing?
help please
The length of the building in the scale drawing is; 31. 25 Inches
From the given, we have that Scale drawing was used 0. 25 inches represents 2 feet
The length of the building = 250 feet
Then, 0. 25 inches = 2 feet
Then, x inches = 250 feet
Now cross multiply
x × 2 = 0. 25 × 2500
Multiply through, we have;
2x = 62. 5
Make 'x' the subject by dividing both sides by 2
2x/2 = 62. 5/ 2
x = 31. 25 Inches
Thus, the length of the building in the scale drawing will be; 31. 25 Inches.
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y = x2 + 5x + 8 y = -x +3 Select the correct choice and fill in any answer boxes in your O A. The solution(s) is/are (Type an ordered pair. Use a comma to separate answe B. There is no solution.
To determine whether or not this system has a solution, we proceed as follows:
[tex]-x+3=x^2+5x+8\Rightarrow x^2+6x+5=0[/tex]Now, we use the quadratic function to solve, that is:
[tex]x=\frac{-(6)\pm\sqrt[]{6^2-4(1)(5)}}{2(1)}\Rightarrow\begin{cases}x=-1 \\ x=-5\end{cases}[/tex]From this, we have that the system has two solutions, we determine which replacing x in one of the functions, that is:
[tex]y_1=-(-1)+3\Rightarrow y_1=4[/tex]One solution is the point (-1, 4).
[tex]y_2=-(-5)+3\Rightarrow y_2=8[/tex]And, another solution is the point (-5, 8).
We can see each solution in the following graph:
The number of people who like a particular video online triples every day after the day the video is posted. If 15 people like the video on the day it is posted, which inequality can be used to find the number of days, t, it takes for the number of people who have liked the video to reach more than 3,000?
The inequality for the expression will be represented by n > 5.
The parameters present shows a geometric sequence. A Geometric sequence is the one in which the ratio between the consecutive terms remains constant. The constant ratio is called common ratio. The nth term of geometric sequence is represented by Tₙ = arⁿ⁻¹ where n is the number of terms, r is common ratio and a is the first term. Here, a = 15 and r = 3. Now, for the people to be more than 3000 the inequality can be written as
arⁿ⁻¹ > 3000
15 (3)ⁿ⁻¹ > 3000
3ⁿ⁻¹ > 200
Taking log on both sides
log 3ⁿ⁻¹ > log 200
(n - 1) > log 200/log 3
n - 1 > 4.82
n > 5.82
Rounding off we get
n > 5 which is required inequality.
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Now, let’s say the children sold 50 cups of lemonade on the first day and 90 cups on the second day. Which proportion can be used to calculate the percent increase in the number of lemonade cups sold?
If the children sold 50 cups of lemonade one the first day and 90 cups on the second day. then the percentage increase in the number of lemonade cups sold 80%
The number of cups of lemonade sold on first day = 50 cups
The number of cups of lemonade sold on second day = 90 cups
The percentage increase = (New value - Old value)/Old value × 100
Substitute the values in the equation
The percentage increase in the number of lemonade cups sold
= [tex]\frac{90-50}{50}[/tex]×100
= 0.8×100
= 80%
Hence, if the children sold 50 cups of lemonade one the first day and 90 cups on the second day. then the percentage increase in the number of lemonade cups sold 80%
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Answer:
90-50/50 = P/100
Step-by-step explanation:
This is the correct answer on T4L!
highest common factor of 350 and 150
Answer: 50
Step-by-step explanation: Common factor of 150 and 350 = 1, 2, 5, 5. Highest common factor of 150 and 350 = 2 × 5 × 5 = 50.
Use the point-slope form of a linear equation to write the
equation of the line.
Slope = 3 through (-4,-7)
Answer:
y +7 = 3(x +4)
Step-by-step explanation:
You want the point-slope equation of the line with slope 3 through point (-4, -7).
Point-slope equationThe point-slope equation of a line with slope m through point (h, k) is ...
y -k = m(x -h)
ApplicationFor m=3 and (h, k) = (-4, -7), this is ...
y -(-7) = 3(x -(-4)) . . . . . substitute for m, h, k
y +7 = 3(x +4)