Answer:
3√10 units
Step-by-step explanation:
[tex] \sqrt{250} = \sqrt{25 \times 10} = \sqrt{25} \sqrt{10} = 5 \sqrt{10} [/tex]
[tex]3x + 2x = 5 \sqrt{10} [/tex]
[tex]5x = 5 \sqrt{10} [/tex]
[tex]x = \sqrt{10} [/tex]
So the length of the longer piece is 3√10 units.
Jordan i working two ummer job, making $13 per hour lifeguarding and $10 per hour walking dog. Lat week Jordan earned a total of $177 and worked 3 more hour lifeguarding than hour walking dog. Determine the number of hour Jordan worked lifeguarding lat week and the number of hour he worked walking dog lat week
Jordan worked 9 hours as lifeguarding
Jordan worked 6 hours walking dog
given that
Jordan making $13 per hour lifeguarding and $10 per hour walking the dog
last week Jordan earned a total of $177
let x be the number of hours she worked walking the dog
let y be the number of hours she worked as a lifeguard
13y+10x=177 -------- (1)
worked 3 more hour lifeguarding than an hour walking dog
y = 3 + x --------(2)
substitute equation 2 in 1
13(3+x) +10x =177
39+13x+10x = 177
39 + 23x = 177
23x = 177 -39
23x = 138
x = 138/23
x = 6
now substitute x=6 in equation 2
y = 3 + 6
y = 9
9 number of hours he worked lifeguarding last week
6 number of hours he worked walking dog last week
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The graph f (x) = x is shifted down 6 and to the right 3 and reflected over the x-axis. Which of the following is the function of the resulting transformation?
The function of the resulting transformation is f(x) = -x - 3 + 6.
Given:
The graph f (x) = x is shifted down 6 and to the right 3 and reflected over the x-axis.
The first transformation:
shifted down 6 units
f(x) = x - 6
second transformation:
x = x + 3.
f(x) = x + 3 - 6
Third transformation:
reflected over the x-axis.
f(x) = -1(x+3-6)
f(x) = -x - 3 + 6.
Therefore the function of the resulting transformation is f(x) = -x - 3 + 6.
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Write the equation of the function in point-slope form.
A line with a slope of 2 and passes through (5,-2)
Emmy bought 53.6 ounces of cat food and 4.7 ounces of dog food. How much pet food did
she buy in all?
Answer:
Step-by-step explanation:
53.6 oz + 4.7 oz
= 58.3 oz in total
Answer:
58.3 ounces
Step-by-step explanation:
53.6 + 4.7 = 58.3
In many countries, cigarette smoking has decreased in the 21st century. The percentage of smokers in Russia can be represented by the equation 36x+100y=346, where y is the percentage of adults who smoke and x is the number of years since 2000. The percentage of smokers in Poland can be represented by the equation 18x+50y=176, where y is the percentage of adults who smoke and x is the number of years since 2000. Determine the solution to the system
The system of equation does not have a solution.
How to solve system of equation?The percentage of smokers in Russia can be represented by the equation 36x+100y=346, where y is the percentage of adults who smoke and x is the number of years since 2000.
The percentage of smokers in Poland can be represented by the equation 18x+50y=176, where y is the percentage of adults who smoke and x is the number of years since 2000.
Let's combine the equation and find the solution.
36x + 100y = 346
18x + 50y = 176
multiply equation(ii) by 2
36x + 100y = 346
36x + 100y = 352
0 = 6
Therefore, the system has no solution.
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147+294+441+575+632+879+1,026
There are 1200 elephants in a herd. Some have pink and green stripes, some are all pink and some are all blue. One third are pure pink. Is it true that 400 elephants are definitely blue? yes no.
It is true that 400 elephants are blue in color. This happens because number of elephants remaining is twice 400.
Given that,
Total number of elephant = 1200
Strips colors available are: Pure Pink
Pure blue
Pink and Green
Pure Pink = 1/3 of 1200
= 1/3 × 1200
= 400
Rest elephant who are definitely blue:
Remaining elephant = Total number of elephant - Pure Pink
= 1200 - 400
= 800
∴ It is true that 400 elephants are blue because the number of elephants remaining twice 400.
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a teacher is teaching two ap statistics classes. on the final exam, the 20 students in the first class averaged 92 while the 25 students in the second class averaged 83. if the teacher combines the classes, what will the average final exam score be?
Answer:
220
Step-by-step explanation:
hope it helps
The required when two classes are combined, the average final exam score is approximately 87.
Number of students in the first class = 20
The average score of the first class = 92
Number of students in the second class = 25
The average score of the second class = 83
Calculate the total number of students:
Total number of students = Number of students in the first class + Number of students in the second class
Total number of students = 20 + 25 = 45
Calculate the total score for both classes:
Total score for the first class = Number of students in the first class * Average score of the first class
Total score for the first class = 20 * 92 = 1840
Total score for the second class = Number of students in the second class * Average score of the second class
Total score for the second class = 25 * 83 = 2075
Calculate the combined total score:
Combined total score = Total score for the first class + Total score for the second class
Combined total score = 1840 + 2075 = 3915
Calculate the average final exam score when the two classes are combined:
Average final exam score = Combined total score / Total number of students
Average final exam score = 3915 / 45
Average final exam score = 87
Therefore, when the two classes are combined, the average final exam score is approximately 87.
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taylor wants to buy a bicycle that cost $48.75 she works for her mom after school to earn money if taylor is payed $4.50 per hour will she be able to buy the bicycle after working 9 hours
Answer:
No, here's why...
Step-by-step explanation:
Multiply 9 by 4.50
you get $40.50
40.50<48.75
she will not be able to but the bicycle
Find the slope (6,-10),(-15,15)
Answer:
-25/21
Step-by-step explanation:
Slope Formula:
m=(y1-y2)/(x1-x2) where m is the slope
m=(-10 - 15)/(6 - (-15))
m=(-(10+15)/(6+15))
m=-25/21
5. Write the equation of the line shown.
Y=________
Answer:
y = ⅓ x
Step-by-Step Explanation:
When y = 1 x = 3 which means y is always ⅓ of x.
The Johnstown Inclined Plane in Pennsylvania is one of the longest and steepest hoists in the world. The railway cars travel a distance of 896.5 feet at an angle of approximately 35.4 degrees, rising to a height of 1693.5 feet above sea level. (Round your answers to two decimal places.)
(a) Find the vertical rise of the inclined plane: 519.33 ft
(b) Find the elevation of the lower end of the inclines plane: _____ ft
(c) The cars move up the mountain at a rate of 300 feet per minute. Find the rate at which they rise vertically: 173.78 ft/min
a. Vertical rise of the inclined plane= 519.35 ft
b. Elevation of the lower end of the inclined plane=1174.15 ft
c. The rate at which they rise vertically is 173.78 ft/min
What is unit rate?
A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.
a. Since the length of the incline = 896.54 ft, and the angle of the incline = 35.4°. Let h be the vertical rise of the incline. From trigonometric identities,
sin35.4° = h/896.54 ⇒ h = 896.54sin35.4° = 519.35 ft
b. Since the top of the incline is 1693,5 ft above sea level, and the vertical height of the incline is 519.35 ft, the elevation of the lower end of the inclined plane is 1693.5ft - 519.35ft = 1174.15 ft
c. The cars move up the mountain at a rate of 300 ft/min along the inclined plane. The rate at which they rise vertically is the vertical component of the velocity = 300sin35.4° ft/min = 173.78 ft/min
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Find the slope of the line \mathrm{y}=5\mathrm{x}+4y=5x+4.
The slope of the line y = 5x + 4 is 5.
Slope i.e. m = 5.
Given, a line of equation
y = 5x + 4
We have to find the slope of the given line,
Now, as we know the slope-intercept form of a line i.e.
y = mx + c
where, m is the slope of the line and c is the y-intercept of the line.
So, using the same form in the line, we get
y = 5x + 4
the slope of the line is 5.
Hence, the slope of the line y = 5x + 4 is 5.
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Given f(x) = 3x + 5, describe how the graph of g compares with the graph of f. g(x) = 3(0.1x) + 5
The following data is gotten from comparing the graph of f(x) = 3x + 5 to graph of g(x) = 3(0.1x) + 5
Both has y intercept of 5
g(x) is a vertical compression of f(x) by a factor of 0.1
How to make the comparisonThe graph of the both linear equation is plotted and attached
solving for y intercept by substituting x = 0 into f(x) = 3x + 5 shows that
f(x) = 5
solving for y intercept by substituting x = 0 into g(x) = 3(0.1x) + 5 shows that
g(x) = 5
examining the both equations, it can show that the slope of f(x) is multiplied by a factor 0.1 this results to vertical shrink
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i really need help with
Find equivalent expressions for 2y + 7 - 5y + 6y - 3 + y
Answer:
4y + 4
Step-by-step explanation:
Place similar together: 2y - 5y + 6y + 1y + 7 -3
Solve: (2-5+6+1)y + 4
4y + 4
Kate is comparing the cost of a fresh lobster dinner at two different restaurants. The first restaurant charges $27 for the meal, plus $3 per pound for the lobster she picks. At the second restaurant, Kate would pay $4 per pound for the lobster, in addition to $25 for the meal. Kate realizes that, in theory, dinner at both restaurants could cost the same amount if the lobster had a certain weight. How much would Kate pay for her dinner? What is the weight?
1) Based on a system of equations, the amount Kate would pay for her dinner at either of the two different restaurants is $33.
2) Based on the same system of equations, the weight of the lobster is 2 pounds.
What is a system of equations?A system of equations indicates two or more equations solved concurrently, at the same time, or simultaneously.
A system of equations is also described as simultaneous equations.
First Restaurant Second Restaurant
Meal charge $27 $25
Lobster per pound $3 $4
Let the weight of the lobster per pound = x
Expressions:The total cost of Kate's dinner at the first restaurant = 27 + 3x
The total cost of Kate's dinner at the second restaurant = 25 + 4x
Equated Expressions:27 + 3x = 25 + 4x
2 = x
Total Costs:First Restaurant = 27 + 3x
= 27 + 3(2)
= $33
Second Restaurant = 25 + 4x
= 25 + 4(2)
= $33
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Express 25p as a percentage of £2
Answer:
0.5
Step-by-step explanation:
If 50% of £2 is £1
and 25% of £1 is 25p
we can workout that 25% of £2 is 0.5
Susan Asked her father for a no-interest loan of $8,000 so she could purchase a used car. She told her father that she would repay the loan at a rate of $250 per month.
The amount remaining on her after one year is $5000 .
In the question ,
it is given that ,
amount taken by Susan from her father = $8000 ,
interest rate charged by Susan father = 0%
amount that Susan will repay her loan per month = $250 .
So , the amount that Susan will repay in 12 months = 12×250
= $3000
So , in 1 year Susan will pay $3000 ,
the amount of loan remaining after 1 year = (loan amount) - (amount paid in 1 year)
the amount of loan remaining after 1 year = 8000 - 3000
= $5000
Therefore , The amount remaining on her after one year is $5000 .
The given question is incomplete , the complete question is
Susan Asked her father for a no-interest loan of $8,000 so she could purchase a used car. She told her father that she would repay the loan at a rate of $250 per month . How much will be remaining on her loan after one year ?
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what direction does this parabola open? (x-4)2=-15(y+18)
The parabola with the equation (x-4)²=-15(y+18) opens downwards.
The equation of the parabola is (x-4)²=-15(y+18)
From the equation we can infer that the parabola has the vertex at (4,-18) and the axis of symmetry is the line x = 4 .
(x-4)²=-15(y+18)
or, x² -8x + 16 = -15y -270
or, 15y = -x² + 8x - 286
The equation is of the general form : y = ax² + bx + c therefore the parabola will have two x values for every y value. So either the parabola will open upwards or downwards.
Now the general form of the parabola we find that the coefficient of the highest power of x is -1 (negative value)
Therefore the graph of the parabola opens downwards as illustrated by the graph of the parabola attached below.
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The set of data in the table below represents a linear function
X
6
-4
-2
y
-7--
--5---
-3/-/-
Which is an equation for this function?
The equation of the function is y = x - [tex]1\frac{1}{3}[/tex]
The first point = (-6, [tex]-7\frac{1}{3}[/tex])
The second point = (-4, [tex]-5\frac{1}{3}[/tex])
Convert the mixed fraction to the simple fraction
The first point = (-6, -22/3)
The second point = (-4, -16/3)
The slope of the line is the change in y coordinates with respect to the change in x coordinates of the line
The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= (-16/3 - (-22/3) / (-4 - (-6)
= 2 / 2
= 1
The point slope form is
[tex]y-y_1=m(x-x_1)[/tex]
y - (-22/3) = 1(x - (-6))
y + 22/3 = x + 6
y = x+ 6 - 22/3
y = x+ -4/3
y = x - 4/3
Convert the simple fraction to mixed fraction
y = x - [tex]1\frac{1}{3}[/tex]
Hence, the equation of the function is y = x - [tex]1\frac{1}{3}[/tex]
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find the value of w. round to the nearest tenth
Answer:
[tex]\pmb {w=13.11}[/tex]Step-by-step explanation:
[tex]\pmb {sin(22)^o=\cfrac{x}{35} }[/tex]
[tex]\pmb {35sin(22)=w}[/tex]
[tex]\pmb {w=13.11}[/tex]
_________________
Hope this helps!
Have a great day! :)
Tony is opening a pizza restaurant and needs to determine the amounts of ingredients he will use in his pizzas. He wants the amount of dough for a medium pizza to be times the amount of dough for a small pizza. And, he wants the amount of dough for a large pizza to be 3/2 times the amount of dough for a small pizza. Also, the amount of dough used for one large pizza should be 5/2 equal to the amount of dough used for one medium and one small pizza. So, he needs to determine how much dough to use for a small pizza. Use this information to complete the following tasks.
Now, use opposite operations on the equation from part B to move one of the terms so they are both on the same side of the equal sign.
Please it worth 43 points
The equation that represents this situation while the variable s representing the amount of dough needed , for a small pizza is (5/2)S = (3/2)S + S .
In the question ,
it is given that
amount of dough for a medium pizza is 3/2 times the amount of dough for small pizza ,
let the amount of dough required for small pizza = S
let the amount of dough required for large pizza = L
let the amount of dough required for medium pizza = M
So , M [tex]=[/tex] (3/2)S
and amount of dough for a large pizza is 5/2 times the amount of dough for small pizza ,
that is
L [tex]=[/tex] (5/2)S
amount of dough used for one large pizza is equal to the amount of dough used for one medium and one small pizza ,
that is L [tex]=[/tex] M [tex]+[/tex] S .
Substituting the value of L and S , we get
(5/2)S [tex]=[/tex] (3/2)S + S
We have a linear equation that is true for all S , there is no unique solution to this equation .
Therefore , The equation that represents this situation is (5/2)S = (3/2)S + S .
The given question is incomplete , the complete question is
Tony is opening a pizza restaurant and needs to determine the amounts of ingredients he will use in his pizzas. He wants the amount of dough for a medium pizza to be 3/2 times the amount of dough for a small pizza. And, he wants the amount of dough for a large pizza to be 5/2 times the amount of dough for a small pizza. Also, the amount of dough used for one large pizza should to be equal to the amount of dough used for one medium and one small pizza. So, he needs to determine how much dough to use for a small pizza. Use this information to complete the following tasks.
Write an equation to represent this situation while the variable s representing the amount of dough needed , for a small pizza .
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Q5.
The diagram shows a rectangle.
B=(x + 4) cm
H=(x-5) cm
The area of the rectangle is 90 cm².
Set up and solve a quadratic equation to work out the value of x.
Answer:
x = 11
Step-by-step explanation:
According to the question:
Base of the rectangle = (x + 4) cm
Height of the rectangle = (x - 5) cm
Area of the rectangle = 90 cm²
Area of rectangle = Height of the rectangle × Base of the rectangle
[tex] \therefore[/tex]
[tex] \rm \implies 90 = (x + 4)(x - 5) \\ \\ \rm \implies 90 = {x}^{2} - x - 20 \\ \\ \rm \implies {x}^{2} - x = 90 + 20 \\ \\ \rm \implies {x}^{2} - x = 110 \\ \\ \rm \implies {x}^{2} - x - 110 = 0 \\ \\ \rm \implies {x}^{2} - 11x + 10x - 110 = 0 \\ \\ \rm \implies x(x - 11) + 10(x - 11) = 0 \\ \\ \rm \implies (x - 11)(x + 10) = 0 \\ \\ \rm \implies x - 11 = 0 \: \: and \: \: x + 10 = 0 \\ \\ \rm \implies x = 11 \: or \: - 10[/tex]
As value of length cannot be negative.
Therefore, value of x should be 11
if the probability that the islanders will beat the rangers in a game is 0.62 what is the probability that the islanders will win exactly one out of three games in a series against the rangers?
Answer : The chance that the Islanders will win n games out of 6 is:
0.47 ^ n + (1 - 0.47) ^ (6 - n) * 6! / n! / (6 - n!)So, the chance of winning 4 games is 0.205605
the chance of winning 5 games is 0.072932
the chance of winning all 6 games is 0.010779
Adding these together we get 0.289316
Rounding to the nearest thousandth we get 0.289 (or 28.9%)891 viewsRelated questions (More answers below)
Step-by-step explanation:
Y+6=7(c-4) in slop intercept form
y = 7c - 34 is slop intercept form of equation .
What is an explanation of the slope-intercept form?
A line's equation can be written in the slope-intercept form such that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are instantly visible. This form is frequently known as the y = mx + b form. A line has the equation 3x + 4y + 5 = 0. The slope intercept form can be used to calculate the line's slope and y-intercept.slop intercept form of equation
y = mx + c
Y+6=7(c-4)
y + 6 = 7c - 28
y = 7c - 28 - 6
y = 7c - 34
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how to solve percent change and percent error problem
The way to calculate the percentage change will be:
Step 1: Take one value and subtract it from another.
Step 2: Subtract the error from the exact or ideal value (not your experimental or measured value). This will result in a decimal number.
Step 3: Multiply the decimal number by 100 to get the percentage.
Step 4: To report your percent error value, use the percent or % symbol.
What is percentage error?The difference between an approximate or measured value and an exact or known value is expressed as a percentage in percent error.
It is a scientific term that describes the difference between a measured or experimental value and a true or exact value.
It's important to divide the new value by the old value to get the percentage change.
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Question 1 (1 point)
Which pair of equations represents lines that are perpendicular
y = 2x+8
y = 2x + 2
Y = 1/2x +4
y = -2x -3
Y = 1/2x + 3
y = 2x -4
Answer:
it would be 69 bhejejejirirooddsskkskskakakakzkzjajbhshdhdjdjeiejeie
Write your answer as a fraction in simplest form
Answer:
-147/100 or mixed number -1 47/100
Step-by-step explanation:
Answer:
-1 47/100 or -147/100
Step-by-step explanation:
Simplify the top which gives you -21/10 and change the sign of -9/14 to a positive and then remove parentheses. Calculate the bottom fractions which is 10/7. Rewrite the fraction then simplify to -147/100
The position of the squirrel can be calculated using the function p (t) = at² + bt + c.
What is the value of a?
What is the value of b?
What is the value of c?
The value of a is 5/19
The value of b is -160/19
The value of c is 960/19
Given,
The quadratic function formula;
p(t) = at² + bt + c
We have to interpret quadratic graphs;
Thus, the equation is now;
p(t) = at² + bt + 0
p(t) = at² + bt
From the graph, we see that when x = 8, y = 0. Thus;
p(8) = a(8²) + 8b + c = 0
64a + 8b + c = 0 ------(1)
From the graph, we know that the axis of symmetry is;
x = -b/2a
Thus;
16 = -b/2a
b = -32a -----(2)
From the graph, we see that when x = 5, y = 15. Thus;
p(8) = a(5²) + 5b + c = 0
25a + 5b + c = 15 ------(3)
Put -32a for b in eq 1 and 3 to get;
64a + 8(-32a) + c = 0
-192a + c = 0 ------(4)
25a + 5(-32a) + c = 15
-135a + c = 15 ------(5)
Subtract eq 4 from eq 5 to get;
192a - 135a = 15
57a = 15
a = 15/57
a = 5/19
Thus;
b = -32(5/19) = -160/19
-135(5/19) + c = 15
15 + (675/19) = c
c = 960/19
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