Given:
Scott can run 20 km in 85 minutes.
To find:
How long will it take Scott to run 52 km?
Solution:
Let us consider x be the number of minutes it will take him to run 52 km.
We know that,
[tex]Speed=\dfrac{Distance}{Time}[/tex]
By using this formula, we get
[tex]Speed=\dfrac{20}{85}[/tex] ...(i)
[tex]Speed=\dfrac{52}{x}[/tex] ...(ii)
On equating (i) and (ii), we get
[tex]\dfrac{20}{85}=\dfrac{52}{x}[/tex]
[tex]20\times x=52\times 85[/tex]
[tex]20x=4420[/tex]
On dividing both sides by 20, we get
[tex]x=\dfrac{4420}{20}[/tex]
[tex]x=221[/tex]
Hence, it will take 221 minutes to run 52 km.
Which angle would be complementary to
The base of an open rectangular box is of length (2x + 5) cm and width x cm.
The area of this base is 58 cm
The height of the open box is (x - 2) cm.
a) Show that 2x + 5x -58 = 0
) Solve the equation 2x + 5x -58 = 0, giving your answers correct
to 2 decimal places
D) Hence calculate the volume of the box, stating the units of your answer.
Answer:
a) x = 8.29 cm
D) V = 1125.27 cm³
Step-by-step explanation:
a) We can solve the equation as follows:
[tex] 2x + 5x - 58 = 0 [/tex]
[tex] 2x + 5x = 58 [/tex]
[tex] x = \frac{58}{7} = 8.29 [/tex]
D) The volume of the box is given by:
[tex] V = l*w*h [/tex]
Where:
l: is the length
w: is the width
h: is the height
The length of the rectangular box is:
[tex] l = (2x + 5) cm = (2*8.29 + 5) cm = 21.58 cm [/tex]
The width is x = 8.29 cm.
And the height is:
[tex] h = (x - 2) cm = (8.29 - 2) cm = 6.29 cm [/tex]
Hence, the volume is:
[tex] V = l*w*h = (21.58*8.29*6.29) cm^{3} = 1125.27 cm^{3} [/tex]
I hope it helps you!
Which region represents the solution to the given system of inequalities?
{y < -1/2x }
[y ≥ 2x+3 }
A
B
C
D
The region D represents the solution of the given system of inequalities.
What is the system of linear inequalities?
A system of linear inequalities is a collection of linear inequalities in the same variables.
How to shade the graph of inequalities?Rearrange the equations so "y" is on the left and everything else on the right. Plot the "y≤ ,y≥ ,y> or y< " line.Shade above the line for a " greater then" and below for the "less than".According to the given equation.
We have system of inequalities.
[tex]y < \frac{-1}{2}x[/tex]
and [tex]y \geq 2x + 3[/tex]
Also, the graph of the inequalities.
Since, y is less than [tex]-\frac{1}{2} x[/tex] shade below the line.
And, for the second inequality.
y is greater than and equal to 2x + 3 therefore, shade the above the line.
So, the common region D we get after the shading.
Hence, region D represents the solution of the given system of inequalities.
Find out more information about system of inequalities:
https://brainly.com/question/19526736
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2/3 of a class are girls.
a) What is the ratio girls to boys in the class?
b) What is the ratio boys to girls in the class?
given f(x)=2/5(6-x)^2 what is the value of f(6)?
Answer:
0
Step-by-step explanation:
f(x) = 2/5(6 - x)²
f(6) = 2/5[6 - (6)]²
f(6) = 2/5(0)²
f(6) = 0
Can someone help me?It's urgent and thank you!
Answer:
x = 9
Step-by-step explanation:
square each side first to get:
8x - 8 = 64
8x = 72
x = 9
Jasmine used the number line to find the distance between 0 and 5. What was Jasmine’s error? Jasmine should have counted from 5 to 0. Jasmine started with the wrong integer. Jasmine gave a negative answer for distance. Jasmine ended with the wrong integer.
Answer:
The answer is "Option C".
Step-by-step explanation:
In this question, the distance value is -5 that's why option c is correct.
Answer:
C. Jasmine gave a negative answer for distance.
Use the explicit formula an = a1 + (n-1)•d to find the 500th term of the sequence below.
24, 31, 38, 45, 52, ...
Step-by-step explanation:
the answer is in the image above
Answer:
a₅₀₀ = 3517
Step-by-step explanation:
a₁ represents the first term and d the common difference
Here a₁ = 24 and d = 31 - 24 = 7 , then
a₅₀₀ = 24 + (499 × 7) = 24 + 3493 = 3517
Miguel made $286 for 13 hours of work.
At the same rate, how much would he make for 7 hours of work?
Answer:
Step-by-step explanation:
The key here is to find out how much he makes per hour. We can find that out using the info given.
286 = 13x so
x = 22 dollars per hour. For 7 hours of work then,
7(22) = $154
Find the equation of the line passing
through the points (2, 4) and (3,2).
Answer:
y=-2x+8
Step-by-step explanation:
first is to find the slope
m=(y2-y1) /(x2-x1)= (2-4)/(3-2)=-2/1= -2
now using the line formula of y=m*x+b, put in one of the points and solve for b.
2= -2*3 + b
2= -6 + b
8 = b
so y= -2*x+8
When x = 1 and y = –2, z =
Answer:
No solution is possible from the information provided
Step-by-step explanation:
Please help us help you by including enough information to answer your question.
Answer:
z = -10
Step-by-step explanation:
trust me
what is 69/2 as a mixed number
Answer:
I think it's 34
Step-by-step explanation:
69/2 = 34.5 = 34
Type the correct answer in the box.
Consider the table below.
х у
-3 0.5
-2
1
-1 2.5
0
5
18.5
Complete the standard form equation representing the quadratic relationship displayed above, where a, b, and care constants.
Answer:
Step-by-step explanation:
Use the standard form equation along with 3 of the coordinates from the table. I used (-1, 2.5), (0, 5), and (1, 8.5). Begin always with the coordinate where you have a 0:
[tex]5=a(0)^2+b(0)+c[/tex] and we get immediately that c = 5. We can use that value as move forward with the next coordinate pair.
[tex]8.5=a(1)^2+b(1)+5[/tex] and
8.5 = a + b + 5 and
3.5 = a + b Hold that thought while we come up with the second equation for this system.
[tex]2.5=a(-1)^2+b(-1)+5[/tex] and
2.5 = a - b + 5 and
-2.5 = a - b Now solve this system using the method of eliination:
a + b = 3.5
+ a - b = -2.5
so
2a = 1 and a = 1/2 Now we can plug that in and solve for b:
a + b = 3.5 becomes
1/2 + b = 3.5 so
b = 3 and the equation is
[tex]y=\frac{1}{2}x^2+3x+5[/tex]
He average price of a home in a neighborhood of mostly leased properties is $259,000. The average monthly rent is $2,500. One home in the neighborhood is leased for $2,800. Using a GRM, what is the value of that home?
Answer:
$290,080
Step-by-step explanation:
Given:
Average price = 259,000
Average monthly rent = 2500
Monthly rent of home = $2800
Gross Rent Multiplier = price per monthly rent
GRM = Price / monthly rent
The GRM = 259000 ÷ 2500
= $103.60
The price = GRM * Monthly rent
Price = $103.60 * $2800
Price = $290,080
Write an equation of a line through the point (2, -1) parallel to y = 4x - 3.
Answer:
y = 4x - 9
Step-by-step explanation:
y = 4x + b
-1 = 4(2) + b
-1 = 8 + b
-9 = b
due today pls helppppp
====================================================
Work Shown:
tan(angle) = opposite/adjacent
tan(C) = AB/BC
tan(theta) = x/BC
tan(23) = (8.1)/BC
BC*tan(23) = 8.1
BC = (8.1)/tan(23)
BC = 19.0824041631723
BC = 19.1
In this case, rounding to 3 sig figs means we round to the nearest tenth.
Make sure your calculator is in degree mode.
Una empresa fabrica protectores faciales, según los estudios de mercado que se han hecho, se ha de vender a S/.9 la unidad. La empresa tiene unos gastos fijos mensuales de local y personal de S/.9000, y además, fabricar cada unidad protector facial cuesta S/. 3. ¿Cuántas unidades ha de vender mensualmente si no quiere tener pérdidas?
Answer:
The number of units sell is 2.
Step-by-step explanation:
selling cost of one unit = $ 0.9
Monthly expense = $ 0.9
Manufacturing cost = $ 0.3
Let the number of unit sell is x.
So,
0.9 x = 0.9 + 0.3 x
0.6 x = 0.9
x = 1.5
So, the number of units sell to get no loss is 2.
If a ⋆ b = ab² - a²b, then 2 ⋆ 3 = i don't kno the answer
Hello,
We know that :
a * b = ab² - a²b
We know that : 2 * 3 = 6 but we want to try this formula.
We have :
a = 2 and b = 3
So :
2 * 3
= 2 * 3² - 2² * 3
= 2 * 9 - 4 * 3
= 18 - 12
= 6
It works :)
Solve the system of equations:
(1) x - y = 3
(2) 7x - y = -3
Answer:
x= 70
and y = 67 then
-70-67 =-3
Answer:
x=-1 y=-4
Step-by-step explanation:
answer is in the photo above
5x+y=1
10x-6=34
pleasee
Answer:
=>x=4
therefore y= -19
Answer:
x = 4, y = - 19
Step-by-step explanation:
Given the 2 equations
5x + y = 1 → (1)
10x - 6 = 34 → (2) , which can be solved as
10x = 40 ( divide both sides by 10 )
x = 4
Substitute x = 4 into (1) and solve for y
5(4) + y = 1
20 + y = 1 ( subtract 20 from both sides )
y = - 19
Complete the sentence:
The intersection of a circle and a triangle can be
A. Six Points
B. Twelve Points
C. Eight Points
D. Circle
Answer:
A. Six Points
Step-by-step explanation:
lines that intersect and form four right angles are called?
Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect. Perpendicular lines are lines that intersect at a right (90 degrees) angle.
there are 105 teachers in a school 19 more are femal than male how what is the proprtion of female teachers
NEED HELP; A group of friends goes out to dinner. The total bill, without tax, is $63. If tax on the meal is 6% and if an 18% tip is left on the $63 total bill, what is the total amount paid?
A. $78.12
B. $78.80
C. $66.78
D. $74.34
4days : 2 weeks simplify
Answer:
2:7
Step-by-step explanation:
ratio as a fraction in simplest form. 2 weeks = 14 days, so 4/14 = 2/7.
Answer:
2 : 7
Step-by-step explanation:
7 days = 1 week
y days = 2 weeks
[tex]\frac{1}{7} :\frac{2}{y}[/tex]
1 × y = 2 × 7
y = 14
4 days : 14 days
4 = 2 × 2
14 = 2 × 7
GCF = 2
4 ÷ 2 = 2
14 ÷ 2 = 7
2 : 7
You bought a shirt for 13.50 that was originally 45.00 in terms of percent what discount did you get the shirt?
A hot air balloon is released and it rises at a speed of 15 mph. A
weather pattern introduces a wind headed west at 20 mph. The
hot air balloon is now redirected. What is the new direction of the
hot air balloon?
Answer:
The direction is 37 degree north of west.
Step-by-step explanation:
velocity of balloon, v = 15 mph upwards
velocity of wind, v' = 20 mph west wards
The direction is given by
[tex]tan\theta = \frac{15}{20}\\\\\theta = 37^o north of west[/tex]
part ion even know of the hardest test
Given:
The equation of a line is:
[tex]y=-\dfrac{5}{7}x+2[/tex]
A line passes through the point (-5,-3) and perpendicular to the given line.
To find:
The equation of the line.
Solution:
Slope intercept form of a line is:
[tex]y=mx+b[/tex] ...(i)
Where, m is the slope and b is the y-intercept.
We have,
[tex]y=-\dfrac{5}{7}x+2[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]m=-\dfrac{5}{7}[/tex]
We know that the product of slopes of two perpendicular lines is always -1.
[tex]m_1\times m_2=-1[/tex]
[tex]-\dfrac{5}{7}\times m_2=-1[/tex]
[tex]m_2=\dfrac{7}{5}[/tex]
Slope of the required line is [tex]\dfrac{7}{5}[/tex] and it passes through the point (-5,-3). So, the equation of the line is:
[tex]y-y_1=m_2(x-x_1)[/tex]
[tex]y-(-3)=\dfrac{7}{5}(x-(-5))[/tex]
[tex]y+3=\dfrac{7}{5}(x+5)[/tex]
Using distributive property, we get
[tex]y+3=\dfrac{7}{5}(x)+\dfrac{7}{5}(5)[/tex]
[tex]y+3=\dfrac{7}{5}x+7[/tex]
[tex]y=\dfrac{7}{5}x+7-3[/tex]
[tex]y=\dfrac{7}{5}x+4[/tex]
Therefore, the equation of the line is [tex]y=\dfrac{7}{5}x+4[/tex]. Hence, option A is correct.
which are the slope and the y-intercept linear function that is represented by the graph?
Answer:
See explanation
Step-by-step explanation:
The question is incomplete, as the graph is not given.
The general step to calculate slope and y intercept is as follows;
Assume any two points on the graph are:
[tex](x_1,y_1) = (5,1)[/tex]
[tex](x_2,y_2) = (1,4)[/tex]
The slope (m) is:
[tex]m = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{4 -1}{1-5}[/tex]
[tex]m = \frac{3}{-4}[/tex]
[tex]m = -\frac{3}{4}[/tex]
The equation of the graph is:
[tex]y = m(x - x_1) + y_1[/tex]
This gives:
[tex]y = -\frac{3}{4}(x - 5) + 1[/tex]
[tex]y = -\frac{3}{4}x +\frac{15}{4} + 1[/tex]
[tex]y = -\frac{3}{4}x +\frac{15+4}{4}[/tex]
[tex]y = -\frac{3}{4}x +\frac{19}{4}[/tex]
To calculate the y intercept; set [tex]x = 0[/tex]
[tex]y = -\frac{3}{4}*0 +\frac{19}{4}[/tex]
[tex]y = \frac{19}{4}[/tex] ---- y intercept
The function h(t) = -16t^2 + h, 0 gives the height (in feet) of a ball dropped from a height of h, 0 after t seconds. A ball is dropped from a height of 12 feet. After how many seconds does the ball hit the floor?
could someone explain how to solve the equation? I know it's h(t) = -16^2 + 12
Answer:
Step-by-step explanation
the answee