Answer:
22.12feet
Step-by-step explanation:
the ladder becomes your hypotenuse,the wall is the height,this forms a right angled triangle and the angle of elevation forms at the base,use sine which is opposite over hypotenuse to get your answer
Subtract: 2 square root -8 -3 square root -18
Answer:
[tex] - 5 \sqrt{ - 2} [/tex]
Step-by-step explanation:
We can write sq root (- 18) as = sq root [3 x 3 x (-2)]
Similarly sq root ( - 8) = sq root [2 x 2 x (-2)]
2 sq root [2 x 2 x (-2)] - 3 sq root [3 x 3 x(-2)]
We simply,
2 x2 sq root (-2) - 3 x 3 sq root (-3)
4 sq root (-2) - 9 sq root (-2)
Bcoz sq root (-2) is common in bot term so
So
Sq root (-2) (4-9)
-5 sq root (-2) answer
What is the slope of the line given by the equation y=-3X?
A. 1/3
B. -1/3
C. -3
D. 3
Answer:
[tex]\boxed{-3}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation is determined by the constant equation [tex]y=mx+b[/tex] where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept of the line.
Therefore, we can use the equation given and implement it to find your slope.
[tex]y=-3x[/tex]
Our equation does not have a y-intercept, [tex]b[/tex]. Therefore, it can just be inferred as [tex]+0[/tex].
Because we do have a [tex]m[/tex], we can then find out what our slope is: [tex]\boxed{-3}[/tex].
Jesse takes two data points from the weight and feed cost data set to calculate a slope, or average rate of change. A rat weighs 3.5 pounds and costs $4.50 per week to feed, while a Beagle weighs 30 pounds and costs $9.20 per week to feed.
Answer:
The slope is [tex]s =[/tex] $0.1774 / pounds
Step-by-step explanation:
From the question we are told that
The weight of the rat is [tex]w_1 = 3.5 \ pound[/tex]
The cost of feeding the rat per week is [tex]c_1 =[/tex]$4.50
The weight of a Beagle is [tex]w_2 = 30 \ pound[/tex]
The cost of feed a Beagle per week is [tex]c_2 =[/tex]$9.20
Now the slope can be evaluated mathematically as
[tex]s = \frac{c_2 -c_1 }{w_2 -w_1 }[/tex]
substituting values
[tex]s = \frac{9.20 -4.50 }{30 -3.5 }[/tex]
[tex]s =[/tex] $0.1774 / pounds
Given: Q = 7m + 3n, R = 11 - 2m, S = n + 5, and T = -m - 3n + 8.
Simplify [Q - R] + [S - T].
10m - 7n - 14
10m + 5n - 24
10m - 5n + 24
10m + 7n - 14
Answer:
The answer is 10m + 7n - 14
Step-by-step explanation:
Q = 7m + 3n
R = 11 - 2m
S = n + 5
T = -m - 3n + 8
[Q - R] + [S - T] is
[ 7m + 3n - (11 - 2m) ] + [ n + 5 - ( - m - 3n+8)]
Solve the terms in the bracket first
That's
( 7m + 3n - 11 + 2m ) + ( n + 5 + m + 3n - 8)
( 9m + 3n - 11 ) + ( m + 4n - 3)
Remove the brackets
That's
9m + 3n - 11 + m + 4n - 3
Group like terms
9m + m + 3n + 4n - 11 - 3
The final answer is
10m + 7n - 14Hope this helps you
A freight train averages 20 miles per hour traveling to its destination with full cars and 30 miles per hour on the return trip with empty cars. What is the train's average speed for the entire trip
Answer:
24mph
Step-by-step explanation:
Let's say the distance between the destination is 10 miles. The train will reach the destination in 30 min for the first round and 20 min the second. Now, we can say, the train took 50 min to go 20 miles. Which is also 24mph. (5min=2miles)
The train's average speed for the entire trip is equal to 25 mph.
Given the following data:
Distance A = 20 milesTime A = 1 hourDistance B = 30 milesTime B = 1 hourTo determine the train's average speed for the entire trip:
First of all, we would find the total distance and total time for the trip respectively.
For total distance:
[tex]Total\;distance = Distance\;A + Distance\;B\\\\Total\;distance = 20+30[/tex]
Total distance = 50 miles
For total time:
[tex]Total\;distance = Time\;A + Time\;B\\\\Total\;distance = 1+1[/tex]
Total time = 1 hour
Mathematically, average speed is given by the formula:
[tex]Average\;speed = \frac{Total\;distance}{Total\;time} \\\\Average\;speed = \frac{50}{2}[/tex]
Average speed = 25 mph.
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I don’t quite understand what to do or how to solve it. Can someone explain please ?
Answer:
True.
Step-by-step explanation:
Remember the vertical line test. Anywhere on that graph, you can draw a vertical line, and it will not touch the function two times. Because of this, it is true.
(04.03 LC
Given the following system of equations:
3x + 5y = 30
X + 3y = 10
Which action creates an equivalent system that will eliminate one variable when they are combined?
Answer:
multiply second equation by (-3)
new system of equations:
3x + 5y = 30
-3x - 9y = -30
Step-by-step explanation:
x + 3y = 10
multiplied by (-3):
-3x - 9y = -30
combinig:
3x+5y + (-3x-9y) = 3x - 3x + 5y - 9y = -4y
10 + (-30) = -20
so: -4y = -20
Answer:
Multiply the second equation by −3 to get −3x − 9y = −30.
Step-by-step explanation:
Find the equation of the line passing through the point (–1, –2) and perpendicular to the line y = –1∕2x + 5. Choices are in the attachment...
Find the coefficient of fourth term of (-x -3)^5
Answer:
-270
Step-by-step explanation:
Here, we want to know the coefficient of the fourth term.
The coefficients according to pascal triangle for the expansion is 1 5 10 10 5 1
So the expansion looks as follows;
1[(-x)^5(-3)^0] + 5[(-x)^4(-3)^1)] + 10[(-x)^3(-3)^2) + 10[(-x)^2(-3)^3] + ...........
So the fourth term we are dealing with is
10[(-x)^2(-3)^3)]
So the value here is
10 * x^2 * -27
= -270 x^2
So the coefficient is -270
They can leave tonight by bus, or they can save two hours by leaving tomorrow morning and using the express train which travels 20 km/h faster than the bus. If the distance between South Central High and Calgary is 800 km, determine how long it will take to travel by bus, rounded to the nearest hour.
Answer:
The bus will take 10 hours to travel from South Central High to Calgary.
Step-by-step explanation:
Let suppose that both bus and express train travels at constant speed, whose kinematic formula is now described:
[tex]v = \frac{\Delta s}{\Delta t}[/tex]
Where:
[tex]v[/tex] - Speed, measured in kilometers per hour.
[tex]\Delta s[/tex] - Travelled distance, measured in kilometers.
[tex]\Delta t[/tex] - Time, measured in hours.
The transportation time is cleared afterwards:
[tex]\Delta t = \frac{\Delta s}{v}[/tex]
The kinematic expressions for the bus and the express bus are, respectively: ([tex]\Delta s = 800\,km[/tex])
Bus
[tex]\Delta t = \frac{800\,km}{v}[/tex]
Express train
[tex]\Delta t - 2\,h = \frac{800\,km}{v + 20\,\frac{km}{h} }[/tex]
By eliminating [tex]\Delta t[/tex]:
[tex]\frac{800\,km}{v} -2\,h = \frac{800\,km}{v+20\,\frac{km}{h} }[/tex]
[tex]\frac{800\,km}{v} - \frac{800\,km}{v+20\,\frac{km}{h} } = 2\,h[/tex]
[tex]800\cdot (v+20)-800\cdot v = 2\cdot v\cdot (v+20)[/tex]
[tex]16000 = 2\cdot v^{2}+40\cdot v[/tex]
[tex]2\cdot v^{2}+40\cdot v -16000 = 0[/tex]
Which is a second-order polynomial and whose roots are:
[tex]v_{1} = 80\,\frac{km}{h}[/tex] and [tex]v_{2} = -100\,\frac{km}{h}[/tex]
Only first root is physically reasonable, as speed is a scalar, that is, a number that is represented only by magnitude. Then, the time taken by the bus to travel from Central High to Calgary is: ([tex]v = 80\,\frac{km}{h}[/tex])
[tex]\Delta t = \frac{800\,km}{80\,\frac{km}{h} }[/tex]
[tex]\Delta t = 10\,h[/tex]
The bus will take 10 hours to travel from South Central High to Calgary.
Irum is sitting on the beach, watching the tide go in and out. Irum's distance from the shoreline (in meters) as a function of time (in hours) is graphed. What is the approximate average rate at which Irum's distance from the shoreline increases, between the 9th and the 13th hour marks?
Answer:
Hi, the Answer is 0.75.
Step-by-step explanation:
it is 0.75 because if you look on the graph, and you calculate the 3/4 slope between the two, 3/4= 0.75
Answer:
A) 0.75 meters per hour
Step-by-step explanation:
The sum of three numbers is 84 The second number is 2 times the first. The third number is 16 less than the second. What is the second number?
Answer:
40
Step-by-step explanation:
First let x represent the first number.
Let 2x represent the second number.
Let 2x-16 represent the third number.
x + 2x + 2x-16 = 84
5x -16 = 84
5x = 84 + 16
5x = 100
Divide both sides of the equation by 5 so that x can stand alone.
[tex]\frac{5x}{5} = \frac{100}{5}[/tex]
x = 20
∴ First number = x = 20
Second number = 2x = 40
Third number = 2x - 16 = 24
For A (1, -1), B(-1,3), and C(4, -1), find a possible location of a fourth point, D, so that a
parallelogram is formed using A, B, C, D in any order as vertices.
Answer: c, b, a, d
Step-by-step explanation: that is correct
Rewrte the expression with a ratational exponent as a radical expression (4^2/5)^1/4
Answer:
Step-by-step explanation:
(4^2/5)^1/4
first multiply the exponent
2/5*1/4=2/20=1/10
4^1/10= 10√4(the ten is on the top to the square root)
look at the image and answer it
Answer:
The circumference of circle is 14π cm.
Step-by-step explanation:
Given that the formula of circumference is C = 2×π×r where r represents radius of circle. In this case, diameter of circle is 14cm so the radius will be 7cm. Then, you have to substitute the value into the formula :
[tex]c = 2 \times \pi \times r[/tex]
[tex]let \: r = 7[/tex]
[tex]c = 2 \times \pi \times 7[/tex]
[tex]c = 14\pi \: \: cm[/tex]
Answer:
14[tex]\pi[/tex]
units = cm
Step-by-step explanation:
circumference = 2 x [tex]\pi[/tex] x r
c = 2 x [tex]\pi[/tex] x 7 - it's 7 because the diameter is 14 and radius is half the diameter
c = 14 x [tex]\pi[/tex]
c = 43.98229715
in terms of pi c = 14 [tex]\pi[/tex]
units = cm
Can somebody please help me!!
Step-by-step explanation:
Simply you replace X and Y by their values
Given: x=-1 y=-4
10 - (-X)^3 + y^2
=10 + X^3 + Y^2
Now replace X and Y
=10 + (-1)^3 + (-4)^2
=10 - 1 + 16
= 25
Complete the equation: x2 + 10x + ___ = 2
Amir wants to buy a $1382 Apple iPhone that is 12% off. What is 1 point
the discounted price before tax? *
Answer:
1273
Step-by-step explanation:
C) the answer on edg is C.
Find the measure of the remote exterior angle. m∠x=(4n−18)°m∠y=(n+8)°m∠z=(133−6n)° m ∠ x = ( 4 n − 18 ) ° m ∠ y = ( n + 8 ) ° m ∠ z = ( 133 − 6 n ) °
Answer:
67°
Step-by-step explanation:
The question is incomplete. Here is the complete question.
Find the measure of the remote exterior angle. m∠x=(4n−18)°, m∠y=(n+8)°, m∠z=(133−6n)° angle Z being the exterior angle.
Before we can get the exterior angle Z, we need to first calculate the value of n.
In geometry, the sum of interior angles is equal to the remote exterior angle.
m∠z = m∠x + m∠y
(133-6n)° = (4n-18)°+(n+8)°
133-6n = 4n-18+n+8
-6n-4n-n = -18-133+8
-11n = -143
n = 143/11
n = 13°
Since the exterior angle m∠z =(133-6n)°
Substituting n = 11 into the equation will give:
m∠z = 133-6(11)
m∠z = 133-66
m∠z = 67°
The remote exterior angle is 67°
Answer: 55
Step-by-step explanation:
write the ratio 4.5: 2.25 in the form n:1
Step-by-step explanation:
you will divide both sides of the ratio I.e the 4.5 and 2.25 by 2.25
Here's a graph of a linear function. Write the
equation that describes that function. Express it in slope-intercept form.
Answer:
y = -2x -5
Step-by-step explanation:
The line crosses the y-axis at -5. So, b = -5.
It goes down 2 units for each 1 unit to the right, so has a slope of ...
m = rise/run = -2/1 = -2
__
The slope-intercept form of the equation of a line is ...
y = mx +b where m is the slope and b is the y-intercept
For the slope and y-intercept shown, the equation is ...
y = -2x -5
Fiona's school is in the shape of a triangle, with three hallways connecting the corners. Fiona enters the building and walks 90 yards through the first hallway to the first corner. Then, she walks 60 yards through the second hallway to the second corner. A triangle is shown. The side lengths are 60 yards, 90 yards, and question mark. The top point is labeled exit and the bottom right point is labeled entrance. The distance between exit and entrance is question mark. What are the possible lengths of the third hallway? between 30 yards and 60 yards between 30 yards and 90 yards between 30 yards and 120 yards between 30 yards and 150 yards
Answer:
bettween 30 and 150 yards
Step-by-step explanation:
test
Answer:
Between 30 yds and 150 yds.
Step-by-step explanation:
Got it right Edge 2021
– StartFraction 5 Over 3 EndFraction v plus 4 equals 8 minus StartFraction 1 Over 3 EndFraction v.(6x – 3) = –
Answer:
v=11/5 or v=2.2
Step-by-step explanation:
The wording of this question is a little confusing but if it says what I think it does (5/3v+4=8-1/3) then this is the answer.
Work out the size of angle x: 38° is at the top of the triangle, 101° is at the bottom right of the triangle, work out the size of angle x which is at the bottom left of the triangle.
Answer: x = 41°
Step-by-step explanation:
The sum of the angles in a triangle equals 180°.
To find the missing angle, subtract the sum of the two given angles from 180.
101 + 38 = 139
180 - 139 = 41
x = 41°
The size of the angle at the bottom left of the triangle is 41°.
What is a triangle?A triangle is a geometric figure which has three edges and three vertices. The sum of a triangle's three angles is 180°.
How to solve this problem?Given that the two angles of the triangle are 38° and 101°. We have to find the size of the other angle which is at the bottom left of the triangle. Let the size of the angle be x°.
We have to solve the equation:
x + 38 + 101 = 180
i.e. x = 180 - (38 + 101) = 180 - 139 = 41°
Therefore, the size of the angle at the bottom left of the triangle is 41°.
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ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
c.) x-2
Step-by-step explanation:
Answer:
X-2
Step-by-step explanation:
Factoring without Combining Like Terms
Try it
Complete the steps to factor 2x2 + 6x + 5x + 15 by grouping.
2x2 + 6x + 5x + 15
Step 1: Group the first two terms and the second two terms.
(2x2 + 6x) + (5x + 15)
Group 1 Group 2
Step 2: What is the greatest common factor of Group 1?
2
Ox
O 2x
Answer:
(x + 3)(2x + 5)
Step-by-step explanation:
Given
2x² + 6x + 5x + 15 ← grouping the terms
= (2x² + 6x) + (5x + 15) ← factor each group
= 2x(x + 3) + 5(x + 3) ← factor out (x + 3) from each term
= (x + 3)(2x + 5) ← in factored form
Answer:
EDG 2021
Step-by-step explanation:
Step 2: C. 2x
Step 3: B. 5
Step 4: C. x + 3
Step 5: A. (x + 3) (2x + 5)
Which equation has the steepest graph?
A. y = 10x-5
B. y=3/4x-9
c. y = -14x+1
D. y = 2x + 8
The equation that has the steepest slope is y = -14x + 1
What is a slope?A slope is the ratio of the change in the y-coordinates to the change in the x-coordinates of a line segment.
Analysis:
A line is said to be the steepest if it has the highest absolute value of the gradient or slope.
From the equations, the coefficient of x in the equations is taken as the slope. y = -14x+ 1 is the equation with the highest absolute value 14. The absolute value means ignoring the minus sign, since it indicates a negative slope.
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Answer:
Y=-14x+1
Step-by-step explanation:
What are the solutions to the system of equations graphed below?
Answer:
B) (2,0) and (0,-4)
Step-by-step explanation:
The answer to the system of equations is where the two intersect on the graph, in this case on the points (2,0) and (0,-4)
Which ordered pair is a solution if the equation? 2x + 3y = 10
Answer:
See below.
Step-by-step explanation:
Try each ordered pair in the equation. Each ordered pair is of the form (x, y). Replace x and y in the equation by values of x and y, respectively, in each ordered pair. Whichever ordered pair makes the equation a true statement is the answer.
For example:
Try (2, 3):
2x + 3y = 10
2(2) + 3(3) = 10
4 + 9 = 10
13 = 10
Since 13 = 10 is a false statement, (2, 3) is not a solution.
Try (2, 2):
2x + 3y = 10
2(2) + 3(2) = 10
4 + 6 = 10
10 = 10
Since 10 = 10 is a true statement, (2, 2) is a solution.
Vincent made a sketch that measures 10 inches by 15 inches. If he creates a new drawing where each of the dimensions is tripled, what will be the perimeter of the new drawing?
Answer:
150 inches
Step-by-step explanation:
Vincent sketch is a rectangle
10 inches by 15 inches
Length=15 inches
Width=10 inches
If each dimension is tripled
Then,
Length=15*3=45
Width=10*3=30
Perimeter of the new drawing=2(length+width)
=2(45+30)
=2(75)
=150 inches