Answer:
The answer is option B
24cmStep-by-step explanation:
Area of a triangle is
[tex] \frac{1}{2} \times b \times h[/tex]
Where b is the base
h is the height
The base of the triangle is 5 times the height is written as
b = 5h
Area of the triangle is 1440cm²
[tex]1440 = \frac{1}{2} \times 5h \times h[/tex]
[tex]1440 = \frac{1}{2} 5 {h}^{2} [/tex]
[tex]2880 = 5 {h}^{2} [/tex]
Divide both sides by 5
[tex] {h}^{2} = 576[/tex]
Find the square root of both sides
[tex]h = \sqrt{576} [/tex]
h = 24cmHope this helps you
Write 2(6² + 4²) as the sum of two perfect square.
Write 10:5 as a ratio in its simplest form
Answer:
its simplest form for the question is 2:1
How many solutions does this system have? 6 x + 3 y = negative 12. y = negative 2 x + 4. one two an infinite number no solution
Answer:
work is shown and pictured
Jack challenged Jill to a race around a curve of a track. Jack took lane 8 with Jill at lane 1. If the radius of lane 1 is half of lane 8, what is the distance in metres Jack has to run if Jill ran a distance of 50m?
Answer:jac ganko
Step-by-step explanation:
Please help me!!!! I really need help!!
Answer:
A. 25°
Hope it helped
if p(x) = x+ 7/ x-1 and q (x) = x^2 + x - 2, what is the product of p(3) and q(2)? a. 50 b. 45 c. 40 d. 20 e. 6
Answer:
d. 20
Step-by-step explanation:
To answer the question given, we will follow the steps below:
we need to first find p(3)
p(x) = x+ 7/ x-1
we will replace all x by 3 in the equation above
p(3) = 3+7 / 3-1
p(3) = 10/2
p(3) = 5
Similarly to find q(2)
q (x) = x^2 + x - 2,
we will replace x by 2 in the equation above
q (2) = 2^2 + 2 - 2
q (2) = 4 + 0
q (2) = 4
The product of p(3) and q(2) = 5 × 4 = 20
Jenny wants to know the perimeter of the bottom of her tent. It is a rectangle with side lengths of 11 ft. And 7 ft. Which is the perimeter of the bottom of her tent?
Answer:
36 ft.
Step-by-step explanation:
11+11+7+7=
22+14= 36
Answer:
36 ft
Step-by-step explanation:
The rectangle's sides lengths are 7 ft and 11 ft, wich are the width and the length.
The formula of the perimeter is:
P= 2w+2L with w the width and L the length
P= 2*7+2*11
P= 14+22
P= 36 ft
The perileter is 36 ft
Which way would you choose to solve 3/x=6/14 ?
Explain your reasoning.
Answer:
I'd cross multiply to solve this equation.
Step-by-step explanation:
Since we have a fraction where we're finding a ratio:
[tex]\frac{3}{x} = \frac{6}{14}[/tex],
I'd find it easiest to cross multiply. This is because we are finding an equivalent to a ratio, so cross multiplication works best here.
Let's solve it.
[tex]14\cdot 3 = 42\\42\div6=7[/tex]
x = 7
Hope this helped!
Write two equivalent expressions using the commutative property that can be used to find the total number of points Dean Scored on his math test
Answer:
2
Step-by-step explanation:
The tee for the fifth hole on a golf course is 375 yards from the tee. On that hole, Marsha hooked her ball to the left, as sketched below. Find the distance between Marsha’s ball and the hole to the nearest tenth of a yard.
Answer:
158.73 yd
Step-by-step explanation:
A picture of the situation is needed, investigating I could find a related one, in the same way the important thing is the solution, the data can be exchanged. I attach the drawing.
Let use the formula of the law of cosine:
c ^ 2 = a ^ 2 + b ^ 2 - 2 * a * b * cos C, to solve the problem
Let the third side be c, we replace:
c ^ 2 = 375 ^ 2 + 240 ^ 2 - 2 * 375 * 240 * cos 16 °
c ^ 2 = 198225 - 173027.10
c ^ 2 = 25197.9
c = 158.73
So the distance is 158.73 yd
Answer: the right answer is 195.4
Step-by-step explanation: this guy does not what's happening
The nth term of a geometric sequence is a sub n =a sub 1 times r ^n-1 , where a sub 1 is the first term and r is the common ratio. Identify a sub 1 and r for each geometric sequence.
Answer/Step-by-step explanation:
Common ratio of a sequence can be gotten by dividing any of the consecutive term in a sequence, by the term before it.
Thus,
For the sequence, [tex] 3, 9, 27. . . [/tex] : [tex] a_1 = 3 [/tex]
[tex] r = \frac{9}{3} = 3 [/tex]
For the sequence, [tex] 8, 4, 2, 1. . . [/tex] : [tex] a_1 = 8 [/tex]
[tex] r = \frac{4}{8} = \frac{1}{2} [/tex]
For the sequence, [tex] -16, 64, -256 . . [/tex] : [tex] a_1 = -16 [/tex]
[tex] r = \frac{64}{-16} = -4 [/tex]
Please help I really need to get it right
Answer:
Alternate interior angles.
17x + 6 = 18x - 1.
x = 7.
Step-by-step explanation:
According to the diagram below, the angles are alternate interior angles.
Since they are alternate interior angles, they are congruent. So, 17x + 6 = 18x - 1.
17x + 6 = 18x - 1
18x - 1 = 17x + 6
x = 7
Hope this helps!
Convert 125 degrees into radians. (NEED ASAP)
Answer:
[tex]\boxed{\frac{25\pi }{36}}[/tex]
Step-by-step explanation:
Use the formula to convert from degrees to radians: [tex]x * \frac{\pi }{180}[/tex], where x is the value in degrees.
[tex]125 * \frac{\pi }{180}[/tex] = [tex]\frac{125\pi }{180}[/tex]
Then, simplify your fraction ⇒ [tex]\frac{125\pi }{180} = \boxed{\frac{25\pi}{36} }[/tex]
I NEED HELP PLZ Event A and event B are independent events. Given that P(B)=13 and P(A∩B)=16, what is P(A)?
Answer:
19
Step-by-step explanation:
sin theta=-1/2 then cos theta=
Answer:
cos 30°= 0.866Step-by-step explanation:
Step one:
Applying the SOH CAH TOA principle
assuming all dimensions are in cm
Step two:
Given data
opposite= 1 cm
hypotenuse= 2 cm
we can now solve for θSin(θ)= opp/hyp
Sin(θ)= 1/2
Sin(θ)= 0.5
θ= sin-1 0.5
θ= 30°
hence from tables cos 30°= 0.866
in how many ways can you select a committee of 3 students out of 10 students ?
I REALLY NEED HELP! PLEASE help me...
Answer:
A. The domain is (1,∞), and the range is (-7,∞)
Step-by-step explanation:
Well lets graph it first,
Look at the image below ↓
By looking at the image we move it 3 units right and 3 units down.
Then it will be located at the point (1,-7).
Meaning for the domain it starts at 1 and goes on for infinity.
And For the range it starts down at -7 and goes down for infinity.
Thus,
the correct answer is choice A.
Hope this helps :)
Answer:
A
Step-by-step explanation:
Solution:-
- First we will go through the guidelines that are followed when a given function [ f ( x ) ] is translated in a cartesian coordinate system domain.
Horizontal shifts:
Left shift: f ( x ) - > f ( x + a ). Right Shift: f ( x ) - > f ( x - a )Where, the constant ( a ) denotes the magnitude of shift
Vertical shifts:
Up shift: f ( x ) - > f ( x ) + bDown Shift: f ( x ) - > f ( x ) - bWhere, the constant ( b ) denotes the magnitude of shift
- The generalized form of a translated function is defined by the combination of both horizontal and vertical shifts as follows:
General: f ( x ) -> f ( x ± a ) ± b
Where, (a) and (b) are constants of respective translation shifts.
- We are given a function H ( x ) is to be translated 3 units to right and 3 units down. Use the above guidelines to determine the translated function H* ( x ) as follows:
[tex]H ( x ) = \sqrt{x+2} - 4\\\\H^* ( x ) = H ( x - 3 ) - 3[/tex]
- Substitute ( x - 3 ) in place of all ( x ) in the given function H ( x ) and subtract ( 3 ) from H ( x ) as follows:
[tex]H^* ( x ) = \sqrt{x-3 + 2} -4 - 3\\\\H^* ( x ) = \sqrt{x-1} -7\\[/tex]
- Now we will look for any transcendental functions in the translated function H*(x). These are " Radicals, fractions, Logs, trigonometric ratios "
- We have a radical - > " square root " in H* ( x ). To find the domain of H*(x) we need to determine for what real values of x is the function H*(x) is defined.
- The square root exist for all only positive numbers. So the terms under the square root must be positive; hence,
[tex]x - 1 \geq 0\\\\x \geq 1[/tex]
- Since the square root is the only transcendental in the given function H*(x) we have a one sided closed interval for the domain of the translated function.
Domain: [ 1 , ∞ ) ... Answer
- The range of the function is the corresponding output of function H*(x) for the domain established above. We can determine this by plugging in the end-points of the defined domain in the translated function H*(x) as follows:
[tex]H^* ( 1 ) = \sqrt{1 - 1} - 7 = -7\\\\H^* ( inf ) = \sqrt{inf - 1} - 7 = inf - 7 = inf\\\\[/tex]
Therefore the range of the function is also a one sided closed interval bounded by x = 1.
Range: [-7 , ∞ ) ... Answer
A steady stream of water flows into a partially-filled rectangular tank. After 6 minutes, there are 87 gallons of water in the tank. After 21 minutes, there are 222 gallons. Write an equation to represent the volume of water in the tank y after x minutes. How much water was in the tank to begin?
Answer: y=9x+33
33 gallons of water to begin with.
Step-by-step explanation:
So we essentially are given two coordinates: (6,87) and (21,222). To find an equation, we simply need to find the slope and y-intercept. We know it's a linear equation because it's a steady stream, meaning a constant slope.
The slope is:
So, the rate at which the stream flows is 9 gallons per minute.
Now, let's find the initial amount of water. To do this, we can use point-slope form. Pick either of the two points. I'm going to use (6,87).
So, there were 33 gallons of water in the tank to begin with.
Answer:
There were 33 gallons.
Step-by-step explanation:
One afternoon Anne leave her house and walk 5 blocks north to the post office then she walk 2 blocks north to the bank finally she walk 3 blocks south to the coffee shop were is the coffee shop relative to her house
Answer:
B
Step-by-step explanation:
Question 5 of 10
Which of the following is the converse of the statement "If it is summer, then
it is warm outside"?
A. If it is warm outside, then it is summer.
B. If it is not warm outside, then it is summer.
O
C. If it is warm outside, then it is not summer.
D. If it is not warm outside, then it is not summer.
hs
Answer:
If it is warm outside, then it is summer
Step-by-step explanation:
To find the converse, interchange the hypothesis and the conclusion
"If it is summer, then it is warm outside"
If it is warm outside, then it is summer
Answer:
A. If it is warm outside, then it is summer
Step-by-step explanation:
statement "If it is summer, then it is warm outside" : warm=summer
A. If it is warm outside, then it is summer. : warm = summer ✓
B. If it is not warm outside, then it is summer. : not warm = summer x
C. If it is warm outside, then it is not summer. : warm =not summer x
D. If it is not warm outside, then it is not summer. : not warm = not summer x
A constant force of 85 N accelerates towards a 10 kg box from a speed of 3.0 m/s to a speed of 7.0 m/s as it goes 14 m along a horizontal floor. What is the coefficient of friction between the box and the floor?
Answer:
Step-by-step explanation:
Let us find the acceleration of box .
v² = u² + 2as
Putting the values
7² = 3² + 2 a x 14
a = 1.43 m /s²
If coefficient of friction be μ
force of friction = μ mg
= μ x 10 x 9.8
= 98μ
Net force pushing the box
= 85 - 98μ
Applying newton's second law
85 - 98μ = 10 x 1.43
98μ = 85 - 14.3
μ = .72
PLEASE HELP: Which is a compound event?
Answer:
The correct option is;
Heads lands 3 times and tales lands 5 times in 8 coin flips
Step-by-step explanation:
A compound event is one in which the probability of more than one outcome or event to have occurred at the same time is sought. The probability of a compound event is the sum of the probabilities of the individual events less the probabilities already captured in both event probabilities
Answering compound event questions can be done by the use of a tabular or diagram format.
Therefore, the compound event in the list is heads lands 3 times and tales lands 5 times in 8 coin flips.
Heather used a graphing utility to find the equation of the line of best fit in this scatter plot. VA PW1ALG131_Using Models from Data After reading equation of the line from the graphing utility, Heather wrote in her notebook that the line of best fit is represented by the equation y = 0.77x + 1.34. Heather likely an error when writing the equation of the line in her notebook because the slope and the y-intercept of the equation she recorded.
The answers are did not make, and both the slope and the y-intercept match if the line of the best fit is represented by the equation y = 0.77x + 1.34
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
We have a line of best fit:
y = 0.77x + 1.34
Here the slope of the line is 0.77 and y-intercept is 1.34
From the graph and line of best fit, we can say heather did not make an error when writing the equation of the line in her notebook because both the slope and the y-intercept match the slope and the y-intercept of the equation she recorded
Thus, the answers are did not make, and both the slope and the y-intercept match if the line of the best fit is represented by the equation y = 0.77x + 1.34
Learn more about the line of best fit here:
brainly.com/question/14279419
#SPJ2
Answer:
Heather likely did not make an error when writing the equation of the line in her notebook because both the slope and the y-intercept match the slope and the y-intercept of the equation she recorded.
Write the following as an inequality:
y is no greater than 4 but more than -2.
Answer:
4>Y>-2 :) ..............
Answer:
[tex]\boxed{-2 < y \leq 4}[/tex]
Step-by-step explanation:
For y is no greater than 4, it would be either less than or equal to 4. So, the inequality for it would be:
y ≤ 4
Now, the inequality for y more than -2:
-2 < y
Combining the inequality:
-2 < y ≤ 4
A box with an open top is to be constructed from a square piece ofcardboard, with sides 6 meters in length, by cutting a square from each of the fourcorners and bending up the sides. Find the dimensions that maximize the volume ofthe box and the maximum volume.
Answer:
Step-by-step explanation:
Let x be the height of the box . x will be cut at four corners .
each side of the box = 6 - 2x
volume of box V = ( 6 - 2 x )² x
V = ( 36 + 4 x² - 24 x ) x
V = 4x³ - 24 x ² + 36 x
For maximum volume
dV / dx = 12 x² - 48 x + 36 = 0
x² - 4 x + 3 = 0
( x - 3 ) ( x - 1 ) = 0
x = 1 , x = 3 ( not possible )
Possible solution x = 1
Volume , for x = 1
V = V = ( 6 - 2 x )² x
V = 4² x 1
= 16 m³.
Kite A B C D is shown. Lines are drawn from point A to point C and from point B to point D and intersect. In the kite, AC = 10 and BD = 6. What is the area of kite ABCD? 15 square units 30 square units 45 square units 60 square units
Answer:
[tex]30 u^{2}[/tex]
Step-by-step explanation:
The computation of the area of kite ABCD is shown below:
Given data
AC = 10 ;
BD = 6
As we can see from the attached figure that the Kite is a quadrilateral as it involves two adjacent sides i.e to be equal
Now the area of quadrilateral when the diagonals are given
So, it is
[tex]\text { area of kite }=\frac{1}{2} \times d_{1} d_{2}[/tex]
where,
[tex]d_{1}=10\ and\ d_{2}=6[/tex]
So, the area of the quadrilateral is
[tex]=\frac{1}{2}(10)(6)\\\\=30 u^{2}[/tex]
Answer:
C
Step-by-step explanation:
I just took the test
What is 1/9 of 63% of 6000?
Answer:
420
Step-by-step explanation:
To find 63% of 6000, we can do 0.63 * 6000 = 3780 because 63% = 0.63.
1/9th of that is 1/9 * 3780 = 420.
Answer:
420
Step-by-step explanation:
Let's first start by finding 63% of 6000 so we can later find 1/9 of that number.
We can set up a percentage proportion.
[tex]\frac{x}{6000} = \frac{63}{100}[/tex]
[tex]6000\cdot63=378000\\378000\div100 = 3780[/tex]
Now to find 1/9 of 3780.
[tex]\frac{1}{9} \cdot \frac{3780}{1}\\\\\frac{3780}{9} = 420[/tex]
So, the answer is 420.
Hope this helped!
Write an expression for the volume and simplify your answer. 3x x+1 x+4
Answer:
volume=3x³+15x²+12x
Step-by-step explanation:
v= l*w*h =(3x )(x+1) (x+4)
v=3x(x²+5x+4)
volume=3x³+15x²+12x
The equation of line l is -3y+4x=9 Write the equation of a line that is parallel to line l and passes through the point (-12,6). a) -3y+4x-69=0 b)-3y+4x-69=0 c)-3y+4x-39=0 d) 3x-3y+66=0
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
- 3y + 4x = 9
3y = 4x - 9
Divide both sides by 3
y = 4/3x - 3
Comparing with the above formula
Slope / m = 4/3
Since the lines are parallel their slope are also the same
So slope of the parallel line l is also 4/3
Equation of the line using point (-12 , 6) is
y - 6 = 4/3(x + 12)
Multiply through by 3
That's
3y - 18 = 4(x + 12)
3y - 18 = 4x + 48
We have the final answer as
4x - 3y + 66 = 0Hope this helps you
defg is a dilation image of defg which is the correct description of the dilation
Answer: Center D I think
Step-by-step explanation: