Answer:
[tex]h=30[/tex]
Step-by-step explanation:
Volume of a cone=1540[tex]cm^{3}[/tex], Radius=7cm.
The height of a cone=h
When we need to find the height of a cone, we can use the formula of the volume of a cone, which is [tex]\frac{1}{3} \pi r^{2} h[/tex] to find the height of a cone.
[tex]1540cm^{3} =\frac{1}{3}\pi r^{2} h[/tex]
Put the pi value=22/7 and the value of radius which is 7 cm into the formula.
[tex]1540cm^{3}=\frac{1}{3}*\frac{22}{7} 7^{2}h[/tex]
[tex]1540cm^{3} =\frac{154}{3}h[/tex]
Move [tex]\frac{154}{3}[/tex] to another side. 1540 divided by [tex]\frac{154}{3}[/tex] to calculate what is the value of h, h is the height of a cone. Like this.
[tex]\frac{1540cm^{3} }{\frac{154}{3} } =h[/tex]
[tex]30=h[/tex]
Rearrange the h.
[tex]h=30[/tex]
I hope you will understand my solution and explanation. If you still cannot get the point, you can ask me anytime! Thank you!
Answer:
The height of the cone is h = 30 cm.
Step-by-step explanation:
The formula for a cone is:
[tex] \\ V = \frac{1}{3}*\pi*r^2*h[/tex]
We have (without using units) and using pi = 22/7:
[tex] \\ 1540 = \frac{1}{3}*\frac{22}{7}*(7)^2*h[/tex]
Which is equals to:
[tex] \\ 1540 = \frac{1}{3}*\frac{22}{7}*(7)*h[/tex]
[tex] \\ 1540 = \frac{1}{3}*22*7*h[/tex]
Well, we have to solve the equation for h:
[tex] \\ \frac{1540*3}{22*7} = h[/tex]
[tex] \\ 30 = h[/tex]
Therefore, the height of the cone is 30 cm.
tate the postulate that verifies is in plane Q when points A and B are in Q.
Answer:
Postulate 3: Through any three points that are not one line, exactly one plane exists. State the postulate that verifies line segment AB is in plane Q when points A and B are in Q.
Step-by-step explanation:
Postulate 4: If two points lie in a plane, the line containing them lies in that plane. hope this helps you :)
In a newspaper, it was reported that yearly robberies in Springfield were down 10% to 90 in 2014 from 2013. How many robberies were there in Springfield in 2013?
Answer:
100.
Step-by-step explanation:
Let the number of robberies be x ( in 2013).
Then x - 0.10x = 90
0.90x = 90
x = 90 / 0.90
= 100.
EMERGENCY HELP! 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:
[tex]y=9x+33[/tex]
33 gallons of water to begin with.
Step-by-step explanation:
So, we are essentially given two coordinates: (6,87) and (21,222). To find an equation, we will 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.
Using the slope formula, the slope is:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}=\frac{222-87}{21-6}=135/15=9[/tex]
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).
Point-slope form is given by:
[tex]y-y_1=m(x-x_1)[/tex]
Substitute:
[tex]y-(87)=9(x-(6))[/tex]
Distribute:
[tex]y-87=9x-54[/tex]
Therefore:
[tex]y=9x+33[/tex]
So, there were 33 gallons of water in the tank to begin with.
Austin walks 2/3 of the way to school and stopped to rest. Devyn walks 4/6 of the way to school and stops for a rest. Where are they in their route to school? Who has traveled further?
Answer:
both are at the same distance
Step-by-step explanation:
Answer:
Austin and Devyn both have 1/3 of the way left on their way to school. They both also have walked the same amount.
Step-by-step explanation:
If Austin has to walk to his school, which could be said as 3/3 and Austin has already walked 2/3. Then if we conduct the equation 3/3-2/3=x. x=1/3. Now Devyn has already walked 4/6 of the way to school. If she has to walk a total of 6/6, then we can again make an equation 6/6-4/6=2/6. Now if we take the distance that they both have left to their school, its 1/3 and 2/6. These are both equavalent fractions because if you scale up 1/3, it equals to 2/6. Since they both have an equal amount of distance to travel, that must mean that they both have covered the same amount of distance already. We can double check to be sure. 2/3 *2/2=4/6. The reason we used 2/2 is because4/2=2 and 6/3=2.
Determine whether the underlined number is a statistic or a parameter. Upper A sample of professors is selected and it is found that Modifying 35 % with underline own a television. Choose the correct statement below. Parameter because the value is a numerical measurement describing a characteristic of a population. Statistic because the value is a numerical measurement describing a characteristic of a population. Parameter because the value is a numerical measurement describing a characteristic of a sample. Statistic because the value is a numerical measurement describing a characteristic of a sample
Answer:
Option : Statistic because the value is a numerical measurement describing a characteristic of a sample.
Step-by-step explanation:
A sample of professors is selected and it is found that Modifying 35 % with underline own a television.
The 35% is the value that summarizes the characteristic of the sample taken from the population. Thus, the value 35% is a statistic.
While a parameter gives a value describing the characteristic of the population itself
Given: Sample proportion is (P)=[tex]35%[/tex]%.
Statistics are the constants that are computed from sample observations alone. This is a simple definition of statistics.
Answer: The correct statement is Statistic because the value is a numerical measurement describing a characteristic of a population.
Explanation: That is, statistic because the value is a numerical measurement describing the characteristic of a sample.
The remaining statements are incorrect.
As parameters are the constants of the population. They describe only the population not the sample.
Learn more: https://brainly.com/question/10211620
Solve the equation for all exact solutions where appropriate. Round approximate answers in degrees to the nearest tenth. Write answers using the least possible nonnegative angle measures. sine theta cosine theta minus sine theta equals 0
A. {270 degree - 360 degree n, where n is any integer}
B. {270 degree + 180 degree n, where n is any integer}
C. {270 degree + 180 degree n, 315 degree + 180 degree n, where n is any integer}
D. {270 degree + 360 degree n, 315 degree + 360 degree n, where n is any integer}
Step-by-step explanation:
The equation is sinθ * cosθ - sinθ = 0
sinθ * cosθ -sinθ = 0sinθ * cosθ = sinθcosθ = sinθ/sinθcosθ = 1θ = 0 + 2kπ
θ = 2kπ where k is any integer
The solutions to the equation are: {0 degree, 180 degree, 360 degree, 360 degree + 180 degree n, where n is any integer}
Hence, the correct option is C.
The given equation is:
sin theta × cos theta - sin theta = 0
We can factor out the sine theta:
sin theta (cos theta - 1) = 0
This means that either sin theta = 0 or cos theta - 1 = 0.
If sin theta = 0, then theta = 0, 180 degrees, 360 degrees, etc.
If cos theta - 1 = 0, then cos theta = 1, which means that theta = 0 degrees and 360 degrees.
Therefore, the solutions to the equation are:
{0 degree, 180 degree, 360 degree, 360 degree + 180 degree n, where n is any integer}
So the answer is C.
Learn more about solutions here: brainly.com/question/30665317
#SPJ2
Which of the following lines the parallel to the line y-9=7(x+5)
A.) y-9=3x+4
B.) y=-9x-5
C.) y+5=7(x-9)
D.) y-9=5(x+4)
Answer:
C.) y + 5 = 7(x - 9)Step-by-step explanation:
Parallel lines have the same slope.
The slope-intercept form of an equation of a line:
y = mx + b
m - slope
b - y-intercept
The point-slope form of an equation of a line:
y - y₁ = m(x - x₁)
(x₁, y₁) - point on a line
m - slope
We have the line y - 9 = 7(x + 5). The slope m = 7.
A) y - 9 = 3x + 4 → m = 3
B) y = -9x - 5 → m = -9
C) y + 5 = 7(x - 9) → m = 7
D) y - 9 = 5(x + 4) → m = 5
The line C) y + 5 = 7(x - 9) has the same slope.
Find the value of x in the triangle
shown below.
X
85
67
Answer:
x = 28 degrees. 180 degrees in a triangle, 180-85-67=28
Answer:
28 degrees
Step-by-step explanation:
The interior angles of a triangle add up to 180 degrees.
The three angles given are: x, 85, and 67.
Therefore, these three angles must add to 180.
x+85+67=180
Combine like terms on the left. Add 85 and 67.
x+ (85+67)=180
x+152=180
We want to find x. We need to get x by itself. 152 is being added to x. The inverse of addition is subtraction. Subtract 152 from both sides.
x+152-152=180-152
x=180-152
x=28
x is 28 degrees.
Find the area of the shape shown below.
Answer:
12 is the total areaStep-by-step explanation:
A of triangle = 1/2 * b * h
b = 6
h = 2
2 * 6 * 0.5
= 12 * 0.5
= 6A of square = l * w
2 * 2
= 4A of Triangle = 1/2 * b * h
2 * 2 * 0.5 =
4 * 0.5
= 22 + 4 + 6
= 6 + 6
= 12The city park department is planning to enclose a play area with fencing. One side of the area will be against an existing building, so no fence is needed there. Find the dimensions of the maximum rectangular area that can be enclosed with 800 meters of fence. Include the units.
Answer:
The maximum rectangular area will have the length 400 meters and width 200 meters with one side of the length against an existing building.
Step-by-step explanation:
From the given information;
The perimeter of a rectangle = 2 (L+B)
here;
L = the length of the side of the fence
B = the width of the fence
So; The perimeter of a rectangle = 2L+2B
we are also being told that;
One side of the area will be against an existing building
i.e
The perimeter of a rectangle is now = L + 2B = 800 meters
L = 800 - 2B
Similarly; Area of a rectangle = L × B
Area of a rectangle = ( 800 - 2B) × B
Area of a rectangle = 800B - 2B²
assuming A(B) to represent the Area;
Then the maximum area A'(B) = 0 ;
Thus,
A'(B) = 800 - 4B = 0
-4B = - 800
4B = 800
B = 200
Therefore; the maximum area have a width = 200 meters and a length 800 - 2(200) = 800 - 400 = 400 meters
Latesha’s mother puts $85 in Latesha’s lunch account at school. Each day Latesha uses $3 from her account for lunch. The table below represents this situation. Latesha’s Lunch Account Day Amount Left in Account ($) 0 $85 1 2 3 4 5 How much is left in Latesha’s lunch account after she has had lunch for 5 days? $15 $67 $70 $82
Answer: it 70
Step-by-step explanation:
Latesha’s mother puts $85 in Latesha’s lunch account at school. Each day Latesha uses $3 from her account for lunch. The table below represents this situation.
How much is left in Latesha’s lunch account after she has had lunch for 5 days?
$15
$67
$70 is correct$82
you tube guests are for hire
Assume that the random variable X is normally distributed, with mean p = 100 and standard deviation o = 15. Compute the
probability P(X > 112).
Answer:
P(X > 112) = 0.21186.
Step-by-step explanation:
We are given that the random variable X is normally distributed, with mean [tex]\mu[/tex] = 100 and standard deviation [tex]\sigma[/tex] = 15.
Let X = a random variable
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean = 100
[tex]\sigma[/tex] = standard deviaton = 15
Now, the probability that the random variable X is greater than 112 is given by = P(X > 112)
P(X > 112) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{112-100}{15}[/tex] ) = P(Z > 0.80) = 1- P(Z [tex]\leq[/tex] 0.80)
= 1 - 0.78814 = 0.21186
The above probability is calculated by looking at the value of x = 0.80 in the z table which has an area of 0.78814.
3 over 3 fourths divided by 5 over 7
Answer:
5.6
Step-by-step explanation:
(3÷3/4)÷5/7
[tex] \frac{3 \times 4}{3} \div \frac{5}{7} [/tex]
[tex]4 \div \frac{5}{7} [/tex]
[tex]4 \times \frac{7}{5} [/tex]
[tex] \frac{28}{5} [/tex]
=5.6
use "keep, change, flip " when dividing a number by a fraction.
keep the whole number
flip the divide sign to multiply
change the placement of number e.g. 5/7 becomes 7/8
then solve
A lake has a small patch of lily pads and every day the patch grows to double its size. It takes 32 days for the patch to cover the lake – how long would it take the patch to cover half the lake?
Answer:
It took 31 days for the patch to cover half the lake
Step-by-step explanation:
The patch grows to double its size everyday
the patch completely covers the lake in 32 days
Since the patch doubles itself everyday, this means that the previous day before the 32nd day, the lake was just half covered.
Therefore, the the patch covered half the lake on the 31st day, i.e it took 31 days for the patch to cover half the lake
Instructions: Find the missing length indicated.
Answer:
? = 3
Step-by-step explanation:
The parallel segments shown divide the sides in the ratio
[tex]\frac{6}{4}[/tex] = [tex]\frac{?}{2}[/tex] ( cross- multiply )
4? = 12 ( divide both sides by 4 )
? = 3
Please help me! I am really struggling with this...
Answer:
44°
Step-by-step explanation:
The secant- secant angle y is half the difference of the measure of its intercepted arcs, that is
[tex]\frac{1}{2}[/tex](BHF - CGJ ) = y , that is
[tex]\frac{1}{2}[/tex](156 - CGH) = 56° ( multiply both sides by 2 )
156 - CGH = 112° , thus
CGH = 156° - 112° = 44°
A car travels 120m along a straight road that is inclined at 8° to the horizontal. Calculate the vertical distance through which the car rises. (Sin 8°= 0.1392)
Answer:
16.704m
Step-by-step explanation:
To solve the above question, we are going to use the Trigonometric function of Sine.
sin θ = Opposite side/Hypotenuse
Where are given θ = 8°
Sin 8° = 0.1392
In the question, we are told that ,
A car travels 120m along a straight road that is inclined at 8° to the horizontal, hence,
Hypotenuse = 120m
We are asked to calculate the vertical distance through which the car rises hence,
Opposite side = vertical distance.
Therefore,
Sin 8° = Opposite/ 120m
Opposite = Sin 8° × 120m
Opposite = 0.1392 × 120m
Opposite = 16.704m
Therefore, the vertical distance through which the car rises is 16.704m
What is the solution to the system of equations graphed below?
Answer:
( 3 , -2 )Option B is the correct option.
Step-by-step explanation:
[tex]y = - 2x + 4...........(i)[/tex]
[tex]y = x - 5..........(ii)[/tex]
Equate ( i ) and ( ii ),
[tex] - 2x + 4 = x - 5[/tex]
Move variable to L.H.S and change its sign
Similarly, Move constant to R.H.S and change its sign
[tex] - 2x - x = - 5 - 4[/tex]
Calculate
[tex] - 3x = - 9[/tex]
Divide both sides of the equation by -3
[tex] \frac{ - 3x}{ - 3} = \frac{ - 9}{ - 3} [/tex]
Any expression divided by itself equals 1
[tex]x = \frac{ - 9}{ - 3} [/tex]
Dividing two negatives equals a positive [tex]( - ) \div ( - ) = ( + )[/tex]
[tex]x = \frac{9}{3} [/tex]
calculate the quotient
[tex]x = 3[/tex]
Value of X is 3
Now, put the value of X in equation ( i ) in order to find the value of y
[tex]y = x - 5[/tex]
plug the value of X
[tex] = 3 - 5[/tex]
Calculate
[tex] = - 2[/tex]
Value of y is -2
So, ( 3 , -2 ) is the solution of the given equation.
Hope this helps ....
Best regards!!
please help I will give brainiest I need your help!!!!
Answer:
Step-by-step explanation:
∠OAB is 90 degrees, tangent and a radius met at 90 degree angle
∠OCB=90 degrees, tan and radius meet at 90 degrees angle
OB=12
find angle BOC:
triangle BOA is right angle triangle:
cos(AOB)=adj/hyp=7/12=54.33
angle B= 180-(90+54.33)=35.67
angle COB=54.33 equal to angle AOB
angle AOC=54.33+54.33=108.66
the sum of angles of circle =360
360-108.66= 251.34( exterior angle at the center AOC)
length of the arc= angle (251.34 degrees*7)
convert degrees to radians=4.386 (251.34/π)
length=r*angle in radian=4.386*7=30.71
( i hope this is the answer)
A pound is approximately 0.45 kilogram. A person weighs 87 kilograms. What is the person’s weight, in pounds, when rounded to the nearest whole number?
Answer:
190
Step-by-step explanation:
the weight is 191 lbs rounded is 190
What is slope and how is it determined from a graph? How do you determine the intercepts from an equation or graph? How can linear equations and functions be written and graphed?
Hey there! I'm happy to help!
The slope is the steepness or incline of a line. From a graph, it is known as the rise over the run between two integer values. If you have a point at (1,1) and a point at (2,2), the rise (vertical difference) between them in 1 unit, and the run (horizontal difference) is 1 unit. 1/1 is 1, so the slope of a line that passes through these points is 1. This means that for every one unit to the right it goes, it goes one unit up.
The intercepts are where the line hits the x and y axes. By looking at a graph, you can find the y-intercept by seeing on what y-value the line intersects with the y-axis, and for the x-intercept you do so with the x-axis.
The slope-intercept equation is y=mx+b. This b is the y-intercept. To find the x-intercept, you plug in the value 0 for y and solve for x. This is because the x-axis is the line y=0, so you will see where the x is if y is equal to 0.
Linear equations and functions can be written in slope intercept form (y=mx+b), standard form (Ax+By=C), and point slope form [tex]y-y_{1} =m(x-x_{1} )[/tex].
They can be graphed by finding the y and x intercepts from the equation and then connecting the points to draw the line!
Have a wonderful day! :D
Please help if you are correct you get brainlyest
Answer:
did you already try A???
Answer:
Probability : [tex]\frac{5}{33}[/tex]
Step-by-step explanation:
The probability of drawing an orange on the first attempt would be 5 / 12, considering that in this first attempt their are 5 oranges present out of a total of 12 fruits. Now after that fruit is chosen their are 4 out of 11 oranges present, such that the probability of drawing an orange on the second attempt would be 4 / 11.
Probability of choosing an orange on the first try : [tex]5 / 12[/tex]
Probability of choosing an orange on the second try : [tex]4 / 11[/tex]
Probability of selecting two oranges in a row ( blindfolded ) : [tex]5 / 12 * 4 / 11[/tex]
[tex]\frac{5}{12}\cdot \frac{4}{11}[/tex] ( cross cancel common factor 4 )
[tex]\frac{5}{3}\cdot \frac{1}{11}[/tex] ( multiply fractions )
[tex]\frac{5\cdot \:1}{3\cdot \:11}[/tex] = [tex]\frac{5}{3\cdot \:11}[/tex] = [tex]\frac{5}{33}[/tex] - the probability of selecting two oranges in a row blindfolded, is [tex]\frac{5}{33}[/tex].
(i) The third and the seventh terms of an A.P. are 20 and 36 respectively. Find the first
term and the common difference,
Answer:
The first term is 12. The common difference is 4.
Step-by-step explanation:
[tex] a_n = a_1 + d(n - 1) [/tex]
The difference between the third and seventh terms is
36 - 20 = 16
The 7th term is the 4th term after the 3rd term, so the common difference is
16/4 = 4
[tex] a_3 = a_1 + 4(3 - 1) [/tex]
[tex] 20 = a_1 + 4(3 - 1) [/tex]
[tex] 20 = a_1 + 8 [/tex]
[tex] a_1 = 12 [/tex]
Answer: The first term is 12. The common difference is 4.
Please help me, I'm so confused
Answer:
C
Step-by-step explanation:
x+4> 8
Subtract 4 from each side
x+4-4>8-4
x > 4
Open circle at 4, line going to the right
━━━━━━━☆☆━━━━━━━
▹ Answer
[tex]Solved - x > 4\\Graphed - C[/tex]
▹ Step-by-Step Explanation
x + 4 > 8
x > 8 -4
x > 4
When graphing inequalities, you have less than, greater than, less than or equal to, and greater than or equal too. When graphing an inequality with less than or greater than, you use an open circle. When graphing an inequality with less than or equal too or greater than or equal too, you used a closed circle.
Since the numbers are positive, we are going to move up the number line therefore leaving us with the answer of C.
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
I would REALLY appreciate if you could help me with this question. I am REALLY stuck...
Answer: D) Construct the perpendicular bisectors for AB and AC.
The intersection of all three perpendicular bisectors will form the circumcenter, which is the center of the circumcircle. This circle goes through all three corner points of the triangle. At minimum, you only need two perpendicular bisectors to get the job done. Choice B is close, but is missing that second perpendicular bisector.
The angle bisectors intersect to form the incenter, which is the center of the incircle (it's the largest possible circle to fit inside the triangle without spilling over).
Answer:
D. Construct the perpendicular of ab and ac
Step-by-step explanation:
Circumscribe a Circle on a Triangle
Construct the perpendicular bisector of one side of the triangle.
Construct the perpendicular bisector of another side.
Where they cross is the center of the Circumscribed circle.
Place compass on the center point, adjust its length to reach any corner of the triangle, and draw your Circumscribed circle
Mark me as brainliest
Determine whether the given lengths can be sides of a right triangle. Which of the following are true statements? The lengths 14, 24 and 26 cannot be sides of a right triangle. The lengths 30, 72, and 78 can be sides of a right triangle. The lengths 14, 24 and 26 can be sides of a right triangle. The lengths 30, 72, and 78 cannot be sides of a right triangle. The lengths 14, 24 and 26 can be sides of a right triangle. The lengths 30, 72, and 78 can be sides of a right triangle. The lengths 14, 24 and 26 cannot be sides of a right triangle. The lengths 30, 72, and 78 cannot be sides of a right triangle.
Answer:
The lengths 14, 24, and 26 cannot be the sides of a right triangle. The lengths 30, 72, 78 can be the sides of a right triangle.
Step-by-step explanation:
To prove that the lengths 14, 24, and 26 cannot be the sides of a right triangle:
a=14, b=24, c=26
Pythagoreon theorem: a^2+b^2=c^2
substitute values in: 14^2+24^2=26^2
simplify: 196+576=676
simplify again: 772=676, which is not true
This proves that the lengths 14, 24, and 26 cannot be the sides of a right triangle.
To prove that the lengths 30, 72, and 78 can be the sides of a right triangle:
a=30, b=72, c=78
Pythagoreon theorem: a^2+b^2=c^2
substitute values in: 30^2+72^2=78^2
simplify: 900+5184=6084
simplify again: 6084=6084, which is true
This proves that the lengths 30, 72, and 78 can be the sides of a right triangle.
Answer:
true, true, false,false, false,true,true,false
See explanations below
Step-by-step explanation:
If three sides can make a RIGHT triangle, then the sum of squares of the two shorter sides EQUALS the square of the third side, using the Pythatorean theorem.
Determine whether the given lengths can be sides of a right triangle. Which of the following are true statements?
The lengths 14, 24 and 26 cannot be sides of a right triangle.
TRUE, A^2+B^2-C^2=4sqrt(6)
The lengths 30, 72, and 78 can be sides of a right triangle.
TRUE, A^2+B^2-C^2= 0
The lengths 14, 24 and 26 can be sides of a right triangle.
FALSE, A^2+B^2-C^2=4sqrt(6)
The lengths 30, 72, and 78 cannot be sides of a right triangle.
FALSE, A^2+B^2-C^2= 0
The lengths 14, 24 and 26 can be sides of a right triangle.
FALSE, A^2+B^2-C^2=4sqrt(6)
The lengths 30, 72, and 78 can be sides of a right triangle.
TRUE, A^2+B^2-C^2= 0
The lengths 14, 24 and 26 cannot be sides of a right triangle.
TRUE, A^2+B^2-C^2=4sqrt(6)
The lengths 30, 72, and 78 cannot be sides of a right triangle.
FALSE, A^2+B^2-C^2= 0
what is the simplified form of the expression (6-4)-9/6
Answer: 1/2
Step-by-step explanation:
solving bracket first we get
2 - 9/6
multiplying and dividing 2 by 6 we get
12/6 - 9/6
=3/6 = 1/2
Answer:
1/2
Step-by-step explanation:
(6-4)-9/6
= (2)-9/6
= 12/6-9/6
= 3/6
= 1/2
PLEASE help me with this question! I really need help...
Answer:
The third: [tex]\bold{\dfrac{x+5}{x+15}}[/tex]Step-by-step explanation:
[tex]x^2+19x+70\ \implies a=1\,,\ b=19\,,\ c=70\\\\x=\frac{-19\pm\sqrt{19^2-4\cdot1\cdot70}}{2\cdot1}=\frac{-19\pm\sqrt{361-280}}{2}=\frac{-19\pm9}{2}\ \Rightarrow\ x_1=-14\,,\ x_2=-5\\\\x^2+19x+70=(x+14)(x+5)\\\\\\x^2-225=x^2-(15)^2=(x-15)(x+15)\\\\\\x^2-5x-150\ \implies a=1\,,\ b=-5\,,\ c=-150\\\\x=\frac{-(-5)\pm\sqrt{(-5)^2-4\cdot1\cdot(-150)}}{2\cdot1}=\frac{5\pm\sqrt{25+600}}{2}=\frac{5\pm25}{2}\ \Rightarrow\ x_1=-10\,,\ x_2=15\\\\x^2-5x-150=(x+10)(x-15)[/tex]
[tex]x^2+24x+140\ \implies a=1\,,\ b=24\,,\ c=140\\\\x=\frac{-24\pm\sqrt{24^2-4\cdot1\cdot140}}{2\cdot1}=\frac{-24\pm\sqrt{576-560}}{2}=\frac{-24\pm4}{2}\ \Rightarrow\ x_1=-14\,,\ x_2=-10\\\\x^2-5x-150=(x+14)(x+10)[/tex]
[tex]\dfrac{x^2+19x+70}{x^2-225}\,\cdot\,\dfrac{x^2-5x-150}{x^2+24x+140}=\dfrac{(x+14)(x+5)}{(x-15)(x+15)}\cdot\dfrac{(x+10)(x-15)}{(x+14)(x+10)}=\\\\\\=\dfrac{(x+14)(x+5)}{(x-15)(x+15)}\cdot\dfrac{x-15}{x+14}=\dfrac{x+5}{x+15}\cdot\dfrac11=\boxed{\dfrac{x+5}{x+15}}[/tex]
Answer:
The answer is option 3.
Step-by-step explanation:
First, you have to factorize the expressions :
[tex] \frac{ {x}^{2} + 19x + 70 }{ {x}^{2} - 225 } \times \frac{ {x}^{2} - 5x - 150}{ {x}^{2}24x + 140 } [/tex]
[tex] = \frac{(x + 5)(x + 14)}{(x + 15)(x - 15)} \times \frac{(x - 15)(x + 10)}{(x + 10)(x + 14)} [/tex]
Next, you have to cut out the common terms like (x + 14), (x - 15) and (x + 10):
[tex] \frac{(x + 5)(x + 14)}{(x + 15)(x - 15)} \times \frac{(x - 15)(x + 10)}{(x + 10)(x + 14)} [/tex]
[tex] = \frac{x + 5}{x + 15} [/tex]
Simplify this problem. |3r−15| if r<5
Answer:
We have the problem:
|3r−15| if r<5
First we see the equality, if r = 5 we have:
I3r - 15I = I3*5 - 15I = I0I = 0.
Then the only restriction that we have is:
I3r - 15I > 0.
now, we could simplify it a bit further:
if r < 5, then the thing inside the absolute value will always be negative:
Then we can write:
I3*r - 15I = -(3*r -15) > 0
multiplying by -1 in both sides
(3r - 15) < 0.
if we keep simplifying this, we will get our initial restriction:
3r - 15 < 0
3r < 15
r < 15/3 = 5
r < 5
A theater group made appearances in two cities. The hotel charge before tax in the second city was $500 higher than in the first. The tax in the first city was 4.5%, and the tax in the second city was 3.5% . The total hotel tax paid for the two cities was $317.50. How much was the hotel charge in each city before tax? First city: Second city:
Answer:
$3750 and $4250
Step-by-step explanation:
x + 500 = y
.045x + .035y = 317.50
.045x + .035(x + 500) = 317.50
.045x + .035x + 17.5 = 317.50
.08x = 300.00
x = 3750
y = 4250