Which expression is equivalent to 2 (14x-37+28x+12.2-5y-17.5)?
A. 84x-16y-10.6
B. 28x-6y-10.6
C. 42x-8y-5.3
D 84x-16y-5.3
Answer:
A. 84x - 16y - 10.6
Explanation:
[tex]\sf \rightarrow 2(14x-3y+28x+12.2-5y-17.5)[/tex]
[tex]\sf \rightarrow 2 (42x-8y-5.3)[/tex]
apply distributive method: a(b + c) = ab + ac
[tex]\sf \rightarrow 2 (42x) -2(8y)-2(5.3)[/tex]
[tex]\sf \rightarrow 84x -16y-10.6[/tex]
f(x) = x+3 f ( x ) = x + 3
Answer + Step-by-step explanation:
y = mx + b where m is the slope and b is the y-intercept
y = x + 3 where m = 1 is the slope and b = 3 is the y-intercept
Table of some points:
| x | 0 | 1 | 2 | 3 |
| y | 3 | 4 | 5 | 6 |
when x = 0, y = 0 + 3 and y = 3
when x = 1, y = 1 + 3 and y = 4
when x = 2, y = 2 + 3 and y = 5
Graph:
One root of f (x) = x cubed 10 x squared minus 25 x minus 250 is x = –10. what are all the roots of the function? use the remainder theorem.
Answer:
x= -10 , x= -5 , x=5
Step-by-step explanation:
we are given function as
x^3+10x^2-25x-250
We are given one of zero is x=-10
we can find all possible factors of 250
so, we will check zeros at x=-5 and x=5
At x=-5:
we can plug x=-5
At x=5:
we can plug x=5
So, other zeros are
x=-5 and x=5
All zeros are
x=-10 , x=-5 , x=5
A circle has a diameter with endpoints (-7, 1) and (-3, 7).
What is the equation of the circle?
r2 = ( x - 3) 2 + ( y + 4) 2
r2 = ( x + 3) 2 + ( y - 4) 2
r2 = ( x + 5) 2 + ( y - 4) 2
r2 = ( x - 5) 2 + ( y + 4) 2
Can someone please teach me how to do this? You can please do like 2 questions and please explain exactly how you got the answers so I can do the rest myself. please
All of these questions require one thing: trigonometric functions.
There are 3 main trigonometric functions, which can only be used on right triangles: sine, cosine, and tangent.
Sine = opposite / hypotenuse
Cosine = adjacent / hypotenuse
Tangent = opposite / adjacent
When trying to figure out what function to use, we always start by looking from the angle. Take problem a, for example. Looking from angle E, of which the value is not given, we have the side opposite and the side adjacent. Therefore, we should use the tangent function.
---The hypotenuse is always the longest side of the triangle. It is never considered the opposite or adjacent side.
Let's set up our function with the given information from problem a.
tan(x) = 9.7 / 5.2
---The tangent of an unknown angle is equal to the quotient of the opposite side and the adjacent side.
Now, solving for the value of x will require a calculator. We'll need to use what's called an inverse trigonometric function. Most calculators have these directly above the regular trigonometric functions, and the inverse functions are accessed using a "second" key.
---Ensure that your calculator is in degrees, not radians!
x = tan^-1(9.7 / 5.2)
x = 61.805 = 62 degrees
Next, let's take a look at problem b. This time, we're solving for a side length instead of an angle. But, we're still going to start by looking from our angle.
Looking from the 38 degree angle, we are given the adjacent side and an unknown hypotenuse. Therefore, we should use the cosine function.
cosine(38) = 53.1 / r
---The cosine of a 38 degree angle is equal to the quotient of 53.1 and an unknown hypotenuse, r.
Use your algebra skills to isolate the variable r.
r * cosine(38) = 53.1
r = 53.1 / cosine(38)
---From here, all you need to do is plug this into your calculator. Since we are solving for a side length (and given an angle), we are just using the regular trigonometric function buttons on the calculator.
r = 67.385 = 67.4 units
Hope this helps!
In a group of 20 pupils, 3 play the flute only.
6 play the piano only.
6 play both instruments.
A student is chosen at random.
What is the probability the student plays neither instrument?
Please answer in fractional form!!
Answer:
[tex]\dfrac{1}{4}[/tex]
Step-by-step explanation:
Given information:
Total number of pupils = 203 pupils play the flute6 pupils play the piano only6 play both instrumentsWe can assume that 3 pupils play the flute only as we have also been told that 6 pupils play both instruments.
To calculate the probability that a randomly chosen pupil plays neither instrument, first determine how many pupils do not play an instrument by subtracting the number of pupils who do play an instrument from the total number of pupils:
⇒ total number of pupils - pupils who play instruments
⇒ 20 - (3 + 6 + 6)
⇒ 20 - 15
⇒ 5
Therefore, 5 pupils do not play the piano and/or flute.
To calculate probability:
[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
Therefore:
[tex]\implies \textsf{Probability of a pupil playing neither instrument} = \dfrac{5}{20}=\dfrac{1}{4}[/tex]
What trigonometric ratio would you use to find the distance from the base of the tower of your keys ? Identify your choice, then calculate the distance
The choice trigonometric ratio is tangent and the distance is 3. 98 meters.
How to determine the trigonometric ratioThe given angle is 86
The opposite side is given as 57 meters
The distance is in the adjacent
Thus, trigonometric ratio to use is the tangent
Tangent = opposite/ adjacent
We have,
tan 86 = 57/x
14. 300 = 57/x
x = 57/ 14. 300
x = 3.i 98 meters
Thus, the choice trigonometric ratio is tangent and the distance is 3. 98 meters.
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An ongoing promotion at a department store gives customers 20\%20%20, percent off the portion of their bill that is over \$100$100dollar sign, 100. Ruby's total bill at the department store after the promotion has been applied is \$250$250dollar sign, 250. If xxx represents the amount of money Ruby would have spent on the same purchase at the department store without the promotion, which of the following equations best models the situation?
The equation best models the situation 100 + 0.8(x - 100) = 250.
The correct option is (D)
What is equation?
An equation in math is an equality relationship between two expressions written on both sides of the equal to sign.
The complete question is:
An ongoing promotion at a department store gives customers 20% off the portion of their bill that is over $100. Ruby's total bill at the department store after the promotion has been applied is $250. If x represents the amount of money Ruby would have spent on the same purchase at the department store without the promotion, which of the following equations best models the situation?
A. 0.2x + 100 = 250
B. 0.8x + 100 = 250
C. 100 + 0.2(x - 100) = 250
D. 100 + 0.8(x - 100) = 250
Given:
Department store gives 20 % off the portion of the bill that is over 100 dollars.
Total bill = 250
let x is the amount of money she would have spent without the promotion.
Then, cost after discount applies = 0.8 ( x - 100 ).
Hence, the equation is 100 + 0.8 (x - 100) = 250.
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You toss a coin and roll a number cube. Find P(heads and an even number.)
Answer:
The events are independent (the outcome of flipping thee coin has no effect on the outcome of rolling the die).
The events are independent (the outcome of flipping thee coin has no effect on the outcome of rolling the die).⇒
The events are independent (the outcome of flipping thee coin has no effect on the outcome of rolling the die).⇒ P(head and an even number)
The events are independent (the outcome of flipping thee coin has no effect on the outcome of rolling the die).⇒ P(head and an even number) = P(head) × P(even number)
P(even number)Assuming a fair coin and a fair die:
P(even number)Assuming a fair coin and a fair die:P(head)
P(even number)Assuming a fair coin and a fair die:P(head) =50%
P(even number)Assuming a fair coin and a fair die:P(head) =50%P(even number)
P(even number)Assuming a fair coin and a fair die:P(head) =50%P(even number) =50%
P(even number)Assuming a fair coin and a fair die:P(head) =50%P(even number) =50% (since half the numbers on a die are even).
P(even number)Assuming a fair coin and a fair die:P(head) =50%P(even number) =50% (since half the numbers on a die are even).P(head and even number)
P(even number)Assuming a fair coin and a fair die:P(head) =50%P(even number) =50% (since half the numbers on a die are even).P(head and even number) =50%×50%=25%
Which equations are true?
Select all that apply
A) -x + (-x) =0
B) x - (-x) = 0
C) None of the above.
The correct answer from the task content is; Choice C; None of the above.
Which of the equations are true?The equations can be evaluated as follows;
A) -x + (-x) =0
-x -x = -2x......Not True
B) x -(-x) = 0
x + x = 2x .....Not True.
On this note, it follows that none of the equations is true.
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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
One leg of a right triangle is 2 inches and the hypotenuse is 6 inches.
Find the area of the triangle.
_[tex]\sqrt{x} \\[/tex]
We can see that the area of the triangle is: 5.65in².
What is a triangle?A triangle is actually known to be a shape that has three sides, three angles and three vertices. It's also known as a plane shape.
In order to find the area of the triangle, we will use Pythagorean Theorem: c² = a² + b².
Where c = hypotenuse = 6in.
b = 2in.
6² = a² + 2²
36 = a² + 4
a² = 36 - 4 = 32
a = √32
Area of the triangle = ½ × base × height.
Where base = √32
height = 2
Thus: A = ½ × √32 × 2
A = √32 = 5.65in².
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Colin walked a distance of 15m in 6 hours. Work out Collin's average speed. Give your answer in miles per hour
2.5 miles/hour
Simply 15/6
Answer:
Colin walks an average speed of 2.5 miles per hour.
Step-by-step explanation:
15/6= 5 miles/2 hours
2.5
x(x+3)-2(-5x+1)x=x^2-3(4-2x)
The answer is no solution
Explanation:
it depends on how you interpret what's written. The way I initially interpreted it*, I was able to use the quadratic formula to find :
[tex]x=\frac{1}{4}-i\frac{\sqrt{455}}{20},\:x=\frac{1}{4}+i\frac{\sqrt{455}}{20}[/tex]
*I interpreted it as: [tex]x\left(x+3\right)-2\left(-5x+1\right)x=x^2-3\left(4-2x\right)[/tex]
but I don't want to say that this is your correct answer, because there are multiple interpretations (like a lot of interpretations)
{this is mostly in response to other answers}
This image of a physics problem shows a block resting on a ramp, . ∠P is the angle between the ramp and the horizontal, and is oriented vertically. Which quantity is equal to cos W?
A. sin p
b. cos p
c. 1 - sin p
d. 1 - cos p
Based on the image description, the quantity that is equal to cos W is sin P.
What is the image about?The image is known to be showing an object on a ramp. Based on it, we can therefore take the angle a to the complementary angle of angle w.
Note that the angle w and angle b are said to be the same via alternate interior angles. Therefore, the quantity that is equal to cos W is sin P.
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Suppose y varies directly as x², and y = 160 when x = 4. Find y when x = 6.
Finding the constant of proportionality :
y = kx²160 = k(4)²k = 10Finding y when x = 6 :
y = 10(6)²y = 10(36)y = 360The value of y is 360 when x = 6.
Divide 140 in the ratio 2:5
Answer:
40 : 100
Step-by-step explanation:
→ Find the sum of the ratio
2 + 5= 7
→ Divide 140 by the answer
140 ÷ 7 = 20
→ Multiply each part of the ratio by 20
40 : 100
There are 39 adults and 26 children registered for a seminar. the seating is to be arranged so each row has the same number of people. all of the people in a row must be in the same age group. how many rows of seats are needed to seat the greatest possible number of participants in each row?
The number of rows of seats needed to seat the greatest possible number of participants in each row is 5
What is Highest Common Factor ?The highest common factor is the highest number that divides the numbers given.
On the basis of given data
Total number of children = 26
Total number of adults = 39
The highest common factor of both the number is 13 ,
Therefore the highest possible number of people that can sit in one row so that the number is in constant in all the rows.
So 2 rows of children of 13 each and
3 rows of adult of 13 each
Which makes the total number of rows = 5
Therefore the number of rows of seats needed to seat the greatest possible number of participants in each row is 5
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P(Ω)
P(A)
0.4
0.1
P(B)
0.2
0.3
Answer:
i dont even have the first one on my computer
Step-by-step explanation:
A roof repairman charges a $60 consult fee, and then $45 per hour to complete repairs. if the homeowner pays a total of $195, how long was the repairman there? answers a: 2 hours b: 2.5 hours c:4 hours d: 3 hours
The time spent by the repairman there will be 3 hours so the correct answer is option D.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that:-
A roof repairman charges a $60 consult fee, and then $45 per hour to complete repairs. if the homeowner pays a total of $195.
The time will be calculated as:-
Total amount = $195
Now the fixed consulting cost will be $60 and will be deducted from the
total amount.
Variable cost = 195 - 60 = 135
The $45 per hour charge so for $145 the time will be:-
Time = 135 / 45
Time = 3 Hours
Therefore the time spent by the repairman there will be 3 hours so the correct answer is option D.
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Approximate the area under the curve y = x^2 from x = 0 to x = 3 using a Right Endpoint approximation with 6 subdivisions.
Will mark brainliest
Subdivide the interval [0, 3] into 6 subintervals of equal length, ∆x = (3 - 0)/6 = 1/2. Then the partition is
[tex]\left[0,\dfrac12\right] \cup \left[\dfrac12,1\right] \cup \left[1,\dfrac32\right] \cup \cdots \cup \left[\dfrac52,3\right][/tex]
The right endpoint of the [tex]i[/tex]-th subinterval is
[tex]r_i = \dfrac12 + (i-1)\times\dfrac12 = \dfrac i2[/tex]
with [tex]i\in\{1,2,3,\ldots,6\}[/tex].
Then the area under the [tex]y=x^2[/tex] on the interval [0, 3] is approximately
[tex]\displaystyle \int_0^3 x^2 \, dx \approx \sum_{i=1}^6 (r_i)^2 \Delta x = \frac18 \sum_{i=1}^6 i^2[/tex]
Recall that
[tex]\displaystyle \sum_{n=1}^N n^2 = \frac{N(N+1)(2N+1)}6[/tex]
Then the approximate value of the area is
[tex]\displaystyle \int_0^3 x^2 \, dx \approx \frac{6\times7\times13}{48} = \boxed{\frac{91}8}[/tex]
The actual value of the area is 9, so this approximation is an overestimation, as is always the case when using a right endpoint sum for an increasing function.
An adult male cheetah runs at a speed of 26 mph. That is 30% faster than his average last month. How fast did the male cheetah run last month?
Sadie makes 1.5 liters of iced tea. She pours of a liter into a pitcher to take to her neighbor. Her sister drinks of the remaining iced tea. How much tea does Sadie’s sister drink?
Answer:
20 mph
Step-by-step explanation:
First problem:
The new speed is 26 mph.
The old speed was x.
The new speed is 30% higher than the old speed.
1.3x = 26
x = 20
Answer: 20 mph
Second problem:
A number, perhaps a percent or a fraction, is missing from the problem.
What is the equation of the line that passes through the point (6,-4) and has a slope
of-?
Answer:
y = -x + 2
Step-by-step explanation:
*Assuming the slope given is -1*
Applying point-slope formula :
y - (-4) = -1 (x - 6)y + 4 = -x + 6y = -x + 2Which expression is equivalent to \frac{r^9}{r^3}
Answer:
[tex]\sf r^6[/tex]
Step-by-step explanation:
Exponent law:[tex]\boxed{\bf \dfrac{a^m}{a^n}=a^{m-n}}[/tex]
In exponent division, if bases are same, subtract the powers.
[tex]\sf \dfrac{r^9}{r^3}=r^{9-3}=r^{6}[/tex]
Solve for x and show your steps. Is the solution extraneous? Check your work to show how you determined if the solution is extraneous or not.
[tex]\sqrt{4x-3}=5[/tex]
Answer:
x = 7
Step-by-step explanation:
[tex](\sqrt{4x-3} )^{2} =5^{2}[/tex]
[tex]4x-3=25[/tex]
[tex]4x=25+3[/tex]
[tex]x=\frac{28}{4}[/tex]
[tex]x=7[/tex]
Hope this helps
graph the line with slope -1/2 passing through the point (5,-3)
Step-by-step explanation:
The graph is shown in the image above.
Answer: Draw a line through the two points (5,-3) and (7,-4)
See the diagram below.
=======================================================
Explanation:
Start at (5,-3). Then move down 1 and to the right 2 units to arrive at (7,-4)
The motion of "down 1, right 2" is from the slope of -1/2
slope = rise/run = -1/2
rise = -1 = go down 1 unit
run = 2 = go 2 units to the right
Two points are the minimum amount needed to draw any line. Plot the two points (5,-3) and (7,-4) and draw a straight line through them as shown in the diagram below. I used GeoGebra to make the graph. Desmos is another tool you could use.
Now that you have x² - 8x 16 = 9 16, apply the square root property to the equation.
The square root property to the equation will be (x – 4)² = 25. And the solutions will be the negative 1 and 9.
What is a quadratic equation?The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2. Then we have
The equation is given below.
x² – 8x + 16 = 9 + 16
Then the equation can be written as
(x – 4)² = 25
x – 4 = ±5
x = 4 ± 5
x = -1, 9
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Y=-5x +6 Y= 3x -2 Find the solution to the system of equations
X = _____
Y= _____
Answer:
x=1, y=1. (1, 1).
Step-by-step explanation:
y=-5x+6
y=3x-2
------------
-5x+6=3x-2
-5x-3x+6=-2
-8x+6=-2
-8x=-2-6
-8x=-8
8x=8
x=8/8=1
y=3(1)-2=3-2=1
1. Use the given conditions to write an equation for the line in point-slope form and general form. Passing through (−4,4) and parallel to the line whose equation is 7x−9y−8=0 Question content area bottom Part 1 The equation of the line in point-slope form is enter your response here. (Type an equation. Use integers or fractions for any numbers in the equation.) Part 2 The equation of the line in general form is enter your response here=0. (Type an expression using x and y as the variables. Simplify your answer. Use integers or fractions for any numbers in the expression.)
1) The equation of the line passing through (−4, 4) and parallel to the line whose equation is 7x − 9y − 8 = 0 is; y - 4 = ⁷/₉(x + 4)
How to find the equation of a line?
1) We are told that the line passes through (−4, 4) and is parallel to the line whose equation is 7x − 9y − 8 = 0
Thus, let us rearrange to find the slope.
7x − 9y − 8 = 0
⇒ 9y = 7x - 8
⇒ y = ⁷/₉x - ⁸/₉
Slope; m = ⁷/₉
Now, the point slope formula is;
y − y₁ = m(x − x₁)
where;
y₁ is the y-coordinate
x₁ is the x-coordinate
m is the slope
Thus the line Passing through (−4,4) is;
y - 4 = ⁷/₉(x + 4)
2) The equation in general form is;
y = 4 + ⁷/₉x + ²⁸/₉
y = ⁷/₉x + ⁶⁴/₉
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If the price of an apple is Rs. 40, find the number of apples that can be brought for Rs. 200.
Answer:
5
Step-by-step explanation:
Divide 200 by 40 to get 5.
Answer:
ig 5 Apples can be Brought with Rs. 200
Step-by-step explanation:
Rs. 40 = 1 apple
Rs. 200 = ? Apple
therefore 5 apples can be brought...
Hope it Helps!!!
Can someone help please?
Thank you.
Answer:
B and C are the answers.
Step-by-step explanation:
3b+b = 4b because the value of B or any variable is 1 so 3 +1 is four and 4b is our answer.
2(2b) the brackets tell the number before brackets should be multiplied and 2 × 2 is 4 so the answer is 4b
