Answer:
The answer is 117/125
Step-by-step explanation:
The identity for the difference of 2 angles as far as cos goes is
cos(α-β) = cosα cosβ + sinα sinβ
We have both alpha and beta in QII. In order to find the sinα, we need the missing leg, the one opposite the reference angle. Applying Pythagorean's Theorem to that right triangle we get that the missing leg is +7 (y values are positive here so the 7 is positive since it is above the y = 0 line). We also have to find the missing leg in beta so we can find the cosβ. Applying Pythagorean's Theorem to that right triangle we get that the missing leg is -4 (negative because x is negative to the left of the origin). Now that we have everything we need to fill in the identity, it looks like this:
[tex](-\frac{24}{25})(-\frac{4}{5})+(\frac{7}{25})(\frac{3}{5})[/tex]
Multiplying that out and then adding gives you
[tex]\frac{96}{125}+\frac{21}{125}=\frac{117}{125}[/tex]
Assume a gas is at a constant temperature. If its initial pressure, final pressure, and initial volume are 150 kPa, 200 kPa, and 25 cm3, respectively, what is its final volume?
A.
20 cm3
B.
25 cm3
C.
33.33 cm3
D.
18.75 cm3
E.
22.5 cm3
Answer:
Option D. 18.75 cm3
Step-by-step explanation:
we know that
The Boyle's law (Ideal gas law) states that Where temperature remains constant, the pressure is inversely proportional to volume.
so
[tex]P1 *V1 = P2 *V2[/tex]
In this problem we have
P1=150 kPa
P2=200 kPa
V1=25 cm³
substitute and solve for V2
[tex](150)(25)= 200*V2[/tex]
[tex]V2=(150)(25)/200=18.75\ cm^{3}[/tex]
Answer:
Option D. 18.75 cm3
Step-by-step explanation:
MARK ME PLS
If a 150 bed facility averages 90% occupancy, and during a 30 day month has total expenses of 202, 500, what is the average cost per resident per day
Answer:
$50/day
Step-by-step explanation:
If 90% of 150 beds are occupied, the .90 × 150 are occupied, or 135 beds. The total expenses for ALL the residents for the month is 202,500. We need the cost per day for all the residents, then when we know that we can find the cost per day of one resident.
202,500 ÷ 30 = $6750 for one day for ALL residents
$6750 ÷ 135 = $50 for one day for a single resident
To find the average cost per resident per day for a facility with an average 90% occupancy rate, multiply the number of beds by the occupancy rate to find the average daily occupancy, then multiply by the number of days in the month to get total resident-days. Finally, divide the total monthly expenses by the total resident-days to get the average daily cost per resident.
Explanation:To calculate the average cost per resident per day in a 150 bed facility with a 90% average occupancy rate over a 30-day month with total expenses of $202,500, we can follow these steps:
Determine the average number of occupied beds per day by multiplying the total number of beds by the occupancy rate.Calculate the total number of resident-days by multiplying the average number of occupied beds by the number of days in the month.Divide the total expenses by the total number of resident-days to find the average cost per resident per day.So, first we find the average number of occupied beds per day:
150 beds × 90% = 135 occupied beds per day.
Next, we calculate the total number of resident-days for the month:
135 occupied beds × 30 days = 4050 resident-days.
Finally, we find the average cost per resident per day:
$202,500 total expenses ÷ 4050 resident-days = $50 per resident per day.
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which description matches the transformations y=cos x undergoes to produce y=-2cos3x?
A. horizontal compression by factor 3, vertical stretch by factor 2, then reflection across the x-axis.
B. horizontal shift left 2 units, then vertical shift up by 3 units.
C. reflection across the y-axis, vertical shift up by 2 units, horizontal shift right by 3 units.
D. horizontal stretch by factor 2, reflection across the x-axis, then vertical stretch by factor 3.
Answer:
horizontal compression by factor 3, vertical stretch by factor 2, then reflection across the x-axis ⇒ answer A
Step-by-step explanation:
* Lets revise some transformation
- A vertical stretching is the stretching of the graph away from
the x-axis
# If k > 1, the graph of y = k•f(x) is the graph of f(x) vertically stretched
by multiplying each of its y-coordinates by k.
# If k should be negative, the vertical stretch is followed by a reflection
across the x-axis.
- A horizontal compression is the squeezing of the graph toward
the y-axis.
# If k > 1, the graph of y = f(k•x) is the graph of f(x) horizontally
compressed by dividing each of its x-coordinates by k.
* Lets solve the problem
∵ y = cos x
∵ y = -2 cos 3x
- At first cos x multiplied by -2
∵ y multiplied by -2
∵ 2 > 1
∴ y = cos x is stretched vertically by factor 2
∵ The factor 2 is negative
∴ y = cos x reflected across the x-axis
∴ The function y = cos x stretched vertically with factor 2 and then
reflected across the x-axis ⇒ (1)
∵ cos x changed to cos 3x
∵ x multiplied by 3
∵ 3 > 1
∴ y = cos x compressed horizontally by factor 3
∴ The function y = cos x compressed horizontally by factor 3 ⇒ (2)
- From (1) and (2)
* The function y = cos x has horizontal compression by factor 3,
vertical stretch by factor 2, then reflection across the x-axis to
produce y = -2 cos 3x
Answer:
It is A
Step-by-step explanation:
AP3x
Which system of equations is represented by the graph?
Answer:
C
Step-by-step explanation:
y=x is a line that has slope 1 meaning it go ups (increases) from left to right.
So that puts us at choice A or C.
Both A or C differ by the numerator for the other function.
We can find the x-intercept for A and C by setting the numerator equal to 0 and solving for x.
Let's do that:
A: -x-10=0 C. -x+10=0
-x=10 -x=-10
x=-10 x=10
A says x-intercept -10
C says x-intercept 10
Your graph intercepts the x-axis at 10 so the answer is C.
A company has determined that it's weekly profit is a function of the number of items that it sells. Which equation could represent the weekly profit in thousands of dollars, why, when the company sells X items?
Answer:
b
Step-by-step explanation:
If θ is an angle in standard position that terminates in Quadrant III such that tanθ = 5/12, then sinθ/2 = _____.
Answer:
[tex]\displaystyle \sin{\frac{\theta}{2}} = \frac{5\sqrt{26}}{26}\approx 0.196[/tex].
Step-by-step explanation:
[tex]\displaystyle \theta\in \left(\pi, \frac{3\pi}{2}\right)[/tex],
such that
[tex]\displaystyle \frac{\theta}{2} \in \left(\frac{\pi}{2}, \frac{3\pi}{4}\right)[/tex].
As a result,
[tex]\displaystyle 0 < \sin{\frac{\theta}{2}} <1[/tex], and[tex]\displaystyle -1 < \cos{\frac{\theta}{2}} <0[/tex].[tex]\displaystyle \tan{\frac{\theta}{2}} = \frac{\sin{\displaystyle \frac{\theta}{2}}}{\displaystyle \cos{\frac{\theta}{2}}}[/tex],
such that
[tex]\displaystyle \tan{\frac{\theta}{2}} <0[/tex].Let
[tex]\displaystyle t = \tan{\frac{\theta}{2}}[/tex].
[tex]t < 0[/tex].
By the double angle identity for tangents.
[tex]\displaystyle \frac{\displaystyle 2\tan{\frac{\theta}{2}}}{1-\displaystyle \left(\tan{\frac{\theta}{2}}\right)^{2}} = \tan{\theta}[/tex].
[tex]\displaystyle \frac{2t}{1 - t^{2}} = \frac{5}{12}[/tex].
[tex]24t = 5 - 5t^{2}[/tex].
Solve this quadratic equation for [tex]t[/tex]:
[tex]\displaystyle t_1 = \frac{1}{5}[/tex], and[tex]t_2 = -5[/tex].Discard [tex]t_1[/tex] for it is not smaller than zero.
Let [tex]\displaystyle s = \sin{\frac{\theta}{2}}[/tex].
[tex]0 < s <1[/tex].
By the definition of tangents:
[tex]\displaystyle \tan{\frac{\theta}{2}} = \frac{\displaystyle \sin{\frac{\theta}{2}}}{\displaystyle \cos{\frac{\theta}{2}}}[/tex].
Apply the Pythagorean Algorithm to express the cosine of [tex]\displaystyle \frac{\theta}{2}[/tex] in terms of [tex]s[/tex]. Note that [tex]\displaystyle \cos{\frac{\theta}{2}}[/tex] is expected to be smaller than zero.
[tex]\displaystyle \cos{\frac{\theta}{2}} = -\sqrt{1 - \left(\sin{\frac{\theta}{2}}\right)^{2}}= - \sqrt{1 - s^{2}}[/tex].
Solve for [tex]s[/tex]:
[tex]\displaystyle \frac{s}{- \sqrt{1 - s^{2}}} = -5[/tex].
[tex]s^{2} =25(1 - s^{2})[/tex].
[tex]\displaystyle s = \sqrt{\frac{25}{26}} = \frac{5\sqrt{26}}{26}[/tex].
Therefore
[tex]\displaystyle \sin{\frac{\theta}{2}} = \frac{5\sqrt{26}}{26}\approx 0.196[/tex].
A point is on a circle if the distance from the center of the circle to the point is equal to the 1.area.2.circumference.3.radius.4.diameter.
The best and most correct answer among the choices provided by the question is 3.) radius. Hope this helps :)
Answer:
3.radius.
Step-by-step explanation:
The area of a circle is the space enclosed by the circle.
The circumference is the total length of the circle when stretched.
The diameter is a line that divides the circle into 2 halves or semicircles.
The radius of a circle is the line drawn from the center of the circle to any part of the circumference or any point on the circle.
The right answer is 3.radius.
Help please; I need the right answer
Answer:
C.
Step-by-step explanation:
[tex]\cos x+\sqrt{2}=-\cos x \\ 2\cos x = -\sqrt 2 \\ \cos x = -\dfrac{\sqrt 2}{2}\\ \\ \Rightarrow x = \pm \arccos\Big(-\dfrac{\sqrt 2}{2}\Big)+2k\pi,\quad x\in \mathbb{Z}\\ \Rightarrow x =\pm\dfrac{3\pi}{4}+2k\pi\\ \\ \\k = -1 \Rightarrow x < 0\\\\ k=0 \Rightarrow x<0 \quad \text{or}\quad \boxed{x = \dfrac{3\pi}{4}} \\ \\k = 1 \Rightarrow x=-\dfrac{3\pi}{4}+2\pi \Rightarrow \boxed{x= \dfrac{5\pi}{4}}\quad \text{or}\quad x > 2\pi[/tex]
Answer:
C
Step-by-step explanation:
Given
cos x + [tex]\sqrt{2}[/tex] = - cosx ( add cosx to both sides )
2cosx +[tex]\sqrt{2}[/tex] = 0 (subtract [tex]\sqrt{2}[/tex] from both sides )
2cosx = - [tex]\sqrt{2}[/tex] ( divide both sides by 2 )
cosx = - [tex]\frac{\sqrt{2} }{2}[/tex]
Since cosx < 0 then x is in the second/ third quadrant
x = [tex]cos^{-1}[/tex] ( [tex]\frac{\sqrt{2} }{2}[/tex] )
= [tex]\frac{\pi }{4}[/tex] ← related acute angle
Hence
x = π - [tex]\frac{\pi }{4}[/tex] = [tex]\frac{3\pi }{4}[/tex] ← second quadrant
or
x = π + [tex]\frac{\pi }{4}[/tex] = [tex]\frac{5\pi }{4}[/tex] ← third quadrant
Help with this question, please ASAP!!
Answer:
the middle set of points
Step-by-step explanation:
A translation < 3, - 4 > means add 3 to the x- coordinate and subtract 4 from the y- coordinate.
Under a reflection in the x- axis
a point (x, y ) → (x, - y )
Hence
X(0, - 2) → X'(0 + 3, - 2 - 4) → X'(3, - 6) → X''(3, 6)
Y(1, 4) → Y'(1 + 3, 4 - 4) → Y'(4, 0) → Y''(4, 0)
Z(5, 3) → Z' (5 + 3, 3 - 4) → Z'(8, - 1) → Z''(8, 1 )
Wich of following are solutions to |x+3|= 4x -7
Answer x= 10/3
Answer:
10/3
Step-by-step explanation:
|x+3|=4x-7
So |-(x+3)|=|x+3|
We are going to try out two cases:
-(x+3)=4x-7 and x+3=4x-7
-x-3=4x-7 3=3x-7
-3=5x-7 10=3x
4=5x x=10/3
x=4/5
We are going to test out both because we could something that isn't actually a solution, this is called extraneous.
First thing I'm going to check is 4x-7 for it being positive.
4(4/5)-7=20/5-7=-15/5=-3 so 4/5 will not work because absolute value result can't be negative
4(10/3)-7=40/3-7=19/3 which is positive
checking |x+3| to see if is 19/3 for x=10/3 we see that is so that is the answer
BRAINLIEST! It would take 4 hours to fill an aquarium using water from 10 taps.
How many hours and minutes would it take if only 6 taps were used?
Please give an explanation of your answer!
Answer:
6 hours and 40 minutes
Step-by-step explanation:
10 taps = 4 hours
( ÷ 10 ) ( × 10 )
1 taps = 40 hours
( × 6 ) ( ÷ 6 )
6 taps = 6.66666666667 hours / 400 minutes
Final answer:
To fill an aquarium initially using 10 taps in 4 hours, using 6 taps would take 6 hours and 40 minutes.
Explanation:
The time it takes to fill the aquarium initially can be calculated by:
Determine the rate of filling using all 10 taps: 1/4 of the aquarium per hour (as 4 hours to fill).
Calculate the rate using 6 taps: 6/10 of the original rate.
Divide the time taken initially (4 hours) by the reduced rate to find the new time.
Therefore, the time it would take to fill the aquarium using only 6 taps is 6.67 hours or 6 hours and 40 minutes.
PLEASE HELP SO I CAN GET THIS OVER WITH!!! WILL GIVE BRAINLIEST!!!!
as a receptionist for a hospital ,one of kelly's tasks is to schedule appoinments. she allots 60 minutes for the first visit and 30 minutes for a follow-up.the doctor cannot perform more than eight follow-ups per day .the hospital has eight hours available for appointments. the first visit costs $120 and the follow up costs $70 let x be the first number of visits and y be the number of followup
determine the number of first visits and follow ups to be scheduled to make the maximum income
Her first visit and follow up 60 mins + 30 mins
The limit is 8 follow ups per day
The hospital has 8 hrs available for appointments
Her first visit cost $120 (60 mins) as her follow up was $70 (30 mins)
X = Visits
Y = Follow-ups
And since her first visit and follow up equals to an hour and 30 mins, meaning for it to all add up into the 8 hrs for the appointment, it'll be... 1 hr, 30 mins/ 3 hrs/ 4 hrs, 30 mins/ 6 hrs/ 7 hrs, 30 mins/ 9 hrs
Eight hours is the limit so that means it equals to 5 visits and 6 follow ups, due to if you want it to be the whole 8 hours.
Claude is so Brainy his brain's nickname is Brainly
What is 7.884 rounded to the nearest hundredth
-----------------------------
The Answer is 7.88
-----------------------------
Answer:
The answer here would be 7.88
Hope this helps!
I need some help. Please help me TYSM!!!
Answer:
D
Step-by-step explanation:
Don't be scared off by this problem. Just read the numbers.
Those A + = 264
Those RH- = 111
The total = 375
Total of everyone typed is 740
Probability = 375 / 740 = 0.50675
Probability = 0.507 to the nearest thousandth.
The cost of apples varies directly with the number of pounds bought. If 2 pounds of apples cost $3.25, how many pounds of apples can be purchased for $9.75
Answer: 6 pounds of apples
Step-by-step explanation:
See photo attached. (:
Determine whether triangle TJD is congruent to triangle SEK
given
T (-4,-2), J (0,5), D (1,-1), S (-1,3), E (3,10), K (4,4)
and explain the reason.
Select one:
a. Yes, by SSS
b. No, by AAS
c. No, by ASA
d. Yes, by SAS
Answer:
I believe it is SSS
Step-by-step explanation:
because all the sides are exactly the same length
In a study, the sample is chosen by putting people's names on a dartboard, and blindly throwing darts to select 5 names. what is the sampling method?
Answer:
Random Sampling
Step-by-step explanation:
Random sampling is when people are chose at random from a population.
Population is the chits that have been put up on the dart board.
Blindly throwing darts to select 5 names is selecting randomly. In this case, there will be no bias involved in it as names are chosen blindly.
!!
Answer: Random sampling method.
Step-by-step explanation:
A random sampling is a sampling technique in which a researcher randomly picks participants for the sample such that the chances for each participants to get selected is equal.
Given : In a study, the sample is chosen by putting people's names on a dartboard, and blindly throwing darts to select 5 names.
Here , the probability to throw dart on any any name is equal because they throwing it blindly.
Thus, this sampling method is a random sampling method.
PLZZZ HURRYYY!!Which graph best represents the solution to the system of equations shown below? y = -4x + 19 y = 2x + 1 A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair 7, 3. A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair 3, 7. A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair negative 3, negative 7. A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair negative 7, negative 3.
Answer:
Two lines are shown intersecting on ordered pair 3, 7.
Step-by-step explanation:
The first of the two lines has a slope of -4 and a y-intercept of 19 (off the top of the graph). It will decrease 4 units for each 1 unit to the right.
The second of the two lines has a slope of +2 and a y-intercept of +1. It will increase 2 units for each 1 unit to the right.
These two lines must intersect in the first quadrant at a point with an x-value less than 5, eliminating the first and last two choices, leaving only the second choice you have listed here.
You would have to examine the graphs to see which has the lines with proper slope and intercept.
My graphing calculator's solution is attached.
two lines are shown intersecting on ordered pair 3, 7.
Really need help on these. I have no idea what to do
Answer:
A
120
Step-by-step explanation:
With all the parallel lines involved, the central figure is a parallelogram. These 4 sided figures have the odd property of having their opposite angles equal.
What that means, in plain English is that <NRL = <NML
Both of these angles = 120
Here's the cruncher. <NRL and <PRK are vertically opposite. They are therefore equal.
The answer to your question is 120 which is A
the answer is A good luck !
A wall of a building is 34 inches wide 16 inches is concrete and 4 inches is limestone what fraction of the wall is brick
Answer:
7/17
Step-by-step explanation:
16 inches of concrete plus 4 inches of limestone come to 20 inches of concrete and limestone combined. Subtracting 20 inches from 34 inches yields 14 inches. 14 inches of the total wall thickness (34 inches) is brick. This fraction is 14/34, or 7/17.
The fraction of the wall made up of brick is found by subtracting the concrete and limestone widths from the total width of the wall. The fraction is 14/34, which simplifies to 7/17.
Explanation:The question is asking us to find the fraction of the wall made up of brick. The total width of the wall is 34 inches. Substrating the concrete and limestone widths from the total width (34 inches - 16 inches for concrete - 4 inches for limestone) we get a result of 14 inches for the brick portion. To express this as a fraction of wall's total width, we place the number 14 (the width of the brick portion) over 34 (the total width of the wall). Therefore, the fraction of the wall that is brick is 14/34, which simplifies to 7/17 when reduced to lowest terms.
Learn more about Fractions here:
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PLS HELP BRAINLIEST WILL BE GIVEN :D
Answer:
56
Step-by-step explanation:
By tracing the lines on the tree diagram, we see the probability of both being red is 0.5 × 0.6 = 0.3.
The probability of both being blue is 0.5 × 0.4 = 0.2.
So we would expect to get both blue 2/3 of the times we get both red.
X = 2/3 (84)
X = 56
describe the translation y=x^2+5
Answer:
The transformation moves the graph of the function up 5 units
Step-by-step explanation:
If we have a function f(x) then the transformation
[tex]g (x) = f (x) + c[/tex] vertically shifts the graph of f(x) c units
If [tex]c> 0[/tex] the graph moves c units up
If [tex]c <0[/tex] the graph moves c units down
In this case the main function is [tex]f (x) = x ^ 2[/tex]
and [tex]g (x) = f (x) + 5 = x ^ 2 +5[/tex]
Therefore the transformation moves the graph of the function up 5 units
ANSWER
[tex]y = {x}^{2} + 5[/tex]
EXPLANATION
The given function is
[tex]y = {x}^{2} + 5[/tex]
The base of this function is
[tex]f(x) = {x}^{2} [/tex]
The translation is of the form.
[tex]y = f(x) + k[/tex]
where k is a vertical translation k units up.
[tex]y = {x}^{2} + 5[/tex]
Therefore the translation is a shift up by 5 units.
given that ABCD is a rhombus, what is the value of x
Answer:
A.) 19.5
Step-by-step explanation:
2^x=3^x+1 what are the exact approximate solutions
Answer:
d.
Step-by-step explanation:
The goal of course is to solve for x. Right now there are 2 of them, one on each side of the equals sign, and they are both in exponential positions. We have to get them out of that position. The way we do that is by taking the natural log of both sides. The power rule then says we can move the exponents down in front.
[tex]ln(2^x)=ln(3^{x+1})[/tex] becomes, after following the power rule:
x ln(2) = (x + 1) ln(3). We will distribute on the right side to get
x ln(2) = x ln(3) + 1 ln(3). The goal is to solve for x, so we will get both of them on the same side:
x ln(2) - x ln(3) = ln(3). We can now factor out the common x on the left to get:
x(ln2 - ln3) = ln3. The rule that "undoes" that division is the quotient rule backwards. Before that was a subtraction problem it was a division, so we put it back that way and get:
[tex]x(\frac{ln(2)}{ln(3)})=ln(3)[/tex]. We can factor out the ln from the left to simplify a bit:
[tex]x[ln(\frac{2}{3})]=ln(3)[/tex]. Divide both sides by ln(2/3) to get the x all alone:
[tex]x=\frac{ln(3)}{ln(\frac{2}{3}) }[/tex]
On your calculator, you will find that this is approximately -2.709
Julia has saved 108 sand dollars and wants to give them away equally to x friends. Write an expression to show how many sand dollars each of Julia’s friends will receive. Then, find the total number of sand dollars each of Julia’s friends will get if Julia gives them to 12 friends.
Answer:
s = 108/x . . . . s = sand dollars each friend getseach of the 12 friends gets 9 sand dollarsStep-by-step explanation:
The point of a fraction is to express the size of something that has been divided into a number of parts equal to the denominator. For example, 1/3 represents the amount when 1 unit is divided into 3 parts.
Here, Julia has 108 that she wants to divide into x parts. The fraction 108/x will tell the size of each part.
__
When x=12, the fraction becomes 108/12 = 9/1 = 9. Each friend gets 9 sand dollars.
please help asap will mark brainliest
Answer:
The fraction is 7/10 and the decimal is 0.7
Step-by-step explanation:
Each incriment represents 1/10, or 0.1.
Answer:
Decimal: 0.7
Fraction: Simplified - 7/10 ; Non-simplified: 70/100
Step-by-step explanation:
There are 9 dashes in-between 0 & 1, meaning that each dash signifies 0.1, and that you are adding 0.1 each time.
The dot is located 7 dashes away from 0. Multiply 7 with 0.1
7 x 0.1 = 0.7
0.7 is your decimal answer.
Change the decimal to a fraction. To do so, move the decimal point to the right two place values and put it over 100. Add 0's if needed.
0.7 = 70/100
As it does not specify you have to simplify, put 70/100. HOWEVER, if it says you have to simplify, simplify. Divide common factors from both the numerator & denominator:
(70/100)/(10/10) = 7/10
7/10 is your simplified fraction. 70/100 is your non-simplified fraction.
~
Hilda is putting new tile in an area of her home. Part of the space is rectangular with a length of 10 feet and a width of 6 feet, and part of the space is triangular with a base of
4 feet and a height of 2 feet.How many square feet of tile will Hilda need to cover the space?
Answer:
64 sq feet
Step-by-step explanation:
Given:
Rectangle Length = 10 feet
Rectangle Width = 6 feet
Triangle Base = 4 feet
Triangle Height = 2 feet
Area of rectangle = Length x Width = 10 x 6 = 60 sq feet
Area of triangle = [tex]\frac{1}{2}[/tex] x Base x Height = [tex]\frac{1}{2}[/tex] x 4 x 2 = 4 sq feet
Total area
= Area of Rectangle + Area of Triangle
= 60 + 4 = 64 sq feet
Answer:
64 ft^2
Step-by-step explanation:
The rectangular area is 10 ft by 6 ft, which comes to 60 ft².
The triangular area is A = (1/2)(base)(height) = (1/2)(4 ft)(2 ft) = 4 ft²
The total area of tile will be 4 ft² + 60 ft², or 64 ft².
Simplify: 5x+50/x+5 • 1/x+10
[tex]\bf \cfrac{5x+50}{x+5}\cdot \cfrac{1}{x+10}\implies \cfrac{5~~\begin{matrix} (x+10) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{x+5}\cdot \cfrac{1}{~~\begin{matrix} x+10 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\implies \cfrac{5}{x+5}[/tex]
Answer:
The correct answer option is C. [tex] \frac { 5 } { x + 5 } [/tex].
Step-by-step explanation:
We are given the following expression and we are to simplify it:
[tex] \frac { 5 x + 5 0 } { x + 5 } . \frac { 1 } { x + 1 0 } [/tex]
We would take the common terms out and then cancel any like terms present in the expression to get the simplest form.
[tex] \frac { 5 ( x + 1 0 ) } { x + 5 } . \frac { 1 } { x + 1 0 } [/tex]
[tex] \frac { 5 } { x + 5 } [/tex]
Therefore, the correct answer option is C. [tex] \frac { 5 } { x + 5 } [/tex].
PLZ HELP MARKIN BRAINIEST!!!
From the graph, when x = 1, y = 57,000.
Replace x with 1 in the equations and see if any of the Y 's equal 57,000 :
y = -2610.82(1) + 47860.82 = 45,250
y = 219(1)^2 - 6,506.78(1) + 59,385 = 219 - 6506.78 + 59385 = 53,097.22
y = 54041.5(0.9)^1 = 48,637.35
y = 10,504.6 (1.1)^1 = 11,555.06
The second equation is the closest. so try another x value to see if it is close to the Y value:
Let's try x = 14:
y = 219(14)^2 - 6506.78(14) + 59,385 = 42924 - 91094.92 + 59385 = 11,214.08
This is close to Y = 12,00 shown on the graph
SO the closest equitation is y = 219x^2 - 6506.78x + 59385
which of these figures must be a rectangle?
Answer:
A rectangle is a parallelogram with at least one right angle is the best choice ⇒ answer A
Step-by-step explanation:
* Lets revise the properties of the rectangle
# Each two opposite sides are parallel
# Each two opposite sides are equal in length
# Its two diagonals bisect each other and equal each other
# Its four angles are right angles
- The parallelogram can be a rectangle if:
# Two adjacent sides are perpendicular to each other means one
angle of its four angles is a right angle
- OR
# Its two diagonals are equal in length
* Lets solve the problem
- We will study the answers to chose the best one
# Answer A
- A rectangle is a parallelogram with at least one right angle
∵ Each tow opposite angles are equal in the rectangle
∵ One of the is right angle means its measure is 90°
∴ The measure of the opposite angle is also 90°
∵ The sum of the measures of the four angles is 360°
∴ The sum of the measures of the other two angles is;
360 - (90 + 90) = 180°
∵ They are equal to each other (opposite angles)
∴ The measure of each one = 180 ÷ 2 = 90°
∴ The measure of the four angles are 90°
∴ The four angles of the rectangle are right angles
* A rectangle is a parallelogram with at least one right angle is the
best choice
Answer:it is A
Step-by-step explanation: