Triangle ABC is inscribed in the circle with arcs shown. find X and the measures of angle A, angle B, Angle C
Answers
The total circumference of a circle = 360°
Therefore,
[tex]\text{arc AB + arc BC+ arc AC}=360^0[/tex]Where,
[tex]\begin{gathered} \text{arc AB=(6x+10)}^0 \\ \text{arc BC=(x+15)}^0 \\ \text{arc AC=((8x-40)}^0 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} (6x+10)^0+(x+15)^0+(8x-40)^0=360^0 \\ 6x^0+x^0+8x^0+10^0+15^0-40^0=360^0 \\ 15x^0-15^0=360^0 \\ 15x^0=360^0+15^0 \\ 15x^0=375^0 \\ \text{divide both sides by }15 \\ \frac{15x}{15}=\frac{375^0}{15} \\ x=25^0 \end{gathered}[/tex][tex]\begin{gathered} \text{arc AB=(6x+10)}^0=(6\times25+10)^0=150^0+10^0=160^0 \\ \text{arc BC=(x+15)}^0=(25^0+15^0)=40^0 \\ \text{arc AC=(8x-40)}^0=(8\times25^0-40^0)=200^0-40^0=160^0 \end{gathered}[/tex]To calculate
[tex]\begin{gathered} \angle A,B,\angle C \\ We\text{ will use the theorem,} \\ \text{The measure of an insribed angle in a circle equals half the measure of the intercepting arc} \\ \end{gathered}[/tex][tex]\begin{gathered} \angle A=\frac{arc\text{ BC}}{2} \\ \angle A=\frac{40^0}{2}=20^0 \end{gathered}[/tex][tex]\begin{gathered} \angle B=\frac{arc\text{ AC}}{2} \\ \angle B=\frac{160^0}{2}=80^0 \end{gathered}[/tex][tex]\begin{gathered} \angle C=\frac{arc\text{ AB}}{2} \\ \angle C=\frac{160^0}{2}=80^0 \end{gathered}[/tex]Hence,
x = 25°
∠ A=20°
∠ B=80°
∠ C=80°
Related Questions
if the growth factor is 1.2, what is the growth rate
Answers
SOLUTION
Step 1 :
In this question, we are meant to know the relationship between Growth factor and Growth Rate.
Growth factor is the factor by which a quantity multiplies itself over time.
Growth rate is the addend by which a quantity increases ( or decreases ) over time.
Step 2 :
From the question, if the growth factor is 1.2 which is also 120 %,
then the growth rate will be ( 120 - 100 ) % = 20 % = 0. 2
CONCLUSION:
The Growth Rate = 0. 2
HELLPPPPLLPPPPPPPPPPPPPPP
Answers
Answer:
a²+13a+40
Step-by-step explanation:
Now the x in the function has been replaced into (a+5) :
(a+5)²+3(a+5) =
(a²+10a+25)+(3a+15) =
a²+13a+40
Hope this helped and have a good day
So I joined a ged class and this is apparently a “high school level” math problem, maybe for people in advanced classes but not regular. Anyway, I need help with solving this. Also the greater than sign with the problem that I’m doing has like an underline under it, which I think means greater than or equal to 3x + 9 > - x + 19
Answers
Given the inequality:
[tex]3x+9\ge-x+19[/tex]Solve for x:
[tex]\begin{gathered} 3x+x\ge19-9 \\ 4x\ge10 \\ x\ge\frac{10}{4} \\ \\ x\ge\frac{5}{2} \end{gathered}[/tex]so, the answer will be:
[tex]\begin{gathered} x\ge\frac{5}{2} \\ x\in\lbrack\frac{2}{5},\infty) \end{gathered}[/tex]a rectangle with a area of s sq feet and a width of 6 in what is the length of the rectangle
Answers
The area of the reactangle is calculates using the following formula:
[tex]A=w\cdot l[/tex]Where
A: area
w: wisth
l: lenght
You can write this formula in terms of the length by dividing the Area by the width:
[tex]l=\frac{A}{w}[/tex]If the area is A=s feet² and the width is w=6 feet, then the length is
[tex]l=\frac{s}{6}[/tex]1 mile= 1,760 yards.1 kilometer= 1,000 metersIf Jose walked 2 miles this morning, about how many kilometers did he walk?
Answers
1 mile= 1.609 km
Then,
2*1.609=3.218 km
He walked 3.218 kilometers
Which inequality is represented by the graph?
Answers
Answer:
it's option c ............
Find an equation of the line.Write the equation in the standard form.Through (8,4); parallel to 7x-y= 2.
Answers
Answer:
7x-y=53
Explanation:
Given the line
[tex]7x-y=2[/tex]Making y the subject of the equation, we have:
y = 7x-2
Therefore, the slope of the line, m=7
• If two lines are parallel, their slopes are equal.
Therefore, the slope of the parallel line = 7
The equation of the parallel line through (8,4) will then be:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-4=7(x-8) \\ y-4=7x-57 \\ 7x-y=-4+57 \\ 7x-y=53 \end{gathered}[/tex]Shandar rents a pickup truck for her house move. She has to pay $96 for the first day, $88 for each additional day she keeps the truck, and 45 cents for each mile she drives. She will also be able to use a $25 coupon. Write an expression that represents the total cost when Shandar keeps the truck for h days and travels a total of p miles.Simplify the expression completely.List the terms in your expression.For each term, identify the coefficient and variable.
Answers
96 first day
88 for each additional day (h)
0.45 for each mile driven (p)
$25 coupon
Expression
Total cost = 96 + 88h + 0.45p - 25
Simplify:
Combine like terms:
TC = 96 - 25 + 88h + 0.45p
TC = 71 + 88h + 0.45p
Terms:
71 = constant
88h = coefficient 88 , variable h
0.45p= coeficcient 0.45 , variable p
The test results for 4 students are 96 83 78 and 83. If one more student's test score of 87 is added, what would increase?A. median B. meanC. modeD. range
Answers
Mean will increase because 87 is greater than 83 and 78, then the eman will be greater
Indicate the transformation that has occurred.2.A. (x,y)-->(-x+3.y-5) C. (x,y) --> (-x,y-5)B. (x,y) --> (x +3,y-5) D. (x,y) --> (x-1,-y)
Answers
So we have a transformation that maps a triangle into another one. This is made by transforming the points X, Y and Z into X', Y' and Z'. In order to find out which of the four options is the correct one we must verify that points X, Y and Z actually transform into X', Y' and Z'.
We have:
[tex]X=(2,5)\rightarrow X^{\prime}=(1,0)[/tex]Let's see which of the four transformations do this. So for A:
[tex]\begin{gathered} (x,y)\rightarrow(-x+3,y-5) \\ X=(2,5)=(x,y) \\ \text{Then} \\ X^{\prime}=(-x+3,y-5)=(-2+3,5-5) \\ X^{\prime}=(1,0) \end{gathered}[/tex]So transformation A is a possible answer, let's see the rest.
For C:
[tex]\begin{gathered} (x,y)\rightarrow(-x,y-5) \\ X=(2,5)=(x,y) \\ \text{Then} \\ X^{\prime}=(-x,y-5)=(-2,5-5) \\ X^{\prime}=(-2,0)\ne(1,0) \end{gathered}[/tex]So the X' that we calculate with transformation C is different that the one we are looking for so we discard this option.
For option B we have:
[tex]\begin{gathered} (x,y)\rightarrow(x+3,y-5) \\ X=(2,5)=(x,y) \\ \text{Then} \\ X^{\prime}=(x+3,y-5)=(2+3,5-5)=(5,0) \\ X^{\prime}=(5,0)\ne(1,0) \end{gathered}[/tex]Like what happened with C, transformation B is discarded.
Let's see what happens with D:
[tex]\begin{gathered} (x,y)\rightarrow(x-1,-y) \\ X=(2,5)=(x,y) \\ \text{Then} \\ X^{\prime}=(x-1,-y)=(2-1,-5)=(1,-5) \\ X^{\prime}=(1,-5)=(1,0) \end{gathered}[/tex]So D is also discarded. This would mean that A is the correct option but just in case, let's check if it tansform points Y=(0,2) and Z=(3,1) into Y'=(3,-3) and Z'=(0,-4):
[tex]\begin{gathered} (x,y)\rightarrow(-x+3,y-5) \\ \text{If} \\ Y=\mleft(0,2\mright) \\ \text{Then} \\ Y^{\prime}=(-0+3,2-5)=(3,-3) \\ \text{If} \\ Z=\mleft(3,1\mright) \\ \text{Then} \\ Z^{\prime}=(-3+3,1-5)=(0,-4) \end{gathered}[/tex]So Y' and Z' are (3,-3) and (0,-4) which definetely means that option A is the correct one.
Franklin is drawing a model of a rectangular swimming pool. He marks two points, A and B, on the coordinate plane and connects them to represent one side of the pool. Points C and D are reflections of B and A, respectively, across the x- axis. Each unit in the coordinate plane represents 1 meter. Draw a rectangle in the coordinate plane yo model the swimming pool. What is the area of the swimming pool?
Answers
Area = base x height
A = 8 x 6 = 48 m²
In the figure shown, what is mzA? Explain.57°; AABC is an isosceles triangle with base angles A and C. m2A = mc.B. 66; AABC is an isosceles triangle with base angles B and C. m2B = m_C = 57, and m2A + m2B + m2 = 180.C. 57. AABC is an equilateral triangle.
Answers
Since ABC is an isosceles triangle with sides AB=AC, then the angle ABC is the same as ACB, an it's equal to 57º.
Since all three internal angles should add up to 180º, then the angle BAC should have a measure of 180-2(57)=66º.
Can you evaluate 3 + (a + 4)(8- b ) when a= 5 and b=6
Answers
The expression to evaluate is:
[tex]3+a+4\mleft(8-b\mright)[/tex]When
a = 5 and b = 6
We simply plug in the values of 5 and 6, into a and b respectivly. And do algebra to get our answer. The process is shown below:
[tex]\begin{gathered} 3+a+4\mleft(8-b\mright) \\ 3+5+4\mleft(8-6\mright) \\ 3+5+4(2) \\ 3+5+8 \\ 16 \end{gathered}[/tex]The answer is 16.
QuestionGiven that cot(0)- 1 and 0 is in Quadrant II, what is sin(0)? Write your answer in exact form. Do not round.Provide your answer below:sin (O)=
Answers
Given:
The trigonometric ratio is given as,
[tex]\cot \theta=-\frac{1}{2}[/tex]The value of θ lies in the second quadrant.
The objective is to find the value of sinθ.
Explanation:
The formula of cotθ is,
[tex]\cot \theta=\frac{\text{adjacent}}{\text{opposite}}=-\frac{1}{2}[/tex]Since, the value of θ lies in second quadrant, the triangle formed for cotθ will be,
Then, the value of x can be calculated as,
[tex]\begin{gathered} x^2=2^2+(-1)^2 \\ x=\sqrt[]{4+1} \\ x=\sqrt[]{5} \end{gathered}[/tex]To find the value of sinθ:
The value of sinθ can be calculated as,
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \sin \theta=\frac{2}{\sqrt[]{5}} \\ \sin \theta=\frac{2}{\sqrt[]{5}}\times\frac{\sqrt[]{5}}{\sqrt[]{5}} \\ \sin \theta=\frac{2\sqrt[]{5}}{5} \end{gathered}[/tex]Hence, the value of sinθ is (2√5)/5.
A bag contains 5 red and 3 blue marbles. Two marbles are drawn simultaneously from the bag. DETERMIN the probability that at least one is red.
Answers
total number of balls = 5 + 3 = 8
The possibilities are:
RR (two red) and RB (one red and one blue)
RR and RB are mutually exclusive
P(RR) =
4. Sales tax in a certain state is 5%. If the sales tax on a new boat was $400, what was the selling price of the boat?
Answers
Sales tax percentage = 5% = 5/100 = 0.05 (decimal form)
Sales tax amount = $400
Multiply the selling price of the boat (x) by the sales tax percentage in decimal form. That expression must be equal to 400.
0.05x = 400
Solve for x:
x = 400/ 0.05
x= $8,000
Please Help!!
Karen was computing the volume of a rectangular prism where v=lwh. In her case w=h. After she multiplied l and w she realized she made w 1/3 larger than it should have been. Since w=h, she lowered the third number by 1/3 of itself and continued to multiply to get the final answer. Betty, who did the same problem with the correct numbers, showed that Karen was off by 12 cubic yards. The correct volume of the prism is __ cu. yds.
Answers
The correct volume of the rectangular prism as calculated by Betty is 108 cubic yards
What is a rectangular prism?A rectangular prism is cuboid and an hexahedron that has 6 faces.
The formula for finding the volume of the rectangular prism is V = l•w•h
Where;
l = Length
w = Width
h = Height
The measurement of the prism, for which Karen is calculating the volume gives;
w = h
The amount larger Karen found that she made the width, which gives;
Width of the cube Karen used = (1 + 1/3) × w
Therefore;
h = (1 + 1/3) × w
The volume becomes;
V' = l × (1 + 1/3) × w × (1 - 1/3) × w = l•w²•(1²-1/3²)
V' = l•w²•(8/9)
The amount by which the volume increased, dV = 12 yd³
Which gives;
l•w²•(8/9) = l•w•h - 12 = l•w² - 12
l•w²•(8/9) - l•w² + 12 = 0
l•w²•(8/9) - l•w² + 12 = 0
l•w²/9 = 12
V = l•w² = 12 × 9 = 108
The correct volume of the prism is 108 cubic yards
Learn more about finding the volume of solids here:
https://brainly.com/question/20284914
#SPJ1
The bacteria in a dish triples every hour. At the start of the experiment therewere 400 bacteria in the dish. When the students checked again there were32,400 bacteria. How much time had passed? (Write your equation and solve forx; y= a • bx).
Answers
Given
The bacteria in a dish triples every hour. At the start of the experiment there
were 400 bacteria in the dish. When the students checked again there were
32,400 bacteria. How much time had passed? (Write your equation and solve for
x; y= a • bx)
Solution
A table is in the shape of a regularhexagon. The perimeter of the table is 12 ftfeet. What is the length of each side ofthe tableA 1 ftB 2 ftC 3 ftD 4 ft
Answers
Solution:
Given the shape of a hexagon;
The perimeter, P, of a hexagon is;
[tex]\begin{gathered} P=6s \\ \\ \text{ Where }s=side\text{ length} \end{gathered}[/tex]Given;
[tex]\begin{gathered} P=12ft \\ \\ s=\frac{12}{6}ft \\ \\ s=2ft \end{gathered}[/tex]CORRECT OPTION: B
calculated the slope (5,-14),(-14,0) help
Answers
the slope can be calculated using the next formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where
(5,-14)=(x1,y1)
(-14,0)=(x2,y2)
then we substitute the values
[tex]m=\frac{0+14}{-14-5}=\frac{14}{-19}=-\frac{14}{19}[/tex]the answer is -14/19
Select the correct answerVector u has its initial point at (15, 22) and its terminal point at (5, 4). Vector v points in a direction opposite that of u, and its magnitude is twicethe magnitude of u. What is the component form of v?OA V=(-20, 36)OB. V=(-20, 52)Ocv = (20, 36)ODV= (20, 52)
Answers
Answer
Option C is correct.
v = (20, 36)
Explanation
If the initial and terminal points of a vector are given, the vector itself is obtained, per coordinate, by doing a terminal point coordinate minus initial point coordinate.
u = [(5 - 15), (4 - 22)]
u = (-10, -18)
Then, we are told that vector v points in the opposite direction as that of vector u and its magnitude is twice that of vector u too.
In mathematical terms,
v = -2u
v = -2 (-10, -18)
v = (20, 36)
Hope this Helps!!!
Jake and Joshua have new jobs selling gift cards at a local convenience store at the cash register, but their pay is different. Jake earns a foundational wage of $6 per hour, as well as $8 for each gift card sold. Joshua gets $4 for each gift card sold and earns a foundational wage of $6 per hour. If they each sell a certain number of gift cards in one hour, they will end up earning the same amount of pay. How many gift cards would that make up to?Write a system of equations, graph them, and type the solution.
Answers
Let x be the number of cards Jake and Joshua sell within one hour. Therefore, their earnings are given by the following expressions,
[tex]\begin{gathered} Ja=6+8x \\ Jo=6+4x \end{gathered}[/tex]Then, set Ja=Jo (both earn the same amount),
[tex]\begin{gathered} Ja=Jo \\ \Rightarrow6+8x=6+4x \end{gathered}[/tex]Solving for x,
[tex]\begin{gathered} \Rightarrow8x=4x \\ \Rightarrow4x=0 \\ \Rightarrow x=0 \end{gathered}[/tex]Then, they will earn the same within one hour only if both sell zero cards within the hour.
Graphing the system of equations,
As one can see, the intersection point is (0,6), which stands for 0 cards and $6
Question60 is 40% of what number?
Answers
let the required number be x then
[tex]\begin{gathered} \frac{60}{x}\times100=40 \\ x=\frac{60}{40}\times100 \\ x=150 \end{gathered}[/tex]So 60 is 40% of 150.
I was doing this with a tutor but there was a connection problem.
Answers
ANSWER:
[tex](x-3)^2+(y+7)^2=113[/tex]The point (7,6) is not on the circle
STEP-BY-STEP EXPLANATION:
(a)
The equation of the circle is given as follows:
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{ where (h,k) is the center and r is the radius } \end{gathered}[/tex]We replace to calculate the radius of the circle, like this:
[tex]\begin{gathered} \mleft(-4-3\mright)^2+\mleft(1-\mleft(-7\mright)\mright)^2=r^2 \\ (-7)^2+(8)^2=r^2 \\ r^2=113 \end{gathered}[/tex]Therefore, the equation would be:
[tex](x-3)^2+(y+7)^2=113[/tex](b)
We replace the point, and if the value is greater than the radius, it means that this point is not on the circle:
[tex]\begin{gathered} (x-3)^2+(y+7)^2\le113 \\ \text{ replacing:} \\ \mleft(7-3\mright)^2+\mleft(6+7\mright)^2\le113 \\ 4^2+13^2\le113 \\ 16+169\le113 \\ 185\le113 \end{gathered}[/tex]Therefore, the point (7,6) is not on the circle
Elena is traveling to visit her grandparents who live 125 miles away.
a. Elena stops for lunch 2/3 of the way. How far has Elena traveled?
b. Elena enters the city where her grandmother lives after 110 miles. Is she more or less than 9/10 of the way there?
PLS PLS PLS HELPP
Answers
Answer:
A. 83 1/3 miles
B. Less than 9/10 of the way there
Step-by-step explanation:
A.
2/3 of the way. "of" means to multiply, so multiply 2/3 and 125.
[tex]\frac{2}{3}[/tex] × [tex]\frac{125}{1}[/tex] = [tex]\frac{250}{3}[/tex]
Simplify by dividing 250 and 3.
250 ÷ 3
[tex]83 \frac{1}{3}[/tex] miles
B.
Multiply 125 by 9/10 then compare the answer to 110 to see if she is more or less than 110 miles.
[tex]\frac{125}{1}[/tex] × [tex]\frac{9}{10}[/tex] [tex]= \frac{1125}{10}[/tex]
Divide 1125 by 10
1125 ÷ 10 = 112.5
Since 9/10 of the distance is 112.5 miles, 110 miles is less than 9/10 of the way there.
While at college orientation, Kate is buying some cans of juice and some cans of soda for the dorm. The juice is $0.60 per can while the soda is $0.75. Kate has $24 of dorm funds all to be spent. What is an equation that represents all the different combinations of juice and soda Kate can buy for $24 and how many different combinations of drinks are possible?
Answers
From the question the following can be derived:
(a)
Let x cans of juice and y cans of soda be purchased for the dorm. Then the cost of the juice and soda is 0.60x + 0.75y. The equation of all the combinations of juice and soda is 0.60x + 0.75y = 24.
(b)
The cost of exactly 24 cans of juice is $24 * 0.60 = $14.40. After this purchase, the remaining sum of money available is $24 - $14.40 = $9.60. This will suffice to buy 12 cans of soda, leaving a balance of $0.80. Thus. the entire money cannot be spent if exactly 24 cans of juice are purchased.
(c)
Below is a graph of the line 0.6x + 0.75y = 24 or 4x + 5y = 160 is plotted. All possible cimbinations of juice and soda will lie on this line. The x-intercept is 40 and the y-intercept is 32. Since neither of x and y can be negative, hence the lower and upper bounds for x are 0 and 40 and the lower ad upper bounds for y are 0 and 32. Also , x has to be multiple of 5 and y has to be a multiple of 4. As may be observed from the graph, only 9 combinations are possible which are (x, y):
(0, 32), (5, 28), (10, 24), (15, 20), (20, 16), (25, 12), (30, 8), (35, 4), (40, 0).
Graph:
([20 + 10.4^2 - 116,870) / (20/ 1/3 x 15 - 10.4/ (116,870/6808))] ^-1
Answers
Answer:
[tex]8\frac{875730264}{8491541359}[/tex]Explanation:
Given the values of the variables below:
• D = 116,870
,• E=1/3
,• L =15
,• M = 20
,• O = 10.4
,• Y = 6,808
We are required to evaluate:
[tex]\begin{gathered} \lbrack(M+O^2-D\div Y)\div(M\div E\cdot L-O\div(D\div Y))\rbrack^{-1} \\ =\mleft(\frac{(M+O^2-D\div Y)}{(M\div E\cdot L-O\div(D\div Y))}\mright)^{-1} \end{gathered}[/tex]Substitute the given values:
[tex]=\mleft(\frac{20+10.4^2-116,870\div6,808}{20\div\frac{1}{3}\cdot15-10.4\div(116,870\div6,808)}\mright)^{-1}[/tex]We simplify using the order of operations PEMDAS.
First, evaluate the parentheses in the denominator.
[tex]=\mleft(\frac{20+10.4^2-116,870\div6,808}{20\div\frac{1}{3}\cdot15-10.4\div\frac{116,870}{6,808}}\mright)^{-1}[/tex]Next, evaluate the exponent(E): 10.4²
[tex]=\mleft(\frac{20+108.16-116,870\div6,808}{20\div\frac{1}{3}\cdot15-10.4\div\frac{116,870}{6,808}}\mright)^{-1}[/tex]Next, we take multiplication and division together:
[tex]\begin{gathered} =\mleft(\frac{20+108.16-\frac{116,870}{6,808}}{20\times3\times15-10.4\times\frac{6808}{116,870}}\mright)^{-1} \\ =\mleft(\frac{20+108.16-\frac{116,870}{6,808}}{900-\frac{13616}{22475}}\mright)^{-1} \end{gathered}[/tex]Finally, take addition and subtraction and then simplify.
[tex]\begin{gathered} =\mleft(\frac{9445541}{85100}\div\frac{20213884}{22475}\mright)^{-1} \\ =(\frac{9445541}{85100}\times\frac{22475}{20213884})^{-1} \\ =(\frac{8491541359}{68808061136})^{-1} \\ =1\div\frac{8491541359}{68808061136}=1\times\frac{68808061136}{8491541359} \\ \\ =\frac{68808061136}{8491541359} \\ =8\frac{875730264}{8491541359} \end{gathered}[/tex]The result of the evaluation is:
[tex]8\frac{875730264}{8491541359}[/tex]I inserted a picture of the question Please don’t ask tons of questions. & please state whether it’s a b c or d
Answers
As given by the question
There are given that the graph of the triangle.
Now,
According to the properties,
If the point (x, y) or (-x, y) rotated about the origin by the angle of 360 degrees.
That means,
There is no difference between rotating 360 degrees clockwise or anti-clockwise around the origin.
Then,
From the vertices of the triangle ABC is:
[tex]\text{A is (-6, 3), B is (-5, 7) and C is (-4, 3).}[/tex]Since the triangle map onto itself
[tex]\begin{gathered} A=A^{\prime} \\ B=B^{\prime} \\ C=C^{\prime} \end{gathered}[/tex]So, the triangle is rotated 360 degrees about the origin
Hence, the correct option is D.
In the diagram, m/ACB = 55°.
E
What is mZECD?
90°
O 55°
180°
D
O 125°
C
B
80
Answers
Answer:
55°
Step-by-step explanation:
Angle ACB and angle ECD are alternate exterior angles and alternate angles have same angle measurements:
If angle ACB = 55°
then angle ECD is also = 55°
Which systems of inequalities represents the number of apartments to be built
Answers
Given that:
- The office building contains 96,000 square feet of space.
- There will be at most 15 one-bedroom units with an area of 800 square feet. The rent of each unit will be $650.
- The remaining units have 1200 square feet of space.
- The remaining units will have two bedrooms. The rent for each unit will be $900.
Let be "x" the number of one-bedroom apartments and "y" the number of two-bedroom apartments.
• The words "at most 15 one-bedroom units" indicates that the number of these apartments will be less than or equal to 15 units:
[tex]x\leq15[/tex]• You know that the remaining units are two-bedroom apartments. And the number of them is greater than or equal to zero. Then, you can set up the second inequality to represent this:
[tex]y\ge0[/tex]• You know the area of each one-bedroom apartment, the area of each two-bedroom apartment, and the total area that the office building contains. The sum of the areas of the apartments must be less than or equal to the total area of the office building.
Then, the inequality that represents this is:
[tex]800x+1200y\leq96,000[/tex]• Therefore, you can set up this System of Inequalities to represent that situation:
[tex]\begin{gathered} \begin{cases}x\leq15 \\ \\ y\ge0 \\ \\ 800x+1200y\leq96,000 \\ \end{cases} \\ \end{gathered}[/tex]Hence, the answer is: Last option.