Answer: x=5, y=15
Step-by-step explanation:
x= cost of a chair
y= cost of a table
The cost of each table and of each chair is x=5, y=15.
We have given that,
Five tables and eight chairs cost $115 three tables and five chairs cost $70.
Determine the cost of each table and of each chair.
What is the variable cost?
A variable cost is a corporate expense that changes in proportion to how much a company produces or sells.
x= cost of a chair
y= cost of a table
Therefore, The cost of each table and of each chair is x=5, y=15.
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your math class is going to test new digital clinometers by measuring the angle of elevation of a kite you will fly. the kite flies to an angle of 50.2° on 520 feet of string. Assuming the the string is taut, how high is the kite to the nearest foot?
A) 624 ft
B) 400 ft
C) 333 ft
D) 677 ft
Check the picture below.
make sure your calculator is in Degree mode.
Thus, the kite is height of 400 ft above the ground.
Hence, option B is correct.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that,
Hypotenuse of tringle = 520 ft
And inclination angle = 50.2 degree
We know that if any one of interior angle is of 90 degree then the angle is said to be right angle triangle.
Since,
sinΘ = (opposite side of Θ)/Hypotenuse
Therefore,
⇒ sin50.2 = Height/520 (since opposite side is height of triangle as shown in figure)
⇒ 0.76 = Height/520
⇒ Height = 395.2 feet ≈ 400ft (in nearest foot)
Hence,
Height of kite is 400 ft.
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Find the distance between the point (-3,-4) and the line 2y=-3x+6
A.sqr13
B.23
C.14
D.23sqr13/13
The distance between the point (-3, -4) and the line 2y = -3x + 6 is 23 ÷ 13.
The distance between the point (-3, -4) and the line given by the equation 2y = -3x + 6 can be found using the point-to-line distance formula:
D = |Ax + By + C| ÷ (A^2 + B^2)
Firstly, we want to put the line equation in the standard form of Ax + By + C = 0. Let us rearrange the given equation of the line to this form:
3x + 2y - 6 = 0
Where A = 3, B = 2, and C = -6. Using the point (-3, -4), we plug the values into the point-to-line distance formula:
D = |3(-3) + 2(-4) - 6| ÷(3^2 + 2^2)
D = |-9 - 8 - 6| ÷(9 + 4)
D = | -23 | ÷ 13
D = 23 /÷ 13
Since ÷ 13 is an irrational number, we can't simplify it further. Therefore, the distance is:
D = 23 ÷ 13
What is the measure of the angle
Answer:
is 235
Step-by-step explanation:
shown in the image attached
Hope this helps
For this case we have that by definition, a flat angle is one that measures 180 degrees. It is observed that a flat angle is formed from the first to the second quadrant.
Now, we must add 55 degrees of the third quadrant, then:
[tex]180 + 55 = 235[/tex]
Thus, the angle formed is 235 degrees.
Answer:
235 degrees
Option A
g(x) = x^3 - x^2 - 4x + 4 what are the zeros, the y-intercept and the end behavior.
I think it's -2,0 1,0 2,0 for the zeros
y-intercept 0,4 but i'm not sure about them and have no clue about the end behavior
Answer:
See explanation
Step-by-step explanation:
Zeros of the function are those values of x, for which g(x)=0, so solve the equation g(x)=0:
[tex]x^3-x^2-4x+4=0\\ \\x^2(x-1)-4(x-1)=0\\ \\(x-1)(x^2-4)=0\\ \\(x-1)(x-2)(x+2)=0\\ \\x_1=-2,\ x_2=1,\ x_3=2[/tex]
Hence, the function has three zeros, x=-2, x=1 and x=2.
To find the y-intercept, substitute x=0:
[tex]y=g(0)=0^3-0^2-4\cdot 0+4=4,[/tex]
so y-intercept is at point (0,4).
The graph of the function shows that when x is infinitely small, then y is infinitely small too and if x is infinitely large, then y is infinitely large too.
Answer:
The zeros: x = 1, -2, 2
The y-intercept: (0, 4)
The end behavior :
x --> + ∞, f(x) --> + ∞
x --> - ∞, f(x) --> - ∞
Step-by-step explanation:
Zero function:
x^3 - x^2 - 4x + 4 = 0
(x^3 - x^2) - (4x - 4) = 0
x^2(x - 1) - 4(x - 1) = 0
(x^2 - 4)(x - 1) = 0
(x + 2)(x - 2)(x - 1) = 0
x + 2 = 0; x = -2
x - 2 = 0; x = 2
x - 1 = 0; x = 1
The zeros: x = 1, -2, 2
The y-intercept when x = 0 so y-intercept = 4 or (0, 4)
The end behavior of a function f(x) : the behavior of the graph of the function at the ends of the x-axis.
As x approaches + ∞, f(x) approaches + ∞
As x approaches - ∞, f(x) approaches - ∞
6! = (4! x (6-4)!) =
Answer:
6! = 720(4! × (6 - 4)!) = 48Step-by-step explanation:
n! = 1 · 2 · 3 · 4 · ... · n
6! = 1 · 2 · 3 · 4 · 5 · 6 = 720
(4! × (6 - 4)!) = (1 · 2 · 3 · 4 × 2!) = 24 × 1 · 2 = 24 × 2 = 48
Complete the statements below using the 2 graphs
Answer:
unit pay 10
slope 10
Step-by-step explanation:
$40/4hr = $10/1hr =10
A sequence is defined by the recursive function f(n + 1) = –10f(n).
If f(1) = 1, what is f(3)?
3
–30
100
–1,000
Answer:
100
Step-by-step explanation:
f(n+1) = -10f(n)
f(1) = 1
f(2) = -10f(1) => f(2) = -10·1 => f(2) = -10
f(3) = -10f(2) => f(3) = -10·(-10) => f(3) = 100
Answer:
100
Step-by-step explanation:
which methods could you use to calculate the y-coordinate of the midpoint of a vertical line segment with endpoints at (0,0) and (0,15)?
A. Count by hand
B. Divide 15 by 2.
C. Add the endpoint.
D. Divide 1 by 15.
The y-coordinate of the midpoint of the vertical line segment is calculated by method B. Divide 15 by 2, which gives the midpoint's y-coordinate as 7.5.
Explanation:To calculate the y-coordinate of the midpoint of a vertical line segment with endpoints at (0,0) and (0,15), you can use the method of dividing the y-coordinates of the endpoints by 2. In this case, you would divide 15 by 2 to find the midpoint's y-coordinate, which is method B. Divide 15 by 2. This is because the midpoint of a line segment is found by averaging the coordinates of the endpoints, and for the y-coordinates you add them together and then divide by 2. So, the calculation is (0 + 15) / 2, which equals 7.5. Thus, the midpoint of the segment is at the point (0, 7.5).
The vertices of ABC are A(-2. 2). B(8.2), and C(O. 8). The perimeter is 22.8 . What is the area in square units ?
Answer:
multiply 22.8 by 22.8
Step-by-step explanation:
Gloria can knit one block of a quilt in 50 minutes. If she knits at the same rate for 5 hours, how many blocks can she knit ?
Answer:
The answer is 6.
Step-by-step explanation:
Remember, Gloria can knit one block in 50 minutes, and they want to know how many blocks she can knit in 5 whole hours.
Which means, that is 5 squares in 4 hours, but we still have the 10 minutes from each of the 50 minutes.
So, you add up the 5 ten minutes (50 minutes) Which gives you a whole square.
Therefore, Gloria can knit 6 squares in 50 minutes.
Gloria can knit 6 blocks in 5 hours if she maintains her knitting rate of one block every 50 minutes.
Gloria can knit one block of a quilt in 50 minutes. To find out how many blocks she can knit in 5 hours, one should first convert the knitting time from hours to minutes. Since there are 60 minutes in an hour, 5 hours is equal to 300 minutes. Next, divide the total available knitting time by the time it takes to knit one block.
300 minutes / 50 minutes per block = 6 blocks
So, if Gloria knits at the same rate, she can knit 6 blocks in 5 hours.
1) Which of the following will give a negative correlation?
a) As time goes on, the number of endangered elephants decreases
b) As speed decreases, the number of accidents decreases
c) As time goes on, the height of a baby increases
d) As time goes on, the height of the plant remains the same
2) Brian made a scatter plot and drew in a line of best fit. The equation of his line was
y = -x + 120, where x represents the number of hours spent exercising in a week and y
represents weight. If someone were to spend 12 hours working out this week, use Brian's
line of best fit to predict a reasonable weight.
a) 120
b) 96
c) 114
d) 216
For number 1 the answer is A because negative correlation means something decrease as times goes on and for number 2 the answer is B because it is the best fit and is not really far away if you sustract.hope this helps. please add brainlist
Find the area of the balcony in square feet . Round to the nearest square foot.
A. 22
B. 85
C. 86
D. 96
16x6=96 square feet
Answer: The answer is D. 96
Step-by-step explanation: Why? well on the paper it shows the balcony 16*6 so the answer is 96 square feet.
I need help asap please ?!
Answer:
B
Step-by-step explanation:
[tex]m+4\leq6[/tex]
We subtract 4 from each side to get [tex]m\leq2[/tex]
Let's plug in a random point such as 0.
[tex]0+4\leq6 \\ \\ 4\leq6[/tex]
Since this is true, the inequality we made is true.
John owns a lawn mowing and landscaping business. The income from the business is given by the function f(x) = 2x + 54, where f(x) is the income in dollars and x is the area in square meters of lawn mowed. If John has earned {204, 344, 450, 482} dollars in the last four months, what are the corresponding areas of lawn he mowed?
A.
{75, 145, 198, 214}
B.
{84, 123, 204, 254}
C.
{70, 135, 184, 195}
D.
{80, 110, 185, 246}
E.
{95, 148, 175, 206}
ANSWER
A. {75, 145, 198, 214}
EXPLANATION
From the given information,the income is given by the function
[tex]f(x) = 2x + 54[/tex]
where f(x) is the income in dollars and x is the area in square meters of lawn mowed.
To find the area that corresponds to John's earnings, we equate the function to the earnings and solve for x.
For the area that corresponds to 204, we have
[tex]2x + 54 = 204[/tex]
[tex]2x = 204 - 54[/tex]
[tex]2x = 150[/tex]
[tex]x = 75[/tex]
For the area that corresponds to 344, we have:
[tex]2x + 54 = 344[/tex]
[tex]2x = 344 - 54[/tex]
[tex]2x=290[/tex]
[tex]x = 145[/tex]
For the area that corresponds to 450, we have
[tex]2x + 54 = 450[/tex]
[tex]2x= 450 - 54[/tex]
[tex]2x =396[/tex]
[tex]x = 198[/tex]
For the area that corresponds to 482, we have
[tex]2x + 54 = 482[/tex]
[tex]2x= 482 - 54[/tex]
[tex]2x = 428[/tex]
[tex]x = 214[/tex]
Therefore the correct answer is A.
The area of the indoor sports exhibition is shown below.
What is its perimeter? m ?
What is its area? m2 ?
Answer:
255.40 m3,097.96 m²Step-by-step explanation:
First, you need to make these conversions:
(Remember that [tex]1m=100cm[/tex])
4,000 cm to m:
[tex](4,000cm)(\frac{1m}{100cm})=40m[/tex]
700 cm to m:
[tex](700cm)(\frac{1m}{100cm})=7m[/tex]
You can observe in the figure that it is formed by two rectangles and a semi-circle.
To calculate the perimeter, you need to add the exterior measures of each figure.
Remember that the circumference of a circle is:
[tex]C=2\pi r[/tex]
Where "r" is the radius
Therefore, the perimeter is:
[tex]P=34m+7m+10m+40m+10m+68m+33m+\frac{(2\pi (17m)}{2}\\P=255.40m[/tex]
To find the area of the indoor sports exhibition, you need to add the areas of the rectangles and the area of the semi-circle.
The area of a rectangle can be calculated with:
[tex]A_r=lw[/tex]
Where "l" is the lenght and "w" is the width.
The area of a semi-circle can be calculated with:
[tex]A_{sc}=\frac{\pi r^2}{2}[/tex]
Where "r" is the radius.
Then, the area of the indoor sports exhibition is:
[tex]A=(40m)(10m)+(68m)(33m)+\frac{\pi (17m)^2}{2}\\A=3,097.96m^2[/tex]
What is P(A or B)...?
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 0.5 + 0.4 - 0.15
P(A or B) = 0.75
Which statement is true?
A.
The x-intercept of f(x) is equal to the x-intercept of g(x).
B.
The y-intercept of f(x) is equal to the y-intercept of g(x).
C.
The y-intercept of f(x) is greater than the y-intercept of g(x).
D.
The x-intercept of f(x) is greater than the x-intercept of g(x).
Answer:
D
Step-by-step explanation:
We can see in the graph f(x) that the x intercept is [tex](1,0)[/tex].
In the table of g(x), we can see that the x intercept is [tex](-1,0)[/tex].
Since [tex]1>-1[/tex], the x intercept of the graph f(x) is greater than the x intercept of graph g(x).
ANSWER
D. The x-intercept of f(x) is greater than the x-intercept of g(x).
EXPLANATION
From the graph, f(x) touches the y-axis at y=-1.
The y-intercept of -1
The graph touches the x-axis at x=1.
This is the x-intercept.
From the table, the y-intercept is the point with x-coordinate of zero.
From the table, x=0 when y=1.
The y-intercept of g(x) is 1.
The x-intercept is where y=0.
The x-intercept is -1.
The x-intercept of f(x), which is 1, is greater than the x-intercept of g(x), which is -1
The correct choice is D.
Can y’all help me with this question?
Answer:
Step-by-step explanation:
the answer is 365,412
A bag contains 5 red marbles, 4 blue marbles, 3 green marbles, and no other marbles. If a marble is chosen at random from the bag, what is the probability that the marble chosen will not be red?
Answer:
A = choosing a red marble
B = choosing a green marble
Probability of A happening = P(A) = 5/(3+5+4) = 5/12
Probability of B happening = P(B) = 4/(3+5+4) = 4/12
Probability of either happening = P(A) + P(B) = 5/12 + 4/12 = 7/12
The key word in their question is red OR green and that is why we add the two probabilities. If they ask the probability of them both happening (if they said red AND green), you would multiply P(A)*P(B).
The probability that the chosen marble is not red is [tex]\frac{7}{12}[/tex].
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur.
What is the formula for the probability?The formula of the probability is
[tex]P(E) = \frac{Number\ of\ favorable\ outcomes}{Total\ number\ of\ outcomes }[/tex]
Where, P(E) is the probability of an event.
According to the given question.
Number of red marbles = 5
Number of blue marbles = 4
Number of green marbles = 3
So,
The total number of marbles in a bag = 5+4+3 = 12
And, the probability that chosen marble is red = [tex]\frac{5}{12}[/tex]
Therefore,
the probability that the chosen marble is not red
[tex]=1-\frac{5}{12} \\[/tex]
[tex]= \frac{12-5}{12}[/tex]
[tex]= \frac{7}{12}[/tex]
Hence, the probability that the chosen marble is not red is [tex]\frac{7}{12}[/tex].
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Jason ran 4 miles in 30 minutes. Which of the following is an equivalent rate of running?
A. 6 miles in 50 minutes
B. 3 miles in 20 minutes
C. 10 miles in 75 minutes D. 8 miles in 80 minutes
Answer:
c
Step-by-step explanation:
30 divided by 4 = 7.5
75 divided by 10 = 7.5
The answer is C. Jason goes 2 miles per every 15 minutes. If Jason goes 10 miles you would multiply 15 by 5 and that is 75.
judy has a piece of wood that is 4 5/8 feet long. she cuts off 3 feet 6 inches of the wood for a project. how much wood, in feet does she have left
there are 12 inches in 1 foot, so 6 inches is really just half a foot, thus 3'6" is really just 3.5' or 3½ feet.
now, let's convert those mixed fractions to improper fractions and then subtract, bearing in mind our LCD will be 8.
[tex]\bf \stackrel{mixed}{4\frac{5}{8}}\implies \cfrac{4\cdot 8+5}{8}\implies \stackrel{improper}{\cfrac{45}{8}}~\hfill \stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{45}{8}-\cfrac{7}{2}\implies \stackrel{\textit{using the LCD of 8}}{\cfrac{(1)45~~-~~(4)7}{8}}\implies \cfrac{45-28}{8}\implies \cfrac{17}{8}\implies 2\frac{1}{8}[/tex]
She has 1 and 1/8 foot of wood left.
3 feet and 6 inches is equal to 3 and 1/2 feet.
3 and 1/2 feet are also equal to 3 and 4/8 feet.
Subtract 3 4/8 from 4 5/8.
4 5/8 - 3 4/8 = 1 1/8.
Hope this helps!
If it does, it would help me a lot if you could make me brainliest.
on a trip to the museum, Lance saw a replica of a circular shield used by ancient Greek soldiers if the circumference of the shield is 100.48 inches, ts radius is inches and the area of the front of the shield is aboutsquare inches
Answer:
If the circumference of the shield is 100.48 inches, its radius is 16 inches and the area of the front of the shield is about 803.84 square inches.
Explanation:
Circumference = 2x r x Pi implies r =Circumference / 2Pi=100.48/2x3.14=16
Area = Pi x r²=3.14 x 16²=804.84
Answer:
If the circumference of the shield is 100.48 inches, its radius is 16 inches and the area of the front of the shield is about 803.84 square inches.
what is 1 3/5 × 2 1/7
Answer:
[tex]\large\boxed{1\dfrac{3}{5}\times2\dfrac{1}{7}=3\dfrac{3}{7}}[/tex]
Step-by-step explanation:
Step 1:
Convert the mixed numbers to the improper fractions:
[tex]1\dfrac{3}{5}=\dfrac{1\cdot5+3}{5}=\dfrac{8}{5}\\\\2\dfrac{1}{7}=\dfrac{2\cdot7+1}{7}=\dfrac{15}{7}[/tex]
Step 2:
We multiply the numbers remembering about simplifying:
[tex]1\dfrac{3}{5}\times2\dfrac{1}{7}=\dfrac{8}{5\!\!\!\!\diagup_1}\times\dfrac{15\!\!\!\!\!\diagup^3}{7}=\dfrac{8\times3}{1\times7}=\dfrac{24}{7}=\dfrac{21+3}{7}=\dfrac{21}{7}+\dfrac{3}{7}=3\dfrac{3}{7}[/tex]
A parking lot has the shape of a rectangle with two isoceles right trangles ( one one each end). What is the area of the parking lot if the rectangle 's dimensions are 45ft by 100ft? A) 5512.5 ft^2 B) 6525 ft^2 C) 8550 ft^2 D) 10012.5ft^2
Answer:
Area of the parking lot = 6525 ft²
Explanation:
Since the two isosceles right-angled triangles have equal bases and heights, therefore, their areas are equal
Therefore:
Area of the parking lot = area of rectangle + 2*area of isosceles triangles
1- getting the area of the rectangle:
Area of rectangle = length * width
We are given that the dimensions of the rectangle are 45 ft and 100 ft
Therefore:
Area of rectangle = 45 * 100 = 4,500 ft²
2- getting the area of the isosceles triangle:
Area of triangle = 0.5 * base * height
From the drawing, we can note that:
base of triangle = height of triangle = smaller side of the rectangle = 45 ft
Therefore:
Area of triangle = 0.5 * 45 * 45 = 1,012.5 ft²
3- getting the total area:
Total area of parking lot = area of rectangle + 2*area of isosceles triangles
Total area of parking lot = 4500 + 2(1012.5)
Total area of parking lot = 6,525 ft²
Hope this helps :)
What is the answer for #4 ?
Answer:
[tex]x>5[/tex] or [tex]x<-5[/tex]
Step-by-step explanation:
Isolate the absolute value term.
[tex]7|\frac{x}{7}|>5 \\ \\ |\frac{x}{7}|>35[/tex]
Take about the absolute value sign.
[tex]\frac{x}{7}>5[/tex] or [tex]-\frac{x}{7}>5[/tex]
Solve for each inequality.
[tex]x>5[/tex] or [tex]x<-5[/tex]
If the scale factor of figure A to figure B is 4:5, find the value of x
Answer:
x is 12
Step-by-step explanation:
Write a proportion
4:5
x:15
or you can write it as 4/5=x/15
Cross multiply and you get 12
The value of x if the scale factor of figure A to figure B is 4:5 is; x = 12
We are given the scale factor of figure A to figure B as 4:5.
By use of similar triangles theorem, we can deduce that the ratio of corresponding sides of figure A to corresponding sides of figure B must be equal to 4:5.Now, looking at both triangles, we can say that;
x:15 = 4:5
Thus,we can write in fraction as;
x/15 = 4/5
x = 15 × 4/5
x = 12
In conclusion, the value of x from the given proportion between both triangles is 12.
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Find the perimeter of a square if half of a diagonal is equal to 8 inches
The perimeter of a square, if half of a diagonal is equal to 8 inches would be [tex]32\sqrt{2}[/tex] inches.
In Mathematics and Geometry, the perimeter of a square can be calculated by using the following formula;
P = 4s
Where:
P is the perimeter of a square.s is the side length of a square.In Mathematics and Geometry, the side length of a square can be calculated by using this mathematical equation (formula);
Diagonal, d = √2s
d/2 = 8
d = 16 inches.
By solving for s, we have the following side length:
s = 16/√2
s = [tex]8\sqrt{2}[/tex] inches.
Now, we can determine the perimeter of the square is given by;
P = 4 × [tex]8\sqrt{2}[/tex] inches.
P = [tex]32\sqrt{2}[/tex] inches.
Which individual is most justified in his or her reasons for not purchasing life insurance
Answer:the anwser is B I am not 100% positive because a seems like it make sense to
Step-by-step explanation:
Shown here is the street map of a particular area. Which street appears to NOT be perpendicular to street B?
A.Street A
B.Street D
C.Street E
D.Street F
Answer:
The awnser is Street A
Step-by-step explanation:
SUPER EASY/////
What is the midpoint of a line segment with the endpoints (8,-3) and (-5,-9)?
For this case we have that by definition, the coordinates of the midpoint are given by:
[tex]M = (\frac {x_ {1} + x_ {2}} {2}, \frac {y_ {1} + y_ {2}} {2})[/tex]
We have the following points:
[tex](x_ {1}, y_ {1}) :( 8, -3)\\(x_ {2}, y_ {2}): (- 5, -9)[/tex]
Substituting the values:
[tex]M = (\frac {8 + (- 5)} {2}, \frac {-3 + (- 9)} {2})\\M = (\frac {8-5} {2}, \frac {-3-9} {2})\\M = (\frac {3} {2}, \frac {-12} {2})\\M = (1.5; -6)[/tex]
Answer:
Option C
Answer:
(1.5, -6) ~apex
Step-by-step explanation: