Answer:
31.2 m^2
Step-by-step explanation:
6m x 5.2m
Match each point of intersection with the system of equations whose solution is at that point
The Match of each point of intersection with the system of equations whose solution is at that point are
y = -2x − 3 / y = 2x − 1 --> Z y = x + 4 / y = -x + 2 --> X y = -2x − 3 / y = x + 4 --> Wy = 2x − 1 / y = -x + 2 --> YWhat is the point of intersection?For the 1st system is:
y = -2x - 3 ------- (1)
y = 2x - 1 (2)
So one need to equate (1) and that of (2) so it will be:
2x - 1 = -2x - 3
Add 2x to both sides
4x - 1 = - 3
Add 1 to both sides
4x = -2
Divide both sides by 4
x = -1/2
- Substitute the value of x in equation (1) or (2)
y = 2( ) - 1
y = -1 - 1
y = -2
Therefore, the point of intersection of the two equations is found to be (-1/2, -2), and it is shown by the letter Z.
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What is the probability that a person orders a sandwich with cheddar cheese?
Answer:
50%
Step-by-step explanation:
3) Calculate the shaded area for the given figure.
DO
—4—
Answer:
10.30089
Step-by-step explanation:
This is true because to find the radius of a circle is pie x r^2 so if the circle is 4 across then the radius is 2 and 2^2 is 4 so pie x 4pie and there is three circles so the total area of all of the circles is 12pie and the area of the rectangle is 48 because it is 4 wide and 12 tall because its height is 3 times its width and 48- 12pie is 10.30089
What is the benefit: cost ratio of a program intervention that cost $1.75 million if the savings as a result of the program were $3 million?
The answer is 12:7 but I don't know how they get to the 12? Can someone please explain me?
The benefit-cost ratio of the program intervention is 12:7. This means that for every $7 spent on the program, $12 worth of benefits are realized.
What is ratio?
A ratio is a way of comparing two or more quantities that are measured in the same units. It is a mathematical expression that shows the relationship between two numbers or quantities.
The benefit-cost ratio (BCR) is a ratio of the total benefits of a program intervention to its total costs. In this case, the BCR can be calculated as:
BCR = Total benefits / Total costs
From the given information, the total cost of the program intervention is $1.75 million, and the savings resulting from the program are $3 million. Therefore, the total benefits are $3 million, and the BCR can be calculated as:
BCR = $3 million / $1.75 million
Simplifying this fraction, we can divide both the numerator and denominator by 0.25 million (or 250,000):
BCR = $12 / $7
Therefore, the benefit-cost ratio of the program intervention is 12:7. This means that for every $7 spent on the program, $12 worth of benefits are realized.
Note that to obtain the ratio of 12:7, we first simplify the fraction by dividing both the numerator and denominator by the highest common factor, which is 250,000 in this case. This gives us a new fraction of 12/7, which can be expressed as the ratio of 12 to 7.
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O is the center of the regular nonagon below. Find its perimeter. Round to the nearest tenth if necessary.
Answer:
Step-by-step explanation:
To find the slope of the line, we need to calculate the rise over the run between two points on the line. Let's choose the two points (0, -3) and (6, 3) as shown in the graph.
Rise = change in y = 3 - (-3) = 6
Run = change in x = 6 - 0 = 6
So the slope of the line is:
slope = rise/run = 6/6 = 1
Therefore, the slope of the line is 1.
For the given triangle, find the missing length(s). Give an exact answer and, where appropriate, an approximation to three
decimal places.
Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
A. Using radicals, the shorter leg is exactly The shorter leg, up to three decimal places, is approximately
B. The shorter leg is exactly No approximation is necessary.
Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
OA. Using radicals, the hypotenuse is exactly The hypotenuse up to three decimal places, is approximately
B. The hypotenuse is exactly No approximation is necessary.
This question: 1 point(s) poss
15
Answer:
Step-by-step explanation:
This is a 30-60-90 triangle so the shorter leg is your x
the longer leg is [tex]x\sqrt{3}[/tex]
and the hypotenuse is 2x
They gave you the longer leg because it is across from the 60, no the 30 angle.
so 16=[tex]x\sqrt{3}[/tex]
x=[tex]\frac{16}{\sqrt{3} }[/tex] you cannot have a root on the bottom so multiply by [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex]
[tex]x=\frac{16\sqrt{3} }{3}[/tex] this is the short leg
the long leg multiply by 2 so long leg = [tex]\frac{32\sqrt{3} }{3}[/tex]
I'LL GIVE THE BRAINLIEST IF YOU ANSWER!
Data Set 1 has a mean of 54 and a MAD of 4. Data Set 2 has a mean of 60 and a MAD of 2.
What can be concluded about the two distributions?
Select each correct answer.
A} The distributions are similar.
B} The distributions are somewhat similar.
C} The means-to-MAD ratio is 3.
D} The means-to-MAD ratio is 1.5.
The two distributions can be concluded as:
The distributions are similar.
The means-to-MAD ratio is 3.
Options A and C are the correct answer.
The MAD (Mean Absolute Deviation) is a measure of variability similar to standard deviation, but it measures the average absolute difference between each value and the mean, regardless of the direction of the deviation.
The means-to-MAD ratio is a measure of how spread out the data is, relative to the mean.
Since the means-to-MAD ratio for Data Set 1 is 3 and the means-to-MAD ratio for Data Set 2 is 30, Data Set 1 is more spread out than Data Set 2.
However, since the ratio is not extremely different (i.e., not greater than 10), the two distributions can still be considered similar.
Thus,
The two distributions can be concluded as:
The distributions are similar.
The means-to-MAD ratio is 3.
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Given the following triangle, if c = 25 and angle A = 20 degrees, find a
The length of the side a is 8.55 units.
Given is a right triangle, the side c which the hypotenuse is 25 units, and an acute angle A is 20°,
We need to find the length of the side a,
Considering the angle, A as reference angle, we have,
Sin A = a / c
Sin 20° = a / 25
a = Sin 20° × 25
a = 8.55
Hence, the length of the side a is 8.55 units.
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Sean and Ezra have a total of $240. Sean and Kezia have a total of $360. The ratio of Ezra's amount to Kezia's amount is 1 : 4. How much money does Sean have?
What is the area of the shaded figure below?
16mm
8 mm
O 448 mm²
O 512 mm²
544 mm²
O. 576 mm²
38 mm
8 mm
8 mm
The area of the shaded part is 704mm²
What is area of shape?The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.
The area of the shaded part = area of the whole shape - area of the unshaded part
Area of the whole shape = l×w
= 54 × 16
= 864mm²
Area(1) of the unshaded part = 1/2bh
= 1/2 ×16×8
= 64mm²
Area( 2) of the unshaded part = 1/2bh
= 1/2 ×8 × 8
= 32mm²
Area(3) of the unshaded part = l×w
= 8×8 = 64mm²
therefore the total area of the unshaded part =
64+32+64 = 160mm²
therefore the area of the shaded part = 864-160 =
704mm²
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Slope of a line with points (-4,2)(0,-4)
It is an exercise of the equation of the line, related to the subject of the slope of a line is a fundamental measurement in analytical geometry and mathematics in general. It is a measure that indicates the inclination of a line, that is, how much the y coordinate changes for each unit that the x coordinate changes. The slope is represented by the letter m and is defined as the quotient between the variation of the y coordinates, divided by the variation of the x coordinates.
The importance of slope extends beyond analytic geometry, and it is used in many other areas of mathematics and science. For example, in physics, slope is used to calculate the velocity and acceleration of a moving object. In statistics and econometrics, slope is used to interpret data and make predictions from it.
Also, slope is used in solving analytic geometry problems. For example, slope can be used to find the equation of a line from two known points, or to determine whether two lines are parallel or perpendicular.
We calculate the slope:
To calculate the slope of the line, we apply the following formula:
m = (y₂ - y₁)/(x₂ - x₁)
Now we find the points of x and y.
x₁ = -4 , y₁ = 2
x₂ = 0 , y₂ = -4
We substitute our data in the slope formula and solve, then
m = (y₂ - y₁)/(x₂ - x₁)
m = (-4 - 2)/(0 - (-4))
m = (-6)/(4)
m = - 1.5
The slope between the points (-4,2) and (0,-4) is -1.5.
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Need help quick please! Thank you!
The cosine of twice the angle is given as follows:
cos(2θ) = -527/625.
How to obtain the cosine of twice the angle?The identity to obtain the cosine of twice the angle is given as follows:
cos(2θ) = cos²(θ) - sin²(θ).
The relation between the sine and the cosine is given as follows:
sin²(θ) + cos²(θ) = 1.
Hence the cosine squared is obtained as follows:
cos²(θ) = (7/25)²
cos²(θ) = 49/625.
The sine squared is given as follows:
sin²(θ) = 1 - cos²(θ)
sin²(θ) = 1 - (49/625)
sin²(θ) = (625/625) - (49/625)
sin²(θ) = 576/625.
Meaning that the cosine of twice the angle is given as follows:
cos(2θ) = cos²(θ) - sin²(θ).
cos(2θ) = 49/625 - 576/625
cos(2θ) = -527/625.
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Need help wit this please
Note that the actual area under the above given curve between x =2 and x = 6 is 12,870 (Option A)
How did we arrive at the above?
To derive the actual arae under the curve, we have to tke the limit as the number of rectangles approaches infinity, which means we need to evaluate:
Limn → ∞ RN
Replacing the given formula for Rn, we get:
Limn →∞ [ 193955n⁴ + 863n³ - 38080n² - 204815n⁴
This will given us:
Limn → ∞ [ 193955n + + 863/n - 38080/n² - 2048/n⁴/15]
Note: As n approaches infinity, the second and 3rd terms will become relative negligible when palced side by side with the 1st term and the fouth term nears zero.
Thus:
Limn → ∞ (193055 / 15) = 12870.33
So Option A is the correct answer when approximated.
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How much paint is needed to cover silo with radius of 3 and
You sit down to take a true-or-false test with 6 questions. If you randomly
guess on all questions, how many possible outcomes are there for the
6-question test?
OA. 36
B. 12
O C. 6
OD. 64
SURMIT
Answer:
Please mark me the brainliest.
Step-by-step explanation:
For each question, there are two possible outcomes: true or false. Therefore, the total number of possible outcomes for a 6-question true-or-false test is 2 x 2 x 2 x 2 x 2 x 2, which is equal to 2^6. Using a calculator, we can find that 2^6 is equal to 64.
Therefore, the answer is option D: 64.
The graph y=x² is shown in red. Then x² +5 is shown
in blue and x²-3 is shown in green. Record your
observations of what happened.
1. Adding different constant terms to
The translations to each graph are described as follows:
y = x² + 5 -> translation of the parent function y = x² up by 5 units.y = x² - 3 -> translation of the parent function y = x² down by 3 units.What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.Hence the meaning of each operation is given as follows:
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I need help with this problem if do thank you a lot
The value of x is equal to 17 degrees.
What is the central angle property?In Mathematics and Geometry, the central angle property states that an inscribed angle is equal to one-half the measure of a central angle that is subtended by the same arc.
Based on the information provided about circle C, the central angle of circle P is represented by m∠C and the inscribed angle is represented by (x + 4)°.
This ultimately implies that, the measure of the central angle is twice (double) the measure of the inscribed angle;
m∠C = 2(x + 4)°.
3x - 9 = 2(x + 4)°.
3x - 9 = 2x + 8
3x - 2x = 8 + 9
x = 17
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This figure shows the dimensions for a package to be shipped. Enter the minimum amount of wrapping paper, in square inches, needed to cover the package. Round your answer to the nearest whole inch.
The minimum amount of wrapping paper, needed to cover the package surface area is 174 square inches.
From the given three dimensional figure,
Total surface area = Area of 2 similar trapeziums + Area of rectangles of 4 different rectangles
We know that, area of a triangle = 1/2 ×Base×Height and area of a rectangle is Length×Breadth.
= 2×1/2(7+3)×3+8×5+8×3+8×3+8×7
= 30+40+24+24+56
= 174 square inches
Therefore, the minimum amount of wrapping paper, needed to cover the package surface area is 174 square inches.
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what is 21/40 into a decimal
Answer: 0.525
Hope this helps. Have a nice day!
A right triangle has side 12 and hypotenuse 20. Use the Pythagorean Theorem to find the length of the third side
Answer:
16
Step-by-step explanation:
The Pythagorean theorem states [tex]a^2+b^2=c^2[/tex], where a and b are the legs of the right triangle. To solve for b, we can convert the equation to [tex]b^2=c^2-a^2[/tex]
Plugging the values in, we get [tex]b^2=400-144=256[/tex]
b=16
Find the volume of the composite object below. QUICK PLEASE
Round your answer to the nearest hundredth.
Do not write the units, only write the number.
Answer:
18573.85
Step-by-step explanation:
Area of rectangle = 42 * 9 * 35 = 13230 cm
Area of half-circle cylinder = 42 * (9^2 * pi) / 2 = 5343.8491 cm
13230 + 5343.8491 = 18573.8491
rounded = 18573.85
Jaeger the goat will be tied by a 15-meter chain to the outside of a 10-meter by 16-meter
rectangular shed that is surrounded by grass. Try three different places to attach the chain to the shed. For each, determine the area of grass that Jaeger could eat. Which of your
locations gives Jaeger the most to eat? (Note: Jaeger cannot walk through the shed.)
a. Sketch each of the solutions of the three different places you happen to pick to attach
the chain to the shed. Accuracy counts. What conclusions can you draw based on
your three test points? Do you see any patterns?
In general, your solution(s) need to have evidence which both supports and helps explain your solution(s). Evidence can include but is not limited to words, pictures, diagrams, tables,
The second location result in the largest area of grass that Jaeger can eat, which is approximately 353.57 square meters.
We may infer from the facts provided that Jaeger the goat will be confined to a 10- by-16-meter rectangular shelter by means of a 15-meter chain. All of the grass along the chain may be consumed by Jaeger. At three separate points in the shed, we are instructed to locate the patch of grass that Jaeger can eat.
Let's consider the three different locations as follows:
Attach the chain to a corner of the shed.
Jaeger can only eat as much grass as is contained inside a quarter-circle with a radius of 15 meters (the length of the chain) if the chain is fastened to a shed corner. This quarter-circle's area is:
Area = (1/4) x π x (15 meters)²
Area = 176.71 square meters (approx)
Affix the chain to the middle of one of the shed's longer sides.
This semicircle's area is:
Area = (1/2) x π x (15 meters)²
Area = 353. 57 square meters (approx)
To the center of one of the shed's shorter sides, fasten the chain.
This circular sector's area will be as follows:
Area = (90/360) x π x (15 meters)²
Area = 176.71 square meters (approx)
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Please help. 8th grade math homework
Completing the table using the rounded values showing the relative frequencies is as follows:
Column Relative Frequency Table
Men Women Total
January - June 25% 25% 25%
July - December 75% 75% 75%
Total 100% 100% 100%
What is the relative frequency?Relative frequency shows the quotient between the number of events and the total number of possible events occurring.
The quotient of relative frequency is expressed over 100 to show the result in percentage terms.
Frequency Table
Men Women Total
January - June 21 19 40
July - December 62 58 120
Total 83 77 160
Column Relative Frequency Table
Men Women Total
January - June 25% (21/83) 25% (19/77) 25% (40/160 x 100)
July - December 75% (62/83) 75% (58/77) 75% (120/160 x 100)
Total 100% 100% 100% (160/160 x 100)
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Find the volume and surface area of a water bottle that has the shape of a cylinder with radius 2 centimeters and height 16 centimeters. Round your answer to two decimal places.
The volume and the surface area of the cylindrical bottle is 200.96 cm³ and 226.08 cm² respectively.
Given that a cylindrical bottle has radius 2 of cm and height of 16 cm.
Surface area = 2 π × radius × (radius + height)
= 2 × 3.14 × 2 × (16+2)
= 12.56 × 18
= 226.08
∴ The surface area of the bottle is 226.08 cm².
Volume = π × radius² × height
= 3.14 × 2² × 16
= 200.96 cm³
∴ The volume of the bottle is 200.96 cm³.
Hence, the volume and the surface area of the cylindrical bottle is 200.96 cm³ and 226.08 cm² respectively.
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
Therefore, the two equations that represent circles with a diameter of 12 units and a center on the y-axis are:
[tex]x^2 + (y - 6)^2 = 6^2[/tex]
and
[tex]x^2 + (y + 6)^2 = 6^2[/tex]
We know that a circle with diameter 12 units has a radius of 6 units. Also, since the center of the circle lies on the y-axis, the x-coordinate of the center is 0.
The equation of a circle with center (0, k) and radius r is given by:
[tex](x - 0)^2 + (y - k)^2 = r^2[/tex]
or simply,
[tex]x^2 + (y - k)^2 = r^2[/tex]
Substituting the values, we have:
Diameter = 12 units → Radius = 6 units
Center lies on the y-axis → x-coordinate of center = 0
So, the equation of the circle is. [tex]x^2 + (y - k)^2= 6^2[/tex], where k is the y-coordinate of the center.
We can now check which of the given equations match this form:
[tex]x^2 + (y - 3)^2 = 36 -- >[/tex]center at (0,3) -> not on y-axis
[tex]x^2 + (y - 5)^2 = 6 -- >[/tex]not a diameter of 12 units
[tex](x – 4)^2 + y^2 = 36 -- >[/tex] center not on y-axis
[tex](x + 6)^2 + y^2 = 144 -- >[/tex] center not on y-axis
[tex]x^2 + (y + 8)^2 = 36 -- >[/tex]center at (0,-8) -> not on y-axis
So, the only equation that represents a circle with a diameter of 12 units and a center on the y-axis is:
[tex]x^2 + (y - k)^2 = 6^2[/tex]
We know that the center is on the y-axis, so the x-coordinate is 0. The distance from the center to the y-axis is 6 units. So, the y-coordinate of the center is either 6 or -6. Thus, we get two equations:
[tex]x^2 + (y - 6)^2 = 6^2[/tex]
and
[tex]x^2 + (y + 6)^2 = 6^2[/tex]
Therefore, the two equations that represent circles with a diameter of 12 units and a center on the y-axis are:
[tex]x^2+ (y - 6)^2 = 6^2[/tex]
and
[tex]x^2 + (y + 6)^2 = 6^2[/tex]
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Determine if the two triangles are necessarily congruent. If so, fill in a flowchart proof to prove that they are.
Triangles ABC and MNO are congruent with each other using Side Side Side Rule of Congruency.
There are four rules of congruency of two triangles.
The rules are:
RHS: where in two right angled triangles, right angle, hypotenuse and another length of side are equal, so they are said to be congruent.
SSS: where in any two triangles if each three sides of a triangle are equal to corresponding sides of another triangle then that triangles are called congruent.
SAS: In two triangles, two sides and angle between them are equal for one triangle to another, so the triangles are said to congruent,
AAS: In two triangles, two angles and one side are equal for one triangle to another, so the triangles are said to congruent,
Here in the picture given that, in triangle ABC and triangle MNO,
AC = MO
AB = NO
BC = MN
So the triangles ABC and MNO are congruent with each other using Side Side Side Rule of Congruency.
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Mary can be 24 cookies one dozen per sheet in her oven in 12 minutes how long would it take her to bake 60 cookies
Which of the following represents the equation of a line that is parallel to the line represented by the equation y=12x+6 ?
Hint: Use the formula sheet to determine the formula(s) needed to solve the problem.
The equation of a line that is parallel to y = 12x + 6 is of the form:
y = 12x + b
What is equation of line?The relationship between the coordinates of each point (x, y) on a line is represented by the equation of a line, which is linear in the variables x and y. All of the points on the line satisfy the equation, in other words.
A line is parallel to the line y = 12x + 6 if and only if it has the same slope as the given line.
The slope-intercept form of the equation of a line is:
y = mx + b
where m is the slope of the line and b is the y-intercept.
Since the given line y = 12x + 6 has a slope of 12, any line that is parallel to it must also have a slope of 12. Therefore, the equation of a line that is parallel to y = 12x + 6 is of the form:
y = 12x + b
where b is any constant.
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A pyramid has a square base with a side length of 7 centimeters. If the volume of the pyramid is 196 cubic centimeters, what is its height in centimeters? 4 cm 12 cm 8 cm 7cm 21 cm
Answer:
The formula for the volume of a pyramid is:
V = (1/3) × base area × height
We know that the base of the pyramid is a square with a side length of 7 centimeters. So, the base area is:
base area = side length squared = 7² = 49 square centimeters
We also know that the volume of the pyramid is 196 cubic centimeters. Plugging these values into the formula above and solving for the height:
196 = (1/3) × 49 × height
588 = 49 × height
height = 588/49
height = 12
Therefore, the height of the pyramid is 12 centimeters.
Solve for x.
35⁰
15 cm
X
x = [?] cm
Round to the nearest hundredth.
Enter
The value of the side x = 26. 316cm
How to determine the valueWe need to know the different trigonometric identities. These identities includes;
sinetangentcotangentsecantcosecantcosineTheir different ratios are given as;
sin θ = opposite/hypotenuse
tan θ = opposite/adjacent
cos θ = adjacent/hypotenuse
From the information given, we have that;
Angle , θ = 35 degrees
Opposite side = 15
Hypotenuse side =
Substitute the values
sin 35 = 15/x
cross multiply
x = 26. 316cm
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