Answer:
[tex]\dfrac{x^2}{4}+\dfrac{y^2}{16}=1[/tex]
Step-by-step explanation:
If the ellipse has its x-intercepts at points (2, 0) and (-2, 0) and y-intercepts at points (0, 4) and (0, -4), then its symmetric across the y-axis and across the x-axis.
Moreover,
[tex]a=2\\ \\b=4[/tex]
The equation of such ellipse is
[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/tex]
Hence, the equation of the ellipse is
[tex]\dfrac{x^2}{2^2}+\dfrac{y^2}{4^2}=1\\ \\ \\\dfrac{x^2}{4}+\dfrac{y^2}{16}=1[/tex]
Find the perimeter of the polygon
The perimeter of a polygon is found by adding up the lengths of all its sides. The given polygon has a perimeter of 600,000 km. A side labeled 'mfi' would be 300,000 km.
Explanation:To find the perimeter of a polygon, you add up the lengths of all its sides. In this case, the given sides of the polygon are 200,000 km, 100,000 km, and 300,000 km. So adding these together gives you a perimeter of 600,000 km for this polygon.
If you're asked to find the length of a missing side (e.g., the side labeled as 'mfi'), you can subtract the lengths of the known sides from the total perimeter. So, 600,000 km (total perimeter) - 100,000 km - 200,000 km = 300,000 km. Therefore, the length of 'mfi' is 300,000 km.
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The perimeter of the polygon shown is approximately 84.91 centimeters.
According to the given image
∠B = ∠D and AB = AD.
To find the perimeter, break the polygon into smaller shapes and find the perimeters of those shapes.
Note that triangle ABD is isosceles since AB = AD, so ∠ABD = ∠ADB. Draw imaginary segments BC and DC, which create two right triangles, ABC and ADC. Since ∠B = ∠D, it is clear that ∠ABC = ∠ADC. Additionally, it is given that BC = 8.5 cm and DC = 7.5 cm.Now, the Perimeter of triangle ABD is calculated in the following way:
AB = AD (given) = 6.5 cm
We can use the Pythagorean theorem on triangle ABD to find BD:
[tex]BD^2 = AB^2 - (\frac{1}{2} \times AD)^2\\BD^2 = 6.5^2 - (\frac{1}{2} \times 6.5)^2\\BD^2 = 25.5625\\BD \approx 5.05 cm[/tex]
So, the Perimeter of triangle ABD is
= AB + AD + BD
[tex]\approx 6.5 cm + 6.5 cm + 5.05 cm \\ \approx 18.05 cm[/tex]
Again, the Perimeter of triangle ABC is
AC = BC + AB = 8.5 cm + 6.5 cm = 15 cm
As ∠ABC is a right angle and AC is the hypotenuse, use the Pythagorean theorem to find AB:
[tex]AB^2 + BC^2 = AC^2\\AB^2 + 8.5^2 = 15^2\\AB^2 = 81\\AB = 9 cm[/tex]
Perimeter of triangle ABC
= AB + BC + AC = 9 cm + 8.5 cm + 15 cm = 32.5 cm
Perimeter of triangle ADC:
Similar to triangle ABC, find AD using the Pythagorean theorem:
[tex]AD^2 + DC^2 = AC^2\\AD^2 + 7.5^2 = 15^2\\AD^2 = 135\\AD = 3\sqrt{5} cm \approx 11.86 cm[/tex]
Perimeter of triangle ADC
= AD + DC + AC = 11.86 cm + 7.5 cm + 15 cm = 34.36 cm
Finally, to find the perimeter of the entire polygon, add the perimeters of the three triangles:
Perimeter of polygon = Perimeter of triangle ABD + Perimeter of triangle ABC + Perimeter of triangle ADC
Perimeter of polygon is
[tex]\approx 18.05 cm + 32.5 cm + 34.36 cm \approx 84.91 cm[/tex]
Therefore, the perimeter of the polygon is approximately 84.91 centimeters.
The diameter of a circle is 18 kilometers. What is the length of a 120° arc?
Final answer:
The length of a 120° arc in a circle with an 18-kilometer diameter is approximately 18.85 kilometers.
Explanation:
The question asks to find the length of a 120° arc, given the diameter of a circle is 18 kilometers. To solve this, we first find the radius of the circle by dividing the diameter by 2, which gives us 9 kilometers.
Knowing the circumference formula is 2πr, we calculate the circumference as 2π(9) or 18π kilometers. Since 360° represents the full circumference, a 120° arc represents one-third of the circle.
Thus, the arc's length is one-third of the circumference: ⅓(18π) = 6π kilometers, which is approximately 18.85 kilometers.
The tables below show four sets of data:
Set A
x
1
2
3
4
5
6
7
8
9
y
10
9
8
7
6
5
4
3
2
Set B
x
1
2
3
4
5
6
7
8
9
y
3
4
5
6
7
8
9
10
11
Set C
x
1
2
3
4
5
6
7
8
9
y
8
6
5
4
3.5
3
2.5
2
2
Set D
x
1
2
3
4
5
6
7
8
9
y
1
2.5
2.5
3
4
5
6
8
9
For which set of data will the scatter plot represent a positive linear association between x and y?
Set A
Set B
Set C
Set D
Answer:
B? sorry if its wrong
Step-by-step explanation:
Answer:
The answer is not set c!
Step-by-step explanation:
Jane sold 100 tickets for her school auction. Adult tickets cost $12 and the children tickets cost $8. Jane collected a total of $944. Write a system of equations for this situation
Answer:
see the explanation
Step-by-step explanation:
Let
x ----> number of adult tickets
y ----> number of children tickets
we know that
Jane sold 100 tickets for her school auction
so
[tex]x+y=100[/tex] ----> equation A
Jane collected a total of $944
[tex]12x+8y=944[/tex] ----> equation B
Solve the system by graphing
Remember that the solution is the intersection point both graphs
using a graphing tool
The solution is the point (36,64)
see the attached figure
therefore
The number of adult tickets sold was 36 and the number of children tickets sold was 64
Write the equation of a line parallel to the line y=2x that passes through the given points. a. (0,4) b.(-2,-1) c.(2,0)
Answer:
ju mmmmmmjjum,,,,i,,,,, enjoy
Step-by-step explanation:
Answer:
its option b: (-2,-1)
Step by step:
y=2x
-2=2(-1)
-2=-2
Infinitely many solutions
Byron's weekly salary is $ 650. He receives a 15% pay raise. What is Byron's new weekly salary?How much was his raise?
Answer:
$747.50
Step-by-step explanation:
650×15/100=$97.50 which is then added to 650 Becoz his pay is 15% rising=747.50
g(x) = 5 - 2.7
What is the domain of g?
Answer:
3
Step-by-step explanation:
What is the equation of points (8,16)
Answer:
86
Step-by-step explanation:
Triangle ABC is a right triangle.
Triangle A B C. Angle A is x degrees, B is 90 degrees, C is (x minus 10) degrees. The exterior angle to angle C is (2 x + 40) degrees.
Which equations can be used to find the value of x? Check all that apply.
x + 90 + (x minus 10) = 180
x + 90 + (2 x + 40) = 180
2 x + 80 = 180
x + 90 = 2 x + 40
(x minus 10) + 90 = 2 x + 40
The equations that can be used to the value of x are 1) x+90+(x-10)=180 and 2) x+90+(2x+40)=180.
Step-by-step explanation:
Two properties can be used to find the value of the x.
1) Sum of Interior angles of a triangle is 180°.
⇒x+90°+(x-10)°=180.
2x+80°=180°.
2x=180°-80°.
2x=100°.
x=50°.
⇒(x-10)°=40°.
2) The Angle of the straight line is 180°.
From the given diagram, BC is a straight line ray with C as intersecting point. this will result in two angles. (refer the diagram).
The sum of those two angles will be 180°.
⇒ (x-10)°+ (2x+40)°=180°.
(3x+30)°=180°.
3x=150°.
x=50°.
∴(x-10)°=40° and (2x+40)° = 140°.
∴The equations that can be used to the value of x are x+90+(x-10)=180 and x+90+(2x+40)=180.
11. Circle all of the examples that are perfect square. (You must circle all correct responses to receive credit)
2
4
0
8
10
12
14
16
18
120
Good evening ,
Answer:
Circle 0 , 4 , 16
Step-by-step explanation:
→ 0 = 0²
→ 4 = 2²
→ 16 = 4²
:)
2b + 8 - 5b + 3 = -13 + 8b - 5
Answer:
The final value of [tex]b=\frac{29}{11}[/tex] .
Step-by-step explanation:
Given:
[tex]2b + 8 - 5b + 3 = -13 + 8b - 5[/tex]
We have to find the value of [tex]b.[/tex]
[tex]2b + 8 - 5b + 3 = -13 + 8b - 5[/tex]
Steps to be followed:
Step 1:Bring all the variables one left side of the equation.Subtract 8b both side.
[tex]2b + 8 - 5b + 3-8b = -13 + 8b - 5-8b[/tex]
[tex]2b - 5b -8b+ 3 +8= -13 - 5[/tex]
Step 2:Add the variable and constants on each side.[tex]2b - 5b -8b+ 3 +8= -13 - 5[/tex]
[tex]-11b+11=-18[/tex]
Step 3:Subtract 11 on both side.[tex]-11b+11=-18[/tex]
[tex]-11b+11-11=-18-11[/tex]
[tex]-11b=-29[/tex]
Step 4:Divide -11 on both sides of the equation.[tex]-11b=-29[/tex]
[tex]b=\frac{-29}{-11} =\frac{29}{11}[/tex]
So the final value of b is 29/11.
Last year a bamboo plant was 17 feet tall. It grew 10 feet this year. How tall is it now?
Answer:
27 is the right answer
Step-by-step explanation:
10+17=27 :)
The graph of f(x) is shown. Estimate f(–3).
f(–3) =
The value estimated for f ( -3 ) from the graph is 12.5
Step-by-step explanation:
The function (f) in the graph defines all point sets in plane as (x, f(x)) form. The graph of equation to be the graph of function. I.e. y = f (x). Hence, graph of f is if the special case for graph of equation.
Given x = - 3 and asked to find f (-3). So, we have to see the point of y mapped (meeting point of y) on the point x = -3. In the graph, the point marked on y straight away to x = - 3 is 12.5.
Answer: 12.5
Step-by-step explanation:
it is the same as the g (x) problem. we sub -3 for x and see what the y value is on graph. At -3, y = 12.5
Brainliest? :)
What is the equation, in slope-intercept form, of the line that is perpendicular to the line
y – 4 = –Two-thirds(x – 6) and passes through the point (−2, −2)?
Answer:
[tex]y=\frac{3}{2}x +1[/tex]
Step-by-step explanation:
We are given;
The equation of a line;
[tex]y-4 = -\frac{2}{3}(x-6)[/tex]
We are required to determine the equation of a line perpendicular to the above line and passing through (-2, -2).
We can get the gradient of a line when given its gradient and a point where it is passing through.In this case;We need to know that the product of gradient of two parallel lines is -1
Therefore, we can get the gradient of the unknown line;m₁× m₂ = -1
Thus;
m₂ = -1 ÷ -2/3
= 3/2
Thus, the gradient is 3/2 and the line passes through (-2,-2)
Thus, to get its equation, we take another point (x,y)
We get;
[tex]\frac{y+2}{x+2}= \frac{3}{2}[/tex]
Then;
[tex]2(y+2)=3(x+2\\2y + 4 = 3x + 6[/tex]
Combining the like terms,
[tex]2y=3x+2[/tex]
In the form of slope-intercept;
[tex]y=\frac{3}{2}x +1[/tex]
orthocenter of the triangle with vertices J(1,0) H(6,0) I(3,6)
Answer:
(3, 1)
Step-by-step explanation:
The orthocenter is the point where the altitudes meet. Since all three altitudes meet there, it is only necessary to look at two of them. A graph helps immensely.
In the attached graph, we notice that segment HJ is horizontal, so the x-coordinate of the orthocenter will be that of point I (x=3).
The segment IJ has a rise of 3 for a run of 1, so its perpendicular through point H will have a rise of 1 for a run of -3. That gets you to point (3, 1) from point H, so (3, 1) is the orthocenter.
Write the following as an exponential expression?
Answer:
Step-by-step explanation:
recall that for a radical expression, the following apply
[tex]\sqrt[x]{y} = y^{\frac{1}{x} }[/tex]
compare this with our case, we can clearly see that
x = 4 and y = 10,
substituting into the above equation gives:
[tex]\sqrt[4]{10} = 10^{\frac{1}{4} }[/tex]
The expression [tex]$\sqrt[4]{10}[/tex] can be written as an exponent as [tex]$(10)^{\frac{1}{4} }[/tex].
What is the general equation of exponential function? What is the general equation of a quadratic equation?The general equation of a exponential relationship is -
y = Aeˣ
The general equation of a quadratic equation is -
y = ax² + bx + c
Given is the following expression -
[tex]$\sqrt[4]{10}[/tex]
We can write the given expression in the form of exponential expression as -
y = [tex]$(10)^{\frac{1}{4} }[/tex]
Therefore, the expression [tex]$\sqrt[4]{10}[/tex] can be written as an exponent as [tex]$(10)^{\frac{1}{4} }[/tex].
To solve more questions on exponential function, visit the link below-
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In a trapezoid ABCD with legs AB and CD, the diagonals intersect each other at point O. Compare the areas of △ABO and △CDO.
ar(ΔABO) = ar(ΔCDO)
Explanation:
The image attached below.
Given ABCD is a trapezoid with legs AB and CD.
AB and CD are non-parallel sides between the parallels AD and BC.
In ΔABD and ΔACD,
We know that, triangles lie between the same base and same parallels are equal in area.
⇒ AD is the common base for ΔABD and ΔACD and they are lie between the same parallels AD and BC.
Hence, ar(ΔABD) = ar(ΔACD) – – – – (1)
Now consider ΔABO and ΔCDO,
Subtract ar(ΔAOD) on both sides of (1), we get
ar(ΔABD) – ar(ΔAOD) = ar(ΔACD) – ar(ΔAOD)
⇒ar(ΔABO) = ar(ΔCDO)
Hence, ar(ΔABO) = ar(ΔCDO).
John scored 5:7 of the goals he attempted at the soccer game. During three games, if John scored 20 goals, how many did he attempt
Answer:
John scored 20 goals he attempted 28.
Step-by-step explanation:
Given:
John scored 5:7 of the goals he attempted at the soccer game.
During three games, if John scored 20 goals.
Now, to find the number of attempts.
Let the number of attempts be [tex]x.[/tex]
The number of goals = 20.
As, given John scored 5:7 of the goals he attempted at the soccer game.
So, 5 is equivalent to 7.
Thus, 20 is equivalent to [tex]x.[/tex]
Now, to solve by using cross multiplication method:
[tex]\frac{5}{7} =\frac{20}{x}[/tex]
By cross multiplying we get:
[tex]5x=140[/tex]
Dividing both sides by 5 we get:
[tex]x=28.[/tex]
Therefore, he attempt 28.
Complete the square x squared +18x-64=0
Answer:
x = -9±√145 (= 3.04 or -21.04)
Step-by-step explanation:
x²+18x-64 = 0 (move the constant to the right side, add 64 to both sides)
x²+18x = 64 (divide the x-term by 2, square it, then add it to both sides)
x²+18x + (18/2)²= 64 + (18/2)² (simplify)
x²+18x + 9²= 64 + 9²
x²+18x + 9²= 64 + 81
x²+18x + 9²= 145 (simplify left side using the property (a+b)² = a²+ 2ab+b²)
(x+9)² = 145 (take square root of both sides)
x+9 = ±√145
x = -9±√145 (= 3.04 or -21.04)
You are told that in a billiards shot, the cue ball was shot at the eight ball, which was 8 inches away. As a result, the eight ball rolled into a pocket, which was 6 inches away.
Knowing that the angle made with the path of the cue ball and the resulting path of the eight ball is larger than 90°, it can be determined that the original distance from the cue ball to the pocket was greater than ____ inches
DISCLAIMER:
I know the answer is 10 but I don't know why, I thought I did the math right but I got 100. I'll give brainliest if you explain it well!
Answer:It is greater than 10 because as you add both distances from the image its greater than 10 by a bit, looking at the angle it gives you a bigger perspective in how far the cue ball is from the pocket
Its basically 8+6 which equals 14 but adding the way the angle is going the distance is shorter than 14 but greater than 10
Answer:
10 inches
Explanation:
correct on edge
Round 1,208.7438 to the nearest hundredth.
A. 1,208.73
B. 1,208.74
C. 1,208.743
D. 1,208.75
Answer:
the answer is 1,208.74
What is the numerator of the simplified sum?
x/x^2 +3x+2 + 3/x+1
Question:
What is the numerator of the simplified sum?
x/x^2 +3x+2 + 3/x+1
Answer & Step-by-step explanation:
The given equation is as follows.
\frac{x}{x^{2}+3x+2} + \frac{3}{x+1}
Taking L.C.M, the equation will become as follows.
\frac{x(x+1)+ 3(x^{2}+3x+2)}{(x^{2}+3x+2)(x+1)} ........ (1)
Factorize the equation x^{2}+3x+2 in the denominator as follows.
x^{2}+3x+2
= x^{2} + 2x + x + 2
= x(x+2) + 1(x + 2)
= (x+1)(x+2) ........ (2)
Put the factors in equation (2) in to equation (1), then the equation will become as follows.
\frac{x(x+1)+ 3(x^{2}+3x+2)}{(x^{2}+3x+2)(x+1)}
= \frac{x^{2}+x +3x^{2}+9x+6)}{(x+1)(x+2)(x+1)}
= \frac{4x^{2}+10x+6}{(x+1)^{2}(x+2)}
Now, factorize the numerator as follows.
\frac{4x^{2}+10x+6}{(x+1)^{2}(x+2)}
= \frac{4x^{2}+4x+6x+6}{(x+1)^{2}(x+2)}
= \frac{4x(x+1) + 6(x+1)}{(x+1)^{2}(x+2)}
= \frac{(4x+6)(x+1)}{(x+1)^{2}(x+2)}
Cancelling (x+1) from both numerator and denominator. Then the equation will be written as follows.
\frac{(4x+6)(x+1)}{(x+1)^{2}(x+2)}
= \frac{(4x+6)}{(x+1)(x+2)}
The numerator of simplified sum is (4x+6).
4x+6
C on Edge 2022
20 characters20 characters20 characters20 characters20 characters20 characters20 characters20 characters
What is an equivalent fraction for 5/10
Answer:
1/2
Step-by-step explanation:
5/10, 5 is HALF of ten so 1/2
Here’s another one thank u all for helping me. I really appreciate it!
Area = Square - Circle
Area of Square = 10² = 100 m²
Area of Circle = π(5²) = 25π m²
Area of Shaded Region = 100 - 25π = 21.5 m² approx.
answer: second choice
What is the value of x and y I’m stuck!!!
Answer:
x = 4 and y = 8
Step-by-step explanation:
Using the tangent and cosine ratios in the right triangle and the exact values
tan30° = [tex]\frac{1}{\sqrt{3} }[/tex], cos30° = [tex]\frac{\sqrt{3} }{2}[/tex]
tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{4\sqrt{3} }[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex] ( cross- multiply )
[tex]\sqrt{3}[/tex] x = 4[tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )
x = 4
-------------------------------------------------------------------
cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4\sqrt{3} }{y}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
[tex]\sqrt{3}[/tex] y = 8[tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )
y = 8
noah has 4 bags of marbles with the same number in each bag. if there are 536 marbles altogether,how many marbles are in each bag?explain how u know
Answer:
There are 134 marbles in each bag.
Step-by-step explanation:
536/4=134
Answer:536 divided by 4 equals 134 marbles in each bag
Step-by-step explanation:
What should be subtracted from 3x^2-4y^2+5xy+20 to obtain x^2+y^2+6xy+20?
Answer:
2x² − 5y² − xy
Step-by-step explanation:
3x²- 4y² + 5xy + 20
−
x² + y² + 6xy + 20
________________
2x² − 5y² − xy + 0
What is 84,396 + 29,760
Answer:
114, 156
Step-by-step explanation:
Answer: 114,156
Step-by-step explanation:
To add 84,396+29,760 you must add each row.
6+0 = 6
9+6 = 15 (Carry up the one)
3+7 = 10 + 1 = 11 (Carry up the one)
4+9 = 13 + 1 = 14 (Carry up the one)
8+2 = 10 + 1 = 11
So the answer will be 114,156
Chen’s report will take 8 and one third hours to complete. He has worked for three fifths of the time doing research. How long has he worked?
Answer:
5 Hours
Step-by-step explanation:
Given:
Chen’s report will take 8 and one third hours to complete.
He has worked for three fifths of the time doing research.
Question asked:
How long has he worked = ?
Solution:
Total hour required to complete the report = [tex]8\frac{1}{3}[/tex] = [tex]\frac{25}{3}[/tex]
He has worked of the total hour = [tex]\frac{3}{5}[/tex]
He has worked = three fifth of the total time doing research.
= [tex]\frac{3}{5} \times\frac{25}{3}[/tex]
= [tex]\frac{75}{15}[/tex]
= [tex]5 hours[/tex]
Thus,he has worked 5 hours doing his research.
Can someone please help me
a^2 + b^2 = c^2
65^2 + 34^2 = c^2
4225 + 1156 = c^2
5381 = c^2
c ≈ 73.3552997404
Hope this helps! ;)