Answer:
the length of major semiaxes a = 8.45 cm and minor semiaxes b= 5.63 cm.
Step-by-step explanation:
Area of ellipse = π*a*b
Let major semiaxes = a and minor semiaxes = b
then a:b = 3:2
a/b = 3/2
=> a = 3/2 b
Putting in the value of formula
150 = π * (3/2)b * b
150 = 3.14 * 1.5b * b
150= 4.71 b^2
150/4.71 = b^2
=> b^2 = 31.8
b= 5.63
a = 3/2 * b
a = 1.5 * 5.63
a = 8.45
So, the length of major semiaxes a = 8.45 cm and minor semiaxes b= 5.63 cm.
Answer:
Major: 8.5 cm
Minor: 5.6 cm
Step-by-step explanation:
PLEASE HELP!
Questions are in attachment below :)
Answer:
Step-by-step explanation:
1 option 2c
1. The equation of a circle with center (h,k) and radius r units is given by
[tex](x-h)^2+(y-k)^2=r^2[/tex]
The given circle has center (5,-2) and a radius r=3 units.
We substitute these values into the formula to get:
[tex](x-5)^2+(y--2)^2=3^2[/tex]
This simplifies to:
[tex](x-5)^2+(y+2)^2=9[/tex]
The correct answer is A.
2. The given circle has center (3,-5) and radius r=8 units.
We substitute the given values into the formula to obtain:
[tex](x-3)^2+(y--5)^2=8^2[/tex]
We simplify to get:
[tex](x-3)^2+(y+5)^2=64[/tex]
The correct answer is C
3. The given circle has equation:
[tex](x+8)^2+(y+9)^2=169[/tex]
We can rewrite this equation as:
[tex](x--8)^2+(y--9)^2=13^2[/tex]
Comparing this to
[tex](x-h)^2+(y-k)^2=r^2[/tex]
The center is (-8,-9) and the radius is 13.
The correct answer is A.
4. The given circle has equation:
[tex](x-7)^2+y^2=225[/tex]
We can rewrite this equation as:
[tex](x-7)^2+(y-0)^2=15^2[/tex]
Comparing this to
[tex](x-h)^2+(y-k)^2=r^2[/tex]
The center is (7,0) and the radius is 15.
The correct answer is B.
5. The given circle has center (-2,6) and passes through (-2,10).
We can use the number line to find the radius.
[tex]r=|10-6|=4[/tex]
[tex](x-h)^2+(y-k)^2=r^2[/tex]
We substitute the center and the radius into the formula to get:
[tex](x--2)^2+(y-6)^2=4^2[/tex]
This simplifies to:
[tex](x+2)^2+(y-6)^2=16[/tex]
The correct answer is A
6. The given circle has center (1,2) and passes through (0,6).
We can use the distance formula to find the radius.
[tex]r=\sqrt{(1-0)^2+(2-6)^2}=\sqrt{17}[/tex]
[tex](x-h)^2+(y-k)^2=r^2[/tex]
We substitute the center and the radius into the formula to get:
[tex](x-1)^2+(y-2)^2=\sqrt{17}^2[/tex]
This simplifies to:
[tex](x-1)^2+(y-2)^2=17[/tex]
The correct answer is C
What is the slope of the line that passes through (-2,7) and (4,9)
[tex]
s=\frac{\Delta{y}}{\Delta{x}}=\frac{9-7}{4+2}=\boxed{\frac{2}{6}=\frac{1}{3}}
[/tex]
Hope this helps.
r3t40
What is the value of s in the figure below?
The value of 's' is calculated using the formula s = re, where e is the angle in radians and r is the radius in meters, which can also be determined statistically.
Explanation:The value of s in the given physics problem represents the distance between two objects separated by an angle, when they are a certain distance r apart. According to the information and by using the formula s = re, where e is the angle in radians and r is the radius in meters (converted from millimeters), we can substitute the known values to find s. Since S = 80×109 N/m² is the shear modulus and given the small value of Kåp, we assume that s will be significantly small compared to 0.040. Additionally, the value of s can also be found using statistical methods, as indicated by a computer or calculator output showing s = 16.4 as the standard deviation in a set of residuals.
After a deposit of $250, a withdrawal of $312, and a
deposit of $15, the balance in a savings account is
$67.50. What was the balance (b) before the deposits
and withdrawal?
Answer:
55
Step-by-step explanation:
A cone has a lateral area 100 pi and total surface area 136 pi. Find its radius.
Answer:
Radius of the cone is 6 unit.
Step-by-step explanation:
Given:
Lateral Surface Area of Cone, LSA = 100π unit²
Total Surface Area of cone, TSA = 136π unit²
Let, r be the radius of cone.
According to the question,
Total Surface area = lateral surface area + Area of circle
136π = 100π + πr²
πr² = 36π
r² = 36
r = 6
Therefore, Radius of the cone is 6 unit.
The radius of the cone is 6 units.
To solve for the radius of the cone, we need to use two formulas: the lateral area (LA) and the total surface area (TSA) of a cone. The given values are:
Lateral area (LA) = 100πTotal surface area (TSA) = 136πWe use the following formulas:
Lateral area (LA) = πrl, where r is the radius and l is the slant height.Total surface area (TSA) = πr² + πrl.From the given values:
100π = πrl (Lateral area)From the first equation, we can express l in terms of r:
l = 100 / r
Substitute l in the second equation:
136 = r² + r(100 / r)
=> 136 = r² + 100
Rearrange the equation to solve for r:
r² = 136 - 100
=> r² = 36
=> r = √36
=> r = 6.
True or false: When it's argument is restricted to (0,2pi), the polar form of a complex number is *not unique*.
Answer:
The CORRECT answer is False
Step-by-step explanation:
I just took the test and got it correct!!
cos x + i sin x in the range 0 to 2pi will be unique so false.
What do you mean by complex number?Complex numbers exist the numbers that exist expressed in the form of a+ib where, a, and b are real numbers, and 'i' exists an imaginary number named “iota”. The value of i = (√-1).
The abbreviated polar form of a complex number exists z = rcis θ, where r = √(x2 + y2) and θ = tan-1 (y/x).
The range is the difference between the highest and lowest values in a set of numbers. To find it, subtract the lowest number in the distribution from the highest.
The range in statistics for a given data set is the difference between the highest and lowest values. For example, if the given data set is {2,5,8,10,3}, then the range will be 10 – 2 = 8. Thus, the range could also be defined as the difference between the highest observation and lowest observation.
Hence, cos x + i sin x in the range 0 to 2pi will be unique so false.
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The Greatest common factor between 14 and 24
The greatest common factor between 14 and 24 is 2 because
The factors of 14 that divides 14 without a remainder are 1,2, and 7
The factors of 24 that divides 14 without a remainder are 1,2,3,4,6,8,and 12
Therefore 2 is the greatest factor between 14 and 24.
For this case we have that by definition, the Greatest Common Factor or GFC of two numbers is given by the biggest factor that divides both without leaving residue. We should look for the GFC of 14 and 24.
14: 1,2,7,14
24: 1,2,3,4,6,8,12,24
Thus, it is observed that the GFC of both numbers is 2.
Answer:
2
Identify the real zeros for f(x) = 3x2 + 2x + 4.
A) 1 and −1
B) 0 and −1
C) no solution
D) infinite solutions
Answer:
c: no solution
Step-by-step explanation:
Final answer:
The function f(x) = 3x^2 + 2x + 4 has no real zeros because the discriminant (b^2 - 4ac) is negative, indicating that the roots of the quadratic equation are complex.
Explanation:
The question asks us to identify the real zeros of the function f(x) = 3x2 + 2x + 4. To find the real zeros, we look for values of x that make f(x) equal to zero. We can approach this by attempting to solve the quadratic equation 3x2 + 2x + 4 = 0 using the quadratic formula, which is x = [-b ± √(b2 - 4ac)]/(2a), where a = 3, b = 2, and c = 4.
Inserting these values into the formula, we get:
x = [-2 ± √((2)2 - 4*3*4)]/(2*3)
x = [-2 ± √(4 - 48)]/(6)
x = [-2 ± √(-44)]/(6)
Since the part under the square root (√(-44)) is negative, this indicates that the solutions for x are complex, not real. Therefore, the equation 3x2 + 2x + 4 has no real solutions.
round 939,515 to the nearest ten
Answer:
939,520
Step-by-step explanation:
You round up because you have a 5 in the tens place and as the saying goes: "Five or more up the score, four or less let it rest"
The number 939,515 rounded to the nearest tens is 939520.
What is rounding off of numbers?We round off numbers to make them easier to remember and it also keeps their value approximately to the place it has been rounded off.
To round off any number to any place we'll look for the digit next to that place and if it is equal to or greater than 5 we'll add one to the previous digit and make all the digits after it zeroes and if the digit is less than 5 we do not add one to the preceding digit and simply make all the digit after it to zeroes.
Given, A number 939515 and we have to round it to the nearest ten.
To round this number to the nearest ten we'll look at the digit at the unit's place.
The digit at the unit place is 5 so we'll add 1 to the tens digit and make the unit digit zero.
Therefore the number 939515 rounded to the nearest tens place is
939520.
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What is the volume of the given prism? Round the answer to the nearest tenth of a centimeter. The figure is not drawn to scale.
To find the volume of a rectangular prism, multiply the 3 side lengths by each other.
Volume = 7.9 x 6.3 x 12.4 = 617.148 cubic cm.
Rounded to the nearest tenth = 617.2 cubic cm.
Answer: [tex]617.1\text{ cm}^3[/tex]
Step-by-step explanation:
In the given picture, we have a rectangular prism.
Height : 7.9 cm
Length = 12.4 cm
Width = 6.3 cm
The volume of a rectangular prism is given by :-
[tex]V=l\times w\times h[/tex], where l is length, w is width and h is height of the prism.
Now, the volume of a rectangular prism will be :-
[tex]V=12.4\times 6.3\times 7.9\\\\\Rightarrow\ V=617.148\approx617.1\text{ cm}^3[/tex]
Hence, the volume of a rectangular prism = [tex]617.1\text{ cm}^3[/tex]
What is the range of the function f(x) = 3x^2 + 6x - 8?
R; all quadratic functions are going to have ranges and domains of *ALL REAL NUMBERS*.
since there are 6.6 laps in a mile, how many laps will you have to make to run 5 miles?
Answer:
33 laps
Step-by-step explanation:
we know that
There are 6.6 laps in a mile
so
using proportion
Find how many laps will you have to make to run 5 miles
so
Let
x ----> the number of laps
[tex]\frac{6.6}{1}\frac{laps}{mile}=\frac{x}{5}\frac{laps}{mile} \\ \\x=6.6*5\\ \\ x=33\ laps[/tex]
what kind of equation is (-2v^2 + v – 3) + (5v^2 + 6v + 4)
Well I guess I can do it tomorrow but I’m not sure if it’s a good
which expression is equivalent to 6 × 2/3
Answer:
[tex]\large\boxed{6\times\dfrac{2}{3}=4}[/tex]
Step-by-step explanation:
[tex]6\times\dfrac{2}{3}=\dfrac{6^{:3}}{1}\times\dfrac{2}{3_{:3}}=\dfrac{2}{1}\times\dfrac{2}{1}=2\times2=4[/tex]
Three times a number increased by 8 is at most 40 more than the number
The verbal statement 'three times a number increased by 8 is at most 40 more than the number' is expressed as the inequality 3x + 8 ≤ x + 40 in mathematical terms. This inequality simplifies to x ≤ 16, indicating that the original number must be 16 or less.
Explanation:The question involves translating a verbal statement into a mathematical inequality. The phrase 'three times a number increased by 8 is at most 40 more than the number' can be represented algebraically. Begin by letting the variable 'x' represent the unknown number. The phrase 'three times a number' translates to '3x', 'increased by 8' means we add 8, and 'is at most' indicates that the expression is less than or equal to something. '40 more than the number' is translated to 'x + 40'. Combining these elements, we have the inequality 3x + 8 ≤ x + 40.
To solve this inequality, we would subtract 'x' from both sides to get 2x + 8 ≤ 40, and then subtract 8 from both sides to find 2x ≤ 32. Next, we would divide both sides by 2 to get x ≤ 16. This tells us that the original number must be 16 or any number less than 16 to satisfy the condition described in the question.
Understanding how to translate verbal statements into mathematical expressions and inequalities is a fundamental math skill. Knowing terms such as 'at most' is crucial for setting up the correct inequality. This situation is an application of basic algebra to interpret and solve problems.
ΔABC undergoes a dilation, with a scale factor of 5, to form ΔA'B'C'.
Side A'B' is 5 times the length of side AB.
What is the area of ΔA'B'C', compared to the area of ΔABC?
A. The area of ΔA'B'C' is 1/5 of the area of ΔABC.
B. The area of ΔA'B'C' is 1/25 of the area of ΔABC.
C. The area of ΔA'B'C' is 25 times the area of ΔABC.
D. The area of ΔA'B'C' is 5 times the area of ΔABC.
Answer:
option C
Step-by-step explanation:
Your friend can clap his hands 28 times in 12 seconds. How many times can your friend clap his hands in 0.5 minutes?
Answer:
70 times
Step-by-step explanation:
12 * 5 = 60
28 * 5 = 140
140/2 = 70
According to the question,
Friend clap,
28 times in 12 seconds.then,
→ [tex]12\times 5 =60 \ times[/tex]
→ [tex]28\times 5 = 140 \ times[/tex]
In 0.5 minutes, he clap.
= [tex]\frac{140}{2}[/tex]
= [tex]70 \ times[/tex]
Thus the response above is appropriate.
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What are the zeros of the function? f(x)=3x^2−24x+36 Enter your answers in the boxes. The zeros of f(x) are and
[tex]
f(x)=3x^2-24x+36 \\
0=3(x-2)(x-6) \\
0=(x-2)(x-6)
[/tex]
There will be 2 solutions.
[tex]
x-2=0\Longrightarrow\boxed{x_1=2} \\
x-6=0\Longrightarrow\boxed{x_2=6}
[/tex]
Hope this helps.
r3t40
The zeros of the function f(x) = 3x^2 - 24x + 36 are found using the quadratic formula to be x = 6 and x = 2.
The zeros of the function f(x) = 3x2 \- 24x + 36 are the values of x for which f(x) equals zero. To find the zeros, we set the quadratic equation equal to zero and solve for x. This can be done using the quadratic formula x = (-b \\pm (sqrt{b2 \(- 4ac})/(2a), where a = 3, b = -24, and c = 36. Applying the quadratic formula:
Calculate the discriminant: \(( -24 )2 \- 4 * 3 * 36 = 576 \- 432 = 144)Take the square root of the discriminant: \sqrt{144} = 12Apply the values to the quadratic formula: \x = (24 \pm 12) / 6Solve for the two possible values of x: \x = 6, \x = 2Therefore, the zeros of the function are x = 6 and x = 2.
A 25-foot long board is to be cut into two parts. The longer part is one foot more than twice the shorter part. How long is each part?
17 and 8
Step-by-step explanation:
8 is the shortest board so multiply 8 by 2 add the 1 foot more gives you 17
In the pulley system shown in this figure, MQ = 30 mm, NP = 10 mm, and QP = 21 mm. Find MN.
MN is 63 mm.
Since triangles MPQ and NQP are similar, we have the following
proportion:
[tex]\frac{MQ}{NP} = \frac{QP}{MN}[/tex]
Substituting the given values, we have:
[tex]\frac{30}{10} = \frac{21}{MN}[/tex]
Solving for MN, we get:
[tex]MN = \frac{21 \times 30}{10} = 63 mm[/tex]
Therefore, MN is 63 mm.
Compare 7 x 10^3 and 2 x 10^3.
Answer
5000
Step-by-step explanation:
You convert the numbers into standard #'s which gets you 7000 and 2000. Subtract 7000 - 2000 and you get 5000.
7x10^3 is 3-1/2 times the size of 2x10^3.
Which of the following statements are true?
1. The difference between -14 and -8.3 is positive.
II. -14 + 8.3 has the same value as the difference between -1.4 and -8.3.
HII. The between -8.3 and -14 has the same value as the difference between -1.4 and -8.3.
É
only
A of the statements are true.
None of the statements are true
Answer:
None of the statements are true
Step-by-step explanation:
Given statements are:
I. The difference between -14 and -8.3 is positive.
II. -14 + 8.3 has the same value as the difference between -1.4 and -8.3.
III. The between -8.3 and -14 has the same value as the difference between -1.4 and -8.3.
Test for statement (I).
difference = -14-(-8.3) = -14+8.3 = -5.7
which is negative so statement I is FALSE.
Test for statement (II).
-14+8.3 = 5.7
difference = -14-(-8.3) = -14+8.3 = -5.7
which are different so statement II is FALSE.
Test for statement (III).
difference = -8.3-(-14) = -8.3+14 = 5.7
which is different than difference value -5.7 for statement I.
so statement III is FALSE.
So the correct choice is "None of the statements are true".
What is the area of the right triangle 8 and 2
Answer:
Step-by-step explanation:
fv xcfvsvsvfber
Answer:
D
Step-by-step explanation:
The area (A) of a triangle is calculated using the formula
A= [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = 8 and h = 2, so
A= 0.5 × 8 × 2 = 8 units² → D
What is the volume of this right cone?
[tex]\bf \textit{volume of a right-circular cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=12\\ h=15 \end{cases}\implies V=\cfrac{\pi (12)^2(15)}{3}\implies V=720\pi[/tex]
please answer these two before 1:20 pm please!!! thank you!!!
Answer:
21. D
22. A
Step-by-step explanation:
Latitude and longitude describe locations on the Earth with respect to the equator and prime meridian. The table shows the latitude and daily high temperatures on the first day of spring for different locations with the same longitude. Which statement describes the slope of the line of best fit for the data? The temperature decreases by about 0.9° for each 1 degree increase north in latitude. The temperature decreases by about 1.7° for each 1 degree increase north in latitude. The temperature increases by about 0.8° for each 1 degree increase north in latitude. The temperature increases by about 1.3° for each 1 degree increase north in latitude.
Answer: B
Step-by-step explanation: edge2022
The volume of box A is 2/5 the volume of box b. What is the height of box A if it has a base area 32 square centimeters
The length of the edge of the bases is x = 4 and x=1.79.
What is the volume of the box?The volume of a rectangular box can be calculated if you know its three dimensions: width, length, and height.
The volume of a box with a square base and a height of 2 cm is 32cm for box A and the volume of a box with a square base and a height of 10cm is 32cm.
What is the length of the edge of the bases?
The volume of the box = length × width × height
Therefore, we are going to make use of Equation (1) to determine the solution to this question, so that we have;
For Box A; We are given our volume to be equal to 32cm^3, height = 2cm, length and width = x cm.
For Box B IS;
[tex]\rm 32 = 2x^2\\\\x^2 = 16\\\\x^2=4^2\\\\x=4[/tex]
Here Length = width.
For box B;
[tex]\rm 32 = 10x^2\\\\x^2=\dfrac{32}{10}\\\\x^2=3.2\\\\x=1.79[/tex]
Hence, the length of the edge of the bases is x = 4 and x=1.79.
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The volume of a sphere is 2 comma 143.57 m cubed. To the nearest meter, what is the radius of the sphere? Use 3.14 for pi.
[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ \cline{1-1} V=2,143.57 \end{cases}\implies 2143.57=\cfrac{4\pi r^3}{3}\implies 6430.71=4\pi r^3 \\\\\\ \cfrac{6430.71}{4\pi }=r^3\implies \sqrt[3]{\cfrac{6430.71}{4\pi }}=r\implies \stackrel{\pi =3.14}{7.9999956 \approx r}\implies \stackrel{\textit{rounded up}}{8=r}[/tex]
Geometry 1-3 Answers if u can
The answer are:
1.D
2.C
3.A
Explanation is in above pictures.
The trajectory of a potato launched from a potato cannon on the ground at an angle of 45 degrees with a speed of 65 meters per second can be modeled by the parabola: y=x-0.0023x^2, where the x-axis is the ground. Find the height point of the trajectory and the horizontal distance the potato travels before hitting the ground.
Step-by-step explanation:
The highest point of a parabola is at the vertex.
x = -b / (2a)
x = -1 / (2×-0.0023)
x ≈ 217.4
y = (217.4) − 0.0023 (217.4)²
y ≈ 108.7
The horizontal distance can be found when the potato lands (y=0):
0 = x − 0.0023x²
0 = x (1 − 0.0023x)
x = 0, x ≈ 434.8
So the potato reaches a maximum height of 108.7 m and travels a horizontal distance of 434.8 m.
The height point of the trajectory is 217.39 meters and the horizontal distance the potato travels before hitting the ground is 434.78 meters.
Explanation:To find the height point of the trajectory and the horizontal distance the potato travels before hitting the ground, we can use the equation y=x-0.0023x^2 to represent the trajectory. Since the trajectory is a parabola, the height point corresponds to the vertex of the parabola. To find the vertex, we can use the formula x = -b / (2a), where a = -0.0023 and b = 1. To find the horizontal distance the potato travels before hitting the ground, we need to find the x-intercepts of the parabola, which correspond to the points where y = 0.
First, let's find the height point:
Using the formula x = -b / (2a) and substituting the values, we get:
x = -1 / (2 * (-0.0023)) = 217.39 meters
Now, let's find the horizontal distance:
Setting y = 0 and solving for x, we get:
0 = x - 0.0023x^2
0 = x(1 - 0.0023x)
x = 0 or x = 434.78 meters
Therefore, the height point of the trajectory is 217.39 meters and the horizontal distance the potato travels before hitting the ground is 434.78 meters.