ANSWER
[tex]\frac{ {y}^{2} }{49} + \frac{ {x}^{2} }{ 16 } = 1[/tex]
EXPLANATION
The given ellipse has a vertex at (0, -7), a co-vertex at (4,0), and a center at the origin.
The equation of an ellipse with vertex on the y-axis and center at the origin is given by
[tex]\frac{ {y}^{2} }{a ^{2} } + \frac{ {x}^{2} }{ {b}^{2} } = 1[/tex]
[tex]\frac{ {y}^{2} }{( - 7) ^{2} } + \frac{ {x}^{2} }{ {4}^{2} } = 1[/tex]
[tex]\frac{ {y}^{2} }{49} + \frac{ {x}^{2} }{ 16 } = 1[/tex]
The equation of the ellipse with a vertex at (0, -7), a co-vertex at (4,0), and a center at the origin is x^2/16 + y^2/49 = 1.
Explanation:To find the equation of the ellipse in standard form, we need to identify the lengths of the major and minor axes. The given vertex at (0, -7) indicates that the semi-major axis length, a, is 7 because the distance from the center to a vertex measures the semi-major axis. Similarly, the co-vertex at (4, 0) represents the semi-minor axis length, b, which is 4.
Since the center is at the origin (0, 0), the standard form of the ellipse equation is given by x^2/b^2 + y^2/a^2 = 1. Plugging the values of a and b, we get x^2/4^2 + y^2/7^2 = 1. So, the equation of the ellipse is x^2/16 + y^2/49 = 1.
Three more than twice the sum of a number and half the number equals 105. Which equation models this relationship?
A 2(x+1/2x)+3=105
B 2x+1/2x+3=105
C 2x+3=1/2x+105
D 2(x+3)=1/2x+105
it's a.
three more is +3 and it equals 105
that already eliminates c and d
next it says twice the sum of a number and half the number
Answer:
a
Step-by-step explanation:
25 POINTS PLEASE HELP
YOU CAN CHOOSE MORE THAN ONE
Select all the correct answers.
A survey of 30 students each from three different high schools was conducted to find the number of hours they spent every month on volunteer work. Based on the median values of the data sets, represented here as dot plots, which conclusions are true?
The students in school 2 generally spend more time doing volunteer work than the students in school 1.
The students in school 1 generally spend more time doing volunteer work than the students in school 2.
The students in school 1 generally spend more time doing volunteer work than the students in school 3.
The students in school 1 generally spend less time doing volunteer work than the students in school 3.
The students in school 3 generally spend more time doing volunteer work than the students in school 2.
From the information given, it is true to state that:
"The students in school 1 generally spend more time doing volunteer work than the students in school 2." (Option B)
What is a dot plot?In statistics, a dot plot, also known as a dot chart is a type of histogram or histogram-like chart that is used to represent data that is relatively small.
It is best used for indicating the statistical relationship between the data and its clusters, outliers, and gaps.
Learn more about dot plots at;
https://brainly.com/question/15853311
#SPJ2
School 2 students generally spend more time on volunteer work than School 1, while School 1 students tend to spend more time than School 3.
Based on the dot plots representing the number of hours spent on volunteer work by students from three different high schools, we can draw some conclusions about the median values of the data sets.
Firstly, comparing School 1 and School 2, it appears that students in School 2 generally spend more time doing volunteer work. This conclusion is supported by the higher frequency of dots in the higher hour range in School 2 compared to School 1.
Next, comparing School 1 and School 3, it seems that students in School 1 generally spend more time on volunteer work. The dot plot for School 1 shows a higher frequency of dots in the higher hour range compared to School 3.
In summary, students in School 2 generally spend more time doing volunteer work than those in School 1, while students in School 1 tend to spend more time on volunteer work than those in School 3.
the table shows the number of boys and girls that have black, blonde, brown, or red hair color. What is the probability that student is a girl with brown hair? (round to the nearest hundredth)
a. 0.20
b. 0.22
c. 0.40
d. 0.44
Answer
The answer is A or 0.20
Step-by-step explanation:
So if you add all the numbers up so (4+4+10+2+5+6+8+1) that would equal=40
8 is the number of girls with brown hair so I would divide 8 by 40
8/40=0.20
Hope this helps!
Answer:
0.20
There are 8 brown-haired girls, out of 40 students.
8
40
(x^2-2)^2-10(x^2-2)+21=0 find one value of x that is a solution to the equation
Answer:
x=3; x=-3; x=√5; x=-√5
Step-by-step explanation:
The equation can be simplified by treating (x^2 - 2) as y. Solving the quadratic equation for y results in y = 4 and y = 7. By substituting these back into the equation and solving for x, we find x = ±sqrt(6) and x = ±sqrt(9). Therefore, one possible solution for x is sqrt(6).
Explanation:The equation provided is a quadratic in the form of x. In this case, let's take: (x^2 - 2) = y. Therefore the equation can be rewritten as: y^2 - 10y + 21 = 0. In order to find the roots of the equation, we should use the quadratic formula: y = [10 ± sqrt((10)^2 - 4*1*21)] / (2*1), which gives us y = 4 and y = 7. Now we substitute back y = (x^2 - 2). This will form two more quadratic equations: x^2 - 2 = 4 and x^2 - 2 = 7. Solving these, we get x = ±sqrt(6) and x = ±sqrt(9). So, one value of x that is a solution to the equation could be sqrt(6).
Learn more about Quadratic Equation here:https://brainly.com/question/26090334
#SPJ2
Graph 8x-2y=-16........
[tex]8x - 2y = - 16 \\ \\ 1. \: 2(4x - y) = - 16 \\ 2. \: 4x - y = - \frac{16}{2} \\ 3. \: 4x - y = - 8 \\ 4. \: 4x = - 8 + y \\ 5. \: 4x = y - 8 \\ 6. \: x = \frac{y - 8}{4} [/tex]
Find center and radius
(x-3)^2+y^2=8
Answer:
Center: (3, 0)Radius: 2√2Step-by-step explanation:
The equation of a circle in standard form:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have the equation:
[tex](x-3)^2+y^2=8\to(x-3)^2+(y-0)^2=(\sqrt8)^2[/tex]
Therefore
the center: [tex](3,\ 0)[/tex]
the radius: [tex]r=\sqrt8\to r=\sqrt{4\cdot2}\to r=\sqrt4\cdot\sqrt2\to r=2\sqrt2[/tex]
square root of 6889 with work
Answer:
83
Step-by-step explanation:
A school bus can hold no more than 40 people. If there are 6 teachers on the bus, write and solve an inequality that shows how many students can be on the bus. Graph the solution on the number line.
Answer: 34 kids in all
Step-by-step explanation:
: 40 - 6 = 34
0 6 34
|------------|----------------------------|
The bus can hold no more than 40 people. 6 are already on so at most, there can be 34 others on board. But the number doesn’t have to be exact.
Which of the following is a sum of cubes?
A)3x^3+8y^6
B)8x^3-27y^6
C)125x^6-9y^3
D)x^3+8y^6
Answer:
D) [tex]x^3+8y^6[/tex]
Step-by-step explanation:
We have been given four choices.
A) [tex]3x^3+8y^6[/tex]
B) [tex]8x^3-27y^6[/tex]
C) [tex]125x^6-9y^3[/tex]
D) [tex]x^3+8y^6[/tex]
Now we need to find about which of the above choices is a sum of cubes.
Basically we need to check which one of the given choices can be represented in cubic form along with addition sign.
3 and 9 can't be written in cubic form unless we use radical numbers.
So the only choice left is D)
D) [tex]x^3+8y^6[/tex]
[tex]=x^3+2^3(y^2)^3[/tex]
[tex]=x^3+(2y^2)^3[/tex]
which is clearly visible as sum of cubes.
The answer is:
D) [tex]x^{3}+8y^{6}[/tex]
Why?We are looking for the expression that can be obtained from a sum of cube factoring, the form of the sum of cubes will be:
[tex]a^{3}+b^{3}=(a+b)(a^{2} -ab+b^{2})[/tex]
The only option that matches with the sum of cubes form is the last option,
D) [tex]x^{3}+8y^{6}[/tex]
and it can be rewritten as the following expression:
[tex]x^{3}+8y^{6}=x^{3}+(2y^{2})^{3}\\\\x^{3}+(2y^{2})^{3}=(x+2y^{2})(x^{2}-2xy^{2}+(2y^{2})^{2})\\\\(x+2y^{2})(x^{2}-2xy^{2}+(2y^{2})^{2})=(x+2y^{2})(x^{2}-2xy^{2}+4y^{4})\\\\(x+2y^{2})(x^{2}-xy^{2}+4y^{4})=x*x^{2}-2x^{2}y^{2}+2xy^{4}+2x^{2}y^{2}-2xy^{4}+8y^{6}\\\\x*x^{2}-2x^{2}y^{2}+2xy^{4}+2x^{2}y^{2}-2xy^{4}+8y^{6}=x^{3}+8y^{6}[/tex]
Therefore, we have that:
[tex]x^{3}+8y^{6}=x^{3}+(2y^{2})^{3}=(x+2y^{2})(x^{2}-2xy^{2}+(2y^{2})^{2})=x^{3}+8y^{6}[/tex]
Hence, the correct answer is:
D) [tex]x^{3}+8y^{6}[/tex]
Have a nice day!
Find the area of the shaded region. Leave your answer in terms of pi.
A. (243pi+162) ft^2
B. (243pi-162) ft^2
C. (27pi+162) ft^2
D. (27pi-162) ft^2
ANSWER
A. (243pi+162) ft^2
EXPLANATION
The area of the shaded region is the sum of the area of the major sector and the area of the isosceles triangle.
Area of major sector
[tex] = \frac{360 - 90}{360} \times \pi \times {18}^{2} [/tex]
[tex] = 243\pi {ft}^{2} [/tex]
The area of the isosceles triangle is calculated using the formula;
[tex] = \frac{1}{2} {r}^{2} \sin( \theta) [/tex]
[tex]= \frac{1}{2} \times {18}^{2} \sin(90 \degree)[/tex]
[tex] = 162 {ft}^{2} [/tex]
The area of the shaded region
[tex] = (243\pi + 162) {ft}^{2} [/tex]
The correct answer is A.
Answer: A
Step-by-step explanation:
1. 49 pic square ft
2. 168 units
3. (4-[tex]\pi[/tex])ft^2
4. 314square ft
5. 22.6 square mm
6. 12 inches
7. 12 [tex]\pi ft^2[/tex]
8. 28.125 [tex]\pi[/tex] square centimeters
9. 22.1 cm
10. (243pi+162) ft^2
Just took the pracitce this will get oyu a 100 hope this helps
A real estate agent received a 6% commission on the selling price of a house. If his commission was $8,880, what was the selling price of the house?
Answer:
6% x = 8,880 : x = selling price of house.
x = $148,000 : solve for x
Step-by-step explanation:
The selling price of the house can be calculated by dividing the commission ($8,880) by the commission rate (0.06). This gives a selling price of $148,000.
Explanation:To solve this problem, you need to understand that the 6% commission the real estate agent received is based on the selling price of the house. You can find the selling price by dividing the commission by the percentage commission expressed as a decimal.
Here's the step-by-step solution:
Convert the 6% commission rate to a decimal by dividing 6 by 100, which gives 0.06.Next, divide the commission amount ($8,880) by the commission rate (0.06). Using this calculation, $8,880 / 0.06, we find that the selling price of the house is $148,000.So, the selling price of the house on which the agent earned an $8,880 commission at a rate of 6% was $148,000.
Learn more about Percentages here:https://brainly.com/question/30697911
#SPJ3
Help Me Please ! This is so confusing .♀️
Answer: -4
Step-by-step explanation:
3-9=-6
-6*5=-30
-30-1=-31
6*-31=-186
-186+2=-184
8-2=6
6*7=42
42+4=46.
-184/46=-4
Answer and Step-by-step explanation:
All you have to do is follow the order of operations.
We do everything in the first set of parenthesis, then we work our way out.
[tex]\frac{6(5(3-9)-1) + 2}{7(8-2)+4}[/tex]
First, we would subtract 9 from 3, and 2 from 8.
3 - 9 equals -6
8 - 2 equals 6
[tex]\frac{6(5(-6)-1) + 2}{7(6)+4}[/tex]
Now, we multiply those numbers.
5 times -6 equals -30
7 times 6 is 42
[tex]\frac{6(-30 -1) + 2}{42+4}[/tex]
Now, we simplify.
-30 minus 1 equals -31
42 + 4 equals 46
[tex]\frac{6(-31) + 2}{46}[/tex]
Multiply -31 by 6, then add 2 to the product.
-31 times 6 equals -186
-186 plus 2 equals -184
[tex]\frac{-184}{46}[/tex]
Finally, we divide.
-184 divided by 46 equals
-4
-4 is the answer to the expression.
I hope this helps!
#teamtrees #PAW (Plant And Water)
First-year students at a school must choose one each of 5 English classes, 4 history classes, 5 math classes, and 3 physical education classes. Find the total number of outcomes
Answer: 68 total outcomes
Final answer:
To find the total number of outcomes, we multiply the number of options for each class type using the fundamental counting principle, resulting in 5 × 4 × 5 × 3 = 300 total outcomes.
Explanation:
The question asks us to find the total number of outcomes for first-year students at a school who must choose one each of 5 English classes, 4 history classes, 5 math classes, and 3 physical education classes. To calculate the total number of outcomes, we use the fundamental counting principle, which states that if there are m ways to do one thing, and n ways to do another, then there are m × n ways of doing both.
In this scenario, the student can choose:
5 English classes
4 history classes
5 math classes
3 physical education classes
Applying the fundamental counting principle, we multiply the number of options for each subject:
5 (English) × 4 (History) × 5 (Math) × 3 (Physical Education) = 300 total outcomes.
simplify-3x +2y + x -5x
Answer:
3x+2y
Step-by-step explanation:
-3x+2y+x-5x
-5x-3x=-8x+x=-7x
-7x+2y
Answer: [tex]-7x+2y[/tex]
Step-by-step explanation:
You have the expression [tex]-3x +2y + x -5x[/tex]
You can observe that this expresssion has two variables. These are:
"x" and "y"
Then, to simplify the expression given, you need to add the like terms (terms that have the same variable), which are:
[tex]-3x[/tex], [tex]-5x[/tex] and [tex]x[/tex]
Therefore, adding the like terms, you get:
[tex](-3x+x-5x)+2y\\-7x+2y[/tex]
Then, the simplified form of [tex]-3x +2y + x -5x[/tex] is:
[tex]-7x+2y[/tex]
This is really stressing me out i need this don’t by tonight for extra credit please help?!!!!!
Answer:
1. 1/6 , 2/9 , 1/4 , 5/18
2. 1/3 , 4/9 , 1/2 , 5/9
3. 5/12 , 5/9 , 5/8 , 25/36
Hope this helps!
Is -2 +-2 A. Positive B. Negative C Both or D None of the above
Answer:
B
Step-by-step explanation:
If I have two dollars of debt (negative) and add 2 more dollars of debt (negative), I now owe 4 dollars in debt (negative).
-2+-2=-4
Answer:
B.) Negative 4
Step-by-step explanation:
A negative plus a negative equales a negative, beacause you aren't adding a positive to cancle out some of the numbers. your just adding more negative.
What is the area of this parallelogram
Answer:
17.15 cm²
Step-by-step explanation:
The area (A) of a parallelogram is calculated using the formula
A = bh ( b is the base and h the perpendicular height )
here b = AE + EB = 1.4 + 3.5 = 4.9 and h = BF = 3.5, hence
A = 4.9 × 3.5 = 17.15
It costs $120 to have a party for 9 people at the skating rink. The cost includes a charge of ,$10 for each person attending the party plus the price of a cake.
How much does the cake cost?
Answer:
The cake costs $30
Step-by-step explanation:
9(10)=90
120-90=30
Which statement represents the transitive property of equality?
The transitive property of equality is correctly represented by option A, stating that if WX = XY and XY = YZ, then WX = YZ.
The correct answer is option A.
The transitive property of equality states that if two quantities are equal to a third quantity, then they are equal to each other. Among the given options, the statement that represents the transitive property is:
A) If WX = XY and XY = YZ, then WX = YZ.
This statement adheres to the transitive property because it asserts that if WX is equal to XY and XY is equal to YZ, then it logically follows that WX must be equal to YZ. This principle is fundamental in mathematics and logic, providing a way to establish equality relationships through a chain of equalities.
On the other hand, options B and C do not correctly represent the transitive property:
Option B is a statement about the equality of angles, and it does not involve the transitive relationship between two quantities.
Option C represents the reflexive property (an equality is always equal to itself) rather than the transitive property.
In conclusion, option A accurately represents the transitive property of equality.
The question probable may be:
Which statement represents the transitive property of equality?
A) If WX = XY and XY = YZ, then WX = YZ
B) If mZA = mZB, then mZB = mZA
C) If WX = XY, then XY = WX
Solve the system of equations.
-5y + 8x = -18
5y + 2x = 58
X = ?
Y= ?
Answer:
x=4 y=10
Step-by-step explanation:
-5y+8x=-18
5y+2x=58
so the first thing you do is cancel out the 5s then you add the 8+2 and -18+58 then you have 10x=40 then you divide both sides by ten. then you plug that four back into an equation so i did 5y+2(4)=58 then 5y+8=58 you subtract 8 from both sides and you have 5y=50 divide both sides by 5 and you get y=10 and that is how you do that
On a quiz show you've made it to the final round. The host explains to you that you can choose from 2 prize plans. In Plan A, you'll win $1,280 guaranteed, plus $40 more for each final round question you answer correctly. Under Plan B, you'll win only $800 guaranteed, but $100 for each question.Complete the following statements (use proper number formatting, such as commas):
The plans will pay the same at
correct questions.
The amount they'll pay at that number of questions is $
.
You think you can answer 9 questions correctly. Which plan should you choose?
D is the answer but I’m not sure
Using Cramer’s Rule, what is the value of x in the system of linear equations below?
Answer:
The answer is the 1st [tex]\frac{\left[\begin{array}{cc}16&3\\8&1\end{array}\right]}{-8}=1[/tex]
Step-by-step explanation:
Lets revise the Cramer's rule
- If the system of equation is ax + by = c and dx + ey = f
- A is the matrix represent this system of equation
- The first column has the coefficients of x, and
the second column has the coefficients of y
∴ A = [tex]\left[\begin{array}{cc}a&b\\d&e\end{array}\right][/tex]
- Ax means replace the column of x by the answers of the equation
∴ Ax = [tex]\left[\begin{array}{ccc}c&b\\f&e\end{array}\right][/tex]
- Ay means replace the column of y by the answers of the equation
∴ Ay = [tex]\left[\begin{array}{ccc}a&c\\d&f\end{array}\right][/tex]
- x = Dx/D, where Dx is the determinant of Ax and D is the determinant
of A
- The determinant of A = ae - bd
- The determinant of Ax = ce - bf
* Now lets solve the problem
∵ x + 3y = 16 and 3x + y = 8
∴ A = [tex]\left[\begin{array}{cc}1&3\\3&1\end{array}\right][/tex]
- Replace the column of x by the answer to get Ax
∴ Ax = [tex]\left[\begin{array}{cc}16&3\\8&1\end{array}\right][/tex]
∵ [tex]x=\frac{Dx}{D}[/tex]
∵ Dx = [tex]\left[\begin{array}{cc}16&3\\8&1\end{array}\right]=(16)(1)-(3)(8)=16-24=-8[/tex]
∵ D = [tex]\left[\begin{array}{cc}1&3\\3&1\end{array}\right]=(1)(1)-(3)(3)=1-9=-8[/tex]
∴ x = [tex]\frac{\left[\begin{array}{cc}16&3\\8&1\end{array}\right]}{-8}=\frac{-8}{-8}=1[/tex]
* x = [tex]\frac{\left[\begin{array}{cc}16&3\\8&1\end{array}\right]}{-8}=1[/tex]
Stare the various transformations. Help needed !!!
Answer:
Step-by-step explanation:
Let's start by simplifying a little:
g(x) = -2[(x − 1)² + 3]
g(x) = -2(x − 1)² - 6
The negative sign in front means a reflection about the x axis. The 2 coefficient means a vertical stretch by a factor of 2. The x−1 means a horizontal shift to the right by 1 unit. And the -6 means a vertical shift down six units.
So the answer is the third one.
Please help me with this. TWO LINES MEET AT A POINT THAT IS ALSO THE ENDPOINT OF TWO RAY'S. SET UP AND SOLVE THE APPROPRIATE EQUATIONS FOR m AND N.
Answer:
m=47, n=52
Step-by-step explanation:
m is equal to 90-43 since 43+m is a right angle (straight angle 180 is composed of two right angles). n is equal to 90-38. If you solve of the missing angle not given a variable, you find n as well because opposite angles are congruent and have the same measure.
PLEASE HELP!!!
SOLVE FOR X ASAP
Answer:38
Step-by-step explanation:
Answer:
x = 1
Step-by-step explanation:
Since the triangle is right use Pythagoras' identity to solve for x
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
The hypotenuse is the side opposite the right angle, thus
x² + 1² = ([tex]\sqrt{2}[/tex])²
x² + 1 = 2 ( subtract 1 from both sides )
x² = 1 ( take the square root of both sides )
x = [tex]\sqrt{1}[/tex] = 1
How long will it take you to ski a distance of 24 miles at a speed of 6 miles per 30 minutes? (Step by step please)
Answer:
4.8 minutes
Step-by-step explanation:
Time = Speed * Distance
Time = 6 mi / 30 min * 24 miles= 1 mi / 5 min * 24 miles = 0,2 mi / min * 24 = 4.8 minutes
Answer:
So if you know that you can complete 6 miles over the course of 30 minutes it is just matter of multipling 30 minutes times 4, this is becasue it takes 4 times your base distance and time to get to yur goal of 24 miles.
30 x 4 equal 120
which you divide by 60 (because you have 60 minutes in one hour)
so it is safe to say that it will take 2 hours of 120 minutes to ski a ditance of 24 miles at a speed of 6 miles per 30 minutes.
Hope this helps!
The sum of the degree measures of any triangle is 180. In a particular isosceles triangle the degree measure of the vertex angle is 112. Find the measure of each base angle
Answer:
34
Step-by-step explanation:
Each of the base angles = x
x + x + 112 = 180 Subtract 112 from both sides. Simplify the left side.
2x + 112 - 112 = 180 - 112 Simplify
2x = 68 Divide by 2
2x/2 = 68/2 Simplify
x = 34
Each of the base angles = 34 degrees.
Faith Franklin sells furniture and earns 8% commission on her total sales. Last month she had $33,500 in sales. How much did she earn?
$2,976.00
$2680.00
$3,015.00
$3685.00
Answer:
$2680.00
Step-by-step explanation:
We are informed that Faith Franklin sells furniture and earns 8% commission on her total sales. She sold $33,500 last month. We are required to determine her earnings for that month;
We simply evaluate 8% of $33,500
[tex]\frac{8}{100}*33500=2680[/tex]
Therefore, she earned $2680.00
A cylindrical container has a radius of 4 inches and a height of 7 inches. to the nearest tenth, what is the volume of the container?
Answer:351.9
Step-by-step explanation:351.9 cm3
V = πr2h
V = π(4)2(7)
V = π(16)(7)
V = 112π
V = 351.858
Final answer:
The volume of the cylindrical container is approximately 352.6 cubic inches.
Explanation:
To find the volume of a cylindrical container, you can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height. In this case, the radius is 4 inches and the height is 7 inches. Plug these values into the formula:
V = 3.14 x (4 inches)² x 7 inches = 3.14 x 16 square inches x 7 inches = 352.64 cubic inches.
Since the question asks for the volume rounded to the nearest tenth, the answer is approximately 352.6 cubic inches.
Which decimal is equivalent to -3 1/8
Answer:
-3.125
Step-by-step explanation:
Answer: this is the correct answer -3.125