Answer:
The true statements are;
1) The center of the ellipse is at (-2, -5)
3) The covertices are at (-2, -4) and (-2, -6)
4) The distance between the center and each focus is 2·√6 units
Step-by-step explanation:
The given graph of the ellipse gives;
1) The location of the center of the ellipse = (-2, -5)
2) The location of the vertices of the ellipse = (-7, -5) and (3, -5)
The distance between the center (-2, -5) and each vertex, d, is given as follows;
d = -2 - (-7) = 5 and d = 3 - (-2) = 5
Therefore, the distance between the center (-2, -5) and each vertex is 5 units
3) The location of the covertices, given in the diagram are (-2, -4), and (-2, -6)
4) The coordinates of the focus of an ellipse = h - c, k
c = √(a² + b²)
Where, for the given ellipse, h = -2, k = -5, c = √(5² - 1²) = √(24) = 2·√6
∴ The location of the focus of the ellipse = (-2 - 2·√6, -5)
The distance between the center and each focus, d = -2 - (-2 - 2·√6) = 2·√6
5) The x-coordinate of the directrices of the ellipse = ± a/e
Where; a = 5
b² = a²·(1 - e²)
∴ e² = 1 - b²/a² = 1 - 1/25 = 24/25
e = 2·√6/5
The directrices = -2 ± 5/(2·√6/5) ≈ -2 ± 5.1
The distance between the center and the directrices ≈ 5.1 units
Therefore, the directrices are vertical lines approximately 5.1 units from the center
Martin had 60kgs of sugar. He put the sugar weighing 3/4 kg. How many packets did he fill ??
Answer:
45kg
Step-by-step explanation:
60.3/4=45
Help? Solve the system of equations.
y = 3x
y = x2 + 3x – 16
solutions: ( );( )
Answer:
(- 4, - 12 ) , (4, 12 )
Step-by-step explanation:
Given the 2 equations
y = 3x → (1)
y = x² + 3x - 16 → (2)
Substitute y = x² + 3x - 16 into (1)
x² + 3x - 16 = 3x ( subtract 3x from both sides )
x² - 16 = 0 ( add 16 to both sides )
x² = 16 ( take the square root of both sides )
x = ± [tex]\sqrt{16}[/tex] = ± 4
Substitute these values into (1) for corresponding values of y
x = - 4 : y = 3 × - 4 = - 12 ⇒ (- 4, - 12 )
x = 4 : y = 3 × 4 = 12 ⇒ (4, 12 )
Can someone help me with this now !
Answer:
its either B or D.
Step-by-step explanation:
could you mark me brainliest pls or even hit the thanks button
What line on a coordinate plane is called the x-axis? Horizontal or Vertical. Please respond as quick as possible
Answer:
it's called the horizontal line
Step-by-step explanation:
also known as y=0
A Rectangle is formed by placing two identical squares side-by-side the area of the rectangle is two cm². What is the perimeter of one square
Answer:
4cm
Step-by-step explanation:
first find the length of the side of one square
the length of the rectangle will be twice the width
let y represent the width
area of a rectangle=length x width
2cm²=2yxy
2cm²=2y²
2cm²/2=2y²/2
1cm²=y²
1√cm²=√y²
1cm=y
perimeter of a square=4xside
4x1cm
4cm
A rhombus is cut along the diagonals to make four triangles.
Which three statements are correct for any rhombus.
A: All four triangles are isosceles.
B: All four triangles are congruent.
C: All four triangles are right-angled.
D: Perimeter of rhombus = 4 times the perimeter of one triangle.
E; Area of rhombus = 4 times the area of one triangle.
Answer:
B: All four triangles are congruent.
C: All four triangles are right-angled.
E; Area of rhombus = 4 times the area of one triangle.
Step-by-step explanation:
A rhombus is a quadrilateral with equal length of sides. It stands on one of its edges, and a simple example is the shape of a diamond. It has two diagonals which bisect the angles of the rhombus.
When a rhombus is cut along its diagonals, the following properties of the shape formed can be observed:
B: All four triangles are congruent.
C: All four triangles are right-angled.
E; Area of rhombus = 4 times the area of one triangle.
What is the following values of:
XZ:
XY:
To get 400 as quotient, what number is to be divided by 16?
400+16
400 -16
400÷16
400× 16
Answer:
400×16
Step-by-step explanation:
let the number be n.
[tex] \frac{n}{16 } = 400 \\ 16 \times \frac{n}{16} = 400 \times 16\\ n = 400 \times 16[/tex]
11 4/5 divided by 3 1/5
A. 3
B. 3 1/2
C. 7/2
D. 4
( Answer within 5-10 minutes to get brainliest! )
Thank you in advance!
I appreciate it all!
Answer:
3.5
Step-by-step explanation:
It's technically 3.69 but 3.5 is the closest answer you can get
25 + 8 (7y - 3) + 3y
Answer:
59y+1
Step-by-step explanation:
25 + 8 (7y - 3) + 3y
Distribute
25+56y-24+3y
Combine like terms
59y+1
Complete the frequency distribution table below.
Answer:
.............soooooooooooooooerrrrrrrrrrrrryyyyyyyyyyyyyyy.......... iiiiiiiii........ doooooooonnnnnnnnntttttttt......... kkkknnnnnooooowwww
Findfind the value of each variable used in the figures if your answer is an integer express it in simples radical form
Answer:
c=2
Step-by-step explanation:
the sides of a 30-60-90 right triangle are in the ratio 1:[tex]\sqrt{3}[/tex]:2
Please help i just need to know how to answer these kind of questions
Answer:
Since you didn't ask for the answer
Step-by-step explanation:
sec(∆)=1/cos(∆)
For the above diagram,cos(∆)=15/17
sec(∆)=1/(15/17)
NOTE:I replaced theta
I need help very quickly, please!!
Answer:
32ft
Step-by-step explanation:
Tan = opp/adj
Tan(65) = n / 15
Tan(65) x 15 = n
n = 32.16 = 32ft
Answer:
32 feet
Step-by-step explanation:
Hi there!
We are given a right triangle and the angle of elevation (one of the acute angles in the triangle) as 65°, as well as one of the legs (sides that make up the right triangle) as 15
We need to find the height of the triangle.
Let's make the height of the triangle (the side we need to find) x
Since we need to find the height of the triangle, let's use tangent. As we have the angle of elevation given, we'll use that.
Recall that tangent is [tex]\frac{opposite}{adjacent}[/tex]
in reference to the angle of elevation, the opposite side is x, and the adjacent side is 15
that means that:
tan(65)=[tex]\frac{x}{15}[/tex]
plug tan(65) into your calculator (make sure it's on degree mode!)
tan(65)≈2.14
2.14=[tex]\frac{x}{15}[/tex]
multiply both sides by 15 to clear the fraction
32.1=x
The problem asks us to round to the nearest foot, so the height of the building is 32 feet
Hope this helps! :)
If f(x)=2x2+3x−6, determine the value of f(2)
Answer: 4
2x2+3(2)−6
lets make sure we do OOO (order of operations correctly)
2x2+3(2)−6
4+3(2)−6
4+6−6
10−6
4
Step-by-step explanation:
Given JKL: XYZ, find x.
Answer:
is there a pic to go along? i need more to this..
Find the range, median, and mode of the following dot plot.
0.11
0.12 0.13
0.14 0.15 0.16 0.17 0.18
Range:
Median:
Mode:
Answer:
Range: 0.07
Median: 0.145
Mode: none
Step-by-step explanation:
Range: largest #- smallest #
Median: middle number (when numbers are in order least to greatest) or when two are middle number you add them, and divide by two
Mode: most occurring number(s) (if there aren't any, no mode)—but if there are multiples such as 2 zeros and 2 ones then 0 and 1 would be the mode
the figure below is a square . Find the length of side x in simplest radical form with a rational denominator.
Answer:
[tex]\sqrt{14}[/tex]
Step-by-step explanation:
In any square with side length [tex]s[/tex], the diagonal of the square is equal to [tex]s\sqrt{2}[/tex]. Since the side length of this square is [tex]\sqrt{7}[/tex], the diagonal is equal to [tex]\sqrt{7}\cdot \sqrt{2}=\boxed{\sqrt{14}}[/tex].
Alternatively, you can form two 45-45-90 triangles with the diagonal of the square. The diagonal acts as the hypotenuse for the both these triangles, and the legs of both triangles are equal to the side length of the square. To find the length of the diagonal, use the Pythagorean Theorem, which states [tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse of the triangle, and [tex]a[/tex] and [tex]b[/tex] are the two legs of the triangle.
In this question, both legs are equal to [tex]\sqrt{7}[/tex], and we're solving for the diagonal, which is the hypotenuse in this case:
[tex]\sqrt{7}^2+\sqrt{7}^2=c^2,\\c^2=14,\\c=\boxed{\sqrt{14}}[/tex]
Louise begins factoring the polynomial, which has four terms. 8x3+24x2+10x+30 2(4x3+12x2+5x+15) 2[4x2(x+3)+5(x+3)] Which is the completely factored form of her polynomial? 8x2(x + 3)2 2x(4x2 + 5) 2(4x2 + 5) (x + 3) 2(4x2 + 5) (x + 3)2
Answer:
[tex]8x3+24x2+10x+30= 2[(4x^2+5)(x+3)][/tex]
Step-by-step explanation:
Given
[tex]8x3+24x2+10x+30= 2(4x^3+12x^2+5x+15)[/tex]
[tex]8x3+24x2+10x+30= 2[4x^2(x+3)+5(x+3)][/tex]
Required
The complete factored form
We have:
[tex]8x3+24x2+10x+30= 2[4x^2(x+3)+5(x+3)][/tex]
Factor out x + 3
[tex]8x3+24x2+10x+30= 2[(4x^2+5)(x+3)][/tex]
The above represents the completely factored form
Answer:
C on edge
Step-by-step explanation:
I took the test
Complete parallel side 2
Height = 8mm
parallel side 1= 5mm
parallel side 2=?
Area = 72 mm
Step-by-step explanation:
Assume length of side 2 = L
Area of parallelogram is Height x L
So, 72 = 8 x L
L = 9
In a quiz, positive marks are given for correct answers and negative marks are given for incorrect answers, If Anju's scores in four successive rounds were -14, 15, -11 and 20. What was her total at the end.
Answer:
10
Step-by-step explanation:
-14+15 leaves a positive 1
-11+20 leaves a positve 9
add.
HURRY !!!!!! Which describes the correlation shown in the scatterplot?
Thang decided to borrow $90 from his local bank to help pay for a car. His loan was for 3 years at a simple interest rate of 40%. How much interest will Thang pay?
Answer:
Step-by-step explanation:
P = 90
r = 40% = 40/100 = 0.4
t = 3 years
It is not clear to me what this means. Is the 40% for each year for 3 years or is the interest rate = 40% period. I know that in some of the poorer countries, this is not an unusual amount to pay for each year he holds the loan.
I will take it as 40% for each year for 3 years.
i = prt = 90 * 0.4 * 3
i = 108
5 out of every 11 children in a school are girls. What is the ratio of girls to boys in the school?
Identify each expression with a sum of x2 + 3x +1.
Answer:
There are no like terms.
Step-by-step explanation:
Next
Unit Pre Test
Submit Test
20
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s)
The equation of a line is 2[v+ 1) = 10x* 3.
The yuntercept of the line is
and the slope of the line is
Answer:gotta go sorry
Step-by-step explanation:
Mohamed and Miguel go to the movie theater and purchase refreshments for their friends. Mohamed spends a total of $18.25 on two bags of popcorn and three
drinks. Miguel spends a total of $27.50 for four bags of popcorn and two drinks.
a) Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink.
b) Using your system from part a), determine and state the price of one bag of popcorn and the price of one drink.
Find MZUVW if mZPVW = 130° and mZUVP = 26.
Solve for x.
3x + 7
2x + 3)
Answer: x = 34
Step-by-step explanation:
2x+3+3x+7=180
5x+10=180
5x=170
x = 34
Mr. O'Donnell goes to the store to buy a shirt. The shirt is $20, but he also has to pay a 9% tax. What is the total price he has to pay?
Answer:
The total price that he has to pay is $21.8.
Step-by-step explanation:
Mr. O'Donnell goes to the store to buy a shirt. The shirt is $20, but he also has to pay a 9% tax.
First you convert the sales tax percentage to its decimal form: in this case 9% becomes 0.09.
To calculate the cost of the tax, the following multiplication must be performed:
cost of product or service* sales tax (in decimal form) = total sales tax
In this case:
$20*0.09= $1.8
Finally, you must add the value of the total sales tax to the cost of the product or service to obtain the total cost. In this case:
$20 + $1.8= $21.8
So, the total price that he has to pay is $21.8.