Answers
Solution:
The vertex equation of an ellipse is;
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]Thus, given the center;
[tex](h,k)=(-2,3)[/tex]Then, the equation whose graph is an ellipse centered at (-2,3) is;
[tex]\frac{(x+2)^2}{12}+\frac{(y-3)^2}{18}=1[/tex]
Related Questions
In the figure below, ∠ABC ≅ ∠DEC and ∠GFE ≅ ∠DCE. Point C is the point of intersection between segment AG and segment BD , while point E is the point of intersection between segment AG and segment DF.
Prove ΔABC ∼ ΔGEF.
Answers
A figure is given with :-
∠ABC ≅ ∠DEC
∠GFE ≅ ∠DCE
Point C is the point of intersection between segment AG and segment BD.
Point E is the point of intersection between segment AG and segment DF.
We have to prove that ΔABC ∼ ΔGEF.
As ∠ABC ≅ ∠DEC
We can write,
∠DEC = ∠FEG (Vertically opposite angles)
Similarly,
As ∠GFE ≅ ∠DCE
We can write,
∠DCE = ∠ ACB (Vertically opposite angles)
Hence,
∠ ACB = ∠DCE = ∠GFE
∠ ACB = ∠GFE
Also,
∠FEG = ∠DEC = ∠ ABC
∠FEG = ∠ ABC
Hence, by using AA corollary, we can write,
ΔABC ∼ ΔGEF
Hence, proved.
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The graph of Ax), shown below, resembles the graph of G(X) = x2, but it hasbeen changed somewhat. Which of the following could be the equation ofFx)?600 = x2-5OTFC) = ?AO A. F(X) = 3(x - 2)2 - 2B. F(x) = -3(x - 2)2 - 2C. F(x) = -3(x+ 2)2 - 2D. F(x) = 3(x + 2)2 - 2
Answers
The correct answer is option C
Explanation
First observation; the graph f(x) is n- shaped, so the coefficient of x^2 must be negative. This means option A and option D cannot be the answer
We have to channel our focus to option B or C
From the graph f(x), when x = -1, f(-1) = -5
Test option B and option C by substituting x= -1 into f(x) and check which options gives -5 as the answer
Testing option c
f(-1) = -3(-1 + 2)^2 -2
=-3(1) -2
= -3 - 2
=-5
f(-1) = -5
Since f(-1) = -5, which gives a correct value as we have on the graph,
Then the answer is option C
The perimeter of a square is 56 cm. What is the approximate length of its diagonal ? 10.6 cm 14.0 cm15.0 cm18.8 cm
Answers
We are given the perimeter of a square. Since a square has all of the sides of the same length the perimeter is, therefore:
[tex]P=4l[/tex]Where "l" is the length of the side. Solving for "l" by dividing both sides by 4:
[tex]\frac{P}{4}=l[/tex]Replacing the value of "P":
[tex]\frac{56}{4}=l[/tex]Solving the operations:
[tex]l=14[/tex]The length of the diagonal of a square is given by:
[tex]d=l\sqrt[]{2}[/tex]Replacing the value of the length we get:
[tex]d=14\sqrt[]{2}[/tex]Solving the operation:
[tex]d=19.8[/tex]Therefore, the length of the diagonal is 19.8 cm.
Find the midpoint of the segment with the given endpoints.(-10,9) and (-3,4)
Answers
Let's apply the midpoint formula
((x1+x2)/2, (y1+y2)/2)
[tex](\frac{-3-10}{2},\frac{4+9}{2})[/tex][tex](\frac{-13}{2},\frac{13}{2})[/tex]suppose we want to choose 6 colors without replacement from 9 distinct colors if the order of choices is not taken into consideration how many ways can this be done and b if the order of the choices is taken into consideration how many ways can this be done
Answers
The first case is when the order of choices is not taken into consideration. If the order of choices is not taken into considerations then it is a case of permutations. So, the number of ways in which 6 colors can be chosen from 9 distinct colors are
The second case is when the order of choices is taken into consideration. If the order of choices is taken into considerations then it is a case of combinations. So, the number of ways in which 6 colors can be chosen from 9 distinct colors are
The perimeter of ΔPQR below is 55 units. What is the length of side QR?P to Q 2x+4 P to R x+3 Q to R has an x there.
Answers
Given:
In ΔPQR, Perimeter is 55 units.
The length of PQ = 2x+4
The length of PR = x+3
The length of Q+R = x
To find the length of QR, that is x:
Perimeter of the triangle formula is,
[tex]P=\text{ Sum of the length of thre}e\text{ sides}[/tex]So, we have
[tex]\begin{gathered} 2x+4+x+3+x=55 \\ 4x+7=55_{} \\ 4x=48 \\ x=12 \end{gathered}[/tex]Then, the length of QR is, 12 units.
If Mike buys 2 pounds of basmati rice and 3.9 pounds of brown rice, how much will he spend? brown rice $3 per lb basmati rice $4 per lb white rice $4 per lb Bhutanese red rice $3 per lb sticky rice $3 per lb
Answers
Mike wants to buy 2 lb of basmati rice and 3.9 lb of brown rice.
The prices are given as
Basmati rice = $4 per lb
Brown rice = $3 per lb
How much will he spend?
Simply multiply the quantity of rice by its price
[tex]\begin{gathered} Basmati\: rice=2\times\$4=\$8 \\ Brown\: rice=3.9\times\$3=\$11.7 \end{gathered}[/tex]So the total amount is
[tex]Total\: amount=\$8+\$11.7=\$19.7[/tex]Therefore, Mike will spend $19.7
there are 4 girls and 16 boys on the dodgeball team. What is the ratio of girls to the total number of kids on the team?
Answers
Given:
The number of girsl is, 4
The number of boys is, 16
Therefore the total number of kids is,
[tex]16+4=20[/tex]Taking the ratio of number of girsl to the tital number of kids, we have,
[tex]\frac{4}{20}=\frac{1}{5}[/tex]The required ratio is 1 : 5.
There are 5 blue marbles, 2 red marbles, and 3 green marbles in a bag. What is theprobability of selecting a red marble? Your answer can be a fraction, decimal orpercent.
Answers
Given
There are 5 blue marbles, 2 red marbles, and 3 green marbles in a bag
[tex]\begin{gathered} \text{Total Marbles =5+2+3} \\ \text{Total Marbles =10} \end{gathered}[/tex]Probability of selecting a red marble
[tex]\text{Probability of selecting a red marble =}\frac{2}{10}=\frac{1}{5}[/tex]The final answer
The probability of selecting a red marble
[tex]\frac{1}{5}[/tex]In the following diagram, AB bisects CD at E. Which of the following must be true?(1) CE is twice the length of CD(2) BE is half the length of AB(3) AE and BE are the same length (4) E is the midpoint of CD
Answers
EXPLANATION:
In the graph we can see that by bisecting point E in line C and D it does not remain in equal parts as if it can be seen in A and B, then the most accurate answer according to the graph would be the following:
(1) CE is twice the length of CD.
Evaluating a Function In Exercises 5-12, evaluate the function at the given value(s) of the independent variable. Simplify the results. 5. f(x) = 3x - 2 (a) f(0) (b) f(5) (c) f(b) (d) f(x - 1)
Answers
Since the given function is
[tex]f(x)=3x-2[/tex]We want to evaluate it at some values of x
a) To find f(0), substitute x by 0
[tex]\begin{gathered} x=0 \\ f(0)=3(0)-2 \\ f(0)=0-2 \\ f(0)=-2 \end{gathered}[/tex]b) To find f(5), substitute x by 5
[tex]\begin{gathered} x=5 \\ f(5)=3(5)-2 \\ f(5)=15-2 \\ f(5)=13 \end{gathered}[/tex]c) To find f(b), substitute x by b
[tex]\begin{gathered} x=b \\ f(b)=3(b)-2 \\ f(b)=3b-2 \end{gathered}[/tex]d) To find f(x-1), substitute x by (x - 1)
[tex]\begin{gathered} x=(x-1) \\ f(x-1)=3(x-1)-2 \end{gathered}[/tex]Simplify it by multiply 3 by the bracket
[tex]\begin{gathered} f(x-1)=3(x)-3(1)-2 \\ f(x-1)=3x-3-2 \end{gathered}[/tex]Add the like term
[tex]\begin{gathered} f(x-1)=3x+(-3-2) \\ f(x-1)=3x+(-5) \\ f(x-1)=3x-5 \end{gathered}[/tex]This graph shows the distance that a robot walks. What is the rate of change of the robot's location?
Answers
Solution:
The rate of change, m, is;
[tex]\begin{gathered} m=\frac{d_2-d_1}{t_2-t_1} \\ \\ \text{ Where }d=distance,t=time \end{gathered}[/tex]Thus;
[tex]\begin{gathered} (1,10),(3,30) \\ \\ m=\frac{30-10}{3-1} \\ \\ m=\frac{20}{2} \\ \\ m=10 \end{gathered}[/tex]ANSWER: (D) 10 feet per minute
use the figure at the right . if JK =3x+18 and NO=18, what is the value of x?
Answers
You have the following information:
JK = 3x + 18
NO = 18
You can notice that segment JM and MK are equal, furthermore, JK = JM + MK.
Then, JK = 2JM. From this expression you obtain:
JM = JK/2
By replacing the given expression for JK you have:
JM = (3x + 18)/2 = 3/2 x + 9
Moreover, you can notice that segments JM and NO are qual. Then, you have:
JM = NO you replace the expressions for JUM and NO
3/2 x + 9 = 18 subtract 9 both sides
3/2 x = 18 - 9
3/2 x = 9 multiply both sides by 2/3
x = 9(2/3)
x = 18/3
x = 6
Hence, the value of x is x = 6
What is the radius for a circle whose equation is x2 + y2 = 36?A. 18B. 36C. 1296D. 6
Answers
Answer:
D. 6
Explanation:
The general equation for a circle centered at the origin (0,0) is:
[tex]x^2+y^2=r^2[/tex]Given the equation of the circle:
[tex]\begin{gathered} x^2+y^2=36 \\ \implies r^2=36 \\ r^2=6^2 \\ r=6 \end{gathered}[/tex]Thus, the radius of the given circle is 6.
Logarithm 9) solve for P ( in terms of Q)Log (P - Q) = lop P - log Q
Answers
we have the expression
[tex]\text{log (P}-Q)=\log P-\log Q[/tex]Applying properties of log right side
[tex]\text{log (P}-Q)=\log (\frac{P}{Q})[/tex]Equate the numbers inside the parenthesis
[tex]P-Q=\frac{P}{Q}_{}[/tex]Solve for P
[tex]P-\frac{P}{Q}=Q[/tex][tex]P\lbrack1-\frac{1}{Q}\rbrack=Q[/tex][tex]P=\frac{Q}{\lbrack1-\frac{1}{Q}\rbrack}[/tex]Simplify
[tex]P=\frac{Q^2}{Q-1}[/tex]Convert the expression from radical form to exponential expression in rational form, multiply and simplify then divide no need to evaluate just simplify
Answers
Solution
Given:
[tex]\sqrt[]{5^7}\text{ }\cdot\sqrt[]{5^6}\div\sqrt[5]{5^3}[/tex]Recall from the law of indices that;
[tex]\begin{gathered} a^{\frac{b}{c}}=\sqrt[c]{a^b}=(\sqrt[c]{a})^b \\ a^{\frac{b}{2}}=\sqrt[]{a^b}^{} \end{gathered}[/tex][tex]undefined[/tex]compute the monthly cost of the cellular phone for use of the following anytime minutes.
Answers
ANSWER:
(a) $29.99
(b) $37.49
(c) $30.24
STEP-BY-STEP EXPLANATION:
We have a function by part to calculate the monthly cost of a cell phone plan.
If the consumption is between 0 and 300 minutes, the value will always be $29.99. While if the consumption is greater than 300 minutes, the value is given by the following equation:
[tex]C\mleft(x\mright)=0.25x-45.01[/tex]Knowing the above, we calculate in each case:
(a) 190 minutes.
It is in the interval between 0 and 300 minutes, therefore, the cost is $29.99.
C (190) = $29.99
(b)
[tex]\begin{gathered} C(330)=0.25\cdot330-45.01 \\ C(330)=82.5-45.01 \\ C(330)=37.49 \end{gathered}[/tex](c)
[tex]\begin{gathered} C(301)=0.25\cdot301-45.01 \\ C(301)=75.25-45.01 \\ C(301)=30.24 \end{gathered}[/tex]How much does a customer pay for three memory cards if the store increases the percent of discount in part (b) by 2%.Part (b) was 5%
Answers
discount was 2%
Cost of 3 mem cards
A + B + C = X
2% of X = X+ (2/100)X
Then
Cost of 2 mem cards= $47.50
5% of $47.50 = $2.375
Cost of 3 mem cards = 47.50 + 47.50/2= 47.50 + 23.75= $71.25
Now find 2% 0f 71.25
= (2/100)x71.25= $1.425
Then
customer pays
$71.25 - $1.425= 69.83
Answer is
customer pays $69.83 for three memory cards
What percent of the runs are intermediate
Answers
Solution
For this case we have the following
[tex]\frac{56}{144}\cdot100=38.89[/tex]If we round to the nearest whole number we got:
39%
Pls help some one and can you explain how you do it
Answers
Answer:
about 37
Step-by-step explanation:
(8x-23) ----> divide
---- ----
8. 8. ------> 8x cancels out and is just x
x- 2.875+34 =. 37
8 Kiara has a bag with 9 oranges. She shares the oranges between 3 friends and herself. Write an equation to model the situation. How many oranges does each person receive?
Answers
9 oranges shared between 4 persons
x = 9/4
Oranges for each person = 9/(number of persons)
In this case, number of persons = 4
Oranges for each person = 9/4
Oranges for each person = 2.25 oranges (also we can write 2 1/4)
PLEASE HELPPP ASAP For the trapezoid below, what is he correct term for RL
Answers
GIVEN:
We are given the diagram showing a trapezoid REWT, with the vertical line RL.
Required;
Identify the correct term for the line RL.
Solution;
The trapezoid has;
RE = Shorter base
TW = Longer base
RL = Altitude (or vertical height).
ANSWER:
The correct answer is option B
[tex]Altitude[/tex]Find the y-intercept and x-intercept of the line 6x-2y=12
Answers
The expression we have is:
[tex]6x-2y=12[/tex]This is the equation of the line.
To find the y-intercept, we need to find the value for y, when x is equal to 0. So we plug x=0 into our equation:
[tex]6(0)-2y=12[/tex]And we solve for y:
[tex]-2y=12[/tex]Divide both sides by -2:
[tex]\begin{gathered} \frac{-2y}{-2}=\frac{12}{-2} \\ y=-6 \end{gathered}[/tex]The y-intercept is at y=-6
In the coordinate form, the y-intercept is (0,-6)
Now, to find the x-intercept, we need to find the value of x, when y=0.
So we plug y=0 into the equation:
[tex]6x-2(0)=12[/tex]And we solve for x:
[tex]6x=12[/tex]Divide both sides by 6:
[tex]\begin{gathered} \frac{6x}{6}=\frac{12}{6} \\ x=2 \end{gathered}[/tex]The x-intercept is at x=2
In coordinate form, the x-intercept is: (2,0)
Answer:
2,-6
Step-by-step explanation:
the app is desmos btw- very helpful
Please break down how to do these pls
Answers
The value of given expressions is -4[tex]x^{-2}[/tex] + 3[tex]y^{0}[/tex] = 19 and 2[tex]x^{0}[/tex][tex]y^{-2}[/tex] = 0.08
Simplifying an equation is simply another way of saying solving a math problem. When you simplify a phrase, you are attempting to write it in the simplest way feasible. In conclusion, there should be no more adding, subtracting, multiplying, or dividing to do.
Given expression 1. -4[tex]x^{-2}[/tex] + 3[tex]y^{0}[/tex] 2. 2[tex]x^{0}[/tex][tex]y^{-2}[/tex]
Expression for x =2 and y=5
-4x-2 + 3y0
= -4(2)-2 + 3(5)0
= 16+3
=19
Now
2x0y-2
= 2(2)0x(5)-2
= 2 x (1/25)
= 2 x 0.04
= 0.08
Therefore the value of given expressions is -4[tex]x^{-2}[/tex] + 3[tex]y^{0}[/tex] = 19 and 2[tex]x^{0}[/tex][tex]y^{-2}[/tex] = 0.08
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Hello! Would you please explain if Questions 7 and 8 are the same? I'm confused if I need to sub x for 23 for number 8
Answers
In question 7, the exercise only wants an explanation, in text form, of the meaning of the substitutions. That is, that the value of x=5 indicates the time that has passed, 5 hours, and that f(5)=32 indicates the number of riders.
In question 8, you need to pick some values for x, make a table with those values and the respective values of the function when you substitute those values of x, and put the points on the graph.
can u tell me what the answer are ????
Answers
Answer:
Step-by-step explanation:
x = 10
y = -1
See pics for explanation:-
Hope it helps :)
need help find the crimcumference of each circles round your answer to the nearest tenth.
Answers
The formula in getting the circumference of a circle is:
[tex]C=2\pi r[/tex]where r = length of the radius and π = 3.14159.
Since the radius is already given in the circle which is 9.9 km, let's use this value to replace "r" in the formula. Use 3.14159 to replace π as well.
[tex]C=2\times3.14159\times9.9km[/tex]Then, multiply.
[tex]C=62.203482km\approx62.2km[/tex]Hence, the circumference of the given circle is approximately 62.2 km.
Can you please help me with this questions Find the critical value t(alpha/2) corresponding to the 95% confidence interval
Answers
Answer:
df = 49
t = 2.01
Explanation:
The degrees of freedom for the t-distribution is always equal to the size of the sample n minus 1, so the degrees of freedom are:
df = n - 1
df = 50 - 1
df = 49
Then, the critical value is t(alpha/2) can be calculated using a t table with 49 degrees of freedom, where
alpha = 100% - 95% = 5%
So, alpha/2 = 5%/2 = 2.5%
Therefore, using a table, we get:
[tex]t_{\frac{\alpha}{2}}=2.01[/tex]So, the answers are:
df = 49
t = 2.01
oq voce precisa esta na foto se for possivel explique em portugues faça passo a passo
Answers
This is a riddle where the left-hand side represents the amount spent and the right-hand side represents the balance.
We have that:
[tex]\text{Total Spent+Current Balance=50}[/tex]Adding the values in the balance column is not really necessary; in fact, it is coincidental in this case that the balances add up to 51.
Identify the slope and y-intercept of the line y = -3(x - 1) + 5. Also, graph this line.
Answers
The slope is -3, and y-intercept is 8
The graph is shown below:
Explanation:Given the line:
y= -3(x - 1) + 5
Let us write this in the form:
y = mx + b
Where m is the slope and b is the y-intercept
Removing the parentheses, we have:
y = -3x + 3 + 5
= -3x + 8
Therefore,
The slope is -3, and y-intercept is 8