Answers
The standard form of the hyperbola:
[tex]\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}\text{ = }1[/tex]The center of the hyperbola is at (h, k) = The point where the lines intersect
(h, k) = (0, 0)
For hyperbola:
c² = a² + b²
b is gotten by tracing the value of a to the intersecting line. Trace 3 down to the x axis. you get 5.
[tex]\begin{gathered} a\text{ = distance from center to vertex} \\ \text{the hyperbola coordinate = (0, a) = }(0,\text{ 3)} \\ \text{the other one = (0, -a) = (0, -3)} \\ \text{Hence, a = 3} \end{gathered}[/tex][tex]\begin{gathered} c\text{ = distance from the center to the focus point} \\ b\text{ = 5 and -b = 5} \\ c^2=3^2+5^2 \end{gathered}[/tex][tex]\begin{gathered} c^2\text{ = 9+25 = 34} \\ c\text{ = }\sqrt[]{34} \\ c\text{ = 5.83} \end{gathered}[/tex]The equation becomes:
[tex]\begin{gathered} \frac{(y-k)^2}{5^2}-\frac{(x-h)^2}{3^2}=\text{ }\frac{(y-0)^2}{5^2}-\frac{(x-0)^2}{3^2} \\ =\text{ }\frac{y^2}{25}-\frac{x^2}{9} \end{gathered}[/tex]Related Questions
What is the missing numerator in 1 1/8=?/16
Answers
Answer:
12
Step-by-step explanation:
12/18 is just. 11/6*2
Which pair of variables would most likely have a positive association?
Answers
Answer:
• The age of a kitten and its weight
,• Temperature and the sales of ice cream
,• The number of notebooks bought and the total cost.
Explanation:
Two variables have a positive association when an increase in the values of one of the variables also leads to an increase in the value of the second variable.
From the given options, those with a positive association are explained below:
(a)The age of a kitten and its weight
The older a kitten gets, the more the weight of the kitten until it gets to adulthood.
(b)Temperature and the sales of ice cream
When the temperature increases, people tend to purchase more ice cream.
(c)The number of notebooks bought and the total cost.
• If 1 notebook costs $5, then:
,• 2 notebooks will cost $10.
As the number of notebooks bought increases, the total cost also increases.
If M is a centroid of triangle WOR and YR =16, what is the length of WR
Answers
If M is a centroid of triangle WOR and YR =16, the length of WR
side will be WR = 48.
What is the triangle's centroid?The centroid of the thing represents its center. A triangle's centroid is the point at which its three medians intersect. It can also be described as the point at which the three medians intersect.The median is a line that connects the midpoints of two sides and the opposite vertex of a triangle. A triangle is a two-dimensional shape with three sides. The three angles add up to 180 degrees.The centroid of a triangle divides the triangle's medians in a 2: 1 ratio.The ratio of the two sides will be given here as:
WY/ YR = 2/1
Determine the value of YR to determine the value of WR.
WY/16 = 2/1
WY = 32
WR will have the following value:
WR = WY+ YR
WR = 32+ 16
WR = 48
As a result, the value of the side WR is 48.
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Dog kennel charges each owner a registration fee + a daily amount for the # of days a dog is boarded. The total bill for 1 owner was 115 for 5 days, another was 151 for boarding for 7 days. Are the following true or false
1. a total cost for 10 days is 180
2. a total cost for 14 days is 277
3. a total cost for 1 day is 43
Answers
Answer:
Find cost difference between the two days
151 - 115 = 36
we can assume it costs 18$ a day
To find registration fee
five days = 18 x 5 = 90$
115 - 90 = 25
The registration fee is 25$
The formula is 18x + 25. Where x is the amount of days the dog is boarded
1. False
2. True
3. True
Cal made the graph at right. Use the graph to write a problem involving fractions.
Answers
We need to come up with a question involving the graph.
Very simple!
We can ask how much time in a day Cal spends for different activities.
We can say:
According to the graph, how much time of the day does Cal spend studying and sleeping?
answering this question:
[tex]\begin{gathered} \frac{1}{8}+\frac{1}{3} \\ =\frac{3(1)+8(1)}{3\times8} \\ =\frac{3+8}{24} \\ =\frac{11}{24} \end{gathered}[/tex]The owner of a small restaurant bought 75 kilograms of rice. Each week, the restaurant uses 4.5 kilograms of rice. Function r gives the remaining amount of rice, in kilograms, as a function of the number of weeks since the restaurant owner bought the rice.6 weeks | kilograms of rice left12 weeks | kilograms of rice leftw weeks | kilograms of rice
Answers
The total kg of rice bought is 75kg
Each week, 4.5kg is used,
Let the number of weeks be represented by n
The remaining amount of rice is represented by r
The relationship between the values above can be given as,
[tex]r=75-4.5n[/tex]For 6 weeks, the kilogram of rice left where n = 6 is,
[tex]\begin{gathered} r=75-4.5n \\ r=75-4.5(6)=75-27=48\operatorname{kg} \end{gathered}[/tex]For 12 weeks, the kilogram of rice left where n = 12 is,
[tex]\begin{gathered} r=75-4.5n \\ r=75-4.5(12)=75-54=21\operatorname{kg} \end{gathered}[/tex]For w weeks, the kilogram of rice left where n = w is,
[tex]\begin{gathered} r=75-4.5n \\ r=75-4.5(w)=75-4.5w \end{gathered}[/tex]Hence, after 6 weeks, the remaining rice left is 48kg
Hence, after 12 weeks, the remaining rice left is 21kg
Hence, after w weeks, the remaining rice left is (75-4.5w)kg
the ladder to the slide is 21 feet high. how long is the slide
Answers
To find the slide we can us the pythagorical theorem that say:
[tex]h=\sqrt[]{l^2_1+l^2_2}[/tex]Where l1 and l2 iare the leg of the triangle so in our problem will be:
[tex]\begin{gathered} h=\sqrt[]{28^2+21^2} \\ h=\sqrt[]{784+441} \\ h=\sqrt[]{1225} \\ h=35 \end{gathered}[/tex]So the slide is 35 ft
This test is timed so i need it quickly
Answers
Answer: D!!
Step-by-step explanation: No explanation so you can move on quickly!!!!:))
Let f(t) = 3 + 2, g(x) = -x^2?, and
he) = x - 2/5. Find the indicated value.
Question 22
Answers
To find h(f(-9)), first, we need to find f(-9) substituting x = -9 into f(x), as follows:
[tex]\begin{gathered} f(x)=3x+2 \\ \text{ Substituting x = -9,} \\ f\mleft(-9\mright)=3(-9)+2 \\ f(-9)=-27+2 \\ f(-9)=-25 \end{gathered}[/tex]Substituting f(-9) = -25 into h(f(-9)), we get h(-25).
To evaluate h(-25) we have to substitute x = -25 into h(x), as follows:
[tex]\begin{gathered} h(x)=\frac{x-2}{5} \\ \text{ Substituting with x = -25,} \\ h(x)=\frac{-25-2}{5} \\ h(x)=-\frac{27}{5} \end{gathered}[/tex]The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).5,4, 16/5... Find the 7th term.
Answers
In order to find the 7th of the sequence, first let's find the common ratio of the sequence.
To do so, let's divide one term by the term before:
[tex]q=\frac{4}{5}[/tex]Now, we can use the following formula to find the 7th term:
[tex]a_n=a_1\cdot q^{n-1}[/tex]For n = 7, we have:
[tex]\begin{gathered} a_7=5\cdot(\frac{4}{5})^6 \\ a_7=1.311 \end{gathered}[/tex]Identify the missing terms in the polynomial.x3-9O x2-term, x-termSO x-termO x4-term, x2-term, x-termO x-term
Answers
We must identify the missing terms in the polynomial:
[tex]x^3-9.[/tex]The general form of a 3th grade polynomial is:
[tex]a_3\cdot x^3+a_2\cdot x^2+a_1\cdot x+a_0.[/tex]We see that the missing terms are x² and x.
Answer
The missing terms are: x2-term, x-term.
In the diagram of LPN below, QM ||PN, QP=32, LM=10, and MN=40. What is the length of LP? L 10 M M 32 40 P N Answet Submit Answer
Answers
This graph shows how fast the international space station travels in orbit around Earth What is the meaning of the point with an x-coordinate of 3?A. In 1 second, the space station travels 3 miles B. In 3 seconds, the space station travels 3 miles in 15 miles.C. The space station travels 3 miles in 15 seconds D. It takes the space st 3 seconds to go 5 miles.
Answers
From the graph, x coordinate 3 mean it takes 3 seconds to travels 15 miles.
Option B is the correct answer.
2
(b) The area of a rectangular painting is 8134 cm².
If the length of the painting is 98 cm, what is its width?
Width of the painting: cm
Answers
Answer:
Step-by-step explanation:
To answer this question do 8134 cm²÷98 cm
8,134÷98=83cm
Which statements about the graph of the function ) =22-X-6 are true? Select two options3The domain of the function is falx2)The range of the function is all real numbersThe verter of the function is7227The function has two x-intercepts.The function is increasing over the interval (-5)
Answers
True statements about the graph of the function f(x) = 2 x 2 - x -6 include:
The range of the function is all real numbers
The function has two x-intercepts.
What is function?In mathematics, functions are the foundation of calculus. Functions are specific types of relationships. In math, a function is represented as a rule that produces a unique output for each input x. In mathematics, mapping or transformation is used to represent a function.
These functions are typically denoted by letters such as k, g, and h. The domain is defined as the set of all the values that the function can accept while it is defined. The range contains all of the values returned by the function in question. The co-domain is the set of values that have the potential to be outputs of a function.
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Write the number in standard notation.5.8 × 10−3
Answers
0.0058
Explanation:The given scientific notation is:
[tex]5.8\times10^{-3}[/tex]This can also be written as:
[tex]\begin{gathered} 5.8\times\frac{1}{1000} \\ \\ =\frac{5.8}{1000} \\ \\ =0.0058 \end{gathered}[/tex]Therefore 5.8 x 10^-3 in standard form is 0.0058
a store pays $10 for a bracelet and the markup is 115%. A customer will also pay 5 and a half sale tax . what will be the total cost to the nearest cent ?
Answers
ANSWER:
$22.68
STEP-BY-STEP EXPLANATION:
Given:
Bracelet = $10
Markup percentage = 115% = 115/100 = 1.15
The markup amount can be calculated as follows:
[tex]\begin{gathered} \text{ markup amount = cost price }\cdot\text{ markup percentage} \\ \text{ replacing} \\ \text{markup amount }=10\cdot1.15=11.5 \end{gathered}[/tex]Therefore, the total price would be:
[tex]t=10+11.5=21.5[/tex]Now we apply sales tax for the price and calculate the price after tax, like this:
[tex]\begin{gathered} t=21.5+21.5\cdot\frac{5.5}{100} \\ t=21.5+1.1825 \\ t=22.6825\cong22.68 \end{gathered}[/tex]$22.68 is the total cost of the bracelet
123456Previous Activity78910Juanita wants to perform row operations on the augmented matrix for the system below.x+ 2y = 3-x+y+z=2y-2z=-3Which matrix should Juanita use to perform the operations?1 2 3 0-⠀⠀⠀⠀-1 1 1 21 -2 -3 0Next A
Answers
The given system of equation is
x + 2y + 0z = 3
- x + y + z = 2
0x + y - 2z = - 3
The augumented matrix is formed by using the coefficient of the variables. The required matrix is shown below
[tex]\begin{bmatrix}{1} & {2} & {0} & {3} \\ {-1} & {1} & {1} & {2} \\ {0} & {1} & {-2} & {-3} \\ {} & {} & {} & {}\end{bmatrix}[/tex]The correct option is the second one
Which of the following graphs shows the preimage P(x)=|x| and the image I(x)=1/2⋅P(x)?
Answers
Given,
The expression for function P(x) is | x |.
The expression for function I(x) is | x |/2.
Required:
The graph of the function.
The graph of the function is,
The function P(x) is represented by black line.
The function I(x) is represented by Red line.
Hence, option A is correct.
What is the generator for the sequence: 81, -27, 9, -3, 1
a. 3
b. -3
c. -1/3
d. 1/3
e. None
Answers
Gianna went shopping for a new camera because of a sale. The price on the tag was $26, but Gianna paid $13 before tax. Find the percent discount.
Answers
The percent discount of the camera is 50%.
What is percentage discount?Percentage discount is a discount that is given to a product or service that is given as an amount per hundred.
In other words, the percent discount is list price minus the sale price then divided by the list price and multiplied by 100 to get a percentage.
Hence,
she bought the camera for $13 but the price tag is $26.
Therefore,
percentage discount = tagged price - sale price / tagged price × 100
tagged price = 26 dollars
sale price = 13 dollars
percentage discount = 26 - 13 / 26 × 100
percentage discount = 13 / 26 × 100
percentage discount = 1 / 2 × 100
Therefore,
percentage discount = 50%
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What is the perimeter, P, of a rectangle that has a length of x + 6 and a width of y-1?OP=x+y+5OP=x+y-7OP=2x + 2y + 10OP=2x+2y-10
Answers
GIVEN
A rectangle with length (x + 6) units and width (y - 1) units.
TO FIND
The perimeter of the rectangle.
SOLUTION
The perimeter of a rectangle is calculated using the formula:
[tex]P=2\left(l+w\right)[/tex]Substitute the values of the length and width into the formula:
[tex]P=2(x+6+y-1)[/tex]Simplify:
[tex]\begin{gathered} P=2(x+y+5) \\ P=2x+2y+10 \end{gathered}[/tex]ANSWER
[tex]P=2x+2y+10[/tex]Yea I do agree that with this one ☝️ I will be coming
Answers
Solution
- The equation for the potential given is:
[tex]V(t)=320e^{-3.1t}[/tex]Question 1:
- To find when the potential is 150V, we simply substitute the value of V = 150 into the equation and then find the corresponding value of t.
- Thus, we have:
[tex]\begin{gathered} V=150 \\ \\ 150=320e^{-3.1t} \\ \\ \text{ Divide both sides by 320} \\ \\ e^{-3.1t}=\frac{150}{320}=\frac{15}{32} \\ \\ \text{ Take the natural log of both sides} \\ \\ \ln e^{-3.1t}=\ln(\frac{15}{32}) \\ \\ -3.1t=\ln(\frac{15}{32}) \\ \\ \text{ Divide both sides by -3.1} \\ \\ t=-\frac{1}{3.1}\ln(\frac{15}{32}) \\ \\ t=0.2444s\text{ \lparen To 4 decimal places\rparen} \end{gathered}[/tex]Question 2:
- The rate at which the changing occurs is gotten by differentiating the function with respects to time.
- That is,
[tex]\begin{gathered} V(t)=320e^{-3.1t} \\ \\ V^{\prime}(t)=\frac{d}{dt}(320e^{-3.1t}) \\ \\ V^{\prime}(t)=320(-3.1e^{-3.1t}) \\ \\ V^{\prime}(t)=-992e^{-3.1t} \end{gathered}[/tex]- Now that we have the expression for the rate of change of potential with time, we can proceed to find how fast the changing of potential V is happening at t = 0.2444s.
- Thus, we have:
[tex]\begin{gathered} V^{\prime}(t)=-992e^{-3.1t} \\ put\text{ }t=0.2444 \\ \\ V^{\prime}(t)=-992e^{-3.1\times0.2444} \\ \\ \therefore V^{\prime}(t)=-465.02125...\approx-465.0\text{ v/s} \end{gathered}[/tex]Question 3:
- The voltage is changing at -50v/s when we substitute V'(t) = -50 into the equation for V'(t).
- We have that:
[tex]\begin{gathered} V^{\prime}(t)=-992e^{-3.1t} \\ \\ V^{\prime}(t)=-50 \\ \\ -50=-992e^{-3.1t} \\ \\ \text{ Divide both sides by -992} \\ \\ e^{-3.1t}=\frac{-50}{-992}=\frac{25}{496} \\ \\ \text{ Take the natural log of both sides} \\ \ln e^{-3.1t}=\ln(\frac{25}{496}) \\ \\ -3.1t=\ln(\frac{25}{496}) \\ \\ \text{ Divide both sides by -3.1} \\ \\ \therefore t=-\frac{1}{3.1}\ln(\frac{25}{496}) \\ \\ t=0.96377...\approx0.9638seconds\text{ \lparen To 4 decimal places\rparen} \end{gathered}[/tex]Final Answers
Question 1: 0.2444 seconds
Question 2: -465.0v/s
Question 3: 0.9638 seconds
What is the variable being tested in an experiment?0 A.response variableO B. placeboO C.control variableOD.explanatory variable
Answers
Given
Variables
Find
Which variable being tested in an experiment
Explanation
The dependent variable is the variable that is being measured or tested in an experiment
response variable is often referred as dependent variable.
Final Answer
hence , the correct option is A.
Can u help me answer question 24 BTW this is lesson 6 the distributive property 24. 5(2x+7) = __________
Answers
We have the following:
[tex]5\mleft(2x+7\mright)=_{}[/tex]We apply the distributive property that tells us that the multiplication of a number by a sum is equal to the sum of the multiplications of said number by each of the addends.
Therefore:
[tex]5(2x+7)=_{}10x+35[/tex]4. A fruit stand sells boxes of apples. Each box weighs the same amount. The table shows the number of boxes and the total number of pounds. AppIGN Number of Boxes Tocal Number of Pounds И. 7 8 72 10 Which of the following correctly describes the relationship in the table? A. Number of boxes + 4 = total number of pounds B. Number of boxes x 9 + total number of pounds C. Number of boxes - 9 total number of pounds D. Number of boxes x 6 = total number of pounds
Answers
From the table it can be observed if we multiply the number of boxes by 9, then it gives total number of pounds for the corresponding number of boxes.
As 4 multiply by 9 is 36, which is total number of pounds for 4 boxes. In similar manner total number of pounds can be obtained for different number of boxes.
So answer is,
[tex]\text{ Number of boxes}\times9=\text{ total number of pounds}[/tex]Option B is correct.
[tex](9x^{2} - 2x) - (5x^{2} -8x-3)[/tex]
Answers
Answer:
[tex]4x^{2} +6x+3[/tex]
Step-by-step explanation:
Distribute and multiply the 1.
[tex]1(9x^{2} -2x) - 1(5x^{2} -8x-3)[/tex]
Collect like terms and sort them in descending order.
[tex]9x^{2} -2x -5x^{2} +8x +3[/tex]
[tex]4x^{2} +6x+3[/tex]
Please help me with these graphs i am not sure which one should be correct in order to explain this to my son. I have attached the pictures of the graph What graph represents the system of linear inequalities?2x+y<1y≥1/2x+2
Answers
The given inequalities are
2x + y < 1
y ≥ x/2 + 2
The first step is to write both inequalities as equations. We have
2x + y = 1
y = x/2 + 2
The next step is to plot the straight line graphs for each equation. Since we are given options, we would find the x and y intercepts of each equation and select the graph that matches them.
Recall, x intercept is the value of x when y is zero
y intercept is the value of y when x is zero
For the first equation,
when x = 0, we have
2(0) + y = 1
0 + y = 1
y = 0. This means that y intercept = 0
when y = 0,
2x + 0 = 1
2x = 1
x = 1/2 = 0.5
This means that x intercept = 0.5
The line representing this equation should pass through the y axis at y = 0 and the x axis at x = 0.5
Also, the line would be dashed(not solid) because the solutions to the inequality do not include the values on the line.
For the second equation,
when x = 0, y = 0/2 + 2 = 0 + 2 = 2
when y = 0, we have
0 = x/2 + 2
x/2 = 0 - 2 = - 2
x = - 2 * 2 = - 4
The line representing this equation should pass through the y axis at y = 2 and the x axis at x = - 4
Also, the line would be a solid line because the solutions to the inequality include the values on the line.
The next step is to determine the shaded region for each inequality. Where the shaded regions overlap is the solution. The shaded regions in each option indicate the solution. We would pick points which we would test in each of the shaded regions
For the first option, let us pick a point in the shaded region. Let us pick x = - 2 and y = 2
We would plug these values in both inequalities and see if they satisfy it.
For the first,
2x + y < 1
y < 1 - 2x
Plugging in x = - 2 and y = 2, we have
2< 1 - 2(-2)
2 < 1 + 4
2 < 5
This is true
For the second,
y≥ x/2 + 2
Plugging in x = - 2 and y = 2, we have
2 ≥ -2/2 + 2
2 ≥ - 1 + 2
2 ≥ 1
This is also true
Thus, the first option is correct
Can someone help me with this geometry question? My instructor said I was wrong?
Answers
If 7 ballpoint pens cost $9.66, how much will 12 pens cost? (100 points)
Answers
Answer:
16.56
Step-by-step explanation:
9.66/7
=1.38 each
1.38x12=16.56
Answer:
16.56
Step-by-step explanation:
