Answer:
$3,500 labor and $3,500 materials
Step-by-step explanation:
furnishings + labor + materials = 10,000
furnishings = 3000
3000 + labor + materials = 10,000
labor = materials
3000 + labor + labor = 10,000
2(labor) = 7,000
labor = 7,000/2
labor = 3,500
labor = materials = 3,500
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle. x = 4 − y2, x = y2 − 4
The region enclosed by the given curve is integrated with respect to y and the area is 21.33 square units.
In this question,
The curves are x = 4 - y^2 -------- (1) and
x = y^2 - 4 ------- (2)
The limits of the integral can be found by solving these two curves simultaneously.
On equating (1) and (2),
[tex]4 - y^2 = y^2 - 4[/tex]
⇒ [tex]4 +4 = y^2 +y^2[/tex]
⇒ [tex]8= 2y^2[/tex]
⇒ [tex]y^2=\frac{8}{2}[/tex]
⇒ [tex]y^2=4[/tex]
⇒ y = +2 or -2
The limits of y is {-2 < y +2} or 2{0 < y < 2}
The diagram below shows the region enclosed by the two curves.
The region enclosed by the given curves can be integrated with respect to y as
[tex]A=2\int\limits^2_0 {[(4-y^{2})-(y^{2}-4 )] } \, dy[/tex]
⇒ [tex]A=2\int\limits^2_0 {[4-y^{2}-y^{2}+4 ] } \, dy[/tex]
⇒ [tex]A=2\int\limits^2_0 {[8-2y^{2} ] } \, dy[/tex]
⇒ [tex]A=2[8y-\frac{2y^{3} }{3} ]\limits^2_0[/tex]
⇒ [tex]A=2[8(2)-\frac{2(2)^{3} }{3} ][/tex]
⇒ [tex]A=2[16-\frac{16}{3} ][/tex]
⇒ [tex]A=2[\frac{48-16}{3} ][/tex]
⇒ [tex]A=2[\frac{32}{3} ][/tex]
⇒ [tex]A=\frac{64}{3}[/tex]
⇒ [tex]A=21.33[/tex]
Hence we can conclude that the region enclosed by the given curve is integrated with respect to y and the area is 21.33 square units.
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(9⋅10
9
)⋅(−2⋅10
−3
)=left parenthesis, 9, dot, 10, start superscript, 9, end superscript, right parenthesis, dot, left parenthesis, minus, 2, dot, 10, start superscript, minus, 3, end superscript, right parenthesis, equals
Choose 1 answer:
Choose 1 answer:
(Choice A, Checked)
A
-18\cdot 10^6−18⋅10
6
minus, 18, dot, 10, start superscript, 6, end superscript
(Choice B)
B
-18 \cdot 10^{5}−18⋅10
5
minus, 18, dot, 10, start superscript, 5, end superscript
(Choice C)
C
18\cdot 10^{-6}18⋅10
−6
18, dot, 10, start superscript, minus, 6, end superscript
(Choice D)
D
18\cdot 10^{-5}18⋅10
−5
Answer:
A. -18·10^6
Step-by-step explanation:
The rules of exponents apply to powers of 10 used in scientific notation. The associative and commutative properties of multiplication also apply.
Application(a^b)(a^c) = a^(b+c)
The numerical product is ...
[tex](9\cdot10^9)\cdot(-2\cdot10^{-3})=(9)(-2)(10^{9-3})=\boxed{-18\cdot10^6}[/tex]
__
Additional comment
Expressed in scientific notation, the result would be ...
[tex]-1.8\cdot10^7[/tex]
Your calculator can perform this multiplication for you.
How do I do this!!!!!
The expected values of the binomial distribution are given as follows:
1. 214.
2. 21.
3. 31.
What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected value of the binomial distribution is:
E(X) = np
For item 1, the parameters are:
p = 3/7, n = 500.
Hence the expected value is:
E(X) = np = 500 x 3/7 = 1500/7 = 214.
For item 2, the parameters are:
p = 0.083, n = 250.
Hence the expected value is:
E(X) = np = 250 x 0.083 = 21.
For item 3, the parameters are:
p = 1/13, n = 400.
Hence the expected value is:
E(X) = np = 400 x 1/13 = 31.
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A study of 860 u.s. atms (automated teller machines) found that the average surcharge for withdrawals from a competing bank was $1.15. (source: public interest research groups) what is known about the atms from a competing bank?
The statement is false as the sample is a few ATMs of the total ATMs in US.
What do you mean by ATM?An automated teller machine, or ATM, is a customized computer that makes it simple for bank account holders to manage their money. One can use it to print a statement of account activity or transactions, check account balances, withdraw or deposit money, and even buy stamps.Customers can carry out simple financial transactions using an automated teller machine (ATM), an electronic banking facility, without the assistance of a branch person or teller.With no assistance from the bank, withdraw money whenever you need to. The consumers' privacy is guaranteed. Rupee withdrawals are quicker than bank withdrawals and do not require standing in long lines. Since no bank employees are involved in the transaction, maintenance costs are lower.Two primary types of automated teller machines (ATMs) exist. One is a basic, straightforward device that lets you check your balance, change your PIN, obtain small statements, and get account notifications. The more sophisticated units offer possibilities for a line of credit and bill payment and cash or check deposits.The sample is only 860 ATMs and not total ATMs in US thus, a sample of 860 ATMs have taken and conducted the survey.
Thus, the statement is false as the sample is a few ATMs of the total ATMs in US.
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Phil and ava both worked 14 hours this week. phil earned $112.70, and ava earned $113.82. ava wants to know how much more per hour she earns than phil. which strategy is appropriate for ava to use?
Answer:
Find out how much each makes per hour and then compare.
Step-by-step explanation:
Phil: 112.70/14 = 8.05 Phil makes $8.05 per hour
Eva: 113.82/1 =8.13 Eva makes $8.13 per hour
Eva makes $0.08 more an hour.
Micheal was asked to give examples of the identity property of addition and the identity property of multiplication. Below are his answers. Identity property of addition: 8 + 1 = 8 identity property of multiplication: 8(0) = 0 What was his mistake
Answer:
Identity property of addition 8 + 0 = 8
Identity property of multiplication 8 x 1 = 8
Step-by-step explanation:
He mixed up his properties. 8 + 1 does not equal 8. I want to know what I can add to 8 and that I would still get 8, the answer is zero.
The identity property of multiplication is showing that any number multiplied by 1 is itself.
Geometry: write formal proofs, ASAP!!!!
Answer:
By the definition of midpoints, AX and CX are congruent. By the definition of segment bisectors, X is the midpoint of BD, and therefore BX and DX are congruent. Since angle AXD and CXB are vertical angles, they are congruent by the vertical angles theorem. By SAS, triangles AXD and CXB are congruent. By CPCTC, angles A and C are congruent. By converse of alternate interior angles theorem, AD is parallel to CB.
The expression above can also be written in the form . For this expression, a = , b = , and c = . b 3 and 5/5
For this expression, the variables are equal to:
a = 15b = 7c = 4What is an expression?An expression is a mathematical equation which shows the relationship existing between two or more numerical quantities or variables.
Given the following expression:
[tex]\sqrt[4]{15^{7} }[/tex]
From the law of indices, we have:
[tex]\sqrt[c]{a^{b} } =a^{\frac{b}{c} } \\\\\sqrt[4]{15^{7} } =15^{\frac{7}{4} }[/tex]
For this expression, the variables are:
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Answer: A = 15, B = 7, C = 4, I got it right
:)
When navigating the maze, the robot will only need to go north, south, east, and west. it can be useful to use the complex plane to represent these directions. when using the complex plane this way, we use numbers such that their magnitude is equal to 1. if we let the value i represent the robot facing due north, what values represent the robot facing east, south, and west?
The values represent the robot facing east, south, and west are 1, -i, -1.
What was the meaning of puzzle?To offer or represent to (someone) a problem difficult to solve or a situation difficult to resolve : challenge mentally also : to exert (oneself, one's mind, etc.) over such a problem or situation they puzzled their wits to find a solution.
given that,
The robot can only go north, south, east and west.
Assuming that the north-south axis corresponds to the y-axis and west-east axis corresponds to x-axis.
Now,
It is provided that the ' i ' represent that robot is facing north.
So, if the robot turns and faces south, it can be seen that he will be facing in the opposite direction of ' i '.
Since, the values on y-axis are negative in that direction.
Hence, South will be represented by ' - i ' .
Moreover, it is given that we use only the numbers whose magnitude is 1. As, west-east axis represents x-axis.
So, the value that represents East will be 1.
(as it is on the positive x-axis ).
Since, west is in the opposite direction of east.
So, West will be represented by -1.
Hence,The values represent the robot facing east, south, and west are 1, -i, -1.
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Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
12.50h = 2500.75
Step-by-step explanation:
He earned $12.50 for 1 hour of work.
For 2 hours, he earned $12.50 × 2.
For 3 hours, he earned $12.50 × 3.
For h hours, he earned $12.50 × h which can be simply written as 12.50h
He earned altogether $2500.75, so 12.50h must equal 2500.75.
Answer: B 12.50h = 2500.75
Answer:
[tex]12.50 h = 2500.75[/tex]
Step-by-step explanation:
We know from the question that the student earned $12.50 per hour.
Using this information, we can say that if the student worked for h hours, they would make a total of 12.50 × h dollars.
We also know that the total money they earned is $2500.75.
∴ Therefore, we can set up the following equation:
12.50 x h = 2500.75
From here, if we want to, we can find the number of hours worked by simply making h the subject of the equation and evaluating:
[tex]h=\frac{2500.75}{12.50}[/tex]
= 200.6 Hours
The area of a circle is 25л ft². What is the circumference, in feet? Express your answer in terms of π.
Answer:
C = 10π ft
Step-by-step explanation:
the circumference (C) of a circle is calculated as
C = 2πr ( r is the radius )
to find r use the area formula, that is
A = πr² = 25π ( divide both sides by π )
r² = 25 ( take square root of both sides )
r = [tex]\sqrt{25}[/tex] = 5
then
C = 2π × 5 = 10π ft
which expression is equivalent to (60x^(20)y^(24))/(30x^(10)y^(12)
a. 2x^(2)y^(2)
b. 2x^(10)y^(12)
c. 30x^(2)y^(2)
d.30x^(10)y^(12)
Answer:
b. 2x^10y^12.
Step-by-step explanation:
(60x^(20)y^(24))/(30x^(10)y^(12)
60 / 30 = 2
x^20 / x^10 = x^(20-10) = x^10
y^(24) / y^(12) = y^(24-12) = y^12.
Thus, the answer is:
2x^10y^12.
Answer:
b. 2x^(10)y^(12)
Step-by-step explanation:
(60x^(20)y^(24))/(30x^(10)y^(12)
when there is division we simplify that by subtracting the power
by using rules of indices
[tex] \frac{x^a}{x^b}=x^{a-b}[/tex]
and number can be divided easily
[tex] \frac{60}{30}*\frac{x^{20}}{x^{10}}*\frac{y^{24}}{y^{12}}[/tex]
[tex] 2*x^{20-10}y^{24-12}[/tex]
[tex] 2x^{10}y^{12}[/tex]
so answer is b. 2x^(10)y^(12)
Which of the following correctly uses absolute value to show the distance between -80 and 15?
O-80-1511-95| = -95 units
1-80+ 15| = |-65| = 65 units
O-80-15| = |-95| = 95 units
O-80 + 15| = |-65| = -65 units
Answer:
C
Step-by-step explanation:
|-80 - 15| = 95
The distance between -80 and 15 is 95
80 to 0 plus 15.
30 POINTS HELP PLS!!!!!!
The lengths of the sides of the rectangles are;
a. (2•x + 3) and (x + 2)
b. (6•x + 2) and (x + 1)
c. (x + (2 + √3)) and (x + (2-√3))
Which method can be used to find the side lengths of the rectangles?The given functions are presented as follows;
a. 2•x² + 7•x + 6
By factoring of the above function we have;
2•x² + 7•x + 6 = (2•x + 3) × (x + 2)
The lengths of the sides of the rectangle are therefore;
(2•x + 3) and (x + 2)b. 6•x² + 7•x + 2
The above function can be factored as follows;
6•x² + 7•x + 2 = (6•x + 2) × (x + 1)
The rectangle side lengths are;
(6•x + 2) and (x + 1)c. x² + 4•x + 1
Using the quadratic formula, the above function can be factored to give;
x² + 4•x + 1 = (x + (2 + √3)) × (x + (2-√3))
The sides of the rectangle are therefore;
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NEED HELP PLEASE ASAP!!!
Find the quotient of 213.21 and 15.8. Round your answer to the nearest tenth.
13.4
1.4
1.3
13.5
Answer:
13.5
Step-by-step explanation:
213.21/15.8 ---> ((213.21)100)/((15.8)100)
21321/1580 = 13 R 781.
781/1580 = 0.49~~~
We only need to be concerned about the tenth and hundredth place digits.
The decimal tells us that it rounds up from 4, so it's 5.
Thus, the answers 13+0.5, which is 13.5
Simplify
sin0 over
1-sin²0
Step-by-step explanation:
sin(0) = 0.
sin^2(0) = sin(0) × sin(0) = 0 × 0 = 0.
∴ sin(0) / 1 - sin^2(0) = 0 / 1 - 0
= 0 / 1
= 0.
There are 6 dogs and 5 cats. In how many different orders can these animals be placed in line if any animal can be next to any other animal?
120=!3÷!6
!2-!5=!3
to 120 modes
pls help questions 5-7
Answer: 0.032, 18, 4224, 7.58
Step-by-step explanation:
5. 5 L = 5000 mL = 5000 [tex]cm^{3}[/tex]
5000/(6*6*6) = 23 r 32 so 5 L of water can fill up 23 cubic tanks length 6 cm and is left with 0.032 L
6. There is (13 - 11) x 20 x 10 = 400 [tex]cm^{3}[/tex] left unoccupied in the box
400/23 = 17.4 so it takes 18 balls to overflow the water
7. 1 mL = 1 [tex]cm^{3}[/tex]
(a) 22 x 12 x 16 = 4224 [tex]cm^{3}[/tex] = 4224 mL
(b) 2 L = 2000 mL = 2000 [tex]cm^{3}[/tex]
22 x 12 = 264
2000/264 = 7.58 cm
Which expression is equivalent to 3square root x^5y?
Answer: Choice B
Work Shown:
[tex]\sqrt[3]{\text{x}^5\text{y}}\\\\(\text{x}^5\text{y})^{\frac{1}{3}}\\\\(\text{x}^5)^{\frac{1}{3}}*(\text{y})^{\frac{1}{3}}\\\\\text{x}^{\frac{5}{3}}\text{y}^{\frac{1}{3}}\\\\[/tex]
Fractions equivalent to 2/100
Answer:
1/50
Steps:
Recall 2 can divide 100
therefore
2/100 = 1/50
In order for you to use the goodnees-of-fit test, the test of independence, or the test of homogeneity, the expected frequencies for each cell needs to be at least:____.
The condition for the expected value in the goodness of fit test is that the expected frequency is at least 5.
According to the statement
we have to find the condition of the expected values in the case of testing of goodness-of-fit test.
So, For this purpose we know that the
The goodness of fit test is of a statistical model describes how well it fits a set of observations. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected.
So, The main condition of the expected value for the goodness of fit test is
For each category, the expected frequency is at least 5.
Without this condition the test is not possible, so overall this the main condition related the goodness of fit test.
So, The condition for the expected value in the goodness of fit test is that the expected frequency is at least 5.
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The functionf (x)is shown in the graph.
What is the equation for f (x)?
Enter your answer in the box.
f(x) =
[tex]f(x)=-\frac{3}{4}x-3[/tex]
What is a graph?A graph is a diagram that depicts the connections between two or more objects. A pie chart is a type of graph. 5. A mathematical function or equation is shown by a curve or line, usually represented using a Cartesian coordinate system.
The equation for f (x):
[tex]y=f(x)=mx+b[/tex]
The slope of the line is m.
The point of intersection of the line with the y-axis is b.
To find the slope first by the following formula:
[tex]=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
Two points of the line: [tex](x_{1} ,y_{1})=(x_{2},y_{2} )[/tex]
[tex](x_{1} ,y_{1})=(-4,0)[/tex]
[tex](x_{2} ,y_{2})=(0,-3)[/tex]
Substituting:
[tex]m=\frac{-3-0}{0-(-4)}[/tex]
[tex]m=-\frac{3}{4}[/tex]
Find the y-intercept Looking at the graph, we find the line intercepts the y-axis at y=-3.
Therefore, b=-3.
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After finding the intercept form of the graph of the given straight line, it can be obtained that [tex]f(x)=-\frac{4}{5}x-3[/tex].
How to find the equation of a straight line in intercept form from its graph?If the graph of a straight line cuts the x-axis at the point [tex](a,0)[/tex] and the y-axis at the point [tex](0,b)[/tex], then the equation of the straight line in intercept form will be [tex]\frac{x}{a}+\frac{y}{b}=1[/tex].
Here, in the given figure, we can see that the graph of [tex]y=f(x)[/tex] is a straight line.
From the graph, we can see that the straight line cuts the x-axis at the point [tex](-3\frac{3}{4},0)=(-\frac{15}{4},0)[/tex] and cuts the y-axis at the point [tex](0,-3)[/tex].
So, here, [tex]a=-\frac{15}{4}[/tex] and [tex]b=-3[/tex].
Hence, the equation of the straight line in intercept form is
[tex]\frac{x}{a}+\frac{y}{b}=1\\\frac{x}{-\frac{15}{4}}+\frac{y}{-3}=1\\\frac{y}{-3}=1+\frac{4x}{15}\\y=-\frac{4}{5}x-3[/tex]
Therefore, finding the intercept form of the given straight line, we obtain that [tex]f(x)=-\frac{4}{5}x-3[/tex].
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There is a balcony that forms part of a circle around a stage, and they need to put up a safety railing. How long of a railing do they need if the radius of the circle is 40 feet, and the arc takes up 45°? Use 3.14 for pi.
The length of the railing needed is 31.4 feet
Calculating the length of an arcFrom the question, we are to determine the length of railing needed
To determine the length of railing needed, we will determine the length of the arc formed by the balcony
Using the formula,
l = θ/360° × 2πr
Where l is the length of the arc
θ is the angle subtended by the arc
and r is the radius
From the given information,
θ = 45°
r = 40 feet
Putting the parameters into the equation, we get
l = 45°/360° × 2 × 3.14 × 40
l = 1/8 × 2 × 3.14 × 40
l = 2 × 3.14 × 5
l = 31.4 feet
Hence, the length of the railing needed is 31.4 feet
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identify all values of that make the equation true.
Please explain them as step by step !!
Thank you!!
Part a
[tex]\frac{2x+1}{x}=\frac{1}{x-2}\\\\(2x+1)(x-2)=x\\\\2x^2 -3x-2=x\\\\2x^2 - 4x-2=0\\\\x^2 - 2x-1=0\\\\x=\frac{2 \pm \sqrt{8}}{2}\\\\x=1 \pm \sqrt{2}[/tex]
Part C
[tex]\frac{x+3}{1-x}=\frac{x+1}{x+2}\\\\(x+3)(x+2)=(1-x)(x+1)\\\\x^2 +5x+6=-x^2 +1\\\\2x^2 + 5x+5=0\\\\x=\frac{-5 \pm \sqrt{-15}}{4}\\\\x=\frac{-5 \pm i\sqrt{15}}{4}[/tex]
Zoey read a novel in 30 days she made it a habit to read 13 pages everyday for the first 20 days. if in the last 10 days she reads 6 pages everyday how many pages are in the book?
Answer:
320 pages.
Step-by-step explanation:
We can simply multiply and add to find how many pages are in the book.
So we have (13 pg * 20 d) + (6 pg * 10 d) = 260 + 60 = 320.
Another way of solving is to set up a proportion for both the 20 and 10 days, find how many pages are read on these days, and add:
[tex]\frac{13pg}{1d}=\frac{xpg}{20d}\\ x=260pages\\\\\frac{6pg}{1d} =\frac{xpg}{10d}\\ x=60pg\\260+60=320[/tex]
What fraction of a clockwise revolution does the hour hand of a clock turn through, when it goes from a) 5 to 11? b)2 to 8? c)10 to 1?
Answer: 1/2, 1/2, 1/4
Step-by-step explanation:
To find the fraction that the hour hand turns of a clockwise revolution, we have to find how long it is going then divide by 12
Ex. a) 11 - 5 = 6, 6/12 = 1/2 so the hour hand turns by 1/2 of a clockwise revolution
b) 8 - 2 = 6, 6/12 = 1/2 so the hour hand turns by 1/2 of a clockwise revolution
c) For this, we have to convert 1 into 13 as 1 - 10 is a negative number
13 - 10 = 3, 3/12 = 1/4 so the hour hand turns by 1/4 of a clockwise revolution
The answers are :
a) 1/2
b) 1/2
c) 1/4
To find the fraction of a clockwise revolution, take the ratio between hours covered and hours covered in one revolution.
a)
Hours covered between 5 and 11 ⇒ 11 - 5 = 6Hours covered in 1 revolution ⇒ 126/12 = 1/2b)
Hours covered between 2 and 8 ⇒ 8 - 2 = 6Hours covered in 1 revolution ⇒ 126/12 = 1/2c)
Hours covered between 10 and 1 ⇒ 13 - 10 = 3 (∴ 12 + 1 = 13)Hours covered in 1 revolution ⇒ 123/12 = 1/4Multiply (x - 3)(x2 + 7x - 2)
Answer:
x^3+4x^2−23x+6
Step by Step:
(x−3)(x2+7x−2)
=(x+−3)(x2+7x+−2)
=(x)(x2)+(x)(7x)+(x)(−2)+(−3)(x2)+(−3)(7x)+(−3)(−2)
=x3+7x2−2x−3x2−21x+6
=x3+4x2−23x+6
Algebra 2 how do you find the frequency?
The frequency of the periodic function is given by: 0.0796.
What are the period and the frequency of a function?The period of a function is given by the distance between it's repetitions.The frequency of a function is found dividing one by the period.From the graph, we have that the period is of 4pi hours, hence the frequency is:
f = 1/4pi = 0.0796.
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1. Sandy has 1.45 L of soft drink in a bottle. She pours the soft drink into glasses with capacity of 0.32 L each. At least how many glasses must she use in order to pour all soft drink out of the bottle?
2. A baker has 5.6 kg of flour. Later he buys 2.5 kg of flour. If he needs 0.48 kg of flour to make a dough, then how many doughs can he make with the flour? How much flour remains (in kg)?
Step-by-step explanation:
1.
how many glasses of 0.32 liter can she fill ?
that means, how often does 0.32 fit into 1.45 ?
that is solved by division :
1.45 / 0.32 = 4.53125
so, she will need at least 5 glasses to completely empty the bottle. the 5th glass will be filled only partly, but that does not matter in that regard.
2.
he has 5.6 kg and adds 2.5 kg. that is 5.6 + 2.5 = 8.1 kg.
1 dough (that means 1 portion of dough as described by his recipe) uses 0.48 kg flour.
how many doughs can he make
so, again, how often does 0.48 fit into 8.1 ?
8.1 / 0.48 = 16.875
he can therefore make 16 full portions of dough. he does not have enough flour for a full 17th.
so, he uses
16×0.48 = 7.68 kg of flour for the 16 doughs.
and he has
8.1 - 7.68 = 0.42 kg of flour left.
Identify an equation in standard form for a hyperbola with center (0, 0), vertex (−5, 0), and focus (−6, 0).
An equation in standard form for a hyperbola with center (0, 0), vertex (-5, 0), and focus (-6, 0) is given by y²/25 - x²/9 = 1.
What is an equation?An equation can be defined as a mathematical expression which is used to show and indicate that two (2) or more numerical quantities are equal.
How to determine the equation of a hyperbola?Mathematically, the equation of a hyperbola in standard form is given by:
[tex]\frac{(y\;-\;k)^2}{a^2} - \frac{(x\;-\;h)^2}{b^2} = 1[/tex]
Given the following data:
Center (h, k) = (0, 0)
Vertex (h+a, k) = (-5, 0)
Foci, F = (h+c, k) = (-6, 0) and F' = (6, 0)
Also, we can logically deduce that the value of a and c are -5 and -6 respectively.
For the value of b, we would apply Pythagorean's theorem:
c² = a² + b²
b² = c² - a²
b² = (-6)² - (-5)²
b² = 36 - 25
b² = 9.
b = √9
b = 3.
Substituting the given parameters into the equation of a hyperbola in standard form, we have;
[tex]\frac{(y\;-\;k)^2}{a^2} - \frac{(x\;-\;h)^2}{b^2} = 1\\\\\frac{(y\;-\;0)^2}{-5^2} - \frac{(x\;-\;0)^2}{3^2} = 1\\\\\frac{y^2}{-5^2} - \frac{x^2}{3^2} = 1\\\\\frac{y^2}{25} - \frac{x^2}{9} = 1[/tex]
y²/25 - x²/9 = 1.
In conclusion, we can logically deduce that an equation in standard form for a hyperbola with center (0, 0), vertex (-5, 0), and focus (-6, 0) is given by y²/25 - x²/9 = 1.
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