keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]7x+9y=5y-6\implies 7x+4y=-6\implies 4y=-7x-6 \\\\\\ y=\cfrac{-7x-6}{4}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{7}{4}}x-\cfrac{3}{2}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-7}{4}} ~\hfill \stackrel{reciprocal}{\cfrac{4}{-7}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{4}{-7}\implies \cfrac{4}{7}}}[/tex]
so we're really looking for the equation oif a line whose slope is 4/7 and it passes through the point (-8 , -6)
[tex](\stackrel{x_1}{-8}~,~\stackrel{y_1}{-6})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{4}{7} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-6)}=\stackrel{m}{ \cfrac{4}{7}}(x-\stackrel{x_1}{(-8)}) \implies y +6= \cfrac{4}{7} (x +8) \\\\\\ y+6=\cfrac{4}{7}x+\cfrac{32}{7}\implies y=\cfrac{4}{7}x+\cfrac{32}{7}-6\implies {\Large \begin{array}{llll} y=\cfrac{4}{7}x-\cfrac{10}{7} \end{array}}[/tex]
Given the following sets, find the set (A UB) n (AUC).U={1, 2, 3, ...,9}A = {1, 2, 4, 8}B = {3, 7, 9)C={1, 2, 3, 4, 6}Select the correct choice below and, if necessary, fill in the answer box to complete your choice.O A. (AUB) n (AUC)=0(Use a comma to separate answers as needed. Use ascending order.)O B. (A UB) n (AUC) is the empty set.
From the data sets given
(A U B) = ( 1, 2 ,3 ,4 , 7, 8 , 9)
(A U C) = (1, 2 ,3 ,4 ,6 ,8)
(A U B) n ( A U C) = ( 1 ,2, 3, 4 ,8)
Just need a simple explanation.
The square roots for each side of the equation are not correct, as the square root of 36 is of -6 or 6, not -36 or 36, hence the correct solutions are:
x = -3 or x = 9.
Are the steps correct?The equation in Step 6 is given as follows:
[tex]\sqrt{(x - 3)^2} = \sqrt{36}[/tex]
Simplifying the square roots, the variable x can be isolated, as follows:
x - 3 = 6.x - 3 = -6.Both -6 and 6 are correct results for the square root of 36, because:
6² = 36.(-6)² = 36.His mistake when removing the square root is that he did not calculate the root, he just removed the square root from the 36, hence the correct solutions will be found as follows:
x - 3 = 6. -> x = 9.x - 3 = -6. -> x = -3.From the (x - 3)² term, the square root is removed along with the square. However 36 = (6)² or (-6)², hence sqrt(36) = 6 or sqrt(36) = -6.;
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What is the solution to the following system of equations?x+y=5Ix-y=1
the initial equation is:
[tex]\begin{gathered} x+y=5 \\ x-y=1 \end{gathered}[/tex]So we can add bout of the equation so:
[tex](x+y)+(x-y)=5+1[/tex]and we simplify it so:
[tex]\begin{gathered} x+x+y-y=6 \\ 2x=6 \end{gathered}[/tex]now we solve for x so:
[tex]\begin{gathered} x=\frac{6}{2} \\ x=3 \end{gathered}[/tex]and with the value of x we can replace it in the first equation so:
[tex]3+y=5[/tex]and we solve for y:
[tex]\begin{gathered} y=5-3 \\ y=2 \end{gathered}[/tex]So the solution is x equal to 3 an y equal to 2
A group of 15 people are ordering pizza.each person want 2 slices and each pizza has 15 slices.how many pizzas should they order
SHOW ALL WORK PLEASE!
Sarah has two similar regular pyramids with pentagon-shaped bases. The smaller has a scale factor of 2:3 when compared to the larger. Only the smaller pyramid is shown.
She calculates the area of the base of the pyramid (through long, hard work) to be 110.11 square units. The height of the pyramid is 15 units. Now she needs to calculate the volume of the pyramid.
(a) Calculate the volume of the pyramid for Sarah.
(b) "Oh, no!" Sarah exclaims. "Now I have to go through all this hard work again to find the volume of the larger pyramid!" Does she? Explain.
(c) Calculate the volume of the larger pyramid for Sarah.
Answer: a) The volume of the pyramid 440.44 cube units
(b) No she doesn't
(c) The volume of the larger pyramid is 1,486.485 cube units
Step-by-step explanation: The given parameters are;
The scale factor of the pyramids, S.F. = 2:3
The base area of the small pyramid, = 110.11 square units
The height of the small pyramid, h₁ = 12 units
(a) The volume of a pyramid, V = (1/3) × Area of base × The height of the pyramid
Therefore;
The volume of the small pyramid, V₁ = (1/3) × 110.11 square units × 12 units
V₁ = 440.44 cube units
The volume of the small pyramid, V₁ = 440.44 cube units
(b) No she does not have to go through all the hard work again to find the volume of the larger pyramid
She only has to make use of the scale factor relationships of the two pyramid to calculate the volume of the larger pyramid
The volume scale factor = (The linear scale factor)³
(c) The linear scale factor of the pyramids = 2:3 = 2/3
Therefore;
The volume scale factor of the pyramids = (2/3)³ = 8/27
To find the volume of the larger pyramid, V₂, from the volume of the smaller pyramid, V₁, we multiply the volume of the smaller pyramid, V₁, by 27/8 as follows;
V₂ = V₁ × (27/8)
Therefore;
The volume of the larger pyramid, V₂ = 440.44 cube units × (27/8) = 1,486.485 cube units
The volume of the larger pyramid, V₂ = 1,486.485 cube units.
PLS GIVE ME BRAINLIESTA DN FRIEND REQUEST ME PLS AND THANK YOU
A, taken two at a time 4) a. ** Evaluate each expression. 5) P2
we have
4P2
the formula is equal to
n!/(n-r)!
n=4
r=2
substitute
4!/(4-2)!
4!/2!=(4*3*2!)/2!
simplify
4*3=12
answer is 12Find the inverse
g(x) =
10 –5x
2
The most appropriate choice for inverse of a function will be given by-
[tex]f^{-1}(x) = \frac{10 - 2x}{5}[/tex]
What is inverse of a function?
At first, it is important to know about function
A function from A to B is a rule that maps to each element of A a unique element of B.
A is called the domain of the function and B is called the co domain of the function.
[tex]f^{-1}[/tex] is said to be the inverse of [tex]f[/tex] if [tex]f[/tex] [tex]o[/tex] [tex]f^{-1}[/tex] = [tex]f^{-1} o[/tex] [tex]f[/tex] = [tex]I[/tex], I is the identity function.
Let g(x) = y
[tex]\frac{10-5x}{2} = y\\10 - 5x = 2y\\5x = 10-2y\\x = \frac{10 - 2y}{5}[/tex]
[tex]f^{-1}(x) = \frac{10 - 2x}{5}[/tex]
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How do you write 6.01 × 10^2 in standard form?
Learning Diagnostic Analytics Recommendations Skill plans Fifth grade > AA.12 Describe relationships among quadrilaterals SZT Complete the sentence below. A rhombus is a rectangle. always sometimes never Submit
A rectangle has 4 right angles.
A rhombus does not have 4 right angles,
So, A rhombus is sometimes a rectangle
Point O is on line segment NP . Given NO =5 and NP =20, determine the length OP .
If the point O is on the line segment NP, then:
[tex]NO+OP=NP[/tex]Replace for the given values and find the length of OP:
[tex]\begin{gathered} 5+OP=20 \\ OP=20-5 \\ OP=15 \end{gathered}[/tex]The length of OP is 15.
Which of these is the northern-most countries? Responses
A Colombia
B Brazil
C Ecuador
D Peru
Gravel is being dumped from a conveyor belt at a rate of 40 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast (in ft/min) is the height of the pile increasing when the pile is 6 ft high? (Round your answer to two decimal places.)
The height of the pile increasing when the pile is 6 ft high is 1.41ft/min (approx.)
Define Volume of cone?
A pyramid having a circular cross section is called a cone. A right cone is a cone with the vertex located above the base's middle. Right circular cone is another name for it. If you know the height and radius of a cone and plug those values into a formula, you can quickly get the volume of a cone. Formula is , V = 1/3 πr²h
We have, dV/dt = 40 ft³/min
h = diameter where, h = 2r
so r = 1/2h
The formula for regular circular cone is,
V = 1/3 πr²h
put the value of r,
V = 1/ 3 * π * (1/2h)² * h
= 1/12 * π * h³
differentiate it, we get
dV/dt = 3/12 * π * h² * dh/dt
dh/dt = (dV/dt)/(3/12*π*h²)
we have, dV/dt = 40 ft³/min and h = 6
Put these values,
dh/dt = 40 / (3/12 * 22/7 * 6²) (∵ π = 22/7)
After solving, we get
dh/dt = 1.41 ft/min
Therefore, The height of the pile increasing when the pile is 6 ft high is 1.41ft/min (approx.)
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The probability of a randomly selected adult in one country being infected with a certain virus is 0.005. In tests for the virus, blood samples from 19 people are combined. What is the probability that
the combined sample tests positive for the virus? ls it unlikely for such a combined sample to test positive? Note that the combined sample tests positive if at least or person has the virus.
The probabilty that the combined sample wil test posiltive is 1.
(Round to three decimal places as needed.)
Answer: there is a 0.095% chance that one of the adults tests positive
Step-by-step explanation:
Let X be a discrete random variable for the outcome of a toss of a coin with sides 0 and 1,with P(X = 0) = 0.5 and P(X = 1) = 0.5. Moreover let Y be another variable associatedwith a biased coin with sides 1 and 2, such that P(Y = 1) = 0.4 and P(Y = 2) = 0.6. IfZ = X + Y , what is P(Z < 3)
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given probabilities
[tex]\begin{gathered} P(X=0)=0.5,P(X=1)=0.5 \\ P(Y=1)=0.4,P(Y=2)=0.6 \\ Z=X+Y \end{gathered}[/tex]STEP 2: Write the formula for calculating the required probability
[tex]P(Z<3)=P(Z=1)+P(Z=2)[/tex]STEP 3: Find P(Z=1)
[tex]\begin{gathered} P(Z=1)=P(X=0)\text{ and }P(Y=1) \\ =0.5\times0.4=0.2 \end{gathered}[/tex]STEP 4: Find P(Z=2)
[tex]\begin{gathered} P(Z=2)=P(X=0)\cdot P(Y=2)\text{ or }\times P(X=1)\cdot P(Y=1) \\ (0.5\times0.6)+(0.5\times0.4) \\ =0.3+0.2=0.5 \end{gathered}[/tex]STEP 5: Find the P(Z<3)
[tex]P(Z<3)=0.5+0.2=0.7[/tex]Hence, the answer is 0.7
3 thousandths times 0.001
the answer would be 3
Solve each proportion.
4/5 = n/2
5/b = 9/5
The value of the first proportion is 1.6 and the value of the second proportion is 2.78.
What is a proportion?A part, piece, or number that is measured in comparison to a total is referred to as a proportion in general. When two ratios are equal, according to the definition of proportion, they are in proportion. A formula or claim shows that two ratios or fractions are equivalent.
According to the question,
The first proportion will be :
4/5 = n/2
n = 8/5
n = 1.6
The second proportion will be :
5/b = 9/5
b = 25/9
b = 2.78
Hence, the value of n will be 1.6 and the value of b will be 2.78 respectively.
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Lana has a three-year lease that requires her to pay $395 rent permonth. What is the total amount she will pay for rent during the term ofher lease?a. $1,185b. $14,220c. $4,740d. $1,422
Step 1. Since Lana Pays the rent monthly, and the lease is for a 3 year period, the first step will be to calculate the number of months that are in 3 years.
Since there are 12 months in just 1 year, we multiply 12 by 3 to get the number of moths in 3 years:
[tex]12\times3=36[/tex]There are 36 months in 3 years.
Step 2. Multiply the number of months by the monthly payment of the rent.
We multiply $395 by the 36 months:
[tex]395\times36[/tex]And the result is:
[tex]395\times36=14,220[/tex]$14,220 is the total amount she will pay for rent during the term of her lease.
Answer:
b. $14,220
For a circle of radius 7 feet, find the arc length of a central angle of 6°.
[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r = 7\\ \theta = 6 \end{cases}\implies s=\cfrac{(6)\pi (7)}{180}\implies s=\cfrac{7\pi }{30}\implies \underset{\textit{about 9 inches}}{s\approx \stackrel{ft}{0.73}}[/tex]
Use the equation A=Pe^rt to answer each question. Show all work. First question
Answer:
$7209.78
Explanation:
To find the amount in the account after 6 years, we will use the following equation
[tex]A=Pe^{rt}[/tex]Where P is the initial amount, r is the interest rate and t is the time in years.
So, replacing P = $5000, r = 6.1% = 0.061, and t = 6 years, we get
[tex]\begin{gathered} A=5000e^{0.061t} \\ A=5000e^{0.061(6)} \\ A=5000e^{0.366} \\ A=5000(1.44) \\ A=7209.78 \end{gathered}[/tex]Therefore, the answer is $7209.78
How many y-values are there for each x-value in the function represent by the graph
Answer: 1
Step-by-step explanation:
If the equation is a function there is one y-value for every x-value
2. Which of the following represents a quadratic function? (Circle all that apply!) (2 pts)a, y = 9x2 + 4x - 6b. y = 3x + 8c. y = 1223 - 6x2 + 4x - 9
A quadratic function is a function in the form,
[tex]\begin{gathered} y=ax^2+bx+c \\ \text{where a, b, c are real } \\ a\ne0 \end{gathered}[/tex]Option A is a quadratic function,
Option B, is not a quadratic function because it is not the form of the equation written above and also,
[tex]a=0[/tex]Option C is also not a quadratic function because it has the highest degree of x to be 3.
In option D the function is given by the function is defined by
[tex]\begin{gathered} y=x^2 \\ \text{thus} \\ a=1\ne0 \end{gathered}[/tex]This implies that the function in option D is a quadratic function
Option E is not a quadratic function
Help please I did them and got all wrong LOL..............
Answer:
1. Choice (2) 13
2. Choice (3) 8.1
3. Choice (3) 95 to 105 ft
4. Choice (3) 96 in
Step-by-step explanation:
All the problems use the Pythagorean theorem
The Pythagorean Theorem states that the sum of the squared sides of a right triangle equals the length of the hypotenuse squared.
[tex]c^{2} = a^{2} + b^{2}[/tex]
or
[tex]c = \sqrt{a^{2} + b^{2}}[/tex]
where c is the hypotenuse and a, b the shorter sides.
This means that given any two of the three sides of a right triangle we can compute the length of the third side
For example if we were given the hypotenuse c and side b, we can solve for side a by:
[tex]a = \sqrt{c^{2} - b^{2}}[/tex]
If we were given side a and asked to solve for side b then
b = \sqrt{c^{2} - a^{2}}
Frankly it does not matter which you choose as side a and side b.
Question 1
The distance from the foot of the ladder to the wall can be taken to be side a and is equal to 8ft
So b = 8ft
The length of the ladder is the hypotenuse c = 15 feet
[tex]a = \sqrt{c^{2} - b^{2}} \\\\a = \sqrt{15^{2} - 8^{2}}\\\\a = \sqrt{225 - 64}\\\\a = \sqrt{161}\\\\a = 12.68857754045 \\\\[/tex]
Rounded to nearest foot, that would be 13 feet So choice (2)
Question 2
The points J and K have the following coordinates as indicated on the graph.
J(-3, 2)
K (1, -5)
The distance between two points is the length of the path connecting them. The shortest path distance is a straight line. In a 2 dimensional plane, the distance between points (X1, Y1) and (X2, Y2) is given by the Pythagorean theorem:
[tex]d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]
For:
(X1, Y1) = (-3, 2)
(X2, Y2) = (1, -5)
[tex]d = \sqrt {(1 - (-3))^2 + (-5 - 2)^2}\\\\d = \sqrt {(4)^2 + (-7)^2}\\\\d = \sqrt {{16} + {49}}\\\\d = \sqrt {65}\\\\d = 8.062258\\\\\text{Rounded to the nearest 10th it would be \boldsymbol{8.1}}\\\\[/tex] So choice (3)
Question 3
This again involves a right triangle as shown in the figure
The sides are a = AC = 60 and b = BC = 80 and we are asked to find the length of AC which is the hypotenuse of ΔABC
Use the Pythagorean Theorem directly
[tex]c = \sqrt{a^{2} + b^{2}}}\\\\a = \sqrt{60^{2} + 80^{2}}\\\\c = \sqrt{3600 + 6400}}\\\\c = \sqrt{10000}}\\\\c = 100}\\\\[/tex]
Answer 100 feet so choice (3): from 95 to 105 ft
Question 4
The brace is one of the shorter sides, with the platform top as the hypotenuse.
Let's use a for the brace, b for the 40 in side and c for the hypotenuse = 104 in
So we have to compute for b using the formula:
[tex]b = \sqrt{c^{2} - a^{2}}[/tex]
Using the given values, this would be:
[tex]b = \sqrt{104^{2} - 40^{2}}\\\\b = \sqrt{10816 - 1600}\\\\b = \sqrt{9216}\\\\b = 96\\\\[/tex]
which would be choice (3)
Find the standard form of the equation of the ellipse satisfying the given conditions.Endpoints of major axis: (4,12) and (4,0)Endpoints of minor axis: (8,6) and (0,6)
The Standard form of the ellipse is given as,
[tex]\frac{(x-a)^2}{a^2}+\text{ }\frac{(y-b)^2}{b^2}\text{ = 1}[/tex]The length of the major axis is given as,
[tex]\begin{gathered} 2a\text{ = 8} \\ a\text{ = }\frac{8}{2} \\ a\text{ = 4} \end{gathered}[/tex]The length of the minor axis is given as,
[tex]\begin{gathered} 2b\text{ = 12} \\ b\text{ = }\frac{12}{2} \\ b\text{ = 6} \end{gathered}[/tex]Therefore the required equation is calculated as,
[tex]\begin{gathered} \frac{(x-4)^2}{4^2}\text{ + }\frac{(y-6)^2}{6^2}\text{ = 1} \\ \frac{(x-4)^2}{16^{}}\text{ + }\frac{(y-6)^2}{36^{}}\text{ = 1} \end{gathered}[/tex]an insurance company claims the probability of surviving a certain type of cancer is 20%. what are the odds of surviving? express your answer in the form a:b
The probability of surviving is given as 20%.
It is required to find the odds of surviving.
Let the event "surviving a certain type of cancer" be X.
It follows that the probability can be written as:
[tex]\begin{gathered} P(X)=20\%=\frac{20}{100}=\frac{\cancel{20}^1}{\cancel{100}^5} \\ \Rightarrow P(X)=\frac{1}{5} \end{gathered}[/tex]Recall that for an event X, the odds in favor of the event happening are given by the ratio:
[tex]\begin{gathered} \frac{P(X)}{P(\overline{X})} \\ \text{Where }P(\overline{X})\text{ is the probability of the event not happening} \end{gathered}[/tex]The probability of event X not happening is given as:
[tex]\begin{gathered} P(\overline{X})=1-P(X) \\ \text{Substitute }P(X)=\frac{1}{5}\text{ into the equation:} \\ P(\overline{X})=1-\frac{1}{5}=\frac{4}{5} \\ \Rightarrow P(\overline{X})=\frac{4}{5} \end{gathered}[/tex]Substitute the probabilities into the odds formula:
[tex]\frac{P\mleft(X\mright)}{P(\overline{X})}=\frac{\frac{1}{5}}{\frac{4}{5}}=\frac{1}{4}[/tex]The odds of surviving is 1:4.
The odds of surviving in the ratio from is 4 : 1.
What are odds in favor and odds against?The odds in favor is the ratio of the number of ways that an outcome can occur compared to how many ways it cannot occur.
The odds against is the ratio of the number of ways that an outcome cannot occur compared to in how many ways it can occur.
Given, An insurance company claims the probability of surviving a certain type of cancer is 20%.
So, The probability of not surviving a certain type of cancer is 80%.
∴ The odds of surviving is 2/8 = 1/4.
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Suppose that the age of all of a country's vice presidents when they took office was recorded. The collection of the ages of all the country's vice presidents when they took office is a A. PopulationB. ParameterC. Sample D. Statistic
Answer:
Population
Explanation:
A population is a complete group that has a common feature. A Sample is a part of that population and a statistic or parameter are measures of the sample or population.
In this case, we have the ages of all the country's vice presidents, so it is a population.
1) Bob’s frog can travel 7 inches per jump, Kim’s frog can travel 9 inches, and Jack’s frog can travel 13 inches. If the 3 frogs start off at point 0 inches, how many inches will it be to the next point that all 3 frogs touch?
2) Two runners run around a circular track. The first runner completes a lap in 6 minutes. The second runner completes the track in 13 minutes. If they both start at the same place and the same time and go in the same direction, after how many minutes will they meet again at the starting place?
Answer:
See below
Step-by-step explanation:
LCM of 7 9 13
Prime factorization
9 = 3 x 3
7 = 7
13 = 13
LCM = 3 x 3 x 7 x 13 = 819 in
LCM of 6 and 13 is similarly 78 min
true or false√3^(3√2) =(108)^1/6
False
Explanations:For the Left Hand side of the expression:
[tex]\sqrt[]{3}^{(3\sqrt[]{2})}[/tex]This can be simplified as:
[tex]\begin{gathered} 3^{\frac{1}{2}(3\sqrt[]{2})} \\ =3^{1.5\sqrt[]{2}} \\ =3^{2.12} \\ =\text{ }10.27 \end{gathered}[/tex]For the Right Hand Side of the expression:
[tex]\begin{gathered} (108)^{\frac{1}{6}} \\ =(108)^{0.167} \\ =\text{ }2.19 \end{gathered}[/tex]Since the Left Hand Side does not equal the Right Hand Side after simplification, the expression is not true
Use the quadratic formula to solve for x.5x? - 7x=2Round your answer to the nearest hundredth.If there is more than one solution, separate them with commas.X == 0DO...Х5?
Given equation:
[tex]5x^2-7x\text{ = 2}[/tex]Re-arranging:
[tex]5x^2-7x\text{ -2 = 0}[/tex]Using quadratic formula:
[tex]x\text{ = }\frac{-b\pm\text{ }\sqrt[]{b^2-4ac}}{2a}[/tex]a = 5, b = -7, c= -2
Substituting into the formula:
[tex]\begin{gathered} x\text{ = }\frac{-(-7)\pm\text{ }\sqrt[]{(-7)^2-4(5)(-2)}}{2\times5} \\ =\text{ }\frac{7\pm\sqrt[]{89}}{10} \end{gathered}[/tex]Writing as a decimal:
[tex]x\text{ = }-0.24\text{ or 1.64 (nearest hundredth)}[/tex]Answer:
x = -0.24, 1.64
Write an exponential function in the form y=ab^xy=ab
x
that goes through points (0, 7)(0,7) and (2, 112)(2,112).
An exponential function in the form y=abˣ is y = 7×4ˣ .
A mathematical function with the formula f (x) = an x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered.
Write the equation of the function:
y = abˣ
For point (0 , 7)
7 = ab⁰
for point (2 , 112)
x = 2
y = 112
Substitute:
112 = ab²
Swap the sides:
ab⁰ = 7
ab² = 112
Find the quotient of the equations:
ab²/ ab⁰ = 112/7
Simplify the equations:
b² = 16
b = ±√16
Split into two equations: b = +√16 or b = -√16
Simplify the radical expression:
b = 4
b = -4
Combine the results: b = 4 or b = -4
Any fraction with a denominator of 1 is equal to its numerator:
a = 7
7 = a (±4)°
Substitute into one of the equations:
a = 7
b = ± 4
y = 7×4ˣ
Hence , y =7×4ˣ is an exponential function with the formula y=abˣ.
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Which degenerate conic is formed when a double cone is sliced through the apex by a plane parallel to the slant edge of the cone?
Circle
Parabola
One line
Two lines
One line is formed when a double cone is sliced through the apex by a plane parallel to the slant edge of the cone.
A rhombus's three-dimensional surface of rotation around one of its symmetry axes is known as a bicone or dicone in geometry. A bicone is a surface made by uniting two right circular cones that are congruent at their bases.
A 3D representation of a double cone {not shown indefinitely stretched). A cone is a three-dimensional geometric structure with a smooth transition from a flat base—often but not always circular—to the point at the top, also known as the apex or vertex.
The part that intersects the plane is only the bus of the cone.
As a result, when a double cone's apex is cut by a plane parallel to the cone's slant edge, one line is created.
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Answer: one line
Step-by-step explanation:
