PLSSS HELP, i couldn’t find an answer for it

The equation of comet's orbit is  [tex]\frac{(y-4)^2}{36} + \frac{x^2}{64}[/tex] =1

A hyperbola is a geometric shape made up of two branches that are symmetric about a center point and asymptotic to two lines called the asymptotes. It is defined by the equation (x^2/a^2) - (y^2/b^2) = 1. It is a type of conic section, similar to a parabola and an ellipse.

If the vertices and foci's of hyperbola have specified coordinates are of the form (0,10) and (0,14)

then

The y-axis serves as the transverse axis.

so

The formula for the equation is:

(y-k)^2/a^2-(x-h)^2/b^2=1

In this issue

The value of the center (h,k) is (0,4)

It follows that (0,a-k)) = (0,10)

a=10-4=6

(0,c-k) equals (0,14)

c=14-4=10

Identify b's value.

b^2=c^2-a^2

b^2=10^2-6^2

b^2=64

therefore

The formula reads as follows:

[tex]\frac{(y-4)^2}{36} + \frac{x^2}{64}[/tex] =1

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Answer:

---------------------------------

Given equation:

Recall the identity for a square of a sum:

Complete the square by adding the missing part:

Answer:

x = -2, x = -4

Step-by-step explanation:

Given quadratic equation:

[tex]x^2+6x+8=0[/tex]

Solve by the method of Completing the Square.

Step 1

When completing the square for a quadratic equation in the form ax²+bx+c=0, the first step is to move the constant to the right side of the equation:

[tex]\implies x^2+6x=-8[/tex]

Step 2

Add the square of half the coefficient of the term in x to both sides to form a perfect square trinomial on the left side:

[tex]\implies x^2+6x+\left(\dfrac{6}{2}\right)^2=-8+\left(\dfrac{6}{2}\right)^2[/tex]

Simplify:

[tex]\implies x^2+6x+3^2=-8+3^2[/tex]

[tex]\implies x^2+6x+9=-8+9[/tex]

[tex]\implies x^2+6x+9=1[/tex]

Step 3

Factor the perfect square trinomial on the left side:

[tex]\implies (x+3)^2=1[/tex]

Step 4

Square root both sides:

[tex]\implies \sqrt{(x+3)^2}=\sqrt{1}[/tex]

[tex]\implies x+3=\pm1[/tex]

Step 5

Subtract 3 from both sides:

[tex]\implies x+3-3=\pm1-3[/tex]

[tex]\implies x=-4, -2[/tex]

Therefore, the solutions of the given quadratic equation are:

[tex]x=-4, \;\; x=-2[/tex]

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Answer:

Step-by-step explanation:

a) To find u1, we can use the term-to-term rule given in the problem:

Un+1 = U²₁ + 5

We know that u1 = 1, so we can substitute that into the equation:

u2 = 1² + 5 = 1 + 5 = 6

b) To find u2, we can use the same term-to-term rule and substitute the value of u1 (which is 6) into the equation:

u3 = 6² + 5 = 36 + 5 = 41

c) To find un, we can use the term-to-term rule and substitute the value of un-1 into the equation.

un = un-1² + 5

It's important to note that the value of n is not given so we can't calculate the value of un.

Therefore, u1 = 6, u2 = 41, and we can't calculate un without knowing the value of n.

The output a needed to satisfy the consumer and interindustry demands is 12 units, and the output b needed to satisfy the consumer and interindustry demands is 6 number of units.

a) Output a = 12 (units)

b) Output b = 6 (units)

1. Calculate the total consumer demand (CD):

CD = 12 + 20 + 8 = 40 (units)

2. Calculate the total interindustry demand (ID):

ID = 4 + 5 + 9 = 18 (units)

3. Calculate the total production (TP):

TP = CD + ID = 40 + 18 = 58 (units)

4. Calculate the output a and b needed to satisfy the consumer and interindustry demands:

a) Output a = TP - ID = 58 - 18 = 40 (units)

b) Output b = CD - Output a = 40 - 12 = 28 (units)

The output a needed to satisfy the consumer and interindustry demands is 12 units, and the output b needed to satisfy the consumer and interindustry demands is 6 number of units.

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Answer:

12. 12 students scored in the 80-89 range

13. 31 students took the maths test

Answer:13/9

Step-by-step explanation:11x/5 -2/3 = 113/45  after adding 2/3 to both sides we have 11x/5 = 143/45. Now we multiply 11x/5 by 9/9 which equals 99x/45 = 143/45. This means 99x = 143 and x =143/99 = 13/9

The length and breadth of the rectangle are 10m and 6m respectively

The shorter side of a rectangle is called its breadth (width) and the longer side is the length.

The area of a rectangle = L×B

and the perimeter = 2(L+B)

where L is the length and B is the breadth

therefore 60 = LB, and B = 60/L

and 32 = 2(L+B)

substitute 60/L for B

32 = 2(L+60/L)

divide both sides by 2

16 = L+60/L

16 =( L²+60)/L

therefore L² +60 = 16L

L² -16L +60= 0

L²-10L-6L +60 = 0

L(L-10)-6(L-10) = 0

L-10 = 0 or L-6 = 0

therefore L = 10 or 6

when L is 10m then B = 60/10 = 6m

when L is 6m then B = 60/6 = 10m

Since the longer side is length then L = 10m and B = 6m

therefore the length and breadth of the rectangle are 10m and 6m respectively.

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The number of hours Alan could trim to earn at least $73 is 11.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

Charges per hour = $7

Equipment fees = $4

The number of hours to earn at least $73.

7t - 4 ≤ 73

Where t is the number of hours.

Now,

7t - 4 ≤ 73

7t ≤ 73 + 4

7t ≤ 77

t ≤ 11

Thus,

The number of hours is 11.

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Answer: C. 3

Step-by-step explanation:

Using the trapezoid midsegment theorem,

[tex]\frac{4x+8x+3}{2}=4x+7.5\\\\\frac{12x+3}{2}=4x+7.5\\\\12x+3=8x+15\\\\4x+3=15\\\\4x=12\\\\x=3[/tex]

The following algebraic expression are trinomial.

The term expression in math is also known as algebraic expression consists of unknown variables, numbers and arithmetic operators.

Here we must know what is meant by trinomial,

The term trinomial is referred as

Here we have given algebraic expression that is written as  x³ + x² - √x is a trinomial with one variable ‘x’ and it having three non-zero terms.

Then the next given algebraic expression which is 2x³ - x², is NOT a trinomial. Because this expression is a binomial with one variable ‘x’, having two non-zero terms.

Then the another given algebraic expression that is 4x³ + x² - 1/x, is a trinomial with one variable ‘x’, having three non-zero terms.

Finally the given algebraic expression which can be written as x⁶ - x +√6, is a trinomial with one variable ‘x’, having three non-zero terms.

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Answer: 26.7

Step-by-step explanation:

[tex]\frac{9.2}{v}=\tan 19^{\circ}\\\\\frac{v}{9.2}=\frac{1}{\tan 19^{\circ}}\\\\v=\frac{9.2}{\tan 19^{\circ}}\\\\v \approx 26.7[/tex]

Answer: The given equation is 9.2/v = tan(19). To solve for v, we can first multiply both sides of the equation by v to get rid of the denominator on the left side. This gives us 9.2 = v * tan(19).

Next, we can divide 9.2 by tan(19) to find the value of v. The value of tan(19) is approximately 0.3420201, so 9.2 / 0.3420201 = 26.884956 (rounded to 1 decimal place).

So the value of v in the equation is approximately 26.9 (to 1 decimal place).

Step-by-step explanation:

The linear equation -2(x - 2) = 4 - 2x has infinitely many solutions

A linear equation is a mathematical statement that describes a relationship between two or more variables and is written in the form of ax + by = c, where a, b and c are constants and x and y are variables. The equation is called "linear" because it is a first degree equation and it describes a straight line when graphed on a coordinate plane.

In this problem, we have to solve for the value of x

-2(x - 2) = 4 - 2x

Open the bracket

-2x + 4 = 4 - 2x

collect like terms

-2x + 2x = 4 - 4

0 = 0

This has an infinitely many solution

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1) The definition of function F(x) is: B. F(x) = -(x + 2)²(x - 2).

2) The standard definition of the cubic function is: A. F(x) = ax³ + bx² + cx + d.

4) The approximate solution to the system of equations is given as follows: A. (-3.43, 6.30).

The Factor Theorem states that a polynomial function with roots(also called zeros) [tex]x_1, x_2, \codts, x_n[/tex], is represented by the product of it's linear factors [tex]x - x_1, x - x_2, \cdots x - x_n[/tex], according to the rule the rule presented as follows:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

From the graph, the roots of the function are given as follows:

Meaning that the cubic function is defined as follows:

F(x) = a(x + 2)²(x - 2).

The y-intercept of the function, numerically, is given as follows:

F(0) = a(2² x (-2))

F(0) = -8a.

The y-intercept is positive, meaning that the leading coefficient is negative, and thus the option B is the correct option.

The general format of a cubic function, with leading coefficient a and constant d positive, is given as follows:

y = ax³ + bx² + cx + d.

Meaning that the correct option for item 2 is given by option A.

The solution to the system of equations is found through graphing, and is the point of intersection of the two functions.

From the graph given by the image presented at the end of the answer, using rounding, the approximate solution for item 4 is given by option A.

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The first five terms of the sequence [tex]a_n = 3n/(n+4)[/tex] are:

3/5, 3/4, 9/7, 3/2, 15/9.

What is a sequence?

A sequence in A.P stands for "Arithmetic Progression" which is a sequence of numbers in which each term is the sum of the previous term and a constant called the common difference.

Now the given expression is

To find the first five terms of the sequence [tex]a_n = 3n/(n+4),[/tex] we need to substitute the values of n from 1 to 5 and solve for [tex]a_n[/tex].

a1 = 3*1/(1+4) = 3/5

a2 = 3*2/(2+4) = 3/4

a3 = 3*3/(3+4) = 9/7

a4 = 3*4/(4+4) = 12/8 = 3/2

a5 = 3*5/(5+4) = 15/9

Hence, the first five terms of the sequence [tex]a_n = 3n/(n+4)[/tex] are:

3/5, 3/4, 9/7, 3/2, 15/9.

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Emmy answered average of 60 out of 75 math problems correctly on the quiz she took last week, meaning she answered a total of 60 problems correctly.

60/75 = 0.8

0.8 x 75 = 60

Emmy took a math quiz last week and answered 60% of the 75 problems correctly. To calculate how many problems Emmy got correct, we need to divide 60 by 75, which gives us 0.8. Then, we multiply 0.8 by 75, which gives us 60. This means that Emmy correctly answered 60 out of 75 math problems on the quiz. This is equivalent to 60%, which is the percentage of problems she got correct. It is important to note that if Emmy had answered any more or any less problems correctly, the percentage of correct answers would have been different. Therefore, it is important to understand the relationship between percentages and total number of problems answered correctly in order to accurately calculate the number of correct answers.

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The circumference of the circle is 23.864

In order to calculate the circumference of a circle, you need to multiply the Diameter of the circle with value of π (pi) which is 3.14.

In the given question,

given, d = 7.6cm

formula : C = d x π

therefore, C = 7.6 x 3.14 = 23.864cm

Write the answer correctly to 3 significant figures.

Alternatively, Circumference can also be calculated by using the value of the radius of the circle. We know, Radius = Diameter/2

Therefore, C = ( 2 x r ) x  π

Symbols:

π = pi ( value = 3.14)

d = diameter

r = radius

C = circumference

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The probability that the first girl is the first to flip a head is; 1/2.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

We are given that if the number of toss required is odd as in one attempt represent odd number , we have following sequence of events

H, TTH, TTTTH.....

The required probability P will be as;

P = 1/2 + (1/2)³ + (1/2)⁵..........

As she flipped it in first go the probability is 1/2.

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For a quadratic function [tex]y=ax^2+bx+c[/tex], we know the vertex of the graph is a maximum if and only if [tex]a < 0[/tex], and a minimum if and only if [tex]a > 0[/tex].

It is easy to see that for a function of the form [tex]y=a(x-h)^2+k[/tex], the vertex of the graph is a maximum if and only if [tex]a < 0[/tex], and a minimum if and only if [tex]a > 0[/tex].

Therefore, the vertex of the graph of [tex]f(x)[/tex] is a maximum, and the vertex of the graph of [tex]g(x)[/tex] is a minimum.

The probability of a senior student taking statistics or calculus is 0.82. This is calculated by adding the probability of a senior student taking statistics (0.15) and a senior student taking calculus (0.35).

p(a or b) = p(a) + p(b) - p(a and b)

p(a) = 15/100 = 0.15

p(b) = 35/100 = 0.35

p(a and b) = 15/100 = 0.15

p(a or b) = 0.15 + 0.35 - 0.15 = 0.82

The probability of a senior student taking either statistics or calculus is 0.82. This is calculated by adding the probability of a senior student taking statistics (0.15) and a senior student taking calculus (0.35) and subtracting the probability of a senior student taking both statistics and calculus (0.15). The probability of a senior student taking statistics is calculated by dividing the number of seniors taking statistics by the total number of students surveyed (15/100 = 0.15). The probability of a senior student taking calculus is calculated by dividing the number of seniors taking calculus by the total number of students surveyed (35/100 = 0.35). The probability of a senior student taking both statistics and calculus is calculated by dividing the number of seniors taking both statistics and calculus by the total number of students surveyed (15/100 = 0.15). Therefore, the probability of a senior student taking either statistics or calculus is 0.82.

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Step-by-step explanation:

we know

[tex]y = mx + c[/tex]

Answer:

y-intercept: -3

slope: 4

equation: y=4x-3

Step-by-step explanation:

To find the y-intercept, it shows in the table of value that when x is 0, y is -3 so y-intercept = -3. To find the slope, find the first differences which is 4.

Answer: 3062 pounds

Step-by-step explanation: 10.5x7x10 is 735 and divided by 0.24 is 3062.2 pounds rounded to 3062

The value of x is: x=88.

Here, given that, 36% of the letters in Pythagoras's alphabet soup are vowels.

33 1/3% of those vowels are "os."

To calculate the percentage of letters that are "os," we first need to find 33 1/3% of 36%.

33 1/3% is equivalent to 1/3. So, we can calculate the percentage of "os" as follows:

Percentage of "os" = (36% * 1/3) = 12%

Now, we know that 12% of the letters in the soup are "os."

Next, Pythagoras removes all the "os" from his soup.

This means that what remains are the non-"os" letters, which are the remaining vowels and consonants.

To calculate the percentage of the original letters that remain, we need to subtract the percentage of "os" from 100%:

Percentage of original letters remaining = 100% - Percentage of "os"

Percentage of original letters remaining = 100% - 12% = 88%

Therefore, x% of the original letters remain, and x is equal to 88.

Hence, The value of x is: x=88.

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Answer:

First number 7

Step-by-step explanation:

First, let's make the first number y and the second number x

Next, we write our equations which are y=1/2x+3 and y=1/4x+5

Then, we set those two equations equal to each other and then solve for x

The first step of the equation is to add/subtract like terms, I subtracted 5 on each side of the equation, our new equation is 1/4x=1/2x-2, I then subtracted 1/2x on each side so now our equation is -1/4x=-2. We then multiply 1/4 by its reciprocal on each side. Its reciprocal is -4.

Now that we know x is equal to 8 now we can fill x into the original equations which were y=1/2x+3 and y=1/4x+5 you don't have to solve both, just one of your choosing.

Therefore your answer! .

The area to determine 142.5  material she will need to create the kite.

Given that

A kite with two top triangles with height = 5 inches

a base = 7.5 inches

The bottom two triangles share the base but have a height = 14 inches

area of sum of all triangle's area

area = b×h /2

A1 = 7.5 × 5 /2

   = 18.75

the other top triangle has the same area so A1+A2 = 18.75 × 2 = 37.5

A3 = 7.5 ×14/2

     = 52.5

the other top triangle has the same area so A3+A4 = 52.5 × 2 = 105

The area of kite A1 + A2 +A3 +A4 = 37.5 +105 = 142.5

The area to determine 142.5  material she will need to create the kite.

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That's  0.20833 of one day./

(5/24 of a day)

The volume of a hemisphere with a radius of 44.9 m is approximately 189582.2 cubic meters, rounded to the nearest tenth.

To calculate the volume of a hemisphere, you can use the formula

V = (2/3)πr^3

where V is the volume, π is pi (approximately 3.14), and r is the radius. In this case, r = 44.9 m.

So, (2/3)π(44.9)^3 = 189582.234 cubic meters.

This is the exact volume, but since the question asked for the volume rounded to the nearest tenth, the final answer would be 189582.234 cubic meters. It's worth mentioning that a hemisphere is half of a sphere, thus, the volume of a full sphere with a radius of 44.9 m would be double of this value.

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The equation of the tangent to the curve x=tan(θ) and y=sec(θ) at the point (1,√2) can be found by both eliminating the parameter and without eliminating the parameter.

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Answer: one is 10 and one is 12. Holy why was this so hard shouldn't this be as SAT/ACT problem?

Step-by-step explanation: 1/X + 1/X+2 = 11/60. THEN DO ALGEBRA THAT TOOK ME FOREVER IT WAS SO HARD.

As per the given distribution the consumer group claims that the difference in proportions has a mean of 0.05.

The term mean in math is defined as the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Here we have given that the consumer group is investigating two brands of popcorn, R and S.

And the population proportion of kernels that will pop for Brand R is 0.90 where as the population proportion of kernels that will pop for Brand S is 0.85.

Then the difference of the mean is calculated as,

=> 0.90 - 0.85

=> 0.05

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So, the coordinates of the images S', R', T' under the translation are (11,9), (-4,-6) and T'(h+4,k-5) respectively.

a) For the point S(7,14), we are given the translation defined by (x,y) -> (x+4, y-5). This means that for any point (x,y), we add 4 to the x-coordinate and subtract 5 from the y-coordinate to find the image of that point. Applying this transformation to the point S(7,14) gives us the image point S'(7+4, 14-5) = S'(11,9). So the coordinates of the image S' is (11,9)

b) For the point R(-8,-1), we are given the same translation defined by (x,y) -> (x+4, y-5). Applying this transformation to the point R(-8,-1) gives us the image point R'(-8+4,-1-5) = R'(-4,-6). So the coordinates of the image R' is (-4,-6)

c) For the point T(h,k), we are given the same translation defined by (x,y) -> (x+4, y-5). Applying this transformation to the point T(h,k) gives us the image point T'(h+4,k-5).

Here h and k are variables and we can't say the coordinates of image point T' without specific values of h and k. But we can say the transformation of point T as T'(h+4,k-5)

So, we have found the coordinates of the images S', R', T' under the translation defined by (x,y) -> (x+4, y-5) as (11,9), (-4,-6) and T'(h+4,k-5) respectively.

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