Which is the graph of x^2/9 + y^2/4 = 1

Since segment AD bisects angle BAC, the value of x is equal to 14.6.

In Mathematics, an angle bisector can be defined as a type of line, ray, or segment, that bisects or divides a line segment exactly into two (2) equal angles.

By applying the angle bisector theorem to this triangle (ΔABC), we have:

AB/BD = AC/DC

19/x = 17/(20 - x)

17x = 19(20 - x)

17x = 380 - 19x

19x + 17x = 380

26x = 380

x = 380/26

x = 14.6.

In conclusion, we can reasonably infer and logically deduce that the value of x in triangle ABC is 14.6.

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Answer:

Step-by-step explanation:

7

3 = 7 - 4

-1 = 3 - 4

-5 = -1 - 4

so the 5th:  -5 - 4 = -9

     the 6th:   -9 - 4 = -13

and the 7th:   -13 - 4 = -17

Answer:

scale factor = 2

Step-by-step explanation:

The scale factor is the ratio of corresponding sides, image to original

Using the bases of the 2 triangles , then the scale factor is

S → L  = \(\frac{4}{2}\) = 2

Answer:

5,000 passengers

Step-by-step explanation:

1. Find out how many trains leave each hour.

6 min – 60/6 = 10 x 200 passengers = 2000

10 min – 60/10 = 6 x 200 passengers = 1200

12 min – 60/12 = 5 x 200 passengers = 1000

15 min – 60/15 = 4 x 200 passengers = 800

2. Add it all up.

2000 + 1200 + 1000 + 800 = 5000 passengers

Answer:

5000

Step-by-step explanation:

6 minute train leaves 10 times

10 x 200 = 2000 passengers

10 minute train leaves 6 times

6x200 = 1200

12 minute train leaves 5 times

5x200 =1000

15 minute train leaves 4 times

4x200 =800

2000+1200+1000+800=5000

assuming more than 1 train can be at the station at once

Answer:

No, all of her work is correct.

Step-by-step explanation:

Answer:

No, all of her work is correct.

Step-by-step explanation:

All of her work is correct.

The first step is showing factorization of √50

The second step is simplifying the factorization

The third step is simplifying the entire radical.

When you take a square root of a square, they cancel out, so:

√5² = 5

We multiply it with our leftover √2 and we get:

5√2

The probability that at least one of the next three babies is a boy is 0.875.

Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.

Probability of the complement of event B:

The probability of the complement of event B is computed as follows:

P(B* )=1-P(B) P(B)=14(1-(0.5x0.5)) = 0.25

The probability of the complement of event B is B) 0.25.

Probability that at least one of the next three babies is a boy:

The probability that at least one of the next three babies is a boy is computed as follows:

at least one of the next three babies is a boy =1-(0.5x0.5x0.5) =1-0.125 = 0.875

The probability that at least one of the next three babies is a boy is D) 0.875.

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The solution of the expression 8⁴/8⁻² will be 262144.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is 8⁴/8⁻². the expression will be solved as,

E = 8⁴/8⁻²

E = 8⁴ x 8²

The same base with the powers are added,

E = 8⁴⁺²

E = 8⁶

E = 262144

Therefore, the solution of the expression 8⁴/8⁻² will be 262144.

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We get that statement (B) is the situation that is represented by the expression 3 + (−7).

We are given an expression:

3 + ( - 7 )

We need to identify the statement that represents the same expression:

For the statement, "A football team lost 3 yards on one play. The team gained 7 yards on the next play.", we get the expression as:

- 3 + 7

For the statement, "A football team gained 3 yards on one play. The team lost 7 yards on the next play.", we get the expression as:

3 + ( - 7 )

For the statement, "A football team gained 3 yards on one play. The team gained 7 yards on the next play.", we get the expression as:

3 + 7

Therefore, we get that statement (B) is the situation that is represented by the expression 3 + (−7).

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Answer:

Divide the number by 100

Step-by-step explanation:

The percentage of a number is it's relation in terms of 100. So to get the percentage of a number you have to divide it by 100

e.g 10 is a number

10/100

That is 0.1%

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Thanks.

Answer:

A= 168 minutes or 2 hours and 48 minutes.

B= 3 tyres

Step-by-step explanation:

The values of r and s is -1 and -4 respectively.

Given that:-

coordinates of j are (-8,-5)

coordinates of l are (6,-11)

coordinates of k are (r-4,2s)

Also, k is the mid-point of jl.

We have to find the values of r and s.

We know that, for  (x,y) and (z,w), the mid-point is ((x+z)/2, (y+w)/2).

Here,

(x,y) = (-8.-5)

(z,w) = (6,-11)

(r-4,2s) = ((x+z)/2,(y+w)/2)

Hence,

(r-4,2s) = ((-8+6)/2,(-5-11)/2)

(r-4,2s) = (-1,-8)

Comparing the coordinates, we get:-

r - 4 = -1

r = -1+4 =3

2s = -8

s =-8/2 = -4

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Answer:

No. It is not possible to construct a triangle with lengths of its sides 4cm, 5cm and 9cm because the sum of two sides is not greater than the third side:

5 + 4 is not greater than 9.

Step-by-step explanation:

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If you rent a car, you should choose Option 3 and accept the fixed price of $50 for gasoline if you expect to drive 150 miles.

1. Total gasoline consumed (gallons):

To calculate the total gasoline consumed, divide the expected distance by the car's fuel efficiency:

Total gasoline consumed = Distance / Fuel efficiency

Total gasoline consumed = 150 miles / 28 miles per gallon

Total gasoline consumed ≈ 5.36 gallons

2. Option 1 cost:

In Option 1, you need to return the car with a full gas tank. Since the car has a 16-gallon tank and you've consumed approximately 5.36 gallons, you need to fill up the remaining 16 - 5.36 = 10.64 gallons.

Option 1 cost = 10.64 gallons * $3.95 per gallon = $42.01

3. Option 2 cost:

In Option 2, you return the car without filling it up and pay $5.45 per gallon. As calculated before, you've consumed approximately 5.36 gallons.

Option 2 cost = 5.36 gallons * $5.45 per gallon = $29.20

4. Option 3 cost:

In Option 3, you accept the fixed price of $50 for gasoline. This fixed price is the most cost-effective option compared to the other two choices.

Therefore, the best choice is Option 3, accepting the fixed price of $50 for gasoline, as it offers a better value for the expected distance of 150 miles.

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Answer:

y = -2x - 8

Here's how I got that:

- You first assign the points -

     (-8, 8) → x1 = -8, y1 = 8

     (1, -10) → x2 = 1, y2 = -10

- Now you plug those points into slope formula and solve-

                          \(s=\frac{y2-y1}{x2-x1}\)

                                   ↓

                       ((-10) - 8)/(1 - (-8))

                                   ↓

                                -18/9

                                   ↓

                           slope = -2

- Now we plug the numbers we got into intercept formula -

                            b = y1 − s ⋅ x1

                                      ↓

                             8 - (-2) · (-8)

                                      ↓

                           y-intercept = -8

           - Put everything together and you get.. -

                                 y = -2x - 8

~That's all folks~

-Siascon

\(\text{Given that,}\\\\(x_1,y_1) = (-8,8) ~ \text{and}~ (x_2,y_2) = (1,-10)\\\\\text{Slope, m}= \dfrac{y_2- y_1}{x_2-x_1} = \dfrac{-10-8}{1+8} = -\dfrac{18}{9} =-2\\\\\\\text{Equation with given points,}\\\\y-y_1 = m(x-x_1)\\\\\implies y = m(x-x_1)+y_1\\\\\implies y = -2(x+8) + 8\\\\\implies y = -2x -16 +8\\\\\implies y = -2x -8\)

Answer:

3 is a13

1 is a31

5 is a14

Step-by-step explanation:

The positions on the matrix are all reflective of these names.

The position of the given numbers in the matrix is required.

The number 3 is at location \(a_{13}\), number 1 is at \(a_{31}\) and number 5 is at \(a_{14}\).

The entries of a matrix are named in the following way

\(\begin{bmatrix}a_{11} & a_{12} & a_{13} & a_{14} & a_{15}\\a_{21} & a_{22} & a_{23} & a_{24} & a_{25}\\a_{31} & a_{32} & a_{33} & a_{34} & a_{35}\end{bmatrix}\)

So, the number 3 is at location \(a_{13}\), number 1 is at \(a_{31}\) and number 5 is at \(a_{14}\).

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The slope for the given coordinate points is 1/2.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

The given coordinates are (3,0) and (-5,-4).

Substitute (x₁, y₁)=(3,0) and (x₂, y₂)=(-5,-4) in slope formula, we get

Slope (m) = (-4-0)/(-5-3)

= -4/(-8)

= 1/2

Therefore, the slope is 1/2.

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The range of x are;

1. x < -30

2. x > 8

3. x > 15

4. x < -2

A relationship between two expressions or values that are not equal to each other is called 'inequality.

1. -130 > 50x +20

-130-20> 50x

-150 > 50x

-150/50 > x

-30 > x

x < -30

2. -8(x-3) < -40

-8x +24< -40

collect like terms

-8x < -64

x > -64/-8

x > 8

3. 2x - 22 > 8

collect like terms

2x > 30

divide both sides by 2

x > 30/2

x > 15

4. -35 < -5(x+9)

-35 < -5x -45

collect like terms

10 < -5x

-2 > x

x < -2

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Answer:

vertical

Step-by-step explanation:

Answer:

4x^2

Step-by-step explanation:

Call the unknown side y

The area of the figure is

8x^3 *y = 32 x^5

Divide each side by 8 x^3

8x^3 *y / 8x^3 = 32 x^5 / 8x^3

y = 4 x^2

The unknown side is 4 x^2

Answer:

4x^2

Step-by-step explanation:

32x^5 / 8x^3 = 4x^2

or 4x^2 * 8x^3 = 32x^5

so 4x^2

Answer:

a line

Step-by-step explanation:

In geometry, we can define a line as a straight one- dimensional figure without thickness but extends infinitely in both directions.

If we are to put it into more understandable words, we can describe a line as the shortest distance between any two points.

A line has a specific definition in geometry. Every other option listed do not have specific definition in geometry.

Answer:

17 + 6h = 71

Step-by-step explanation:

17 dollars for a bike + 6 times the amount of hours will equal the total that he gave.

to manipulate this equation to find h, isolate it first.

6h = 71 - 17

6h = 54

h = 54/6

h = 9

Answer:

A. 2.25

Step-by-step explanation:

-3x + 10 = 5x - 8 (Given)

10 = 8x - 8 (Added 3x on both sides)

18 = 8x (Added 8 on both sides)

2.25 = x (Divided 8 on both sides)

Answer:

(6,2)

Step-by-step explanation:

(-2+8, -3+5)

The determinant of a 4x4 matrix is calculated using the Laplace Expansion method, which involves expanding the determinant along one row or column.

The formula for the determinant of a 4x4 matrix is:det(A) =\(a11 * a22 * a33 * a44 – a11 * a22 * a34 * a43 + a11 * a23 * a34 * a42 – a11 * a23 * a32 * a44 + a12 * a23 * a32 * a44 – a12 * a23 * a34 * a41 + a12 * a21 * a34 * a43 – a12 * a21 * a33 * a44 + a13 * a21 * a33 * a44 – a13 * a21 * a34 * a42 + a13 * a22 * a34 * a41 – a13 * a22 * a31 * a44 + a14 * a22 * a31 * a43 – a14 * a22 * a33 * a41 + a14 * a23 * a33 * a42 – a14 * a23 * a31 * a42\)To calculate the determinant of a 4x4 matrix, take the sum of the products of the elements in each row/column and its corresponding minor, then multiply each product by the sign of the term (+ or -). For example, if A is a 4x4 matrix, then the determinant is: det(A) =\(a11 * |A11| - a12 * |A12| + a13 * |A13| - a14 *\)|A14|.The minors A11, A12, A13 and A14 are the 3x3 matrices obtained by deleting the first row and first column from A. The values of the minors are calculated by applying the Laplace Expansion method to each minor.

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Answer:

-49152

Step-by-step explanation:

The pattern is:

multiply for 4

then:

-3, -12, -48, -192, -768, -3072, -12288, -49152

Answer:

y=-2x+15

Step-by-step explanation:

Hi there!

We are given that m=-2, b=15, and we want to write the equation of the line, given these values

We can write the line in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept, since we are given the values of both m and b.

Since we know the values of m and b (-2 and 15 respectively), we can substitute those numbers in as the variables they equal to.

Substitute -2 as m:

y=-2x+b

Substitute 15 as b:

y=-2x+15

Hope this helps!

Answer:

Step-by-step explanation:

the answer is 42.80 , 2.28 is what they saved and i got the .80 cents because i rounded up from .78

The original price of a swimsuit is 47.90.

What is an expression?

Expression in math is defined as the collection of the numbers, variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that;

The price of a swimsuit after discount of 5% = 45.50

Now, Let the original price of swimsuit = x

Then we can formulate;

x - 5% of x = 45.50

( x - 5x/100 ) = 45.50

(100x - 5x)/100 = 45.50

95x / 100 = 45.50

95x = 45.50 × 100

95x = 4550

x = 4550 ÷ 95

x = 47.895

After round to the nearest cent,

x = 47.90

Thus, The original price of a swimsuit is 47.90.

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The critical value for this two-tailed test is 2.6759.

To conduct a two-tailed test at the 0.01 level of significance with a sample of 55 observations, we use the t-distribution because the population standard deviation is unknown. The critical value is determined by dividing the significance level (0.01) by 2 to account for both tails of the distribution. This gives an alpha level of 0.005. Using the degrees of freedom for a sample of size 55 (54 degrees of freedom), we find the corresponding critical value from a t-distribution table or calculator. In this case, the critical value is approximately 2.6759 when rounded to four decimal places.Since the population standard deviation is unknown, we'll use the t-distribution instead of the standard normal distribution. The degrees of freedom for a sample of size 55 is 54. Using a t-distribution table or a statistical calculator, the critical value for an alpha level of 0.005 and 54 degrees of freedom is approximately 2.6759 (rounded to four decimal places).

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Answer:

Part A: D. \(3x+x=180\)

Part B: Smaller angle \(=45^{\circ}\), larger angle \(=135^{\circ}\)

Explanation:

The term supplementary is used when the sum of two angles add to \(180^{\circ}\).

Part A:

From the information given that the "angles are supplementary" and the "measure of one angle is 3 times the measure of the other", the equation to find for x can be written as:

\(3x+x=180\)

Part B:

To find the measure of each angle, we can first find the measure of the smaller angle \(x\):

\(3x+x=180\)

\(4x=180\)

\(x=45^{\circ}\)

\(\therefore\) The smaller angle is \(45^{\circ}\)

Since the measure of the larger angle is \(3\) times the measure of the smaller angle:

Larger angle \(=3x\)

\(=3(45)\)

\(=135^{\circ}\)

\(\therefore\) The measure of the larger angle is \(135^{\circ}\)

Hope this helps :)

Answer:

\(2p^2\)

Step-by-step explanation:

Step 1: Apply the exponentiation property:

\((8p^6)^\frac{1}{3} = 8^\frac{1}{3} * (p^6)^\frac{1}{3}\)

Step 2: Simplify the cube root of 8:

The cube root of 8 is 2:

\(8^\frac{1}{3} =2\)

Step 3: Simplify the cube root of \((p^6)\):

The cube root of \((p^6)\) is \(p^\frac{6}{3} =p^2\)

Step 4: Combine the simplified terms:

\(2 * p^2\)

So, the simplified expression is \(2p^2\).