An ellipse has a center at the origin, a vertex along the major axis at (20, 0), and a focus at (16, 0). The equation of the ellipse is in the form below. What is the value of b in the equation? (Enter a positive number.)

The linear equality represented by the graphis [tex]\boxed{{\mathbf{y > }}\frac{{\mathbf{2}}}{{\mathbf{3}}}{\mathbf{x + 3}}}[/tex] and it matches with [tex]\boxed{{\mathbf{OPTION C}}}[/tex].

Further explanation:

From given graph, theline passes through points [tex]\left({3,5}\right)[/tex]  and [tex]\left({ - 3,1}\right)[/tex] as shown below in Figure 1.

The slope of a line passes through points [tex]\left({{x_1},{y_1}}\right)[/tex] and [tex]\left({{x_2},{y_2}}\right)[/tex] is calculated as follows:

[tex]m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}{\text{}}[/tex]   ......(1)

Here, the slope of a line is denoted as  and points are [tex]\left({{x_1},{y_1}}\right)[/tex] and [tex]\left({{x_2},{y_2}}\right)[/tex].

Substitute [tex]3[/tex] for [tex]{x_1}[/tex] , [tex]5[/tex] for [tex]{y_1}[/tex] , [tex]-3[/tex] for [tex]{x_2}[/tex] and [tex]1[/tex] for [tex]{y_2}[/tex] in equation (1) to obtain the slope of a line that passes through points [tex]\left( {3,5}\right)[/tex] and [tex]\left({ - 3,1}\right)[/tex].

[tex]\begin{aligned}m&=\frac{{1 - 5}}{{ - 3 - 3}}\\&=\frac{{ - 4}}{{ - 6}}\\&=\frac{2}{3}\\\end{aligned}[/tex]

Therefore, the slope is [tex]\frac{2}{3}[/tex].

The point-slope form of the equation of a line with slope   passes through point  is represented as follows:

[tex]y - {y_1} = m\left({x - {x_1}}\right){\text{}}[/tex]         ......(2)

Substitute [tex]3[/tex] for [tex]{x_1}[/tex] , [tex]5[/tex] for [tex]{y_1}[/tex] and [tex]\frac{2}{3}[/tex] for [tex]m[/tex] in equation (2) to obtain the equation of line.

[tex]\begin{aligned}y - 5 = \frac{2}{3}\left({x - 3} \right)\\3\left( {y - 5} \right) = 2x - 6\\3y - 15 = 2x - 6\\3y = 2x - 6 + 15\\\end{aligned}[/tex]

Further simplify the above equation.

[tex]\begin{aligned}3y=2x + 9\\y=\frac{2}{3}x+\frac{9}{3}\\y=\frac{2}{3}x + 3\\\end{aligned}[/tex]

Therefore, the value of [tex]y[/tex] is [tex]\dfrac{2}{3}x + 3[/tex].

Since the shaded part in Figure 1 is above the equation of line [tex]y = \dfrac{2}{3}x + 3[/tex], therefore, greater than sign is used instead of is equal to

Therefore, the inequality is [tex]y > \dfrac{2}{3}x + 3[/tex].

Now, the four options are given below.

[tex]\begin{aligned}{\text{OPTION A}}\to y < \frac{2}{3}x + 3 \hfill \\{\text{OPTION B}} \to y > \frac{3}{2}x + 3 \hfill \\{\text{OPTION C}} \to y > \frac{2}{3}x + 3 \hfill \\{\text{OPTION D}}\to y < \frac{3}{2}x + 3 \hfill\\\end{aligned}[/tex]

Since OPTION C matches the obtained equation that is [tex]y > \dfrac{2}{3}x + 3[/tex].

Thus, the linear equality represented by the graph is [tex]\boxed{{\mathbf{y > }}\frac{{\mathbf{2}}}{{\mathbf{3}}}{\mathbf{x + 3}}}[/tex]and it matches with [tex]\boxed{{\mathbf{OPTION C}}}[/tex]

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Answer Details:

Grade: Junior High School

Subject: Mathematics

Chapter: Coordinate Geometry

Keywords: Coordinate Geometry, linear equation, system of linear equations in two variables, variables, mathematics,equation of line, line, passes through point, inequality

The angles are within the range of angles are 120°, 110°, 130°  and  120°, 120°, 120°

From the given options, the angles are within the range of angles are 120°, 110°, 130°  and  120°, 120°, 120°

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6 inches is the answer
P= 2( L+W)

Answer: 6 inches

Step-by-step explanation:

Given: The perimeter of the rectangle = 40 inches

Let the unknown side be w.

And the bottom side l=14 in.

We know that the perimeter of rectangle is given by :-

[tex]\text{Perimeter}=2(l+w)\\\Rightarrow40=2(14+w)\\\Rightarrow\frac{40}{2}=14+w\\\\Rightarrow20=14+w\\\Rightarrow\ w=20-14)\\\Rightarrow w=6\ in.[/tex]

Hence, the  the length of w = 6 inches.

48-36 =12

60-48=12

 36/12 =3

48/12=4

60/12=5

 the maximum number of bowls is 12

Answer:

12

Step-by-step explanation:

Answer:

(MAD) Mean Absolute Deviation: 3.28

Step-by-step explanation:

Mean: 4 + 5 + 8 + 10 + 15 = 42/5 = 8.4

8.4 - 4 = 4.4

8.4 - 5 = 3.4

8.4 - 8 = 0.4

8.4 - 10 = 1.6

8.4 - 15 = 6.6

Mean Absolute Deviation: 4.4 + 3.4 + 0.4 + 1.6 + 6.6 = 16.4/5 = 3.28

"Our proportionality constant would be how much the rope stretches versus the weight being hung.  This is set up by simply dividing the two numbers.  

9.6 inches / 8 pounds  

or for every pound hung, it will stretch 1.2 inches  so we know if it stretches 6 inches, we can set up an equation  6 inches = 1.2 [inches/pound] * pounds solve for weight  to get 5 pounds being hung from the rope."

Answer: 9.6 inches / 8 pounds  

Step-by-step explanation: I got it right

Final answer:

The probability of selecting a heart or a face card from a standard deck of cards is approximately 42.31%, which is significantly higher than the probability of selecting just a heart suit face card, which is about 5.77%.

Explanation:

To calculate the probability of selecting a heart or a face card, we first need to count the number of favorable outcomes. There are 13 hearts in a deck of cards and 12 face cards (Jacks, Queens, and Kings, with 3 in each suit). However, there are overlap cards that are both hearts and face cards (Jack, Queen, King of Hearts), which amount to 3 cards. We must subtract these to avoid double counting. So, the formula to find the total number of favorable outcomes is:

Favorable outcomes = Total hearts + Total face cards - Overlap of hearts and face cards

Favorable outcomes = 13 (hearts) + 12 (face cards) - 3 (heart face cards) = 22

Next, we calculate the probability:

P(A) = Favorable outcomes / Total number of cards

P(A) = 22 / 52 ≈ 0.4231 or 42.31%

This is the probability of selecting a heart or a face card from a standard deck. Comparing this to the probability of selecting a heart suit face card (which is 3/52 or about 5.77%), it is clear that selecting a heart or a face card is much more likely.

Therefore, the probability of selecting either a heart or a face card is less than the probability of drawing only heart-suit face cards, since the number of favorable outcomes for the latter is smaller.

Answer:

The correct option is 4.

Step-by-step explanation:

It is given that Point Q is on the coordinate 24, R is on the coordinate 28, S is on the coordinate 29, T is on the coordinate 42.

Total numbers lie on line QT is

[tex]42-24=18[/tex]

The numbers lie on line ST is

[tex]42-29=13[/tex]

The probability that a point chosen at random on QT is on ST is

[tex]P=\frac{\text{The numbers lie on line ST}}{\text{Total numbers lie on line QT}}\times 100[/tex]

[tex]P=\frac{13}{18}}\times 100[/tex]

[tex]P=72.222\approx 72.2\%[/tex]

The probability that a point chosen at random on QT is on ST is 72.2%. Therefore option 4 is correct.

Answer: its  410439

(all u need to do is subtract!)

The correct answer is: 5 over 15 multiplied by 4 over 14

Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Given this, Deja draws a marble from the bag randomly without looking.

The total number of marbles in the bag is:

5 + 8 + 2 = 15

Deja draws a marble from the bag randomly without looking. Therefore, the probability of drawing a red marble in the first trial is:

P(red on first draw) = 5/15

Deja draws another marble from the bag without replacing the first one. Therefore,

The probability of drawing a red marble in the second trial, given that she drew a red marble in the first trial, is:

P(red on second draw | red on first draw) = 4/14

We multiply these probabilities because the events are independent (i.e., the outcome of the first draw does not affect the outcome of the second draw).

Therefore, the expression that shows the probability of drawing red marbles in both trials is:

= P(red on the first draw) × P(red on second draw | red on the first draw)

= (5/15) × (4/14) = 4/63

So the correct answer is: 5 over 15 multiplied by 4 over 14.

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#SPJ3

1 pound = 16 ounces

16 * 5.5 = 88 ounces per day

88*7 = 616 ounces per week

616 * 2 = 1232 ounces in 2 weeks

30 = 3/5

 so 1/5 = 10 miles

there are 20/5 in 4 inches

 10*20 = 200

 they are 200 miles apart

Answer:

Obtuse triangle sets

B. 5, 13, 19

C. 12, 14, 25

Step-by-step explanation:

The Pythagorean inequality for the sides of the triangle to be an obtuse:

[tex]a^2 + b^2 < c^2[/tex], where a, b and c are the sides of the triangle.

The other Pythagorean inequalities are:

[tex]a^2 + b^2 > c^2[/tex], for Acute triangle

[tex]a^2 + b^2 = c^2[/tex], for Right triangle

Now let's check which set of the given sets satisfy the above inequality.

Option A

4, 5, 6

Here a = 4, b = 5 and c = 6

[tex]4^2 + 5^2 < 6^2\\16 + 25 < 36\\41 < 36\\[/tex]

Which is not true.

Here [tex]a^2 + b^2 > c^2[/tex], So this is Acute triangle

Option B

5, 13, 19

Here a = 5, b = 13 and c = 19

[tex]5^2 + 13^2 < 19^2\\25 + 169 < 361\\194 < 361\\[/tex]

Which is true. This is Obtuse triangle

Option C

Here a = 12, b = 14 and c = 25

[tex]12^2 + 14^2 < 25^2\\144 + 196 < 625\\340 < 625\\[/tex]

Which is true. This is obtuse triangle.

Option D

Here a = 21, b = 72 and c = 75

[tex]21^2 + 72^2 < 75^2\\441 + 5184 < 5625\\5625 < 5625\\[/tex]

Which is not true for obtuse.

Here [tex]a^2 + b^2 = c^2[/tex], for Right triangle

So this is Right triangle.

Answer:

c

Step-by-step explanation:

just did it

Answer:

The answer is $3(0.50+1.00)

Step-by-step explanation:

Robert bought 3 pounds of bananas at $0.50 per pound which can be expressed as:

[tex]3*0.50[/tex]

And 3 pounds of apples at $1.00 per pound which can be expressed as:

[tex]3*1.00[/tex]

As Robert bought the apples and bananas, you can add both expressions:

[tex]3*0.50 + 3*1.00[/tex]

This expression can be factorized as:

[tex]3(0.50+1.00)[/tex]

or

[tex]3(1.50)[/tex]

Both expressions will give you the same result, which is $4.50.