in each diagram the line BD bisects angle ABC. Find the measure of angle ABC​

Answer:

Center [tex]= (0,0)[/tex]

Vertices  [tex]=(-\sqrt{7},0)\text{ and }(\sqrt{7},0)[/tex]

Foci [tex]=(-2,0)\text{ and }(2,0)[/tex].

Step-by-step explanation:

The standard form of an ellipse is

[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/tex]    ...(1)

where, a>b, (0,0) is center, (±a,0) are vertices and (±c,0) are foci.

[tex]c=\sqrt{a^2-b^2}[/tex]

The given equation of ellipse is

[tex]3x^2+7y^2=21[/tex]

Divide both sides by 21.

[tex]\dfrac{3x^2+7y^2}{21}=\dfrac{21}{21}[/tex]

[tex]\dfrac{x^2}{7}+\dfrac{y^2}{3}=1[/tex]    ...(2)

On comparing (1) and (2), we get

[tex]a^2=7,b^2=3[/tex]

[tex]a=\sqrt{7},b=\sqrt{3}[/tex]

Now,

[tex]c=\sqrt{a^2-b^2}=\sqrt{7-3}=\sqrt{4}=2[/tex]

Therefore,

Center [tex]= (0,0)[/tex]

Vertices [tex]=(\pm a,0)=(\pm \sqrt{7},0}=(-\sqrt{7},0)\text{ and }(\sqrt{7},0)[/tex]

Foci [tex]=(\pm c, 0)=(\pm 2,0)=(-2,0)\text{ and }(2,0)[/tex].

Answer:

first is square and second in not rectangle I think it is trapezium

Answer: y=-(3x-2)= -3x+2

The intercept with y is 2

The intercept with x is 2/3

Answer:

1764 ways

Step-by-step explanation:

Given:

Men = 9

Women = 7

Required Men: 3

Required Women: 2

'

Required

Total Possible Outcome

The total possible outcome can be determine as follows;

Total = (Selection of Men) and (Selection of Women)

Calculating Selection of Men;

Let n represent total number of men; This implies that n = 9;

Let r represent number of men to select; This implies that r = 3;

The selection can be done in the following ways;

[tex]Male = nCr[/tex]

Where [tex]nCr = \frac{n!}{r!(n-r)!}[/tex]

[tex]Male = 9C3[/tex]

[tex]Male = \frac{9!}{3!(9-3)!}[/tex]

[tex]Male = \frac{9!}{3!(6)!}[/tex]

[tex]Male = \frac{9 * 8 * 7 * 6!}{3!6!}[/tex]

[tex]Male = \frac{9 * 8 * 7}{3!}[/tex]

[tex]Male = \frac{9 * 8 * 7}{3*2*1}[/tex]

[tex]Male = 84 ways[/tex]

Calculating Selection of Women;

Let n represent total number of men; This implies that n = 7;

Let r represent number of men to select; This implies that r = 2;

The selection can be done in the following ways;

[tex]Female = nCr[/tex]

Where [tex]nCr = \frac{n!}{r!(n-r)!}[/tex]

[tex]Female = 7C2[/tex]

[tex]Female = \frac{7!}{2!(7-2)!}}[/tex]

[tex]Female = \frac{7!}{2!(5)!}[/tex]

[tex]Female = \frac{7 * 6 * 5!}{2!5!}[/tex]

[tex]Female = \frac{7 * 6}{2!}[/tex]

[tex]Female = \frac{42}{2*1}[/tex]

[tex]Female = 21 ways[/tex]

Recall that

Total = (Selection of Men) and (Selection of Women)

Hence,

[tex]Total = 84 * 21[/tex]

[tex]Total = 1764 ways[/tex]

Answer:

1

Step-by-step explanation:

-3a+4 =7

-4. _4

-3a=3

divide by -3 on both sides

a=-1

3+4=7

Answer:

a= [tex]-3\frac{2}{3}[/tex] or ≈ -3.66

Step-by-step explanation:

-(3a+4)=7

-3a-4=7

Add 4 to both sides

-3a=11

Multiply both sides by -1

3a= -11

Divide both sides by 3

a= [tex]-3\frac{2}{3}[/tex]

Answer:

1. 4

2. -4

3. -4

Step-by-step explanation:

Let's look carefully at each problem and explain it.

1. (-2)^2

This means find the square of the number -2. Since the square of a number means multiplying the number by itself, then

(-2)^2 means the product (-2) * (-2),

and since the product of two negative numbers is positive, then

(-2)^2 = (-2) * (-2) = 4

Answer is 4.

2. -2^2

Here, the exponent applies only to the 2, not to -2. This problem means square 2 and then take the opposite of the product. This can be written as

-(2^2)

-2^2 = -(2^2) = -(2 * 2) = -(4) = -4

Answer is -4.

3. -(2)^2

This is the same as problem 2 above. You square the 2 first, then take its negative.

-(2)^2 = -(2^2) = -(2 * 2) = -(4) = -4

Answer is -4

Answer:

1.785 cm / min

Step-by-step explanation:

We have to the following equation:

V = A * L

The volume is equal to the area times the length, now, if we derive with respect to time we have:

dV / dt = dA / dt * L

Now, the area of a trapezoid is:

A = (Upper base + Lower base) / 2 * height

Now we have:

Upper base = 40 + h

Lower base = 40

Replacing we have:

A = (40 + h + 40) / 2 * h

A = (h ^ 2) / 2 + 40 * h

Now, we derive and we are left:

dA / dt = d [(h ^ 2) / 2 + 40 * h] / dh * dh / dt

dA / dt = (h + 40) * dh / dt

we replace dA / dt:

dV / dt = [(h + 40) * dh / dt] * L

We have that dV / dt is equal to 0.1 m ^ 3 / min, we know that 1m ^ 3 is equal to 10 ^ 6 cm ^ 3, therefore:

dV / dt = 10 ^ 5 cm ^ 3 / min

in addition L is equal to 8 m or what is equal to 800 cm, and also h at the required moment is 30 cm

we replace everything and we have:

10 ^ 5 = 800 * (30 +40) * dh / dt

dh / dt = 10 ^ 5/56000

dh / dt = 1.785 cm / min

Answer:

A≈896.81

Step-by-step explanation:

This is an approximate answer. Use the formula SA = pi, radius, slant height + pi, radius squared. Plug it in in PEMDAS order.

P.S. SOmeone please tell me if this is wrong I will fix it. Thanks!

Answer:

[tex]26.14yd^2[/tex]

Step-by-step explanation:

Triangle

[tex]A=\frac{h_bb}{2} \\=\frac{4*6}{2} \\=12yd^2\\\\A=\frac{1}{2} \pi r^2\\=\frac{1}{2} \pi 3^2\\=14.14yd^2\\\\12+14.14=26.14yd^2[/tex]

Answer:

Step-by-step explanation:

The area of a circle knowing the diameter is 28.2743, now divide between 2: 14,13715

Now the area of the triangle give us: 9.238

9.238 + 14,13715 = 23.37515

The procedure is in the images

App used: CalculateMyFigure

Answer:

g(5)=17

Step-by-step explanation:

g(x)=3x+2

Let x = 5

g(5) = 3*5+2

      = 15+2

      = 17

Answer:

17

Step-by-step explanation:

Just substitute 5 into the position of X

Answer:

Step-by-step explanation:

this is a radical equation:

when x=1 y=0

reflected about x

-sqrt(x)

right 1 unit

-sqrt(x-1)

it looks like y-int is about (0,1/3)

vertically compressed by a factor of 1/3

-(1/3)sqrt(x-1)

if you think the y-int is more (0,1/4), then

the function is vertically compressed by a factor of 1/4

-0.25sqrt(x-1)

Answer:

i) x= -0.25, x=1.25

ii)x=1.5, x= -0.5     (notice the negative signs)

Step-by-step explanation:

So, to simply solve this(or estimate), notice what the equations say at the end of them!

0 and 2, and also notice the equations are exactly the same as the graph's.

This means, by substitution, we are look for the x-values at y=0, and at y=2

(because they are exactly the same, in those instances, we can just replace the equation with the value of 0, or 2 because they are equal)

Then all we have to do is imagine the lines of y=0(x-axis) and y=2, and find where the parabola intersects those lines.

And so, just find where they intersect, and you have got it!

Hope this helps!

Answer:

A

Step-by-step explanation:

[tex]\sqrt{(-5 - (-1))^{2} + (7 - 2)^{2} } = \sqrt{41}[/tex]

So the right answer is √41

please see the attached picture for full solution

Hope this helps

Answer:

maximum point: (0, 4)

x-intercepts: (2, 0), (-2, 0)

y-intercepts: (0, 4)

Answer:

(2,5)

Step-by-step explanation:

Choose values for  x  and substitute in to find the corresponding  y  values.

(2) - 2y = -8

2 = 2y - 8

10 = 2y

5 = y

(2,5)

Answer:

a)   45

The sequence  3 , 5, 9 , 15 , 23 , 33 , 45

Step-by-step explanation:

Given The sequence  3 , 5, 9 , 15 , 23 , 33

First term = 3

Add 2  of first term  

Second term  = 3 +2 = 5

Add 4  of second term  

Third term = 5 + 4 = 9

Add 6  of Third term  

Fourth term  = 9 + 6 = 15

Add 8 of  fourth term

fifth term = 15 + 8 = 23

Add 10 of fifth term

sixth term = 23 + 10 = 33

Add 12 of sixth term

seventh term = 33 +12 = 45

Final answer:-

Now the sequence   3​, 5​, 9​, 15​, 23​, 33​, ​__45___

Answer:

4th option is the correct answer

35 inches

Step-by-step Explanation:

[tex]w = 4 \frac{3}{8} = \frac{35}{8} \: in \\ \\ l = 3 \times \frac{35}{8} = \frac{105}{8} \: in \\ \\ perimeter \: of \: rectangle \\ = 2\bigg(l + w \bigg) \\ \\ = 2\bigg( \frac{105}{8}+ \frac{35}{8} \bigg) \\ \\ = 2 \times \frac{140}{8} \\ \\ = \frac{140}{4} \\ \\perimeter \: of \: rectangle = 35 \: in[/tex]

Answer:

Step-by-step explanation:

From Rule 6: Jennie is at Seat 4 and next to Harvey; and by rule 1 (Harvey has a higher seat number than Jennie)

From Rule 2:  Peter is across from Harvey.

Since Seat 5 is across from Seat 1

From Rule 7: Peter is next to Lia.

Therefore, Lia can either be in Seat 2 or Seat 8, but by Rule 3 (Neither Joyce nor Lia is in seat 8), therefore, Lia is in Seat 2.

By Rule 5: Lia is next to Kenny, therefore:

From Rule 4: Rick is across from Kenny, and Rick is also next to Joyce.

Seat 7 is across from Seat 3, therefore:

Since Rick is also next to Joyce (and by Rule 3, Joyce cannot be on Seat 8)

Therefore, we have:

Seat 1: Peter

Seat 2: Lia

Seat 3: Kenny

Seat 4: Jennie

Seat 5: Harvey

Seat 6: Joyce

Seat 7: Rick

Since Mark has the remaining seat, Mark is on Seat 8.

Answer: 3.3%

Step-by-step explanation:

Amount = prt / 100

3075.21 = (2152 x r x 13)/100

Answer:

the answer is letter c

Step-by-step explanation:

Answer:

(1,–1), (4, –2), (9, –3)

Step-by-step explanation:

In the picture attached, the plot of the function f(x) = -√x is shown.

To verify which points lie on the line we compute the following table.

x    √x    f(x) = -√x

1     1        -1

4    2       -2

9    3       -3

The points which lie on the graph will be (1,–1), (4, –2), and (9, –3) so the correct answer is option D.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

In the picture attached, the plot of the function f(x) = -√x is shown. To verify which points lie on the line we compute the following table.

x    √x    f(x) = -√x

1     1        -1

4    2       -2

9    3       -3

We can see that the above points are satisfying the function. Therefore points that lie on the graph will be (1,–1), (4, –2), and (9, –3) so the correct answer is option D.

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Answer:

30 3/8 pounds of shortening used.

Step-by-step explanation:

20 1/2 + 29 3/4 +18 1/8 + 16 + 5 1/4 = 89.625

120- 89.625 = 30.375 pounds

0.375 as a fraction = 3/8 + 30

Therefore the total shortening used = 30 3/8 pounds

How many pounds of shortening are used in this cake mix is maximum figure as we found exact 0.375

We can do this by multiplying the 0.375 x 2 = 0.750  = 3/4

Then counteracting 4 = 1 to 8 = 1 and keeping the top fraction.

1/2 of 3/4 = 3/8

3/8 x 2 = 0.75

0.75 /2 = 0.375

Answer:

50%

is the probability of this question

Answer:

25%

Step-by-step explanation:

We have 4 choices when flipping two coins, HH, HT, TH and TT where H and T are heads and tails respectively. The only option where both coins will not land on heads is TT so the probability is 1/4 = 25%.

Answer:

40cm^2

Step-by-step explanation:

A=a+b/2×h

A=6+10/2*5

A=16cm/2*5cm

A=8cm*5cm

A=40cm^2

Answer:

B. 10

Step-by-step explanation:

The median is the middle number, so to find it, we must list the numbers from smallest to largest :

5, 5, 8, 11, 15, 21, 27, 34, 55

The median is 15

The mode is what number occurs most often, which is 5.

The difference will be found by subtracting 5 from 15:

15-5=10

Answer:

10

Step-by-step explanation: you have to find the median number and subtract by 5

5,5,8,11,15,21,27,5

also the median is middle number subtract by 5 because it want the difference number of electoral votes per state

15-5=10

Answer: 63 square units

Step-by-step explanation:

Area of a parellelogram = b x h

7 x 9 = 63 square units

Answer:

63

The triangle can be moved to the other side making the parallelogram a rectangle with a length and width of 7 and 9

7 x 9 = 63

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

15 minutes more, as 60-45mins = 15 minutes

Step-by-step explanation:hope it helps

It will take 15 more minutes for the journey than the expected.

Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.

Speed is a scalar quantity as it only has magnitude and no direction.

Given that,

The distance from Raj's house to the airport is 30 miles.

He expects the taxi to travel at an average speed of 40 mph.

If he travels at a speed of 40 mph, let t be the time taken.

Speed = Distance / Time

40 = 30 / t

t =  = 0.75 hours = 45 minutes

If Raj's taxi actually travels at an average speed of 30 mph, let t' be the time taken.

30 = 30 / t'

t' = 1 hour = 60 minutes.

t' - t = 60 - 45 = 15 minutes

Hence the journey takes 15 more minutes than expected.

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