If DB = 4 and DC = 6, find AD.

2
2
3

Answer:

D

Step-by-step explanation:

Given that the ratio of side lengths = 8 : 3, then

ratio of volumes = 8³ : 3³ = 512 : 27 → D

ANSWER

The correct answer is option D.

EXPLANATION

The given pyramids are similar and the side lengths are in the ratio 8:3

Volume is in cubic units, therefore the volume of the two similar pyramids are in the ratio;

[tex] {8}^{3} : {3}^{3} [/tex]

This simplifies to

[tex]512 : 27[/tex]

The correct answer is option D.

10 ~ Spinning A 3

I hope this helps!~ I tried

Honestly I feel like it is 10.

Answer:

4th bubble

Step-by-step explanation:

First FOIL: f(x) = x² + 3x - 4. Then convert from Standard Form [y = Ax² + Bx + C] to Vertex Form [y = A(X - H)² + K], where (h, k) is the vertex and -h gives the OPPOSITE terms of what they really are. So, you do this by completing the square [½B]²:

Remember, -h gives the OPPOSITE terms of what they really are, so your vertex is (-1½, -6¼).

If you are ever in need of assistance, do not hesitate to let me know by subscribing to my channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.

Answer:

No. of sweets Sue has = (18-x) -5

No. of sweets Tony has = (18+x)/2

Step-by-step explanation:

Sue has sweets = 18

Tony has sweets = 18

Sue give Tony  sweets = x

Sweets left for Sue = 18 - x

Sweets for Tony = 18 + x

Sue eats 5 sweets = (18-x) -5

Tony eat half of his sweets = (18 +x)/2

No. of sweets Sue has = (18-x) -5

No. of sweets Tony has = (18+x)/2

Answer:

D) 26

Step-by-step explanation:

f(x) = 3x^2 - 6x + 2

Let x = -2

f(-2) = 3(-2)^2 - 6(-2) + 2

      =3(4) +12+2

      = 12 +12+2

     =26

For this case we have a function of the form [tex]y = f (x).[/tex]

Where:

[tex]f (x) = 3x ^ 2-6x + 2.[/tex]

We must find the value of the function when [tex]x = -2.[/tex]

Substituting we have:

[tex]f (-2) = 3 (-2) ^ 2-6 (-2) +2\\f (-2) = 3 * 4 + 12 + 2\\f (-2) = 12 + 12 + 2\\f (-2) = 26[/tex]

Thus, the value of the function is 26.

Answer:

26

Option D

(N-2)180

(130-2)180

128 x 180

23040

Final answer:

The sum of the interior angles of a convex 130-gon is 23040 degrees, calculated using the formula S = (n - 2) × 180° with n equal to the number of sides.

Explanation:

The sum of the interior angles of any polygon can be calculated by using the formula S = (n - 2) × 180°, where S is the sum of the interior angles and n is the number of sides in the polygon. In the case of a convex 130-gon, with n = 130, the calculation would be S = (130 - 2) × 180°. This simplifies to S = 128 × 180°, which is S = 23040°. Therefore, the sum of the interior angles of a convex 130-gon is 23040 degrees.

Answer:

3. Additive

4. [tex]x<2[/tex]

5. Graph the linear line. Then, make the line dotted and shade below the line.

Step-by-step explanation:

3. Adding -15 to both sides to isolate the variable.

4.

[tex]-3x+8>2x-2\\5x<10\\x<2[/tex]

Answer:

B. points A and B

Step-by-step explanation:

"Rate of change" is just a fancy name for slope.

The question asks for points on the graph having a slope of 5.  We know a slope of 5 is a positive (goes up from left to right) and it's quite steep.

By looking at the graph, we see that to have a slope of 5, it has to take place in the first half of the graph.

Let's look at the possible options:

A. Points D and F: From point D to point F, you're going down, so the slope is negative.  NO

B. Points A and B: goes up, pretty steep.  Let's calculate the slope.

Point A: (2,1), Point B: (3,6)

Slope = (6 - 1) / (3 - 2) = 5 / 1 = 5

We found it!

C. Points B and C: goes up, pretty steep too.  Let's calculate the slope:

Point B: (3,6) , Point C: (4,9)

Slope = (9 - 6) / (4 - 3) = 3 / 1 = 3, NO, not the slope we're looking for

D. Points C and E: goes down, NO,  not what we want.

Answer:

60+6= 66, 66/3= 22 in 6 years time his father will be 44 years. now his father age will 38 and George age will be 22

The present age of the father is 42 years and George is 18 years.

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

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the sum of the present ages of George and his father is 60 years. In 6 years his father will be twice as old as George will be.

Make the two linear equations and solve them to get the present ages.

G + F = 60

2 ( G + 6 ) = F + 6

2G + 12 = F + 6

2G + 12 = 60 - G + 6

3G = 54

G = 18 years

Father's age will be,

F = 60 - 18

F = 42 years

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Answer:

[tex]226.08\ in^{2}[/tex]  or  [tex]72\pi\ in^{2}[/tex]

Step-by-step explanation:

we know that

The lateral area of a cylinder ( curved area of the vase) is equal to

[tex]LA=2\pi rh[/tex]

we have

[tex]r=6/2=3\ in[/tex] ------> the radius is half the diameter

[tex]h=12\ in[/tex]

substitute the values

[tex]LA=2\pi (3)(12)=72\pi\ in^{2}[/tex] -----> exact value

assume

[tex]\pi=3.14[/tex]

[tex]72(3.14)=226.08\ in^{2}[/tex] ----> approximate value

Answer:

7

Step-by-step explanation:

Answer:

Part A) The slope is undefined

Part B) The equation of the line is [tex]x=p[/tex]

Part C) None y-intercept

Part D) The slope of a line perpendicular to the given line is equal to zero

Step-by-step explanation:

we have that

Describe

A) slope of the line

B) equation of the line

C) y-intercept

D) slope of a line perpendicular to the given line

Part A) slope of the line

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

[tex](p,a)\ (p,-a)[/tex]

Substitute the values

[tex]m=\frac{-a-a}{p-p}[/tex]

[tex]m=\frac{-2a}{0}[/tex]  -----> the slope is undefined

Its a vertical line (parallel to the y-axis)

Part B) Equation of the line

we know that

The equation of a vertical line is equal to the x-coordinate of the points through which the line passes.

so

[tex]x=p[/tex]

Part C) The y-intercept

The y-intercept is the value of y when the value of x is equal to zero

The vertical line not intercept the y-axis

so

None y-intercept

Part D) slope of a line perpendicular to the given line

A line perpendicular to the given line is a horizontal line (parallel to the x-axis)

therefore

The slope is equal to zero

Answer:

Option C.

The measure of the complement angle is [tex]18\°[/tex]

Step-by-step explanation:

Let

x-----> the angle

we know that

The complement of an angle is equal to [tex](90-x)\°[/tex]

The supplement of an angle is equal to [tex](180-x)\°[/tex]

we have

The complement of an angle is one-sixth the measure of the supplement of the angle

[tex](90-x)\°=(1/6)(180-x)\°[/tex]

solve for x

[tex](540-6x)\°=(180-x)\°\\ (6x-x)=(540-180)\°\\ (5x)=(360)\°\\ x=72\°[/tex]

Find the measure of the complement angle

[tex](90-x)\° ----> (90-72)=18\°[/tex]

Answer:

Option C. 18

Step-by-step explanation:

Answer:

Option D. minor arc

Step-by-step explanation:

we know that

In a circle the measure of minor arc plus the measure of major arc is equal to 360 degrees

The measure of minor arc is less than 180 degrees

The measure of major arc is greater than 180 degrees

In this problem

Arc BDC is a major arc

Arc BC is a minor arc

Answer: You take $18.80 divide by 2 =$9.40 then $18.80+$9.40=$28.20

$28.20 x's 5.5=$$155.10

$18.80 x's 40=$752.00

then add 752.00+155.10=$907.10

Step-by-step explanation:

Answer:

The length L is 10 cm

Step-by-step explanation:

We need to find the length of the arc subtended by a central angle of 2 radians and the circle has radius of 5cm.

So, the formula used will be:

l = r  Θ

Where L= length of arc

r= radius of circle

and  Θ is angle

In The given question

L=?

r = 5 cm

Θ = 2 radians

Putting values in formula:

L = r  Θ

L = 5 * 2

L = 10 cm

So, the length L is 10 cm

Final answer:

The length of the arc subtended by a central angle of 2 radians in a circle of radius 5 cm is 5 cm.

Explanation:

The length of an arc subtended by a central angle can be found using the formula:

Length of arc = (central angle / 2π) × circumference of the circle

In this case, the central angle is 2 radians and the radius of the circle is 5 cm. The circumference of the circle is given by 2πr, where r is the radius. So, the length of the arc can be calculated as:

Length of arc = (2 / 2π) × (2π × 5) = 5 cm

The answer is (-4,3) so C

Answer:

[tex]\boxed{\text{c) (-4, 3)}}[/tex]

Step-by-step explanation:

When you reflect a point (x, y) across the y-axis, the y-coordinate remains the same, but the x-coordinate gets the opposite sign: it becomes (-x, y).

Thus, if a point A, say, (4, 3) is reflected across the y-axis, its reflection A' is at

[tex]\boxed{\textbf{(-4, 3)}}[/tex]

Answer:

V=167.5 cubic mm

Step-by-step explanation:

Volume of the Cone is given with the formula

[tex]V=\frac{1}{3} \pi r^2h[/tex]

though we are not specified what is radius and which one is the height , we are assuming that ,

Height = 10 mm

Radius = 4 mm

Substituting these values in the formula we get

[tex]V=\frac{1}{3} \pi 4^2 \times 10[/tex]

[tex]V=\frac{1}{3} \pi 160[/tex]

[tex]V=\frac{160 \times 3.14}{3}[/tex]

[tex]V=\frac{160 \times 3.14}{3}[/tex]

[tex]V=\frac{502.40}{3}[/tex]

[tex]V=167.5[/tex]

Answer:

1. Not simplified correctly. It  is (3/7)x + 1

2. Not simplified correctly. It is (3/x)

3. Not Simplified correctly. I believe it is as simplified as it can get

Step-by-step explanation: When a polynomial is over a denominator, ALL elements of the polynomial is affected

A unit circle has radius 1, and thus circumference [tex]2\pi[/tex].

Since an angle of [tex]\frac{\pi}{4}[/tex] is one eighth of a whole turn, the length of an arc that subtends an angle of  [tex]\frac{\pi}{4}[/tex] radians will be one eighth of the whole circumference:

[tex]l = \dfrac{2\pi}{8} = \frac{\pi}{4}[/tex]

In fact, the radians have the property that, in the unit circle, the length of the arc is exactly the measure of the angle. In general, you have

[tex]l = r\cdot\alpha[/tex]

where l is the length of the arc, r is the radius and [tex]\alpha[/tex] is the angle in radians. So, if [tex]r=1[/tex], you have [tex]l=\alpha[/tex]

The length of an arc in a unit circle that subtends an angle of π/4 radians is simply π/4, because in a unit circle, the length of an arc is the angle (in radians) multiplied by the radius (which is 1).

In Mathematics, particularly in the study of a unit circle, an interesting concept to learn is the length of an arc that subtends an angle. Here, the given angle is π/4 radians. In a unit circle, the length of an arc can be calculated by simply multiplying the angle (in radians) by the radius of the circle. In this case, since the radius is 1 (as it's a unit circle), the length of the arc is simply the measurement of the angle in radians, which is π/4.

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Final answer:

Eudora's balance at the end of the year will be $7,750.03.

Explanation:

To calculate Eudora's balance at the end of the year, we need to calculate the interest for each period separately and then add them together. The credit card offers an introductory APR of 7.8% for the first 3 months, so we will calculate the interest for this period first.

Step 1: Calculate the interest for the introductory period:

Interest = Balance * Introductory APR * (Introductory Period / 12) = $6400 * 0.078 * (3/12) = $156.00

Since the card compounds interest monthly, we need to calculate the interest for each month of the remaining 9 months at the standard APR of 26.5%:

Step 2: Calculate the interest for each month of the remaining 9 months:

Interest for each month = Balance * Standard APR / 12 = $6400 * 0.265 / 12 = $139.67

Step 3: Add up the interest for the introductory period and the remaining 9 months:

Total interest = Interest for the introductory period + (Interest for each month * Number of months) = $156.00 + ($139.67 * 9) = $1,350.03

Step 4: Calculate the final balance at the end of the year:

Final balance = Balance + Total interest = $6400 + $1,350.03 = $7,750.03

Therefore, Eudora's balance at the end of the year will be $7,750.03.

Step-by-step explanation:

cos 330°=cos ( 360 -30)

In fourth quad the value of cos A is positive .

All angles when subtracted by multiple of 180° or (π) the function remain same

cos (30°)=√3/2

Also-

Cos(330)=Cos(360–30)

since Cos(360-x)=cos(x) where x is in degree

Cos(330)=Cos(30)= √ 3 /2 ~ 0.866

Answer:

Answer:

cos ( 330 º ) = √ 3 /2

Explanation:

Remember that  

cos ( a − b ) = cos ( a ) cos ( b ) + sin ( a ) sin ( b )

and that  

330 º = 360 º − 30 º , so

cos ( 330 º ) = cos ( 360 º − 30 º ) = cos ( 360 º ) cos ( 30 º ) + sin ( 360 º ) sin ( 30 º )

The cosine, sine, tangent and secant of 360º equal the cosine, sine, tangent and secant of 0º respectively. We know that  

sin 0 º  is 0, and that  cos 0 º = 1  so

cos ( 330 º ) = 1 ⋅ cos ( 30 º ) + 0 ⋅ sin ( 30 º )

cos ( 330 º ) = √ 3 /2

Hope This Helps!  Have A Nice Day!!

Answer:

6x(x - 2)

Step-by-step explanation:

Find the common factors of 6x² - 12x, which is 6x.

Answer:

x=-3 ;       x= 4

Step-by-step explanation:

zeros of the function are the value of x at which the function becomes zero. Or graphically when the graph line crosses the x-axis those values of x are the zeros of the function.

Finding zeros of given function f(x)= x^2-x-12/ x^2+x-12 by substituting f(x)=0

0=  x^2-x-12/ x^2+x-12

0= (x+3)(x-4)/(x-3)(x+4)

(x+3)(x-4)=0

(x+3)=0  ; (x-4)=0

x=-3 ;       x= 4

the zeros of the function f(x)= x^2-x-12/ x^2+x-12 are at point x=-3 and x= 4 !

Answer:

-3,4

Step-by-step explanation:

A.P.E.X

Answer:

Your answer will be C. y= 4x-1

Step-by-step explanation:

On the x value side, the numbers represent what to fill in x with, and y should be the output of it.

For example :

4(1) = 4 - 1 = 3

4(2) = 8 - 1 = 7

4(3) = 12 -1 = 11

Hope this helps and was correct

This  y = 4x-1, equation is  represented by the table

On the x value side, the numbers represent what to fill in x with, and y should be the output of it.

For example :

4(1) = 4 - 1 = 3

4(2) = 8 - 1 = 7

4(3) = 12 -1 = 11

The correct answer is option C.

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Subtract 8 from both sides

-3x < 15 - 8

Simplify 15 - 8 to 7

-3x < 7

Divide both sides by -3

= x > -7/3

Answer:

x > - 2 1/3

Step-by-step explanation:

- 3x + 8 < 15

- 3x < 7

x > - 2 1/3

Answer:

95086

Step-by-step explanation:

We let the population one year ago be x, the relationship between x and the present population is;

(105/100)*x = 104832

This is because the present population exceeds the population one year ago by 5%.

therefore,

1.05*x =  104832

x = 99840

We now let the population two years ago be y, the relationship between y and the population one year ago is;

(105/100)*y = 99840

This is because the population one year ago exceeds the population two years ago by 5%.

Therefore,

1.05*y = 99840

y = 95085.7

Rounding to the nearest whole number;

95086

Answer:

C.) 0.555

Step-by-step explanation:

This is annoying because we're dealing with decimals.

So, we need to know how density works. Density works by dividing mass (g) by volume (ml).

Since the empty bottle has a mass of 4,850g and the bottle + the liquid have a total mass of 6.160g, we'll subtract the bottle's mass from the total mass, giving us 1.310g. Again, we divide mass by volume to obtain density (which should be listed as g/ml).

1.310 ÷ 2.360 = ~0.555

Therefore, your answer is 0.555

The density of the liquid in the bottle is calculated by dividing the mass of the liquid (found by subtracting the mass of the empty bottle from the total mass when full) by its volume. The correct answer is C) 0.555 ml.

The subject here is density, which is a physical property of a substance that can be calculated by its mass over its volume. In your case, you are being asked to find the density of the liquid inside the bottle. This can be done by first, finding the mass of the liquid alone, then dividing that by the volume of the liquid given in the question.

The mass of the liquid can be found by subtracting the mass of the empty bottle from the total mass of the bottle when full (6.160g - 4.850g = 1.310g). The volume of the liquid is already given as 2.360 ml.

Finally, you compute the density by dividing the mass of the liquid by its volume (1.310g / 2.360 ml = 0.555 g/ml).

So, the correct choice is C) 0.555 ml.

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Answer:

Second option: This is a perfect cube.

Fourth option: The side length is 6 centimeters.

Fifth option: Taking the cube root of the volume will determine the side length.

Step-by-step explanation:

You know that the volume of a cube can be calculated with:

[tex]V=s^3[/tex]

Where s is the lenght of any side of the cube.

Since you know the volume of this cube, you can calculate the side lenght by  solving for "s". You can make this taking the cube root of the volume.

Therefore, you get that the side lenght of this cube is:

[tex]s=\sqrt[3]{216cm^3}[/tex]

[tex]s=6cm[/tex]  

(Since it has exact cube root, it is a perfect cube)

Answer:

B,D,E

Step-by-step explanation:

Answer:

3rd Quadrant

Step-by-step explanation:

The "i" in complex numbers behave same as the y in real numbers, so basically this number translated in real would be same as (-14,-5).

To graph this, we have to go -14 units in x direction and -5 units in y direction. Basically, 14 units to the left and then 5 units down. That will place us in 3rd quadrant.

Hence, -14 -5i will fall in the 3rd quadrant of the complex plane.

Answer:

C. III

Step-by-step explanation: