If twice the age of son is added to age of father, the sum is 56. But if twice the age of the father is added to the age of son, the sum is 82. Find the ages of father and son.

Answer: 7 cm

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

14:8 = 14/8 = 7/4

28:10 = 28/10 = 14/5

Since the fractions are not equal, it is not a proportion.

Answer: no

is the sign that you mean ÷ ?

if so:

-3×7÷5×1/7

= -21÷5×1/7

=-21/5 × 1/7

= (-21×1) / (5×7)

= -21/35

=-3/5

=-0.6

Step-by-step explanation:

just think back to the standard circle of radius = 1.

there the trigonometric functions are all represented as sides of right-angled triangles, where the radius is the baseline.

just like the triangle we are seeing here.

the only difference : the baseline (radius) is 17 and not 1.

and that is fine. everything is as in the standard circle, but multiplied by the radius (which is also true for the standard circle, but multiplying by 1 does not change anything, right ?).

a)

angle A is or focus. so, just imagine the triangle turned counterclockwise by 90° (so that AC is horizontal and CB is vertical).

do you see it now ?

sin is the vertical leg, cos the horizontal leg. and the leg lengths here are the standard functions multiplied by the radius.

so,

17 × sin A = 8

sin A = 8/17 = 0.470588235... ≈ 0.47

b)

17 × cos A = 15

cos A = 15/17 = 0.882352941... ≈ 0.88

c)

now B is our focus. imagine the triangle being mirrored at point B, so that B is left, and AC is right. your see it now ?

tan B = sin B / cos B

sin B = 15/17 = 0.882352941... ≈ 0.88

cos B = 8/17 = 0.470588235... ≈ 0.47

tan B = 15/17 / 8/17 = 15/8 = 1.875 ≈ 1.88

d)

cos B = 8/17 = 0.470588235... ≈ 0.47

Answer:

The max height is 11.25 feet and the ball will take 1.464 seconds to hit the ground

Step-by-step explanation:

The quickest way to solve this equation is by using the equation that you gave, which is h(t)= -16t^2 + v0t + h0. This equation models the trajectory of the football, which means that at the equation's vertex, we can model what the height of the ball is. Along with that, by finding the positive root of where h(t) = 0, we can find how long it will take for the ball to hit the ground.

First, lets find h0 and v(0)

h0 is the initial height of the ball. So we know that the ball leaves your hand of 5 feet, so h0 = 5. Similarly, the initial velocity is 20 ft/sec, so v0 = 20.

Plugging 5 in for h0 and 20 for v0, we get h(t) = -16t^2 + 20t + 5.

Second, find max height.

To find the vertex of a parabola, use -b/2a to find the time, and plug that into h(t) to get the height.

b=20

a=-16

t = -b/2a = -20/2(-16) = .625 seconds

h(.625) = 11.25 feet

The max height is 11.25 feet

Third, find how long.

To find this, we need to find the t-intercepts of the equation.

set h(t) = 0

-16t^2 + 20t + 5 = 0

Use quadratic formula to find t

t = (- 20 ± [tex]\sqrt{20^{2} - 4(-16)(5)}[/tex])/2(-16)

t = {1.464}, -.214

The ball will take 1.464 seconds to hit the ground.

Answer:

22 is the perimeter.

Step-by-step explanation:

You find the perimeter by adding up all of the sides of a shape. 9 + 9 = 18. 18 + 4 = 22.

Answer: 5/9

Step-by-step explanation:   10             6

                                              ------  x ----------- = 5

                                                12           9         -----

                                                                            9

Answer:

[tex]10.4\: \sf cm^2\:(3\:sf)[/tex]

Step-by-step explanation:

[tex]\Large\boxed{\sf Formulae}[/tex]

Sine Rule

[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

Cosine rule

[tex]c^2=a^2+b^2-2ab\cos C[/tex]

Area of a triangle

[tex]\textsf{Area of a triangle}=\dfrac12ab\sin C[/tex]

where:

[tex]\Large\boxed{\sf Calculation}[/tex]

To find the area of ΔBCD, find:

Then use the sine rule for area of a triangle

Calculate length CD using cosine rule:

[tex]\implies CD^2=4.9^2+3.8^2-2(4.9)(3.8)\cos 80^{\circ}[/tex]

[tex]\implies CD^2=31.98334186...[/tex]

[tex]\implies CD=5.655381673...\:\sf cm[/tex]

Calculate ∠ADC using sine rule:

[tex]\implies \dfrac{\sin 80}{CD}=\dfrac{\sin ADC}{4.9}[/tex]

[tex]\implies ADC=\sin^{-1}\left(\dfrac{4.9 \sin 80}{CD}\right)=58.568949^{\circ}[/tex]

Therefore, ∠CDB = 180° - 58.568949° = 121.431051°

Use sine rule to calculate DB:

[tex]\implies \dfrac{DB}{\sin 25}=\dfrac{CD}{\sin CBD}[/tex]

[tex]\implies DB=\dfrac{5.655381673\sin25}{\sin 33.568949}=4.322471258..\: \sf cm[/tex]

[tex]\Large\boxed{\sf Solution}[/tex]

Use the sine rule for area of a triangle to find area of ΔBCD:

[tex]\implies A=\dfrac12(CD)(DB)\sin CDB[/tex]

[tex]\implies A=\dfrac12(5.655381673)(4.322471258)\sin (121.431051)[/tex]

[tex]\implies A=10.4\: \sf cm^2\:(3\:sf)[/tex]

Answer:

6+12=18

Step-by-step explanation:

the area of the smaller rectangle+the area of the bigger rectangle=18

area square= side²

= (x-6)²

= x²-12x+36

Answer:

36

Formula:
Side² = Area
Step-by-Step Explanation
-6 x -6 = 36

Answer:

3

Step-by-step explanation:

If each packet has 500 grams, and each person eats 100 grams, then one packet will feed five people (500/100=5). Since he will be buying pasta for 12 people, he will need to buy three packets, because 3*500=1500 grams. While there is some extra, buying only two packets would result in not enough pasta.

Answer:

360°

Step-by-step explanation:

the sum of the exterior angles of any polygon = 360°

Based on observation, in this polyhedron, there are a total of six vertices, nine edges, and five faces.

In geometry, this refers to the point where two line meet. In this case, the vertices are A, B, C, D, E, F for a total of six vertices.

This term refers to line segments, for example the line between B and C is an edge. Based on this, there are nine edges in this shape.

This refers to flat surfaces; in this, case the total of flat surfaces are five.

Learn more about geometry in: https://brainly.com/question/16836055

Answer:

.858 cm^2

Step-by-step explanation:

Area of square - area of circle = grey corner areas

(2 * 2)  - ( pi * 1^2 ) =

4 - pi = .858 cm^2

Here is the Answer:

Step-by-step explanation:

The required distance between the take-off point and the water tower is 1980.1 feet.

Given that,
A plane took off and rose at an angle of 8º with the horizontal ground. As the plane flies over a water tower, it has covered a distance from the take-off point of 2000 feet.
To determine how far apart are the take-off point and the water tower.​

These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operation.

Here,
Now,
The distance flying over inclination is 2000 feet at an angle of 8° with horizontal.
Now,
Required horizontal distance = 2000 * cos 8°
                                            = 1980.1 feet.

Thus, the required distance between the take-off point and the water tower is 1980.1 feet.

Learn more about trigonometry equations here:

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Step-by-step explanation:

By the secant-secant theorem, (AC)(BC)=(DC)(x+DC)

Substituting in the given values, (21)(9)=(8)(8+x)

So, 189=64+8x, meaning x = 15.625, or about 15.63.

Answer:

15.42, 25.49, 46.19

Step-by-step explanation:

although 32.28, 40.40 could also be considered

Answer:

The price is $29.75

Step-by-step explanation:

Because it is 15 percent off, that means that the jeans are priced at 100%-15%=85%. To convert a percent to a decimal, move the decimal two places to the left. This gives us .85. Multiply 35 by .85 and you will get 29.75. Hope this helps!

Answer:

30 degrees

Step-by-step explanation:

The angles of each side of a hexagon is 120 degrees.

The sum of interior angles in a shape is (n-2) * 180.

So,

(6-2) * 180 = 4 * 180 = 720 degrees

This is the total degrees of the hexagon.

Dividing the total degrees by 6 angles gives us 120 degrees for each angle.

Angle AEF = angle FED - angle AED.

Angle FED = 120 degrees

Angle AED = 90 degrees

120 - 90 = 30 degrees

Step-by-step explanation:

5.21× 3.4 = 17.714

thank u

Answer:

32 and 56?

Step-by-step explanation:

32 and 56 are related to 8.

32=8x4

56=8x7

The number that would fill a whole number of packages of hamburger buns is 32 ad 56.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

18, 32, 44, 56

We need to find which number can be evenly divided by 8 because there are 8 hamburger buns in a package.

Now,

18 is not divisible by 8, because 8 x 2 = 16, and 18 is greater than 16.

32 is divisible by 8 because 8 x 4 = 32.

44 is not divisible by 8, because 8 x 5 = 40, and 44 is greater than 40.

56 is divisible by 8 because 8 x 7 = 56.

Therefore,

32 and 56 would fill a whole number of packages of hamburger buns.

Learn more about expressions here:

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Answer:

Area= 7

Explanation: area of triangle is A=bh/2

b=2 h=7

7 x 2 = 14/2 = 7

Answer:

c; 63 square cm

Step-by-step explanation:

the area of a trapezoid can be described by the equation a = (1/2)(h)(b1 + b2)

this means the height times base 1 and base 2 added together divided by 2

(1/2)(6)(8 + 13) is the equation

this can become 3(21)

which is ultimitaly 63

Answer:

it's gonna be 63cm^2

Step-by-step explanation:

First, were gonna find the area of the rectangular portion, which is 8x6, which is 48cm^2

Next, well do the triangle part. So, we have to subtract 13-8 to get the width of the triangle.

Next, we have to find the area for the triangle. The formula is length x width / 2.

So, we have to multiply 6x5 to get 30.

Then, well divide it by 2, which will give us 15cm^2

Finally, we add the areas of rectangle and the triangle together. 15 + 48 is 63.

Bada-bing, bada-boom, we got 63cm^2 as our answer :)

Answer:

probably the answer to the following question is B and C I hove this helps because this numbers cannot be fraction only decimal

Answer:

(x-4) (x-1)

Step-by-step explanation:

X-4=0

x=4

X-1=0

X=1