Find the solution to the system of equations.

Answer:

see explanation

Step-by-step explanation:

Using Pythagoras' identity on the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

AC² = AB² + BC² , substitute values

AC² = 9² + 12² = 81 + 144 = 225 ( take the square root of both sides )

AC = [tex]\sqrt{225}[/tex] = 15 cm

-------------------------------------------

The area of Δ ABC is calculated as

A = [tex]\frac{1}{2}[/tex] × BC × AB = [tex]\frac{1}{2}[/tex] × 12 × 9 = 6 × 9 = 54 cm²

Answer:

There is not enough information to compare the volume of the prisms.

Step-by-step explanation:

To find the volume of rectangular prisms, the length , width and height must be given. The volume of rectangular prisms is gotten by multiplying the three dimension: length, width and height which is expressed in cubic units. To compare the two volumes, the three dimensions must be given.

Hence, there is not enough information to compare.

Answer:

[tex]x = 49.8^\circ\\y = 54.6^\circ[/tex]

Step-by-step explanation:

Kindly refer to the image attached in the answer region for labeling of triangle.

AB = 16

BC = 19

AC = 15

[tex]\angle ABC = x^\circ\\\angle ACB = y^\circ[/tex]

We have to find the angles x and y i.e. [tex]\angle B \text{ and }\angle C[/tex].

Formula for cosine rule:

[tex]cos B = \dfrac{a^{2}+c^{2}-b^{2}}{2ac}[/tex]

Where  

a is the side opposite to [tex]\angle A[/tex],

b is the side opposite to [tex]\angle B[/tex]  and

c is the side opposite to [tex]\angle C[/tex].

[tex]\Rightarrow cos x = \dfrac{19^{2}+16^{2}-15^{2}}{2 \times 19 \times 16}\\\Rightarrow cos x = \dfrac{392}{608} \\\Rightarrow x = 49.8^\circ[/tex]

Similarly, for finding the value of y:

[tex]cos C = \dfrac{a^{2}+b^{2}-c^{2}}{2ab}\\\Rightarrow cos y = \dfrac{19^{2}+15^{2}-16^{2}}{2 \times 19 \times 15}\\\Rightarrow cos y = \dfrac{330}{570}\\\Rightarrow y = 54.6^\circ[/tex]

Hence, the values are:

[tex]x = 49.8^\circ\\y = 54.6^\circ[/tex]

Answer:

Step 1: Variables are q for quarters and d for dimes. So d = dimes and q = quarters

Step 2: The two equations that form a system of equations are:

[tex]\left \{ {{0.1d+.25q=3.70} \atop {d+q=19}} \right.[/tex]

Step 3: Work is shown on the attachment and on the step-by-step explanation

Step 4: Given the context of the problem, the solution of the amount of dimes and quarters, which is 7 dimes and 12 quarters, is needed to satisfy both systems to concur that there was 7 dimes and 12 quarters in a sum of money that amounted to $3.70 with 19 coins in total.

Step-by-step explanation:

Step 1: To first attempt to solve this, we must have to set up two variables for the amount of value a quarter and a dime has. So since a quarter is worth 0.25¢ in and a dime is worth 0.10¢, then we can set up one of the equations to be:

[tex]0.1d + .25q = 3.70[/tex]

And we set it to equal the $3.70 because that's the amount that the sum of money totals to.

Step 2: Now to get the other side of the equation, we use the variables again, d and q and set that to equal 19 because that is the amount of coins that there is in total.

Step 3: Now that we have both equations, we can solve the problem now.

[tex]\left \{ {{0.1d+.25q=3.70} \atop {d+q=19}} \right.[/tex]

Let's first solve this equation by setting one of the side's variables the same absolute value, but not the same integer value so that we can cross it off. I will choose the equation [tex]d+q=19[/tex] to be multiplied by -.1 so that we can cross off both 0.1d and -0.1d after the result of the multiplication:

[tex]\left \{ {{0.1d+.25q=3.70} \atop {-.1d+-.1q=-1.9}} \right.[/tex]

Now, lets cross off everything that we can, and add up the variables together. This includes adding .25q + (-.1q) and adding 3.70 + -1.9.

Now we have:

[tex]\left \{ {{.25q=3.70} \atop {-.1q=-1.9}} \right.[/tex]

Now, what we do from here is add the left side and the right side side to get one equation, which is:

[tex].15q=1.8[/tex]

Finally, we divide both sides to get q=12, which means that there are 12 quarters. Since there are 19 coins in total, we can subtract 12 from 9 to get the remaining amount of dimes, which is 7.

In conclusion, q=12 and d=7.

My written work is also provided in the attachment!!!

Step 4: What does this mean in the context of the question?

This basically means that the solution of the amount of dimes and quarters, which is 7 dimes and 12 quarters, is needed to satisfy both systems to concur that there was 7 dimes and 12 quarters in a sum of money that amounted to $3.70 with 19 coins in total.

In simpler terms, this means that we need 7 dimes and 12 quarters to satisfy that there was a sum of money that amounted to $3.70 with 19 coins in total .

Answer:

Step-by-step explanation:

We will use the area of the circle to find the radius of the circle since that's all that that is useful for! If the area of the circle is 56 cm squared, then

[tex]56=\pi r^2[/tex]  and

[tex]\frac{56}{\pi}=r^2[/tex]  and

[tex]17.82535363=r^2[/tex] so

r = 4.222 cm

Now that we know that, we will use that.  But first, if we have a square circumscribed in a circle, then we know that from the center of the circle to any of the vertices of the square is the radius of the circle, 4.222. If we split that square into 4 triangles, pull one of those triangles out, we have a right triangle...45-45-90 to be specific.  Just for the sake of argument, put the 90 degree angle as the vertex angle of that right triangle and then split THAT triangle in half by dropping an altitude from the vertex angle to the base.  We still have a 45-45-90 triangle, but now the vertex angle is 45, one of the base angles is 90, and the other base angle is 45.  The hypotenuse of that triangle is the length of the radius we just found.  If the base angle is 45 and the hypotenuse is 4.222, we can use right triangle trig to find the length of the base of that triangle which, consequently, is half of the length of x, our unknown.

[tex]sin(45)=\frac{x}{4.222}[/tex] and

4.222 sin(45) = x so

x = 2.9854

But don't forget that that x is only half the length of one of the sides of the square.  So multiply it by 2 to get that the side length, which is x, is

x = 5.97

it is b.9 because u have to multiply (w×h×l)/3

Answer:

9

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

Answer:

Length l = 8 m

The length of one side of the square is 8 m

Step-by-step explanation:

The area of a rectangle is;

Area = length × breadth

Given;

Length = 32 m

Breadth = 2 m

Area of the rectangle can be expressed as;

A = 32 × 2 = 64 m^2

Area of a square is;

Area = length × length = l^2

Since the area of the square is equal to the area of the rectangle, then the area of the square is 64 m^2

A = l^2

64 = l^2

l = √64

l = 8 m

The length of one side of the square is 8 m

Answer:

3X=180    and   or   5X=300

X being the constant of how many miles they traveled per hour (which is 60)

Step-by-step explanation:

Not the best but hoped it helped

Answer:

y = 60x

Step-by-step explanation:

Just did it on Edmentum and got it right

Answer:

x = 42 and y = 92

Step-by-step explanation:

Since there are parallel lines, then

x = 42 ( Alternate angles )

The external angle of a triangle is equal to the sum of the 2 opposite interior angles.

134° is an external angle to the triangle, thus

x + y = 134 , that is

42 + y = 134 ( subtract 42 from both sides )

y = 92

----------------------------------------------------

(b)

The sum of the interior angles of a polygon are

sum = 180° (n - 2) ← n is the number of sides

Here n = 7, thus

sum = 180° × 5 = 900°

Answer:

(3) 49

Step-by-step explanation:

The circle diagram is attached below. angle mVS = 146°

and  angle mST =  64°.

mWT = 360 -64 - 146 = 150 (angle at a point)

∠ VWS = 73° = mVS / 2

MVW = 180 - 146 = 34 (angle in a straight line)

MVW = 180 -73 - 34 = 73° (angle in a triangle)

∠TMR = 180 - 64 = 116° (angle on a straight line)

∠VMT = 116 + 34 = 150°

∠ MVT = ∠ MTV (base angles of an isosceles triangle)

150 +2∠ mTV = 180

∠ MTV = 15°

∠RVW = 73 - 15 = 58°

∠RVW + ∠ VWS  + ∠VRW = 180

∠VRW  = 180 - 58 - 73 = 49

area of rectangle : length x width

1) 7 x 5 = 35

area = 35 in^2

2) area of trapezoid : (a+b)h/2

area = 272 cm^2

3) area = 45.5 in^2

4) area of rhombus : base x height

area =  80 m^2

5) area = 108 cm^2

Answer:

number one is 35in its important to say inches after but in the abbreviation

Step-by-step explanation:

if you need to show your work then put on the side of it

  7in

x 5in

-------

  35in

Answer:

my best guess even though no answers i would say bout 12

Step-by-step explanation:

The maximum amount of water that the bottle can hold is approximately 263.8938 cubic inches.

A cone is a three-dimensional geometric form with a flat base and a smooth, tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that link the base's points to the apex, which is a common point on a plane that does not include the base.

To find the maximum amount of water that the bottle can hold, we need to calculate the volumes of the cylinder and the cone and add them together.

The volume of the cylinder:

V_cylinder = πr²h

where r is the radius (half of the diameter) of the base, and h is the height of the cylinder.

The radius of the cylinder base is 6/2 = 3 inches, and the height of the cylinder is 8.5 inches, so:

V_cylinder = π(3)²(8.5)

V_cylinder ≈ 226.1947 cubic inches

Volume of the cone:

V_cone = (1/3)πr²h

where r is the radius of the base of the cone, and h is the height of the cone.

The radius of the base of the cone is also 3 inches, and the height of the cone can be found by subtracting the height of the cylinder from the total height of the bottle:

h_cone = total height - height of cylinder = 12.5 - 8.5 = 4 inches

So:

V_cone = (1/3)π(3)²(4)

V_cone ≈ 37.6991 cubic inches

Total volume:

V_total = V_cylinder + V_cone

V_total ≈ 226.1947 + 37.6991

V_total ≈ 263.8938 cubic inches

Therefore, the maximum amount of water that the bottle can hold is approximately 263.8938 cubic inches.

To learn more about the cone;

brainly.com/question/16394302

#SPJ3

Answer:

[tex]a=6[/tex]

Step-by-step explanation:

[tex]-6(2+a)=-48\\-6*2 = -12\\-6*a = -6a\\\rightarrow -12-6a=-48\\-12+12-6a=-48+12\\\rightarrow-6a=-36\\\frac{-6a}{-6}=\frac{-36}{-6} \\\boxed {a=6}[/tex]

Brainilest Appreciated!

Answer:

When you dilate a shape by a scale factor of 2, you are just multiply the coordinates by 2.

So the points become:

A(2, 3)  ===>  A'(4, 6)

B(3, 5)  ===>  B'(6, 10)

C(7,4)   ===>  C'(14,8)

Answer:

Solve the equation for  x  by finding  a ,  b , and  c  of the quadratic then applying the quadratic formula.

Step-by-step explanation:

Exact Form:

x = -5±√ 5/2

Decimal Form:

x  =  − 1.38196601 … ,  − 3.61803398 …

Answer:

36

Step-by-step explanation:

36 is the only one that is a perfect square, via 6*6

A)

X/3 -2 = 6

Add 2 to both sides:

X/3 = 8

Multiply both sides by 3:

X = 24

B)

X/5 +1 = 5

Subtract 1 from both sides:

X/5 = 4

Multiply both sides by 5:

X = 20

Answer:

a) 24.

b) 20.

Step-by-step explanation:

a) x/3 - 2 = 6

x/3 = 6 + 2 = 8

x = 3*8

x = 24.

b).  x/5 + 1 = 5

x/5 = 5 - 1 = 4

x = 5*4

x = 20.

Answer:

Brianna

Step-by-step explanation:

Hope this helps E2020

Answer: The answer is none of the above

Step-by-step explanation: I did it on khan academy

Answer: 3 positive integers.

Step-by-step explanation:

This can be translated to:

"how many integer numbers have the same number of digits in their cubes and squares?"

for example, a number that will be an option is 2:

Because 2*2 = 4

               2*2*2 = 8

the square and cube of 2 have the same number of digits.

3 for example:

3*3 = 9

3*3*3 = 27

does not match the condition.

1 does match it, obviusly.

0 is not positive, so we can ignore it.

let's see 4.

4*4 = 16

4*4*4 = 64

So 4 is other number that matches the condition.

Now, 5:

5*5 = 25

5*5*5 = 125

5 does not match the condition, and any number upper than 5 also does not match the condition.

so the numbers we have are 1, 2 and 4.

so we have 3 integers.

Answer:

(x-9)(x-3)

Step-by-step explanation:

Look to the number on the right, 27, and list out the factors. (1 and 27, 3 and 9, -1 and -27, -3 and -9)

Next, find the factors that would equal the middle number, -12, when added. -3 and -9 add to -12. Therefore, choose these numbers and put them in the form (x-9)(x-3).

Answer:

D

Step-by-step explanation:

edge2022

Answer:

312 employees participated in the training

Step-by-step explanation:

Given;

employee to instructor ratio is 24 to 2

there are 26 instructors for the training

let the total number of instructors be I = 26

let the total number of employees be e = ?

employee to instructor ratio is 24 to 2, e : I = 24 : 2

e : I = 24 : 2  = e : 26

[tex]\frac{24}{2} = \frac{e}{26} \\\\e = 12 *26\\\\e = 312[/tex]

Therefore, the total number of employees who participated in the training is 312

Answer:

First one

Step-by-step explanation:

5sin(3pix)+8=4

5sin(3pix) = -4

sin(3pi x) = -0.8

Basic angle: sin^-1(0.8) = 0.927295218

3pi x = pi+0.927295218, 2pi-0.927295218

3pi x = 4.068887872, 5.355890089, 4.068887872 + 2pi, 5.355890089 + 2pi, 4.068887872 + 4pi, 5.355890089 + 4pi,

x = above values/3pi

x = 0.43217, 0.568, 1.0984, 1.235, 1.765, 1.9016

Answer:

i think its both the cone and the semi cirle on top

Answer:

1/6

Step-by-step explanation:

Since you are rolling the die only one time there is only one way of you getting a 6 and that is rolling an actual 6. There are six sides to the die so you take the one 6 out of the the others and there is your probability.

Answer:

5/36

Step-by-step explanation:

I got it right

Answer:

3XY

Step-by-step explanation:

Answer:

The answer is 904.778 [tex]ft^3[/tex].

Step-by-step explanation:

-You first need the formula for the volume of a cylinder:

[tex]V = \pi r^2h[/tex]

-Take the radius and the height of the cylinder for the formula:

[tex]V = \pi 6^2 8[/tex]

-Then, you solve the formula:

[tex]V = \pi 6^2 8[/tex]

[tex]V = \pi \times 6^2 \times 8[/tex]

[tex]V = \pi \times 36 \times 8[/tex]

[tex]V = \pi \times 288[/tex]

[tex]V = 288\pi \approx 904.778[/tex]

So, the answer is 904.778 [tex]ft^3[/tex].

Answer:

2.30 = ?

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp side/ hypotenuse

sin 50 = ? / 3

Multiply each side by 3

3 sin 50 = ?

2.298133329 = ?

To the nearest hundredth

2.30 = ?

Step-by-step explanation:

Negative four

-4

Equal to x

-4=x

Divided by five

-4=x/5

Plus six

-4=x/5 +6

Interpretation in the picture above

Solution

Multiply through with 5

5×-4=5×x/5 + 5×6 as shown in the second picture

-20=x+30

Collect like terms

-20-30=x

-50=x or x=-50