Two angles have measures of (x + 14)º and (3x – 15). What value of x will make the angles congruent? ​

Answer:

117/108

Step-by-step explanation:

First, let's find the area of the shaded parts. Since the shaded squares and triangles are the same size, then all shaded squares have sides 3 in. by 3 in. because the shaded square in the middle has sides 3 in. by 3 in.

We can also see that the shaded triangles have legs 6 in. and 6 in. because one of the shaded triangles in the figure are labeled 6 in by 6 in.

Now we can find the area of the shaded square and triangle (area of a square is side^2 while the area of a triangle is base*height/2).

Shaded Square Area: 3^2 = 9 in^2

Shaded Triangle Area: 6*6/2 = 18 in^2

There are 5 shaded squares and 4 shaded triangles, so we can determine the shaded area now:

Shaded Area: 9*5 + 18*4 = 45 + 72 = 117 in^2

Now we need to find the area of the white rectangles and the area of the white triangles. We can see that the sides of the white rectangles are 6 in. and 3 in. We can also see that the sides of the white triangles are 3 in and 3 in.

Now we can find the area of the white rectangle and the white triangle.

White Triangle Area: 3*3/2 = 9/2 = 4.5 in^2

White Rectangle Area: 3*6 = 18 in^2

There are 4 white rectangles and 8 white triangles, so we can determine the white area now:

White Area: 4*18 + 8*4.5 = 72 + 36 = 108 in^2

The ratio of the area of the shaded pieces to the area of the white pieces is 117/108.

Answer:

12/5 is the answer of your questions

thank you!!

Answer:

24

Step-by-step explanation:

Use the triangle area formula: A=1/2 (base)(height)

Plug in what we know: 216=1/2(18)(h)

Solve for h: (1/2)(18)=9.

216/9=24.

So, h=24

To check, plug it into the formula: 1/2(18)(24)= 216

there is no drawing how should I do

Answer:

It is larger by [tex]4*10^2[/tex]  times

Step-by-step explanation:

You use exponential division for this problem

first, divide 8 by 2

8/2 = 4

Then, look at 10^9 and 10^7

The bases of those numbers are the same, so you can just subtract the exponents since you're dividing.

[tex]10^9 / 10^7 = 10^{9-7} = 10^2[/tex]

Combine those two together to get:

4 * 10^2

Answer:

8

Step-by-step explanation:

8+12+4+3+14+1+9+13=64, 64/8=8

Answer:

44.6

Step-by-step explanation:

First, to answer this question, we need to find the mean of this data set. When finding the mean, you use the same process you use when averaging.

So we would do: 8 + 12 + 4 + 3 + 14 + 1 + 9 + 13/8

Our new fraction turns into 64/8, which we can then divide to give us 52.625. We can round up our new number to give us 52.6

We now need to find the absolute value of the difference between each data value and mean. In simple terms, we use the answer we got from our fraction and subtract it from each number in our cluster of numbers/data set. Keep in mind when subtracting you will get some negative numbers, but in this scenario we take away any negative sings, so we don't end up with any negative numbers.

8 - 52.6 = -44.6 = 44.6

12 - 52.6 = -40.6 = 40.6

4 - 52.6 = -48.6 = 48.6

3 - 52.6 = -49.6 = 49.6

14 - 52.6 = -38.6 = 38.6

1 - 52.6 = -51.6 = 51.6

9 - 52.6 = -43.6 = 43.6

13 - 52.6 = -39.6 = 39.6

Finally, we need to to the same process we used in our first step, just use the new numbers we have instead of our old numbers.

This gives us 356.8/8, which when divided, will leave us with 44.6.

Therefore, our answer is 44.6

Answer:

Step-by-step explanation:

what does each block mean

Answer:

  D.  y = 1.5x +5

Step-by-step explanation:

The offered answer choices are equations in slope-intercept form. The constant in the equation is the y-intercept, the value of distance when time is zero.

   y = mx +b . . . . m is slope; b is y-intercept

__

The table tells you that the distance value is 5 when the time value is 0. In the equation, that means ...

  b = 5

Only one answer choice matches:

  y = 1.5x +5

The only solution that is true about the dependent system of equations is "There are infinitely many solutions".

Inconsistent System

For a  system of equations to have no real solution, the lines of the equations must be parallel to each other.

Consistent System

1. Dependent Consistent System

For a system of the equation to be a Dependent Consistent System the system must have multiple solutions for which the lines of the equation must be coinciding.

2. Independent Consistent System

For a system of equations to be an Independent Consistent System, the system must have one unique solution for which the lines of the equation must intersect at a particular.

As discussed above the Dependent consistent system has infinitely many solutions as their line are coinciding, therefore, the only solution that is true about the dependent system of equations is "There are infinitely many solutions".

Learn more about the System of equations:

https://brainly.com/question/12895249

#SPJ1

Answer:

A = 5 [tex]\frac{5}{6}[/tex] ft²

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height ) , then

A = [tex]\frac{1}{2}[/tex] × 5 × 2 [tex]\frac{1}{3}[/tex] ← convert to improper fraction

   = [tex]\frac{5}{2}[/tex] × [tex]\frac{7}{3}[/tex]

   = [tex]\frac{5(7)}{2(3)}[/tex]

   = [tex]\frac{35}{6}[/tex]

   = 5 [tex]\frac{5}{6}[/tex] ft²

Answer:

the answer to 2/5x+7=-11 is X=-45

Step-by-step explanation:

Multiply both sides by 5 to get rid of the division giving you 2x+35=-55

isolate the x Value by moving all non x numbers to one side giving you 2x=-90

divide by 2 to get X alone giving you x=-45

Answer:

The answer is C and D.

Step-by-step explanation:

(-4)^1/2 = undefined

(-16)^1/4 = undefined

(-32)^1/5 = -2

(-8)^1/3 = -2

Answer:

the answer should be 1,600,000

Step-by-step explanation:

hope this helps ya!!

Answer:

Step-by-step explanation:

1,5x0,000   x holds the place that you'll want to note if it's 5 or larger, to determine if you round up or down.   Because in the problem you've been given, it's an 8,   so round up

1,600,000  is the answer then.  

Answer:

Look up the website for those answers, I've gotten those type of worksheets before.

Step-by-step explanation:

There should be a pdf or document of the answers and if you can't find it I'll help you!

[tex]I=\displaystyle \int ^{\pi}_{\tfrac{\pi}3} \dfrac{ \sin x}{1 + \cos^2 x} dx\\ \\\\\text{let,}\\\\~~~~~u=\cos x\\\\\implies \dfrac{du}{dx} =-\sin x\\ \\\implies \sin x~~ dx = -du\\\\\text{When}~~ x = \pi , ~~ u = \cos \pi = -1\\\\\text{When}~~ x = \dfrac{\pi}3 , ~~u = \cos \dfrac{\pi}3 =\dfrac 12\\ \\\\I =- \displaystyle \int ^{-1}_{\tfrac 12} \dfrac{du}{1+u^2}\\\\\\[/tex]

  [tex]=\displaystyle \int ^{\tfrac 12}_{-1} \dfrac{du}{1+u^2}~~~~~~~~~~;\left[\displaystyle \int^{a}_b f(x) dx = - \displaystyle \int^{b}_a f(x) dx ,~ b < a\right]\\\\\\=\left[\tan^{-1} u \right]^{\tfrac 12}_{-1}~~~~~~~~;\left[ \ddisplaystyle \int \dfrac{dx}{ 1+ x^2} = \tan^{-1} x + C \right]\\\\\\=\tan^{-1} \left( \dfrac 12 \right) + \tan^{-1} 1\\\\\\=\tan^{-1} \left( \dfrac 12 \right) + \dfrac{\pi}4 \\\\\\=1.249[/tex]

Answer:

Given equation:  [tex]y=x^2+1[/tex]

Therefore, we can say that any point on the curve has the coordinates [tex](a, a^2+1)[/tex]  (where a is any constant)

To find the gradient of the tangent to the curve at any given point, differentiate the equation.

Given equation:

[tex]y=x^2+1[/tex]

[tex]\implies \dfrac{dy}{dx}=2x[/tex]

Therefore, the gradient at point [tex](a, a^2+1)[/tex] is [tex]2a[/tex]

Using the point-slope form of linear equation, we can create a general equation of the tangent at point [tex](a, a^2+1)[/tex]:

[tex]\begin{aligned}y-y_1 & =m(x-x_1)\\ \implies y-(a^2+1)& =2a(x-a)\end{aligned}[/tex]

[tex]\implies y=2ax-2a^2+a^2+1[/tex]

[tex]\implies y=2ax-a^2+1[/tex]

Given that the tangents pass through point (-1, -3), input this into the general equation of the tangent:

[tex]\begin{aligned}y &=2ax-a^2+1\\ \implies -3 & =2a(-1)-a^2+1\end{aligned}[/tex]

[tex]\implies 0=-2a-a^2+1+3[/tex]

[tex]\implies a^2+2a-4=0[/tex]

Use the quadratic formula to solve for a:

[tex]\implies a=\dfrac{-2\pm\sqrt{2^2-4(1)(-4)}}{2(1)}[/tex]

[tex]\implies a=\dfrac{-2\pm2\sqrt{5}}{2}[/tex]

[tex]\implies a=-1 \pm \sqrt{5}[/tex]

Input the found values of a into the general equation of the tangent to create the equations of the two lines:

[tex]\begin{aligned}a=-1+\sqrt{5}\implies y & =2(-1+\sqrt{5})x-(-1+\sqrt{5})^2+1\\ y & =(-2+2\sqrt{5})x-(6-2\sqrt{5})+1\\ y & =(-2+2\sqrt{5})x+2\sqrt{5}-5 \end{aligned}[/tex]

[tex]\begin{aligned}a=-1-\sqrt{5}\implies y & =2(-1-\sqrt{5})x-(-1-\sqrt{5})^2+1\\ y & =(-2-2\sqrt{5})x-(6+2\sqrt{5})+1\\ y & =(-2-2\sqrt{5})x-2\sqrt{5}-5 \end{aligned}[/tex]

Therefore, the equations of the two lines that pass through the point (-1, -3) and are tangent to the graph of [tex]y=x^2+1[/tex] are:

[tex]y=(-2+2\sqrt{5})x+2\sqrt{5}-5[/tex]

[tex]y=(-2-2\sqrt{5})x-2\sqrt{5}-5[/tex]

We are asked to solve the integral:

[tex]{:\implies \quad \displaystyle \sf \int \dfrac{dx}{\cos^{2}(x)-\tan (x)\cos^{2}(x)}}[/tex]

Re write as

[tex]{:\implies \quad \displaystyle \sf \int \dfrac{dx}{\cos^{2}(x)\{1-\tan (x)\}}}[/tex]

Using (1/cos x) = sec(x), we have

[tex]{:\implies \quad \displaystyle \sf \int \dfrac{\sec^{2}(x)dx}{1-\tan (x)}}[/tex]

Now, substitute 1 - tan (x) = t, so that -dt = sec²(x) dx

[tex]{:\implies \quad \displaystyle \sf -\int \dfrac{1}{t}dt}[/tex]

[tex]{:\implies \quad \sf log|t|+C}[/tex]

[tex]{:\implies \quad \boxed{\displaystyle \bf \int \dfrac{dx}{\cos^{2}(x)-\tan (x)\cos^{2}(x)}=-log|1-\tan (x)|+C}}[/tex]

Where, C is any Arbitrary Constant

Answer:

  radius: 14.96 in

  length: 47 in

Step-by-step explanation:

The dimensions of the package with maximum volume can be found by differentiating the volume function, subject to the constraint on the dimensions.

__

The volume of the cylindrical package is ...

  V = πr²h

The constraint on the dimensions is ...

  circumference + length = 141 inches

  2πr +h = 141 . . . . . at maximum volume

Solving the second equation for h, we can write the volume function in terms of r alone:

  h = 141 -2πr

  V = πr²(141 -2πr) . . . . substitute for h

  V = 141πr² -2π²r³ . . . eliminate parentheses

__

Differentiating with respect to radius, we find the radius at maximum volume must satisfy ...

  V' = 282πr -6π²r² = 0

Dividing by 6πr, we can simplify this to ...

  47 -πr = 0

  r = 47/π ≈ 14.96 . . . . inches (radius)

  h = 141 -2πr = 47 . . . inches (length)

This is about optimization problems in mathematics.

Dimensions; Height = 48 inches; Radius =  48/π inches

We are told the combined length and girth is 144 inches.

Girth is same as perimeter which is circumference of the circular side.

Thus; Girth = 2πr

If length of cylinder is h, then we have;

2πr + h = 144

h = 144 - 2πr

Now, to find the dimensions at which the max volume can be sent;

Volume of cylinder; V = πr²h

Let us put 144 - 2πr for h to get;

V = πr²(144 - 2πr)

V = 144πr² - 2π²r³

Differentiating with respect to r gives;

dV/dr = 288πr - 6π²r²

Radius for max volume will be when dV/dr = 0

Thus; 288πr - 6π²r² = 0

Add 6π²r² to both sides to get;

288πr = 6π²r²

Rearranging gives;

288/6 = (π²r²)/πr

48 = πr

r = 48/π inches

Put 48/π for r in h = 144 - 2πr to get;

h = 144 - 2π(48/π)

h = 144 - 96

h = 48 inches

Step-by-step explanation:

Answer:

3x-5?

Step-by-step explanation:

I hope im right.

Answer:

Step-by-step explanation:

The rate of change is defined as the derivative of the function, or also known as the slope. The derivative here would be 3. Another function which has the same rate of change would be any function with a slope of 3. A few example are:

f(x) = 3x + 1

f(x) = 3x + 2

Answer:

(x - 4)^2 + (y - 6)^2 = 100

Answer:

$2.25 per lb

Step-by-step explanation:

x = 4.50/2

x = $2.25 per lb

Answer:

( 2, 60 )

Step-by-step explanation:

→ Read along the x - axis and then the y axis

Answer:

5mm

Step-by-step explanation:

Because, the radius is: It is the line between any point on the circle and the midpoint of the circle..

Answer:

Step-by-step explanation:

h=b+2(assume h is hieght and b is base)

b*(b+2)=60

bb+2b=60

b=-1+√61

h=1+√61

Answer:

base=10

height=12

Step-by-step explanation:

Area of triangle formula is given by: A = (1/2)*b*h

where b: base of the triangle

           h: height of the triangle

Given that: h=b+2

                  A= 60 square yards

Solution:

60= (1/2)*b*(b+2)

[tex]\frac{b(b+2)}{2}[/tex] = 60

b²+2b=120

b²+2b-120=0

We got the quadratic equation: b²+2b-120=0

solve it to find b:  

Let x: coefficient of b² (x=1)

Let y: coefficient of b  (y=2)

Let z: constant (z= -120)

discriminant= y² - 4xz = 4 - 4(1)(-120) = 484

discriminant>0 so the equation has two roots:

b1= (-y-redical discriminant)/2x = (-2-redical(484))/2 = -12

b2= (-y+redical discriminant)/2x = (-2+redical(484))/2 = 10

b1= -12 is rejected because the base can't be negative

So b2=base=10

Now that we found the base, substitute to get the height:

h= b+2 = 10+2 =12

So height=12

radius= 7 ft

the circumference of the circle.

[tex]c = 2\pi \: r[/tex]

[tex]c = 2 \times \pi \times 7[/tex]

[tex]c = 43.9823[/tex]

[tex]c = 43.98 \: ft[/tex]

therefore, the circumference of the circle is 43.98 ft

Answer:

The answer is c

Step-by-step explanation: