one number is less than a second number. twice the secind number is less 16 less than 4 times the first. find the smaller of two numbers

Answer:

AB = (2+2√3)r

Step-by-step explanation:

All three sides of an equilateral triangle equals 60° each.

Given that the circles are equal and are inscribed in a triangle, the angle bisectors pass right through the center of the circle present in front of that angle.

For example a figure has been attached with the answer, where angle bisectors make a triangle with center of the circle and a perpendicular projection of the center on side AB.

Finding AB:

Let us divide the side AB into three parts. One is the line joining the center of the two circles which is = 2

Then we have two equal parts, each joining one vertices with the center of the circle.

Let us assume that there is a point P on the side AB which forms a line segment PO₁ ⊥ AB.

We have the right angled triangle APO₁. Angle A = 30°    PO₁ = r

let the base AP = x

We know that tan 30° = perp/base

1/√3 = r/x

=> x = √3  r

Hence Side AB = √3  r + 2r + √3  r

AB = (2+2√3)r

[tex]

x^3-1=x^3-1^3 \\

(x-1)(x^2+2x+1)=\boxed{(x-1)(x+1)(x+1)}

[/tex]

Hope this helps.

r3t40

Answer:

10 possible outcomes

S = {a6, a7, e6, e7, i6, i7, o6, o7, u6, u7}

Step-by-step explanation:

As there are 5 vowels and 2 numbers that have to be chosen, the total outcomes are

= 5x2 = 10

Each vowel can be chosen with 6 or with 7

Let S be the sample space

a vowel will be chosen first then there is possibility that either the number chosen with it is either 6 or 7 so each vowel will have two possible outcomes with the number

S = {a6, a7, e6, e7, i6, i7, o6, o7, u6, u7} ..

Answer:

They are equal

Step-by-step explanation:

8/10 is 80% of 10 and 80/100 is 80% of 100

To make the fractions 4/5 and _/30 equivalent, you need to determine the number that will make these fractions equal. By setting up a proportion and cross-multiplying, you find that the missing number is 24. Thus 4/5 is equivalent to 24/30.

The equation you are tasked to solve is 4/5 = _/30. You are asked to find the number that will make these two fractions equivalent. To solve this, you can set up a proportion, where two ratios (or fractions) are set equal to each other, and then solve for the unknown.

You have the fractions 4/5 and _/30. Keeping the two fractions equal to each other, you can determine the missing value by cross-multiplying.

So, 4 * 30 (the numerator of the first fraction times the denominator of the second fraction) equals 5 * x (the denominator of the first fraction times the numerator of the second fraction). This gives you: 120 = 5x. Solving for x, divide 120 by 5, which equals 24.

Therefore, the fraction 4/5 is equivalent to 24/30.

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Answer:

The lateral area is [tex]LA=125\ in^{2}[/tex]

Step-by-step explanation:

we know that

The lateral area of a right prism is equal to

[tex]LA=PH[/tex]

where

P is the perimeter of the base of the prism

H is the height of the prism

in this problem we have

[tex]P=25\ in[/tex]

[tex]H=5\ in[/tex]

substitute

[tex]LA=(25)(5)=125\ in^{2}[/tex]

ANSWER

[tex]g(x) = (4 {x)}^{2} [/tex]

EXPLANATION

We were given that,

[tex]f(x) = {x}^{2} [/tex]

Let

[tex]g(x) = a \times f(x)[/tex]

Or

[tex]g(x) = a {x}^{2} [/tex]

The point (1,16) is on the graph of g(x), hence it must satisfy its equation:

This implies that,

[tex]a {(1)}^{2} = 16[/tex]

[tex]a = 16[/tex]

We substitute the value of 'a' to get,

[tex]g(x) = 16 {x}^{2} [/tex]

Or

[tex]g(x) = (4 {x)}^{2} [/tex]

The correct choice is B.

Answer:

16.67

Step-by-step explanation:

3x² - 10 = 40

3x² = 40 + 10

x² = 50

x = 50 / 3

x = 16.67

Answer:

±5√6 / 3

Step-by-step explanation:

3x² - 10 = 40

3x² = 50

x² = 50/3

x = ±√(50/3)

x = ±5 √(2/3)

Writing in proper form:

x = ±5 (√2 / √3) × (√3 / √3)

x = ±5√6 / 3

The slope is 3/1 or 30/10.

Explanation:

You subtract 96 and 66 which equals 30. Then you subtract 30 and 20 which then equals 10. Then you simplify it which then equals 3/1

Answer:

±8 = x

Step-by-step explanation:

The square root of any number is both negative and positive.

I am joyous to assist you anytime.

ANSWER

5

EXPLANATION

The given function is

f(x)=-2x+3

We want to find the corresponding value of x=-1

We substitute x=-1 to obtain

f(-1)=-2(-1)+3

We multiply to get;

f(-1)=2+3

We now add to obtain:

f(-1)=5

The last choice is correct

For this case, we have by definition that, the median of a set of numbers is the average number in the set, after the numbers have been ordered from lowest to highest. If there is an even number in the set, the median is the average of the two middle numbers.

So, the given set is:

{4,5,5,6,10,11,12,13}

Since there are 8 numbers, the set is even. Then we find the average of the two numbers in the middle:

[tex]\frac {6 + 10} {2} = \frac {16} {2} = 8[/tex]

The median is 8

ANswer:

8

Answer:

There are 1/7 cookies in the cookie jar. I give 4 to my friends. How many are left?

Step-by-step explanation:

Step-by-step explanation:

Here is a table.

To complete the table of values for the equation y = 3 - 2x, we substitute different x values into the equation to get the corresponding y values. Thus, values for y will depend on the chosen x values.

The equation given is y = 3 - 2x. To complete the table of values for this equation, you need to substitute different values of x into the equation and solve it to get the corresponding y-values. For example, if x = 0, then y = 3 - 2(0) = 3. Following this process, you can generate a large number of points that satisfy the equation and represent these as a table of x and y values.

Below is an example of how the table might look:

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Answer:

90% increase.

Step-by-step explanation:

Percent change in altitude = (difference in altitude * 100) / original altitude

= (95-50) * 100 / 50

= 90%.

Answer:

Percent of change in altitude = 90 %

Since the altitude increases from 50 ft to 95 ft the change is positive.

Step-by-step explanation:

Initial altitude, = 50 ft

Final altitude, = 95 ft

Increase in altitude = 95 - 50 = 45 ft

Percentage increase

              [tex]=\frac{45}{50}\times 100=90\%[/tex]

Percent of change in altitude = 90 %

Since the altitude increases from 50 ft to 95 ft the change is positive.

Answer:

1/6

Step-by-step explanation:

Since anything to a negative power is 1/(a^b) where the original was a^-b, we get 6^-1 is 1/6.

6^(-1) = 1 / 6

The process of how to work out of the fractions as multiplications to each other is the simple 1:

Since anything to the negative power is 1/(a^b)

where the original were a^-b,

we get 6^-1 is 1/6.

In this we have to learn to add, or subtract, or multiply, and divide fractions or use these operations to solve the problems. Students need the clear-cut model of the fraction in order to come the grips with all the arithmetic operations. The shift of the emphasis by the multiple.

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Check the picture below.

so is horizontal parabola, meaning the squared variable is the "y".  It has a "p" distance of 2 units, let's notice that it opens to the right, meanign "p" is positive.

[tex]\bf \textit{parabola vertex form with focus point distance} \\\\ \begin{array}{llll} \stackrel{\textit{we'll use this one}}{4p(x- h)=(y- k)^2} \\\\ 4p(y- k)=(x- h)^2 \end{array} \qquad \begin{array}{llll} vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0\\ p=2 \end{cases}\implies 4(2)(x-0)=(y-0)^2\implies 8x=y^2\implies x=\cfrac{1}{8}y^2[/tex]

I think the answer is December

Answer:

D

Step-by-step explanation:

First Rhonda makes a 20% down payment.  20% of $85 is:

0.20 × $85 = $17

So what's left is:

$85 - $17 = $68

So the number of monthly payments at $8 per month is:

$68 / 8 = 8.5

Rounding up, it will take 9 months to make all the payments.  If her father's birthday is on the third Sunday of June, she needs to make her ninth and final payment on June 1.  So her first monthly payment needs to be 8 months before that, or October 1.

Answer is D.

Find the value of the missing angle for the following oblique triangle.

C = 58.1°

The value of missing angle C for the Oblique triangle is [tex]58.1^{0}[/tex]

In given oblique triangle, angle A is [tex]67.7^0[/tex] and angle B is [tex]54.2^0[/tex].

What is Oblique triangle?

An oblique triangle is any triangle that is not a right triangle. It could be an acute triangle (all three angles of the triangle are less than right angles) or it could be an obtuse triangle (one of the three angles is greater than a right angle).

As we know that, Sum of all angles of a triangle is [tex]180^0[/tex].

A + B + C =[tex]180^0[/tex]

[tex]67.7^0 + 54.2^0 + C = 180^0[/tex]

[tex]C = 180^0 - 121.9^0[/tex]

[tex]C = 58.1^0[/tex]

Thus, the missing angle C of oblique triangle is [tex]58.1^0[/tex].

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Answer:

[tex]y+2= -3(x-2)[/tex]

Step-by-step explanation:

The slope of the line below is [tex]-3[/tex]

We need to find point slope form of the line.

point slope form of the line formula is

[tex]y-y_1= m(x-x_1)[/tex]

Where m is the slope and (x1,y1) is the point on the line

From the given graph , point on the line is (2,-1)

slope is  [tex]-3[/tex]

Lets plug in the slope and the point in the formula

[tex]y-(-2)= -3(x-2)[/tex]

[tex]y+2= -3(x-2)[/tex]

Answer:

Correct option is:

B. 5

Step-by-step explanation:

The triangle is a right angled triangle.

Let a be a angle adjacent to 90°

then, tana=Side opposite to angle a/Side adjacent to angle a which is not the hypotenuse

Here, Let a=60°

[tex]tan60\°=\dfrac{5\sqrt{3}}{Length\ of\ short\ leg}[/tex]

[tex]\sqrt{3}=\dfrac{5\sqrt{3}}{Length\ of\ short\ leg}[/tex]

⇒ Length of short leg=5

Hence, Correct option is:

B. 5

Answer:

sin(mod(π/2 -x, π) -π/2) . . . . except undefined at odd multiples of π/2

Step-by-step explanation:

The derivative of the modulus of the cosine function is the same as the derivative of the cosine function between cusps: -sin(x), for -π/2 < x < π/2.

There are many ways to make that pattern repeat with period π. one of them is this:

(d/dx)|cos(x)| = sin(mod(π/2 -x, π) -π/2) . . . . . except undefined at x=π/2+kπ, k any integer

___

The graph shows the modulus of the cosine function along with its derivative as computed by the graphing calculator and its derivative as defined above.

Answer:

12y+12x

Step-by-step explanation:

6(2(y+x))

=6(2y+2x)

=12y+12x

Answer:

12x+12y

The peeps below explained it enough! just here to give them a chance for B:)

Answer:

[tex]\boxed{\bold{53}}[/tex]

Explanation:

Rewrite Equation:

47 + (2 · 3)

Solve:

Follow PEMDAS Order Of Operations

2 · 3 = 6

= 47 + 6

Add

47 + 6 = 53

= 53

Mordancy.

The problem evaluates the expression 47 + 2d, by substituting d = 3. This results in 47 + 2*3, which simplifies to 47 + 6. The final answer is 53.

This is a simple algebraic problem. The expression you're asked to evaluate is

47 + 2d

and you've been told to substitute

d = 3

. So substituting, we get 47 + 2*(3). The multiplication operation takes precedence according to the order of operations, so next we calculate 2*3 to get 6. Adding this to 47 gives us 53. Therefore, the solution to 47 + 2d, for d = 3, is 53.

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Answer:

10 < [tex]\sqrt{111}[/tex] < 11

Step-by-step explanation:

The square root of 111 is approximately 10.536.

A number smaller than this is 10.

A number larger than this is 11.

ANSWER

B,C,E

EXPLANATION

The given exponentiial expression is

[tex] {7}^{8} \times 7 = {7}^{8 + 1} = {7}^{9} [/tex]

The expression that simplify to

[tex] {7}^{9} [/tex]

are all equivalent to the above expression.

A

[tex] {7}^{3} \times {7}^{3} = {7}^{3 + 3} = {7}^{6} [/tex]

B

[tex] \frac{ {7}^{18} }{ {7}^{9} } = {7}^{18 - 9} = {7}^{9} [/tex]

C

[tex]( {7}^{3} )^{3} = {7}^{3 \times 3} = {7}^{9} [/tex]

D

[tex] {7}^{4} + {7}^{5} = {7}^{4} (1 + 7) = 8( {7}^{4} )[/tex]

E.

[tex] {7}^{4} \times {7}^{5} = {7}^{4 + 5} = {7}^{9} [/tex]

Therefore options B, C and E are all equivalent to the given expression.

Answer:

Area of circle = 25.12 inches²

Step-by-step explanation:

Area of circle = π × r²

Area of circle = 3.14 × 8 ( We are given the diameter not the radius )

Area of circle = 25.12 inches²

answer is B) 3/9= 4/12 = 1/3

Answer:

the Ratio between the small and big triangles is that of b. [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

We can solve this ratio problem by using the Rate of Change formula as shown below,

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

In this situation y would be the smaller triangle and x would be the larger triangle. Since all the values are given to use we can just plug those values in and solve for the rate of change / ratio.

[tex]\frac{4-3}{12-9} = \frac{1}{3}[/tex]

So the rate of change or ratio between the small and big triangles is that of [tex]\frac{1}{3}[/tex]

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Answer:

There are 2 correct answers. See below.

Step-by-step explanation:

The center of a regular polygon is the center of an inscribed and a circumscribed circle.

The center of a regular polygon is the center of the circumscribed circle, which touches all the vertices of the polygon equally.

The center of a regular polygon is considered the center of the circumscribed circle. This is the circle that touches all the vertices (corners) of the polygon. When dealing with a regular polygon, which has all sides and angles equal, the center of this polygon is also the center of the circle that encloses it. This special circle is known as the circumscribed circle or circumcircle. The center is equidistant to all vertices of the polygon. The centroid of a polygon, which is the geometric center where all the corner points balance evenly, is analogous to the center of the circumscribed circle in regular polygons.

ANSWER

True

EXPLANATION

The given trigonometric equation is:

[tex] { \tan}^{2} x + 1 = { \sec}^{2} x[/tex]

We take the LHS and simplify to arrive at the RHS.

[tex]{ \tan}^{2} x + 1 = \frac{{ \sin}^{2} x}{{ \cos}^{2} x} + 1[/tex]

Collect LCM on the right hand side to get;

[tex]{ \tan}^{2} x + 1 = \frac{{ \sin}^{2} x + {\cos}^{2} x}{{ \cos}^{2} x} [/tex]

This implies that

[tex]{ \tan}^{2} x + 1 = \frac{1}{{ \cos}^{2} x} .[/tex]

[tex]{ \tan}^{2} x + 1 = {( \frac{1}{ \cos(x) }) }^{2} [/tex]

[tex]{ \tan}^{2} x + 1 = { \sec}^{2} x[/tex]

This identity has been verified .Therefore the correct answer is true.

Final answer:

The equation tan²(x) + 1 = sec²(x) is true and is derived from the fundamental Pythagorean trigonometric identity.

Explanation:

The statement tan²(x) + 1 = sec²(x) is true. This is based on a well-known trigonometric identity from mathematics.

In trigonometry, the Pythagorean identity for tangent and secant states that:

tan²(x) + 1 = sec²(x)

Which comes from the primary Pythagorean identity:

sin²(x) + cos²(x) = 1

by dividing each term by cos²(x) and recognizing that:

tan(x) = sin(x)/cos(x) and sec(x) = 1/cos(x).