Mateo is thinking of a whole number .If he multiplies his number by 3, the answer is less than 30 .If he multiplies his number by 6, the answer is more that 40.There is more than one number that Mateo could be thinking off.
What is the sum of all of the numbers Mateo could be thinking of?

Answer:

42 m²

Step-by-step explanation:

Area of triangle = 1/2(b · h)

b = 7 m

h = 12 m

Let's solve

1/2(7 · 12) = 42 m²

So, the area of the triangle is 42 m²

Step-by-step explanation:

[tex] \tan( \alpha ) + \frac{1}{ \tan( \alpha ) } [/tex]

[tex] \frac{ { \tan( \alpha ) }^{2} + 1 }{ \tan( \alpha ) } [/tex]

use the identity

[tex] { \tan( \alpha ) }^{2} + 1 = { \sec( \alpha ) }^{2} [/tex]

so we have

[tex] \frac{ { \sec( \alpha ) }^{2} }{ \tan( \alpha ) } [/tex]

now we use the following id.

[tex] \sec( \alpha ) = \frac{1}{ \cos( \alpha ) } \: and \: \: \tan( \alpha) = \frac{ \sin( \alpha ) }{ \cos( \alpha ) } [/tex]

then, back to what we had

[tex] \frac{ \frac{1}{ { \cos( \alpha ) }^{2} } }{ \frac{ \sin( \alpha ) }{ \cos( \alpha ) } } [/tex]

and finally, this equals to what we wanted to prove

[tex] \frac{1}{ \sin( \alpha ) \cos( \alpha ) } [/tex]

Answer:

See below for proof.

Step-by-step explanation:

To prove the given trigonometric equation, we can use the following tangent trigonometric identities:

[tex]\boxed{\tan \theta=\dfrac{\sin \theta}{\cos \theta}}[/tex]     [tex]\boxed{\dfrac{1}{\tan \theta}=\dfrac{\cos \theta}{\sin \theta}}[/tex]

Therefore:

[tex]\tan \theta + \dfrac{1}{\tan \theta}=\dfrac{\sin \theta}{\cos \theta}+\dfrac{\cos \theta}{\sin \theta}[/tex]

Add the fractions on the right side of the equation:

[tex]\begin{aligned}\tan \theta + \dfrac{1}{\tan \theta}&=\dfrac{\sin \theta}{\cos \theta}+\dfrac{\cos \theta}{\sin \theta}\\\\ &=\dfrac{\sin \theta \cdot \sin \theta}{\cos \theta \cdot \sin \theta}+\dfrac{\cos \theta \cdot \cos \theta}{\sin \theta \cdot \cos \theta}\\\\ &=\dfrac{\sin^2 \theta }{\sin \theta \cos \theta}+\dfrac{\cos^2 \theta }{\sin \theta \cos \theta}\\\\&=\dfrac{\sin^2 \theta + \cos^2\theta}{\sin \theta \cos\theta}\end{aligned}[/tex]

Apply the identity sin²θ + cos²θ = 1:

[tex]\begin{aligned}\tan \theta + \dfrac{1}{\tan \theta}&=\dfrac{\sin \theta}{\cos \theta}+\dfrac{\cos \theta}{\sin \theta}\\\\ &=\dfrac{\sin \theta \cdot \sin \theta}{\cos \theta \cdot \sin \theta}+\dfrac{\cos \theta \cdot \cos \theta}{\sin \theta \cdot \cos \theta}\\\\ &=\dfrac{\sin^2 \theta }{\sin \theta \cos \theta}+\dfrac{\cos^2 \theta }{\sin \theta \cos \theta}\\\\&=\dfrac{\sin^2 \theta + \cos^2\theta}{\sin \theta \cos\theta}\\\\&=\dfrac{1}{\sin \theta \cos\theta}\end{aligned}[/tex]

Therefore, we have proved that:

[tex]\tan \theta + \dfrac{1}{\tan \theta}=\dfrac{1}{\sin \theta \cos\theta}[/tex]

The simplified answers are:

[tex]f(g(x)) = 6x + 2[/tex]

[tex]g(f(x)) = 6x + 9[/tex]

A function is a rule that assigns a unique output value to each input value. It is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. The input values are often referred to as the domain of the function, while the output values are referred to as the range.

To find f(g(x)), we first need to evaluate g(x) and then use the result as the input for f(x). So:

[tex]f(g(x)) = f(2x - 1)[/tex](substituting [tex]g(x) = 2x - 1)[/tex]

[tex]= 3(2x - 1) + 5[/tex](substituting[tex]f(x) = 3x + 5)[/tex]

[tex]= 6x - 3 + 5[/tex]

[tex]= 6x + 2[/tex]

Therefore, [tex]f(g(x)) = 6x + 2.[/tex]

To find g(f(x)), we follow a similar procedure:

[tex]g(f(x)) = g(3x + 5)[/tex] (substituting[tex]f(x) = 3x + 5)[/tex]

[tex]= 2(3x + 5) - 1[/tex] (substituting [tex]g(x) = 2x - 1)[/tex]

[tex]= 6x + 10 - 1[/tex]

[tex]= 6x + 9[/tex]

Therefore, [tex]g(f(x)) = 6x + 9[/tex].

So, the simplified answers are:

[tex]f(g(x)) = 6x + 2[/tex]

[tex]g(f(x)) = 6x + 9[/tex]

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Answer: the top left and top right are similar

Step-by-step explanation:

Similar means the sides are proportional meaning you multiplied the small one by the same number to get a shape that is "similar" (same angles, same shape just bigger or smaller.

So the first one, you multiply both sides by 2  (3x2) and (5x2) = 6x10 so yes similar

the second one isn't same shape so it is not similar

the third one doesn't have the same angles so it's not the same shape

the fourth one is not multiplied by same number to be increased

the fifth one is similar because it's the same shape but 3 times bigger

the bottom shape is the same exact shape but just flipped so it is congruent not similar

On solving the query we can say that The Yankees' chances of losing function when they score fewer than 5 runs are therefore around 0.33, or 33% (rounded to the nearest thousandth).

Mathematics is concerned with numbers and their variations, equations and related structures, shapes and their places, and possible placements for them. The relationship between a collection of inputs, each of which has an associated output, is referred to as a "function". An relationship between inputs and outputs, where each input yields a single, distinct output, is called a function. Each function has a domain and a codomain, often known as a scope. The letter f is frequently used to represent functions (x). X is the input. The four main types of functions that are offered are on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

P(A), P(B), and P(C) are all equal to 0.55.

The following formula may be used to determine the likelihood that the Yankees will lose when they score fewer than 5 runs:

P(C and not B) / P(not B) = P(C | not B)

We are aware of:

not B = the opposite of the occurrence B is the scenario in which the Yankees fail to score five runs in a game.

P(not B) = P(B) - 1.

Now, we may compute P(C | not B) using the formula below:

P(C and not B) / P(not B) = P(C | not B)

P(C | not B) is equal to 0.1419 / (1 - 0.57).

P(C | not B) = 0.1420 / 0.4330 P(C | not B) = 0.331

The Yankees' chances of losing when they score fewer than 5 runs are therefore around 0.33, or 33% (rounded to the nearest thousandth).

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On solving the query we can say that The Yankees' chances of losing function when they score fewer than 5 runs are therefore around 0.33, or 33% (rounded to the nearest thousandth).

What is function?

Mathematics is concerned with numbers and their variations, equations and related structures, shapes and their places, and possible placements for them. The relationship between a collection of inputs, each of which has an associated output, is referred to as a "function". An relationship between inputs and outputs, where each input yields a single, distinct output, is called a function. Each function has a domain and a codomain, often known as a scope. The letter f is frequently used to represent functions (x). X is the input. The four main types of functions that are offered are on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

P(A), P(B), and P(C) are all equal to 0.55.

The following formula may be used to determine the likelihood that the Yankees will lose when they score fewer than 5 runs:

P(C and not B) / P(not B) = P(C I not B)

We are aware of:

not B = the opposite of the occurrence B is the scenario in which the Yankees fail to score five runs in a game.

P(not B) = P(B)-1.

Now, we may compute P(C I not B) using the formula below:

P(C and not B)/ P(not B) = P(C I not B)

P(C❘ not B) is equal to 0.1419/(1 -0.57).

P(C❘ not B) 0.1420/0.4330 P(C❘ not B) = 0.331

The Yankees' chances of losing when they score

fewer than 5 runs are therefore around 0.33, or

33% (rounded to the nearest thousandth).

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1. The coordinates of Y is at Y(10, 0).

2. The equation for diagonal is y = 3/2x - 15

3. The equation for diagonal passing through Z is y = 7/2x - 35.

As from the coordinates of Y is at Y(10, 0).

2. The equation for diagonal is

(y - 0)= (4-10)/ (-4-0) (x - 10)

y= (-6)/ (-4) (x-10)

y = 3/2 (x-10)

y = 3/2x - 15

3. The equation for diagonal passing through Z

(y - 0)= (3-10)/ (-2-0) (x - 10)

y= (-7) / (-2) (x-10)

y = 7/2(x-10)

y = 7/2x - 35

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Answer:

Critical Numbers: 5 and 8

Minimums is f(4)

Maximum is f(5)

Step-by-step explanation:

Take the derivative of the function using the power rule to get

[tex]6x^2-78x+240\\x^2-13x+40\\(x-5)(x-8)[/tex]

This gives you the critical numbers then you have to evaluate at all points:

[tex]f(4) = 464 \\f(5) = 475\\f(8) = 448\\f(9) = 459[/tex]

Showing the minimum is f(4) and the maximum is f(5)

The equations among the answer choices which represent lines parallel to y = 6x + 2 are; Choice A; 12x - 2y = 4 and Choice B; y = 6x - 12.

It follows from the task content that the equations which are parallel to the given equation of the line; y = 6x + 2 is to be determined.

The slope of the given line is 6 by comparison with; y = mx + c where m = slope.

The given equations which are not in slope-intercept form can be expressed in slope intercept form as follows;

A). 12x - 2y = 4; y = 6x -2

B). y = 6x - 12

C). 6y = -x - 1; y = -x/6 - 1/6

D). y = 3x + 2

E). y = -x/6 + 7

Therefore, the equations which are parallel to; y = 6x + 2 as they have the same slope are;

Choice A; 12x - 2y = 4 and Choice B; y = 6x - 12.

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Answer:

Ginger cookie.

Oatmeal — Chocolate — Lemon — Ginger

Answer:

To find the interest earned by Wayne, we can use the simple interest formula:

I = P * r * t

Where:

I = interest earned

P = principal amount

r = interest rate per year

t = time period in years

In this case, we know that:

P = 4000 (the principal amount)

r is unknown (we'll come back to this)

t = 8 years (the time period)

We also know that the interest earned is 4.6, so we can substitute these values into the formula and solve for r:

4.6 = 4000 * r * 8

r = 4.6 / (4000 * 8) = 0.00014375

Now that we know the interest rate per year, we can use the simple interest formula to find the total interest earned by Wayne:

I = P * r * t = 4000 * 0.00014375 * 8 = 4.6

So Wayne earned 4.6 in interest over 8 years.

To find the total amount on the account, we can simply add the interest to the principal:

Total amount = Principal + Interest = 4000 + 4.6 = 4004.6

So the total amount on the account after 8 years is 4004.6.

Answer: The total amount on Wayne's account after 8 years is $5,472.

Step-by-step explanation:

To calculate the interest earned by Wayne, we can use the formula:

I = P * r * t

Where I is the interest, P is the principal amount, r is the interest rate, and t is the time in years.

In this case, Wayne earns 4.6% simple interest for 8 years on 4000. So, P = 4000, r = 0.046 (since 4.6% is equivalent to 0.046), and t = 8.

I = 4000 * 0.046 * 8

I = 1472

Therefore, Wayne earns $1,472 in interest.

To calculate the total amount on the account, we can add the interest to the principal:

Total amount = Principal + Interest

Total amount = 4000 + 1472

Total amount = $5,472

Therefore, the total amount on Wayne's account after 8 years is $5,472.

Answer:

1/6  

Step-by-step explanation:

The area of the circle is 100π in².

The area of the circle is the space occupied by the circle in a two-dimensional plane.

The area of the circle is calculated as,

Area = πr²

Given that the circumference of a circle is 20π in.

The radius of the circle is calculated  as,

C = 2πr

C = 2 x π x r

20π = 2 x π x r

r = 10 in

The area is calculated as,

Area = πr²

Area = π x ( 10)²

Area = 100π in²

Therefore, the area of the circle will be 100π in².

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Answer: 2, 7, 3, 7, 9, 3, 10, 3, 6, 5, 3, 7, 2, 5, 8

Answer:

2, 7, 3, 7, 9, 3, 10, 3, 6, 5, 3, 7, 2, 5, 8

14, 6, 5, 3, 7, 2, 4, 9, 6, 7, 3, 6, 5, 11, 3

Step-by-step explanation: Study Island

Helpful to try ratios

Example : 10 to 15 has 3-7 stars so that strongly supports random samples

Answer:

Step-by-step explanation:

The line for main street is 180 degrees.

If angle 3 is 110 degrees.

Angle 5 would be 180 - 110.

180 - 110

70.

Answer: 70 degrees.

Answer: P*0.06*(50/360) = 11900

Step-by-step explanation: good luck

Answer:

  1428000

Step-by-step explanation:

You want the principal that would result in interest of 11900 at a rate of 6% for a period of 50 days.

Ordinary interest is calculated on the basis of 360 days per year. The fraction of a year represented by 50 days is 50/360, so the interest formula tells us ...

  I = Prt . . . . . . . where P is the principal at rate r for t years

  11900 = P·0.06·(50/360)

  P = 11900/(0.06·50/360) = 1428000

The principal amount is 1428000.

Answer: 300/1

Step-by-step explanation:

You take the numerator and divide it by one because it will equal the numerator.

The value of x and line BD are 2.4 and 31.6

A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

Since the opposite sides of parallelogram are equal , AB = DC

13x-20 = 2x+6

13x -2x = 6+20

11x= 26

x = 26/11 = 2 4/11 = 2.4

BD = 2( 5x+4)

= 2(5 × 26/11 +4)

2( 130/11+4)

= 260/11 +8

= 31.6

therefore the values of x and BD are 2.4 and 31.6

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The probability that Jennifer selects a blue cube is 1/4 or 25%.

The probability that Jennifer selects a blue cube can be found by dividing the number of blue cubes by the total number of cubes:

P(selecting a blue cube) = number of blue cubes / total number of cubes

We are given that there are 5 blue cubes out of a total of 20 cubes:

P(selecting a blue cube) = 5/20

Simplifying this fraction by dividing both the numerator and denominator by 5, we get:

P(selecting a blue cube) = 1/4

Therefore, the probability that Jennifer selects a blue cube is 1/4 or 25%.

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Answer:

Step-by-step explanation:

To find the missing values, we can use the ROI formula:

ROI = Margin x Turnover

We are given that ROI is 70%. We can use this to solve for the missing values:

Margin x Turnover = 70%

We can rearrange this equation to solve for Margin:

Margin = ROI / Turnover

To find Turnover, we can use the formula:

Turnover = Sales / Average Operating Assets

Plugging in the given values, we get:

Turnover = $300,000 / $187,500 = 1.6

Now we can solve for Margin:

Margin = 70% / 1.6 = 43.75%

Therefore, the closest option is B) 40%.

Answer:

Step-by-step explanation:

01 hour 33 minutes

Answer:

Pythagorean identity: sin²Ф + cos²Ф = 1

Step-by-step explanation:

The sine, cosine, and tangent values of an angle in a right-angled triangle are related by the Pythagorean identity, a fundamental trigonometric identity: sin²Ф + cos²Ф = 1

Given: cos(a) = 0.4 (we can use this to identify sin(a) ),

sin²(a) + (0.4)² = 1

sin²(a) = 1 - (0.4)²

sin²(a) = 1 - 0.16

sin²(a) = 0.84

Taking sq. roots on both sides will give,

sin(a) = ±√0.84

Sine is positive in the first and second quadrants, which leads us to the following conclusion:

sin(a) = +√0.84

Thus, rounding to two decimal places, sin(a) is almost equal to 0.917 or 0.92.

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Answer:

The first statement goes with the middle equation

The second statement goes with the third equation.

The third statement goes with the first equation.

Step-by-step explanation:

1st statement:

There is only one adult and we know the cost of his/her skates.  It is $4.  We have 5 children but we do not know what the cost of their skates are so we use the variable x to stand for the cost of the skates.

2nd statement:

To find the profit, we would take what we sold the bags for and subtract out the cost of making the bags.  The variable would stand for the number of bags sold.

3rd statement:

It starts out 16 degrees and every hour falls 4 degrees.  The variable stands for how many hours have passed.

Helping in the name of Jesus.

Answer:

x=140

Step-by-step explanation:

The equation to calculate what divided by 5 equals 28 is as follows:

X/5 = 28

Where X is the answer. When we solve the equation by multiplying each side by 5, you get get:

X = 140

The statement which is true about the minimum values of the two quadratic functions presented in the question is f(x) and g(x) have the same minimum value. Therefore, the correct option is option C.

When  [tex]tan(\theta) = 1[/tex] , the value of  [tex]sin(\theta)[/tex] in quadrant III is [tex]\frac{-1}{\sqrt{2} }[/tex]. Therefore the correct option is option B.

First picture

Finding the vertex of each function, to determine the minimum values of functions. The vertex of a quadratic function in the form [tex]f(x) = ax^{2} +bx + c[/tex] can be find by the coordinates [tex](\frac{-b}{\ 2a} , f(\frac{-b}{\ 2a} ))[/tex].

For function [tex]f(x) = x^{2} +4x - 4[/tex], a = 1, b = 4. Substituting these values in vertex formula,

[tex]x = \frac{-b}{\ 2a} = \frac{-4}{\ (2\ *\ 1)} = -2[/tex]

Finding the value of f(-2):

[tex]f(-2) = (-2)^{2} + 4(-2) - 4[/tex]

= 4 - 8 - 4

= -8

So the vertex of f(x) is (-2, -8), and the minimum value is -8.

For function g(x)

From the values, the minimum value of g(x) is -8, which occurs when x = 0.

Comparing the minimum values of f(x) and g(x),

Minimum value of f(x) is -8

Minimum value of g(x) is -8

Therefore, the correct answer is: C. f(x) and g(x) have the same minimum value.

Second picture

In Quadrant III, x-coordinate and y-coordinate both are negative.

[tex]tan(\theta) = \frac{sin(\theta)}{cos(\theta)} = 1[/tex]

Since, [tex]cos(\theta)[/tex] is negative and [tex]tan(\theta) = 1[/tex], using the Pythagorean identity to find [tex]cos(\theta)[/tex],

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

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

[tex]cos^2(\theta) = \frac{1}{2}[/tex]

[tex]cos(\theta) = \sqrt{\frac{1}{2} }[/tex]

[tex]cos(theta) = -\frac{\ 1}{\sqrt{2} }[/tex]

⇒ [tex]sin(\theta) = tan(\theta) * cos(\theta)[/tex]

[tex]sin(\theta) = 1 * (-\frac{1}{\sqrt{2} } )[/tex]

[tex]sin(\theta) = -\frac{\ 1}{\sqrt{2} }[/tex]

Therefore, in Quadrant III, [tex]sin(\theta) = -\frac{\ 1}{\sqrt{2} }[/tex]

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Answer: -2/3, 2/3, 0, 4-i, and 4+i.

Step-by-step explanation:

A polynomial function of degree 5 with rational coefficients and the given zeros -2/3, 2/3, 0, and 4-i must have a complex conjugate of 4-i as another zero. Complex zeros of a polynomial with real coefficients always come in conjugate pairs. So, the other zero is 4+i.

Now we have all the zeros of the polynomial: -2/3, 2/3, 0, 4-i, and 4+i.

The exponential equation that models the situation is; y = 2,716·(0.85)ˣ

The amount of battery charge that will be in the phone after 6 hours therefore is 1024 milliamperes

An exponential equation is an equation that has the input variable as an exponent; y = a·bˣ

The rate at which the cell phone battery is losing battery charge = 15% per hour

The capacity of the iPhone X starts at 2,716 milliamperes

Therefore, the rate at which at which the battery is discharging is an exponential relationship. The equation that models the situation can therefore be expressed as follows;

y = 2,716 × (1 - 0.15)ˣ = 2,716 × (0.85)ˣ

Where;

y = The current battery charge

x = The number of hours the battery has been losing battery charge

When x = 6, we get;

y = 2,716 × (0.85)⁶ ≈ 1024

y = 1024

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The overall free throw success rate in the entire game is 25%

A rate is a ratio that compares two different quantities which have different units.

Success rate of free = number of free throw made ÷ total number of free throws × 100

In the first half,

represent the total free throw by x

40 = 2/x × 100

40x = 200

x = 200/20

x = 5

In the second half;

20 = 3/x × 100

20x = 300

x = 300/20

x = 15

Therefore the total success rate of free throw = total number of free throw made ÷ total number of free throws × 100

= (3+2)/(15+5)

= 5/20 × 100

= 25%

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