Evaluate a + b for a = 2 and b = 3.

Answer:

see below

Step-by-step explanation:

x < 4

x is less than 4

Since it is less than, there is an open circle at 4

less than means the line goes to the left

Answer:

Since, when a function f(x) is reflected across x-axis then resultant function is -f(x), and reflected across y-axis then resultant function is f(-x),

Also, In translation of f(x),

If the transformed function is,

g(x) = f(x+a)

If a is positive then function is shifted a unit left,

If a is negative then function is shifted a unit right,

While, if transformed function is,

g(x) = f(x) + a

If a is positive then function is shifted a unit up,

If a is negative then function is shifted a unit right,

Here, the given parent function is,

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

Hence, by the above explanation we can match the unction formula with the corresponding transformation, shown below,

1. [tex]y=-x^2-1[/tex]  : Reflected across the y-axis

2. [tex]y=-(x - 1)^2 - 1[/tex]  : Translated right by 1 unit

3. [tex]y= x^2 +1[/tex] : Reflected across the x-axis

4.[tex]y=-x^2[/tex]  : Translated up by 1 unit

5. [tex]y=-(x+ 1)^2 - 1[/tex]  : Translated left by 1 unit

6. [tex]y=-x2 - 2[/tex]  : Translated down by 1 unit

Answer:

Uhm, you can write anything. Most poems don't even have to have a rhyme in them.

Just think of anything that can make some since.

Answer:

Hey Buddy here is one of the rhyme I made

Hope it helps

Step-by-step explanation:

When we open a math book,

Rocky jumps in horror and says " Look!

What do you mean by f(x) and g(x)?

I think its worst than a T-Rex"

At that moment our class nerd says "Those are functions!

And they both have no distinctions"

The teacher being happy tells the nerd to explain it

We all wanted to quit but our teacher was strict.

He started off by telling that there different types of functions

like monomial, binomial, trinomial and polynomial functions.

But as soon as he was going to say his second sentence

The bell rang and that was the bell of independence.

Answer:

B just took it.

Step-by-step explanation:

The fact that all right angles can be bisected is not a postulate of Euclidean geometry.

Euclidean geometry is the classical form of geometry first described by Euclid in his work Elements. He gathered all the mathematical knowledge known to the Greeks at the time, today his work presents itself as the first known axiomatization in the history of mathematics.

Originally, it was only cultivated on a plane and in three-dimensional space, at the same time linking it with the physical world that it was supposed to describe, thus preventing the possibility of studying other varieties of geometry.

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Answer:

θ = 240

and

cos(θ) = -0.5

Step-by-step explanation:

Theta is in the third quadrant, that meansit goes from 180 to 270 degrees

Then,

cos^2 (θ) =1/4

cos (θ) = ± 1/2

θ = arccos(0.5)

θ = 60

But in the third quadrant

θ = 180 + 60  = 240

θ = 240

and

cos(θ) = -0.5

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x\cdot 3^{-4}=32\implies x\cdot \cfrac{1}{3^4}=32\implies \cfrac{x}{81}=32\implies x=2592[/tex]

Answer:

x = 2592

Step-by-step explanation:

Equation: x * 3⁻⁴ = 32

Simplify: x/81 = 32

Multiply: x = 2592

The solution is:: the area cross sectional area of triangle form in the cone is 80ft²

Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

Given in the question,

radius of cone's base = 8ft

             cone's base = base of triangle

height of cone = 10 ft

height of cone = height of triangle

Area of triangle

Area = 1/2(h)(b)

here h = height of triangle

       b = base of triangle

A = 1/2(8)(10)

A = 40ft²

Since the section is 2 similar triangles back to back around the vertical center

so the area cross sectional area of triangle form in the cone is 2(40)ft² = 80ft²

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complete question:

You have a cone with a radius of 8 ft and a height of 10 ft. Find the area of the triangle formed by a perpendicular cross-section through the cone’s center.

For this case we must solve the following linear equation:

[tex]- \frac {1} {4} x + 5 = \frac {3} {4}[/tex]

Subtracting 5 from both sides of the equation we have:

[tex]- \frac {1} {4} x = \frac {3} {4} -5\\- \frac {1} {4} x = \frac {3-20} {4}\\- \frac {1} {4} x = - \frac {17} {4}[/tex]

Multiplying by 4 on both sides of the equation:

[tex]-x = -17[/tex]

Multiplying by -1 on both sides of the equation we have:

[tex]x = 17[/tex]

Answer:

[tex]x = 17[/tex]

Answer: [tex]x=17[/tex]

Step-by-step explanation:

You need to solve for the variable "x":

The first step is to subtract 5 from both side of the equation, then:

[tex]-\frac{1}{4}x+5-5=\frac{3}{4}-5\\\\-\frac{1}{4}x=-\frac{17}{4}[/tex]

The final step is to multiply both sides of the equation by -4.

Therefore, the value of the variable "x" is the following:

[tex](-4)(-\frac{1}{4}x)=(-\frac{17}{4})(-4)\\\\x=17[/tex]

Answer:

y-intercept is 4.

Step-by-step explanation:

Given,

Equation of the line,

[tex]y=\frac{4}{3}x+1[/tex]

∵ Equation of a line is y = mx + c, where m is the slope of the line,

By comparing,

The slope of the above line is [tex]\frac{4}{3}[/tex],

Let m' is the slope of the line perpendicular to above line,

[tex]\implies m'\times \frac{4}{3}=-1[/tex]

[tex]\implies m' = -\frac{3}{4}[/tex]

Now, the equation of a line passes through a point [tex](x_1,y_1)[/tex] is,

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

So, the equation of the perpendicular line having slope [tex]-\frac{3}{4}[/tex] and passes through ( 4,1) is,

[tex]y-1=-\frac{3}{4}(x-4)\implies y=-\frac{3}{4}x+3+1\implies y=-\frac{3}{4}x+4[/tex]

For y-intercept,

x = 0,

⇒ y = 4

Hence, the y-intercept of the perpendicular line is 4.

Answer:

(2,1)

Step-by-step explanation:

So the first thing you want to do is substitute. You want to plug in the equation for y in for the y value above.

So you would do 3x+4(x-1)=10. As you can see we took the bottom equation and put it in for the top equation. We did this so we only have x s and no y s.

Now you would solve. You would distribute first. You would get 3x+4x-4=10. Now combine like terms. 3+4 is 7 so you would get 7x-4=10.The next thing you want to do is get the 7x by itself so move the 4.You would get 7x=14. Now divided both sides by 7 because you want to get the x by itself.

You would get x=2. Now for the y value just plug it in for an equation above. The easier one would be y=x-1. y=(2)-1 will equal 1. You write your final answer in (x,y) style. Your final answer will then be (2,1)

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}3x+4y=10&(1)\\y=x-1&(2)\end{array}\right\\\\\text{Substitute (2) to (1):}\\\\3x+4(x-1)=10\qquad\text{use the distributive property}\\3x+4x-4=10\qquad\text{add 4 to both sides}\\7x=14\qquad\text{divide both sides by 7}\\x=2\\\\\text{put the value of x to (2):}\\\\y=2-1\\y=1[/tex]

Answer:

9

Step-by-step explanation:

Common ratio is found by raking the second term and dividing by the first term

9/1 = 9

We can check by taking the third term and dividing by the second term

81/9 = 9

The common ratio is 9

Answer:

b

Step-by-step explanation:

[tex]\log_96561=4[/tex]

Answer:

(-5,-2)

Step-by-step explanation:

because the point is 5 to the left of the origin and 2 down from the origin

Answer:

13 is your answer

Step-by-step explanation:

x - 8.1 = 5.3

  +8.1    +8.1         Add 8.1 to both sides

x     =     13.4

Which if you want the whole number i'd be 13, Because if your rounding the 3, 4 won't bump the 3 up any because 4 isn't greater than 5.

Hope my answer has helped you!

Answer:

x=13

Step-by-step explanation:

A quick rough estimate could be obtained by adding 8 to both sides:

x = 5.3 + 8, or x = 13 (approx.)

The exact solution is x = 8.1 + 5.3 = 13.4 (which rounds down to 13).

Answer:

d

Step-by-step explanation:

im very smart (def did not get it wrong and it showed me the answer)

Answer:

see explanation

Step-by-step explanation:

Each term in the second factor is multiplied by each term in the first factor, that is

x²(2x² + 3x - 1) + 3x(2x² + 3x - 1) + 2(2x² + 3x - 1)

Distribute all 3 parenthesis

= 2[tex]x^{4}[/tex] + 3x³ - x² + 6x³ + 9x² - 3x + 4x² + 6x - 2

Collect like terms

= 2[tex]x^{4}[/tex] +9x³ + 12x² + 3x - 2

Answer:

2x^4+9x^3-7x^2-6x-2

Step-by-step explanation:

=2x^4+3x^3-x^2+6x^3+9x^2-3x-x^2-3x-2

Simplify

=2x^4+9x^3-7x^2-6x-2

We're looking for a model of the form

[tex]y=a\cos(b(x-c))+d[/tex]

[tex]a[/tex] is the amplitude, equal to half the difference between the maximum and minimum hours of daylight:

[tex]a=\dfrac{15.3-9.1}2=3.1[/tex]

[tex]b[/tex] determines the period of the cosine function. The period itself is [tex]\dfrac{2\pi}b[/tex], which we want equal to 365, so that

[tex]365=\dfrac{2\pi}b\implies b=\dfrac{2\pi}{365}[/tex]

(so that the value in the second box should be 365)

[tex]c[/tex] determines the horizontal shift of the cosine function. We'll come back to this in a moment.

[tex]d[/tex] represents the vertical shift of the function. The standard function is bounded between -1 and 1:

[tex]-1\le\cos x\le1[/tex]

Our new function has an amplitude of 3.1, so that

[tex]-3.1\le3.1\cos x\le3.1[/tex]

We want the range of values to fall between 15.3 and 9.1, so we want to pick [tex]d[/tex] such that

[tex]\begin{cases}-3.1+d=9.1\\3.1+d=15.3\end{cases}\implies d=12.2[/tex]

So the current model is

[tex]y=3.1\cos\left(\dfrac{2\pi}{365}x\right)+12.2[/tex]

[tex]c[/tex] represents the horizontal shift of the function. [tex]x=0[/tex] represents the first day of the year, which according to the current model tells us we should expect [tex]3.1\cos0+12.2=15.3[/tex] hours of daylight on the first day of the year. But this conflicts with the data. We want this maximum to occur on the 172nd day of the year, so we shift the model by this amount, and the model is

[tex]y=\boxed{3.1}\cos\left(\dfrac{2\pi}{\boxed{365}}}(x-\boxed{172})\right)+\boxed{12.2}[/tex]

Final answer:

To use the distributive property for the expression 5(2x - 1), multiply each term inside the parentheses by 5, resulting in the equivalent expression 10x - 5.

Explanation:

To use the distributive property to write an expression equivalent to 5(2x - 1), you simply multiply each term inside the parentheses by the factor outside, which is 5 in this case. So, you will multiply 5 by 2x and then 5 by -1.

Multiply 5 by 2x: 5 × 2x = 10x.

Multiply 5 by -1: 5 × -1 = -5.

Combine the two results to get the equivalent expression: 10x - 5.

Therefore, using the distributive property, the expression equivalent to 5(2x - 1) is 10x - 5.

[tex]\bf (\stackrel{x_1}{1}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{16}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{16-9}{-3-1}\implies \cfrac{7}{-4}\implies -\cfrac{7}{4}[/tex]

Answer:

[tex]\huge\boxed{-\frac{7}{4}}[/tex]

Step-by-step explanation:

Slope formula

[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\displaystyle\frac{16-9}{(-3)-1}=\frac{7}{-4}=-\frac{7}{4}[/tex]

Therefore, the slope is [tex]\displaystyle -\frac{7}{4}[/tex], [tex]\displaystyle -\frac{7}{4}[/tex] is the correct answer.

[tex]\bf (\stackrel{x_1}{1}~,~\stackrel{y_1}{4})~\hspace{10em} slope = m\implies -2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-4=-2(x-1)[/tex]

Answer:

Step-by-step explanation:

6|x| + 25 = 15

6|x| = 15 - 25

6|x| = -10

|x| = - [tex]\frac{10}{6}[/tex]

By definition, the absolute value of any number must be positive, hence  | x| can never be negative, there is no solution.

Answer:

g>5

Step-by-step explanation:

5g>25 Take this equation, using the division property of equality, divide both sides by 5, leaving you with

g>5

Answer:

g > 5

Step-by-step explanation:

Divide by 5 both sides.

Since there is no negatives the sign stays the same.

Answer:

Step-by-step explanation:

This is not a linear function. This is actually an exponential function.

Answer:

A

Step-by-step explanation:

trust me bro

The equation to determine the temperature in Bangor is 3x + 22 = 82. Solving the equation gives the temperature in Bangor as 20 degrees.

To write an equation to determine the temperature in Bangor, let's assume the temperature in Bangor is represented by the variable 'x'. The temperature in Miami is 22 degrees warmer than three times the temperature in Bangor. So, we can write the equation as follows:

3x + 22 = 82

Now, to find the temperature in Bangor, we need to solve for 'x'. We can do this by subtracting 22 from both sides:

3x = 82 - 22

3x = 60

Finally, divide both sides of the equation by 3 to solve for 'x':

x = 60 ÷ 3

x = 20

Therefore, the temperature in Bangor is 20 degrees.

Final answer:

The correct equation to find the temperature in Bangor, Maine, given the temperature in Miami, Florida, is 3x + 22 = 82. After solving, the temperature in Bangor is found to be 20 degrees Fahrenheit.

Explanation:

The temperature in Miami, Florida is given as 82 degrees Fahrenheit. According to the problem statement, this temperature is 22 degrees warmer than three times the temperature in Bangor, Maine. Thus, we can express this relationship algebraically as:

Miami temperature = 3 × Bangor temperature + 22

Substituting the known Miami temperature into the equation, we have:

82 = 3 × Bangor temperature + 22

To solve for the temperature in Bangor, we need to subtract 22 from both sides of the equation:

82 - 22 = 3 × Bangor temperature

60 = 3 × Bangor temperature

Finally, divide both sides by 3 to get the temperature in Bangor:

Bangor temperature = 60 / 3

Bangor temperature = 20 degrees Fahrenheit

Therefore, the correct equation to determine the temperature in Bangor is:

3x + 22 = 82

Answer:

63 % for cats and 37 % for dogs

Step-by-step explanation:

Here is the set up:

Let p = percent of change

(72 - 14)/72 = p/100

Solve for p.

ANSWER

[tex]{ (- 6745)}^{ \frac{1}{7} } [/tex]

EXPLANATION

If we have an exponential expression of the form:

[tex] { (- x)}^{ \frac{1}{n} } [/tex]

then, the result is a real number, if and only if n is an odd number.

We analyze the options and find out that,the first option is where n is odd, because we have n=7.

Hence the only option that is equivalent to a real number is

[tex] { (- 6745)}^{ \frac{1}{7} } [/tex]

The correct choice is A.

Real numbers encompass all positive and negative integers, fractions, and decimals excluding imaginary numbers. In the given options, options B depicting a set of positive integers and C depicting a decimal number are examples of real numbers.

In mathematics, a real number includes all positive and negative integers, fractions, and decimals without imaginary components. From the provided options, options B and C directly depict real numbers. Option B declares the values of x as a set of positive integers from 1 to 14.

While C represents a real number as a decimal 0.9417. To further understand, real numbers are embedded in our daily calculations, for instance, if you own 1 apple, spend $14, or measure a distance of 0.9417 km, these are all instances of real numbers.

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Answer:

The length of the rectangular park is [tex]1.2\ mi[/tex] and the width of the rectangular park is [tex]0.3\ mi[/tex]

Step-by-step explanation:

Let

x ----> the length of the rectangular park

y ---> the width of the rectangular park

we know that

The perimeter is equal to

[tex]P=2(x+y)[/tex]

[tex]P=3\ mi[/tex]

so

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

[tex]x=4y[/tex] ----> equation B

substitute equation B in equation A and solve for y

[tex]3=2(4y+y)[/tex]

[tex]3=10y[/tex]

[tex]y=0.3\ mi[/tex]

Find the value of x

[tex]x=4(0.3)=1.2\ mi[/tex]

therefore

The length of the rectangular park is [tex]1.2\ mi[/tex] and the width of the rectangular park is [tex]0.3\ mi[/tex]

Final answer:

To determine the dimensions of a park with a 3-mile perimeter where the length is 4 times the width, we set up the equation 3 = 2l + 2w, substitute l = 4w into it, and solve for width and length. The calculations show the park is 1.2 miles long and 0.3 miles wide.

Explanation:

The student has asked for help to find the dimensions of a rectangular-shaped park with a 3-mile perimeter where the length is 4 times the width. To solve this, we will use the formula for the perimeter of a rectangle P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.

Since we know the perimeter is 3 miles, we can set up the equation 3 = 2l + 2w. Because the length is 4 times the width, we can also say that l = 4w. Substituting into the first equation, we get 3 = 2(4w) + 2w, which simplifies to 3 = 10w. To find the width, we divide both sides by 10, resulting in w = 0.3 miles. Then, using l = 4w, we find that the length l is 1.2 miles.

Therefore, the dimensions of the park are 1.2 miles long and 0.3 miles wide.

The answer is:

The airplane will travel 8800 feet in 10 seconds.

It's a conversion exercise, we need to be careful in order to solve it with no mistakes.

First:

We need to remember that 1 hour is equal to 60 minutes, and 1 minute is equal to 60 seconds, so, to calculate how many seconds are in one hour, we need to perform the following operation:

[tex]Time=1hour*\frac{60minutes}{1hour}*\frac{60seconds}{nminute}=3600seconds[/tex]

Second:

We need to convert from miles to feet, we need to remember that 1 mil is equal to 5280 feet.

So, solving we have:

[tex]Speed=600\frac{miles}{hour}*\frac{1hour}{3600seconds}*\frac{5280ft}{1mile}=880\frac{ft}{seconds}[/tex]

Now, calculating how many feet does it travel in 10 seconds, we have:

[tex]distance=speed*time\\\\distance=880\frac{ft}{seconds}*10seconds=8800ft[/tex]

We have that the airplane will travel 8800 feet in 10 seconds.

Have a nice day!