I can't figure this out I need helppp!!!!

Answer: Option C i.e. 22.1 is correct

Step-by-step explanation:

The given expression follows pemdas rule

PEMDAS:

P for Paranthesis

E for Exponents

M for Multiplication

D for division

A for Addition

S for Subtraction

Given :24 -12 /2 *3.2

=  24-12/2*3.2     [Multiplication]

= 24- 12/6.4      [Division]

=24-1.875         [Subtraction]

=22.125

So the answer is C. 22.1

In this exercise we have to use the knowledge of finance to calculate the monthly amount of insurance, so the best alternative that represents this amount is:

Option C

In this exercise we want to calculate the monthly insurance payment amount, so from the given values ​​we find:

[tex]Payment= (Bodily Injury)+ (Property Damage)+ (Collision)+(Comprehensive)[/tex]

Substituting the values ​​in the formula given above we find that:

[tex]Payment= 22.5 + 120.5 + 415.25 + 100 \\= 658.25\\658.25/12 = 54.854[/tex]

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The equation q=r+rst can be rearranged to isolate t, with the final solution being t=(q-r)/rs.

To solve for t in the equation q=r+rst, first, you need to isolate t on one side of the equation. You can do this by subtracting r from both sides so that you have q-r=rst. Next, divide both sides by rs, which gives you the final solution: t=(q-r)/rs.

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Final answer:

To find the equation of a line perpendicular to another, determine the slope of the original line and use the negative reciprocal of that slope for the perpendicular line. Choose a point on the perpendicular line, and apply the point-slope form to get the equation.

Explanation:

The process of finding a perpendicular line involves first understanding the slope of the given line. To find the equation of a line that is perpendicular to another, you need to identify the slope (m) of the original line and use the fact that the slopes of perpendicular lines are negative reciprocals of each other (meaning if the slope of the first line is m, the slope of the line perpendicular to it will be -1/m). In the context of vectors and analytical methods in physics, components can help describe forces or directions. If we consider the example of a skier on a slope, breaking down the weight force into components parallel and perpendicular to the slope helps analyze the motion. However, for strictly finding a perpendicular line in mathematics, we focus on the slopes of the lines. Suppose you have the equation of the original line. If it is in the format y = mx + b, where m is the slope and b is the y-intercept, you can find the slope of the perpendicular line by taking the negative reciprocal of m. If the slope is not readily apparent, you might need to rearrange the equation into this format. Once you have the slope of the perpendicular line, choose a point through which the line passes (this could be the original point or any particular point you're given). Then, use the point-slope form (y - y1) = m(x - x1) to write the equation of the line.

f(x) = 3x^2-x

F(-2)

 replace x with -2

3(-2)^2 - -2 =

3*4 +2 = 14

 Answer is 14

There were 6 trucks.

if you multiply 6 * 5 = 30.

Hopes this helps mark me as the Brainliest please.!!!!   

:) 

Answer:

Hello!

Great question!

The correct answer would be "Common Factor."

Step-by-step explanation:

It is a common factor when it is a factor of two (or more) numbers.

The number which can be divided out of each term in an expression is called the GCF or greatest common factor of that number.

GCF or greatest common factor is the common number which all the term has in a group of terms. It is the number which can divide each number of the group.

For example, let a group of number as,

[tex]\{1,2,4,8,16\}[/tex]

The number which can be divided out of each term in this data is 16 which is the greater common factor of this data set.

Thus, the number which can be divided out of each term in an expression is called the GCF or greatest common factor of that number.

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Answer:

The probability of the event below of rolling a 5 is 0.0625.

Step-by-step explanation:

Given is : A probability experiment consists of rolling a fair 16​-sided die. Find the probability of the event below of rolling a 5.

Total number of faces = 16

So, there is only one way for rolling a 5 on a die

And the probability of rolling a 5 on a die = [tex]\frac{1}{16}[/tex]

= 0.0625

The value of x in the figure given is E. √70.

The answer is E. √70.

The two triangles are similar by the AAA Similarity Theorem, since they have two pairs of congruent angles, namely ∠ABD and ∠CAD, and ∠BAD and ∠CDA.

Since the triangles are similar, the ratio of corresponding sides is constant. In particular, the ratio of AD to CD is the same as the ratio of BD to AD.

We are given that AD = 14 and CD = 20, so the ratio of AD to CD is 14/20. We are also given that BD = x, so the ratio of BD to AD is x/14.

Setting these two ratios equal to each other, we get x/14 = 14/20, which simplifies to x = √70.

Here is a proof that shows why the two triangles are similar:

AAA Similarity: Triangles ABD and CAD have two pairs of congruent angles, namely <ADB> and <CAD>, because they are both right angles.

SSS Similarity: Triangles ABD and CAD have three pairs of corresponding sides that are proportional, namely AD/CD = 14/20, BD/AD = x/14, and AB/CD = √70/20. Therefore, the two triangles are similar by the SSS Similarity Theorem.

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The rate of change of the quadratic function over the interval −4≤x≤−2 is 2.

To find the rate of change of the quadratic function [tex]$f(x)=x^2+4 x+5$[/tex] , over the interval −4≤x≤−2, we need to find the average rate of change over that interval.

The average rate of change of a function f(x) over an interval [a,b] is given by:

[tex]Average Rate of Change =\frac{f(b)-f(a)}{b-a}$[/tex]

So, in this case:

a=−4

b=−2

We calculate f(−4) and f(−2):

[tex]$\begin{aligned} & f(-4)=(-4)^2+4(-4)+5=16-16+5=5 \\ & f(-2)=(-2)^2+4(-2)+5=4-8+5=1\end{aligned}$[/tex]

Now we can find the rate of change:

Rate of Change = [tex]$\frac{1-5}{-2-(-4)}=\frac{-4}{-2}=2$[/tex]

The average rate of change of the function f(x)=x² + 4x + 5 over the interval from x = -4 to x = -2 is -2.

The rate of change for the quadratic function f(x)=x² + 4x + 5 over the interval from x = -4 to x = -2 can be calculated using the average rate of change formula. This formula is given by:

Rate of Change = [f(x2) - f(x1)] / (x2 - x1)

Where x1 = -4 and x2 = -2. We first calculate f(-4) and f(-2) by plugging these values into the function:

f(-4) = (-4)² + 4(-4) + 5 = 16 - 16 + 5 = 5

f(-2) = (-2)² + 4(-2) + 5 = 4 - 8 + 5 = 1

Now we use these results in our rate of change formula:

Rate of Change = (1 - 5) / (-2 + 4) = -4 / 2 = -2

The average rate of change of the function f(x) over the interval from x = -4 to x = -2 is -2.

Answer:

You need to buy 6.5 cubic yards.

Step-by-step explanation:

You want to put a 5 inch thick layer of topsoil for a new 23 ft by 18 ft garden.

We know 1 yard = 3 feet or 1 yard = 36 inches

Then 1 inch = [tex]1/36[/tex] yard.

1 feet = 1/3 yard

The volume of the layer of the topsoil is given by:

= [tex]5(1/36)(23)(1/3)(18)(1/3)[/tex] cubic yards

[tex]2070/324=6.39[/tex] cubic yards

Now, the store only sells increments of 1/4 = 0.25 cubic yards.

So, we need to buy [tex]6.39/0.25=25.56[/tex] increments

Rounded to 26 increments.

Therefore, we need to buy 26 increments of 1/4 cubic yards.

That becomes 6.5 cubic yards.

To apply the Pythagorean Theorem, you need the lengths of the two legs of a right triangle. Trigonometric ratios involve the angles and ratios of sides in a right triangle. Examples are provided for both methods.

In order to apply the Pythagorean Theorem, you need the lengths of the two legs of a right triangle. The theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. For example, if we have a triangle with legs of lengths 3 and 4, we can use the theorem to find the length of the hypotenuse. The square of the hypotenuse is 3^2 + 4^2 = 9 + 16 = 25, so the hypotenuse has a length of 5.

Trigonometric ratios, on the other hand, involve the angles of the right triangle and ratios of its sides. The three main trigonometric ratios are sine, cosine, and tangent. For example, if we have a right triangle with an angle of 30 degrees and one leg of length 5, we can use trigonometry to find the length of the other leg. The sine of the angle is given by the ratio of the opposite side (the leg we want to find) to the hypotenuse. So, sin(30 degrees) = opposite / hypotenuse = x / 5. Solving for x, we get x = 5 * sin(30 degrees) = 5 * 0.5 = 2.5.

Unit circle : a circle with radius of one. Unit circle is centered at the origin.

Use the formula cot x = base / perpendicular, where x is the angle. Substituting x,y and t to the formula, we get cot (t) = x / y.

To find the trigonometric function values for a point on the unit circle corresponding to a real number t involves using the x and y coordinates, which are derived from the cosine and sine functions at that angle t.

The student's question involves finding the values of trigonometric functions for a point p(x, y) on the unit circle that corresponds to a real number t. This typically involves understanding the relationship between the coordinates of a point on the unit circle and the trigonometric functions sin, cos, and tan. In this context, x(t) and y(t) are understood as the x and y coordinates of a point on the unit circle at a certain angle t. The point p(x, y) would be given by the cosine and sine functions: x(t) = cos(t) and y(t) = sin(t). In more advanced contexts, these functions can take different forms like x(t) = A cos(wt + p) where A, w, and p are constants. The solution to trigonometric equations may involve differential equations or complex numbers in such cases.

The number line for [tex]\fbox{\begin\\\ \bf \text{option 1}\\\end{minispace}}[/tex] represents the solution for the equation [tex]|x+4|=2[/tex].

Further explanation:

The equation is given as follows:

[tex]|x+4|=2[/tex]

In the above equation [tex]||[/tex] represents the modulus function.

Modulus function is defined as a function which gives positive value of the function for any real value of [tex]x[/tex].

For example: The function [tex]y=|x|[/tex] is a modulus function in which [tex]y>0[/tex] and [tex]x<0[/tex] or [tex]x>0[/tex].

In the given equation [tex]|x+4|[/tex]  is a modulus expression.  

There are two cases formed for [tex]|x+4|[/tex].

First case:  [tex]x>-4[/tex]

If [tex]x>-4[/tex] then [tex]|x+4|\rightarrow (x+4)[/tex].

Substitute [tex]|x+4|=(x+4)[/tex] in [tex]|x+4|=2[/tex].

[tex]\begin{aligned}x+4&=2\\x&=2-4\\&=-2\end{aligned}[/tex]

Therefore, for [tex]x>-4[/tex] the value of [tex]x[/tex] which satisfies the equation [tex]|x+4|=2[/tex] is [tex]x=-2[/tex].

Second case:  [tex]x<-4[/tex]

If [tex]x<-4[/tex] then [tex]|x+4|\rightarrow -(x+4)[/tex].

Substitute [tex]|x+4|=-(x+4)[/tex] in [tex]|x+4|=2[/tex].

[tex]\begin{aligned}-(x+4)&=2\\-x-4&=2\\-x&=2+4\\-x&=6\\x&=-6\end{aligned}[/tex]

Therefore, for [tex]x<-4[/tex] the value of [tex]x[/tex] which satisfies the equation [tex]|x+4|=2[/tex] is [tex]x=-6[/tex].

This implies that the solution for the equation [tex]|x+4|=2[/tex] or the value of [tex]x[/tex] which satisfies the given equation are [tex]\fbox{\begin\\\ \math x=-2\ \text{and}\ x=-6\\\end{minispace}}[/tex].

Option 1:

The number line in option 1 shows that the solutions of the equation [tex]|x+4|=2[/tex] are [tex]x=-2[/tex] and [tex]x=-6[/tex].

As per our calculation made above the solutions for the equation [tex]|x+4|=2[/tex] are [tex]x=-2[/tex] and [tex]x=-6[/tex].

This implies that option 1 is correct.

Option 2:

The number line in option 2 shows that the solutions of the equation [tex]|x+4|=2[/tex] are [tex]x=2[/tex] and [tex]x=4[/tex].

As per our calculation made above the solutions for the equation [tex]|x+4|=2[/tex] are [tex]x=-2[/tex] and [tex]x=-6[/tex].

This implies that option 2 is incorrect.

Option 3:

The number line in option 3 shows that the solutions of the equation [tex]|x+4|=2[/tex] are [tex]x=2[/tex] and [tex]x=6[/tex].

As per our calculation made above the solutions for the equation [tex]|x+4|=2[/tex] are [tex]x=-2[/tex] and [tex]x=-6[/tex].

This implies that option 3 is incorrect.

Option 4:

The number line in option 4 shows that the solutions of the equation [tex]|x+4|=2[/tex] are [tex]x=-2[/tex] and [tex]x=-4[/tex].

As per our calculation made above the solutions for the equation [tex]|x+4|=2[/tex] are [tex]x=-2[/tex] and [tex]x=-6[/tex].

This implies that option 4 is incorrect.

Therefore, the number line for [tex]\fbox{\begin\\\ \bf \text{option 1}\\\end{minispace}}[/tex] represents the solution for the equation [tex]|x+4|=2[/tex].

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Answer details:

Grade: High school

Subject: Mathematics

Chapter: Functions

Keywords: Functions, modulus, modulus function, number line, real line, |x+4|=2, equation, root, zeroes, solutions,  absolute function, x=-6 and x=-2.

Option A is correct, the values of [tex]x[/tex] staisfying the given equation [tex]|x+4|=2[/tex] are [tex]-2[/tex] and [tex]-6[/tex].

Modulus function always returns a positive value to the equation.

Here, [tex]|x+4|[/tex] will give positive result if [tex]x>-4[/tex] and negative value if, [tex]x<-4[/tex].

Case 1: When [tex]x>-4[/tex]

According to the given equation,

[tex]|x+4|=2\\x=2-4\\x=-2[/tex]

So, the value of [tex]x[/tex] which satisfies the given equation [tex]|x+4|=2[/tex] for [tex]x>-4[/tex] is [tex]x=-2[/tex].

Case 2: When [tex]x<-4[/tex]

According to the given equation,

[tex]|x+4|=2\\-x-4=2\\x=-6[/tex]

So, the value of [tex]x[/tex] which satisfies the given equation [tex]|x+4|=2[/tex] for [tex]x<-4[/tex] is [tex]x=-6[/tex].

Hence, the values of [tex]x[/tex] staisfying the given equation [tex]|x+4|=2[/tex] are [tex]-2[/tex] and [tex]-6[/tex].

Now, according to the options, Option A is correct.

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