2(-4^2) - 2(2^4) + 3^2 - -4^2 + 2^4 = ? Please explain, I got 41 but I highly doubt I'm right.

Answer:

Introduction, Methodology, Results, Discussion.

Step-by-step explanation:

yes

there are 60 minutes per hour

24/60 = 0.4 miles per minute

0.4*5 = 2

they will ride 2 miles in 5 minutes

Answer:  The positive number is  [tex]\dfrac{1}{2}.[/tex]

Step-by-step explanation:  We are given to find the positive number that is twice it's own square.

Let x denotes the required number.

Then, according to the given information, we have

[tex]x=2x^2\\\\\Rightarrow 2x^2-x=0\\\\\Rightarrow x(2x-1)=0\\\\\Rightarrow x=0,~~2x-1=0\\\\\Rightarrow x=0,~\dfrac{1}{2}.[/tex]

Sine 0 is not considered as a positive number, so the required positive number is [tex]\dfrac{1}{2}.[/tex]

Thus, the positive number is [tex]\dfrac{1}{2}.[/tex]

The name of the shape graphed by the function r ^ 2 = 9 cos (2 theta) is called the “lemniscate”. A lemniscate is a plane curve with a feature shape which consists of two loops that meet at a central point. The curve is also sometimes called as the lemniscate of Bernoulli.

Explanation:

The period of coskθ is 2π/k. In this case, k = 2 therefore the period is π.

r ^ 2 = 9 cos 2θ ≥0 → cos 2θ ≥0. So easily one period can be chosen as θ ∈ [0, π] wherein cos 2θ ≥0.

As cos(2(−θ)) = cos2θ, the graph is symmetrical about the initial line.

Also, as cos (2(pi-theta) = cos 2theta, the graph is symmetrical about the vertical θ = π/2

A Table for half period [0,π4/] is adequate for the shape in Quarter1

Use symmetry for the other three quarters:

(r, θ) : (0,3)(3/√√2,π/8)(3√2/2,π/6)(0,π/4)

Answer:

lemniscate

Step-by-step explanation:

a p e x

Answer: 12 and 36

Step-by-step explanation: The best way to approach a word problem like this is to break it down sentence by sentence.

We know that the sum of two numbers is 48 so we can move on to the next sentence. Now, let's take a look at the second sentence. One number is 3 times as large as the other.

This sentence tells us what variables we are going to use to represent our numbers.

So if we use x to represent one of our numbers, and one number is 3 times as large as the other, we can use 3x to represent our other number. Also, make sure to always label your variables.

X ⇒ first number

3x ⇒ second number

Now let's look back at the first sentence. "The sum of two numbers is 48". This sentence tells us how we will set up our equation. "The sum" if our variables are X and 3x will be X + 3x = 48.

Keep in mind, the word "is" means equal.

Now we have the following equation and we can solve for X.

X + 3x = 48

We start by simplifying on the left side to get 4x.

Now we have the following equation.

4x = 48

÷4    ÷4   ← divide both sides of the equation by 4

 X = 12

So our first number, X, is 12 and our second number will be 3 × 12 or 36.

Therefore, our two numbers are 12 and 36.

To solve this problem, let us first define what probability means in this case. It would be:

Probability = (number of colors to choose from) / (total number of colors)

There are a total of 5 colors on the spinner. The number of colors to choose from spins 1 to 8 would be 5 out of 5, while for the last spin 9 the number of colors to choose from would only be brown so that would be 1 out of 5. The total probability would be the product of the probability of each spins, therefore:

Probability = 1st spin * 2nd spin * 3rd spin * 4th spin * 5th spin * 6th spin * 7th spin * 8th spin * 9th spin

Probability = (5/5) *(5/5) *(5/5) *(5/5) *(5/5) *(5/5) *(5/5) *(5/5) * (1/5)

Probability = 0.2

There is a 20% chance to get brown on the last spin.

Answer:

1/5

Step-by-step explanation:

Think of it like this. If there is five spots it can potentially land on, and only 1 brown spot, the answer would be 20 %, or as a fraction, 1/5.

Hence, the area of shaded region is:

72 square inches.

We have to find the area of the shaded region i.e. we have to find the area of a triangle.

Clearly the shaded triangle is in the shape of a right triangle.

we will firstly find the dimension of the triangle in order to find it's area.

Clearly the base(b) of a triangle is 36/4= 9 inches.

( since the side of the rectangle of length 36 inches is divided into 4 equal parts)

similarly the height(h) of the right triangle is:

48/3=16 inches.

( since the side of rectangle of measure 48 inches is divided into 3 equal parts)

Hence, the area of triangle is calculated as:

[tex]Area=\dfrac{1}{2}\times b\times h\\\\\\Area=\dfrac{1}{2}\times 9\times 16\\\\Area=72\text{square\ inches}[/tex]

Hence, the area of shaded region is:

72 square inches.

Answer:

The absolute value of a number is the distance the number is from 0 on a number line. Since distance is never negative, absolute value is never negative.Step-by-step explanation:

Answer:

(c) The graph starts flat but curves steeply upward.

Step-by-step explanation:

(a) The graph is a straight line that has a slope of 8

In the table, the value y increases. there is no constant increase in y

So The graph is not a straight line

(b) The graph is a horizontal line at y = 16

For y=16 graph, the value of y remains the same

The value of y changes in the table

So the graph is not a horizontal line

(c) The graph starts flat but curves steeply upward.

The value of y on the table increases rapidly. So we can say that graph starts flat and curves steeply upward.

(d) The graph is a parabola that opens upward.

There is no vertex mentioned in the table. the y values goes on increasing.

In parabola, the graph increases and then decreases or vice versa .

So the graph of given table is not a parabola

Answer:

The first one hopefully :)

Step-by-step explanation:

The equation showing the relationship between milliliters of sugar (c) and the number of flavor packages (f) is c = 150f, derived from the recipe's ratio.

The relationship between milliliters of sugar (c) and the number of flavor packages (f) can be expressed with the equation c = 150f. This equation comes from the ratio provided in the recipe, which states that for every 2 flavor packages, 300 ml of sugar is needed. So, if 1 flavor package corresponds to 150 ml of sugar (since 300 ml is for 2 packages), the equation can be derived by multiplying the number of flavor packages by 150 ml to find the milliliters of sugar.

Three interior angles of the given triangle are 60°, 30°, and 90°.

A triangle is a two-dimensional geometrical figure that has three sides, three vertices, and three interior angles.

Given,  two exterior angles of a triangle are 120° and 150°.

Therefore, the first interior angle is

[tex]= (180 - 120)[/tex] degrees

[tex]= 60[/tex] degrees

The second interior angle is

[tex]= (180 - 150)[/tex] degrees

[tex]= 30[/tex] degrees

The third interior angle is

[tex]= [180 - (60+30)][/tex] degrees

= 90 degrees

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Answer:

[tex]y= 470 - 50x[/tex]

Step-by-step explanation:

Wayne needs to drive 470 miles to reach Milwaukee. Suppose he drives at a constant speed of 50 miles per hour.

Let x represents the number of hours he drives and y represents the distance in miles.

constant speed is 50 miles per hour.

Distance =speed x time

speed is 50 miles per hour and time is x

So distance = [tex]50x[/tex]

Wayne needs to drive 470 miles to reach Milwaukee.

To find out y, we need to subtract 50x from 470

[tex]y= 470 - 50x[/tex]

Answer:

the last one

y = 470 - 50x

Answer:

[tex]w(w+2)=48[/tex] can be used by John.

Step-by-step explanation:

John has 48 square centimeter tiles he wants to use to create a mosaic.

We can say that 48 square cm is the area of the rectangle.

Let the width of the mosaic be = w

So, given is, He wants the mosaic to be rectangular with a length that is 2 centimeters longer than the width.

[tex]l=w+2[/tex]

Now area of rectangle is given as = [tex]length\times width[/tex]

[tex]48=l\times w[/tex]

Substituting l= w+2

[tex]48=(w+2)\times w[/tex] square cm

Hence, the equation John can use to solve and find w, the greatest width in centimeters he can use for the mosaic is :

[tex]w(w+2)=48[/tex]

Answer:

∠1≅∠5 by Corresponding angles for parallel line p and q cut by traversal r

∠5≅∠13 by Corresponding angles for parallel line r and s cut by traversal q

∠10≅∠14 by Corresponding angles for parallel line p and q cut by traversal s

∠13≅∠16 by Vertical angles theorem

The given pairs of congruent angles can be matched with their reasons as follows:

Given:

[tex]r \parallel s\\\\p \parallel q[/tex]

From the image,

1. [tex]\angle 5 $ and \angle 13[/tex] share the same corner along transversal q that cuts across lines r and s. Hence, both angles correspond to each other.

2. [tex]\angle 10 $ and \angle 14[/tex] share the same corner along transversal s that cuts across lines p and q. Hence, both angles correspond to each other.

3. [tex]\angle 13 $ and \angle 16[/tex] share the same vertex angle and are just directly opposite each other. Thus, they are vertically opposite each other and are therefore equal by the vertical angles theorem.

4. [tex]\angle 1 $ and \angle 5[/tex] share the same corner along transversal r that cuts across lines p and q. Hence, both angles correspond to each other.

In summary, the given pairs of congruent angles can be matched with their reasons as follows:

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To solve this problem, we assume that velocity is a linear function of time:
v(t) = m t + b
where
v = velocity

t = time

m = slope of line

b = y-intercept of line equation

When t = 2 hours, v = 18 km/h, therefore:
2 m + b = 18         (1)

When t = 4 hours,  v = 4 km/h, therefore
4 m + b = 4          (2)

Subtract (1) from (2) to obtain
4 m – 2 m = 4 - 18
2 m = -14
m = -7

From (1), calculate for b:
b = 18 – 2(-7) = 32

Part A. The equation in standard form is therefore:
v = -7 t + 32

Part B. To graph the equation for the first 8 hours, we create a table as shown below. Assign values of t from 0 to 8 hours then calculate the corresponding velocity.

By using the concept of function, it can be concluded that-

The domain and range of the given function is the set of real numbers

What is a function

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here the given linear function is

f(x) =[tex]\frac{2}{7}x - 2[/tex]

The graph has been attached here

As the given function is a linear function with a non zero slope, the domain and range is the set of real numbers.

So, the domain and range of the given function is the set of real numbers

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The explicit formula for this geometric sequence is: a_n = 3 (-2)^{n-1}. he common ratio is negative, so the domain is all odd positive integers.

Explicit formula:

The explicit formula for a geometric sequence is of the form: a_n = a_1 r^{n-1}

In this case, the first term is 3 and the common ratio is −2. Therefore, the explicit formula for this geometric sequence is:

a_n = 3 (-2)^{n-1}

Restrictions to the domain:

The domain of a geometric sequence is all positive integers, unless the common ratio is negative. In this case, the common ratio is negative, so the domain is all odd positive integers.

Example:

Using the explicit formula, we can find the fourth term of the sequence as follows:

a_4 = 3 (-2)^{4-1} = 3 (-2)^3 = -24

We can also verify that the domain of the sequence is all odd positive integers by checking the first few terms:

n | a_n

1 | 3

2 | -6

3 | 12

4 | -24

5 | 48

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Final answer:

In similar triangles MNO and XYZ, corresponding angles are congruent (M with X, N with Y, O with Z) and corresponding sides are in proportion (MN to XY, NO to YZ, MO to XZ).

Explanation:

If triangles MNO and XYZ are similar (denoted as MNO ~ XYZ), then their corresponding parts are congruent. Corresponding parts include angles and sides that match between the two triangles due to their similarity in shape and proportion. In similar triangles, corresponding angles are congruent, while corresponding sides are in proportion.

The corresponding congruent angles would be angle M and angle X, angle N and angle Y, and angle O and angle Z. For the sides, the lengths are proportional, which means that the ratio of MN to XY is the same as the ratio of NO to YZ, which is also the same as the ratio of MO to XZ.

Final answer:

In similar triangles MNO and XYZ, the corresponding congruent parts are angles M, N, O congruent to angles X, Y, Z respectively and sides MN, NO, OM proportional to sides XY, YZ, ZX respectively.

Explanation:

If triangles MNO and XYZ are similar (denoted as MNO ~ XYZ), it indicates that they have the same shape but not necessarily the same size. This means that their corresponding angles are congruent, and their corresponding sides are in proportion.

The corresponding congruent parts would be:

Angle M is congruent to Angle X

Angle N is congruent to Angle Y

Angle O is congruent to Angle Z

Side MN is proportional to Side XY

Remember, while the angles are congruent, the sides are proportional, which means the length of the sides of one triangle is some multiple or fraction of the lengths of the corresponding sides of the other triangle.