A Design Was Constructed By Using Two Rectangles, ABCD And A'B'C'D'. RectangleA'B'C'D' Is The Result (2024)

Step 1

Sketch the vector V.

[tex]v=-2i\text{ +5j}[/tex]

Step 2

Find the magnitude of the vector. The magnitude of a vector is given as;

[tex]\begin{gathered} |v|=\sqrt{(i)^2+(j)^2} \\ i=-2 \\ j=5 \\ \left|a+bi\right|\:=\sqrt{\left(a+bi\right)\left(a-bi\right)}=\sqrt{a^2+b^2} \end{gathered}[/tex][tex]\begin{gathered} |v|=\sqrt{(-2)^2+(5)^2} \\ |v|=\sqrt{4+25} \\ |v|=\sqrt{29} \end{gathered}[/tex]

Therefore, the magnitude is given as;

[tex]|v|=\sqrt{29}[/tex]

First we find the speed in mi/h.

We know that 20 h 45 min is equal to 20.75 hours, then the speed is

[tex]\frac{1452.8\text{ mi}}{20.75\text{ h}}=70.01\text{ mi/h}[/tex]

Now we convert the speed to ft/min:

[tex]70.01\text{ mi/h}\cdot\frac{1\text{ h}}{60\text{ min}}\cdot\frac{5280\text{ ft}}{1\text{ mi}}=6161.27\text{ ft/min}[/tex]

Therefore you would have to drive at a speed of 6161.27 ft/min

Answer:

-1

Step-by-step explanation:

[tex]\frac{\frac{64}{-12+4}}{(6)^2+(-30)+2} \\ \\ =\frac{\frac{64}{-8}}{36-30+2} \\ \\ =\frac{-8}{8} \\ \\ =-1[/tex]

[tex]\begin{gathered} \text{From the scatterplot, we can s}ee, \\ \text{The size of the class is depent on the test score.} \\ \text{Higher the test score obtain in the smaller classes.} \\ Thus,\text{the answer C is correct.} \end{gathered}[/tex]

Value of total assests is ;

$85,000 +$2,500 +$18,500 +$7000=$113,000

Value of total liabilities = $62,000 + $9,500 = $71,000

Net worth = $ 113,000-$71,500 =$41,500

Given,

The equation is y=x^2-9.

The values of x are -4, -2, 0, 2, 4.

The odered pair are,

At x= - 4,

The value of y is,

[tex]y=(-4)^2-9=7[/tex]

The ordered pair is (-4, 7).

At x= - 2,

The value of y is,

[tex]y=(-2)^2-9=-5[/tex]

The ordered pair is (-2, -5).

At x= 0,

The value of y is,

[tex]y=(0)^2-9=-9[/tex]

The ordered pair is (0, -9).

At x= 2,

The value of y is,

[tex]y=(2)^2-9=-5[/tex]

The ordered pair is (2, -5).

At x= 4,

The value of y is,

[tex]y=(4)^2-9=7[/tex]

The ordered pair is (4, 7).

The corresponding graph is,

First, lets find how many students want the supreme pizza. Let 'x' be the number of those students. Then, given the information, we have:

[tex]x+17+19=50[/tex]

solving for 'x', we get:

[tex]\begin{gathered} x+17+19=50 \\ \Rightarrow x+36=50 \\ \Rightarrow x=50-36=14 \\ x=14 \end{gathered}[/tex]

we have that x = 14 students want a supreme pizza.

Now, if we suppose that the 50 students are the 100%, then, using a rule of three, we get:

[tex]\begin{gathered} 50\rightarrow100\% \\ 14\rightarrow y\% \\ \Rightarrow y=\frac{14\cdot100}{50}=\frac{1400}{50}=28 \\ y=28\% \end{gathered}[/tex]

therefore, 28% of the students want a supreme pizza

B

1) Examining the Arithmetic Sequence:

(-5,-14, -23,-32,-41,..)

We have the following information:

a_1 = -5

Common ratio:-9

2) From these data, we have the Explicit formula:

[tex]a_n=-5_{}-9(n-1)[/tex]

3) Looking at the options we have some formulas, so we can state that the equation that would generate the Arithmetic Sequence is described in option B

The equation of a circle is given by:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

3.

Using the points (4, 0), (0, 2) and (0, 0), we have:

[tex]\begin{gathered} (0,0)\colon \\ h^2+k^2=r^2 \\ (0,2)\colon \\ h^2+(2-k)^2=r^2 \\ h^2+4-2k+k^2=r^2 \\ \text{Comparing both equations:} \\ h^2+k^2=h^2+4-2k+k^2 \\ 4-2k=0 \\ k=2 \\ (4,0)\colon \\ (4-h)^2+k^2=r^2 \\ 16-8h+h^2+4=r^2 \\ \text{Comparing this last equation with the first one:} \\ 16-8h+h^2+4=h^2+4 \\ 16-8h=0 \\ h=2 \\ \\ h^2+k^2=r^2 \\ r^2=4+4=8 \end{gathered}[/tex]

So the equation of this circle is:

[tex](x-2)^2+(y-2)^2=8[/tex]

Note that:

The control variable is the variable that does not change (that is, constant ) in an experiment. It does not take part in the experiment

The response variable is the dependent variable that determines the outcome of the experiment.

The treatment of an experiment is the independent variable, and it determines the outcome of the experiment.

From the illustration given in this exercise, the control variable, the response variable, and the treatments are identified below with reasons.

1) The control variable = The mathematical abilities of the students

Reason: The students chosen for the experiment must have the same mathematical abilities to prevent bias in the results of the experiment.

2) The response variable = Math test scores

Reason: The maths test scores of the two groups of students are the outcomes of the experiment, hence the response variable.

3) The treatment for the experiment = Wearing of school uniforms

Reason: Wearing of school uniforms is the treatment that the two groups of students were subjected to in order to confirm if their will be any effects on their Maths test scores.

(3x - 3)

3(x - 1)

[6(x - 10)]

6x + 6 times -10

simplify 6 times -10 to -60

6x - 60

Answer: Your result (without simplifying) is actually 2/36, so you would shade two boxes out of the 36 shown.

NOTE: For problem #19, you have 6 boxes for shading, so each box represents 3 increments (3x6=18 boxes). For your result of 5/18, you should only shade the first box and 2/3 of the next box (the other four boxes should be unshaded).

Hope this helps!

Step-by-step explanation:

Direct Variation is of the form (directly proportional);

[tex]\begin{gathered} y\propto x \\ y=kx \end{gathered}[/tex]

While indirect variation (inversely proportional) is of the form;

[tex]\begin{gathered} y\propto\frac{1}{x} \\ y=\frac{k}{x} \end{gathered}[/tex]

So, for each of the given question we want to determine if they are direct or indirect variation;

1.

[tex]\begin{gathered} 6x-5y=-4 \\ -5y=-4-6x \\ -5y=-6x-4 \\ y=\frac{-6x-4}{-5} \\ y=\frac{6}{5}x+\frac{4}{5} \end{gathered}[/tex]

Therefore, this is a Direct variation with proportionality constant;

[tex]k=\frac{6}{5}[/tex]

2.

[tex]\begin{gathered} 2y=14x \\ y=\frac{14x}{2} \\ y=7x \end{gathered}[/tex]

Therefore, this is a Direct variation with proportionality constant;

[tex]k=7[/tex]

ANSWER:

(a)

A. The domain of the given function is {yly is a real number, y ≠ 1}

(b)

[tex]\begin{equation*} D=\left(-\infty\:,\:1\right)\cup\left(1,\:\infty\:\right) \end{equation*}[/tex]

STEP-BY-STEP EXPLANATION:

We have the following function:

[tex]f(y)=\frac{y}{y-1}[/tex]

The domain of a function, are the input values of the function, in this case, it corresponds to the values that y can take.

Since it is a rational function and it cannot take values that make the denominator zero, so we set the denominator equal to zero, like this:

[tex]\begin{gathered} y-1=0 \\ \\ y\ne1 \end{gathered}[/tex]

(a)

That means that y can take the value of all reals except 1.

So the correct answer is:

A. The domain of the given function is {yly is a real number, y ≠ 1}

(b)

In its interval form it would be:

[tex]D=\left(-\infty\:,\:1\right)\cup\left(1,\:\infty\:\right)[/tex]

Answer:

The graph that has a range of all real numbers greater than or equal to -1 is the graph below (top middle graph).

Explanation:

Since the range or the y-values of the graph must be greater than or equal to -1, then the graph must be increasing starting from y = -1.

Out of the 4 graphs, only the two graphs in the middle shows a graph that is increasing.

The graph at the top part is increasing starting from y = -1 while the graph at the bottom part is increasing starting from y = 1 hence, the answer is the graph at the top middle part.

The simplified value of the given expression in the form of a fraction is [tex]\frac{5}{8\cdot(x+1)^2\cdot x^3}[/tex] .

The given expression is: [tex]\frac{15x^2y}{(x+1)^3}\cdot\frac{(x+1)}{24x^5y}[/tex]

we will use the properties of exponents to simplify the expression.

Taking the powers of the like terms and combining we get :

[tex]\implies \frac{15x^2y}{(x+1)^3}\cdot\frac{(x+1)}{24x^5y}[/tex]

[tex]\implies \frac{15}{24} \times \frac{x^{2-5}y^{(1-1)}}{(x+1)^{3-2}}[/tex]

[tex]\implies \frac{5}{8\cdot(x+1)^2\cdot x^3}\\[/tex]

Therefore we get the simplified equation for the expression.

Expressions are mathematical statements that comprise either numbers, variables, or both and at least two terms associated by an operator. Mathematical operations include addition, subtraction, multiplication, and division.

In mathematics, there are two different types of expressions: algebraic expressions, which also include variables, and numerical expressions, which solely comprise numbers. A set sum of money appears to be a constant.

A variable is a symbol that has no predetermined value. A term may consist of one constant, one variable, or a combination of variables and constants multiplied or divided. A number that is additionally multiplied by a variable is referred to as the coefficient in an expression.

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A. The function f(-2) is larger than f(2)

B. The function f(4) is smaller than f(0)

Given,

The function; f(x) = x²- 5x + 1

We have to find;

A. The larger is f(2) or f(-2)

Here,

f(2) = 2²- 5 x 2 + 1 = 4 - 10 + 1 = - 6 + 1 = -5

f(-2) = -2²- 5 x -2 + 1 = 4 + 10 + 1 = 15

That is,

The function f(-2) is larger than f(2)

B. The smaller is f(0) or f(4)

Here,

f(0) = 0²- 5 x 0 + 1 = 0 - 0 + 1 = 1

f(4) = 4²- 5 x 4 + 1 = 16 - 20 + 1 = - 4 + 1 = -3

That is,

The function f(4) is smaller than f(0)

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point = (6,-2)

Parallel to y= 2/3x+4

If 2 lines are parallel, both have the same slope

Slope intercept form:

y= mx +b

where:

m= slope

b= y intercept

so, for y= 2/3x+4

slope = 2/3

So far we have

y= 2/3x +b

Replace x,y by the coordinate point given (6,-2) and solve for b:

-2 = 2/3 (6) + b

-2 = 4 + b

-2-4 = b

-6 = b

Final equation:

y= 2/3x - 6

Given:

[tex]y=\mleft(\frac{5}{2}\mright)^x[/tex]

To sketch the graph:

First find the three points.

Put x=-1 we get,

[tex]\begin{gathered} y=(\frac{5}{2})^{-1} \\ =\frac{2}{5} \\ =0.4 \end{gathered}[/tex]

Put x=0 we get,

[tex]\begin{gathered} y=(\frac{5}{2})^0 \\ =1 \end{gathered}[/tex]

Put x=1 we get,

[tex]\begin{gathered} y=(\frac{5}{2})^1 \\ =2.5 \end{gathered}[/tex]

Therefore, the three points are, (-1, 0.4), (0, 1), and (1, 2.5).

The graph is,

The graph of the function:

[tex]f(x)=\cot (x+\frac{\pi}{6})[/tex]

is shown below:

By graphing at least one full period of the function, we would take the limit of the function as:

[tex]-\pi\le x\le\pi[/tex]

Hence, the graph of at least one full period is:

you can evaluate a percentage like follow.

the 16% of 575 is 0.16(575)=345

the 102% of 250 will be 750

Starting with the expression:

[tex](4\times3)+23\times4-3[/tex]

Solve parenthesis first. Since 4 times 3 equals 12, then the expression is equal to:

[tex]12+23\times4-3[/tex]

Next, solve for multiplications. In this case, solve 23 times 4:

[tex]12+92-3[/tex]

Finally, solve additions and substractions from left to right:

[tex]\begin{gathered} 12+92-3=104-3 \\ =101 \end{gathered}[/tex]

Therefore:

[tex](4\times3)+23\times4-3=101[/tex]

Barney spent $70 on 3 shirts and 2 pairs of pants

Robin bought 1 shirt and 4 pairs of pants for $90

Let x be the cost for each shirt

Let y be the cost for each pair of pants

3x+2y=70 (1)

x+4y=90 (2)

Having this system of equations, we can graph on the graph calculator:

The solution of two linear equations corresponds to the intersection of the two lines because the coordinate pair naming every point on a graph is a solution to its corresponding equation:

In this case the solution is: (10, 20) and corresponds to the cost of the shirt and pant.

Shirt: $10

Pant:$20

Answer:

(x+4)(x-5)

Step-by-step explanation:

Second order polynomial in the following format:

ax² + bx + c = 0

Has roots x¹ and x².

Can be factored as:

(x - x¹)(x - x²)

So, we have to find the roots.

Finding the roots:

Bhaskara formula, which is:

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

In the polynomial given in this question:

a = 1, b = -1, c = -20

So

[tex]x=\frac{-(-1)\pm\sqrt{(-1)^2-4\ast1\ast(-20)}}{2}=\frac{1\pm\sqrt{81}}{2}[/tex]

The roots are:

[tex]x^1=\frac{1+9}{2}=5,x^2=\frac{1-9}{2}=-4[/tex]

The factored form is:

(x - x¹)(x - x²) = (x - (-4))(x - 5) = (x+4)(x-5)

Answer:

Step-by-step explanation:

I hope this helps! :) If it does could you please mark me brainliest?

Answer:

Slope : -1

y = intercept : (0,31)

Step-by-step explanation:

The ship's horizontal distance from the lighthouse is: 1930.59 feet.

What is tangent or tan in trigonometry?

The ratio of the side opposite the angle we know or want to know over the side next to that angle is known as the tangent, which is sometimes abbreviated as T-A-N. The side touching the angle that is NOT the hypotenuse, or the side opposite the right angle, is the neighboring side.

Given in the question,

Height of lighthouse = 135 feet,

angle of elevation = 4 degree,

We know that, tan Θ = perpendicular/ base

Here, height is perpendicular and distance is base,

Putting the values,

tan4° = 135/B

B = 1930.59 feet

Therefore, distance is 1930.59 feet.

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Answer:The answer is 1930.59

Step-by-step explanation:

5 markers -------> $6.55

4 markers -------> x

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. The function h measures the height.

. The units on h meters.

. h'(t) measures the velocity

. The units on h'(t) are meters per second

. The units on t are seconds

Como cada uno de los hermanos le regalará un trozo de twizzler a su padre, ékl tendra tres twizzlers. En milímetros eso es

[tex](3)(100)=300\text{ mm}[/tex]

Ahora tenemos que convertir los milimetros a centímetros. Recordemos que un centímetro tiene 10 milímetros. Entonces, tenemos que dividir la cantidad total de milímetros entre 10.

[tex]\frac{300}{10}=30[/tex]

Por lo tanto el padre tendrá 30 cm de twizzler en total.

The simple interest formula is given by:

[tex]FV=PV(1+in)[/tex]

FV: future value

PV: present value

i: interest rate

n: interest periods

We have from the question:

FV: $5000

PV: ?

i: 5.8%

n: 9.

Then:

[tex]5000=PV(1+(0.058\cdot9))[/tex]

Thus

[tex]PV=\frac{5000}{1.522}\Rightarrow PV=3285.15[/tex]

Then, we should invest in $3285.15 to have $5000 in 9 years.