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The area of rectangle ABCD is 18 square units.

Step 1: Calculate the length of the rectangle.

The length of the rectangle is the distance between points A and B (or C and D). Using the distance formula:

[tex]\[ \text{Length} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]

For the points A(-5,2) and B(-5,4), the length is:

[tex]\[ \text{Length} = \sqrt{(-5 - (-5))^2 + (4 - 2)^2} \][/tex]

[tex]\[ \text{Length} = \sqrt{(0)^2 + (2)^2} \][/tex]

[tex]\[ \text{Length} = \sqrt{0 + 4} \][/tex]

[tex]\[ \text{Length} = \sqrt{4} \][/tex]

[tex]\[ \text{Length} = 2 \][/tex]

Step 2: Calculate the width of the rectangle.

The width of the rectangle is the distance between points B and C (or A and D).

For the points B(-5,4) and C(4,4), the width is:

[tex]\[ \text{Width} = \sqrt{(4 - (-5))^2 + (4 - 4)^2} \][/tex]

[tex]\[ \text{Width} = \sqrt{(4 + 5)^2 + (0)^2} \][/tex]

[tex]\[ \text{Width} = \sqrt{9^2 + 0} \][/tex]

[tex]\[ \text{Width} = \sqrt{81} \][/tex]

[tex]\[ \text{Width} = 9 \][/tex]

Step 3: Calculate the area using length and width.

Now that we have the length and width of the rectangle, we can use the formula:

[tex]\[ \text{Area} = \text{Length} \times \text{Width} \][/tex]

[tex]\[ \text{Area} = 2 \times 9 \][/tex]

[tex]\[ \text{Area} = 18 \][/tex]

The length of the rectangle, calculated as the distance between points A and B (or C and D), is 2 units. The width of the rectangle, calculated as the distance between points B and C (or A and D), is 9 units. Multiplying the length and width together gives us the area of the rectangle, which is 18 square units. Therefore, the correct answer is that the area of rectangle ABCD is 18 square units.

Complete question :

RECTANGLE ABCD has vertices A(-5,2) B(-5,4) C(4,4) D(4,2) calculate the area.

[tex]\bf \cfrac{Melanie}{Jacob}\qquad \stackrel{ratio}{\cfrac{4.1}{20.5}}\qquad \qquad \cfrac{4.1}{20.5}=\cfrac{m}{5}\implies 20.5=20.5m \\\\\\ \cfrac{20.5}{20.5}=m\implies 1=m[/tex]

1. [tex]x[/tex] in quadrant IV means [tex]\sin x<0[/tex], so

[tex]\cos^2x+\sin^2x=1\implies\sin x=-\sqrt{1-\cos^2x}=-\dfrac{\sqrt3}2[/tex]

2. [tex]x[/tex] in quadrant I means [tex]\cos x>0[/tex]. Then

[tex]\cos x=\sqrt{1-\sin^2x}=\dfrac{\sqrt2}2[/tex]

3. [tex]x[/tex] in quadrant II means [tex]\sin x>0[/tex]. Then

[tex]\tan x=\dfrac{\sin x}{\cos x}=\dfrac{\sqrt{1-\cos^2x}}{-\frac12}=\dfrac{\frac{\sqrt3}2}{-\frac12}=-\sqrt3[/tex]

4. If [tex]\sin x=-1[/tex], then [tex]\cos x=0[/tex], so [tex]\tan x[/tex] is undefined.

Answer:

probably 6////////////

Answer:

The answer is 6

Step-by-step explanation:

In a year there is 365 days.

From the first condition, 6x + 2 = to a unknown number of coins

From the second condition, 7x + 4 = to the same number of unknown coins.

The number which satisfies this given condition is 326 coins.

If we divide this number by 8 to share it among 8 students =

326 ÷ 8 = 40 coins/ student and 6 coins remaining. Therefore, the answer is

6 Coins

For this case we have by definition, that the volume of a cone is given by:

[tex]V = \frac {1} {3} * \pi * r ^ 2 * h[/tex]

Where:

A: It is the cone radius

h: It's the height

They tell us that the diameter is 21 m, then the radius is half the diameter, that is: 10.5m. The height is 4m. Substituting the data:

[tex]V = \frac {1} {3} * \pi * (10.5) ^ 2 * 4\\V = \frac {1} {3} * \pi * 110.25 * 4\\V = 147 \pi[/tex].

Finally, the volume of the cube is[tex]147 \pi \ m ^ 3[/tex]

ANswer:

Option B

Answer:

147[tex]\pi[/tex]m^3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Going from (1, -2) to (3,6), x increases by 2 and y increases by 8.  Thus, the slope m of this line is m = rise / run = 8/2 = 4.

I think you meant, "What is the EQUATION of the line that passes through the point (-1, 1) and is parallel to a line that passes through

(3, 6) and (1, -2)?  We have seen that this slope is -4.  

Starting with the point-slope equation of a line, we have:

y - 6 = -4(x - 3)

Answer:

B. 1

Step-by-step explanation:

they only cross at one point... look below

ANSWER

B. 1

EXPLANATION

The given system of equations is;

–2x + 4y = –7

y= -1/2x + 5

We rewrite the first equation is slope intercept form:

4y = 2x–7

[tex]y = \frac{1}{2}x - \frac{7}{4} [/tex]

The two equations have different slopes.

This means that they will intersect at one point in the XY plane.

Hence the system has a unique solution.

Answer:

∠XMZ = 74°

Step-by-step explanation:

Since the arcs XZ and BC are congruent, then

∠BNC = ∠XMZ ← substitute values

6x - 88 = 3x - 7 ( subtract 3x from both sides )

3x - 88 = - 7 ( add 88 to both sides )

3x = 81 ( divide both sides by 3 )

x = 27

Hence

∠XMZ = 3x - 7 = (3 × 27) - 7 = 81 - 7 = 74°

Answer:

To complete the square move the non-x term to the right

2x^2 + 13x = -20 then divide equation by x^2 coefficient

x^2 + 6.5x = -10

then coefficient of x (which is 6.5) divide by 2 (3.25) square the number

=10.5625 Then add 10.5625 to both sides of the equation:

x^2 + 6.5x + 10.5625 = -10 + 10.5625

x^2 + 6.5x + 10.5625 = .5625

Take the square root of both sides

(x + 3.25)^2 = .75

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

12/4 = 3

so

(a^2/b^3)^4 = a^8 / b^12

An exponential expression refers to an expression where a base number is raised to a certain power or exponent. The exponent indicates how many times the base number is repeated as a factor. Exponential expressions can be simplified or evaluated using the rules of exponents.

In mathematics, an exponential expression refers to an expression where a base number is raised to a certain power, or exponent. The exponent indicates how many times the base number is repeated as a factor. For example, in the expression 23, 2 is the base and 3 is the exponent, so it means that 2 is repeated as a factor three times. Exponential expressions can be simplified or evaluated using the rules of exponents.

For example, in the expression 42, 4 is the base and 2 is the exponent, so it means that 4 is repeated as a factor two times. This can be evaluated as 42 = 4 x 4 = 16.

Exponential expressions are commonly used in various mathematical applications, such as in compound interest, population growth, and scientific calculations.

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Answer:

b= -1

Step-by-step explanation:

Step 1: Find out value of x

x-2 = 0

x= 2

Step 2: Substitute value of x in the equation

x^3 + bx^2-  4 = 0

(2)^3 + b (2)^2 - 4 = 0

8 + 4b - 4=0

4 - 4b = 0

4b = -4

b = -1

Answer: 16% as a fraction is 4/25

Step-by-step explanation:

convert 16% into a decimal then put it over 100 and simplify which gives you 4/25

Answer: [tex]=\frac{4}{25}[/tex]

Step-by-step explanation:

First, you need to convert 16% to decimal form. To do this, you must divide it by 100. Then, the numerator will be 16 and the denominator will be 100:

[tex]=\frac{16}{100}[/tex]

And finally, you need to simplify the fraction by reducing it. Notice that the numerator and the denominator can be both divided by 4. Then, dividing by 4 you get:

[tex]=\frac{4}{25}[/tex]

Since the numerator and the denominator cannot be divided by the same number anymore, then the fraction is simplified.

Therefore, the fraction equal to 16% (simplified) is:

[tex]=\frac{4}{25}[/tex]

Answer:

The answer in the procedure

Step-by-step explanation:

Let

x ----> the dog walking hours

y ----> the car washing hours

we know that

The system of linear inequalities is equal to

[tex]x+y\leq20[/tex] -----> inequality A

[tex]9x+10y\geq 90[/tex] -----> inequality B

Solve the system of inequalities by graphing

The solution is the shaded area

see the attached figure

Two possible combinations of hours are

(10,10) and (0,9)

Verify

For (10,10)

Substitute the value of x and the value of y in both inequalities

Inequality A

[tex]10+10\leq20[/tex]

[tex]20\leq20[/tex]  -----> is true

Inequality B

[tex]9(10)+10(10)\geq 90[/tex]

[tex]190\geq 90[/tex] ----> is true

therefore

(10,10) is a possible solution

For (0.9)

Substitute the value of x and the value of y in both inequalities

Inequality A

[tex]0+9\leq20[/tex]

[tex]9\leq20[/tex]  -----> is true

Inequality B

[tex]9(0)+10(9)\geq 90[/tex]

[tex]90\geq 90[/tex] ----> is true

therefore

(0,9) is a possible solution

Final answer:

The situation can be described by two inequalities: x + y <= 20 and 9x + 10y >= 90. Two possible combinations of hours that meet these requirements are 0 hours of dog walking and 9 hours of car washing, or 8 hours of dog walking and 2 hours of car washing.

Explanation:

To represent this situation with a system of linear inequalities, we will let x be the number of hours working as a dog walker and y be the number of hours working as a car wash attendant. The two inequalities based on the constraints of the problem are:

x + y \<= 20 (because you can't work more than 20 hours).

9x + 10y >= 90 (because you need to earn at least $90).

Solving this system can be done graphically or algebraically. Let's see two possible solutions:

If you want to work at both jobs, you could work 8 hours dog walking (x=8) and 2 hours at the car wash (y=2). This means you would earn 8*$9 + 2*$10 = $92, which is also enough to cover the expenses.

neither even or odd, odd, even

Answer:

Odd, neither, neither

Step-by-step explanation:

A function is even if f(x) = f(-x).  That means that it passes through the origin and is symmetrical about the y-axis.

A function is odd if f(x) = -f(-x).  That means that it passes through the origin and is symmetrical about the origin.

The first graph, the line, passes through the origin and is symmetrical about the origin.  So it is odd.

The second graph does not pass through the origin, nor is it symmetrical.  So it is neither odd nor even.

The third graph does not pass through the origin, nor is it symmetrical about the y-axis.  So it is neither odd nor even.

Answer:

its cos:48/80

Step-by-step explanation:

cos-1(48/80)=53.13

For this case we have by definition of trigonometric relations that the cosine of an angle is given by the leg adjacent to said angle on the hypotenuse of the triangle. So:

[tex]Cos (Y) = \frac {64} {80} = \frac {32} {40} = \frac {16} {20} = \frac {8} {10} = \frac {4} {5}[/tex]

After simplifying we have to:

[tex]Cos (Y) = \frac {4} {5}[/tex]

ANswer:

[tex]Cos (Y) = \frac {4} {5}=0.8[/tex]

Answer:

The first 6 terms are -7,-14,-28,-56,-112,-224

Step-by-step explanation:

The given sequence is defined recursively by:

[tex]a_1=-7[/tex] and [tex]a_n=2(a_{n-1})[/tex]

When n=2

[tex]a_2=2(a_{2-1})[/tex]

[tex]a_2=2(a_{1})[/tex]

[tex]a_2=2(-7)=-14[/tex]

When n=3

[tex]a_3=2(a_{3-1})[/tex]

[tex]a_3=2(a_{2})[/tex]

[tex]a_3=2(-14)=-28[/tex]

When n=4

[tex]a_4=2(a_{4-1})[/tex]

[tex]a_4=2(a_{3})[/tex]

[tex]a_4=2(-28)=-56[/tex]

When n=5

[tex]a_5=2(a_{5-1})[/tex]

[tex]a_5=2(a_{4})[/tex]

[tex]a_5=2(-56)=-112[/tex]

When n=6

[tex]a_6=2(a_{6-1})[/tex]

[tex]a_6=2(a_{5})[/tex]

[tex]a_6=2(-112)=-224[/tex]

The first 6 terms are -7,-14,-28,-56,-112,-224

180-40-60=80 degrees

Answer:

-28

Step-by-step explanation:

(5+2) = 7

7 + 2 - 40 = -31

-31 + 3 = -28

Answer:

Is needed [tex]452.32\ ft^{2}[/tex] of sheet metal to build this tank

Step-by-step explanation:

we know that

To find how much sheet metal is needed to build this tank including the top, calculate the lateral area of the cone plus the lateral area of the cylinder plus the area of the top of the cylinder

[tex]A=\pi rl+2\pi rh1+\pi r^{2}[/tex]

we have

[tex]r=5\ ft[/tex]

[tex]h1=8\ ft[/tex] ----> height of the cylinder

[tex]h2=6\ ft[/tex] ----> height of the cone

Find the slant height of the cone l

Applying Pythagoras Theorem

[tex]l^{2}=r^{2}+h2^{2}[/tex]

substitute

[tex]l^{2}=5^{2}+6^{2}[/tex]

[tex]l^{2}=61[/tex]

[tex]l=\sqrt{61}\ ft[/tex]

assume

[tex]\pi =3.14[/tex]

[tex]A=(3.14)(5)(\sqrt{61})+2(3.14)(5)(8)+(3.14)(5)^{2}[/tex]

[tex]A=122.62+251.2+78.5=452.32\ ft^{2}[/tex]

Answer:

  72°

Step-by-step explanation:

You correctly found x, but the measure of the angle is ...

  4x-22 = 4·23.5-22 = 72°

___

or (6x-69)° = (141-69)° = 72°

Answer:

the solution is (-1, 2)

Step-by-step explanation:

Let's solve the system

(3x + 4y = 5)

(2x - 3y = -8)

using the method of elimination by addition and subtraction.  Notice that if we multiply all terms of the first equation by 3 and all terms of the second by 4, y as a variable will temporarily disappear:

  9x + 12y = 15

  8x - 12y  = -32

-----------------------

 17x       = - 17, so x = -1.  

Replacing x in the second equation by -1, we get:

2(-1) - 3y = -8, or

2 + 3y = 8,

or 3y = 6.  Thus, y = 2, and the solution is (-1, 2).

The solution to the given system of equations is x = -1 and y = 2. We found these values using the elimination method, first by making the coefficients of x in both equations the same, then eliminating x and solving for y, and finally substituting y = 2 into the first equation and solving for x.

To solve the given system of equations, we can use the elimination method. First, we need to make the coefficients of either x or y the same in both equations. We can do so by multiplying the first equation by 2 and the second equation by 3:

⟹ (3x * 2 + 4y * 2 = 5 * 2) and (2x * 3 - 3y * 3 = -8 * 3)

When simplified, we get:

⟹ 6x + 8y = 10 and 6x - 9y = -24

Now, we subtract the second equation from the first one to eliminate x:

⟹ (6x + 8y) - (6x - 9y) = 10 - (-24)

⟹ 17y = 34

Finally, we solve for y by dividing both sides of the equation by 17:

⟹ y = 34 / 17

⟹ y = 2

Substitute y = 2 into the first original equation:

⟹ 3x + 4 * 2 = 5

⟹ 3x + 8 = 5

⟹ 3x = -3,

On simplifying, we get x = -1. So, the solution to the system is x = -1, y = 2.

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Answer:

The triangle ABC is reflected over the line y = x ⇒ answer B

Step-by-step explanation:

* Lets revise some transformation

- If point (x , y) reflected across the x-axis

∴ Its image is (x , -y)

- If point (x , y) reflected across the y-axis

∴ Its image is (-x , y)

- If point (x , y) reflected across the line y = x

∴ Its image is (y , x)

- If point (x , y) reflected across the line y = -x

∴ Its image is (-y , -x)

- If point (x , y) rotated about the origin by angle 90° anti-clock wise

∴ Its image is (-y , x)

- If point (x , y) rotated about the origin by angle 90° clock wise

∴ Its image is (y , -x)

- If point (x , y) rotated about the origin by angle 180°

∴ Its image is (-x , -y)

* There is no difference between rotating 180° clockwise or  

anti-clockwise around the origin

* Lets find the vertices of ABC and A'B'C' to solve the problem

- In Δ ABC

# A = (5 , -5) , B = (5 , -4) , C = (2 , -4)

- In Δ A'B'C'

# A' = (-5 , 5) , B = (-4 , 5) , C = (-4 , 2)

∵ The image of (5 , -5) is (-5 , 5)

∵ The image of (5 , -4) is (-4 , 5)

∵ The image of (2 , -4) is (-4 , 2)

∴ The point (x , y) is (y , x)

- From the rule above

∴ The triangle ABC is reflected over the line y = x

Answer:

The triangle ABC is reflected over the line y = x ⇒ answer B

Step-by-step explanation:

Answer:

3/5

Step-by-step explanation:

There are 10 letters in the word "statistics".

Out of which, there are 3 s's and 3 t's.  

So, the question asks what's the probability to get a S or a T out of 10 letters.

Since the number of S's (3) and the number of T's equal 6, that means you have 6 chances out of 10 to pick an S or a T.

6/10 or if we simplify/reduce it... we get 3/5.

the correct answer is 3/5

The question is asking for the probability of selecting either an 's' or a 't' from the word 'statistics'. To solve this, we need to look at the total number of each letter and the total number of letters in the word. The word 'statistics' has 10 letters in total, with 3 's' letters and 3 't' letters.

To calculate the probability, we add the number of 's' letters to the number of 't' letters, which gives us 6. Then we divide this sum by the total number of letters in the word:

Probability('s' or 't') = (Number of 's' + Number of 't') / Total number of letters

Probability('s' or 't') = (3 + 3) / 10 = 6/10 = 3/5.

Thus, the correct answer is 3/5, meaning there is a 60% chance of picking either an 's' or a 't' from the word 'statistics'.

Answer:

y = (1/12)x^2

Step-by-step explanation:

The vertex of this parabola is halfway between (0, 3) and the directrix, y = -3; that is, it's at (0, 0).

The applicable equation for this vertical parabola is 4py = x^2, where p is the distance between the vertex and the focus.  Here that distance is p = 3.

Thus, 4py = x^2 becomes 4(3)y = x^2, or 12y = x^2, or y = (1/12)x^2.

The answer is: y = (1/12)x^2.

The equation of the parabola with focus (a,b) and directrix y=c is

(x−a)2+b2−c2=2(b−c)y

The equation for a parabola with its focus at (0, 3) and a directrix of y = -3 i.e:

The vertex of this parabola is halfway between (0, 3) and the directrix, y = -3; that is, it's at (0, 0).

The applicable equation for this vertical parabola is 4py = x^2, where p is the distance between the vertex and the focus.  Here that distance is p = 3.

Thus, 4py = x^2 becomes 4(3)y = x^2, or 12y = x^2, or y = (1/12)x^2.

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Answer:

  51.3°

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you ...

  Tan = Opposite/Adjacent

For angle y, the opposite side is 10 cm, and the adjacent side is 8 cm. Then you have ...

  tan(y) = (10 cm)/(8 cm)

  y = arctan(1.25) ≈ 51.3402° ≈ 51.3°

Answer:

Monthly interest rate is r=0,004375

Monthly principal c=590,625

Step-by-step explanation:

Monthly interest payment rate :

[tex]r=\frac{5.25}{12}:100=0,0004375[/tex]

Now, we need to find monthly principal payment : [tex]c=\frac{rP}{1-(1+r)^{-N}}[/tex]

Use this rule : [tex]N=30*12=360[/tex]

P=108000

r=0,004375

[tex]c=\frac{0.004375*108000}{1-(1+0.004375)^{-360}} =\frac{472.5}{0.8}=590,625[/tex]

Answer: 596.38

Step-by-step explanation:

ANSWER

The explicit rule is

[tex]f(n) = 45+9n [/tex]

EXPLANATION

The given sequence is :

54,63,72,81,...

The first term of this sequence is

[tex]a = 54[/tex]

The common difference is

[tex]d =63 - 54 = 9[/tex]

The explicit rule is given by:

[tex]f(n) = a + d(n - 1)[/tex][tex]f(n) = 54+9(n -1 )[/tex]

We expand to get:

[tex]f(n) = 54+9n -9[/tex]

[tex]f(n) = 45+9n [/tex]

None of them is correct .

Answer:Neither Maxim nor Salma

Step-by-step explanation:

i just answered ed the question

Answer:

a. the answer is incorrect

b. 1

Step-by-step explanation:

step 1) 6x=48

step 2) 48/6

step 3)x=3

Answer:

56.07 degrees

Step-by-step explanation:

This is a classic problem involving right triangle trig.  We are looking for the angle that has a side opposite it with a measure of 55 m and a side adjacent to it with a measure of 37 m.  This is the tangent ratio of the missing angle.  Our equation then looks like this:

[tex]tan\theta=\frac{55}{37}[/tex]

To find a missing angle on your calculator in degree mode, hit 2nd then tan and you'll see "tan^-1(  " on your display.  After the open parenthesis, enter your fraction and hit the enter button to get the angle measure.  56.07°

Answer:47. 72°

Step-by-step explanation:

from the attached figure below; adjacent =37 hypotenuse=55

θ = ?

From trig. formular,

cos θ = adjacent / hypotenuse

cos θ = 37 / 55

cos θ =0. 6727

θ = cos⁻¹ (0. 6727)

θ = 47. 72°

The angle of elavation is 47. 72°