Match the systems of equations with their solution sets. y + 12 = x2 + x x + y = 3 y − 15 = x2 + 4x x − y = 1 y + 5 = x2 − 3x 2x + y = 1 y − 6 = x2 − 3x x + 2y = 2 y − 17 = x2 − 9x -x + y = 1 y − 15 = -x2 + 4x x + y = 1 Solution Set Linear-Quadratic System of Equations {(-2, 3), (7, -6)} arrowRight {(-5, 8), (3, 0)} arrowRight {(-2, 5), (3, -5)} arrowRight {(2, 3), (8, 9)} arrowRight

The correct rectangular equivalence of 3sqrt(2)·cis(7pi/4 ) is:

3sqrt(2)·cos( 7pi/4 ) + i·sqrt(2)·sin( 7pi/4 )  =  3 - 3i.

David mistakenly interchanged the Sin function and the Cos function when he was calculating the problem.

Hence the correct rectangular equivalence is:

3sqrt(2)·cos( 7pi/4 ) + i·sqrt(2)·sin( 7pi/4 )  =  3 - 3i.

An equation is rectangular in form when it is comprised of Variables like X and Y and can be represented on a Cartesian Plane.

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2/40 = 1/20.
We are able to simplify by dividing 2 and 40 by the greatest common factor (GCF), which was 2. We know this because 2 and 40 can be divided by 2.
2cm is 1/20th of 40cm.

Answer:

The speed of aeroplane =875 miles/hr and the speed of wind =125 miles/hr.

Step-by-step explanation:

Let’s assume the speed of the plane =x miles/hr

And let the speed of wind =y miles/hr

So, the speed of the aeroplane in the direction of wind =(x+y) miles/hr

Speed of the aeroplane in the opposite direction of wind =(x–y) miles/hr

We know that, distance=speed×time

Then according to the given conditions, we have

3300=(x+y)×(3+(18/60))

here convert 18mins to hour by dividing by 60 and add to 3hrs.

⇒x+y= 3300/3.3

⇒x+y=1000 … (i)

And,

3300=(x-y)×(4+(24/60))

here convert 24mins to hour by dividing by 60 and add to 4hrs.

⇒x-y= 3300/4.4

⇒x-y=750 … (ii)

Adding equation (i) and (ii), we get

2x=1750

⇒x= 1750/2

=875

Substituting the value of x in equation (ii), we get

875−y=750

⇒y=875-750

⇒y=125

Therefore, the speed of aeroplane =875 miles/hr and the speed of wind =125 miles/hr.

The teacher will use 3 rolls only to have perfect measurements.

1 yard = 3 feet

4 large bulletin boards are there each needing 9 yards of border.
That means 4 large bulletin boards in total need

9×4 yards of border

= 36 yards of border

= 108 feet of border

Also, there is a small bulletin board that only needs 12 feet border

Hence, in total there is a need for

108 + 12 = 120 feet border.

The border is sold in 40-foot rolls.
Hence, there is a need for 120/40 rolls

i.e. 3 rolls

Hence, the teacher will use 3 rolls only.  

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Answer:

The answer is 3

Step-by-step explanation:

The vertices of an inscribed square of a circle are located on the circumference and on perpendicular diameters

The vertices of a square inscribed in a circle can be located as follows;

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Double angle identity for sine:

[tex]\sin(2x) = 2 \sin(x) \cos(x)[/tex]

[tex]\implies 2 \sin(\theta) - \sin(2\theta) \cos(\theta) = 2 \sin(\theta) - 2 \sin(\theta) \cos^2(\theta)[/tex]

Factorize the left side.

[tex]2 \sin(\theta) - 2 \sin(\theta) \cos^2(\theta) = 2 \sin(\theta) \left(1 - \cos^2(\theta)\right)[/tex]

Pythagorean identity:

[tex]\cos^2(x) + \sin^2(x) = 1[/tex]

[tex]\implies 2 \sin(\theta) \left(1 - \cos^2(\theta)\right) = 2 \sin^3(\theta)[/tex]

so that

[tex]\boxed{2 \sin(\theta) - \sin(2\theta) \cos(\theta) = 2 \sin^3(\theta)}[/tex]

The solution to the system of equations is x = -1.4 and y = 1.6

The system of equations is given as:

-3x + 3y = 9

2x - 7y = -14

Divide the first equation by  3

-x + y = 3

Make y the subject

y = 3 + x

Substitute y = 3 + x in 2x - 7y = -14

2x - 7(3 + x) = -14

Expand

2x - 21 - 7x = -14

Evaluate the like terms

-5x = 7

Divide by -5

x = -1.4

Substitute x = -1.4 in y = 3 + x

y = 3 - 1.4

Evaluate

y = 1.6

Hence, the solution to the system of equations is x = -1.4 and y = 1.6

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Answer:

Question:

Estimate the solution to the system of equations.

You can use the interactive graph below to find the solution.

⎪y=−2x−5

⎨y=2x−2

ANSWER:

CORRECT (SELECTED)

x= -3/4

y= -3 1/2

​

Answer:

x=7

Step-by-step explanation:

3x + 0,25x + 0,10 (2x) +0,05 (x + 3) = 24,65

<=> 3x+0,25x+0,2x+0,05x+0,15=24,65

<=> 3,5x=24,5

<=> x=7

Answer:

Height is 40√2 m or 56.57 m

Explanation:

Use Pythagoras theorem: a² + b² = c²

where 'a' and 'b' are the legs and 'c' is the hypotenuse

Here given:

Substitute values:

(20)² + (h)² = 60²

400 + h² = 3600

h² = 3600 - 400

h² = 3200

h = √3200

h = 40√2

h = 56.6 meter

Answer: A

Step-by-step explanation:

Following the first two steps of the sequence of transformations,

[tex]A(-4,-2) \longrightarrow (-2,-1) \longrightarrow (-2,1)[/tex]

We need to map this onto D(1,1), which involves a translation 3 units right.

In the similarity transformation of ΔABC to ΔDFE, ΔABC was dilated by a scale factor of [1/2 ], reflected across the [x-axis ], and moved through the translation [(X+3, Y+0)].

So, correct option is: A.

Here, we have,

from the given fugre we get,

A =( -4, -2)

Following the first two steps of the sequence of transformations,

Dilated by a factor of 1/2 => A' = ( -2, -1)

reflected across the X-axis => A''=( -2, 1)

and moved through the translation becomes D = ( 1,1)

We need to map this onto D(1,1), which involves a translation 3 units right.

so, translation=> ( -2 + 3, 1+0) => (X+3, Y+0)

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Answer:

Step-by-step explanation:

The ratio is 1 : 3, so we multiply the numbers by 3

4 * 3 = 12

3 * 3 = 9

So, the length is 12 and the width is 9.

12 * 9 = 108

So the area is 108

Hope this helps!

The answer is: True

[tex] \\ \\ \\ [/tex]

Answer:

Step-by-step explanation:

The Crusades were a series of religious wars initiated, supported, and sometimes directed by the Latin Church in the medieval period. The best known of these Crusades are those to the Holy Land in the period between 1095 and 1291 that were intended to recover Jerusalem and its surrounding area from Islamic rule.

Taking into account the rule of three, 1110,4275 Mexican pesos was 81.35 dollars worth and 6.67 dollars was 91.03 Mexican pesos worth.

The rule of three is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them.

That is, what is intended with it is to find the fourth term of a proportion knowing the other three.  

If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other) , the direct rule of three must be applied.

To solve a direct rule of three, the following expression must be followed, being a, b and c known data and x the variable to be calculated:

a ⇒ b

c ⇒ x

So: [tex]x=\frac{cxb}{a}[/tex]

On October 23, 2011, one U.S. dollar was worth 13.65 Mexican pesos. So, you can apply the following rules of three:

1 dollar ⇒ 13.65 Mexican pesos

81.35 dollars ⇒ x

So: [tex]x=\frac{81.35 dollarsx13.65 Mexican pesos}{1 dollar}[/tex]

Solving:

x= 1110,4275 Mexican pesos

13.65 Mexican pesos ⇒ 1 dollar

91.03 Mexican pesos ⇒ x

So: [tex]x=\frac{91.03 Mexican pesosx 1 dollar}{13.65 Mexican pesos}[/tex]

Solving:

x= 6.67 dollars

In summary, 1110,4275 Mexican pesos was 81.35 dollars worth and 6.67 dollars was 91.03 Mexican pesos worth.

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The amount of money invested at 12% was $4327 while $1442 was invested at 7%.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the amount invested at 12% and y represent the amount invested at 7%, hence:

x + y = 5679   (1)

Also:

0.12x = 0.07y + 407.5   (2)

From both equations:

x = 4327, y = 1442

The amount of money invested at 12% was $4327 while $1442 was invested at 7%.

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Using the areas of the circles, the probability of landing in the shaded area of the picture is of 1/81.

The area of a circle of diameter d is given as follows:

[tex]A = 0.25\pi d^2[/tex].

For the smaller circle, the diameter is d = 6, hence the area is:

[tex]A_s = 0.25\pi \times 6^2 = 9\pi[/tex]

For the larger circle, the diameter is d = 54, hence the area is:

[tex]A_l = 0.25\pi \times 54^2 = 729\pi[/tex]

Hence the probability(desired area divided by total area) is:

[tex]p = \frac{9\pi}{729\pi} = \frac{1}{81}[/tex].

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Answer:

puede ser su raiz que seria 90.79

Step-by-step explanation:

Answer:

Your answer is -2/-3

The formula to calculate slope is y2-y1/x2-x1

I think it will help you

Answer:

-1/2

Step-by-step explanation:

[tex] m = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]

[tex]m = \dfrac{0 - 5}{10 - 0} = \dfrac{-5}{10} = -\dfrac{1}{2}[/tex]

Answer: slope = -1/2

According to the empirical rule, the percent of the data points that are below 100 is; 95.44%

We are given;

Mean; μ = 88

Standard deviation; σ = 6

Sample mean; x' = 100

Formula for z-score is;

z = (x' -  μ)/σ

z = (100 - 88)/6

z = 2

Now, from the empirical rule of normal distribution graph attached, we see that at z = 2, the percentage is 95.44%. However, we want to find the percentage that lie below 100. Thus, this is 95.44%

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The total surface area of a cylinder with radius 4 and height 8 is 96π.

It follows from the task content that the total surface area of the cylinder is to be determined. The total surface area of the cylinder is given by the formular;

S=2πr(r+h)

S=2πr(r+h)

= 2 × π × 4(4 + 8)

= 2 × π × 4(12)

= 2π × 48

= 96π

Hence, the total surface area of the cylinder in terms of π is; 96π.

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Answer:

A

Step-by-step explanation:

False . The equation a= 2√3 ft.;c = 4 ft is: A= 2√3 ft².

Given:

a = 2√3 ft,

c = 4 ft,

Lengths of the sides of a right triangle = a and b

Hypotenuse= c

Hence:

c²=a²+b²

4²=(2√3)²+b²

16=12+b²

4=b²

b=2

Area of triangle

A=1/2×a×b

A=1/2×2√3×2

A=4√3÷2

A=2√3 sq.ft

The Area of the triangle is 2√3 ft².

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Answer:

The perimeter of the parallelogram is 2πr

Step-by-step explanation:

The area of the circle should be the same as the area of the parallelogram. Therefore, the area of the circle cannot equal the area of the parallelogram.

Hope this helps. (:

Answer:

18 ft.

Step-by-step explanation:

Area: 216 sq. ft.

1 side: 12 ft.

Area=l x w

216=12 x ?

216/12 = x

x = 18

Answer:

its D hope this helps

Step-by-step explanation:

pls mark brainliest

Answer:

Step-by-step explanation:

First, we will find the midpoint for the x - coordinate first.

Midpoint (x) = [tex]\frac{-1+(-6)}{2} \\=\frac{-1-6}{2} \\=\frac{-7}{2} \\=-3.5[/tex]

Now we will find the midpoint for the y - coordinate.

Midpoint (y) = [tex]\frac{-6+5}{2} \\=\frac{-1}{2} \\=-0.5[/tex]

Therefore from these 2 values we know that the midpoint of this 2 points is (-3.5,-0.5)

Answer:

Exact Form:

1/243

Decimal Form:

0.00411522…

The total number of grapes bought in a day is 1600 .

An equation is a mathematical statement which relates two algebraic expression with an equal sign.

It is given that

34 customers buy a bag of grapes at Jery's Market.

There are an average of 47 grapes in each bag.

Let the no. of grapes = x

Then

x = 34 * 47

x = 1598

rounded to the nearest ten

The total number of grapes bought in a day is 1600 .

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