Consider the equation and the following ordered pairs: (6,y) and (x,1).

y=−2x+5

By performing some simple mathematical operations, the answers to all the subparts are:

So, the answers after multiplication are:

Therefore, by performing some simple mathematical operations, the answers to all the subparts are:

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The distance between the eyes and the distance to the image of the toes will be 273.80 cm.

Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides.

According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Given that It is 163 cm from your eyes to your toes. You're standing 220 cm in front of a tall mirror.

The distance between the image of toes and eyes will be calculated as,

H² = P² + B²

H= √(P² + B²)

H = √(163² + 220²)

H = √(26569+48400)

H = √74969

H = 273.80 cm

Therefore, the distance between the eyes and the distance to the image of the toes will be 273.80 cm.

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Answer:  1 question Solve for x

x=

3

−y−2z−10

​

Solve for y

y=−3x−2z−10

Step-by-step explanation: Steps for Solving Linear Equation

3x+y+2z=−10

Subtract y from both sides.

3x+2z=−10−y

Subtract 2z from both sides.

3x=−10−y−2z

The equation is in standard form.

3x=−y−2z−10

Divide both sides by 3.

3

3x

​

=

3

−y−2z−10

​

Dividing by 3 undoes the multiplication by 3.

x=

3

−y−2z−10

​

The zeroes of the parabola is -1, -5.

What is parabola and zeroes of parabola?

A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.

The equation of parabola can be expressed in two different ways, such as the standard form and the vertex form. The standard form of parabola equation is expressed as follows:

f(x) = y= ax2 + bx + c

To find zeroes of parabola

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

Given equation is

f(x) = [tex]x^{2} +6x+5[/tex]

a = 1, b = 6, c = 5

x = -6 ±[tex]\sqrt{36-4(5)}[/tex]/2

x = -6 ±[tex]\sqrt{16} /2[/tex]

x = -6 ± 4 /2

hence,

x = -6-4/2 and x = -6 +4/2

x = -5 or x = -1

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Considering the definition of an equation and the way to solve it, the equation is y +(-3)=-8 and the solution is -5.

An equation is an algebraic equality in which letters appear with unknown value.

In an equation appears:

The solution of a equation means determining the value that satisfies it. In this way, by changing the unknown to the solution, the equality must be true. To solve an equation, keep in mind:

Being "y" a number, and knowing that sum of a number and -3 is -8, the equation in this case is:

y + (-3)= -8

Solving:

y -3= -8

y= -8 +3

y= -5

Finally, the number "y" is -5.

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After solving the given equation for r, the value of r is √T/4π.

So, the formula equation is:

Now, solve for r as follows:

Therefore, after solving the given equation for r, the value of r is √T/4π.

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The measure of angle B is x, while the measure of angle A is 2·x. The 70° measure of angle C and the angle sum property of the interior angles of a triangle indicates that angle B is [tex]36.\overline 6^{\circ}[/tex] and angle A is [tex]73.\overline 3^{\circ}[/tex]

The interior angles of a triangle are the angles formed by the sides sides of the triangle.

The question can be solved by making use of the known properties of a triangle.

The angle sum property of the interior angles in a triangle gives;

The sum of the interior angles of a triangle is 180°

Therefore; x + 2·x + 70 = 180

3·x = 180° - 70° = 110°

[tex]x = \dfrac{110^{\circ}}{3} = 36\frac{2}{3} ^{\circ}[/tex]

The measure of angle A is 2·x

Which gives;

[tex]A = 2 \times 36\frac{2}{3} ^{\circ} = 73\frac{1}{3} ^{\circ} = 73.\overline 3^{\circ}[/tex]

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Answer: mode is 94

Step-by-step explanation:

The math shows the world is designed, and that design is symmetry and spirals.

How is math found in nature What is the significance of mathematical patterns in nature?

Mathematics is seen in many beautiful patterns in nature, such as symmetry and spirals. Both are aesthetically appealing and proportional. Symmetry can be radial, where the lines of symmetry intersect a central point such as a daisy or a starfish.

Here,

If Hailey used math to describe the design in nature: the number of legs insects and spiders have, the number of petals on flowers, and even the patterns of spots on some animals. The math shows the world is designed, and that design is symmetry and spirals.

Hence, the math shows the world is designed, and that design is symmetry and spirals.

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The percentage is the indicating hundredth thus the percentage of people speeding on this road who noticed the sign would be 84% - 75% = 9%.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

As per the given,

Percentage of people who notice the speed limit = 84%

The percentage of people who notice the sign and follow the speed limit is 75%.

Therefore, 84% - 75%  = 9% are the percentage speeding and noticed.

Hence "The percentage is the indicating hundredth thus the percentage of people speeding on this road who noticed the sign would be 84% - 75% = 9%".

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The dimensions of the cup that minimize the construction cost are 2 x 2 x 5 in

Given:  Capacity = 20 in³, cost of material for the side = 12¢/in² and cost of material for the base = 60¢/in²

In order to calculate the dimension of the cup

Let h and x represent the height and square base respectively

Thus, the capacity (volume) of the pencil cup is can be represented as:

V = x²h     (where V = 20)

20 = x²h

h = 20/x²

At minimum cost, we have:

C(x) = 60x² +  12(4xh)

C(x) = 60x² +  48xh         (put h = 20/x²)

C(x) = 60x² +  48x(20/x²)

C(x) = 60x² +  960/x

Differentiating with respect to x, we have:

C(x) = 120x - 960/x²      (multiply through by x²)

120x³-960 = 0

120x³ = 960

x³ = 960/120

x³ = 8

x = ∛8 = 2 in

For the height:

h = 20/x²

h = 20/2²

h = 20/4 = 5 in

dimensions = 2 x 2 x 5 in

Therefore, the dimensions of the cup that minimize the construction cost are a 2 x 2  square base and  height of 5 in

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The equations that can be used are y(y - 5) = 750, y² - 5y = 750, and (y + 25)(y – 30) = 0.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Length = y

Width = y - 5

Area = 750

The area of a rectangle is written as,

Length x Width = Area

y x (y - 5) = 750

y² - 5y = 750

y² - 5y - 750 = 0

(y + 25)(y – 30) = 0

The equations that can be used are y(y - 5) = 750, y² - 5y = 750, and (y + 25)(y – 30) = 0.

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Answer:

150 adult tickets where sold

Step-by-step explanation:

If we multiply 150 times 3 that gives us 450, which acounts for all the students. And 150 is the number thats left of adults that adds up to 600.

The angular value of x is 3° as per the given the given information in the question.

An angle in Euclidean geometry is the figure produced by two rays, called the sides of the angle, that have a common termination, called the vertex of the angle. Angles formed by two rays lie in the plane containing the rays. Angles are also generated by the intersection of two planes. These are referred to as dihedral angles. Two intersecting curves can also define an angle, which is the angle of the rays lying tangent to the respective curves at their point of intersection.

Given,

m ∠GQP=80

m ∠RQP=3+59x

m ∠RQG=32x+4

From the figure,

m ∠RQG+ m ∠GQP= m ∠RQP

32x+4+80°=3+59x

27x=81°

x=3°

Therefore, the value of x=3°

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Answer: [tex]\frac{4\sqrt{x} }{t^2}[/tex]

Step-by-step explanation:

You can start by either applying the exponent to both the numerator and denominator (exponent rule), or make things simpler by dividing first. Doing the latter allows me to show both properties. Since the terms in the fraction are being multiplied, we can divide common terms which will leave us with [tex]\frac{16x}{t^4}[/tex] on the inside. Now that it is simplified, we can apply the exponent. We will end up with 4x^1/2 in the numerator and t^2 in the denominator. If the exponent seems daunting, it is also helpful to know that raising something to the exponent of 1/2 is basically taking the square root of it.

The Perimeter of triangle CED  is 57 in.

What is a parallelogram?

A parallelogram is the name given to a quadrilateral in geometry. In a parallelogram, the opposing sides are parallel and of equal length. The rhombus, rectangle, and square are just a few shapes that are parallelograms.

Having two sets of parallel sides makes a quadrilateral a parallelogram. A parallelogram has opposite sides that are the same length and angles that are the same size. Additionally, the internal angles on the same transverse side are supplementary. 360 degrees are equal to the total of all internal angles.

Two parallel pairs of sides make up a parallelogram, a quadrilateral. Four right angles form a parallelogram called a rectangle.

Rhombus: An equal-length parallelogram with four sides.

The diagonals of a parallelogram bisect each other AC = 2 CE

Substitute AC= 34 into AC = 2CE =34 = 2CE

Calculate 34 = 2 CE=>  CE = 17

The diagonals of a parallelogram bisect each other BD = 2DE

Substitute BD= 28 into BD = 2DE =>  28 = 2DE

Calculate 28 = 2DE  => DE = 14

Opposite sides of parallelogram are congruent AB = CD

Substitute AB = 26 into AB = CD =>  CD = 26

Perimeter of a triangle PΔCDE = CE + CD + DE

Substitute  CE = 17, DE = 14, CD = 26.

PΔCDE = CE + CD + DE

PΔCDE = 17+ 26 + 14

PΔCDE = 57 in

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The probability that the student will pass the test, using the binomial distribution, is of:

0.172 = 17.2%.

The formula that gives the probability of x successes is presented as follows:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters of the formula are listed as follows:

In the context of this problem, the values of these parameters are given as follows:

The probability of passing is given by:

P(X ≥ 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).

In which:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 7) = C_{10,7}.(0.5)^{7}.(0.5)^{3} = 0.1172[/tex]

[tex]P(X = 8) = C_{10,8}.(0.5)^{8}.(0.5)^{2} = 0.0440[/tex]

[tex]P(X = 9) = C_{10,9}.(0.5)^{9}.(0.5)^{1} = 0.0098[/tex]

[tex]P(X = 10) = C_{10,10}.(0.5)^{10}.(0.5)^{0} = 0.0010[/tex]

Then:

P(X ≥ 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.1172 + 0.0440 + 0.0098 + 0.0010 = 0.172 = 17.2%.

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The factors of 6x²y-10xy+15x-25​ are (3x-5)(2xy+5).

According to the question,

We have the following expression:

6x²y-10xy+15x-25​

In this expression, we can not use any identity to solve it further.

Now, in order to find the factors of this expression, we will find the common terms from the first two terms and one common factor from the last two terms.

Taking 2xy as a common factor from first two terms and 5x as a common factor from the last two terms:

2xy(3x-5)+5(3x-5)

Taking (3x-5) as a common factor from the above expression:

(3x-5) (2xy+5)

Hence, the factors of 6x²y-10xy+15x-25​ are (3x-5)(2xy+5).

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Answer: over budget by $64



Step-by-step explanation:

$99 coat

$75 Shoes

$240 tv

Total=414

total-budget=

Budget =$350

414-350

= 64

The grams of fat that are contained in one serving of the low-fat yogurt are: 3.7968g.

To obtain the number of grams of fat that is contained in one serving of the low-fat yogurt, we need to first note the percentage content of the low-fat version of yogurt.

100 - 45.75% = 54.25% or 0.5425

Since one serving of the yogurt contains 7g of fat, then the low-fat serving will be equal to:

7g × 0.5425  = 3.7968

So, the total gram of fat for one serving of the low-fat yogurt is equal to:

3.7968g

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Answer: 17%

Step-by-step explanation:

If you add up 34%, 23%, 5%, & 25% that would equal 83%, if you subtract the 83% from 100%, you would get 17%.The 17% is equivalent to 510. So Rachel Teeter will have $510 in her savings account.

Answer:

Store B

Step-by-step explanation:

Store A: $2.50 ÷ 2 = $1.25

Store B: $3.25 ÷ 3 = $1.08 (to nearest cent)

Store B offers the better deal.

Check the picture below.

Answer:  y intercept:  (0, -1/7)

Step-by-step explanation:

First you start with y = 10x - 1/7

Since your finding the y-intercept, you turn the 10x into a 0

So you would have y = -1/7

So y = -1/7

is your answer!

⇒[tex]\frac{d}{dx} (e^{x} )= e^{x} *\frac{d}{dx} (x)\\\frac{d}{dx} (e^{x} )=e^{x}*1\\\frac{d}{dx} (e^{x} )=e^{x}[/tex]

⇒Note this is all applied due to chain rule.

Answer:

[tex] = \frac{8(x + 3) {}^{2} }{2(x + 3)} = 4(x + 3) = 4x + 12[/tex]

Hopefully this will help u

Step-by-step explanation:

To purchase $12,200 worth of restaurant equipment for her business, Linda made a down payment of $1600 and took out a business loan for the rest. After 3 years of paying monthly payments of $322.48, she finally paid off the loan.

(a) What was the total amount Linda ended up paying for the equipment

(including the down payment and monthly payments)?

How much on loan:

12,200 - 1,600 = $10,600 loan amount

How much paid on loan:

$322.48 * 3 years * 12 months = $11,608.28 amount paid on loan

Total paid:

= loan amount + amount paid on loan

$10,600 + $$11,608.28

= $22,208.28 paid overall

________________________________________

(b) How much interest did Linda pay on the loan?

= loan amount - amount  paid on loan

= $11,608.28 - $10,600

= $1,009.28 paid in interest

If they took 1 hour and 35 minutes to complete the test and finished at 1:20 they started at 11:45.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, The total time of the math test Raven took was 1 hour and 35 minutes.

Now he finishes the test at 1:20.

So, One hour before the time was 12:20.

20 minutes before that was exactly 12:00 and 15 minutes before that was

11:45 so a total of 1 hour and 35 minutes.

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