Write the equation of the line passing through the given point that is

perpendicular to the given line.


20. y = 3/3x - 2; (-2,4)

21. -2x + 7y = 14; (-3, -7)

22. 3x - 8y = 16; (-3, 1)

23. 4x+ y = 7; (4,2)

⇒Find the sum of  12t+8 and [tex]t^{2} -10t+3[/tex]

⇒For sum we add:

[tex]=(12t+8)+(t^{2} -10t+3)\\=12t-10t+8+3+t^{2} \\=2t+11+t^{2}[/tex]

⇒The next step is to subtract [tex]9t^{3} -3t+8[/tex] and [tex]t^{2} -8t+4[/tex] from the answer we got above.

[tex]=(2t+11+t^{2} )-(9t^{3} -3t+8)-(t^{2} -8t+4)\\=2t+11+t^{2} -9t^{3} +3t-8-t^{2} +8t-4\\=2t+3t+8t+11-8-4+t^{2} -t^{2} -9t^{3} \\=13t-1-9t^{3} \\[/tex]

⇒The answer  is shown above.

The functions representing exponential growth or decay are f(x) = 3²ˣ⁺¹, f(x) = 0.8ˣ⁻⁰, f(x) = π⁴ˣ, f(x) = (4/9)ˣ, f(x) = -(3)ˣ, f(x) = (-3)ˣ

An exponential function is defined by the formula f(x) = aˣ, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.

The exponential function is an important mathematical function which is of the form f(x) = aˣ

Where a>0 and a is not equal to 1, and x is any real number.

If the variable is negative, the function is undefined for -1 < x < 1.

Here,

An exponential curve grows, or decay depends on the exponential function. Any quantity that grows or decays by a fixed per cent at regular intervals should possess either exponential growth or exponential decay.

In the question, the functions that are exponential are

f(x) = 3²ˣ⁺¹, f(x) = 0.8ˣ⁻⁰, f(x) = π⁴ˣ, f(x) = (4/9)ˣ, f(x) = -(3)ˣ, f(x) = (-3)ˣ

Learn more on exponential function here;

https://brainly.com/question/2456547

#SPJ1

The solution of the given expression will be 9/16.

Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given an expression, [-3*(10+(-7))]²÷[(3-(-9)]²

[-3*(10+(-7))]²÷[(3-(-9)]² = (-9)²/12²

= 9/16

Hence, The solution of the given expression will be 9/16.

For more references on expression, click;

https://brainly.com/question/14083225

#SPJ1

The area and perimeter of the composite figures are as follows;

Figure 1;

Perimeter = 70 km

Area = 200 km²

Figure 2

Perimeter = 28 cm

Area = 24 cm²

Figure 3

Perimeter = 40 m

Area = 88 m²

Figure 4

Perimeter = 64 m

Area = 96 m²

The area of a composite figure is the sum of the areas of the parts or simple figures that make up the figure.

Figure 1

The perimeter = 10 + 10 + 5 + 20 + 5 + 10 + 10 = 70

The area = 10 × (10 + 5) + 10 × 5 = 200

Figure 2

Figure 3

Figure 4

Learn more about finding the area and perimeter of composite figures here:

https://brainly.com/question/27699952

#SPJ1

Using the definition of isosceles and equilateral triangles:

12. x = 77°; y = 58°; z = 122°

13. x = 60°; y = 120°; z = 60°

All three sides and angles of an equilateral triangle are equal in measure. On the other hand, two sides and two base angles of an isosceles triangle are equal to each other.

12. x = 1/2(180 - 26) [based on the definition of isosceles triangle]

x = 1/2(154)

x = 77°

y = 1/2(180 - (90 - 26)) [based on the definition of isosceles triangle]

y = 1/2(180 - 64)

y = 1/2(116)

y = 58°

z = 180 - 58 [base angles of isosceles triangle are equal]

z = 122°

13. Each interior angle of an equilateral triangle is equal to 60 degrees.

Therefore, x = the measure of one interior angle

x = 60°

y = 180 - 60 [linear pair]

y = 120°

The base angles of the triangle that has two equal sides would be 60° [180 - 120]

Therefore:

z = 180 - 2(60)

z = 60°

Learn more about equilateral and isosceles triangles on:

https://brainly.com/question/17264112

#SPJ1

The system of linear equations shows that the adult tickets was 155 and children ticket was 259

In algebra, a system of equations comprises two or more equations and seeks common solutions to the equations. "A system of linear equations is a set of equations which are satisfied by the same set of variables."

To solve this problem, we can set up two equations for this

Let;

x + y = 414 ...eq(i)

47x + 22y = 12983 ...eq(ii)

Solving both equations; the values of x and y are 155 and 259 respectively

Learn more on system of linear equation here;

https://brainly.com/question/13729904

#SPJ1

x + 2 = 10

x + 2 - 2 = 10 - 2

x = 8

x - 2 = 10

x - 2 + 2 = 10 + 2

x = 12

2x = 10

2x/2 = 10/2

x = 5

x/2 = 10

x/2 × 2 = 10 × 2

x = 20

Your answer is -5.

Hope this helps.

If two cones are similar, then the height of the larger cone will be equal to 3 cm.

An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely encompass the surface of a compact figure. The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.

As per the data provided in the question,

For volume, the scale factor is,

k³ = 27/8

For length, the scale factor is,

k = ∛27/8

k = 3/2

Then the height of the larger will be,

h = 3/2 × 2

h = 3 cm.

To know more about Area:

https://brainly.com/question/27683633

#SPJ1

El polígono regular tiene las características de un pentágono, cuya medida de ángulo central es 72° y la suma de todos los ángulos centrales es igual a 360°.

En este problema debemos determinar que polígono regular tiene un ángulo central con medida de 72°, la suma de todos los ángulos centrales de un polígono es igual a 360°. El número de lados del polígono se puede determinar mediante la siguiente operación:

n = 360° / θ

Donde θ es la medida del ángulo central, en grados.

Si sabemos que θ = 72°, entonces el número de lados del polígono:

n = 360° / 72°

n = 5

El polígono regular es un pentágono.

Para aprender más sobre polígonos regulares: https://brainly.com/question/23936721

#SPJ1

Answer: 105 words

Step-by-step explanation:

15x7=105

The volume of the solid generated by revolving the region bounded by y = x and y = x²-3x about the x-axis will be x³/3-3x²/2+c.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that,

y = x²-3x

The volume of the solid generated by revolving the region bounded by y = x and y = x²-3x about the x-axis is obtained as,

[tex]=\int\:x^2-3x \ dx \\\\ = \int \:x^2dx-\int \:3xdx \\\\ =\frac{x^3}{3}-\frac{3x^2}{2} \\\\ =\frac{x^3}{3}-\frac{3x^2}{2}+C[/tex]

Thus, the volume of the solid generated by revolving the region bounded by y = x and y = x²-3x about the x-axis will be x³/3-3x²/2+c.

Learn more about the equation here,

https://brainly.com/question/10413253

#SPJ2

Answer:

137.11 mg

Step-by-step explanation:

divide 200 mg by 2 = 100 mg

divide 100 by 1590 = 0.0628930818

multiply this by 1000 = 62.8930818

subtract 62.8930818 from 200 = 137.1069182

137.1069182 rounded to 2 decimal places is 137.11 mg

therefore, the answer is 137.11 mg

The number of pencils that will be in the large package, given the ratio of the pencils to pens in the package, is 25 pencils

In the original package, the ratio was such that there was 4 pens for every 10 pencils. This means that the number of pencils per pen was:

= 10 / 4

= 2. 5 pencils per pen

If there is a larger package with the same ratio and the number of pens in the package is 10 pens, then the number of pencils would be:

= Number of pens x Pencils per pen

= 10 x 2.5

= 25 pencils

Find out more on ratios at https://brainly.com/question/21207992

#SPJ1

Answer:

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

Given is a quadratic equation:

A quadratic equation has no real solutions if its discriminant is negative.

The discriminant of ax² + bx + c is:

Apply to given equation:

Find the value of n when D < 0:

Using percentage formula, the mark up price on the microscope is £49

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Markup shows how much more a company's selling price is than the amount the item costs the company. In general, the higher the markup, the more revenue a company makes. Markup is the retail price for a product minus its cost, but the margin percentage is calculated differently.

Let's find 50% of £98

50 / 100 = x / 98

0.5 = x / 98

x = 0.5 * 98

x = 49

The mark up price is £49

Learn more on percentage here;

https://brainly.com/question/24877689

#SPJ1

The series of transformations that would map Figure M onto Figure N will be firstly rotated about the origin and then translated upward by 3 units.

What is a transformation of a shape?

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the structure and/or location of the object.

From before the refers to the object's initial condition, and Picture, after transformation, refers to the object's ultimate structure and location.

Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.

If the geometry is rotated, then there is no change in angles.

The translation does not change the shape and size of the geometry. But changes the location.

The series of transformations that would map Figure M onto Figure N will be firstly rotated about the origin and then translated upward by 3 units.

More about the transformation of the shape link is given below.

brainly.com/question/27224339

#SPJ1

Disclaimer

The question given by you is incomplete, so a similar question have been solved here and the image is attached.

Determine a series of transformations that would map Figure M onto Figure N.

Answer:

18

Step-by-step explanation:

If 4 out of 10 wore glasses, then 6 out of 10 did not wear classes.  This would be 60% or .6

.6x30 = 18

By adding the two given fractions we will see that 1/2 of the students either walked or came by bus

Let's say that there are N students in total. We know that a fraction of 1/8 of these N students walk to school.

And a fraction of 3/8 of the students go by bus to the school.

Then the fraction that either walks or came by bus to school is given by the addition between the two fractions above, then we just need to solve.

f = 3/8 + 1/8

We can see that we have the same denominator in both fractions, so we can directly add the numerators:

f = (3 + 1)/8 = 4/8

Now we can simplify the fraction to get:

f = 1/2

Learn more about fractions:

https://brainly.com/question/11562149

#SPJ1

Answer:

26.009

Step-by-step explanation:

Let's break it down

(2*10) + (6*1) + (9*1/1000)

20+6+0.009

26.009

Hundreds- 0

Tens- 2

Ones- 6

Tenths- 0

Hundredths- 0

Thousandths- 9

Answer:

26.009

Step-by-step explanation:

since 2 is being multiplied by ten there are 2 tens

And since 6 is being multiplied by 1 there are 6 ones

and since 9 is being multiplied by 1/1000 there are 9 thousandths

And the rest of the place values are zero and should be written like

26.009

Hopes this helps please mark brainliest

The given expression 1-tan(a) is simplified as (cos(a)-sin(a))/cos(a).

The given trigonometric expression is 1-tan(a).

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

We know that, tanθ=sinθ/cosθ

Now, 1-tan(a) =1-sin(a)/cos(a)

= (cos(a)-sin(a))/cos(a)

Therefore, the given expression 1-tan(a) is simplified as (cos(a)-sin(a))/cos(a).

Learn more about the trigonometric ratios here:

https://brainly.com/question/25122825.

#SPJ1

not defined because 848 has no unit

The exponential function f(x)=(1/8)^-x can be evaluated to give us:

An exponential function  serves as Mathematical function in the form f (x) = ax hving “x” as  variable,the conceptis the concept of  exponential function.

The given function is f(x)=(1/8)^-x

Then f(2)=(1/8)^-2 = 1/(1/8)^2 =1/(1/64) =64

f(-3)=(1/8)^-(-3) = 1/512

f(-3)=(1/8)^-(1/2) =[tex]\frac{1}{\sqrt{\frac{1}{8} } }[/tex]

Learn more about exponential function here: https://brainly.com/question/2456547

#SPJ1

Answer:

You can write a statement of proportionality without any additional information:

... weight = k × length . . . . . . . . for some constant k

If you need to know the specific weight of a specific length, then you need to know the constant of proportionality (the value of k).

Step-by-step explanation:

Answer:

55 Hot dogs were sold

Step-by-step explanation:

Let d = hot dogs

Let h = hamburgers

d + h = 175

d + 1.50h = 235

Re-write

d + h = 175 for d and then substitute this into the second equation

d = 175 - h

d + 1.5 h = 235

175 - h + 1.50h = 235  Combine like terms

175 + .5h = 235  Subtract 175 from both sides

.5 h = 60  Divide both sides by .5

h = 120

120 Hamburgers were sold.  

Plug in 120 for h to solve for hot does

d + h = 175

d + 120 = 175  Subtract 120 from both sides

d = 55

Check

d + 1.5h = 235

55 + 1.5(120) = 235

55 + 180 = 235

235=235

Answer:

22/27

Step-by-step explanation:

5 play nothing.

27 - 5 = 22

22 play basketball only or baseball only or both.

p(plays baseball or basketball) = 22/27

The first angle in a triangle is three times that of a second angle. The second angle is two times that of the third angle. The ratio of the angles in the triangle is 1:2:3.

When two rays are joined at one point, they produce the geometric shape known as an angle. The vertex is the shared point between the two rays, which are known as the arms or sides of the angle. When two rays meet at a point, they make an angle. An "angle" is the term used to describe the "opening" between these two rays, and it is symbolised by the symbol. Angles are typically expressed as 60°, 90°, etc. and are measured in degrees.

Given,

A first angle of let x

2x = 2nd angle

3x = 3rd angle

Angle sum = 180

x + 2x + 3x = 180

6x = 180

Dividing,

x = 30°

2x = 2(30)

2nd angle = 60

3x = 3(30)

3rd angle = 90

30°, 60°, and 90° are the three angles.

Ratio 1:2:3

To learn more about angle, visit:

https://brainly.com/question/28451077

#SPJ1

The cos, tan, sec, csc and cot of the angle θ in quadrant IV are 3/5, -4/3, 5/3, -5/4 and -3/4 respectively

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Given that: sin(θ) = -4/5 and θ is in quadrant 4.

Using this information, we can sketch the location of the angle θ in the quadrant (See the attached image). Therefore:

(a) cos(θ) = 3/5     (adj/hyp)

(b) tan(θ) = -4/3     (opp/adj)

(c) sec(θ) = 1/cos(θ) = 5/3

(d) csc(θ) = 1/sin(θ) = -5/4

(e) cot(θ) = 1/tan(θ) = -3/4

Learn more about Trigonometry on:

https://brainly.com/question/11967894

#SPJ1