How dose breaking up the multiplication problem above by place value help you solve the problem

For exponential equation a^1/n = r option D is true i.e. r^n=a.

What are exponential equations?

Exponents are used in exponential equations, as the name implies. We already know that the exponent of a number (base) specifies how many times the number (base) has been multiplied. But what happens if a number is variable? When the power is a variable in an equation, it is referred to as an exponential equation.

For example, 3^x = 81, 5^x - 3 = 625, 62^y - 7 = 121, etc are some examples of exponential equations.

Exponential equations are classified into three categories. These are :

As given,

                 a^1/n=r

Now we take 1/n from left side of exponential equation to right side i.e.

      a=r^n   (As a^1/2 = 4 ---> a=4^2)

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Answer:

The sum of any triangle's angles is always 180 degrees, so take the equations and add them together, equal to 180.

(2v- 20 + 2v - 15 + 31 = 180)

v = 46

Answer:

46°

Step-by-step explanation:

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

Check the picture below.

Answer:

Step-by-step explanation:

We will have to convert this to vertex form.

First we add y to both sides.

y = 3x^2 + 9x - 3

The vertex form is y = a(x – h)^2 + k

y = 3(x^2 + 3x) - 3

We need to complete the square now, and half if 3 is 1.5, and 1.5^2 is 2.25, so we add 2.25 inside the parentheses but we have to be careful, because if we subtract 2.25 from outside the parentheses it wouldn't work because the 2.25 inside the parentheses is being multiplied by 3, so we have to subtract 2.25*3=6.75 from the outside.

y=3(x^2 + 3x + 2.25) - 9.75

we can simplify this now to

y=3(x + 1.5)^2 - 9.75

and now this is vertex form. From here it is incredibly easy to get the vertex. Just take the x value required to make the total in the parentheses zero, so in this problem it would be -1.5 (Because (-1.5+1.5)^2 is zero) and then you have your x coordinate. From there we just take k, which in this problem is -9.75, and it is the y value of our vertex.

In conclusion, the vertex is (-1.5. -9.75)

Considering the expression of a line, the equation of the line that passes through the points (-3,7) and (4,-7) is y= -2x +1.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope can be calculated using:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope m and one of the points in the expression of a line, the value of the ordinate to the origin can be obtained.

In this case, being (x₁, y₁)= (-3, 7) and (x₂, y₂)= (4, -7), the slope m can be calculated as:

m= (-7 - 7)÷ (4 - (-3))

m= (-7 - 7)÷ (4 +3)

m= (-14)÷ 7

m= -2

Considering point 1 and the slope m, you obtain:

7= (-2)× (-3) + b

7= 6+b

7 -6= b

1= b

Finally, the equation of the line is y= -2x +1.

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Total no of people = 118

Women = 49 (d)

Men = 118- 49 = 69 (a)

Total no of people like tea = 63

Total no of people do not like tea = 118-63 = 55

No of Men do not like tea = 33(c)

No of Women do not like tea = 55- 33 = 22 (f)

No.of Women like tea = 49-22 = 27 (e)

No . of men like tea = 69 - 33 = 36(b)

5. If  Jackson bought an ultra-slim Television. The size of this screen is 17.69.

6.  If the ramp has a 550 incline and the height of the ramp is 15m. The height of the ramp is -68.24.

5. Size of the screen

Pythagorean theorem

c²= a² + b²

c² = 12² + 13²

c²= 144+169

c = √313

c = 17.69

6. Height

Using SOH CAH TOA

sin550= 15/x

x= 15/sin550

x= 15/-0.2195

x= -68.24

Therefore the size is 17.69  and the height is -68.24.

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The equation of the line of best fit for this data-set is given as follows:

y = 10x + 60.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the coefficients are given as follows:

The function goes through point (0,60), hence the intercept b of the line of fit is given as follows:

b = 60.

When x increases by 2, from 0 to 2, y increases by 20, from 60 to 80, hence the slope m is obtained as follows:

m = 20/2 = 10.

Hence the line of fit is given as follows:

y = 10x + 60.

Meaning that the third option is correct.

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Answer:

y = 10x + 60.

Step-by-step explanation:

The largest possible whole-number length for the third-side is 27 .

What is whole number ?

Whole numbers are made up of all the ordinal numbers and 0. Natural numbers are the names given to counting numbers in mathematics. Thus, the definition of a whole number is a grouping of all natural numbers plus 0. Along with zero, all positive integers are also considered whole numbers.

There are no fractions, decimals, or negative integers in whole numbers, which are actual numbers. There is no fraction or decimal equivalent to zero. It is neutral; neither good nor bad. The whole-number rule is observed by zero.

All natural numbers and 0 are included in the category of whole numbers. They are a subset of real numbers, which exclude negative numbers, decimals, and fractions. Whole numbers include counting numerals as well.

Consider a triangle with side lengths a , b ,c such that a < b < c

a = 18 and b = 10 are the two known sides

Let c be the missing side length

The missing side has the property that...

a - b < c < a + b

18 - 10 < c < 18 + 10

8 < c < 28

Meaning that if c is a whole number then it can take on any of these values { 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 }

So c = 27 is the largest possible third side, where only whole number sides are considered.

We can't have a third side of 28 because the two other sides add to a+b = 10 + 18 = 28 and a triangle wouldn't form (instead only a straight line would).

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The angle measures of x are given as follows:

13) x = 50º.

14) x = 40º.

15) x = 112º.

16) x = 32º.

17) x = 22º.

18) x = 120º.

For item 13, at the triangle at the right, we have that the sum of the measures of the internal angles of a triangle is of 180º, hence:

43 + 57 + y = 180

y = 80º.

Meaning that x is the base angle of an isosceles triangle, for which the top angle is of 80º, hence:

2x + 80 = 180

2x = 100

x = 50º.

For item 14, we have that the third angle in the triangle with angles 50º and 80º is the complement of x, hence:

50 + 80 + 90 - x = 180

x = 40º.

For item 15, the internal angles are given as follows:

2y + 44 = 180

2y = 136

y = 136/2

y = 68.

The external angle is supplementary with it's internal angle, hence:

x = 180 - 68 = 112º.

For item 16, the internal angles of the triangle are given as follows:

Hence:

90 + x + 58 = 180

x = 32º.

For item 17, the internal angles are given as follows:

Hence the value of x is obtained as follows:

180 - (6x - 7) + 2x + 103 - x = 180

-6x + 7 + 2x + 103 - x = 0

5x = 110

x = 22º.

For item 18, we have an equilateral triangle, hence the internal angles are of 60º and the external angles, representing the value of x, are given as follows:

x = 180 - 60 = 120º.

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The answers are given below.

In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.

Given:

1) 2Sin(9θ).Cos(5θ)=1/2(Sin14θ+Sin4θ)

2) Sin(3θ)Sin(5θ)Cos(3θ)Cos(5θ)=1/2(Sin8θ+Sin2θ)

3)Cos6θ+Cos4θ=2Cos5θCosθ

4)Sin(13θ/2)+Sin9θ=2Sin(11θ/2)Sinθ

5)Cosθ=2√5/5

6)Cos2θ=23/2

7)Tan(π/12)=2-√3

8)Sin(165°)=√6-√2 /4

9)Cos(5π/18)Cos(2π/9)-Sin(5π/18)Sin(2π/9)=Cos(π/2)

                                                                      =0

Hence, these are the answers .

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Answer:0.39685026299

Step-by-step explanation:

...... calculator

Answer:

V = 157 in³

Step-by-step explanation:

the volume (V) of a cone is calculated as

V = [tex]\frac{1}{3}[/tex] πr²h ( r is the radius and h the height )

here diameter = 10 , then r = 10 ÷ 2 = 5 , then

V = [tex]\frac{1}{3}[/tex] × 3.14 × 5² × 6 ( cancel 3 and 6 by 3 )

  = 3.14 × 25 × 2

 = 3.14 × 50

= 157 in³

Answer:

48% of students picked a vanilla cupcake

Step-by-step explanation:

We can get 48% from this question by turning this data into a fraction

27 students picked vanilla out of a total amount of 50

= 27/50

= 48%

This equals a percentage of 48% of students picking a vanilla cupcake

Answer:

48%

Step-by-step explanation:

The framed poster will cover 156 square inches of space on a wall. So the answer is D.

What is the Rectangle?

A rectangle is a four-sided geometric shape with four right angles. The opposite sides of a rectangle are of equal length, and the opposite sides are of equal width. It is defined by its length and width. The length is the longer side of the rectangle and the width is the shorter side. The area of a rectangle is found by multiplying the length by the width, and the perimeter is found by adding the lengths of all four sides.

The poster itself is 12 inches by 9 inches, so it covers a total area of 129 = 108 square inches.

However, we also need to include the area covered by the frame.

The frame is 1 inch wide on all four sides of the poster.

So, the total area covered by the frame is 41*12 = 48 square inches.

To find the total area covered by the poster and the frame, we add the area of the poster to the area of the frame:

108 + 48 = 156 square inches

Therefore, The framed poster will cover 156 square inches of space on a wall. So the answer is D.

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Answer:

2nd choice

Step-by-step explanation:

m/54.2 = 82.5/271

Cross multiply:

m(271) = (82.5)(54.2)

m = 4471.5/271 = 16.5

The probability of selecting a chip with an even number, given that the chip is black, is 1/10.

The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.

Given:

An experiment involves selecting a numbered chip, some black and some white, from a bag of chips.

The probability of selecting a black chip with an even number is 1/2.

Let P(B and E) = 1/2

The probability of selecting a black chip is 3/5.

P(B) = 3/5

The probability of selecting a chip with an even number given that the chip is black

P(W) = 3/5 - 1/2

        = 6-5/10

        = 1/10

Therefore, the probability is 1/10.

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The fractions from the given options that is less than 1/2 hence option A.

The concept that will be used is division of the numerator by the denominator. The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line.

The given fraction is 1/2, if we convert to decimal, by dividing the numerator by the denominator  we have 0.5

Then we can conert the given options one after the other.

Option A ; 3/8 = 0.375

Option B = 5/8 = 0.625

Now from the result we can see that 0.375  < 0.5 < 0.625 , hence option A is correct.

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Answer:

We use decimals every day while dealing with money, weight, length, etc. Decimal numbers are used in situations where more precision is required than whole numbers can provide. For example, when we calculate our weight on the weighing machine, we do not always find the weight equal to a whole number on the scale.

Step-by-step explanation:

Hope this helps!

The volume of the cylinder is 169.7. (Option C)

Based on the provided information, let the radius of the cylinder be r and diameter of the cylinder be 2r. The diameter and height of the circular cylinder is the same. When examining the cross section of the cone and cylinder, there are two similar triangles. Hence,

(15 – 2r)/15 = r/5

5(15 – 2r)= 15r

75 – 10r = 15r

r = 3

Volume of the cylinder = πr^2h where r is the radius of the cylinder and h is the height of cylinder. As h = 2r, Hence,

V = πr^2(2r) = (22/7)(3^2)(6) = 169.7

Note: The question is incomplete as the options are incorrect. The correct options are A) 127.5 B) 151.6 C) 169.7 D) 168.5

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Answer:

0.125 gallons

Step-by-step explanation:

1/2 quart is equal to 0.125 gallons.

Answer:

½ quart = 0.125 gallons

Step-by-step explanation:

We know that,

→ 1 quart = 0.25 gallons

Then 1/2 quarts will equals,

→ 1 quart = 0.25 gallons

→ 1 q = 0.25 gal

→ 1/2 q = (0.25/2) gal

→ 1/2 q = 0.125 gal

Hence, answer is 0.125 gal.

The expression of the numbers as negative or positive is as follows;

6. ¹/₄

7. -15 yards

8. +6 pounds

9. +535 pounds

10. -9 degrees.

11. -²/₃ of the crowd

12. +$20

13. -10 points

14. -570

15. - ½

11. -350 feet

12. -500 miles

13. +10 feet

14. -13 degrees

15. + 20 miles

We can express numbers in this regards as either positive or negative with a positive number indicating a gain while a negative number indicates a loss.

Thus;

6. One-fourth of the students brought their hunch to school is expressed as; ¹/₄

7. After the penalty, there was a loss of 15 yards on the play is expressed as; -15 yards

8. He gained 6 pounds of muscle is expressed as; +6 pounds

9. He made a 535 deposit into a bank account is expressed as; +535 pounds

10. The temperature was 9 degrees below zero is expressed as; -9 degrees.

11. Two-thirds of the crewed left the stadium is expressed as; -²/₃ of the crowd

12. She received $20 on her birthday is a gain and expressed as; +$20

13. The student lost 10 points on the final exam is a loss and expressed as; -10 points

14. He made a 570 withdrawal from a bank account is a loss and is expressed as; -570

15. One-half of the gallon of milk is gone is a loss and is expressed as; - ½

Write the number that represents the given scenario. (DOK 1)

11. A submarine is 350 feet below sea level is negative and is expressed as; -350 feet

12. The family traveled 500 miles south on a road trip is in the negative y-axis and is; -500 miles

13. A rabbit hops 10 feet forward is positive movement and is; +10 feet

14. The temperature dropped 13 degrees is a loss and is expressed as -13 degrees

15. A hot air balloon traveled 20 miles north is in the positive direction and is expressed as; + 20 miles

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Answer: 7 and 6

Step-by-step explanation: 7 x 6 = 42

15 pound of dog food will feed 27 dogs

At the dog shelter, 36 dogs are fed in a day

These 36 dogs will be fed with 20 pound bag of dog food

Therefore the number of dogs that can be fed with 15 pound of dog food can be calculated as follows

= 36/20

= 1.8

The next step is to multiply 1.8 by 15

= 1.8 × 15

= 27

Hence 27 dogs will be fed with 15 pound of dog food

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The slope of the relationship is m = 5. Hence option A is the correct option.

What is the relationship?

A collection of ordered pairs having one item from each set makes up a relation between two sets. If the ordered pair (x,y) is present in the relationship and the objects x and y come from different sets, then the objects are said to be connected. One kind of relationship is a function.

Given linear relationship:

x             y

-2           -12

-1            -7

0             -2

1               3

2              8

The slope of the linear relationship that passes through the points (x₁, y₁) and (x₂, y₂) is [(y₂ - y₁)/(x₂ - x₁)].

Here, x₁ = -2 , y₁ = -12, x₂ = -1, y₂ = -7

The slope is (-7 - (-12))/(-1 - (-2))

=(-7 + 12)/(-1 + 2)

= 5/1

= 5

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The perimeter of rectangle ABCD will be 112 centimeters.

Let W be the rectangle's width and L its length.

The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be

Perimeter of the rectangle = 2(L + W) units

In the following rectangle ABCD, the sum of the lengths of AB, BC, and CD is 90 cm. The sum of the lengths of BC, CD, and AD is 78 cm.

We know that in a rectangle ABCD, AB = CD, and BC = AD. Then we have

AB + BC + CD = 90

2 AB + BC = 90                    ...1

BC + CD + DA = 78

2 BC + AB = 78               ...2

From equations 1 and 2, we have

3AB + 3BC = 168

AB + BC = 56

2(AB + BC) = 112 cm

P = 112 cm

The perimeter of rectangle ABCD will be 112 centimeters.

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The length of the cylinder for the condition is 11.66 cm

One of the fundamental three-dimensional shapes in geometry is the cylinder, which has two distant, parallel circular bases. At a predetermined distance from the centre, a curved surface connects the two circular bases. The axis of the cylinder is the line segment connecting the centres of two circular bases. The height of the cylinder is defined as the distance between the two circular bases.

Given the height of the pencil = 10 cm

and kept diagonally in cylinder,

and radius of cylinder = 3 cm

the relation between height, radius and diagonal of cylinder is

d² = h² + (2r)²

h² = d² - (2r)²

where d is diagonal and r is radius

h² = 10² + (2 x 3)²

h² = 100 + 36

h² = 136

h = √136

h = 11.66 cm

Hence height of cylinder is  11.66 cm.

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the image of question is  attached.

Answer:

Answer:height = √919.539cm

Step-by-step explanation:

we have to find height from slant height

we have to find height from slant heightso the formula is height= v(I²-r²)

we have to find height from slant heightso the formula is height= v(I²-r²)slant height I = 10 cm = 100 cm

we have to find height from slant heightso the formula is height= v(I²-r²)slant height I = 10 cm = 100 cmradius r = 3 cm = 9cm

we have to find height from slant heightso the formula is height= v(I²-r²)slant height I = 10 cm = 100 cmradius r = 3 cm = 9cmheight = √(100-9)

we have to find height from slant heightso the formula is height= v(I²-r²)slant height I = 10 cm = 100 cmradius r = 3 cm = 9cmheight = √(100-9)height = √91

we have to find height from slant heightso the formula is height= v(I²-r²)slant height I = 10 cm = 100 cmradius r = 3 cm = 9cmheight = √(100-9)height = √91height = 9.539 cm

Note

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The missing side in the triangle is 13 units which is the hypotenuse. The values of sine, cosine, and tangent of the referenced angle are 5/13, 12/13, and 5/12 respectively.

Trigonometry is the branch of mathematics that deals with particular functions of angles and how to apply them in calculations. There are six widely used angles-related trigonometric functions. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant(csc) are their respective names and acronyms.

In the given triangle the reference angle is θ.

So, the adjacent side (P) has a length of 12 units. The opposite (B) is the side having a length of 5 units. So, the hypotenuse will be

Then, acc to Pythagoras theorem, the hypotenuse (H) will be

H² = P² + B²

H² = 5² + 12²

H² = 25 + 144

H² = 169

H = √169

H = 13 units

This is the missing side of the given triangle.

The sine is

sinθ = opposite/ hypotenuse

= 5/13

cosθ = adjacent/ hypotenuse

= 12/13

tanθ = opposite/ adjacent

= 5/12

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Answer: The solution for k is -3/4.

To solve the equation, you can follow these steps:

Add 10k to both sides of the equation: -6k - 10 = 10 - 10k becomes -6k = 20

Divide both sides by -6: -6k/-6 = 20/-6 becomes k = -3/4

Step-by-step explanation: