How do you find out if a number is a multiple of 8?

Answer:

y = 13

Step-by-step explanation:

given (7, 33 ) is a solution of the top equation, then

x = 7, y = 33 satisfies the equation , that is

33 = 7a + 5 ( subtract 5 from both sides )

28 = 7a ( divide both sides by 4 )

4 = a

then

y = 4x + 5 ← top equation

substitute y = 4x + 5 into the other equation

9x + 2(4x + 5) = 44

9x + 8x + 10 = 44

17x + 10 = 44 ( subtract 10 from both sides )

17x = 34 ( divide both sides by 17 )

x = 2

substitute x = 2 into the top equation for value of y

y = 4x + 5 = 4(2) + 5 = 8 + 5 = 13

The volume of the pyramid is 3.5 cubic centimeters.

The volume of a pyramid can be calculated using the formula:

V = (1/3) * Base area * Height

Where Base area is the area of the base of the pyramid, and Height is the distance from the base to the apex of the pyramid.

Given that the area of the base of the pyramid is 4.6 cm^2 and the height of the pyramid is 2.3 cm, we can substitute these values into the formula and solve for the volume:

V = (1/3) * 4.6 cm^2 * 2.3 cm = 3.53 cm^3

So the volume of the pyramid is 3.53 cubic centimeters. Rounded to the nearest tenth of a cubic centimeter, the volume is 3.5 cm^3.

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Answer:11

Step-by-step explanation:

77 divided by 7 is 11.

Answer:

Step-by-step explanation:

As 9: 16.2

Then 6: EF   Lets take EF as side x

9:16.2 as

6:x    CROSS MULTIPLY ( 9×x and 16.2×6)

Cross multiplying gives you: 9x and 97.2

Then divide both answers by 9 ( 97.2÷9 and 9x÷9)

This gives you x=10.8 which is side EF

To find side AB ADD 9 and 6 to get 15 and subtract this from 36 and you get 21.

Using the same method to find EF find DE and you will get 37.8

Therefore, perimeter becomes:

16.2 + 37.8 + 10.8 = 64.8

HOPE THIS HELPS

Answer:

P△DEF=64,8

Step-by-step explanation:

P△ABC=36, AC=9, BC=6 → AB=21

AB/DE=BC/EF=AC/DF

AC/DF=9/16,2; AB/DE=21/DE ⇒ DE=(21*16,2)/9=37,8

AC/DF=9/16,2; BC/EF=6/EF ⇒ EF=(6*16,2)/9=10,8

P△DEF=16,2+37,8+10,8=64,8

The computer is worth $800 when it is created, $600 when it is used for the first time, and $450 when it is used for the second time.

A mathematical equation is a formula that connects two statements using the equal sign (=) to denote equivalence. An algebraic equation is a mathematical statement that establishes the equality of two mathematical expressions. For example, the variables 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14. Mathematical equations are used to express the connection between two phrases on either side of a letter.

given

This equation can be used to represent the value of the computer: price of the computer one year ago x (1 - rate of decline)

The computer's current market value 0 = $800

Computer value at time 1 is $800 multiplied by 3/14 by 1 to get $600.

The computer's current market value 2 = $600 x 3/4 = $450

Computer value at time 3: $450 multiplied by 3/4, or $337.50

The computer is worth $800 when it is created, $600 when it is used for the first time, and $450 when it is used for the second time.

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Therefore , the solution of the given problem of expression comes out to be  0.8x is the required expression.

Multiplying, dividing, adding, and subtracting are necessary math operations. When combined, the following expression would appear: A mathematical operator, some data, and an equation Values, variables, and functions make up a statement of fact's constituent parts, such as additions, deductions, multiplications, divisions, etc. It is possible to contrast and compare words and phrases.

Here,

Given :

Let x be the original price

To find the expression after 20 % discount :

=> x * 20/100 = 0.2x

So,

New price:

=> x - 0.2x

or

=> 0.8x

Therefore , the solution of the given problem of expression comes out to be  0.8x is the required expression.

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Answer:

First question(unnumbered):
 [tex]\mathrm{Choice \; (B) : \;\;\dfrac{1}{2}}[/tex]

Question 48

[tex]\mathrm{Choice \;(C)\;\; (x, y) = \left(-1, \dfrac{3}{2}\right)}[/tex]

Question 49
[tex]\mathrm{Choice \; (D)\;\;-1}[/tex]

Step-by-step explanation:

The imaginary variable i is [tex]\sqrt{-1}[/tex] and [tex]i^2 = -1[/tex]

For the unnumbered first question we have

the equation
[tex]\dfrac{1}{1-i}[/tex]

Multiply numerator and denominator by [tex]i + 1[/tex]

[tex]\rightarrow \dfrac{1\cdot \left(1+i\right)}{\left(1-i\right)\left(1+i\right)}\\\\\\= \dfrac{1 + i}{1 - i^2} \;\;\;\;\;\;\;since \;(a +b)(a-b) = a^2 - b^2\\\\\textrm{Since $i^2 = -1$, the denominator becomes:}\\\\1-i^2 = 1 -(-1) = 2\\\\\\[/tex]

Therefore ,

[tex]\dfrac{1}{1-i} = \dfrac{1 + i}{2}\\\\= \dfrac{1}{2} + \dfrac{i}{2}\\\\[/tex]

The real part is [tex]\dfrac{1}{2}[/tex]   and the imaginary part is [tex]\dfrac{i}{2}[/tex]

Answer to first question is: ) [tex]\dfrac{1}{2}[/tex]
-------------------------------------------------------------------------

#48

Solve [tex](x, y)[/tex]  for [tex]2y\:+\:xi\:=\:4+x-i[/tex] for  [tex]$x,y\in\mathbb{R}$[/tex]

For the equation

[tex]2y\:+\:xi\:=\:4+x-i[/tex]

Move the the x and i terms from the right to left side:

[tex]2y + xi - x + i = 4\\\\2y - x +xi + i =4\\\\[/tex]

Since this works out to a real number, the imaginary part is 0

So

[tex]xi + i = 0\\\\xi = -i\\\\x = \dfrac{-i}{i}\\\\x = -1[/tex]

and the real part

[tex]2y - x = 4[/tex]

Substitute for x = -1 in the above to get
[tex]2y -(-1) = 4\\\\2y + 1 = 4\\\\2y = 4-1\\\\2y = 3\\\\y = \dfrac{3}{2}\\\\[/tex]

[tex](x, y) = \left(-1, \dfrac{3}{2}\right)[/tex]
which is choice (C)

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

#49

For [tex]$a,b\in\mathb{R}$[/tex]

[tex]a+ib\:=\:\left(2-i\right)^2 \\\\[/tex]

Expand [tex]x(2-i)^2[/tex]

[tex]= 2^2 - 2.2.i +i^2\\\\[/tex]

Since i² = -1 this works out to:
[tex]4 - 4i -1[/tex]

[tex]3 - 4i[/tex]

Therefore
[tex]a + ib = 3 - 4i\\\\[/tex]

Equation real part on left to the real part on the right :
[tex]a = 3[/tex]

Equation imaginary part on left to the imaginary part on the right :
[tex]ib = 4i[/tex]

[tex]b = -4[/tex]

[tex](a + b) = (3 +(-4))\\\\= 3 - 4 \\\\= -1\\\\[/tex]

This would be option (D)

a) The equation that fits the story is given as follows:

2x/5 = 28.

b) The length of the racetrack is given as follows: 70 meters.

c) Antonio had to go 42 meters farther to reach the finish line.

The length of the race track is obtained applying the proportions in the context of this problem.

His car stops 10m past the starting line. After he fixes a wheel, the car goes 2/5 the racetrack’s total distance and then stops for good. It is 38m from the starting line, hence the distance driven during this entire period is of:

38 - 10 - 28 m.

28 m is 2/5 of the track length, which is going to be called x, hence the equation is given as follows:

2x/5 = 28.

The track length is then obtained as follows:

2x = 5 x 28

x = 5 x 14

x = 70 meters.

Thus the remaining distance is of:

70 - 28 = 42 meters.

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Answer:

Step-by-step explanation:

y = (a-3)x+5

Answer:    

y=3x+5

Step-by-step explanation:

The system of linear equation is x + y = 16 and y = 2x + 4. Dakota sold 4 items and Cody sold 12 items

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

Let x represent the number of items Dakota sold and y represent the number of items Cody sold.

Dakota and Cody sold a total of 16 items, hence:

x + y = 16

y = 16 - x    (1)

Also, Cody sold four more than twice the number of items Dakota sold, hence:

y = 2x + 4   (2)

substituting y = 16 - x:

16 - x = 2x + 4

3x = 12

x = 4

y = 16 - x = 16 - 4 = 12

Dakota sold 4 items and Cody sold 12 items

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The value of (7²-√81) + √125) is 45

Squares are the numbers, generated after multiplying a value by itself. Whereas square root of a number is value which on getting multiplied by itself gives the original value. Hence, both are vice-versa methods. For example, the square of 2 is 4 and the square root of 4 is 2.Similarly, the square of 4 is 16 and the square root of 16 is 4.

A perfect square is a number, from a given number system, that can be expressed as the square of a number from the same number system. Therefore 4, 16, 25 are examples of perfect squares

7²-√81) + √125 is calculated as

49- 9+ 5 = 45

Therefore the value of 7²-√81) + √125 = 45

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Answer: Congruent figures can slide, flip, or turn.

(Translate, reflect, or rotate)

Corresponding Angles are congruent. (Not always)

Corresponding Sides have a scale factor.

Corresponding Sides are Congruent. (Only if they have the same side and shape)

Corresponding Angles have a scale factor. (I Dont Know about this one)

All transformations (translation, reflection,

rotation, and dilation) result in congruent figures. (It would be similar to the pre-image)

i hope this helps sorry I can't do much but i think it might just be the 3 without the bolded words behind it

The measure of the angle ∠G of the isosceles triangle will be 51°.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The two triangular legs and their opposing angles are congruent in an isosceles triangle.

In triangles △GHI, IG ≅ HI, and the measure of the angle ∠H = 51°. Then the measure of the angle ∠G will be given as,

The two sides of the triangle △GHI will be congruent. Then the triangle is known as an isosceles triangle.

If IG ≅ HI, then the measure of the angle ∠G ≅ ∠H.

The measure of the angle ∠G of the isosceles triangle will be 51°.

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The GCF of 10 and 4x is 2.

The greatest common factor (GCF) of two or more numbers is the largest number that divides evenly into each of them. Factoring a number means breaking it down into its prime factors. That is;

10 = 2 * 5 , we can see that 2 and 5 are the prime factors of 10.

4x = 4 * x, we can see that 4 and x are the prime factors of 4x.

Since 2 is the only common factor between 10 and 4x, we can conclude that 2 is the GCF of 10 and 4x.

It means that 2 is the greatest number that divides into both 10 and 4x with a remainder.

Therefore, the GCF of 10 and 4x is 2.

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Answer:

  j = 1.5

Step-by-step explanation:

You want to solve the equation 0.3j-(0.1j-3) + 0.1 = 2 (j+0.1) + 0.2 for the value of j.

It usually works well to simplify such an equation as the first step. That means eliminating parentheses and combining like terms.

  0.3j-(0.1j-3) + 0.1 = 2 (j+0.1) + 0.2 . . . . . . given

  0.3j -0.1j +3 +0.1 = 2j +0.2 +0.2 . . . . . . eliminate parentheses

  0.2j +3.1 = 2j +0.4 . . . . . . . . . . . . collect terms

  2.7 = 1.8j . . . . . . . . . . . subtract (0.2j +0.4)

  1.5 = j . . . . . . . . . divide by 1.8

The solution is j = 1.5.

__

Additional comment

You are often taught to solve this kind of 3-step equation by subtracting the unwanted variable term and the unwanted constant term in two steps. (The third step is dividing by the coefficient of the variable.) Here, we show those subtractions being done both at once.

The variable term we choose to subtract is the one with the smallest coefficient. That way, the result of the subtraction (1.8j) leaves the coefficient of the variable as a positive number.

Sometimes the variable term on the right is subtracted, so you end up with a "j = " equation. In that case, the equation you would be solving as the last step is ...

  -1.8j = -2.7

which requires arithmetic with negative numbers. Negative numbers tend to be associated with more mistakes, so we choose not to go there.

The exponential function that models the data is f(x) = 8(1/2)ˣ

The general form of exponential function is given by:

f(x) = abˣ

Where a is the initial value of output variable, b is the growth or decay factor and x is the value of input variable

From the table:

when x = 0, f(x) = 8:

f(x) = abˣ

8 = ab⁰      (remember: b⁰ = 1)

8 = a

a = 8

when x = 1, f(x) = 4:

f(x) = abˣ

4 = 8 × b¹

4 = 8b

b = 4/8

b = 1/2

Thus, substituting a and b into f(x) = abˣ will give the exponential function that models the data:

f(x) = 8(1/2)ˣ

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You get a quadratic equation when the square of the expression that comes after b plus b times that same expression not squared plus c equals 0.

Any equation in algebra that can be written in standard form as

ax^2+bx+c=0,

where x stands for an unknown integer and a, b, and c are known quantities, where a 0, is considered a quadratic equation.

The coefficients of the equation are the numbers a, b, and c, which can be separated by naming them, respectively, the quadratic coefficient, the linear coefficient, and the constant coefficient or free term.

Due to the fact that the solutions lie where the parabola crosses the x-axis, quadratic equations frequently have two solutions.

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Answer: r= 1/5 and s = 2/5

Step-by-step explanation:

trust me

The median number of pets per family is 2.

Median number is the middle value of a set of numbers when they are arranged in numerical order. It is also known as the middle number or the 50th percentile. The median number is used to find the middle value when there is an odd number of values in the set, or to find the average of the two middle values when there is an even number of values in the set.

This can be determined by looking at the graph and counting the number of families in each bar.

The bar with 2 pets has the most families, and is the median number.

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The money market account earns 8/4 = 2% interest per quarter.

In one year, there are 4 quarters.

so, the formula to calculate the balance after 8 years is:

A = P (1 + r/n)^(nt)

where A is the final balance, P is the principal (initial investment), r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years the money is invested for.

Substituting in the given values,

A = 1000 (1 + .02)^(4*8)

A = 1000 (1.02)^32

A = 1000 (1.8587)

A = 1858.7

So after 8 years, Ed will have earned $1858.7.

The solution to the simplification of each of the fractions are;

1) ³/₄ * ¹¹/₅

2) 1 ³/₅ miles

3) 1¹/₈ yards

1) We are told that;

Caleb has 2¹/₅ yards of rope

Quantity of rope used by Caleb = ³/₄

Thus;

³/₄ of 2¹/₅ simply means that we will multiply both.

2¹/₅ can also be expressed as 11/5. Thus, we now have;

³/₄ * ¹¹/₅

2) Number of miles mary hiked = 6²/₅ miles = 32/5 miles

He stopped at 1/4 of the way.

Thus;

Number of miles before stopping = 1/4 * 32/5 = 8/5

= 1 ³/₅ miles

3) The area is gotten by;

A = length * width

A = 1¹/₂ * ³/₄

= 3/2 * 3/4

= 9/8

= 1¹/₈ yards

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The account balance in seven years will be $9,382.32.

Balance in math is the idea of equal parts on either side of a given equation. The concept of balance is used in algebraic equations and inequalities where the two sides of the equation must be equal in order for the equation to be true. Balance is an important concept to learn in math, as it is used to solve many problems. Balance can also be used in geometry to understand symmetry and shapes, as well as in calculus to understand derivatives and integrals. Balance is a fundamental concept in math that can be used in a variety of ways.

This can be calculated by multiplying the initial deposit of $850 by (1 + 0.029/12)^84, which is equal to 9,382.3198.

After rounding to the nearest hundredths place, the answer is $9,382.32.

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Answer:

$1,041.06

Step-by-step explanation:

Got it right.

According to the venn diagram, the circle surrounds four pizzas. Ham is present in Meat Feast, Scorcher, Hawaiian, and Capricciosa.

The Venn diagram, a frequent style of diagram showing logical connections between sets, was made popular by John Venn in the 1880s. Diagrams are used to teach fundamental set theory and to show simple set relationships in probability, logic, statistics, linguistics, and computer science. The relationships between two or more groups of elements are shown in a Venn diagram by overlapping circles and other shapes. When arranging information graphically, it is frequently advantageous to emphasize the similarities and differences between components. The intersection of two large circles forms the central empty area of a Venn diagram.

given

From the image,

ham is an ingredient in Meat feast, Scorcher, Hawaiian, and Capricciosa.

According to the venn diagram, the circle surrounds four pizzas. Ham is present in Meat Feast, Scorcher, Hawaiian, and Capricciosa.

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Answer: 6

Step-by-step explanation:

The expression (−4)⁸(−4)⁻⁵(-4)⁰ written as a single power is given by (- 4)³.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the expression as -

(−4)⁸(−4)⁻⁵(-4)⁰

The given expression is -

(−4)⁸(−4)⁻⁵(-4)⁰

(- 4)⁸ ⁻ ⁵ ⁺ ⁰

(- 4)³

Therefore, the expression (−4)⁸(−4)⁻⁵(-4)⁰ written as a single power is given by (- 4)³.

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Answer:

25x+125< 500 15 fewer seats

Step-by-step explanation

this is number 1

The Implicit Differentiation of 5x^2-xy-4y^2=0 is Dy/Dx= (5x-y)/(-4y)

Using implicit differentiation, Dy/Dx can be found by taking the derivative of both sides with respect to x.

On the left side, the derivative with respect to x of 5x2 is 10x and the derivative with respect to x of -xy is -y.

On the right side, the derivative of 4y2 with respect to x is 0.

Therefore, the equation becomes 10x - y = 0.

Solving for y gives y = 10x.

Substituting this into the original equation, we get 5x2 - 10x2 - 4(10x)2 = 0, which simplifies to -5x2 - 40x2 = 0.

Finally, we can solve for Dy/Dx:

Dy/Dx= (5x-10x)/(-4(10x))

Dy/Dx= (5x-y)/(-4y)

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The additive inverse of (-3) + (-6) is (3 + 6) which is 9

The additive inverse of a number is its opposite, or the number that when added to the original number results in zero. In other words, it is the number that can "cancel out" the original number and make it disappear.

For example, the additive inverse of 3 is -3, because 3 + (-3) = 0. Similarly, the additive inverse of -6 is 6, because -6 + 6 = 0.

Now, for the given expression, the additive inverse of (-3) + (-6) is the number that can "cancel out" the expression and make it disappear. By adding the additive inverse of each term of the given expression we would get 0. Therefore the additive inverse of (-3) + (-6) is (3 + 6) which is 9.

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