Math 5th grade
The rule for an input/output table is output = x + 2

Answer:

To find the sum of the two expressions, we can combine like terms. In this case, we have two terms with a coefficient of -3y² and two terms with a coefficient of -3y, so we can combine them to get:

(-3y² + -3y²) + (-3y + -3y) + (2y² + 9y + 4)

Simplifying the expression gives us:

-6y² - 6y + 2y² + 9y + 4

Combining the like terms again gives us:

-4y² + 15y + 4

Therefore, the sum of the two expressions is -4y² + 15y + 4. This is already in simplest form.

10 pints is equal to 5 quarts.

Given that there are 10 pints.

We need to convert pints to quarts.

To convert pints to quarts, we need to keep in mind that there are 2 pints in 1 quart.

Given that we have 10 pints, we can divide this value by 2 to obtain the equivalent amount in quarts:

10 pints / 2 pints per quart

= 5 quarts

Therefore, 10 pints is equal to 5 quarts.

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An inequality's solution is a value that makes the inequality true. There are various ways to resolve an inequality.

The solution set is the collection of all possible solutions to an inequality. The meaning of the symbol / is "is not greater than or equal to." A relationship between two expressions or values that is not equal to each other is known as inequality in mathematics.

So inequality results from an imbalance. in order to demonstrate that substituting one or more variables into an inequality or equation "works out". This means that the equation or inequality can be reduced to a true statement.

A number sentence proves that two numerical expressions are equal. When two numerical expressions are equivalent, a number sentence is said to be true (that is, both evaluate to the same number). Otherwise, it is alleged to be false.

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The maximum number of cars that can be installed on the frame is 30.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

given, A Ferris wheel frame can withstand a weight of 6000 kg. It has cars that seat two people, and each car can withstand a maximum weight of 200 kg. since we are neglecting the weight of the cars.

Let "x" be the number of cars that can be installed

thus,

200x < 6000

x < 6000/200

x < 30

therefore, The number of cars that can be installed on the frame is 30.

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The box will accelerate down the ramp at a rate of 0.063 m/s²

To find the acceleration of the box down the ramp, you can use the equation:

a = g sin(θ) - (μ g cos(θ)) / m

In this equation, "a" is the acceleration of the box, "g" is the acceleration due to gravity (9.8 m/s²), "θ" is the angle of the ramp with respect to the horizontal, "μ" is the coefficient of friction between the box and the ramp, and "m" is the mass of the box.

Plugging in the values that you know, you get:

a = 9.8 × sin(24.7) - (0.211 × 9.8 × cos(24.7)) / 34.9

This simplifies to:

a = 4.095 - 1.87/ 34.9 = 0.063 m/s²

Thus, the box will travel down the ramp at a speed of 0.063 m/s².

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Answer:

k should equal 2 and above

Step-by-step explanation:

A product of 6 is 12 which is 6 * 2 so therefore k should equal anything above 2

Answer:

A, D

Step-by-step explanation:

A) To solve you only need to add 3 to both sides.

B) You need to use the division property of inequality and divide both sides by 22

C) You need to use the multiplication property of inequality and multiply both sides by 10/8

D) To solve you only need to add 8.25 to both sides.

E) You need to use the addition property of inequality and add 1/3 to both sides.

Answer:

x = 2

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion, that is

[tex]\frac{EC}{BC}[/tex] = [tex]\frac{DE}{AB}[/tex] ( substitute values )

[tex]\frac{2x+3}{13x-1.5}[/tex] = [tex]\frac{6}{21}[/tex] ( cross- multiply )

6(13x - 1.5) = 21(2x + 3) ← distribute parenthesis on both sides

78x - 9 = 42x + 63 ( subtract 42x from both sides )

36x - 9 = 63 ( add 9 to both sides )

36x = 72 ( divide both sides by 36 )

x = 2

Answer:

Step-by-step explanation:

FALSE

An obtuse-angled triangle is a triangle in which one of the interior angles measures more than 90° degrees

Answer:

If HG = HK, then HG = HK. This statement is true by definition, as both sides of the equation are equal to the same value.

If KHJ = KJH, then KHJ = KJH. This statement is also true by definition, as both sides of the equation are equal to the same combination of letters.

Answer:

-600 is the sum of the arithmetic SERIES till [tex]S_{12}[/tex]

Step-by-step explanation:

Since this is a SERIES you would use the finite arithmetic SERIES formula

which is [tex]S_{n} = \frac{n}{2} (2a_{1} +d(n-1))[/tex]

[tex]S_{12} = \frac{12}{2} (2(-6) + -8(12-1))[/tex]

[tex]S_{12} = 6(-12 + -8(11))[/tex]

[tex]S_{12} = 6(-12 + -88)[/tex]

[tex]S_{12} = 6(-100)[/tex]

[tex]S_{12} = 600[/tex]

Therefore, the sum of the SERIES would be -600. Hope this helps!

The future value of the $1000 annuity payment is $7,715.61.

An annuity is when a series of payment is made over a period of time. The future value of the annuity would be a function of the amount deposited each year, the interest rate earned and the duration of the investment.

Future value = Quarterly deposit x annuity factor

Annuity factor = (1 + r)^n] - 1} / r

Where:

Future value = 1000 x  [{(1 + 0.1^(6} - 1 ] / 0.1 = $7,715.61

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It will take 9 years to double the money at 9% per annum

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

Given:

let P = 100

Interest = 100

Apply formula of interest

Interest= (P x R x T) ÷ 100

100= (100x 9 xT )÷100

T= 11.11 years

In case of annually compounded interest let us assume that Rs 100 to[tex](1.09)^ 9 =(1.09)^T[/tex] become 200 . Apply formula

A=P[tex](1+R/100)^T[/tex]

200=100 [tex](1+9/100)^T[/tex]

200=100 [tex](109/100)^T[/tex]

2 =  [tex](109/100)^T[/tex]

[tex](1.09)^ 9 =(1.09)^T[/tex]

On Comparing

T= 9 years.

Hence, It will take 9 years.

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Answer:

Tristan 0.1 miles/min

Step-by-step explanation:

Divide distance and time

David =0.074 miles/min

Jalen = 0.09 miles/min

Hope this helps

The time that it will take the ink to diffuse a distance of 10⁻⁴ cm is; 10⁻³ seconds

The subject of a formula is defined as the variable that is being worked out. It can be recognized as the letter that is on its own on one side of the equals sign. For example, in the formula for the area of a rectangle;

A = base * height , the subject of the formula is  A.

We are given t as the subject of a formula written as;

t = x²/2D

Where;

t is time in seconds that it takes molecules to diffuse a distance a centimeters.

D is the diffusion coefficient

We are given;

D = 10⁻⁵ cm²/s

Distance of diffusion; x = 10⁻⁴ cm

Thus;

t = (10⁻⁴ )²/10⁻⁵

t = 10⁻⁸/10⁻⁵

t = 10⁻⁸⁺⁵

t = 10⁻³ = 0.001 seconds

That is the time we conclude it will take the ink to diffuse.

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We can see here that AC and BC are:

AC = 5cm

BC = 3cm

A triangle is a three-sided polygon, and it is one of the basic shapes in geometry. In a triangle, three straight lines, called sides, are connected end-to-end to form the shape. The point where two sides meet is called a vertex, and there are three vertices in a triangle.

There are several types of triangles, each with their own specific properties. The most common classification of triangles is based on their side lengths.

Using Sine Rule, we have:

[tex]\frac{a}{Sin A} = \frac{b}{Sin B}[/tex] where:

Sin A = Sin 30° = 0.5

Sin B = Sin 80° =  0.9848

a = x cm

b = 5cm

Thus, inserting the the above values into the Sine Rule equation, we have:

[tex]\frac{x}{0.5} = \frac{5}{0.9848}[/tex]

Cross-multiplying, we have:

0.9848x = 5×0.5

0.9848x = 2.5

∴ x = 2.5 ÷ 0.9848 = 2.538cm

≈ 3cm.

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The line of best fit for the scatterplot below passes through D) S and Q pair of points.

A scatter plot is a type of plot or mathematical diagram that uses Cartesian coordinates to display values for typically two variables for a set of data. It is also known as a scatter graph, scatter chart, scattergram, or scatter diagram.

One more variable can be shown if the points are color-, shape-, or size-coded. The data are represented as a set of points, where each point's position on the horizontal axis is determined by the value of one variable, and its position on the vertical axis by the value of the other variable.

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Answer:

Step-by-step explanation: Half of 70 is 35 so there are 35 Sixth-grader and then you do 70 multiplied by 30% and get 21

The required answer is,

Percentage of green = 37%.

The surface area of a cylinder can be defined as the total space covered by the flat surfaces of the bases of the cylinder and its curved surface.

A=2πrh+2πr2

r Radius

h Height

Here, we have,

Surface area of a cylinder = πr² + 2πr h

With r = 22 and h = (6 + 10) = 16

Area = π * 22² + 2 * π * 22 * 16

Area = 1520.728 + 2211.968

Area = 3732.696 in²

Now,

Percentage of green = surface area of green ÷ total surface area

Surface area of green = 2πr h

Surface area of green = 2 * π * 22 * 10

Surface area of green = 1382.48

Percentage of green = 1382.48 / 3732.696 * 100%

Hence, the required answer is,

Percentage of green = 37%

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Answer:  Choice 2. x = 5 ± i √5

Step-by-step explanation:

Use the formula

(b/2)^2

in order to create a new term. Solve for x by using this term to complete the square.

Hope this helps!

The width of the given rectangle is; 7 units

Let the length of the rectangle be x and let the width be y.

We are told that the length of a rectangle is the sum of the width and 2. Thus;

x = y + 2

Now, formula for area of rectangle is;

A = length * width

Thus;

A = y(y + 2)

Now, we are told that the area is 63 square units and as such;

y(y + 2) = 63

y² + 2y - 63 = 0

Factorizing gives us;

(y + 9)(y - 7) = 0

Thus; y = 7

x = 7 + 2

x = 9

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Answer:

75 = 4w

Step-by-step explanation:

Let w = width

Let w + 5 = length

Let p = perimeter ( Perimeter is given: 70 ft. )

Write the formula to find the perimeter of a rectangle

p = 2 ( l + w )

Sub the numbers in

70 = 2 [(w+5) + (w)]

Simplify the equation

70 = 2 (2w + 5)

70 = 4w + 5

75 = 4w

The number of pupils that chose English as their favorite subject is 26

From the table given, we can see that we have to fill the space before the addition of the numbers.

For the number of girls that chose English, we have;

= Total number of girls - sum of Maths and Sciences

= 38 - (20 + 12)

= 38 - 32 = 6

For the number of boys that chose English, we have;

= Total for Maths - Girls that chose Maths

= 25 - 20 = 5

Also,

Total pupils for all the courses - total for girls

= 70 -38 = 32

Then,

= 32 - ( 5 + 7)

= 32 - 12 = 20

Total pupils that chose English

= 20 + 6

= 26 pupils

Thus, the number is 26

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Answer:

b = 4

Step-by-step explanation:

b^3=64

3√b = √64

b = 4

Answer:

b = 4

Step-by-step explanation:

Answer:

See below for solution

When I post this I lose the formatting but you should be able to figure it out

Step-by-step explanation:

Part a

p               q                    ∼ ( p ∨ ∼ q ) → ∼ p
------------------------------------------------------------

True True                     True

True False                    True

False True                     True

False False                    True

Part b

p                q             r                      p → ( q → r )
-----------------------------------------------------------------

True         True        True                 True

True          True        False               False

True          False       True                True

True          False       False               True

False         True        True                True

False         True        False               True

False         False      True                 True

False         False  False                True

Part c

p               q             r            ( p → q ) → r
-----------------------------------------------------------

True True True True

True True False False

True False True True

True False False True

False True True True

False True False False

False False True True

False False False False

Part d

p               q             (p → q)→(p ∧ q)
---------------------------------------------------

True True                      True

True False                     True

False True                       False

False False                      False

The shaded region that represents the subset of the students at North High School will be C.

Sets are groups of clearly specified components. The number of items in a finite set is denoted by a curly bracket.

John Venn introduced the Venn diagram in the 1880s, which is a type of diagram that displays the logical relationship between sets. The illustrations are used in probability, logic, statistics, linguistics, and computer science to demonstrate basic set connections and to teach rudimentary set theory.

The shaded region that represents the subset of the students at North High School who play sports OR make the honor roll will be given by the intersection region.

The shaded region that represents the subset of the students at North High School will be C.

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The solution of the given inequality is x<6.5. Therefore, option D is the correct answer.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is x/x-6 >13.

Multiply x-6 on both the sides of an inequality, we get

x>13(x-6)

x>13x-78

Add 78 on both the sides of an inequality, we get

x+78>13x

Subtract x on both the sides of an inequality, we get

78>12x

12x<78

x<6.5

Therefore, option D is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

This rational inequality can be used to determine the number of seconds, , that a beginning ice-skater can skate before losing his or her footing. x/x-6 >13  If Charlene has never ice-skated before, which inequality describes the number of seconds she can expect to skate before losing her footing?

A. 6>x>6.5

B. x<6

C. x<0

D. x<6.5

E. x<6

Answer:

Wrong option

Step-by-step explanation:

✓2-✓(10^2*2)

✓2-10✓2

whose value is in negative and doesn't match with your options