Helpppp
(5-√11) : 3 √7

18.75 inches is the length of the rectangle and 18.75 inches is the width of rectangle.

The area of Rectangle is length times of width.

The perimeter of a rectangle is 50 inches.

Perimeter=2(Length+Width)

Length=3W

Perimeter=50 inches

50=2(3W+W)

50=2(4W)

50=8W

Divide both sides by 8

50/8=W

W=6.25

Length=3(6.25)=18.75.

Hence, the length of rectangle is 18.75 inches and width is 6.25 inches.

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According to the given statement, there were 58 children, 29 adults and 64 students.

Algebraically speaking, an equation is indeed a statement that establishes the equivalence of two mathematical equations.

Let there be x number of children, y number of students and x/2 number of adults. Forming the first equation based on number of students -

x + y + x/2 = 151 : Equation 1

Multiply equation 1 with 2

2x + 2y + x = 302 : Equation 2

3x + 2y = 302 : Equation 3

y = (302 - 3x)/2 : Equation 4

Forming second equation based on cost -

5x + 7y + 12x/2 = 1086 : Equation 5

Rewriting this equation

5x + 7y + 6x = 1086 : Equation 6

11x + 7y = 1086 : Equation 7

Keep the value of y from equation 4 in equation 7

11x + 7(302 - 3x)/2 = 1086

11x + (2114 - 21x)/2 = 1086

22x + 2114 - 21x = 2172

x = 2172 - 2114

x = 58

Now,

y = (302 - 3x)/2

y = (302 - 3×58)/2

y = 128/2

y = 64

Number of adults = 58/2

Number of adults = 29

Thus, there were 58 children, 29 adults and 64 students.

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The missing terms will be 0.5, 2, and 7.5 respectibily.

What is equivalent ratio?

The concept of a ratio in mathematics is the divisional comparison of two quantities, the antecedent and consequent. As an illustration, each ingredient must be added according to a ratio during cooking. So, we may argue that a ratio is employed to represent one quantity as a portion of another. The ratio can be written as a fraction as well. If the ratio a:b is a fraction, its form is a/b. As a result, it is simple to compare two or more equivalent ratios expressed as equivalent fractions.

1st ratio is 8:16 = 1/2

So the following terms will be 1:0.5

For 4 it will be 4:2.

For15 it will be 15:7.5.

Hence, The missing terms will be 0.5, 2, and 7.5 respectibily.

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The steps to solve the 3 linear equations with 2 variables is shown below .

In the question ,

it is asked that how can we find the solution of 3 linear equations that have 2 variables .

Step (1) : Pick any two pair of linear equations ,

Step(2) : Then use addition and subtraction to eliminate the Same Variable from the equations .

Step(3) : In step 2 we will get the value of 1 variable ,

Step(4) : Substituting the value of the variable in Step(2) in the third linear equation ,

we will get the value of other variable also .

Therefore , the value of both the variable can be found by the above steps .

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The verbal expression of 0.25r+0.6s is 0.25 multiplied by r plus 0.6 multiplied by s

An algebraic expression can be described as an expression that is made up of coefficients, factors, terms, constants and variables.

These expressions are also known to be made up of some arithmetic and mathematical operations, which includes;

Examples of algebraic expressions:

2x + y

3x + 7

4z + 1

Given the expression:

0.25r+0.6s

It is written in words as;

0.25 multiplied by r plus 0.6 multiplied by s

Hence, algebraic expressions are made up of constants and terms

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Complete question:

0.25r+0.6s. What is the verbal expression

The roots of the quadratic equation x² - 8x + 16 = 0 are real and equal which is 4.

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

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The quadratic equation is given below.

x² - 8x + 16 = 0

The value of the discriminant is given as,

D = b² - 4ac

D = (-8)² - 4(1)(16)

D = 64 - 64

D = 0

The roots of the equation are calculated as,

x² - 8x + 16 = 0

x² - 4x - 4x + 16 = 0

x(x - 4) - 4(x - 4) = 0

(x - 4)(x - 4) = 0

x = 4, 4

The roots of the quadratic equation x² - 8x + 16 = 0 are real and equal which is 4.

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Answer:

false

Step-by-step explanation:

5²+6²=61.

>

Square root of 61 is 7.81 and not 12 so the points will not meet

Answer: 46%

Step-by-step explanation:

On rolling a standard die , the probability of getting a even number and less than 4 is  1/6 .

In the question ,

it is given that ,

a standard die is rolled ,

the total outcomes is {1 , 2 , 3 , 4 , 5 , 6} .

the even numbers are {2,4,6} .

and the outcome that are less than 4 is only {2} .

so , the number of favorable outcome is only 1 .

and total number of outcome is 6 ;

So , the probability is = (favorable outcome)/(total outcome)

Substituting the value from above ,

we get ,

probability is = 1/6 .

Therefore , the required probability is  1/6 .

The given question is incomplete , the complete question is

You roll a standard die. What is the probability of getting a even number and less than 4 ?

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The measure of each of the acute angles of the right triangle is 32° and 58°.

A right triangle is a kind of triangle which has a right angle (90°) and two acute angles (less than 90°).

Let x = measure of one of the acute angles

If the measure of one acute angle of a right triangle is 6 less than twice the measure of the other acute angle, then

measure of the other acute angle = 2x - 6

The sum of all the angles of any triangle is equal to 180°. Hence,

90° + x + 2x - 6 = 180°

Solve for the value of x.

3x = 96

x = 32

Solve for the measure of the other acute angle.

2x - 6 = 2(32) - 6 = 58

Hence, the two angles are 32° and 58°.

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Yes, the given expressions are equivalent.

What is the equivalent expression?

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.

We have,

9(4 - x)

and 36 - 9x

Are these equivalent expressions?

9(4 - x) = 36 - 9x

36 - 9x = 36 - 9x

So, LHS = RHS = 36 - 9x

Therefore, the expression 9(4 - x) and 36 - 9x  are equivalent expressions.

Hence, yes the given expressions are equivalent.

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Answer:

Step-by-step explanation:

66 minutes

Answer

Step by step explanation

Answer:

Option C is the correct answer

C) 150 m

Step-by-step explanation:

Speed = Distance ÷ Time

Distance = Speed × Time

d = 10 × 15

d = 150 m

Thus, The speed of the object is 150 m.

Answer:

d=150m

Step-by-step explanation:

Speed = Distance /Time 

10= d/155

d= 150m

Answer:

     [tex]\frac{16}{25}[/tex]

Step-by-step explanation:

[tex]\frac{5*(\frac{4}{5})^{2}*\frac{3}{5} }{3}[/tex]

= [tex]\frac{\frac{5}{1} *\frac{16}{25}*\frac{3}{5} }{3}[/tex]

= [tex]\frac{\frac{5*16*3}{1*25*5} }{3}[/tex]

= [tex]\frac{\frac{240}{125} }{3}[/tex]

= [tex]\frac{\frac{48}{25} }{3}[/tex]

= [tex]\frac{48}{25} /\frac{3}{1}[/tex]

= [tex]\frac{48}{25} *\frac{1}{3}[/tex]

= [tex]\frac{48*1}{25*3}[/tex]

= [tex]\frac{48}{75}[/tex]

= [tex]\frac{16}{25}[/tex]

The transformations that map the strip pattern onto itself is a horizontal translation, a reflection across a vertical line, a reflection across a horizontal line, a glide reflection, and a 180°. Option A is the correct option.

The strip pattern can be mapped onto itself in two different ways.

Hence, the transformations that map the strip pattern onto itself can be achieved through a horizontal translation, a reflection across a vertical line, a reflection across a horizontal line, a glide reflection, and a 180°.

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The equivalent fraction is defined below and the few equivalent fractions of 1/2 are 2/4 , 3/6... .

In the question ,

it is given that the fraction is 1/2 .

The Equivalent Fractions are defined as the fractions that have different numerators and denominators but are equal to same value  and

A fraction is a part of the whole ; Equivalent fractions represent the same portion of that whole.

the fraction is 1/2 ,

to find the equivalent fraction , we multiply numerator and denominator by 2 ,

we get , 2/4

on multiplying by 3 , we get

= 3/6 .

Therefore , the equivalent fractions of 1/2 are 2/4 , 3/6 ...

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A function is a mathematical expression that describes the relationship between an input and an output.

The function table is a visual, graded table with cells for input and cells for output that are organized into rows and columns.

Function tables have three variables components. There is the input, the function and the output. Function tables are created so that one of the three components is unknown and the other two serve as the clues to solving the table.

The rule of a function table is the mathematical operation that describes the relationship between the input and the output. The rule must be consistently applied to all input/output parts.

A traditional function table is made using two rows, with the top row being the input cells and bottom row being the ouput celss. Each column represents a signal input/output relationship.

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Answer:

37.7

Step-by-step explanation:

Circumference = π × d = 3.14 × 12 = 37.68

Answer:

37.7

Step-by-step explanation:

circumference = πd

12(3.14) = 37.7 (nearest 1 d.p.)

The constant of proportionality representing the distance travelled by the runner is equivalent to 9.1.

The general equation of a straight line is -

The equation can also be used to represent direct proportionality as -

m is called constant of proportionality

Given is a table that shows the distance traveled by a runner.

We can write the constant of proportionality as -

m = (13.65 - 4.55)/(1.5 - 0.5)

m = 9.1

Therefore, the constant of proportionality for the data that shows the distance travelled by the runner will be 9.1.

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Answer:

1428.33333 yards

Step-by-step explanation:

1 foot = 0.33333 yards

4285 feet = 4285*0.33333 = 1428.33333 yards

The solution to this problem is the p-value must be higher than 0.05.

A confidence interval in frequentist statistics is a range of estimates for an unobserved parameter. The most common confidence level for computing confidence intervals is 95%, however other levels, including 90% or 99%, are sporadically employed.

Here ,

In this given problem we can see confidence interval has 0 in it.

So,

Since the confidence interval comprises 0, the null hypothesis should be rejected.

When the p-value exceeds the level of significance, the null hypothesis is only rejected.

Since alpha=0.05 in this case, the p-value must be higher than 0.05.

Thus, the p-value must be higher than 0.05.

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Answer:

[tex]\text{as x} \to \infty, \ \text{y} \to -\infty\\\\\text{as x} \to -\infty, \ \text{y} \to \infty[/tex]

Rises to the left; falls to the right

============================================================

Explanation:

The leading term is what determines the end behavior of any polynomial function.

The leading term has the largest exponent. The other terms will have no effect on the end behavior.

As x gets really large in the positive direction, so does x^3. But the -2 out front will flip to have y go to negative infinity.

Therefore:  [tex]\text{as x} \to \infty, \ \text{y} \to -\infty[/tex]

We can informally think of this as "falls to the right".

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

As x heads to the left, x^3 becomes further negative. But -2 out front makes -2x^3 to be positive.

So [tex]\text{as x} \to -\infty, \ \text{y} \to \infty[/tex] aka "rises to the left".

Whatever x does, y does the opposite. If x goes positive, then y goes negative and vice versa.

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

The end behavior is therefore

[tex]\text{as x} \to \infty, \ \text{y} \to -\infty\\\\\text{as x} \to -\infty, \ \text{y} \to \infty[/tex]

x and y are opposite.

We can summarize that notation as saying "rises to the left, falls to the right".

See the graph below. I used GeoGebra to make the graph, but you can use Desmos or any other tool you prefer.

The correct statement is:

x= 125, 180 - (63+62) =55 and 180-55=125

What are interior angles?

An Interior Angle is an angle inside a shape.

The basic polygonal shape of a triangle has three sides and three interior angles. It is one of the fundamental shapes in geometry . It has three connected vertices. Triangles can be divided into a variety of categories according on their sides and angles.

The sum of the diagonal internal angles in a triangle determines its outer angle.

And also,

In a triangle, the sum of the interior angles is always 180°.

So, x= 125 ( Because 63+62=125 ) , 180 - (63+62) =55 and 180-55=125

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The steps to solve a word problem are to read, plan and solve the problem.

1. Read: After reading the issue, decide what the question is trying to get to.

Read the issue at least twice.

Highlight or highlight important words, phrases, and numbers. Put an end to unimportant information.

2. Plan: Consider what the narrative is requesting of you. What facts are provided to you, and what do you need to learn?

Make a drawing.

Keywords may be underlined or circled. (Use crayons or highlighters to color-code important numbers and words.)

Put your own words in the question's place.

3. Solve: Which approach—addition, subtraction, multiplication, or division—could you use to uncover the information that is missing?

Create and solve a numerical sentence.

Employ counters.

Produce charts

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Answer:

w(3n)=12n+2

Step-by-step explanation:

. Explanation: to evaluate w(3n) substitute n=3n into w(n). ⇒w(3n)=4(3n)+2=12n+2.

Answer:

It takes 38.5 years for money to quadruple when invested at an annual interest rate of 1.8% compounded continuously.