Rohan used the model below to show
1.38 ÷ 3

Three groups of cubes are shown with 4 groups of tens and 3 ones in each group.

Part A
Rohan made an error in his model. Explain his error. Include the correct grouping for the model.

The graph of the given absolute function is attached below and the end points (-5,0) (0, 5) of the rays are marked in it.

Absolute value function:

The  function that contains an algebraic expression within absolute value symbols is called as absolute value function.

Given,

Here we have the absolute value function f(x) = |-x - 5|

Now, we have to plot the graph for this function and we have to mark the end point of the rays.

Here the given function is written as,

=> f(x) = | -x - 5|

In order to plot the graph for the function we need the table of values to point it on the graph,

For that we have to take following sample values,

When x = -5, then f(-5) = |-5 -5| = 0

When x = 0,  then f(0) = |0 - 5| = 5

Therefore, the end points of the rays are (-5,0) and (0,5)

Now, we have to plot these values on the graph.

Then we get the graph like the following.

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Answer:$12

Step-by-step explanation:

1.75/3= 0.6 (1dp)

0.6 x 20 = 12

Answer:

$11.67

Step-by-step explanation:

3 oranges = 1.75

1 orange = 0.58333333333

20*0.58333333333 = 11.6666667

Answer:

41

Step-by-step explanation:

9² + 40² = 1681

the s.r of 1681 is 41

We s.r the answer because we need the singular of C, not C²

Hope this helps

24 pints of 55% pure fruit juice and 16 pints of 80% pure fruit juice will be required to make 40 pints of a mixture that is 65% pure fruit juice.

According to the question,

We have the following information:

The first type is 55% pure fruit juice, and the second type is 80% pure fruit juice. The company is attempting to produce a fruit drink that contains 65% pure fruit juice.

Now, let's take x pints of 55% pure fruit juice and y pints of 80% pure fruit juice will be required to make 40 pints of a mixture that is 65% pure fruit juice.

So, we have:

x+y = 40

x = 40-y ...(1)

55x/100+80y/100 = 40*65/100

55x+80y = 40*65

Putting the value of x from equation 1:

55(40-y)+80y = 2600

2200-55y+80y = 2600

2200+25y = 2600

25y = 2600-2200

25y = 400

y = 400/25

y = 16 pints

Putting this value in equation 1:

x = 40-y

x = 40-16

x = 24 pints

Hence, 24 pints of 55% pure fruit juice and 16 pints of 80% pure fruit juice will be required to make 40 pints of a mixture that is 65% pure fruit juice.

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The value of x in the algebraic equation x = 15.3568 - 1(1+x)^25 is 0.115

Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.

These basic mathematical operations (+, -, ×, and ÷) we use in our everyday life. Whether we need to calculate the annual budget or distribute something equally to a number of people, for every such aspect of our life, we use arithmetic operations.

In this case, we have to solve for x in the algebraic equation using mathematical operation.

x = 15.3568 - (1 + x)^25

Collect like terms

x + (1+x)^25 = 15.3568

Solving for x

x = 0.115

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Answer:

a + (a+1)²

Step-by-step explanation:

The following of the number "a" is:

a+1

Then:

The sum of a number with the square of its following algebraic language is:

a + (a+1)²

The algebraic expression for the sum of a number with the square of its following number can be written as:

Where x is the given number and (x + 1 )² represents the square of the following number.

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Answer: 22

Step-by-step explanation:

3 times 5 then add 7

The given set written on set builder notation is:

{x| x ∈ R, 3 ≤ x ≤ 9}

We want to write the given set using set builder notation, the set is the set of all real numbers that are greater than or equal to 3 and less or equal to 9.

So the set can be written as an inequality as:

3 ≤ x ≤ 9

To define the set using the set builder notation, we also need to clarify that x belongs to the real number set, this is x ∈ R.

Then the set that we need to write is:

{x| x ∈ R, 3 ≤ x ≤ 9}

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Answer:

11 seconds

Step-by-step explanation:

[tex] - 16 {t}^{2} + 1936 = 0[/tex]

[tex] - 16 {t}^{2} = - 1936[/tex]

[tex] {t}^{2} = 121[/tex]

[tex]t = 11[/tex]

The best compatible number to use for 24 x 18 = 432.

24 can be written as 25

18 can be written as 20.

So,

20 x 25 = 500

Option B is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The number of roses in one centerpiece = 18 roses.

The number of roses in 24 centerpieces.

= 24 x 18

= 432

The best compatible number to use for 24 x 18 = 432.

24 can be written as 25

18 can be written as 20.

So,

20 x 25 = 500

Thus,

The best compatible number to use for 24 x 18 = 432.

24 can be written as 25

18 can be written as 20.

So,

20 x 25 = 500

Option B is the correct answer.

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If he borrowed $1400 at 9% simple interest to be paid back in 2 years. The  interest he will pay is $1,663.34.

Using this formula

Interest = Principal ( 1+ Interest rate)^ time

Where:

Interest =?

Principal = $1400

Interest rate = 9% or 0.09

Time = 2 years

Let plug in the formula

Interest = $1,400 ( 1+ 0.09) ^ 2

Interest = $1,400 ( 1.09) ^2

Interest = $1,400 ( 1.1881)

Interest = $1,663.34

Therefore he will pay the amount of $1,663.34 as interest.

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Difference quotient for f(x) = √x at (16,4) is  √16+h - 4 / h

Difference quotient is mathematical operation used to solve derivation of function by using following formula :

difference quotient = [tex]\frac{f(x+ h) - f(x) }{h}[/tex]

For the function f(x) =  √x at point (16,4)

f(x +h) = [tex]\sqrt{x+h}[/tex]  

putting value in formula

difference quotient =  [tex]\frac{\sqrt{x+h} -\sqrt{x} }{h}[/tex]

now , putting x = 16 ,

difference quotient = √16+h - √16 / h

taking square root of 16 ,

= √16+h - 4 / h

So, the required Difference quotient for the function at (16,4) is √16+h - 4 / h

option (d) is correct

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The expression 3 tens 8 ones × 1000 can be evaluated and the value is; 38,000.

It follows from the task content that the value of the expression represented by the word phrase as given is to be determined.

On this note, it follows that we have;

First, 3 tens and 8 ones can be written as;

(3 × 10) + (8 × 1)

= 30 + 8

= 38.

Therefore, the result of the evaluation is; 38 × 1000 = 38, 000.

Ultimately, the result of the expression is; 38,000.

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After flipping a fair coin, when 'H' represents the heads and 'T' represents the tails the probability of heads P(H) = 1/2 and probability of tails P(T) = 1/2.

As given in the question,

After flipping a fair coin, when 'H' represents the heads and 'T' represents the tails ,

Number of total outcomes = { H , T }

Total number of outcomes = 2

Number of favourable outcomes to represent heads = 1

Number of favourable outcomes to represent tails = 1

Probability =(Number of favourable outcomes)/ (Total number of outcomes)

Probability of getting heads from the total outcomes is equal to

P(H) = 1 / 2

Probability of getting tails from the total outcomes is equal to

P(T) = 1/2

Therefore, after flipping a fair coin, when 'H' represents the heads and 'T' represents the tails the probability of heads P(H) = 1/2 and probability of tails P(T) = 1/2.

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Answer:

13685

Step-by-step explanation:

8050 x 0.70 = 5635

8050 + 5635 = 13685

[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{0}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{0}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-6)}}} \implies \cfrac{0 +3}{2 +6} \implies \cfrac{ 3 }{ 8 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{ \cfrac{3 }{ 8 }}(x-\stackrel{x_1}{(-6)}) \implies {\large \begin{array}{llll} y +3 = \cfrac{3 }{ 8 } ( x +6) \end{array}}[/tex]

My answer and step by step explanation is provided as an attachment.

Answer: base = 23  height = 31

Step-by-step explanation:

Area of triangle = (bh)/2

A = 356.5 cm2

h = b+8

356.5 = (b(b+8)) / 2

2(356.5) = b2 + 8b

0 = b2 + 8b - 713

Use quadratic equation to solve for b (there are on-line quadratic equation solvers, or you can do it manually)

b = -31 , 23

23 is the base    23 + 8 = 31 = height

Answer:

Step-by-step explanation:

Formula for geometric sequence is:

[tex]a_{n} =a_{1} (r)^{n-1}[/tex]

Now we substitute the values in:

[tex]165=a_{1} (3)^{3-1}[/tex]

165=a1(-2x3)^2

165=a1x9

Answer is 23

Answer:

Domain: (negative infinity, positive infinity)

Range: (negative infinity, 1]

Step-by-step explanation:

Answer:

She needs 8 cups of soil
one cup per pot

Step-by-step explanation:

The equation of the graph is y = 2[tex]x^{2}[/tex] + 9x + 4

A quadratic equation is a second-order polynomial equation in a single variable x

a[tex]x^{2}[/tex]+bx +c=0

with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

From the graph the roots of the equation are -4 and -1/2

so if x = -4, them x + 4 = 0 is a factor,

Also, if x = -1/2, then x + 1/2 = 0 is a factor

Multiply and expand the two factors

(x + 4)(x + 1/2) = 0

[tex]x^{2}[/tex] + x/2 +4x + 2 = 0

multiply through by 2

2[tex]x^{2}[/tex] + x +8x + 4 = 0

2[tex]x^{2}[/tex]  +9x +4 = 0

In conclusion, the equation of the function in standard form is 2[tex]x^{2}[/tex]  +9x +4 = 0

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The unknown side and angle of the triangle is as follows:

A right angle triangle is a triangle that has one of its angles as 90 degrees. The side of a right angle triangle can be found using trigonometric ratios.

Hence, let's find x, y and z.

The sum of angles in a triangle is 180 degrees.

Hence,

180 - 27 - 90 = x

x = 63 degrees.

sin 63° = opposite / hypotenuse

sin 63 = y / 35

cross multiply

y = 35 sin 63

y = 31.1852283466

y = 31.19 units

sin 27 = z / 35

z = 35 sin 27

z = 15.8896674909

z = 15.89 units

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Answer:

Question 1:

The angle m∠DOX is greater than 90 degrees, but less than 135 degrees.

Looking at the diagram we see that:

m∠DOX = 120 degrees.

Question 2:

The angle m∠COX is the sum of two angles that in total are 80 degrees.

Therefore, the equation is:

m∠COX = m∠AOX + m∠COA

Question 3:

The BOA angle measurement is given by:

BOA = 60 - 40

BOA = 20 degrees

Therefore, an angle that measures 20 degrees is:

BOA.

Question 4:

From the previous question we have:

m∠BOA = 60 - 40

m∠BOA = 20

The measure of m∠BOA is 20 degrees

Question 5:

The measure of the angle EOD is given by:

m∠EOD = 140 - 120

m∠EOD = 20 degrees

THANKS

50

4.8

(41 votes)

Step-by-step explanation:

The perimeter of the triangle ABC with respect to the given information is 78.

Whether it be a two-dimensional shape or a one-dimensional length, a perimeter is a closed path that contains, surrounds, or delineates it. A circle's or an ellipse's circumference is its furthest boundary. Numerous real-world uses exist for calculating perimeter. Adding the lengths of all the sides and edges that surround a shape yields its perimeter. It is calculated using linear length units like centimeters, meters, inches, and feet.

Given,

In triangle QRS,

A is the midpoint of QR, B is the midpoint of RS, and C is the midpoint of SQ.

And also given that QA=10, BR=15, SQ=28

Let p represent the triangle ABC's perimeter.

QR + RS +SQ = p

2(QA) + 2(BR) + SQ = p

2(10) +  2(15)+ 28 = p

20 + 30+ 28 = p

78=p

Therefore, the perimeter of triangle ABC is 78

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Answer:

3 * (8 + (n - 1)*x*1/3 ) = 3 * ( 0 )

..

The values that make the inequality -2h ≤ -40 true are

Equivalent form of the inequality is written as

Inequality is a means of representing the relationship existing between the positive and negative parts of equations, using other terms aside exactly using only "equal to"

solving the inequality

-2h ≤ -40

dividing through by a negative number changes the inequality

diving through by -2 gives

h ≥ 20

Therefore, h are values greater than 20 and 23, 25, and 30 are all greater than or equal to 20

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The expected value for the game is -12.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

The probability of rolling a 2 or 5:

= P(2 or 5)

= 1/6 + 1/6 = 1/3

The probability of not rolling a 2 or 5:

= 1 - 1/3

= 2/3

The expected return:

= (1/3)(36) + (2/3)(-36)

= 12 - 24

= -12

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Answer:

45

Step-by-step explanation:

Number of Latvian footballers(n¹) = 36

Numer of footballers of other nationalities(n²)=36/4=9

Now total number of footballers= n¹+n²= 36+9 =45