eight toy makers each carved 25 blocks and 15 cars how many toys did they crave in all

Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

The length of the railing is 105.81 inches.

Given,

The stair has 7 steps

The rise of each step = 8.5 inches

The tread of each step = 12.5 inches

Slope of each step = x

We have to find the length of the railing.

Length of railing = 7x

Then,

Slope of step, x can be determined using Pythagorean theorem.

Let rise be the height of the right angled triangle and tread be the base of the triangle

Then,

Hypotenuse= Slope, x  = \(\sqrt{Rise^{2} + Tread^{2} }\)

x = \(\sqrt{8.5^{2}+ 12.5^{2} }\)

x = \(\sqrt{72.25 + 156.25}\)

x = √228.5

x = 15.12 inches

That is,

The slope, x of one step is 15.12 inches

Now,

Length of the railing = 7x = 7 × 15.12 = 105.81 inches

Therefore,

The length of the railing is 105.81 inches.

Learn more about Pythagorean theorem here;

https://brainly.com/question/14930619

#SPJ1

Answer:

x=39 degrees

Step-by-step explanation:

x + 31 equals 2x - 8 because both pair of expressions must add up to 180

Answer:

-232 ft

Step-by-step explanation:

there is not sufficient evidence to claim that the variance of the battery life population is different than 4 hours2 at a significance level of 0.05.

answer is D. None of the above.

To test if there is significant evidence to claim that the variance of the battery life population is different than 4 hours2, we can use a chi-square test.This is how the test statistic is computed:

X2 = (n-1)*(s2/σ2)

where n is the sample size, s2 is the sample variance and σ2 is the population variance.

In this case, n = 16, s2 = 3.25 and σ2 = 4

X2 = (16-1)*(3.25/4) = 12.1875

The critical value of X2 with 15 degrees of freedom and α = 0.05 is 24.996. Therefore, since 12.1875 < 24.996, we fail to reject the null hypothesis, and there is not sufficient evidence to claim that the variance of the battery life population is different than 4 hours2 at a significance level of 0.05.

Learn more about variance here

https://brainly.com/question/13708253

#SPJ4

Answer:

2.5

Step-by-step explanation:

the length has increased by 7.5/3 = 2.5.

so the scale factor is 2.5

Answer:

any line with a slope of 3 is parallel.

Step-by-step explanation:

Answer:

z³=27

³√z³=³√27

z=3

Step-by-step explanation:

z³=27

³√z³=³√27

z=3

Answer:

-3i^2

Step-by-step explanation:

(-3i^2) ^3=-(3*(-1)) ^3=-(-3)^3=-(-27)=27

We have shown that C is the image of A by dilation with center B and ratio 3.

Now, To show that C is the image of A by dilation with center B and ratio 3, we need to follow these steps:

Firstly, Find the vector AB by subtracting the coordinates of B from the coordinates of A:

AB = A - B = (6 - 3, 4 - 7) = (3, -3)

Multiply the vector AB by the dilation ratio of 3:

3 AB = 3 (3, -3)  = (9, -9)

Add the resulting vector to the coordinates of the center B:

BC = B + 3 AB = (3, 7) + (9, -9)

BC = (12, -2)

Hence, Compare the resulting point BC to the coordinates of C to show that they are the same:

BC = (12, -2) = C

Therefore, we have shown that C is the image of A by dilation with center B and ratio 3.

Learn more about the coordinate visit:

https://brainly.com/question/24394007

#SPJ1

We provide recruitment solutions for your Future Talent and Volume Hiring needs. Platform. Services.

Define Decimal place?

To learn more about decimal place refers to:

https://brainly.com/question/29423712

#SPJ1

Answer:

49%

Step-by-step explanation:

Well, you would just divide the "male democrat" category and the "male total" category and then move the decimal over 2 spaces, because you need to multiply by 100 to turn your answer into a percent, so:

\(\frac{600}{1222}=0.49\)

Then once you multiply by 100, or move the decimal to the left 2 spaces, it becomes:

49%

Answer: Uhm, omkay sirs

Step-by-step explanation:

For the linear function y = 2/3x + 1, we have that:

a) The slope is of 2/3 and the intercept is of 1.

b) The y-intercept is marked at y = 1 on the y-axis.

c) Using the slope and the intercept, point (3,3) is the second point used to graph the function.

d) The graph of the linear function y = 2/3x + 1 is given at the end of the answer.

A linear function, in slope-intercept format, is modeled as follows:

y = mx + b

In which:

For this problem, the function is:

y = 2/3x + 1.

Then, form item a, we have that:

For item b, the y-intercept of b = 1 means that the function crosses the y-axis at b = 1.

For item c, we have to consider that the slope is of 2/3, meaning that when y increases by 2, x increases by 3. Point (0,1) is on the graph of the function, hence point (3,3) will also be, as x increases by 3 from 0 to 3 and y increases by 2 from 1 to 3.

Considering the discussion above, the graph of the function is given at the end of the answer, with the intercept and point (3,3) labeled.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

Answer:

Y=6x-75

Step-by-step explanation:

If you take the beginning amount spent which is $75 you would want that on the graph to be in the negatives. With it starting in the negatives it will show you whether the amount of cars (x) will cause a profit or a deficit.

For instance, say they washed 7 cars (x=7). You would take 6 and multiply it by 7 to get 42. Then you would take 42 and take away 75 to find the profit/deficit. 42-75= -33

This shows that washing 7 cars will cause them to lose $33.

If you take another situation where they wash 15 cars (x=15). In this case they would earn a total of $15.

we have the equations

y=(1/4)x+4

y=-2x-5

Remember that

when solving a system by graphing, the solution is the intersection point both graphs

so

using a graphing tool

see the attached figure

please wait a minute to draw the system

The number of weeks to produce 225 units will be 10.

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

The given expression for the number of the unit produced is written as below,

s(t) = 14√4t + 44

For 225 units the number of weeks required will be calculated as:-

s(t) = 14√4t + 44

225 = 14√4t + 44

181 = 14√4t

4√t = (181 / 14 )

√t = ( 181 / 56 )

t = ( 181 / 56 )²

t = 10 weeks

Therefore, the number of weeks to produce 225 units will be 10.

To know more about an expression follow

https://brainly.com/question/723406

#SPJ1

Equations are expressions with equal values

The solution of the equation is -11/3

The equation is given as:

\(\frac{-2}{x + 4} = \frac{4}{x + 3}\)

Cross multiply

\(-2x - 6 = 4x + 16\)

Collect the like terms

\(-4x - 2x = 16 + 6\)

Evaluate the like terms

\(-6x =22\)

Divide through by -6

\(x =-\frac{11}{3}\)

Hence, the solution of the equation is -11/3

Read more about equations at:

https://brainly.com/question/7784687

Answer: \(-\frac{11}{3}\)

Step-by-step explanation:

Answer:

no,i don't think about it

Answer:

108°

Step-by-step explanation:

From the diagram,

Angle X + Angle CXD = 180°

Angle X + 72° = 180°

Angle X = 180° - 72° = 108°

Answer:

its c

Step-by-step explanation:

Answer:

The height = 18 inches

Step-by-step explanation:

The volume = area of the base × height

Area of the base = 40.5 inches²

The volume = 729 inches³

729 = 40.5 × height

Height = 729 ÷ 40.5 = 18 inches

Candy spends £2.65, has 2/3 left and Candy has £7.95 money to start with.

Given that Candy spends £2.65 and has 2/3 of the initial amount left, we are required to find how much money Candy has to start with.

Solution:Let the initial amount of money Candy has be x.

Then, the amount of money spent by Candy = £2.65

Amount of money left with Candy = 2/3 of the initial amount

∴ Money left = 2/3 × x

Amount of money spent + money left = initial amount of money

Candy spends £2.65:2/3 of the initial amount left

= £ (x - 2.65)∴ 2/3 × x

= x - 2.65⇒ 2x/3

= x - 2.65⇒ 2x

= 3x - 7.95⇒ 3x - 2x

= 7.95⇒ x = 7.95

Hence, Candy has £7.95 to start with.

Know more about  money   here:

https://brainly.com/question/24373500

#SPJ8

To find the distance above the ground at which the tack is, we need to calculate the vertical displacement of the front wheel when the tack was picked up.

First, let's determine the circumference of the front wheel. The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter. Given that the diameter is 26 inches, we can calculate the circumference:

C = π × 26

C ≈ 81.64 inches

This means that for every complete revolution of the wheel, Devon travels a distance of approximately 81.64 inches.

Next, we need to determine how many complete revolutions the front wheel made as Devon rolled another 100 feet (1200 inches). Since the circumference of the wheel is 81.64 inches, we can divide 1200 inches by 81.64 inches to find the number of revolutions:

1200 / 81.64 ≈ 14.68 revolutions

Now, we know that the tack was picked up after one full revolution. Therefore, out of the 14.68 revolutions, 13 complete revolutions have occurred. The tack is located at the point where the 14th revolution starts.

Since each revolution covers a distance equal to the circumference of the wheel, the vertical displacement of the tack is the height of the wheel, which is the radius of the wheel. The radius is half the diameter, so in this case, it is 26 / 2 = 13 inches.

Therefore, the tack is located 13 inches above the ground.

For more such questions on distance

https://brainly.com/question/26550516

#SPJ8

For the given expression, the variable is p, coefficient is 17 and the exponent is 5.

Expression:

Expression refer the algebraic expression that consists of variables, numbers and math operators.

Given,

Here we have the expression 17p⁵

Now, we have to find the exponent, coefficient and variable.

As per the definition of exponent, the term exponent refers the power value of the expression.

So, the exponent is 5.

And the definition of coefficient is an integer that is written along with a variable or it is multiplied by the variable.

So, the coefficient is 17.

And the variable of this expression is p.

To know more about Expression here.

https://brainly.com/question/14083225

#SPJ1

The expression which is used to represents the statement "one-more than the quotient of a number x" and 4 is "x/4 + 1".

A "Quotient" is the result of a division operation between two numbers, where one number is divided by another. It represents the number of times one number is contained within another number.

An "Expression" is defined as "mathematical-phrase" which contain numbers, variables, and operators such as addition, subtraction, multiplication, and division. It can also contain functions and other mathematical symbols.

The quotient of a number"x" and 4 can be written as x/4.

So, one more than the quotient of a number x and 4 can be represented by the expression:

⇒ x/4 + 1,

Therefore, required mathematical expression is "x/4 + 1".

Learn more about Expression here

https://brainly.com/question/30553495

#SPJ1

The given question is incomplete, the complete question is

Write an expression to represent : One more than the quotient of a number x and 4.