7. (a) A homeowner wishes to replace the three identical steps leading to her front door with a ramp. Each step is 10 cm high and 35 cm long. Find the length of the ramp. Give your answer correct to one decimal place.​

Answer:

3

Step-by-step explanation:

Answer:

226a³b² - 824ab³ + 984b⁴

Step-by-step explanation:

We can factorize the given expression by expanding the two binomials and then combining like terms.

First, expand the two binomials:

10ab (a − 2b)³ +24ab² (3a − 6b)² = 10ab(a³ - 6a²b + 12ab² - 8b³) + 24ab²(9a² - 36ab + 36b²)

Then, combine like terms:

= 10ab(a³ - 6a²b + 12ab² - 8b³) + 24ab²(9a² - 36ab + 36b²)

= (10a³b - 60a²b² + 120ab³ - 80b⁴) + (216a³b² - 864ab³ + 864b⁴)

= (10a³b + 216a³b² - 60a²b² - 864ab³ + 120ab³ + 864b⁴ - 80b⁴)

= (10a³b + 216a³b² - 60a²b² - 864ab³ + 120ab³ + 864b⁴ - 80b⁴)

= (10a³b - 60a²b² + 120ab³ - 80b⁴) + (216a³b² - 864ab³ + 864b⁴)

= (10a³b + 216a³b² - 60a²b² - 864ab³ + 120ab³ + 864b⁴ - 80b⁴)

= (10a³b - 60a²b² + 120ab³ - 80b⁴) + (216a³b² - 864ab³ + 864b⁴)

= 226a³b² - 824ab³ + 984b⁴

False

The parent function is the simplest function within a family of functions that defines the general form of that family.

Parent Functions

Parent functions are given in terms of y and x, where y is the output and x is the input. In linear functions, b represents a constant, specifically the y-intercept. Since the form y=b does not have an input it cannot be the parent function of linear lines. The graph of y=b would be a horizontal line with no slope. This does not define the general form of most linear functions. Additionally, since the slope has been changed to zero, it is not considered the simplest form of linear functions.

Linear Parent Function

The true parent function of linear functions is y=x. This function is the simplest linear function and has no transformations. Additionally, when graphed it is a diagonal line that defines the general shape of lines.

To create new linear functions the parent function, y=x, can be transformed by changing the coefficient of x to change the slope or by adding a constant to shift the graph vertically.

Answer: I'm sorry if it's wrong I'm pretty sure it's ≥ if not I'm sorry

Step-by-step explanation:

Step-by-step explanation:

the area of a trapezoid is

(a + b)/2 × x

a and b being the 2 bases. and x, as requested, is the height.

A

it does not matter which base is which, as long as we keep using them consistently.

so, let's assume a is the first base :

a = x + 5

and then for the second base

b = 2x - 1

now we use that in the main formula :

(x + 5 + 2x - 1)/2 × x = (3x + 4)/2 × x = (3x² + 4x)/2

A = (3/2)x² + (4/2)x = (3/2)x² + 2x ft²

B

now the height is increased by 4 ft.

that means we need to replace x by x + 4.

(3/2)(x+4)² + 2(x+4) = (3/2)(x² + 8x + 16) + 2x + 8 =

= (3/2)x² + (24/2)x + (48/2) + 2x + 8 =

= (3/2)x² + 12x + 24 + 2x + 8 =

= (3/2)x² + 14x + 32 ft²

with x being the original height, of course.

The total number of students in the student body is 110.

Percentage is the ratio of an amount expressed as a number out of 100. The sign that is used to represent percentage is %.

In order to convert a number to percentage, multiply the number by 100. Percentage is a measure of frequency.

In order to determine the total number of students in the student body, divide the number of students that watch TV everyday by the given percentage.

Number of students in the student body = number of students that watch TV everyday / percentage

88 / 80%

= 88 / 0.8 = 110

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A line has a slope of 5. it passes through the points (-5, -1) and (x,9) than the value of x is -3

We are going to use the fact that when a line passes through two points : [tex](x1,y1) and (x2,y2)[/tex]

the slope is given by the following formula:

[tex]slope=y2-y1/x2-x1[/tex]

In the present case, the slope is 5 and the points are (-5, -1) and (x, 9)

Hence,

[tex]5=9-(-1)/x-(-5)[/tex]

[tex]5=10/x+5\\x+5=10/5\\x+5=2\\x=-3[/tex]

Thus, the value of x is -3 when it travels between the coordinates (-5, -1) and (x, 9).

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Answer: 6

Step-by-step explanation:

Answer: To compare the level of support for the new after-school club between teachers and students, we can calculate the percentage of individuals in each group that responded "yes" to the proposal.

For teachers: 13 out of 20 is equivalent to 13/20 = 0.65 or 65%

For students: 37 out of 50 is equivalent to 37/50 = 0.74 or 74%

Based on the percentage of individuals in each group that responded "yes," we can see that students are more in favor of the new after-school club than teachers. 74% of students responded "yes" to the proposal, while only 65% of teachers responded "yes."

It's worth mentioning that it's important to keep in mind that this comparison is based on the sample size of teachers and students that responded to the survey and not the whole population, also if the sample size isn't representative of the population and not randomly selected it can't be generalized.

Step-by-step explanation:

when a fraction has a small numerator and a bigger denominator, the percent would be a proper fraction.

A percentage is a number or ratio that can be expressed as a fraction of 100 in mathematics. If we need to calculate the percentage of a number, divide it by the whole and multiply by 100.

As a result, the percentage denotes a part per hundred. The term % refers to one hundred percent. The symbol “%” represents it.

Therefore, When a fraction has a small numerator and a large denominator, it is a proper fraction.

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As a result, the answer to the given angle problem can be found by comparing the position, measurement, and congruence of two or more angles.

When two lines come together at a common point, an angle is created. They are expressed as a number of degrees, denoted by the symbol °. Acute, right, obtuse, and reflex angles are the other three significant types of angles. 360 degrees make up a circle. A 720° angle indicates that the object has completed two full rotations.

Here,

You can compare angles and take into account their relationships to other angles in addition to calculating degrees or radians.

Since we are comparing the position, measurement, and congruence of two or more angles, we refer to them as having "angle relationships."

For instance, two lines or line segments that cross each other create two pairs of vertical angles.

When a transversal intersects two parallel lines, complex angle relationships, such as alternating interior angles, matching angles, and so forth, result.

As a result, the answer to the given angle problem can be found by comparing the position, measurement, and congruence of two or more angles.

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The sale price of the item is given by the equation A = $ 26.40

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the sale price of the item be represented as A

Now , the equation will be

The original price of the item = $ 33

An item on sale costs 80% of the original price

So , the sale price of the item A = 80 % x original price of the item

Substituting the values in the equation , we get

The sale price of the item A = ( 80 / 100 ) x 33

The sale price of the item A = 0.80 x 33

The sale price of the item A = $ 26.40

Therefore , the value of A is $ 26.40

Hence , the sale price is $ 26.40

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These two perpendicular bisectors will meet at (1, 5, 1). These are the coordinates of the triangle's circumcenter.

the triangle's circle's center. It is the point where the "perpendicular bisectors," or lines parallel to the centre of both sides, cross.

The intersection of any two perpendicular bisectors of any two triangle sides is known as the circumcenter of a triangle ABC.

The equation y=1 is the perpendicular bisector of sides B(3,0) and C(3,2). Because AB's midpoint is at 3,1 and its slope is unknown. The perpendicular bisector has zero slope. The equation for such a line is y=y1.

The equation for the perpendicular bisector of A(0,0) and B is also x=1.5 (3,0). The reason is that AB has a midpoint of zero slope and (1.5,0). The perpendicular bisector's slope won't be clearly defined. The equation for such a line is x=x1.

These two perpendicular bisectors will meet at (1, 5, 1). These are the coordinates of the triangle's circumcenter.

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Answer:

To find the coordinates of the point on the x-axis that is reflected over the x-axis from the point P, you can use the formula (x, -y). In this case, the x-coordinate of point P is 4, so the x-coordinate of the reflected point will also be 4. The y-coordinate of point P is 7, so the y-coordinate of the reflected point will be -7. Therefore, the coordinates of the reflected point are (4, -7).

If it cost the shoe factory $26.47 to make a pair of Purple Pedi running shoes and the mall sells them for $128.98 then 3.87 is the percent mark-up.

The gross profit of a unit is determined by subtracting its cost to produce or acquire for resale from its sales price to determine the markup percentage. The markup percentage is computed as (12 - 8) / 8 and equals 50% if an item is priced at $12 but costs the manufacturer $8 to produce.

Some individuals will inform you that a 5% markup equates to a markup of 5% of the price your customer pays. In your illustration, this is stating that you add a specific amount to your cost, $62, to arrive at a price of $P for your customer, and the amount you added is 5% of $P. This means that your cost of $62 is 95% of the price of P.

($128.98 - $26.47)/ $26.47

= 3.87.

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The solution to the equations is

Addition : 2.49 + 6.7 = 9.19  ;  6.7 + 2.49 = 9.19

Subtraction : 9.19 - 6.7 = 2.49  ;  9.19 - 2.49 = 6.7

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the three decimals be represented as set x = { 2.49 , 6.7 , 9.19 }

Now , the addition facts are given by equations ,

2.49 + 6.7 = 9.19  be equation (1)

6.7 + 2.49 = 9.19   be equation (2)

And , the subtraction facts are given by the equations ,

9.19 - 6.7 = 2.49  be equation (3)

9.19 - 2.49 = 6.7  be equation (4)

Hence , the equations are solved

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Answer: y = 2x-8

Step-by-step explanation:

Let's try to determine by substitution method. Starting from the first equation:

y = 2x-8

2·0-8 = -8

2·1-8 = -6

2·3-8 = -2

2·4-8 = 0

The first equation satisfies the conditions of the table.

The two numbers that come next in the sequence 5,5,10,15,25, are 40 and 65.

To calculate this , You can figure it out by taking the first number, which is 5. However, since the previous number is 0, the sum is 5, and you proceed in the same manner.

5 + 5 = 10

(5 + 10) = 15

(10 + 15) = 25

(15 + 25) = 40

(25 + 40) = 65

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The quadratic equation 4(x² − 5) − 1 = 3 has its solutions to be are √6 and -√6

From the question, we have the following parameters that can be used in our computation:

4(x 2−5)−1=3

Express properly

This gives

4(x² − 5) − 1 = 3

Subtract -1 from both sides of the equation

So, we have the following representation

4(x² − 5) = 4

Divide both sides by 4

This gives

x² − 5 = 1

Subtract -5 from both sides of the equation

So, we have the following representation

x² = 6

Take the square root of both sides

x = ±√6

Hence, the solution is ±√6

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Answer:

30,34,38,42,46,50,54,58,62,66,70

The solution for y in the equation √(7 - x)² + (9 - y)² is infinite many solutions

From the question, we have the following parameters that can be used in our computation:

√(7-x)²+(9-y)²

Express tthe equation properly

So, we have the following representation

√(7 - x)² + (9 - y)²

The above is an expression, not an equation

This means that the value of the variable y can take any value and the equation will be true

In other words, it means that the variable y has infinite many solutions because it is not an equation but it is an expression

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At the end of the eighth year, the amount Mr. Smith withdrew was $41,757.68.

The amount that Mr. Smith withdrew at the end of the eighth year is a product of a series of computations, involving future value determination.

In this situation, we have used an online finance calculator to determine the future value of the investment at each leg.

N (# of periods) = 20 years

I/Y (Interest per year) = 6%

PV (Present Value) = $0

PMT (Periodic Deposits) = $1,800

Results:

FV = $66,214.06

Sum of all periodic payments = $36,000 ($1,800 x 20)

Total Interest = $30,214.06

N (# of periods) = 5 years

I/Y (Interest per year) = 6%

PV (Present Value) = $,

PMT (Periodic Withdrawal) = $-7500

Results:

FV = $46,331.15

Sum of all periodic payments = $-37,500 ($7,500 x 5)

Total Interest $17,617.09

N (# of periods) = 2 years

I/Y (Interest per year) = 6%

PV (Present Value) = $46,331.15

PMT (Periodic Withdrawal) = $-5000

Results:

FV (Final Withdrawal) = $41,757.68

Sum of all periodic payments = $-10,000 ($5,000 x 2)

Total Interest = $5,426.53

Thus, the amount of $41,757.68 was withdrawn by Mr. Smith at the end.

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Answer:

The mechanic spent 12 hours on the repair.

Step-by-step explanation:

The mechanic spent 12 hours on the repair.

Answer:

73

Step-by-step explanation:

so basically this process is rather easy, okay what u have to do is find the area but since u cant u just have to try your best and go over the answer with a friend, oh you have none? Sorry for assuming, so just ask siri if you have 0 friends, the formula should look a little like this:

A=l*w or A=b*h

which than u would have to add up the circumference (sorry for not mentioning that earlier) so the new formula would be a little like this

A+C=

than thats your answer (it should be 12.)

The length of the side CD is 5.195 cm and the Area of ΔABC is 31.17 cm²

The basic trigonometric functions are;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the given triangle ABC, we can see that it is a right angle triangle where ∠ACD = 60°, and as such, ∠CAD = 30°.

Thus;

BC/AC = tan 30°

6/AC = 0.5774

AC = 10.39cm

Thus;

CD/AC = cos 60

CD = 10.39 * 0.5

CD = 5.195 cm

Formula for area of a triangle is;

Area = ¹/₂ * base * height

Area = ¹/₂ * 6 * 10.39

Area = 31.17 cm²

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Answer:

x = 45°

Step-by-step explanation:

x° + 45° + 90° = 180°

x° + 135° = 180°

x° = 180° – 135°

x° = 45°

i hope this helped

The closest to the number of yards of ribbon Mario had altogether will be ;

⇒ 11 yards

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

Given that;

Mario had 8 1/5 yards of ribbon for a project.

And, Sue gave him 2 3/4 more yards of ribbon.

Now,

Since, Mario had 8 1/5 yards of ribbon for a project.

And, Sue gave him 2 3/4 more yards of ribbon.

Hence, Total ribbon for the project Mario have = 8 1/5 yards + 2 3/4 yards

                                                                        = 41/5 + 11/4

                                                                        = (164 + 55) / 20

                                                                         = 219 / 20 yards

                                                                         = 10.95 yards

                                                                         ≈ 11 yards

Thus, Total ribbon for the project Mario have = 11 yards

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Answer: C

Step-by-step explanation: it says that it's smaller or equal to x and x is smaller than 17