10. How many feet from the base of a house must a 39-foot ladder be placed so that the top of the ladder will
reach a point on the house 36 feet from the ground? Draw a picture!

After evaluating the algebraic expression we can infer that both students were correct.

An algebraic expression in mathematics is one that was produced utilizing integer variables, constants, and algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)

On the other hand, transcendental numbers, such and e, are not algebraic because they are not generated from integer constants and algebraic operations. While the definition of e necessitates an infinite number of algebraic operations, the creation of is frequently done as a geometric expression .

If an expression can be converted into a rational fraction using the characteristics of the arithmetic operations, it is said to be rational expression (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions).

The expression 5a/2a+3 is the quotient of the terms as it can be written as 5a ÷ ( 2a+3 ).

Again the expression 2a +3 is a sum with only two terms.

Hence both students were correct.

To learn more about expression visit:

https://brainly.com/question/14083225

#SPJ1

After evaluating the algebraic expression we can infer that both students were correct.

An algebraic expression in mathematics is one that was produced utilizing integer variables, constants, and algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)

On the other hand, transcendental numbers, such and e, are not algebraic because they are not generated from integer constants and algebraic operations. While the definition of e necessitates an infinite number of algebraic operations, the creation of is frequently done as a geometric expression .

If an expression can be converted into a rational fraction using the characteristics of the arithmetic operations, it is said to be rational expression (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions).

The expression 5a/2a+3 is the quotient of the terms as it can be written as 5a ÷ ( 2a+3 ).

Again the expression 2a +3 is a sum with only two terms.

Hence both students were correct.

To learn more about expression visit:

brainly.com/question/14083225

#SPJ1

The equation that represents the lines through (2, -4) and (0, 4) is y = -4x + 4

It is crucial to note that the equation of a line is expressed as;

y = mx+ c

Where;

From the information given, we have the point as;

(2, -4) and (0, 4)

Now, let's determine the slope

The formula for determining the slope or gradient of a line is expressed as;

Slope, m = y2 - y1/x2 - y1

Now, substitute the values into the formula

Slope, m = 4 -(-4)/0 -2

expand the bracket

Slope, m = 4 + 4/-2

Add the values

Slope, m = 8/-2

Slope, m = -4

To determine the intercept, use the points of x and y

-4 = -4(2) + c

expand the bracket

-4 = -8 + c

c = -4 + 8

c = 8

The equation of the line is;

y = -4x + 4

Thus, the equation of the line is y = -4x + 4

Learn more about equation of a line here:

https://brainly.com/question/13763238

#SPJ1

The carpenter will not be able to complete his work because the ladder reach 14.1 ft up the wall.

In this question, we have been given a carpenter has a 15 foot ladder. For safety, the bottom of his ladder must be placed 5 feet from the wall.

Consider the following diagram.

In right triangle ABC, AC represents the length of the ladder, CB is the distance between wall and the bottom of the ladder.

Using Pythagoras theorem,

AC² = AB² + BC²

15² = 5² + AB²

225 - 25 = AB²

AB = √200

AB = 14.1 ft                  ............(1)

We have been given that in order to complete his work, the ladder must reach 14.5 feet up the wall.

From (1), we can see that the ladder will reach 14.1 ft up the wall.

This means, under these conditions, the carpenter will not be able to complete his work.

Therefore, the carpenter will not be able to complete his work because the ladder reach 14.1 ft up the wall.

Learn more about the Pythagoras theorem here:

https://brainly.com/question/13965522

#SPJ1

The value of the smiley face given the values of the rectangle, triangle and star is 908.

In order to solve this question, take note of the BODMAS rule. The BODMAS rule gives the order in which mathematical operations should be solved.

The value of the rectangle would be determined first using the third equation provided in the question. let a represent the value of a rectangle.

(4 x a) + (2 x a) - (3 x a) = 15

4a + 2a - 3a = 15

3a = 15

a = 15 / 3

a = 5

The next step is to determine the value of the triangle. The second equation would be used. Let b represent the value of the triangle.

(3 x 5) + (4 x b) = 47

15 + 4b = 47

4b = 47 - 15

4b = 32

b = 32 / 4

b= 8

Now, determine the value of the star using the first equation. Let the value of the star be represented with c.

5 + (3 x 8) - c = 17

5 + 24 - c = 17

29 - c = 17

c = 29 - 17

c = 12

Now, the value of the smiley face can be determined using the last equation:

12 x (8  + 12 - 5) + 8(8 . 12 - 5)

12 x (15) + 8(91)

180 + 728 = 908

To learn more about addition, please check: https://brainly.com/question/349488

#SPJ1

Answer:

y=5x-13

Step-by-step explanation:

1. (3,2) = x,y

2. substitute each x and y digit into y=mx+b format

3. 2=5(3)+b

4. solve for 2=5(3)+b which equals b=-13

5. ANSWER IS SOLVED WHEN ANSWERED IN y=mx+b FORMAT

5. y=5x-13

Answer:

Answer:

SAS postulate

Step-by-step explanation:

AD (common)

AC = BD (both are diameters)

Angle COD = Ange AOD (vertically opposite angles)

Angle CAD = Angle BAD (angle on the circumference is half the angle at the centre)

Therefore, ABD and DCA are congruent by SAS postulate

Step-by-step explanation:

not even 30 points lol it says 18 ANYWAYS hope this helps

Both of the blanks given in the table can be filled in by the ratio 18/1.

Here, we are given a table as shown in the image given above.

There is a proportional relationship given between Demi's test scores and her studying time.

When she studies for 3 hours, her test score is 54.

Thus, the ratio of her test score to hours studying is - 54/3

= 18/1

Similarly, when she studies for 4 hours, her test score is 72.

Thus, the ratio of her test score to hours studying is - 72/4

= 18/1

Thus, both of the blanks given in the table can be filled in by the ratio 18/1.

Learn more about proportionality here-

https://brainly.com/question/24868934

#SPJ1

Answer:

3x+1y=0

Step-by-step explanation:

the equation of a straight line on a graph is y= mx+c
where m is the gradient and c is the y intercept.

we know that the line passes through (1,-3) and has a gradient of 3, therefore we can substitute these values into the equation.

-3 = 3*1 +c
3 = 3+c
c = 3-3 = 0
therefore the equation of this line is y = 3x+0

now we have to write this in the form ax+by=c

3x+1y=0

Answer: 11/16

Step-by-step explanation:

1/8=2/16

1/4=4/16

5/16=5/16

add it all together

5x + 10 is the simplified form of the expression 2( 3x + 4 ) - ( x - 2 ).

Given the expression in question;

2( 3x + 4 ) - ( x - 2 )

To expand and simplify, get rid of the first parenthesis using distributive property.

2( 3x + 4 ) - ( x - 2 )

3x( 2 ) + 4 ( 2 ) - ( x - 2 )

6x + 8 - ( x - 2 )

For the second parenthesis, the negative sign before it affects everything inside it, hence;

6x + 8 - ( x ) - ( - 2 )

6x + 8 - x + 2

Collect like terms

6x - x + 8 + 2

Add 6x and -x

5x + 8 + 2

Add 8 and 2

5x + 10

Therefore, the simplified form of the expression is 5x + 10.

Learn how to simplify more expressions here: https://brainly.com/question/27122308

#SPJ1

The solution to the inequality |2x - 3| > 5 is: x < -1 or x > 4

Therefore, the correct option is A) x < -1 or x > 4.

Given that we need to find the solution to the inequality |2x – 3| > 5

To solve the inequality |2x - 3| > 5, we can break it down into two cases:

Case 1: 2x - 3 > 5

In this case, we have:

2x - 3 > 5

2x > 5 + 3

2x > 8

x > 4

Case 2: -(2x - 3) > 5

In this case, we have:

-(2x - 3) > 5

-2x + 3 > 5

-2x > 5 - 3

-2x > 2

x < -1 (remember to reverse the inequality when multiplying or dividing by a negative number)

Combining the solutions from both cases, we find that the solution to the inequality |2x - 3| > 5 is:

x < -1 or x > 4

Therefore, the correct option is A) x < -1 or x > 4.

Learn more about inequality click;

https://brainly.com/question/20383699

#SPJ2

The equation of the inverse function is f'1(x) = x^2 + 6 and the domain is all set of real numbers

The function f(x) is given as

f(x) = √x -6

Rewrite as

y = √x -6

Switch/swap the positions of x and y in the above equation

The equation becomes

x = √y -6

Make y the subject of the formula in the above equation

The equation becomes

y - 6 = x^2

Add 6 to both sides

y = x^2 + 6

Rewrite as an inverse function

f'1(x) = x^2 + 6

Hence, the inverse function is f'1(x) = x^2 + 6

Read more about inverse equations at:

brainly.com/question/14391067

#SPJ1

Answer:

f(×)=(×+6)^2;×>-6 there we go..

The trials in a binomial experiment are the steps. the likelihood of each trial being successful is. What is the likelihood of success? The probability of success is P=1.42.

The binomial distribution is used to summarise the number of trials or observations where each trial has the same probability of attaining a certain value.. When flipping a coin, the probability of witnessing a certain number of successful outcomes in a specified number of trials is determined by the binomial distribution; as there are only two possible outcomes, the likelihood of flipping a coin is 12 or 0.5 for each trial we do.

based on the facts provided;

here ,

n=500 ,p=0.4,q=0.6, X=number of successes

when n*p and n*q>5 then we can use normal approximations

here n*p=500*0.4=200 >5 ,n*q=500*0.6=300>5

so we can use normal approximation

mean =200

variance =200*0.6=120,

std. deviation=120^1/2

we need to find

P(185<=X<=220), applying continuity correction factor

P(184.5<=X<=220.5)

Z=(X-mean)/std. dev~N(0,1)

P((184.5–200)/10.95<=Z<=(220.5–200)/10.95)

=P(-1.42<=Z<=1.87)

to know more about binomial visit;

https://brainly.com/question/15345198

#SPJ9

Answer: 84

Step-by-step explanation:

Bhamini =

42 x 6 = 25.2

25.2 x 1/3 = 84

Chas =

252.84 - 42 = 126

Bhamini gets £84!

Hope this answered your question, don't ell Mr Gohil I helped you lol.

Answer provided by Zack.

the equation of the line will be x + y = 0 and it is being graphed.

Point on the line = (1, -1)

Slope of the perpendicular line = 1

So, the slope of the line will be

m × 1 = - 1

m = - 1

Equation of the line will be given by:

y - y₁ = m (x - x₁)

y - (- 1) = (- 1) (x - 1)

y + 1 = - x + 1

x + y = 0

We have graphed the equation.

Therefore, we get that, the equation of the line will be x + y = 0 and it is being graphed.

Learn more about equation here:

https://brainly.com/question/1214333

#SPJ1

70 people can get share from the chocolate.

Real estate investment trusts, limited partnerships, and mutual funds all employ shares as a sort of unit. A share is an immovable unit of capital that symbolizes the ownership connection between the company and the shareholder. The denominated value of a share is its face value, which could not be the same as the share's market value.

The capital of a firm consists of the whole face value of its issued shares.

Total amount of chocolate purchased = 10 kg

Amount of chocolate each friend want =1/7 kg

So, number of people who can get share = 10 / (1/7)

                                                                     = (10×7)/1

                                                                     = 70 people

To know more about share please visit:

https://brainly.com/question/28392295

#SPJ10

Answer: 9 inches

Step-by-step explanation:

       We know that the area of a square can be solved with the following formula when s is the length of one side. We will plug in our known values and solve:

        a = s²

        (81) = s²

        [tex]\sqrt{81}[/tex] = s

        9 in = s

       One side of the rug is equal to 9 inches.

Margie can make 13 bows with her ribbon.

In the US, a foot is used to measure length or distance. "Feet" is the plural form of the single unit of measurement known as "foot." Foot or feet are denoted by the letter ft.

Margie has 15 feet of ribbon.

To make a bow for a bouquet, it takes 7/8 of a foot of ribbon for a bouquet.

1 bow = 7/8 × 1 foot

Therefore, the number of bows Margie can make with the ribbon will be:

Number of bows = 7/8 × 15 feet

Number of bows = 13.125 ≈ 13

Hence, Margie can make 13 bows with her ribbon.

Learn more about foot here:

https://brainly.com/question/876758

#SPJ1

Answer:

Michael age is 13 and keanus age is 39

Step-by-step explanation:

Michael is 1/3 of keanus age

so Michael is 1 and keanus is 3 so if u add them all up it's 4 so 52 divide by 4 it's 13 so Michael is 13 and if you times three it will be 39, and if u add their age together it adds up to 52 so it's 13

Answer:

C=38.48+0.5x

about 143 miles

Step-by-step explanation:

$38.48 base cost plus $.50 per mile, so after x miles, it would be 0.5x

so C=38.48+0.5x

to find how many miles Paul can travel

we set 110=38.48+0.5x

then solve

x=143.04

so Paul can travel about 143 miles

The equation of line in slope intercept form can be written as y = mx + c where m is the slope of line and c is the y intercept.

We are given three equations namely y = 2x -2, y = -x + 1 and y = x - 4 and we need to determine the description of equation, slope and y intercept. The equation y = 2x - 2 is the equation of straight line. If we compare this equation with the slope intercept form of line then, m = 2 and c = -2. Thus, slope is 2 and y intercept is -2. The equation y = -x +1 is the equation of straight line. If we compare this equation with the slope intercept form of line then, m = -1 and c = 1. Thus, slope is -1 and y intercept is 1. This equation y = x - 4is the equation of straight line. If we compare this equation with the slope intercept form of line then, m = 1 and c = -4. Thus, slope is 1 and y intercept is -4. The graphs of the equation are attached below.

Learn more about Slope intercept form at:

brainly.com/question/9317111

#SPJ9

Answer:

Multiply 5/2 to both sides

Step-by-step explanation:

Doing so 'cancels' out the coefficient of (z+1) on the left-hand side.

Answer:

Step-by-step explanation:

If the diagonal of a square is 11.3 meters, approximately what is the perimeter of the

square?

find the area with the formula ½ × d ^ 2 Square units, take the square root of the result and find the side, multiply by 4 and you have the perimeter.

1/2 11.3^2 =

1/2 127,69 =

63.845 m²

√63.845 =

7.99 m

7.99 * 4 =

31.96 m

The domain and the range of the graph are x >= 1 and -∝ < y < ∝, respectively

The domain of the function is the set of input values of the graph

The range of a function is the set of output values of the graph.

The domain

On the graph of the function, we can see that:

The x values start from 1 and it extends indefinitely to the right

This means that the domain is x >= 1

The range

On the graph of the function, we can see that:

The y values extend indefinitely on all sides of the coordinate plane

This means that the range is -∝ < y < ∝

Read more about domain and range at

brainly.com/question/2264373

#SPJ1

If Maran made 160 candy apples, spending $120 on ingredients and supplies while selling all the candy apples for $480, then the two statements that are true are:

B. Maran spent $0.75 on each candy apple (Cost Price), and

E. Maran sold each candy apple for $3 (Selling Price).

As per the question statement, Maran made 160 candy apples, spending $120 on ingredients and supplies while selling all the candy apples for $480.

We are required to identify the two true statements from a the set of 5 statements, provided in the question itself, related to the per candy cost price, sell price and profit of Maran.

Since he made 160 candy apples, spending $120 on ingredients and supplies, therefore, the cost price of per candy will be $(120/160) = $0.75, i.e., Statement B that Maran spent $0.75 on each candy apple is True.

Also, he sold all 160 candies for a total of $480, therefore, the sell price of each candy is $(480/160) = $3. Hence, Statement E that Maran sold each candy apple for $3., is also true.

Now, since the cost price of each candy is $0.75 and the sell price of the same is $3, then Maran made a profit of $(3 - 0.75) = $2.25 per candy. But statement D mentions that Maran earned a profit of $3 on each candy sold, which is false.

To learn more about Cost Prices & Selling Prices, click on the link below.

https://brainly.com/question/28017453

#SPJ1

Total surface area of cylinder is 303.34 [tex]cm^{2}[/tex]

A cylinder is a 3D solid shape made up of two bases that are parallel and identical and are connected by a curved surface. These bases resemble spherical disks. The axis of the cylinder shape is a line drawn through the center or connecting the centers of two circular bases.

The surface area of a cylinder is

SA = [tex]2\pi r^{2}[/tex] + 2πrh

where:

r = radius

h = height

This formula comes from adding the areas of the surfaces of the cylinder.  It has two flat circular faces and a rounded face.

If we cut the cylinder from the circular face symmetrically, the surface area for one piece will be

SA = 2[[tex]\frac{\pi r^{2} }{2}[/tex]]  +  ([tex]\frac{2\pi r}{2}[/tex])h  +  2rh

We will have 2-half flat circular faces, a flat rectangular surface, and half of the rounded surface.

Simplify the SA formula.

SA = [tex]\pi r^{2}[/tex] + πrh + 2rh

SA = r(πr + πh + 2h)

Substitute the values into this formula.

SA = 3(3π + 8π + (2×8))

SA = 3(11π + 16)

SA = 33π + 48

SA = 151.67[tex]cm^{2}[/tex]

Since we have 2 pieces, multiply this result by 2.

2(151.67[tex]cm^{2}[/tex]) = 303.34[tex]cm^{2}[/tex]

Total surface area is 303.34[tex]cm^{2}[/tex]

To learn more about surface area visit :

brainly.com/question/2835293

#SPJ9

After Applying Laws of Exponents we can write as [tex](6yz)^{-4}[/tex]

The exponent of a number indicates how many times a number has been multiplied by itself. For instance, 34 indicates that we have multiplied 3 four times. Its full form is 3 3 3 3. Exponent is another name for a number's power. A whole number, fraction, negative number, or decimal are all acceptable.

Exponents with distinct bases and the same powers can be multiplied by multiplying the bases and writing the power outside of the brackets.

[tex]a^{n}[/tex] .[tex]b^{n}[/tex] =[tex](a.b)^{n}[/tex]

=[tex]3y^{-4}[/tex] . [tex]2z^{-4}[/tex]

=[tex]3y^{-4}[/tex] . [tex]2z^{-4}[/tex]

= [tex](6yz)^{-4}[/tex]

To know more about law of exponents visit :

brainly.com/question/15993626

#SPJ9

Answer:

136 ,24 ,180 ,34

Step-by-step explanation: