AB= 6 cm, AC = 12 cm
Calculate the length of CD.
Give your answer to 3 significant figures.
C
D
55°
12 cm
B 6 cm
A

The greatest number of rectangles 6cm×4cm that can be cut from a metal that measure 16cm×20cm is 13 rectangles.

A rectangle is a plane shape that has pair of opposite sides equala and parallel.

To calculate the greatest number of rectangles, we use the formula below.

Formula:

Where:

Ferom  the question,

Given:

Substitute these values into equation 1

Hence, the greatest number of rectangles is 13 rectangles.

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The standard form of the equation y = -2/3 x - 1 is 2x + 3y = -3.

The standard form for linear equations in two variables is Ax + By = C. Where,

The equation is represented in slope intercept form. So, let' represent it in standard form.

Therefore,

y = - 2 / 3 x - 1

add 2 / 3 x to both sides of the equation

y = - 2 / 3 x - 1

y + 2 / 3 x  = - 2 / 3 x + 2 / 3 x - 1

y + 2 / 3 x  = - 1

Let's multiply all through by 3 to eliminate the fraction

y + 2 / 3 x  = - 1

3y + 3(2 / 3 x) = -3

Therefore, the standard form equation is 2x + 3y = -3

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Answer:

add 54 to the numerator and 61 to the denominator because after you add it the fraction, it should be 60/90: simplified to 2/3 if you divide the numerator and denominator by 30.

The number that must be added to the numerator and denominator is 40.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Fraction = 6/29

The new fraction = 2/3

Now,

(6 + x)/(29 + x) = 2/3

3(6 + x) = 2(29 + x)

18 + 3x = 58 + 2x

3x - 2x = 58 - 18

x = 40

Thus,

The number x is 40.

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The values of x, y and z in the given Rhombus are

x = -98, y = 36 and z = -97/4.

Given, the figure shown is a rhombus

as, the opposite angles of the rhombus are equal

So, 3y - 1 = 107

3y = 107 + 1

3y = 108

y = 36

and (-x - 8) = (-4z - 7)

x + 8 = 4z + 7

x - 4z = -1

also, the sum of the opposite angles of the rhombus is 180°.

So, (-x - 8) + (-4z - 7) = 180

-x - 4z = 180 + 15

x + 4z = -195

On adding the equations, we get

2x = -196

x = -98

and z = -97/4

Hence, the values of x, y and z are

x = -98, y = 36 and z = -97/4.

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The minimum cost will be at (2.5 , 3) and the minimum cost be $25.

Given, a landscaping contractor plans to use the least expensive combination of two brands of fertilizer.

A package of Brand X costs $16 and contains 12 oz of phosphates and 10 oz of nitrates.

A package of Brand Y costs $7 and contains 10 oz of phosphates and 5 oz of nitrates.

The lawn requires at least 60 oz of phosphates and 40 oz of nitrates.

Let the number of Brand X packages be, x

the number of Brand Y packages be, y

According to the question,

12x + 10y ≥ 60 = 6x + 5y ≥ 30

10x + 5y ≥ 40 = 2x + y ≥ 8

x ≥ 0

y ≥ 0

Z = 16x + 7y

On solving the equations, we get

6x + 5y = 30

6x + 3y = 24

On subtracting, we get

2y = 6

y = 3

and x = 2.5

So, minimum cost will be at (2.5 , 3) and the minimum cost be

Z = 16(2.5) + 7(3)

Z = 4 + 21

Z = 25

Hence, the minimum cost will be at (2.5 , 3) and the minimum cost be $25.

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Answer:

the correct answer is -32+43

Step-by-step explanation:

I just know

Answer:

3. line XZ is congruent to line XZ | reflexive property
4. triangle WXZ is congruent to triangle YZX | HL (i think)
5. angle WXZ is congruent to angle YXZ | CPCTC

Step-by-step explanation:

The height of the sunflower after 9 weeks is 52 inches and the function that represent the height of the sunflower after w weeks = 25 + 3w weeks.

Sophia planted a tiny sunflower in her backyard at the start of spring.

When she planted the sunflower,

The height of the sunflower = Initial height of the sunflower = 25 inches.

Now, The sunflower then began to grow at a rate of 3 inches per week.

Thus, the growth rate of the sunflower = 3 inches/week

The growth in 9 weeks = 3*9 = 27 inches,

The height of the sunflower after 9 weeks = initial height + growth = 25 +27 = 52 inches.

The growth in w week = 3w inches,

The height of the sunflower after w weeks = initial height + growth = 25 + 3w inches.

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The expression a⁷- a is divisible by 7 if a is an integer.

Given that,

7 divides a^7−a

To find that if a is an integer, then 7 divides a^7 -a or a⁷- a is divisible by the number 7

We can write, where k is an integer

a^7−a=7k

a(a^6−1)=7k

Now if a=k then

a^6−1=7

a^6=8

and a=±1.414 so a^7−a=9.898

If a is not equal to k then

a(a^6−1)=a(a^3+1)(a^3−1)=7k

since a(a+1)(a−1) is the not product of 3 consecutive integers, the expression is divisible by 7.

Hence, The expression a⁷- a is divisible by 7 if a is an integer.

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Answer:1712

Step-by-step explanation:  is 1712

Answer:no image I can’t see on mobile

Step-by-step explanation:

h

Answer: -1

Step-by-step e

Using x only once in the inequality, the inequality expression is 8 > x > 2

The mathematical statement is given as

8 is greater than x, and x is greater than 2.

In mathematical expressions, greater than can be represented as >

So, we have the following representations

8 > x, and x > 2

Next, we combine the inequality expressions

This becomes

8 > x > 2

Hence, the inequality expression is 8 > x > 2

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Answer:

*Note: Perimeter is equal to the sum of all side lengths

1.   3cm + 3cm + 5cm + 4cm = 6cm + 9cm = 15cm

2.   3.5cm + 3cm + 3.5cm + 3.5cm + 3cm + 3.5cm

      = 6cm + 7cm + 7cm = 6cm + 14cm = 20cm

3.   2cm + 3cm + 3cm + 3cm + 5cm + 6cm = 5cm + 6cm + 11cm

      = 11cm + 11cm = 22cm

7.   9cm + 9cm + 9cm = 27cm

8.   Perimeter of a rectangle = 2 times the length plus 2 times the width

     P = 2(60m) + 2(48m) = 120m + 96m = 216m

9.   1 roll of 16m of wire = $3,214

     216m/16m = 13.5 rolls of wire

     13.5 rolls($3,214) = $43,389

Solving each pair of expression shows that

(1/5)^2 + 1 ≠ 2 * 12 / 25

( 1 + 1/4 )^2 = 2 - 7/16

Putting equals sign implies that the the expression in left hand side of the equation is equal to the expression on the right hand side

If they are not equal the sigh to be used is not not equal to

(1/5)^2 + 1 & 2 * 12 / 25

1/25 + 1 & 24/25

26/25 ≠ 24/25

( 1 + 1/4 )^2 & 2 - 7/16

(5/4)^2 & 25/16

25/16 = 25/16

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The answers are:

Q1 = x < -1

Q2 = x ≤ 2

Q3 = x > -2

Q4 = x > 0

Code = 4776

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

Solve for x.

3 < -5x + 2x

3 < -3x

Divide both sides by 3.

1 < -x

Change sign.

x < -1

18 ≥ 5x  + 4x

18 ≥ 9x

Divide both sides by 9.

2 ≥ x

-6x - 16 < 2x

Add 16 on both sides.

-6x < 2x + 16
Subtract 2x on both sides.

-6x - 2x < 16

-8x < 16

Divide both sides by 8.

-x < 2

Change sign.

x > -2

(1/2)x - 4 > -4

1/2x > -4 + 4

1/2x > 0

x > 0

Code = 4776

Thus,

The answers are:

Q1 = x < -1

Q2 = x ≤ 2

Q3 = x > -2

Q4 = x > 0

Code = 4776

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The side lengths of the fence he can build with the greatest area inside are of:

75 yards and 75 yards.

Considering a rectangle of length l and width w, we have that the area and the perimeter of the rectangle are given as follows:

A farmer has 300 yards of fencing, hence the perimeter is:

P = 300.

Then:

2(l + w) = 300

l + w = 150

l = 150 - w.

Then the equation giving the area of the fence is:

A = lw

A = w(150 - w)

A = -w² + 150w.

Which is a quadratic equation with coefficients given by:

a = -1, b = 150.

The width that will give the highest possible area is the x-coordinate of the vertex, hence:

w = -150/(2(-1)) = 75 yards.

The length is of:

l = 150 - w = 150 - 75 = 75 yards.

Which means that the third option is correct.

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9,603.75 cm² is the area of the given triangle.

So, the perimeter of the triangle is 392 cm.

Then, let the rest 2 sides be x, where x = x.

Now, we know that the rest 2 equal sides are of length 98.5 cm.

Now, calculate the area as follows:

Therefore, 9,603.75 cm² is the area of the given triangle.

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The required simplified solution of the given subtraction is 16/25. Option D is correct.

Given that,
To Subtract. and determine the lower terms,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
= 47/50 - 3/10
= [47 - 3×5] / 50
= [47 - 15] /50
= 32 / 50
= 16 / 25

The required simplified solution of the given subtraction is 16/25. Option D is correct.

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Answer:

d) 16/25

Step-by-step explanation:

The problem is,

→ (47/50) - (3/10)

Let's solve the problem,

→ (47/50) - (3/10)

→ (47/50) - (15/50)

→ (47 - 15)/50

→ 32/50

→ (32 ÷ 2)/(50 ÷ 2)

→ 16/25

Hence, answer is 16/25.

The expression that gives the volume of the Sphere with radius 7  is  (4/3)π(7³) , the correct option is (a) .

In the question ,

it is given that

the radius of the sphere is 7 .

we need to find the expression that represents  the Volume of the Sphere when radius is 7 .

the formula for the Volume of the Sphere is (4/3)π(r³) .

Substituting the value of radius = 7 , in the formula ,

we get ,

Volume = (4/3)π(7³)

Therefore , The expression that gives the volume of the Sphere with radius 7 is  (4/3)π(7³) .

The given question is incomplete , the complete question is

Which expression gives the volume of a sphere with radius 7 ?

(a) (4/3)π(7³)

(b) (4/3)π(7²)

(c) 4π(7²)

(d) 4π(7³)

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The graph of the function is y - 1 = x, not y = x - 1.

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

Given, y = (x - 1).

When x = 1, y = 0 ⇒ (1, 0).

When x = 2, y = 1 ⇒ (2, 1).

When x = 3, y = 2 ⇒ (3, 2).

When x = 4, y = 3 ⇒ (4, 3).

When x = 5, y = 4 ⇒ (5, 4)

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The slope of the graph above is [tex]-\frac{4}{3}[/tex]

The slope of a line is the change in the dependent variable with respect to the change in the independent variable. The slope of a line is rise over run.

Therefore,

slope = m = y₂ - y₁ / x₂ - x₁

Hence, using the coordinates on the graph let's find the slope of the graph.

(-2, 1)(1, -3)

Therefore,

x₁ = - 2

x₂ = 1

y₁ = 1

y₂ = - 3

Hence,

[tex]slope = \frac{-3-1}{1-(-2)}[/tex]

[tex]slope = \frac{-4}{1+2}[/tex]

[tex]slope = \frac{-4}{3}[/tex]

Therefore, the slope of the line is [tex]-\frac{4}{3}[/tex]

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The total number of members there is 199

Two kinds of logical reasoning are often distinguished in addition to formal deduction: induction and abduction. Given a precondition or premise, a conclusion or logical consequence and a rule or material conditional that implies the conclusion given the precondition, one can explain the following.

Since the number of members of the band is <200. the members are arranged in rows and 3 will be left out

therefore assume the members on row are 200- 3= 197, but 197 is a prime number ,therefore we choose the closet number to 197 which is 196.

therefore the total number of members = 196+3= 199.

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The measure of the smallest angle of the quadrilateral is  60° .

In the question ,

it is given that ,

the angle measure of the quadrilateral are in the ratio 4 : 5 : 6 : 9 .

So , the measure of the largest angle is = 9x

and the measure of the smallest angle is = 4x .

we know that the sum of the measure of all the angles of the quadrilateral is 360° .

that means ,

4x + 5x + 6x + 9x = 360°

24x = 360

dividing both sides by 24 ,

x = 360/24

x = 15 .

the smallest angle is = 4(15) = 60°

Therefore ,  The measure of the smallest angle of the quadrilateral is  60° .

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Answer:

-6n-4+3<17

-6n-1<17

-6n<17+1

-6n<18

DIVIDE BOTH SIDE WITH THE COEFFICIENT OF n WHICH IS (-6)

-6n =18

-6 -6

n= -3

The inverse function of the given function will be f(x)⁻¹ = ( 10 ) / ( 9x - 99).

From the question, we have

f(x) = ( 10/9x) + 11

x = ( 10 / 9y ) + 11

x - 11 = ( 10 / 9y )

9y / 10 = ( 1 / ( x - 11 )

9y = 10 / ( x - 11 )

y = ( 10 ) / ( 9x - 99 )

Inverse function :

The expression that established the relationship between the dependent variable and the independent variable is referred to as a function. An inverse function is a function that is applied to the value of y after switching the values of two variables, x and y.

Complete question:

What is the inverse of function f?

f(x) = 10/9x+11

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The amount to be invested today in order to have $600 in 20 years is $189.66.

When an account pays interest that is compounded quarterly, it means that both the amount invested and the interest that has already been earned increases in value four times in a year.

In order to determine the amount to be invested today, determine the present value of $600.

The formula for calculating present value:

P = FV / [(1 + r)^nm]

Where:

P = 600 / [(1.0145)^80] = $189.66

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Answer: it is 200

Step-by-step explanation:

The valid conclusion about statement A and statement B is "If Figure A is a parallelogram, then Figure A’s angles sum to 360°".

The correct answer option is option D.

A conditional statement can be defined a statement that is written in the form “If A then B,” where A and B are sentences.

For this conditional statement:

Sentence A is called the hypothesis

Sentence B is called the conclusion.

Hypothesis: This is an assumption taken to be true for the purpose of argument or investigation.

Conclusion: This is the proposition that follows as a necessary consequence of the premises in an argument or syllogism.

Hence, “If A then B” means that B must be true whenever A is true.

Therefore, if a figure is a parallelogram, then it is a quadrilateral; If a figure is a quadrilateral, then its angles sum to 360°.

It can be concluded that if a figure is a parallelogram, then it's angles must sum to 360°.

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The total cookies she baked altogether is 28 cookies

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.

Half of the cookies is placed on the table, 6 is eaten by my dog, half is eaten by my brother and I ate the last 4, the means my brother ate 4 cookies too.

Therefore the total cookies put on the plate is 6+4+4= 14cookies

half of all the cookies were put in the plate,

therefore the total cookies made is 14×2= 28cookies.

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