A right-angled triangle has sides of lengths (x+5)cm, (x-3)cm and 9cm. Calculate the value of x. Give your answer to 3 significant figures. (Quadratic Formula)

Answer:

£200

Step-by-step explanation:

The ratio is 2:5

we then have

80:x

Because one side of the ratio was multiplied by 40 we have to do the same to the other

20*5=200

therefore our new ratio is

80:200

Ollie gets £200

Answer:

B

Step-by-step explanation:

Inequalities of the type | x | ≤ a, have solution of the form

- a ≤ x ≤ a , so

| x | ≤ 4

- 4 ≤ x ≤ 4

The values of x are between - 4 and + 4, but can equal - 4 and 4 since the symbol is ' less than or equal to '

This is indicated on a number line by solid circles, where not equal to are denoted by open circles.

Thus the solution is Graph B

Answer:

1/a3 is the simplify expression for the equation

Answer:

15 boys

Step-by-step explanation:

start by dividing 20 by 4

you get 5

5 times 3 next

now you have 15

Answer:

25 girls and boys

Step-by-step explanation:

There are 3 boys for every 4 girls

To find the rate we must

Divide 20 by 4 then multiply that by 3

20 divided by 4 is 5

5 times 3 is 15

15 boys went on the field trip

20 girls went on the field trip

The total number of students is 25 girls and boys

Answer:

Part A:

I have attached the graph of this system of inequalities.

Part B:

Plug in (8,10) into both equations

10 > 3(8) + 10

10 > 24 + 10

10 > 34

This is false!

10 < (-3/4)(8) - 1

10 < (-3)(2) - 1

10 < -6 - 1

10 < -7

This is also false!

So, (8,10) is not included in the solution area for the system.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

whenever you see a (as in ax^2 + bx+c) as a number other than 1, you should see if you can factor that out

2(6x^2 -x -1)

= 2(3x+1) (2x-1)

Answer:

2\(3x+1)(2x-1\)

Step-by-step explanation:

Answer:

8 Books

Step-by-step explanation:

First find how many she had before buying 8 more-

12 - 8 = 4

Then multiply that by 2

4 x 2 = 8

The had 8 books to begin with

Answer:C

Step-by-step explanation:

Transformation involves changing the position of a shape

The transformations and the order in which they were applied are:

A. 90° counter-clockwise rotation, then reflected across the y-axis

From the figure, the coordinate of RST is:

[tex]R= (2,4)[/tex]

[tex]S = (2,8)[/tex]

[tex]T =(-6,8)[/tex]

Using R to illustrate the transformation.

We have

[tex]R= (2,4)[/tex]

First, R is rotated 90 degrees counterclockwise

The rule of this transformation is:

[tex](x,y) \to (-y,x)[/tex]

So, we have:

[tex](2,4) \to (-4,2)[/tex]

Next, the point is reflected across the y-axis.

The rule of this transformation is:

[tex](x,y) \to (-x,y)[/tex]

So, we have:

[tex](-4,2) \to (4,2)[/tex]

From the question, we have the coordinate of R" to be;

[tex]R: =(4,2)[/tex] --- same as the result of the above sequence

Hence, option (A) is correct

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Answer:

The first set of ordered pairs is a function, because no two ordered pairs have the same first coordinates with different second coordinates. The second example is not a function, because it contains the ordered pairs (1,2) and (1,5). These have the same first coordinate and different second coordinates

Answer:

f(-2) = 9

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

f(x) = -3x² - 5x + 11

f(-2) is x = -2

Step 2: Evaluate

Answer:

[tex]y > 4x - 3 = y + 3 > 4x \\ let \: take \: (0.0) \\ 0 + 4 > 4 \times 0 \\ 4 > 0 \\ solution = (0.0)[/tex]

The length of the rectangular prism is L = 4x/5

A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.

The volume of a prism is the product of its base area and height

Volume of Prism = B x h

where B = base area of prism

h = height of prism

Given data ,

The formula for the volume of a rectangular prism is V = lwh, where l, w, and h are the length, width, and height of the prism, respectively.

In this problem, we are given that the volume of the prism is 7/(x - 3/5x) and the width and height are 2/x and 4/x, respectively.

So we can substitute these values into the formula for the volume and solve for the length:

V = lwh

7/(x - 3/5x) = l * (2/x) * (4/x)

Multiplying both sides by (x - 3/5x), we get:

7 = l * 8/(5x² - 3x)

Simplifying, we get:

l = 56x²/(5x² - 3x)

Now we need to check if this solution satisfies the condition that the width is 2/x and the height is 4/x:

w = 2/x, h = 4/x

V = lwh = (56x²/(5x² - 3x)) * (2/x) * (4/x) = 7/(x - 3/5x)

So the solution is correct.

Hence , the length of the prism is 56x²/(5x² - 3x), which can be simplified to 32x²/40x or 4x/5

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Answer:

Inequality (1) → y > 2x

inequality (2) → x ≥ -2

Step-by-step explanation:

If the inequality (1) is a dotted line passing through origin.

Since, shaded area is above the dotted line,

Equation of the inequality will be in the form of y > mx +b

Here m = slope of the dotted line

b = y-intercept

Since, this line is passing through the origin,

Therefore, y-intercept = 0

Slope 'm' of the line = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]

                                 = [tex]\frac{2}{1}[/tex]

                             m = 2

Inequality (1) → y > 2x

Second inequality is represented by the shaded area on the right side of  the dark vertical line, x = -2,

Therefore, inequality 2 will be → x ≥ -2

Answer: x≽-2 and y>2x

Answer:

L=16.8

w = 8.8

Step-by-step explanation:

L = x +8

w = x

x(x+8) = 148

x^2 + 8x = 148

x^2 + 8x - 148 =0

a = 1

b = 8

c = - 148

x = [tex]\frac{-8 +/- \sqrt{8^2 + 4*1*(-148)} }{2}[/tex]

(x - 8.8)(x + 16.8) =  0

(x + 16.8) is an extraneous root.

x = 8.8 which is the width

L = 16.8

Answer:

Step-by-step explanation:

3x + 5y = 7         {subtract 3x from both sides}

5y = -3x + 7        {divide both sides by 5}

y = -³/₅x + ⁷/₅        ←  slope-intercept form

y=m₁x+b₁   ║   y=m₂x+b₂   ⇔    m₁ = m₂

{Two lines are parallel if  their slopes are equal}

y = -³/₅x + ⁷/₅     ⇒   m₁ = -³/₅    ⇒    m₂ = -³/₅

(-1, 3)  ⇒  x₁ = -1,  y₁ = 3

The point-slope form:

y - 3 = -³/₅(x - (-1))

y - 3 = -³/₅(x + 1)           {myltiply both sides by 5}

5y - 15 = -3x - 3           {add 3x to both sides}

3x + 5y - 15 = - 3        {add 15 to both sides}

3x + 5y = 12

Answer:

2. Carbon-Dioxide and Nitrogen

3.After the Earth's surface had cooled to a temperature below the boiling point of water, rain began to fall for centuries. As the water drained into the great hollows and gaps in the Earth's surface, the primeval ocean came into existence.

Step-by-step explanation:

The forces of gravity prevented the water from leaving the planet.

Lauren can drive farther on 40 gallons of gasoline than Melissa because her car is more fuel efficient.

What is miles?

Miles are a unit of measurement used to measure distances, typically between two points. Miles are typically used to measure the length of a journey, such as how many miles it is from one city to another. Miles can also be used to measure the length of a route or the total distance that a person has traveled. In the United States, a mile is equal to 5,280 feet or 1.61 kilometers.

Lauren:

10 gallons : 320 miles

40 gallons : x miles

x = 1280 miles

Melissa:

8 gallons : 280 miles

40 gallons : y miles

y = 1120 miles

Since Lauren can drive 1280 miles on 40 gallons of gasoline, she can drive farther than Melissa, who can only drive 1120 miles on the same amount of gasoline. This is because Lauren’s car has higher fuel efficiency, meaning it uses less gasoline for the same distance.

In conclusion, Lauren can drive farther on 40 gallons of gasoline than Melissa because her car is more fuel efficient. This difference in fuel efficiency can be seen in the ratio tables, which show that Lauren can travel 160 miles farther than Melissa on the same amount of gasoline.

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Answer: Its the pink one and the green one

hope that was helpful!

Step-by-step explanation:

Answer:

pink, dark blue, and red

Step-by-step explanation:

Answer:

the largest one is f or francium.

Answer:

-40

Step-by-step explanation:

Multiply both sides by the reciprocal of 9/10 to get rid of the fraction

[tex]\frac{10}{9}[/tex]×[tex]\frac{9}{10}[/tex]×y=-36 ×[tex]\frac{10}{9}[/tex]

y=-36×[tex]\frac{10}{9}[/tex]

y=[tex]\frac{-360}{9}[/tex]

y=-40

Answer:

Por tanto, la cantidad de ingredientes necesarios para 6 personas es:

450 g de queso, 15 ml de leche, 150 g de azúcar, 150 g de mantequilla y 75 g de harina.

Step-by-step explanation:

Por lo tanto:

Para queso

4 personas = 300g de queso

6 personas = x

Cruz multiplicar

4x = 6 × 300g

x = 6 × 300 g / 4

x = 450 g de queso

Por 10ml de leche

4 personas = 10 ml de leche

6 personas = x

Cruz multiplicar

4x = 6 × 10 ml

x = 6 × 10 ml / 4

x = 15 ml

Por 100 g de azúcar

4 personas = 100 g de azúcar

6 personas = x

4x = 6 × 100g

x = 6 × 100 g / 4

x = 150 g de azúcar.

Por 100 g de mantequilla

4 personas = 100 g de mantequilla

6 personas = x

4x = 6 × 100g

x = 6 × 100 g / 4

x = 150 g de mantequilla

Por 50 g de harina

4 personas = 50 g de queso

6 personas = x

4x = 6 × 50g

x = 6 × 50 g / 4

x = 75 g de queso.

Por tanto, la cantidad de ingredientes necesarios para 6 personas es:

450 g de queso, 15 ml de leche, 150 g de azúcar, 150 g de mantequilla y 75 g de harina.

Answer:

24%

Step-by-step explanation:

24/100 =.24 which as a percent is 24%

Answer:

x = -25i

x = 25i

Answer:D

Step-by-step explanation:

D, the  X values repeat for 7.

Answer:

2

Step-by-step explanation:

Experimental probability : (Number of times event occur / total number of trials)

Total Number of trials = (3 + 4 + 6 + 3) = 16

Experimental probability :

For 1: P(1) :

3/16

For 2 : P(2) :

4/16 = 1/4

For 3: P(3)

6 /16 = 3/8

For 4 : P(4)

3 / 16

Theoretical probability :

The Theoretical probability of 1, 2, 3 and 4 are the same ;

Theoretical probability =

(Required outcome / Total possible outcomes)

For each of 1 - 4

Theoretical probability = 1 /4

Experimental probability of P(2) = 1/ 4 and is Hence, the same as the Theoretical probability

Answer:

Option H

Step-by-step explanation:

Option F

If two lines are cut by a transversal so that a pair of corresponding angles are congruent, then the lines are parallel.

True.

Option G

If two lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then the lines are parallel.

True

Option H

If two line are cut by a transversal so that a pair of vertical angles are congruent, then the lines are parallel.

Since, vertical angles don't prove the lines cut by a transversal are parallel.

So the statement is False.

Option J

If two lines are are cut by a transversal so that a pair of same side interior angles are supplementary, then the lines are parallel.

True.

Answer:

21

Step-by-step explanation: