There are 80 oranges and apples, and 5% of them are apples. William takes out some of the oranges, so apple make up 20% of the remaining pieces of fruit. How many oranges did he take out

Answer:

m+g[tex]\leq[/tex]40

12m + 14g[tex]\geq[/tex]250

Step-by-step explanation:

Jordan is paid $12 per hour for mowing lawns and $14 per hour for planting gardens.

Let m represents the number of hours mowing lawns and g represents the number of hours planting gardens.

He can work a maximum of 40 hours per week, and would like to earn at least $250 this week.

Then, the system of the inequality becomes

m+g[tex]\leq[/tex]40

12m + 14g[tex]\geq[/tex]250

Answer:

x = 24

. So, first number = 7 * 24 = 168. and second number = 4 * 24 = 96. Therefore the numbers are 168 and 96.

Answer:

42 and 24

Step-by-step explanation:

The numbers in ratio 7 : 4 = 7x : 4x ( x is a multiplier ) , then

7x - 4x = 18 ( difference of 2 numbers is 18 )

3x = 18 ( divide both sides by 3 )

x = 6

Then

7x = 7 × 6 = 42

4x = 4 × 6 = 24

The numbers are 42 and 24

Answer: To find an equation for a parabola that passes through three specific points, we can use the method of algebraic manipulation.

Since the parabola is symmetric about the y-axis, the equation of the parabola will have the form y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.

Given three points (-2,7), (1, 10), and (2,27), we can use the vertex form of the equation and substitute the x, y values of the three points to find the values of a, h and k

y = a(x-h)^2 + k

Since it is passing through (-2,7), we can substitute the values of x and y in the equation and get

7 = a(-2 - h)^2 + k

It passing through (1, 10), we can substitute the values of x and y in the equation and get

10 = a(1 - h)^2 + k

It passing through (2,27), we can substitute the values of x and y in the equation and get

27 = a(2 - h)^2 + k

Now we have three equations with three variables, we can solve it using any of the techniques such as substitution, elimination or matrix. But the final equation will be in the form of y= a(x-h)^2 + k

Here, x= (-2, 1, 2) and y = (7, 10, 27) . Therefore it has a unique parabola passing through these points.

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

they are alternative exterior angles meaning they are equal.so you can solve by doing

7x-40=5x+10

isolate the terms by adding like terms. ( add 40 from the left side of the equation to the right.)

so it would look like this.

7x=5x+10+40. (the 40 was negative on the left side so you have to do the inverse to move it) do the same with the 5x.

now you have

2x=50. divide 50 by 2 to get your final answer .

Answer:

12

Step-by-step explanation: i think

Answer: The tree is 27 feet tall.

Step-by-step explanation:

Here's what we know:

6/10 = x/45 (a 6 foot object creating a 10 shadow is equivalent to something else making a 45 shadow)

We need to isolate x. Multiply both sides by 45:

6*45/10 = x

We can factor out a 2:

3*45/5 = x

We can also factor out a 5:

3*9/1 = x

27 = x

The tree is 27 feet tall.

The scale model door of 2.4 inches is 9.3 ft tall in the actual building.

By scaling, we can create a drawing of an object that corresponds to the object's true size. In geometry, scaling refers to either growing or reducing figures in order to preserve their fundamental shape.

By multiplying the numerator of one fraction by the denominator of another and the first term's denominator by the numerator of another, we can do cross multiplication.

Given that:

16 inches = 62 ft

2.4 inches = x ft

To calculate the actual value cross multiply the values:

[tex]x= \frac{(62)(2.4)}{16} \\\\x= 9.3 ft[/tex]

Hence, the actual door is 9.3 ft tall.

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If Ojemba is sitting on a sled on the side of a hill inclined at 60° and  weight of Ojemba and sled is 160 pounds , then magnitude of force needed for Mandisa to keep sled from sliding down the hill is 355.59 N   .

the inclination angle of the the side of the hill is = 60° ;

the compound mass of Ojemba and Sled is = 160 pounds ,

On conversion we get the mass in Kg is = 72.57 Kg .

the acceleration due to gravity is , [tex]g = 9.8 m/s^{2}[/tex] ;

The force required for Mandisa to keep sled from sliding down the hill can be calculated by the formula ;

[tex]F = mgSin\theta[/tex] , Substituting the values ,

we get ;

[tex]F = 72.57\times 9.8\times Sin(30\textdegree)[/tex]

[tex]F = 72.57\times 9.8\times \frac{1}{2}[/tex] ;

So , [tex]F = 355.59 N[/tex] .

The required magnitude of the force is 355.59 N .

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Answer:

20

Step-by-step explanation:

https://www.calculatorsoup.com/calculators/geometry-plane/distance-two-points.php

Answer:

20 i think i forgot but, hopefully u get it right

Step-by-step explanation:

Enlargements of the picture or reductions of the image are both types of dilations.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size.

A dilation is a transformation that yields a different-sized picture with the same general shape as the original. Enlargements are dilations that result in a bigger picture. Reduction is the name for a dilatation that shrinks the picture. The initial figure is stretched or contracted by a dilatation.

The angles of the dilated picture relative to the pre-image stay constant, which is one of the primary characteristics of dilated images.

Even in the enlarged picture, parallel and perpendicular lines are still discernible.

A dilated image's side's midway matches the pre-exactly. image's

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Scrooge sees out of his window when Marley's ghost leaves as all the spirits of people whom Scrooge has not met before in his life. Thus, option B is correct.

Although ghosts are typically thought of as lone, human-like essences, and there have been reports of ghostly battalions, ghosts that resemble animals instead than people.

Here, we have,

Scrooge discovers "the air filled with phantoms" outside s windowsill after Marley's Apparition hath left it. Some of these imprisoned spirits were people Scrooge had indeed known. It resembles an incredible image of the metropolis that Scrooge has already been familiar with. Scrooge is compelled to agree.

Scrooge responds with the ghost's request to peek out just the balcony. He observes a mass of ghosts, each one imprisoned in bonds. As both they and Marley vanish into darkness, they sob at their failure to live noble, compassionate lives and their incapacity to help other people in need.

Therefore, option B is the correct option.

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The value of x using Pythagorean theorem is 14.05 units

An equation shows how two or more numbers and variables are related to each other.

Pythagoras theorem shows the relationship between the sides of a right angled triangle. It is given by:

hypotenuse² = adjacent² + opposite²

In the diagram, using Pythagoras theorem:

22² = (x + 1)² + (x + 2)²

484 = x² + 2x + 1 + (x² + 4x + 4)

2x² + 6x + 5 = 484

2x² + 6x - 479 = 0

x = 14.05

The value of x is 14.05 units

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The object will hit the ground after 5.01 seconds.

When an object is propelled upward from ground level with an initial velocity of 80.1 feet per second then its height h in feet t seconds later is giving by the equation,

h= -16t^2+ (80.1)t

When the object hit the ground, the height of the object h would be zero.

To find: time (t) when h = 0

Substitute h = 0 in given equation.

h = -16t^2+ (80.1)t

0 = -16t^2+ (80.1)t

16t^2 -  (80.1)t = 0

t (16t - 80.1) = 0

t = 0  or  16t - 80.1 = 0

t = 0   OR   t = (80.1)/16

t = 0 OR t = 5.01

Therefore, it will hit the ground after 5.01 seconds.

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The formula for K in terms of F is [tex]K = \frac{5}{9} (F-32) + 273[/tex]

The given expression:

[tex]F = \frac{9}{5} (K-273) + 32[/tex]

To find the formula for K

The formula for K is obtained by making K the subject of the formula as shown below:

[tex]F = \frac{9}{5} (K-273) + 32[/tex]

subtract 32 from LHS.

[tex]F-32 = \frac{9}{5} (K-273)[/tex]

multiply 5 with LHS

[tex]5(F-32) = 9(K-273)[/tex]

Take numerator 9 to LHS

[tex]\frac{5}{9}(F-32) = K-273[/tex]

take -273 from RHS to LHS

[tex]\frac{5}{9}(F-32) + 273 = K[/tex]

Thus the formula for K in terms of F is [tex]K = \frac{5}{9} (F-32) + 273[/tex]

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Answer:

Step-by-step explanation:

[tex]y=x^2+2x-2\\\\y=x^2+2x+1-1-2\\\\\bold{y=(x+1)^2-3}[/tex]

a = 1 > 0  ← it means the parabla opens up, so, the vertex is minimum

The vertex form is  y = a(x - h)² + k, where (h, k) is the vertex

So, from  y = (x + 1)² - 3   the vertex is:  (-1, -3)

When the trinomial 3x² - x - 10  is factored completely, one of its factors is 3x+5.

Solving the given trinomial 3x² - x - 10.

=>3x² - 6x+5x - 10

=>3x(x-2)+5(x-2)

=>(3x+5)(x-2)

The two factors of the given trinomial 3x² - x - 10 is (3x+5) and (x-2), but according to the given options, the correct answer is option C - 3x+5.

Thus, When the trinomial 3x² - x - 10  is factored completely, one of its factors is 3x+5.

Complete question: 3x² - x - 10

When this trinomial is factored completely, one of its factors is

A) x + 2

B) x - 5

C) 3x + 5

D) 3x - 2

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The equation to determine the length and the width of the rug is

21 = W² - 4W.

A rectangle is a quadrilateral with four right angles in the Euclidean plane. It may alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides.

A quadrilateral is a rectangle.

A rectangle's opposing sides are equal and parallel to one another.

Each vertex of a rectangle has a 90° internal angle.

360° is the total of all interior angles.

The diagonals cut each other in half.

The diagonals are all the same length.

The Pythagorean theorem may be used to determine the length of the diagonals.

A rectangle is also referred to as a parallelogram since its sides are parallel.

While all parallelograms are rectangles, not all rectangles are parallelograms.

The length of the rug is l ft

Then the width of the rug will be l-4 ft

So the are will be l*(l-4) = [tex]l\x^{2} - 4l[/tex]

We know area is 21

so the equation is 21 = [tex]l\x^{2} - 4l[/tex]  (Option a)

And after solving the equation the lenght is7m and breadth is 3 m.

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Answer:

The Volume of a Sphere is equal to 2 times the volume of a cone.

Step-by-step explanation:

The volume of a sphere: 4/3 π r^3

The volume of a cone: 1/3 π r^2 h  

r is the radius

h is the height

In this case, the height can be replaced by the 2r or the diameter, since it would correspond exactly to the height of the sphere of radius r.

So then,

sphere       and    cone

4/3 π r^3             1/3 π r^2 h  

                           1/3 π r^2 * 2r

                           2/3 π r^3    

Ratio sphere : cone

4/3: 2/3

2:1

Therefore the volume of the sphere is twice that of the cone or equal to twice the volume of the cone

Answer:

11.25

Step-by-step explanation:

It says if the teams were equal, so divide 45/4 to get 11.25

Answer:

Step-by-step explanation:

11 students on each team

1 student is left out

11x4 = 44

Answer:  

a = 1.5  

VW = 9 ft  

Step-by-step explanation:  

Since the tangent lines connect both circles, we know that the line VU and VX are congruent (equal). Thus, we can set them equal to each other and solve for a:

a + 4 = a² + 0.25                            Set equal  

a² - a = 3.75                                    Isolate a values  

a² - a + 0.25 = 3.75 + 0.25            Complete the square  

(a + 0.5)² = 4                                  Factor  

a + 0.5 = 2                                     Simplify  

a = 1.5

Now we need to calculate VW, but thats easy because its equal to TV, and since we know a, we can just plug it in:

((1.5) + 7.5) ft  

9 ft

The total amount for Elizabeth's purchase after 10 percent discount on her total bill is 33 dollars and 84 cents which is equivalent to 34 dollars.

What is percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.

Elizabeth bought the grocery for a total of 37 dollars and 60 cents.

She has a coupon of 10% discount.

Which means, she can get 10% discount on her total bill.

The amount of her total bill is $37.60.

So, calculate using percentage, the value of 10% of $37.60.

=(10 × 37.60/100)

= 376/100

= 3.76

So, Elizabeth would get a discount of $3.76 on her total bill -

= 37.60 - 3.76

= 33.84

Therefore, after the discount Elizabeth's total bill is $33.84 ≈ $34.

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A book cost $2.00.

In Maths, a variable is an alphabet or term that represents an unknown number or unknown value or unknown quantity. The variables are specially used in the case of algebraic expression or algebra. For example, x+9=4 is a linear equation where x is a variable, where 9 and 4 are constants.

Variables may be classified into two main categories: categorical and numeric. Each category is then classified in two subcategories: nominal or ordinal for categorical variables, discrete or continuous for numeric variables.

Given the no of books purchased by

Alana =4

Petra =2

Angus = 16

So, the total price of 4 books of Alana =$4

Total price for Petra = $2

Total price of Alana and Petra =4x+2x

=6x

Total price for Angus = 16x

But given Angus received a discount  of $15

So price post discount = 16x- 15

According to the question

16x-15 = 6x +5

Adding 15 both sides

16x +15-15 = 6x + 5+15

16x= 6x+20

Subtracting 6x both sides

16x - 6x = 6x - 6x + 20

10x = 20

i.e x=2

Cost of one book = $2

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Answer:

231 and 52.8

Step-by-step explanation:

Given that

Hamza decided the price of the item would be increased by 10 percent

We need to find out the price that normally at 210 pounds and the price that normally at 48 pounds

So,

The price that normally at 210 pounds is

= 210 + 210 × 10%

= 210 +  21

= 231

And, the price that normally at 48

= 48 + 48 × 10%

= 48 + 4.8

= 52.8

Answer:

hurry

Step-by-step explanation:

Answer:

  Manuel can make 5 batches of muffins using Recipe 1

Step-by-step explanation:

You want to know the value of b in the equation 2b = 10, where b is the number of batches of muffins Manuel can make using recipe 1.

Divide both sides of the given equation by 2 so solve for the value of b.

  (2b)/2 = (10)/2

  b = 5

Manuel can make 5 batches of muffins using Recipe 1.

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Answer:

Hope that helps! :)

-Aphrodite

Step-by-step explanation:

Answer:

D)

hope this helped

Step-by-step explanation:

The length is 11.5 cm.

The sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse

Given: diagonal = 20 cm

In ABC,

AC² = BC² + AB²

AC²= x² + x²

AC²= 2x²

AC= √2 x

IN ACF,

AF² = AC² +CF²

20²=  2x² + x²

400= 3x²

400/3= x²

x= 11.5

hence, length is 11.5 cm.

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Answer:

50 inches

Step-by-step explanation:

Hi there!

[tex]P=2l+2w[/tex] where l is the length of the rectangle and w is the width of the rectangle

Plug in the length (15 inches) and width (10 inches)

[tex]P=2(15)+2(10)\\P=30+20\\P=50[/tex]

Therefore, the perimeter of the frame is 50 inches.

I hope this helps!