A rectangle has a length of √7 meters and a width of (2√5 - √15) meters. What is its area?

Light and emotional variables are affected by eye dilation. Under typical conditions, pupils are meant to dilate as a result of changes in lighting and psychological factors.

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Step-by-step explanation:

well,

y = x²

would give us

y = 5² = 25

(5, 25)

but we have

(5, 18) so, what is the difference ?

we see that y is reduced by 7 units.

so,

y = x² - 7

the whole curve is moved down by 7 units.

The range of a function is the set of all possible outputs (y-values) for a given input (x-value).

Given the function f(x) = [x+3]-5, we can see that the function first adds 3 to x and then subtracts 5. The square bracket notation around (x+3) indicates that the function is taking the greatest integer less than or equal to (x+3).

For any input x, the output of the function will always be the greatest integer less than or equal to (x+3) - 5. Therefore, the output of the function is always an integer less than or equal to -2.

So the range of the function is [-5, -2] U (-2, ∞)

Option A) [-5,∞) is incorrect as the range starts with -5 but the function output is always less than or equal to -2.

Option B) (-5,∞) is incorrect as the function output is always less than or equal to -2.

Option C) [3,∞) is incorrect as the function output is always less than or equal to -2.

Option D) (3,∞) is incorrect as the function output is always less than or equal to -2.

The correct answer is (-2, ∞)

Answer:

I think it's (4,4) but I could be wrong

Step-by-step explanation:

ΔABC is the required triangle in which AB = 4 cm, BC = 7 cm and AC = 5 cm.

To see the attachment.

Now, According to the question:

Let us assume that given sides are :

BC = 7 cm, AB = 4 cm and AC = 5 cm

Steps of construction

Step I Draw a line BC = 7 cm.

Step II With center B and radius 4 cm draw an arc.

Step III With center C and radius 5 cm, draw an arc which cuts the previous arc at A.

Step IV Join AB and AC.

Hence, ΔABC is the required triangle in which AB = 4 cm, BC = 7 cm and AC = 5 cm.

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Answer: To find the area that 1.6 litres of paint will cover, we can use the unit rate. The unit rate is a way to compare different quantities by finding how much of one quantity corresponds to one unit of another quantity.

We know that 750ml of paint covers an area of 12 m2, this means that the unit rate of paint:area is 750ml:12m^2

We can use this to find the area that 1.6 litres of paint will cover.

First we should convert the 1.6 litres of paint to milliliters, since we have the unit rate in ml:

1.6 litres = 1.6*1000 ml = 1600 ml

Now we can use the unit rate to find the area that 1.6 litres of paint will cover:

Area = (1600 ml paint) * (12 m2/750ml paint) = 21.333 m2

So, 1.6 litres of paint will cover approximately 21.333 m^2

Note that you could also use the proportion (750ml/12m^2) = (1600ml/x) to find the value of x.

Step-by-step explanation:

The time taken by the ball to reach the ground is 11.5 seconds.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Suppose a ball was dropped from a TV tower 2120 feet high. The time it takes an object to free-fall from the top of this tower to the ground can be represented by the equation s = -16t² + 2120.

The time will be calculated as,

s = -16t² + 2120

Equate with zero as the ball reaches the ground the height s becomes zero.

-16t² + 2120 = 0

-16t² = -2120

t² = 2120 / 16

t² = 132.5

t = √132.5

t = 11.5 seconds

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The solutions of x² + 4x > 77 is x < –11 or x > 7

An equation is a mathematical expression that states that two algebraic expressions must be equal in nature. Finding the value of a variable in an equation indicates the process of solving an equation. The solution of the equation is the value that was determined while solving the equation.

Here we have

x² + 4x > 77  

Subtract -77 from both sides

=> x² + 4x - 77 > 77 - 77  

=> x² + 4x - 77 > 0

The above expression can be factorized as follows

=>  x² + 11x - 7x - 77 > 0     [ Split middle term ]

=> x(x + 11) - 7(x + 11) > 0  

=> (x + 11) (x - 7) > 0

=> (x + 11) > 0              (x - 7) > 0

=> x < -11                       x > 0

Therefore,

The solutions of x² + 4x > 77 is x < –11 or x > 7

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Answer:

4 (8+r)

Step-by-step explanation:

The 4 (four) quadrants in order are: Quadrant I, Quadrant II, Quadrant III, and Quadrant IV.

A coordinate plane is divided into four sections called quadrants. These quadrants are numbered I, II, III, and IV in a counterclockwise direction, starting with the top right.

Quadrant I is the top right section of the coordinate plane, and it contains all the points where the x-coordinate and y-coordinate are positive.

Quadrant II is the top left section of the coordinate plane, and it contains all the points where the x-coordinate is negative and the y-coordinate is positive.

Quadrant III is the bottom left section of the coordinate plane, and it contains all the points where the x-coordinate and y-coordinate are negative.

Quadrant IV is the bottom right section of the coordinate plane, and it contains all the points where the x-coordinate is positive and the y-coordinate is negative.

Understanding this concept is important for solving mathematical problems, especially in algebra and geometry.

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Answer:

First question:

y intercept = 3

slope = -1/3

y = -1/3x+3

Second Question:

y intercept = -3

slope = -3/2

y = -3/2x=3

Third Question:

y intercept = -1

slope = 3

y = 3x-1

youre welcome buddy :)

So, the probability that the two biscuits are not the same type is 0.15 or 15%.

To find the probability that the two biscuits are not the same type, we need to calculate the probability that Sue takes one biscuit of each type.

First, we will calculate the probability that Sue takes one plain biscuit, one chocolate biscuit, and one currant biscuit.

The probability of Sue taking one plain biscuit is 12/20, since there are 12 plain biscuits out of a total of 20.

The probability of Sue taking one chocolate biscuit after taking a plain biscuit is 5/19, since there are now 5 chocolate biscuits out of 19 remaining.

The probability of Sue taking one currant biscuit after taking a plain and chocolate biscuit is 3/18, since there are now 3 currant biscuits out of 18 remaining.

To find the overall probability that Sue takes one biscuit of each type, we multiply the individual probabilities together:

P = (12/20) * (5/19) * (3/18) = 0.15

So, the probability that the two biscuits are not the same type is 0.15 or 15%.

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The null hypothesis is: H0: p ≤ 0.31

The alternative hypothesis is : H1: p > 0.31

A common statistical theory called the null hypothesis asserts that there is no statistical link or significance between two sets of observed data and measurable events for a given single observed variable.

The null states that the probability of the readers have the personal computers have to be lower than or equal to 31 percent.

What is the alternative hypothesis?

An alternate hypothesis is a claim that the two variables have some kind of statistical relationship.

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Answer:3/8 was left over

Step-by-step explanation: 3/8 plus 1/4 x 2 equals  5/8... remainder 3/8

Answer:

3/8 (this is the answer)

There are 2 types of images namely virtual and real image

The point where light rays from an object meet or appear to contact after reflection or refraction is sometimes referred to as the image. In this concept, a "object" might be anything that light rays are emanating from.

Real images and virtual images are the two types of images. The method by which they are created distinguishes a genuine image from a virtual image. Light beams must converge to create an actual image, whereas they must diverge to create a virtual image.

Real images are those that are created when light rays collide at a specific location after being reflected or refracted by a mirror or lens.

Virtual pictures are those that only seem to form when viewed from behind a mirror. Behind the mirror, the picture is not actually there. When light beams are refracted or reflected, a virtual picture is created.

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Answer: 2/5, 4/5, -4/5, 8/5, -16/5

I dunno that's what I got I could be wrong

The volume of a sphere, to the nearest cubic meter is; 44 cubic meter

We are given that the formula for the volume of a sphere is;

V = [1/(6√π)]S^(3/2)

where;

V is volume

S is the surface area of the sphere

π = 3.14

We are given that  surface area is 60 square meters. Thus, we will now have;

V = [1/(6√3.14)]60^(3/2)

V = 43.713 m³

Approximating to the nearest cubic meter gives;

V = 44 cubic meter

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Answer:1280

Step-by-step explanation:

75% of something is 960 you can use trial and error to find the amount by just doing 75% of a number a little higher than what you got

The additive inverse of 8 /- 13 is -8 /+ 13. This means that when you add 8 /- 13 to its additive inverse, the result is 0.

The additive inverse of 8 /- 13 is its opposite number. This means that the sign of the number must be flipped. The inverse of 8 /- 13 is -8 /+ 13. To find the inverse of a number, you must switch the sign of the number from positive to negative or from negative to positive.

When two numbers are added together, the result will be zero if the numbers are opposites. This means that 8 /- 13 and its inverse, -8 /+ 13, when added together, will equal 0. This is because the two numbers have the same value but opposite signs. The positive 8 is cancelled out by the negative 8, and the negative 13 is cancelled out by the positive 13, leaving 0.

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Brayden's total earning by walking lap around a track is $35, if he walks 2+1/2 = 5/2 laps per day for 7 days.

Per day walking of brayden = 5/2 laps

7 days walking of brayden = 5/2 × 7 = 35/2 laps

As per the question statement he earns $1 per lap if he walk less than 16 laps and $2 per lap if hi walks 16 or more lap. Since the total walking of brayden is more than 16 laps, so he will earn at the rate of $2 per lap. So total earning will be,

= 2× 35/2

= $35

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Total Seeds required 9.33 kg  and she has 10 kg.so, she has enough grass seed to make a lawn 10m by 14 m.

If you're fortunate enough to have a rectangular lawn, determining the size is straightforward. Multiply the length and breadth measurements together to get the total. You now have your region/area.

So, Maisie knows that she needs 3 kg of grass seed to make a rectangular lawn 5 m by 9m.

Grass seed is sold in 2 kg boxes,

Maisie wants to make a rectangular lawn 10 m by 14 m,

She has 5 boxes of grass seed

To Find, Has Maisie got enough grass seed to make a lawn 10m by 14 m

Solution:

3 kg of grass seed to make a rectangular lawn 5 m by 9m.

=> 3 kg  of grass seed  needed for 5 x 9 = 45 m²

=>  1 m² required  = 3/45  kg seed

a rectangular lawn 10 m by 14 m,

area = 10 x 14 = 140 m²

Hence 140 m² required = 140 x  3/45  =  9.33 kg

Grass seed is sold in 2 kg boxes,

She has 5 boxes of grass seed

Hence total seeds = 5 x 2 = 10 kg

Therefore, total seeds required 9.33 kg  and she has 10 kg.so, she has enough grass seed to make a lawn 10m by 14 m.

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Answer: triangle 1's 1/2 length* triangle 1's width+triangle 2's 1/2 length* triangle 2's width+triangle 3's 1/2 length* triangle 3's width

Step-by-step explanation: triangle 1/2 length* triangle width=triangle area.

The value of x in the given equation x² = 9 is x = ± 3.

In x² = 9, we need to remove the power of 2 in order to separate just x.

This implies finding the square root √x² which is equal to x.

However, there are 2 possible answers to any square root, a positive or a negative answer.

x = √9

x = ± 3

0r we can solve this equation by the splitting method.

Rearrange the equation

x² = 9

(x - 3)(x + 3) = 0

On solving, we get

x = +3 and x = -3

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The solution to this ¾ divided by 4 is 0.1875.

To visualize the question we are trying to solve, let's put 3/4 and 4 side-by-side so it's easier to see:

3/4÷4

The numbers in 3/4 divided by 4 are labeled below:

3 = numerator

4 = denominator

4 = whole number

All we need to do here is keep the numerator exactly the same (3) and multiply the denominator by the whole number:

3/4 x4= 3/16.

Once you have your final fraction, just divide the numerator by the denominator to get your answer in decimal form:

3/16=0.1875

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Answer:

1 inch

Step-by-step explanation:

It's 1 inch because you minus 20 inch by 19 inch and get 1 inch

Answer:

Use direct variation method of mathematics

The length of the rectangle is 25 cm and the width is 10 cm.

We shall represent the length and width of the original rectangle with x and y respectively so that the perimeter is;

2(x + y) = 70 {divide through by 2}

x + y = 35...(1)

length of new rectangle = x - 5

width of new rectangle = y + 5

area of new rectangle:

(x - 5)(y + 5) = xy + 50

xy + 5x - 5y - 25 = xy + 50

xy - xy + 5x - 5y = 50 + 25

5x - 5y = 75 {divide through by 5}

x - y = 15...(2)

add equations (1) and (2) we have;

x + y + x - y = 35 + 15

2x = 50 {divide through by 2}

x = 25

substitute 25 for x in equation (1), we have;

25 + y = 35

y = 35 - 25 {subtract 25 from both sides}

y = 10

Therefore, have the length and width of the original rectangle to be x = 25 cm and y = 10 cm respectively.

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Answer:

One glass of milk: 15 carbs

One snack bar: 13 carbs

Step-by-step explanation:

This problem is an example of systems of linear equations. We can set this problem up by defining variable. I used [tex]m[/tex] for the glass of milk and [tex]b[/tex] for the snack bar.

First, we have: 4 glasses of milk and 2 snacks bar have a total of 86 carbs. We can write this as

[tex]4m+2b=86[/tex]

Next: 2 glasses of milk and 3 snack bars have a total of 69 carbs.

We can write this as

[tex]2m+3b=69[/tex]

Now we set it up.

[tex]4m+2b=86[/tex]

[tex]2m+3b=69[/tex]

By dividing both sides of the first equation by 2, we can use the subtraction method to get rid of the variable [tex]m[/tex]. Now we have

[tex]2m+b=43[/tex]

[tex]2m+3b=69[/tex]

Subtract like terms and solve for [tex]b[/tex]

[tex]-2b=-26[/tex]

[tex]b=13[/tex]

Now we substitute [tex]b[/tex] back into the original equation to find [tex]m[/tex].

[tex]2m+(13)=43[/tex]

[tex]2m=30[/tex]

[tex]m=15[/tex]

There you have it. I hope this helps!

When we multiply any number by zero, the outcome is always a zero, according to the definition of the zero property of multiplication, examples as 8 x 0 = 0.

When we multiply any number by zero, the end result is always a zero, according to the definition of the zero property of multiplication. Zero need not always be the first or second number. When multiplied by another number, it could be anywhere. This indicates that the outcome of the multiplication is unaffected by the placement of the digit zero.

All different kinds of numbers fall under the umbrella of this property. They could be fractional, decimal, or integer numbers. Thus, the results of some such numbers will be as follows:

10 x 0 = 0         6.4 x 0 = 0

½ x 0 = 0         1 x 2 x 3  = 0

A non-example of property 0 is: 5 × 1 = 5, the number is not multiplied by 0, therefore, it does not denote the zero property of multiplication.

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Compete question is: Give non-example of the property 0.

There are two triangles, triangle abc and triangle def. Side ab is congruent to side de, side ac is congruent to side df. Angle cab is congruent to angle fde. The length of the side bc is (x-4).  The value of x is 23.

The value of x can be calculate as follows:

Given that the triangles are congruent and moreover

Considering that

AB = DE

AC = DF

so,

The third will be compatible as well.

so,

BC = AE

x - 4 = 19

x = 19 + 4

x = 23

Therefore , the value of x is 23. When there are two triangles, triangle abc and triangle def. Side ab is congruent to side de, side ac is congruent to side df. Angle cab is congruent to angle fde. The length of the side bc is (x-4).

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