3. A train travels 20 km at a uniform speed of 60 km/h and the next 20 km at a uniform speed of 80km/h. Calculate its average speed.​

Sally's class haven't raised $2,000 as the amount made is $958. The estimated value is $1900. The amount needed is $42.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

In this case, Sally's class is raising money for charity with a goal of raising $2,000. They raise $997 at a bake sale and $961 at a car wash. Sally wants to see if they raised enough money to meet their goal. The amount made will be:

= $997 + $961

= $1958

They have not made $2000. The amount left is:

= $2000 - $1958

= $42

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Answer:

[tex]14v+7=7(2v+1)[/tex]

Step-by-step explanation:

break down the equation 14v +7

Answer:

7(2v+1)

Step-by-step explanation:

7 goes into 14 twice and into itself once so its factorised as 7(2v+1) you can do the multiplication to test it .

By evaluating the quadratic equation we can get some points, and with them we can estimate the graph.

The graph can be seen in the image at the end.

Here we want to graph the function:

y = x^2 + 2x - 2

To do so, we can evaluate the quadratic equation in some values of x to get points, and then just connect the points with a general parabola.

when x = 0

y = 0^2 + 2*0 - 2 = -2

So the point is (0, -2)

when x = 1

y = 1^2 + 2*1 - 2 = 1 + 2 - 2 = 1

So the point is (1, 1)

when x = -1

y = (-1)^2 + 2*(-1) - 2

y = 1 - 2-  2 = -3

So the point is (-1, -3)

when x = -2

y = (-2)^2 + 2*(-2) - 2

y = 4 - 4 - 2 = -2

So we have the point (-2, -2)

And so on..., eventually, you will get enough points to connect, and you should get something like:

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The equation written is: x + 18 + x = 84

The lengths of each piece of the cable are: 33 meters and 51 meters.

To write an equation, let the unknown quantity be represented as a variable, which would be used in creating an algebraic expression.

For example, we are given the following:

Length of a cable = 84 meters

The length of one the pieces that the cable is cut into is represented as x.

The second pieces = x + 18 meters.

The equation that would be created for this problem would be:

x + 18 + x = 84

Solve for x:

2x + 18 = 84

2x = 84 - 18

2x = 66

2x/2 = 66/2

x = 33

The length of one of the pieces = 33 meters

Length of the second piece = x + 18 = 33 + 18 = 51 meters.

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Using the exterior angle theorem which involves the use of two interior angles in the polygon, the value of angle ACD in the triangle is 150 degrees

An exterior angle of a polygon is an angle that is formed outside of the polygon by extending one of its sides. It is the supplementary angle of an interior angle.

Exterior angle theorem states that the sum of two interior angles is equal to one exterior angle.

Using that theorem in this problem;

∠ACD = 33 + 117

∠ACD = 150°

The value of angle ACD in the triangle is equal to 150 degrees

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Cells share many cοmmon features, yet they can look wildly different. In fact, cells have adapted οver billions of years to a wide array of environments and functional rοles.

The lοwest common element of life is a cell. Some cells function as independent entities, while οthers are a component of multicellular οrganisms.

Nucleic acids, prteins, carbohydrates, and lipids make up the four main types of οrganic molecules that all οrganisms are composed of. In part because they arrive in distinct, distinguishable packets, cells are regarded as the fundamental building blοcks of life.

The reasοn for this is that, like a hοuse's walls, the cell membrane that surrounds every cell acts as a definite border between its interiοr and exterior envirοnments. The plasma membrane is anοther name for the cell membrane. Phοspholipids are a framework οf fat-based molecules that serve as the fοundation of cell membranes.

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Yes, rectangles and squares are similar polygons.

Similar polygons are two or more polygons with the same shape but different sizes. This means that the sides of the polygons are proportional, and the angles are congruent. The formula to determine if two polygons are similar is A/a = B/b = C/c = D/d = …, where A, B, C, and D are the sides of one polygon and a, b, c, and d are the sides of the other polygon. For instance, if a rectangle has sides of 4 and 8, and a square has sides of 6 and 6, the ratio of the sides of the rectangle to the sides of the square is 4/6 = 8/6. This means that the two shapes are similar.

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Claire's current account balance would be -$50.

The amount that Clare has in his bank account initially = $150

The amount that he used from his bank account to buy the bike =  $200

As we can see that the amount that Clare used to buy the bike is more than the amount that he has in his account, therefore his account balance becomes negative, that is:

$150 - $200 = -$50

Here, it means that Clare has to pay the bank the amount of $50 that he used more than the amount that he had in his account.

Therefore, Claire's account balance would be -$50.

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3/4 divided by 2 in the fraction is equal to 3/8.

A fraction is used to represent the portion of the whole quantity. Also, we know that every integer is a rational number and any whole number can be written in the form of n/1, where n is any whole number.

On the given data, we need to use the concept of the division of fractions.

3/4 ÷ 2

=3/4 × 1/2 [ Reciprocal of 2 is 1/2]

=3/8

Therefore, 3/4 divided by 2 in the fraction is equal to 3/8.

Once you have your final fraction, just divide the numerator by the denominator to get your answer in decimal form: 3/8=0.375

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Answer:

Step-by-step explanation: .

Using the cosine rule calculate the magnitude of angle B when did the b=20.8cm c= 14.5cm and a= 9.3cm is [tex]\approx 37.02364^{\circ}[/tex]

​

Given,

b=20.8cm c= 14.5cm and a= 9.3cm

[tex]\gamma=\cos ^{-1}\left(\frac{a^2+b^2-c^2}{2 a b}\right)[/tex]

[tex]=\cos ^{-1}\left(\frac{9.3^2+20.8^2-14.5^2}{2 \cdot 9.3 \cdot 20.8}\right)[/tex]

[tex]\approx 37.02364^{\circ}[/tex]

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The volume of the biggest possible cube inside the right cylinder is approximately 1193.243 cubic centimeters.

Cubes are hexahedrons with one same side length and only right angles. In this case, the cube is constrained by cross area of right cylinder in accordance to image attached below. The maximum possible volume for a cube inside the cylinder is described by following expression:

V = (√2 / 2)³ · R³

Where:

If we know that R = 15 cm, then the volume of biggest possible cube is:

V = (√2 / 2)³ · (15 cm)³

V ≈ 1193.243 cm³

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Answer:

I don't get it please elaborate!

Step by Step Explanation:

Thank you!

Answer:

8.8 feet per second

Step-by-step explanation:

1 mile = 5280 feet

3600 seconds = 1 hour

6 mph = 5280(6)/3600 = 528/60 8.8 feet per second

The equation of the line perpendicular to the line A is given by the

x-4y +29=0

What is the general equation of a Straight line?

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

Given is a  Line A pass through the point (1,5) and (5,7).

Find the equation of the line perpendicular to A that pae through point (-1,7)

line A is y= 1/4 x+c

x-4y +4c=0

it passes through ( -1,7)

c= 29/4

equation becomes x-4y +29=0

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Answer:

See below

Step-by-step explanation:

I'm guessing this is what you're looking for:

[tex]45^2=(40+5)^2=(40+5)(40+5)=40(40)+2(40)(5)+5(5)=1600+400+25=2025[/tex]

The fraction of Jon original pay is 4/10

Jon earns  £90  one week

The following week he earns  £130

His pay rise is

130-90

= 40

The fraction of his original pay is

= 40/100

= 4/10

Hence the fraction of Jon original pay is 4/10

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Square root of 4 is not a polynomial. It is a quadratic function. Functions containing other operations like square root is not a polynomial.

A polynomial need not have any square root.  polynomial is a finite sequence form. it must contain no square roots of variables, no fractional or negative powers on the variables, and no variables in the denominators of any fractions. Polynomial are sums and differences of polynomial terms. For an expression to be a polynomial term, any variables in the expression must have whole number powers. It should not have any square root, cube root or any negative values. Quadratic function can have square root cube roots and fraction values.

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Water molecules with a mass of 3.34 * (10 )23 weigh 9.911 grams.

Firstly, you wish to transform the quantity of water molecules you have into the quantity of moles.

Undoubtedly, you are aware

Number of Particles = Mole Ratio x Avogadro's Constant

Avogadro's constant is equal to 3.34 * (10) 23 / 6.02  * (10) 23 when the number of moles is equal to the number of particles.

=0.55

so 0.55 moles

Consequently, mass/molar mass = number of moles.

Since we must determine the mass, we can use the formula Mass = Number of Moles x Molar Mass.

H 2 O's molar mass is calculated as H - 2(1.01) = 2.02 O- 16 18.02

Consequently, 18.02 g/mol is the molar mass.

We now possess the necessary values to determine the mass because of this.

Mass =  0.55 × 18.02

Mass = 9.911

As a result, the 3.34 mass

There are 9.911 grams in 3.34 * (10 )23 water molecules.

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the other equation is missing, the solution cannot be found.

What is Rate?

A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.

When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.

Determined to finish her milkshake before Diego, Lin now drinks her 12 ounce milkshake at a rate of an ounce per second.

Rate= 1/3 ounce milkshake per second

Initial = 20 ounces

Lin's condition is thus represented by the equation:

[tex]y = \frac{1}{3} x +20[/tex]

Since the other equation is missing, the solution cannot be found.

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The number of images that will be formed when two mirrors are positioned at an angle of 45 degrees is 7.

The formula that you have provided for calculating the number of images formed by two mirrors positioned at a specific angle is (360/n) - 1, where n is the angle between the mirrors in degrees.

When two mirrors are positioned at an angle of 45 degrees, n = 45. So, using the formula, the number of images formed would be: (360/45) -1 = 8 - 1= 7

It's important to note that this formula only gives you the approximate number of images that will be formed. In reality, due to the nature of light and the reflective properties of mirrors, it is impossible to determine the exact number of images that will be formed.

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The symmetric of -15 is 15.

When we talk about symmetric, we must remember that it means the opposite of a number, that is, we take as a basis the number line where we have zero (0) as the central number, on one side the negative infinite numbers (-) and on the other, the positive infinite number (+), see the attached image.

In order to solve this type of exercise, just change the signs of the number in question, if it is negative it will become positive and vice versa.

[tex] \bold{- 15 = + 15}[/tex]

Answer:

9/4

Step-by-step explanation:

Use the process of elimination. Divide each number's numerator by its denominator; if the outcome repeats itself, it isn't a terminating decimal. Therefore, when you divide 9/4, it equals 2.25, which is a terminating decimal.

The 4 types of triangle with respect to angle measurement :

Acute Triangle

Obtuse Triangle

Right triangle

Equivalent triangle

A triangle is said to be equilateral if each of its three sides is the same length. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.

A triangle having three acute angles is known as an acute triangle. A triangle having one obtuse angle and two acute angles is known as an obtuse triangle. No Euclidean triangle may contain more than one obtuse angle because in Euclidean geometry, a triangle's angles must add up to 180°.

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

Obtuse-angled triangles or obtuse triangles are triangles with any one of its angles being an obtuse angle or more than 90°. Only 180° is equivalent to the internal angles of an acute triangle.

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There are four different triangles for measuring angles:

sharp triangle

Sharp triangle

correct triangle

comparable triangle

If all three sides of a triangle are the same length, the triangle is equilateral. Equiangular triangles are equilateral triangles in well-known Euclidean geometry. His three internal angles, which are all 60 degrees, are therefore consistent with one another.

An acute triangle is a triangle having three acute angles. Obtuse triangles are those with one obtuse angle and two acute angles. Euclidean geometry mandates that the total of all the angles of a triangle be 180°, hence a triangle cannot have more than one obtuse angle.

A right triangle, also known as a right triangle, right triangle, right triangle, right triangle, right triangle, or formerly right triangle, is a triangle with one or two right sides. The basis of trigonometry is the relationship between the sides of a right triangle and different angles.

An obtuse or obtuse triangle is a triangle with one of its angles obtuse or greater than 90°. An acute triangle has only 180° interior angles.

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The 4 physical properties of solutions are:

1) Concentration

2) Solubility

3) Viscosity

4) Transparency

In chemistry, a solution is a homogeneous mixture of two or more substances. The four common physical properties of solutions are:

1) Concentration: The amount of solute present in a given amount of solvent, typically measured in molarity, molality, or mass percentage.

2) Solubility: The maximum amount of solute that can be dissolved in a given amount of solvent at a specific temperature and pressure.

3) Viscosity: The resistance of a fluid to flow, which can be affected by the presence of a solute.

4) Transparency or Opacity: The property of a solution by which it allows light to pass through it or not.

These are the 4 common physical properties of solutions, but there are many other physical properties that can be used to describe solutions depending on the context.

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Answer:

see explanation

Step-by-step explanation:

given the system of equations

x + 3y = 76 → (1)

x + y = 36 → (2)

1

subtracting (2) from (1) term by term will eliminate x

(x - x) + (3y - y) = 76 - 36

0 + 2y = 40

2y = 40 ( divide both sides by 2 )

y = 20

3

substitute y = 20 into either of the 2 equations and solve for x

substituting into (2)

x + 20 = 36 ( subtract 20 from both sides )

x = 16

4

that is 16 students bought orange juice and 20 bought a sandwich

As a check

substitute the values for x and y into the equations and if both sides are equal then they are the solution

(1) :  16 + 3(20) = 16 + 60 = 76 ← True

(2) : 16 + 20 = 36 ← True

since both equations are true, then

x = 16 and y = 20 are the solutions to the system

David's annual gross pay is $2 730.00 * 12 = $32 760.00.

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Answer:

(-3,5)

Step-by-step explanation:

8x+3(23+6x)=-9

x=-3

y=23+6x(-3)

y=5

(-3,5)

A quadrilateral is a four-sided shape. The perimeter of a quadrilateral is the sum of all its sides. If the perimeter of a quadrilateral is 54 cm, and we know that all four sides are equal, we can divide 54 by 4 to find the length of each side.

54 cm / 4 = 13.5 cmTherefore, the length of each side of the quadrilateral is 13.5 cm.

It's important to note that this is only one possibility, since quadrilaterals can have different shapes and different side lengths.

Answer:

25 :)

Step-by-step explanation: