The diagram shows a right-angled triangle.

All the measurements are in centimetres.

The area of the triangle is 18cm^2

Work out the length of the shortest side of the triangle.You must show all your working

Therefore, as a result square root property can be used to solve a quadratic equation.

Describe equation.

To create an equation, the equal sign is placed between two numerical or variable expressions, as in 4x+9=25.

The answer is a number that may be used in an equation to replace the variable.

According to the given question:

In order to isolate the variable being solved,

the square exponents are removed using the Square Root Property.

The positive and negative values of the number that, when multiplied by itself, equals x are provided by the formula x=±√c x = ± c.

Therefore , as a result square root property can be used to solve a quadratic equation.

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The volume of the pyramid with the given base area of square and height of the cube is given by: V = ( 1/3) × ( y)² × (h).

As given in the question,

Base of the given pyramid is square in shape.

Base area of the pyramid is given by:

Let 'y' be the side length of the square base.

Area of the square base = ( side length )²

                                         = y²

let 'h' be the height of the cube

Volume (V) of the pyramid = ( 1/3 ) × Base area × height

⇒Volume of the pyramid = ( 1/3 ) ×  y² × h

Therefore, the volume of the pyramid with square base and height of the cube is equal to Volume of the pyramid = ( 1/3 ) ×  y² × h.

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The equation 3x2 + Kx - 30 has equal roots when the discriminant (D) of the equation is equal to zero.

The discriminant of a quadratic equation is given by the formula D = b2 - 4ac, where a = 3, b = K, and c = -30.

Substituting these values into the formula, we get:

D = K2 - 4(3)(-30)

D = K2 + 360

Therefore, K2 = -360, and K = √(-360) = 6√(-5)

Therefore, the value of k for which the roots of the equation 3x2 + Kx - 30 are equal is 6√(-5).

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The mileage for which company A charge less than company B , m < 65 ( an Inequality using the number of miles driven).

The subtraction property of inequality is applied when an inequality holds the addition operator previously, i.e

x + a < b => x + a - a < b - a

=> x< b - a.

The division property of inequality is mainly applied to the shift coefficient of the variable to another side of the inequality, i.e

2x< b => 2x/2<b/2

⇒ x< b/2.

We have, ryan is going to rent a truck for one day. There are two companies say company A and company B, in which ryan have to choose one for rent a truck for one day.

Let , Total cost charged by company A = $a

Total cost charged by company B = b

The number of miles driven = m miles

For Company A, initail fee = $40 and

Additional charge = .80 cents/mile driven

so, a = 40 + 0.8m --(1)

For Company B, initail fee = $53 and

Additional charge = .60 cents/mile driven

so, b = 53 + 0.6m --(2)

We want to know the mileage at which company A charges less than B i.e a < b

Now, using equation (1) and (2) ,

40 + 0.8m < 53 + 0.6m

Simplify the above Inequality,

=> 40 + 0.8 m - 40 < 53 - 40 + 0.6 m

=> 0.8 m < 13 + 0.6 m

=> 0.8 m - 0.6 m < 13 + 0.6 m - 0.6 m

=> 0.2 m < 13

=> m < 13/0.2

=> m < 130/2 = 65

Hence, required Inequality is m< 65.

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Complete question :

ryan is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices.

Company A charges an initial fee of $40 and an additional .80 cents for every mile driven.

Company B charges an initial fee of $53 and an additional .60 cents for every mile driven.

For what mileages will Company A charge less than Company B? Write your answer as an inequality, using m for the number of miles driven

Answer: 8x + 2xy

Step-by-step explanation:

9x - x + 4xy - 2xy

8x + 2xy

We can only compare the 9x with -x and the 4xy with the -2xy

The easiest way to quantify data variability is to look at the range, or the difference between the greatest and smallest value.

The difference between the highest and lowest values for a given data set is the statistics' range. The difference between the highest and lowest observation could likewise be used to describe the range.The sample interval is defined as the highest value less the smallest value. A crucial indicator of variability for continuous variables is the sample range.

here ,

Use an en dash (not an em dash or a hyphen) with no spaces between them.

If at least one number in the range is between 1 and 100, such as 3-11, 68-70, or 83-343, use all the digits (i.e., no elision).

Use all the numbers to represent multiples of 100, such as 100-127, 310-329, or 2,220-2,254.

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So the value of the line integral given point scale is [tex]\frac{15}{16}[/tex] -4cos6-6 .

To evaluate the line integral X signed by ideas oversee. Where C is the line segment from 2 to 36

First we find the vector determined by the two points

So ,

36 -2 = 34

Starting point is 2.

The segment can be para militarized as vitally equal to 2+3T+40 =3T 2+40 .

They belonging to close interval 0- one. Next we find the derivative of the Para militarism action y¹T= 34.

This implies the strength of y¹T = [tex]\sqrt{3^{2}+4^{2} }[/tex]

= 5

Finally we calculate the integral X signed by ideas oversee which is equal to treaty sign 2+ 40×DT Over 0- one.

Now report 2+ 40 equal to you. So implies 4DT is equal to DU and when T is equal to zero.

20=U

So next this integral becomes 15×2 to 6 Juju -2 x 4.

Comes out to be 15 x 16. 0-2. Sign your deal. Now applying integration by parts.

We have 15 x 16. 0-2 cause you plus integration of causal deal Limit 2- 6.

Now we have 15/16. On applying the limits -4 cos six plus sign 6- sign too.

So therefore final answer becomes [tex]\frac{15}{16}[/tex] -4cos6-6 .

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When a prism and pyramid have the same base and height, their volumes are inversely proportional: the volume of the pyramid is one-third that of the prism.

A pyramid is a three-dimensional object that has faces made of triangles and a base made of polygons. The base is the bottom, while the faces are the sides.

A prism is a three-dimensional object having two identically shaped and sized polygonal bases and rectangular sides. In the actual world, a cardboard box serves as an illustration of a prism.

When a pyramid and a prism have bases and heights that are equivalent, the pyramid can fit inside the prism.

In reality, when this is the case, the pyramid occupies precisely one-third of the prism's volume. When a prism and pyramid have the same base and height, their volumes are inversely proportional: the volume of the pyramid is one-third that of the prism.

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No, negative infinity and positive infinity are not the same. Negative infinity is a amount of number that is less than any other number, while positive infinity is a number that is greater than any other number.

Negative infinity is a number that is less than any other number. It is represented by a negative sign followed by an infinity symbol, and it is usually written as "-∞". Negative infinity is the opposite of positive infinity, which is a number that is greater than any other number. Positive infinity is usually written as "+∞". Negative infinity is used in mathematics to signify the smallest possible number or the lower limit of a range, while positive infinity is used to signify the largest possible number or the upper limit of a range. The two numbers are not the same, as they represent opposite extremes of a range. Negative infinity is the lowest possible number and positive infinity is the highest possible number.

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The ratio of the error is; 0.3333

The Percent error of the given problem is;  33.33%

We are given;

Amount spent by John on shopping = $75

Amount expected to spend = $100

Since this is what was given then it means we will have the following;

The approximate value to be spent = 100 dollars

Exact Value  spent = 75 dollars

Therefore, the error made is;

Error = Approximate value - Exact value  

Error = 100 - 75

Error =  25 dollars

Thus, the error when it is absolute is;

Absolute Error = ±25 dollars

Now, the ratio will be;

Ratio(e) = Error/exact value spent

e = 25/75 = 0.3333

Percent Error = error * 100%

Percent error = 0.3333 * 100%

Percent error =  33.33%

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We can find out the missing values of the sides of a triangle by using trigonometry functions like sin, cos, and tan.

If one angle and perpendicular are given then the other side means hypotenuse can be found out by sin function.

Sin Ф = perpendicular/hypotenuse

If one angle and hypotenuse are given then the other side means base can be found out by the Cos function.

CosФ = base/ hypotenuse

If one angle and base are given then the other side means perpendicular can be found out by the tan function.

Tan Ф= perpendicular/ base

Therefore the missing sides can be found by trigonometric function while one angle is given.

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The equation of the line that is parallel to the line y = - 5x + 3 will be y = - 5x + c.

Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as ax + by + d = 0.

The equation of the line is given below.

y = - 5x + 3

Then the equation of the line that is parallel to the line y = - 5x + 3 will be written as,

y = - 5x + c

The equation of the line that is parallel to the line y = - 5x + 3 will be y = - 5x + c.

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Answer:

f(x)=19

Step-by-step explanation:

x=-5

f(x)=-3(-5)+4

f(x)=15+4

f(x)=19

I think this is how you do it, but I haven't done these problems in a while so I could be incorrect.

The number of tickets sold will be equal to 29.

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.

Let x represent the number of child tickets that were sold

Let y represent the number of adult tickets that were sold

5.30x +9.40y= 1206

The number of adult tickets sold was three times greater than the number of child tickets,

y= 3x

Substitute 3x for y in the equation,

5.40x + 9.40y= 974.40

5.40x + 9.40(3x)= 974.40

5.40x + 28.2x= 974.40

33.6x= 974.40

Divide both sides by the coefficient of x which is 33.5,

x= 974.40/33.6

x = 29

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Find the slopes and their product should be - 1 for the diagonals to be perpendicular.

The points p and q have zero y-coordinate, so they are on the y-axis.

The points r and s have same y-coordinate b, so they are on the parallel line to the y-axis.

The points p and r are opposite to each-other, similarly points s and q are opposite points. So the diagonals are pr and qs. This is also known from the order of vertices in the name of the quadrilateral.

Slopes are:

The product of slopes:

The diagonals are perpendicular if:

Answer: I think it's 13

Step-by-step explanation: So we need to fill in the distance formula. It's d=√((x_2-x_1)²+(y_2-y_1)²).

-6=x_1

-3=y_1

6=x_2

2=y_2

Now you plug in your coordinates to the formula, so you get d=√((6--6)²+(2--3²)

(6-(-6)²=144

(2-(-3²)=-7

So now 144+25=169

The square root of 169 is 13, so d=13. That should be your answer! Let me know if it's right

The range of possibilities for variation or the boundaries between them: the price spectrum for steel; many different styles. the size or scope of a process, action, or operation .

The range of values between the highest and lowest values for a certain data collection is known as the statistical range. It is also possible to show the range by comparing the highest and lowest observational values. The sample interval is found by subtracting the highest value from the lowest. For continuously varying variables, the sample range is a key measure of variability.

here ,

Between the lowest and greatest numbers, there is a range. In the example, the lowest value is 2, and the highest is 9.

The range therefore equals 9 x 2 = 8.

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Answer:

[tex] \sf \: 375g \: is \: 2.5\% \: of \: 15kg[/tex]

Step-by-step explanation:

Conversion of 15 kg into grams,

→ 1 kg = 1000 g

→ 15 kg = 15000 g

Let's find the percentage,

→ (375g ÷ 15kg) × 100

→ (375/15000) × 100

→ 0.025 × 100

→ 2.5%

Hence, the answer is 2.5%.

The root of the graph of f(x) = [tex](x-5)^{3} + (x+2)^{2}[/tex] touches the x axis at -2 and 5.

What is root of graph ?

A rooted graph is a graph in which one node is labeled in a special way so as to distinguish it from other nodes. The special node is called the root of the graph.

What is axis ?

An axis in mathematics is defined as a line that is used to make or mark measurements.

Have given ,  f(x) = [tex](x-5)^{3} + (x+2)^{2}[/tex]

⇒ [tex](x-5)^{3} * (x+2)^{2}[/tex]= 0.

But if ab = 0 ⇒ either a = 0 or b = 0 or both zero.

⇒ [tex](x-5)^{3}[/tex]= 0 and \[tex](x+2)^{2}[/tex] = 0

⇒ (x - 5) = 0 and x + 2 = 0

⇒ x = 5 and x = - 2.

The root of the graph of f(x) = [tex](x-5)^{3} + (x+2)^{2}[/tex] touches the x axis at -2 and 5.

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The slope of a line that is parallel to x + y = -4 is: -1.

If we have two lines that are parallel to each other, their slopes will be the same.

For example, if the slope of one line is 4, the slope of the line that is parallel to the line will also have a slope of 4.

To find the slope of the equation, x + y = -4, rewrite it in slope-intercept form, y = mx + b:

x + y = -4

y = -x - 4 [subtraction property of quality]

The slope is therefore -1. Therefore, the slope of the line that is parallel to the line whose equation is x + y = -4 is: -1.

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6) According to the time and work concept, 18 hours would be taken for James to complete the work.

Knowing the formulas can immediately lead you to a solution upon reading the question. Therefore, knowing the formula for any topic in numerical ability simplifies the solution and associated calculations.

Here are a few of these essential time and work formulas for your reference.

Work Performed = Time Required Rate of Work

Work Rate = 1 / Time Taken

Duration = 1 / Rate of Work

If a piece of work is completed in x number of days, then the amount of work completed in one day is equal to 1/x. Total Work Completed = Number of Days Efficiency.

Time and Productivity are inversely proportional to one another X:

if y is the ratio of the number of men needed to complete a piece of work, then y:x is the ratio of the time required by those men to complete the work.

If x number of people can complete W1 work in D1 days while working T1 hours per day, and y number of people can complete W2 work in D2 days while working T2 hours per day, then the relationship between them is Time and Work Formula i..e;

[tex]\frac{M1.D1.T1}{W1} =\frac{M2.D2.T2}{W2}[/tex]

Monica can do the work in 9 hours so she does a work of 1/9 in an hour.

The same work done by Monica and James takes 6 hours so they both can do a 1/6 th of work in an hour.

Developing the relation:

[tex]\frac{1}{9}+\frac{1}{x}=\frac{1}{6}[/tex]

here, the speed of Monica is 1/9 and the speed of James in completing the work is 1/x and the speed of them both is 1/6

So solving this equation we get ,

[tex]6x+54 = 9x[/tex]

[tex]3x = 54\\x=18\\[/tex]

So the speed of James in completing the work is 1/18th in an hour So he takes 18 hours to complete the whole work by himself alone.

According to the time and work concept, 18 hours would be taken for James to complete the work.

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The five ways to prove the congruence theorem are listed as,

Here we have to find the 5 ways to prove congruence.

As we all know that, according to the concept of triangle, then term congruence referred as if two shapes are congruent if and only if they have the exactly the same sides and exactly the same angles.

Based on these we have derived 5 sub theorem, from the congruence theorem, they are listed as,

1) SSS   (side, side, side)

2) SAS   (side, angle, side)

3) ASA   (angle, side, angle)

4) AAS   (angle, angle, side)

5) HL   (hypotenuse, leg)

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Option A, C, and E are the correct option.

What is midpoint?

The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.

Given, the coordinate of the vertices of AB line segment are A(9, 5) and B(15, 2).

The formula midpoint of the points (x₁, y₁) and (x₂, y₂) is ((x₁ +x₂)/2 , (y₁ + y₂)/2) .

The midpoint of the line segment AB is ((9 + 15)/2, (5+2)/2)

= (24/2 , 7/2)

= (12, 3.5)

The slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is (y₁ - y₂)/(x₁ + x₂).

The slope of the line AB is (5 - 2)/(9 - 15) = 3/(-6) = -1/2.

The slope of perpendicular line of a line with slope m is = -1/m.

The slope of perpendicular bisector is - 1/( -1/2) = 2

The distance of midpoint from the endpoints is equal. The perpendicular bisector of the line passes through the midpoint.

The distance of midpoint from the endpoints of the segment to any point on the perpendiculars bisector are equal.

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Answer:

5 per day

Step-by-step explanation:

Step-by-step explanation:

Find the arithmetic sequence for -16,-21,-26,-31

-21 - (-16) = -5

-26 - (-21) = -5

-31 - (-26) = -5

Answer:

Each following number is five less than the previous.

Answer: they would cost  £5.25

Step-by-step explanation:  £2.25 divided by 3 = 0.75 0.75x7=  £5.25

Answer:

Step-by-step explanation:

360

Answer:

x ≤ 2

Step-by-step explanation:

Brainliest pls btw did it help

The  average rate of change in concentration of b from t= 0 s to t = 212 s as calculated from the data given above is 0.004811  m/s.

The average rate of change is given by the formula ,

concentration change / time change.

First we will calculate the rate of change for A

rate change = 0.140 - 0.650 = -0.510 M

time difference = 212 s − 0 s = 212 s

Rate of concentration change = -0.510 M / 212 s = -0.002405 M/s

The - sign indicates that the [A] is decreasing with time.

In order to calculate the concentration rate of B we will write it in the form of stoichiometry

B = 2 x 0.002405 = +0.004811 m /s

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