How do you find the length of the third side of a triangle for Class 7?

The value of x in the equation 1.5 (x + 4) - 3 = 4.5 (x - 2) is 4.

The BODMAS rule is a rule used to simplify a mathematical equation. BODMAS itself is an abbreviation of the Bracket, Order, Division, Multiplication, Addition, and Subtraction. This rule indicates the sequence in which a mathematical equation should be solved.

As we want to find the value of x, firstly we have to simplify the equation by applying the BODMAS rule to the given equation:

1.5 (x + 4) - 3 = 4.5 (x - 2)

Since there's no Bracket, Order dan Division part that can be solved, so the first step is applying the Multiply part:

  1.5x + 6 - 3 = 4.5x - 9

Then we apply the addition and subtraction part:

   1.5x - 4.5x = - 9 - 6 + 3

              - 3x = - 12

                  x = 4

Thus, the value of x in the equation 1.5 (x + 4) - 3 = 4.5 (x - 2) is 4.

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Jacob poured 39/20 liters of water into the pitcher to make it 2 7/10 liters

An equation is an expression showing two or more numbers and variables linked together by a mathematical operation. Types of equations are linear, quadratic, cubic and so on depending on the degree of the variable.

Let x represent the amount of water that Jacob pour into the pitcher.

There is 3/4 liter of water in a pitcher. Then, Jacob pours more water into the pitcher. Now there are 2 7/10 liters of water in the pitcher.

2 7/10 liters = 27/10 liters

The equation is given as:

x + 3/4 = 27/10

x = 39/20

Jacob poured 39/20 liters of water into the pitcher

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7 pints of white paint were used to paint her bedroom wall. This is a great way to ensure that the bedroom wall is painted to her desired color scheme with the right amount of blue and white paint.

The total amount of paint used is 9.5 pints.

One fourth of 9.5 pints is 2.375 pints of blue paint.

The remaining amount of paint is 9.5 - 2.375 = 7.125 pints of white paint.

Therefore, 7 pints of white paint were used to paint her bedroom wall.

Ivania used 9.5 pints of blue and white paint to paint her bedroom wall. One fourth of this amount was blue paint, meaning 2.375 pints of blue paint were used. This leaves the remaining amount of paint as 9.5 - 2.375 = 7.125 pints of white paint. Therefore, 7 pints of white paint were used to paint her bedroom wall. This means that the majority of the paint used was white paint, with only a quarter of the paint used being blue. This is a great way to ensure that the bedroom wall is painted to her desired color scheme with the right amount of blue and white paint.

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The percent of the bug eaten each day is 67% and the percent of the bug remaining each day is 33%.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

f(x) = 500 (0.67)ˣ

Part A :

x = 0 ⇒ f(x) = 500 (0.67)⁰ = 500

x = 1 ⇒ f(x) = 500 (0.67)¹ = 335

x = 2 ⇒ f(x) = 500 (0.67)² = 224.45

x = 3 ⇒ f(x) = 500 (0.67)³ = 150.3815

Part B :

Here 0.67 is the decay rate.

That is the rate of decay of the bug is 0.67.

67% of the bugs are decaying with each day.

Part C :

Percent of bugs remaining each day = 100% - 67% = 33%

Part D:

f(x) < 40

500 (0.67)ˣ < 40

(0.67)ˣ < 40 / 500

(0.67)ˣ < 0.08

Taking logarithms on both sides,

㏒ (0.67)ˣ < ㏒ 0.08

x ㏒ (0.67) < ㏒ 0.08

x (-0.1739) < (-1.0969)

Dividing doth sides by (-0.1739), the sign of inequality changes because of dividing by a negative number.

x > 6.3

Hence the percentage of the bugs eaten and remained are calculated.

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The area of the trapezium shown is 57.97 cm²

An equation is an expression that shows the relationship between variables and numbers.

The area for a two dimensional shape is the amount of space occupied for that shape.

The area of a trapezium is given by:

Area = (1/2)(sum opposite base) * height

For the trapezium shown, the parallel sides have a measure of 17 inches and 31 inches respectively. The height is 11.7 inches:

Area = (1/2)(7.9 + 10.8)(6.2) = 57.97 cm²

The area is 57.97 cm²

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So on solving the provided question, we can say that fraction we have are  [tex]4\frac{2a}{3} + \frac{1a}{4} - \frac{1a}{a} (b - 7)[/tex]   = 14/6

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

here the fraction we have are

[tex]4\frac{2a}{3} + \frac{1a}{4} - \frac{1a}{a} (b - 7)[/tex]

12/3 + 12/4 + 15/2

14/6

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The exponential model indicates that plastic production has increased by 4.9% per year.

Fit an exponential model to this data

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[tex](4x - 8) - (3x + 10)[/tex]

Distribute negative sign:

[tex]4x-8+-1(3x)+(-1)(10)[/tex]

[tex]4x-8-3x-10[/tex]

Combine Like Terms:

[tex](4x-3x)+(-8-10)[/tex]

[tex]=\fbox{x - 18}[/tex]

Answer:

[tex]x - 18[/tex]

[tex]4x - 8 - 3x - 10 \\ 4x - 3x - 8 \times 10 \\ x - 18[/tex]

The value of 20.25 ÷ 0.9 in standard form is 2.25×10¹

The standard form of a number is a way of writing the number in a form that follows certain rules. Any number that can be written as a decimal number, between 1.0 and 10.0, multiplied by a power of 10, is said to be in standard form.

This means that writing a value in the form 35.77× 10³ is very wrong in standard form because 35.77 is less than 10. But instead we write it in the form 3.577×10⁴, now 3.577 is less than 10.

The value of 20.25÷ 0.9 = 22.5

but this is not in standard form because 22.5 is greater than 10. By putting it in standard form, we divide it by 10 and multiply it by 10 again

This means that 22.5 = 2.25×10¹

Therefore 20.25 ÷ 0.9 in standard form is 2.25 × 10¹

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The graph of Linear equation with colors lines black, orange, green and blue is shown in figure.

The equation of line in point-slope form passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Given that;

Linear equation with colors lines black orange green and blue.

Now, We know that;

The graph of linear equation is always a straight line.

Hence, The graph of Linear equation with colors lines black orange green and blue is shown in figure with straight line.

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The coordinates of the point P on directed line segment AB that partitions AB in the ratio of 3:5 in simplest form is x = -1/2 and y = 3[tex]\frac{1}{4}[/tex].

When the numerator and denominator have no common factors other than one, the fraction is in its simplest form. Use division to find the simplest form of a fraction.

Given set of points

A(-2, 5)

B(2, 3)

ratio 3:5  or  r = 3/5

We will use the following formula to find the coordinate

[tex]$x=\frac{x_1+r x _2}{1+r}[/tex]

[tex]$y=\frac{y _1+r y _2}{1+r}$[/tex]

Substitute the values in the formula

[tex]$ x=\frac{-2+(3 / 5) 2}{1+3 / 5}[/tex]                 [tex]$y=\frac{5+(3 / 5) 3}{1+(3 / 5)}[/tex]

[tex]$x=\frac{-2+6 / 5}{5+3 / 5}[/tex]                     [tex]$ y=\frac{59 / 5}{5+8 / 5}$[/tex]

[tex]$x=\frac{-10+6 / 5}{8 / 5}[/tex]                   [tex]$ y=\frac{25+9 / 5}{8 / 5}$[/tex]

[tex]$x=\frac{-4}{8}[/tex]                               [tex]$y=\frac{17}{4}$[/tex]

x = -1/2                               y = 3[tex]\frac{1}{4}[/tex]

Thus, the coordinates of the point P on directed line segment AB that partitions AB in the ratio of 3:5 in simplest form is x = -1/2 and y = 3[tex]\frac{1}{4}[/tex].

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Full question:

Given the points A(-2, 5) and B(2, 3), find the coordinates of the point P on directed line segment AB that partitions AB in the ratio of 3: 5. Write the answer in lowest simplified fraction if necessary.

The LCM of the numbers 1 - x² and (x - 1)³ is (1 - x²)(x - 1)

An equation is a expression that shows the relationship between numbers and variables.

The least common multiple (LCM) of a set of numbers is the smallest number that can be divisible by the set of numbers

Given the numbers:

1 - x² and (x - 1)³

(1 - x²) = (1 - x)(1 + x) = -1(x - 1)(x + 1)

(x - 1)³ = (x - 1)(x - 1)(x - 1)

The LCM = -1(x + 1)(x - 1)(x - 1) = -1(x² - 1)(x - 1) = (1 - x²)(x - 1)

The LCM is (1 - x²)(x - 1)

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Answer: First=Undefined (if you had a typo, please respond and I will edit)

Second=3.5

Step-by-step explanation:

-|b=2a|

-|-8=2(2.5)|

-8=5

Undefined

3|b+6|-|a|

3|-8+6|-|2.5|

3|-2|-2.5

3*2-2.5

6-2.5

3.5

The length of line WX in both rectangles  is 10.5 ft. The right option is (D) 10.5.

A rectangle is a plane shape with fours sides, having two opposite sides equal and parallel.

To calculate the length of WX, we use the formula below.

Note: Rectangle RSTV is similar to rectanngle WXYZ. And the ratio of their corresponding Lengths are equal.

Formula:

From the question,

Given:

Substitute these values into equation 1 and solve for WX

Hence, the length of line WX is 10.5 ft

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Answer:

[tex]12x^3-16x^2[/tex]

Step-by-step explanation:

[tex]10x^3-15x^2+2x^3-x^2=12x^3-16x^2[/tex]

The time taken by 3 electricians to complete the work is 9 1/3 hours.

When one quantity's value rises relative to another's decrease or vice versa, it is said that the two are inversely proportionate.

It implies that the two quantities exhibit opposing behaviors in nature. For instance, the relationship between time and speed is inverse.

If x and y are inversely proportionate to each other

=> x ∝ 1/y  

=> xy = k    [ where 'k' is proportionality constant ]

Here we have

The time required to complete a job varies inversely to the number of people working. It took 4 hours for 7 electricians to wire a building.

Let x be the time and y be the number of people

Given that the time required to complete a job varies inversely to the number of people working.  

=> xy = k ---- (1)  [ Since they are inversely proportional to each other ]    

Given that it took 4 hours for 7 electricians to wire a building.  

=> 4(7) = k  

=> k = 28

Substitute k = 28 given number of electricians y = 3 in equation (1)

=> x (3) = 28

=> x = 28/3 = 9 1/3hrs

Therefore,

The time taken by 3 electricians to complete the work is 9 1/3 hours.

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The cost to customer after seven months of service is equal to $171.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

Next, we would set up or write an equation that shows the relationship between the months of service and the total charges as follows;

y - 81 = 18(x - 2)

By making "y" the subject of formula, we have the following:

y = 18x - 36 + 81

y = 18x + 45

After seven (7) months of service, the cost is given by:

y = 18(7) + 45

y = $171.

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Therefore , the solution of the given problem of triangle comes out to be is 22 miles away.

Given its three sides and three vertices, a triangles is a polygon. A fundamental geometric shape, it. Triangle ABC refers to a triangle that has the points A, B, and C as its corners. When four parts are not collinear, a solitary plane and triangle are discovered in geometric shapes. Triangles are known as polygons because of their upper right and three corners. A triangle's three points of intersection are referred to as its corners. By multiplying triple triangle angles, 180 degrees can be obtained.

Here,

The given number indicates that FG is 8 & GH is 14.

FG + GH = FH thanks to the segment addition postulate.

In the equation FG Plus GH = FH, 8 should be used in place of FG and 14 should be used in place of GH.

This results in FH = 8 + 14 => FH = 22.

Therefore, is 22 miles away.

Therefore , the solution of the given problem of triangle comes out to be is 22 miles away.

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The complete question is " Find FH in the given triangle FGH where FG=8,GH=14 and the FH is the equal to sum of FG and GH"

Number of servings Cate can have is given by the equation A = 16 servings

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of servings be represented as A

Now , the equation will be

The number of cups of rice Cate has = 2 cups

The number of cups of servings Cate divides = 1/8 cups

So ,

The number of servings A = number of cups of rice Cate has / number of cups of servings Cate divides

Substituting the values in the equation , we get

The number of servings A = 2 / ( 1/8 )

On simplifying the equation , we get

The number of servings A = 2 x 8

The number of servings A = 16 servings

Therefore , the value of A is 16 servings

Hence , the number of servings is 16 servings

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Mariu buy computer for £915. 00 each and ell them for £2081. 00 each. then the total profit on the ale of 13 computer is £15158.00

What is a simple definition of profit?

the excess of returns over expenditure in a transaction or series of transactions. especially : the excess of the selling price of goods over their cost. 3. : net income usually for a given period of time.

The profit on the sale of 1 computer is the difference between the selling price and the buying price.

Profit on 1 computer:

£2081.00 - £915.00 = £1166.00

The profit on 13 computers is 13 times the profit on 1 computer.

13 × £1166.00 = £15158.00

£15158.00

hence Mariu buy computer for £915. 00 each and ell them for £2081. 00 each.then the total profit on the ale of 13 computer is £15158.00

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Answer:

x=-9ln(1/2)/[ln(4)-ln(1/2)]

Step-by-step explanation:

4^{x}=(1/2)^{x-9}

ln(4^{x})=ln((1/2)^{x-9})

xln(4)=(x-9)ln(1/2)

xln(4)=xln(1/2)-9ln(1/2)

xln(4)-xln(1/2)=-9ln(1/2)

x[ln(4)-ln(1/2)]=-9ln(1/2)

x=-9ln(1/2)/[ln(4)-ln(1/2)]

Step-by-step explanation:

multiply both equations with factors so that the terms of the targeted variable (in our case x) have the same constant factor. and then we can subtract one equation from the other, abd the variable is eliminated in the result.

in our case the least common multiple of 4 and 9 is 36.

so, we multiply equation 1 by 9, and equation 2 by 4, abd then we subtract

36x - 54y = 90

- 36x + 8y = 28

-------------------------

0 -62y = 62

so, x is "eliminated", and we can solve for y : y = -1.

and then we can use one of the original equations to solve for x.

e.g.

9x + 2×-1 = 7

9x - 2 = 7

9x = 9

x = 1

Answer:

First, we'll need to find the LCM (least common multiple) which, in this case, is 36. Now that we know this, we can get 4x and 9x to be 36x and -36x so that they can cancel out. To do this, we have to multiply Equation 1 by 9 and Equation 2 by -4.

9(4x - 6y = 10) is equivilant to 36x - 54y = 90

-4(9x + 2y = 7) is equivilant to -36x - 8y = -28

Now that we have our new system of equations, we can proceed with the process of elimination! The first step is to add the two equations together. This will result in:

-62y = 62 we have successfully eliminated x!

The last step will be to divide both sides by -62

-62y/-62 = 62/-62

y = -1

Answer:

A, B,D

Step-by-step explanation:

Answer: x=-28

Step-by-step explanation:

Answer: -28

Step-by-step explanation:

1.5x+3=-39

      -3    -3

1.5x=-42

__     __

1.5     1.5

x = -28

lines mean divide

Assuming Boden does not add or take out any money, he would have $470.4 in the account after 4​ years.

Mathematically, simple interest can be calculated by using this formula:

S.I = PRT or S.I = A - P

Where:

Substituting the given parameters into the simple interest formula, we have;

S.I = 400 × 4.4/100 × 4

S.I = 400 × 0.044 × 4

S.I = $70.4.

Next, we would calculate the future value as follows;

S.I = A - P

Future value, A = S.I + P

Future value, A = $70.4 + $400

Future value, A = $470.4.

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Answer:

16

Step-by-step explanation:

option c 16 is the answer

Answer:

2/3<85

I hope I help you in this ans and tq.

The 5 exponents are as Zero, Unity, Negative, Fractional and Reciprocal exponent. They are defined by the mathematical properties of the number when it is raised to a certain power.

Understanding these exponents is important for solving mathematical problems, especially in algebra and calculus.

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The measurement 63.42 feet after conversion  is  760.92 inches.

What is conversion of measurement?

By multiplying or dividing a number, a conversion factor can be used to change one set of units to another. If a conversion is required, the right conversion factor to an equivalent value must be applied. The correct conversion factor, for instance, is 12 inches to 1 foot when converting between inches and feet.

Here the given measurement is ,

=> 63.41 feet

To convert feet into inches we need to multiply by 12. Then

=> 63.41 × 12 = 760.92 inches.

Hence the given measurement into inches 760.92 inches.

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Answer:

C

Step-by-step explanation:

The graph passes through [tex](-2,-5)[/tex] but not [tex](2,5)[/tex].

The line is steep, and has a slope of more than 1.