x² - 10x = 100
Use a trial and improvement method to find this solution.
Give your answer correct to 1 decimal place.
You must show all your working.
Show your working
Answer

Answer: 2x3-1

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]x[/tex] x 25/100=30

25/100[tex]x[/tex]=30

25[tex]x[/tex]=3000

[tex]x[/tex]=300/25

[tex]x[/tex]=120

The final price of the car when Mark sells a car that has been marked up $450 is $2452.50.

From the information, Mark sells a car that has been marked up $450, which was 25% of the buying price.

He also has to charge a 9% sales tax on the selling price of the car. The final price of the car will be:

= Original price + Mark up + Tax

= $1800 + $450 + (9% × $1800 + $450)

= $1800 + $450 + $202.50

= $2452.50

The price is $2452.50.

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she would have four seeds left because 6 seeds times six pots would equal 36 seeds so subtract 36 from forty to get four

Step-by-step explanation:

Answer:4

Step-by-step explanation:6x6=36+4=40

The angle W equal to 24.3

In a triangle sum of three angles is equal to 180

W = (3x-24) degree

C = (4x-11) degree

T = 2x degree

3x-24+4x-11+2x=180

9x-35=180

9x=180-35

9x= 145

x=16.1

substitute the value of x in W equation

W = 3(16.1)-24 = 24.3

The value of angle W is 24.3

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The length of the Hypotenuse is, [tex]\sqrt{5}x[/tex] units.

What is Pythagoras Theorem?

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

Let the one leg of a right triangle is twice as long as the other.

Suppose the shorter leg is x.

So the longer leg is 2x.

Let, the hypotenuse is h.

By Pythagoras Theorem,

[tex]x^2 + (2x)^2 = h^2\\x^2 + 4x^2 = h^2\\5x^2 = h^2\\h = \sqrt{5} x[/tex]

Hence, the hypotenuse as a function of the length of the shorter leg, is [tex]\sqrt{5}x[/tex] units.

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Probability that the arrow will stop on the same letter twice = 1/3 (c).

What is probability?

The area of arithmetic called likelihood deals with numerical representations of the chance that a happening can occur or that an announcement is true.

Main body:

Given : Maria will spin the arrow on the spinner 2 times.

To find : What is the probability that the arrow will stop on the same letter twice.

Solution : We have given a spinner that spin twice and stop on the same letter.

Formula for probability = no. of favourable outcome/ total outcomes

Here, total part of spinner = 3 and it spin two times

So, total possible outcome = 6.  Arrow stay on same letter twice( favorable outcome) =2.

Plugging the values in formula :

Probability =  2/6

Probability =  1/3

Therefore,  probability that the arrow will stop on the same letter twice =  (c).

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Using simple mathematical operations, we know that the lift will carry 1,120 more children than adults in a day.

A mathematical function known as an operation converts zero or more input values into a precisely defined output value.

The quantity of operands affects the operation's arity.

parentheses, exponents, multiplication, division, and PEMDAS.

So, to calculate how many more children the lift carries in a day:

The number of adults the lift can carry is 24.

The number of children the lift can carry is 40.

The lift carries people at full capacity 70 times.

Now, calculate as follows:

24 × 70 = 1,680

40 × 70 = 2,800

Difference:

2,800 - 1,680 = 1,120

Therefore, using simple mathematical operations, we know that the lift will carry 1,120 more children than adults in a day.

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The width of the enlarged photo is 12 inches

The length of the original photo = 10 inches

The width of the original photo = 8 inches

The length of the enlarged photo = 15 inches

The width of the enlarged photo = x

Then the proportion of the length and width of the original and enlarged photo will be

10 / 8 = 15 / x

Cross multiply the terms

10x = 15 × 8

Multiply the terms in the equation
10x = 120

Divide both side of the equation by 10

10x / 10 = 120 / 10

x = 120 / 10

Divide the terms

x = 12 inches

Hence, the width of the enlarged photo is 12 inches

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Answer:

0.9*0.8=0.72

Step-by-step explanation:

there are 9 squares across the top and 8 square downward so the only equation similar to this is the first equation.

Answer: 0.9 x 0.8 = 0.72

Step-by-step explanation:

dark gray is 9 x 8, divide both numbers by 10, you get 0.9 x 0.8 = 0.72

The cost is the cost per pound times the number of pounds minus the coupon.

If [tex]p[/tex] pounds are purchased, she will pay [tex]3.50p-3.25[/tex].

If 3 pounds are purchased, she will pay 3.50(3)-3.25=7.25.

Answer:

12 - D = X

Step-by-step explanation:

Im not REALLY x2 sure but hope its helpful

The value of n is calculated as -14 which was found using the slope formula and given data.

When coordinates are provided, the following formulae can be used to determine a line's slope:

Step 1: Determine the line's coordinates.

Step 2: Enter their values into the equation slope(m) = (y₂-y₁)/(x₂-x₁).

Given: There is a line that contains the points (-9, n) (-10, 5).

We need to find the value of n.

We know that,

slope(m) = (y₂-y₁)/(x₂-x₁)

           -9   = (5-n)/(-10+9)

           -9(-10+9) = 5-n

           90-81 = 5-n

           9+5 = -n

              n = -14

Therefore, the value of n is -14 which was found using the slope formula and given data.

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Five minutes into the descent the airplane has an altitude of 500 feet.

Given that an airplane at 3,000 feet begins to descend at a rate of

500 feet per minute, it is required to write an equation to model the situation and find the altitude of the airplane after 5 minutes.

First, we can model the situation through a linear equation of the form

y = mx + b.

Then, we must identify each variable:

y = A = Altitude

m = decrease per minute = 500

x = t = minute-time

b = Airplane height = 3,000

Now, we set up the equation, substituting y, m, x, and b into the linear equation, as the situation models the descent of the airplane the slope must be negative; thus:

A(t) = 3,000 − 500t

Lastly, we must find the altitude when if t = 5:

A(5) = 3,000 − 500(5)

Solving, we obtain:

A(5)=3,000 − 2,500 = 500

Hence the answer is, Five minutes into the descent the airplane has an altitude of 500 feet.

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The expected population of a city in 4 years is 581,000.

Current population (P) = 528 000.

Rate of growth (r) = 2.4%

Time t = 4 years

Expected population (A) = ?

The formula used is-

A = P(1 + r/100)∧t

Put the values.

A = 528 000(1 + 2.4/100)∧4

A = 528 000 x (1.042)∧4

A = 581,000

Thus, the expected population  of a city in 4 years is 581,000.

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The cost per ticket is $9, the cost of 5 ice cream cones is $14.58 and the cost of 12 bananas is $4.8.

a.

4 movie tickets cost $36.

cost per ticket = 36/4

= $9,

The cost per ticket is $9.

b.

3 ice cream cones cost $8.75.

1 ice cream cost = 8.75/3

= 2.916

5 ice cream cost = 2.916*5

= $14.58.

The cost of 5 ice cream cones is $14.58.

c.

5 bananas cost $2.00.

1 banana cost = 2/5

= 0.4

12 bananas cost = 0.4*12

= $4.8.

The cost of 12 bananas is $4.8.

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Answer: $931

Step-by-step explanation:

Since $980 is 100% of the price and the cash discount is 5% we can calculate the cash price of the portrait like this:

$980 full price* (1 - .05 discount) = $931

Answer:

Step-by-step explanation:

A = 75000(1 + (0.06 × 10)) = 120000

A = $120,000.00

B = 24000(1 + (0.07 × 0.75)) = 25260

B = $25,260.00

B=9 months

Answer:

2:45

Step-by-step explanation:

1 hour has 60 minutes so:

number of hours in 1000minutes:

1000/60=16.6666hours

so 16 hours + 0.6666 hours

convert 0.6666 hours to minutes;

0.6666x60=39.99minutes=40 minutes(rounded)

10:05+16hours+40 minutes

2:05+40minutes=2:45

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Answer:

Answer number 3

y=-9x+5

The minimum measurement is 12.85 and the maximum measurement is 12.94 that would be equal to 12.9.

What is rounding of decimal numbers?

Look at the next digit in the correct position to determine how to round a number; if it is less than 5, round down, and if it is 5 or more, round up. The term "rounding decimals" describes the accurate rounding of decimal figures. To the nearest whole, tenth, or hundredth, we can round decimals.

Given, An ostrich egg has a width of 12.9 cm to the nearest tenth of a centimeter.

We have to find the minimum and maximum possible measurements.

If you're rounding to the nearest tenth of a centimeter, 12.85 centimeters is the smallest measurement that would equal 12.9 centimeters.

And 12.94 centimeters is the maximum measurement that would be equal to 12.9.

Therefore, the minimum measurement is 12.85 and the maximum measurement is 12.94.

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Answer:

[tex]68 = 2 \times 2 \times 17[/tex]

Answer:

First, know that this is a downwards parabola graph.

Answer: x=30 degrees

Step-by-step explanation:

A triangle has 180 degrees, so:

90+x+20+x+10=180

90+2x+30=180

2x+30=90

2x=60

x=30

The claim of invertible metrix is true and others are false.

In the given value we have to check which is true and which is false for the eigenvalues.

The eigenvalues are 2, 2, 5.

(1) First check the matrix is certainly invertible.

The matrix is invertible when the probuct of eigenvalues does not equal to zero.

invertible of A = 2*2*5

invertible of A = 20 which is not equal to zero.

So the matrix is certainly invertible. The claim is true.

(2) Now we check the matrix is certainly diagonalizable.

We note that the eigen value 2 has an algebraic multiplicity of 2 (number of repetitions), but we are unsure if the accompanying eigen vectors likewise have a count of two (geometric multiplicity)

The sum of the algebraic multiplicities must equal the sum of the geometric multiplicities in order for A to be diagonalizable.

In this instance, there is no evidence to support the geometric multiplicity of the eigenvalue 2. Therefore, we are unable to affirm that A is diagonalizable.

Consequently, the claim is false.

(3) Now we check the matrix is certainly not diagonalizable.

If the homogeneous equation from (A-⋋I)x=0 when the eigen value ⋋=2 is substituted x+y+z=0, then the solution set is x=-k-m where y=k, z=m are the parameters.

So it can be written as

[tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =k\left[\begin{array}{ccc}-1\\1\\0\end{array}\right] +m\left[\begin{array}{ccc}-1\\0\\1\end{array}\right][/tex]

Putting k=1 and m=1, then the corresponding eigen vectors for ⋋=2 are [tex]\left[\begin{array}{ccc}-1\\1\\0\end{array}\right],\left[\begin{array}{ccc}-1\\0\\1\end{array}\right][/tex]

So the geometric multiplicity of the eigen value ⋋=2 is 2.

The algebraic multiplicity = Geometric multiplicity we can see the given matrix A is diagonalizable.

So the statement is false.

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Answer:

Y= x+1

Step-by-step explanation:

m=2-1/ 1-0; m=1

Y-2= 1(x-1)

Y= x-1+2

Y= x+1

The total amount that Chau spent on video game and DVD rentals in the past month is $31.70.

Given that Chau rented 5 video games and 4 DVDs and the rental price for each video game was $3.30 while the rental price for each DVD was $3.80.

The Total amount that was spent will be:

= Amount spent on video games + Amount on DVD

= (5 × $3.30) + (4 × $3.80)

= $16.50 + $15.20

= $31.70

The amount is $31.70.

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