The area of triangle ABC is 4√2 m².

Work out the value of x.
Give your answer correct
to 3 significant figures.
Note: Please make sure your final line says x =

Answer:

Wouldn't she have had 5 cats before? Adding 2 other cats would make it 7, which fits the "more than 5 cats" requirement.

Answer: No solution

Distribute the parenthesis

3x-15=2x-10+x

Combine like terms

3x-15=3x-10

This answer has no solution for x.

The value of the function (h-g)(2.1) is -3.51

The equations of the functions are given as:

Let g(x)= 2x^2+3x-9 and h(x)=x^2+2x-6

To calculate or find (h-g)(2.1), we start by calculating h(2.1) and g(2.1)

This is calculated as follows:

g(2.1)= 2(2.1)^2+3(2.1)-9

Evaluate

g(2.1)= 6.12

h(2.1)=(2.1)^2+2(2.1)-6

Evaluate

h(2.1)=2.61

The function is then calculated as:

(h-g)(2.1) = h(2.1) - g(2.1)

This gives

(h-g)(2.1) = 2.61 - 6.12

Evaluate the difference

(h-g)(2.1) = -3.51

Hence, the value of the function (h-g)(2.1) is -3.51

As a breakdown

g(x)= 2x^2+3x-9

h(x)=x^2+2x-6

g(2.1)= 2(2.1)^2+3(2.1)-9

g(2.1)= 6.12

h(2.1)=(2.1)^2+2(2.1)-6

h(2.1)=2.61

(h-g)(2.1) = h(2.1) - g(2.1)

(h-g)(2.1) = 2.61 - 6.12

(h-g)(2.1) = -3.51

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Answer:

15740000 million dollars in profit in year 4

Step-by-step explanation:

Now since you didn't provide the table, im going to have to assume the years are going to be the X while the Y is going to be profit.

Using the equation you provided y=-0.34x^2+4.43x +3.46, we can simply put 4 as our x value (since x represents years) and we would get 15.74. Now you have to remember to convert it into millions to show the profit so 15.74 times 1,000,000 would be 15740000 million dollars

Answer:

Positive

Step-by-step explanation:

5a < 2a

Divide 2 on both sides

5/2a < a

Answer:

336 ways

Step-by-step explanation:

Use nPk which is [tex]\frac{n!}{(n-k)!}[/tex]. This is [tex]\frac{8!}{5!}[/tex]. This becomes 8×7×6 as the 8! and 5! cancel out. 8×7×6 is 336.

Total number of possible 3-topping pizzas are 336 ways.

In more general terms, if we have n items total and want to pick k in a certain order, we get: n! / (n – k)! And this is the permutation formula: The number of ways k items can be ordered from n items: P(n,k) = n (n – k)!

Given that,

Total number of items n = 8

number of picking item k = 3

Now,

p(n,k) = [tex]\frac{n!}{(n -k)!}[/tex]

p(8,5) =  [tex]\frac{8!}{(8 -3)!}[/tex]

         = [tex]\frac{8!}{5!}[/tex]

         = [tex]\frac{8.7.6.5! }{5! }[/tex]

         = 8 × 7 ×6

p(8,5) = 336 ways

Hence, Total number of possible 3-topping pizzas are 336 ways.

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Answer:

B={1,2,3,4,6and12}

n (B) =6

Step-by-step explanation:

Factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12.

Hope it helps!

The board with a length of 4.8 feet would require 5 pounds of pressure to break.

An equation is an expression that shows the relationship between two or more numbers and variables. An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.

Let p represent the pressure and l represent the length.

l ∝ 1/p

l = k/p (k is constant)

When l = 3, p = 8, hence:

3 = k/8

k = 24

For p = 5:

l = k/p = 24/5 = 4.8 feet

The board with a length of 4.8 feet would require 5 pounds of pressure to break.

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Answer:

See attached image.

Step-by-step explanation:

If x=y, the (x,y) = (x,x) or (y,y).  All points have the same x and y values.

Answer:

Step-by-step explanation:

Measure the angle between the lines

It should be 90 degrees,

Answer:

0

Step-by-step explanation:

54m² - 54m² = 0

Water is 0

Considering the equation of the parabola, the coefficients are given as follows: p = 5, q = -20, r = 19.

The graph is the one given at the side of the question.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

In this problem, the turning point is (2,-1), hence h = 2, k = -1, and the equation has the following format:

y = a(x - 2)² - 1

The curve passes through (3,4), that is, when x = 3, y = 4, and we use it to find a.

y = a(x - 2)² - 1

4 = a(3 - 2)² - 1

a = 5.

Hence the equation is:

y = 5(x - 2)² - 1

Placing it into standard form, we have that:

y = 5(x² - 4x + 4) - 1

y = 5x² - 20x + 19

Hence the coefficients are:

p = 5, q = -20, r = 19.

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The length of one edge of the cube exists 6 centimeters.

The lateral surface area of a cube exists

[tex]$A=4 a^{5}$[/tex]

where a stands the length of one edge of a cube.

It exists given that the lateral surface area of the square stands at 144 square centimeters.

Substitute A = 144 in the above formula.

[tex]$144=4 a^{2}[/tex]

Divide both sides by  4.

[tex]$36=a^{2}[/tex]

Taking square root on both sides.

[tex]$\sqrt{36}=\sqrt{a^{2}}[/tex]

6 = a

The length of one edge of the cube exists 6 centimeters.

Therefore, the correct answer is option c. 6 cm.

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Answer:

800÷100 = 8

65×8=520

[tex]\frac{520}{800}[/tex]

another way:

100%-65%=35%

35% = 0.35

800×0.35= 280

800-280=520

another way:

65% = 0.65

0.65×800=520

Hope it helped! :)

A function of random variables utilized to calculate a parameter of distribution exists as an unbiased estimator.

A function of random variables utilized to calculate a parameter of distribution exists as an unbiased estimator.

An unbiased estimator exists in which the difference between the estimator and the population parameter grows smaller as the sample size grows larger. This simply indicates that an unbiased estimator catches the true population value of the parameter on average, this exists because the mean of its sampling distribution exists the truth.

Also, we comprehend that the bias of an estimator (b) that estimates a parameter (p) exists given by; E(b) - p

Therefore, an unbiased estimator exists as an estimator that contains an expected value that exists equivalent to the parameter i.e the value of its bias exists equivalent to zero.

Generally, in statistical analysis, the sample mean exists as an unbiased estimator of the population mean while the sample variance exists as an unbiased estimator of the population variance.

Therefore, the correct answer is an unbiased estimator.

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If a plot of land in the shape of a horizontal ellipse has a pole at each focus. the foci are 16 feet from the center. if the plot of land is 40 feet across one axis, how long is it across the other axis is: c. 24 feet.

Using Pythagoreans theorem formula

a²=b²+c²

Where:

c=16 feet

a=40/2=20 feet

Hence:

20²=b²+16²

b²=20²-16²

b²=400-256

b²=√144

b=12

2b=12×2

2b=24 feet

Therefore if the plot of land is 40 feet across one axis, how long is it across the other axis is: c. 24 feet.

The complete question is are:

A plot of land in the shape of a horizontal ellipse has a pole at each focus. The foci are 16 feet from the center. If the plot of land is 40 feet across one axis, how long is it across the other axis?

a. 34 feet

b. 46 feet

c. 24 feet

d. 30 feet

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Answer:

0.5%

Step-by-step explanation:

Answer:

t = G/(a + h)

t(a + h) = G

a + h = G/t

a = (G/t) - h

t = (G/a) + h

t - h = G/a

a(t - h) = G

a = G/(t - h)

f(x) = 3^x

f(4) = 3^4

f(4) = 3 * 3 * 3 * 3

f(4) = 9 * 9

f(4) = 81

Hope this helps!

The computation shows that the total distance will be 260.52km.

From the information given, it was stated that the race has 78 laps through the town of Monte Carlo and that each lap of the race has a distance of 3.34 km.

Therefore, the total distance will be:

= 78 × 3.34

= 260.52 km

Therefore, the distance is 260.52km.

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Answer:

14 children

Step-by-step explanation:

Half the children like pets and a quarter of the children do not, so another quarter does not have preference. Let x = total number of children, and we would have this equation.

0.25x = 7

x = 28

Since we are asked to give the number of children who like pets, 28/2 = 14 is the answer.

Answer:

(-3,1)

Step-by-step explanation:

9x+8y=-19

7x+9y=-12

I'll assume the question is to find the solution to these equations.  The solution will be the point (x,y) where the two lines intersect.  The intersection is the one point that satisfies both equations (the smae value of (x,y) works in both.

We can either solve matematically of graph to find the intersection.  I'll do both, and hope the answers are identical.

Matematically

Rearrange either equation to isolate one of the variables (either x or y).  I'll take the second and isolate x:

7x+9y=-12

7x = -9y - 12

x = (-9y - 12)/7

Now use this definition of x in the other equation:

9x+8y=-19

9((-9y - 12)/7) + 8y = -19

(-81y - 108)/7 + 8y = -19

-81y - 108 + 56y = - 133

-25y = -25

y = 1

If y = 1, then:

9x+8y=-19

9x+8(1)=-19

9x = -27

x = -3

The solution is (-3,1)

Graphing

Graph both lines and look for the intersection.  The attached graph shows the lines cross at (-3,1).

The solution, bu both approachjes, is (-3,1)

Based on the orbital period of the planet in earth years, and the distance it is rotating, the mass of the star that the planet is orbiting is 3 solar masses.

Because the sun is so heavy, it needed to have a special unit that could adequately reflect this mass.

Solar masses was the term that scientists came up with. In terms of the Earth's mass, a single solar mass means that the body is 333,000 times the mass of the Earth.

When given the orbital period of a planet, and the distance it is orbiting around a sun, you can find the solar mass by the formula:

= Distance planet is rotating³ - Orbital period²

Solving gives:

= 1.2³ / 0.76²

= 2.99

= 3 solar masses

In conclusion the mass of the star is 3 solar masses

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Answer:

3 solar masses

Step-by-step explanation:

just did it and got it right

Answer:

8/15

Step-by-step explanation:

possibilities/ sample size=16 girls/30 "learners"=8/15

Taylor series is [tex]f(x) = ln2 + \sum_{n=1)^{\infty}(-1)^{n-1} \frac{(n-1)!}{n!(9)^{n}(x9)^{2} }[/tex]

To find the Taylor series for f(x) = ln(x) centering at 9, we need to observe the pattern for the first four derivatives of f(x). From there, we can create a general equation for f(n). Starting with f(x), we have

f(x) = ln(x)

[tex]f^{1}(x)= \frac{1}{x} \\f^{2}(x)= -\frac{1}{x^{2} }\\f^{3}(x)= -\frac{2}{x^{3} }\\f^{4}(x)= \frac{-6}{x^{4} }[/tex]

.

.

.

Since we need to have it centered at 9, we must take the value of f(9), and so on.

f(9) = ln(9)

[tex]f^{1}(9)= \frac{1}{9} \\f^{2}(9)= -\frac{1}{9^{2} }\\f^{3}(x)= -\frac{1(2)}{9^{3} }\\f^{4}(x)= \frac{-1(2)(3)}{9^{4} }[/tex]

.

.

.

Following the pattern, we can see that for [tex]f^{n}(x)[/tex],

[tex]f^{n}(x)=(-1)^{n-1}\frac{1.2.3.4.5...........(n-1)}{9^{n} } \\f^{n}(x)=(-1)^{n-1}\frac{(n-1)!}{9^{n}}[/tex]

This applies for n ≥ 1, Expressing f(x) in summation, we have

[tex]\sum_{n=0}^{\infinite} \frac{f^{n}(9) }{n!} (x-9)^{2}[/tex]

Combining ln2 with the rest of series, we have

[tex]f(x) = ln2 + \sum_{n=1)^{\infty}(-1)^{n-1} \frac{(n-1)!}{n!(9)^{n}(x9)^{2} }[/tex]

Taylor series is [tex]f(x) = ln2 + \sum_{n=1)^{\infty}(-1)^{n-1} \frac{(n-1)!}{n!(9)^{n}(x9)^{2} }[/tex]

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The distance the player is from the right post is = 5.1 meters

The Pythagorean theorem states that the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.

Formula for the Pythagorean theorem =

a²= b²+c²

From the diagram given,

The hypotenuse (a) = x²

b= 1.82²

c = 4.8²

x² = 1.82² + 4.8²

x²= 3.3124 + 23.04

x²= 26.3524

a= √26.3524

a= 5.1 meters.

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The identity Sin(α)/Tan(α) = Cos(α) is valid

Trigonometry is study of triangles. All trigonometric ratios are defined using the sides of the right triangle, such as an adjacent side, opposite side, and hypotenuse side. Three major of them are as follows :-

Sine Function:

sin(θ) = Opposite / Hypotenuse

Cosine Function:

cos(θ) = Adjacent / Hypotenuse

Tangent Function:

tan(θ) = Opposite / Adjacent

Lets prove this identity by proceeding with the LHS

= Sin(α)/Tan(α)

= Sin(α)/ (Sin(α)/Cos(α)) (Tan(α) = Sin(α)/Cos(α))

= Sin(α)xCos(α) / Sin(α)

= Cos(α)

Hence verified

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