The area of this rectangle is 132 square units.
h = 11
What is the base of the re
angle?

Please help begging u ..

Answer:

Step-by-step explanation:

If the longest side is 6.2 cm, and it is twice the length of the shortest, then we can write an equation as 2x=6.2, where x is the short side length.

Then, since a triangle has 3 sides, the medium side length is 14.5-6.2-x.

Hope that helped,

-sirswagger21

To find the area between the graphs of y = x - 17 and y = -2x + 14 over the interval 1 ≤ x ≤ 19, we need to find the intersection points first.

Setting the two equations equal to each other, we have:

x - 17 = -2x + 14

Simplifying the equation:

3x = 31

x = 31/3

The intersection point occurs at (31/3, (31/3) - 17).

To find the area, we integrate the difference of the two functions over the given interval:

Area = ∫(x - 17) - (-2x + 14) dx

= ∫(3x - 31) dx

Evaluating the integral over the interval 1 to 19 will give us the desired area between the graphs.

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Answer:

13.4 inches

Step-by-step explanation:

Firstly you should calculate the diagonal of lower square using pythahoras theorem

I.e diagonal = (89)^1/2

Now calculate distance by simple arithmetic

X=Xx + Xy

= (89)^1/2 + 4

= 13.4

Answer:

√105 inches

Step-by-step explanation:

The diagonal of the bottom is the hypotenuse of a right triangle with legs measuring 5 and 8.

a² + b² = c²

5² + 8² = c²

c² = 89

c = √89

The path of the spider is the hypotenuse of a right triangle whose legs measure √89 and 4.

a² + b² = c²

(√89)² + 4² = c²

89 + 16 = c²

c² = 105

c = √105

A characteristic of the classical approach to probability include the following: D. probabilities assume outcomes of an experiment are equally likely.

In Science, an experiment is a scientific investigation which typically involves the process of manipulating an independent variable (the cause), in order to determine or measure the dependent variable (the effect).

In Mathematics and statistics, an expected value is sometimes referred to as the long-term mean (average) of a discrete random variable, E(X) and it can be calculated by taking the weighted average of all the outcomes of the discrete random variable with respect to their probabilities.

In this context, we can logically deduce that a characteristic of the classical approach to probability is that most times probabilities assume outcomes (results) of an experiment are equally likely.

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The given information provides a square thin plane lamina with side length 4 cm, which is earthed along three sides.

(i) Deriving expressions for the potential and electric field strength:

Electric Field Strength (E):

E = -∇V, where ∇ represents the gradient operator and V(x, y) = sin(πx/2a)sin(πy/2a).

Now, let's calculate the components of the electric field E using the partial derivatives:

E = -(∂V/∂x)î - (∂V/∂y)ĵ

= -[(πcos(πx/2a))/2a]î - [(πcos(πy/2a))/2a]ĵ

= -(π/2a)cos(πx/2a)î - (π/2a)cos(πy/2a)ĵ.

(ii) Calculating the values at the center of the plate:

Voltage at the center of the square:

V(x, y) = sin(πx/2a)sin(πy/2a)

V(0.02, 0.02) = sin(π/4)sin(π/4) = 0.5V.

Vector E field at the center of the square:

E = -(π/2a)cos(πx/2a)î - (π/2a)cos(πy/2a)ĵ

E(0.02, 0.02) = -(π/2(0.04))cos(π/4)î - (π/2(0.04))cos(π/4)ĵ

= -19.63î - 19.63ĵ V/m.

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Answer:

The first graph represents a slope of 1/4

Step-by-step explanation:

To find the slope, you do rise/run. That would mean, you would need to move 1 unit up and 4 units to the right to get to your next point. First choice shows that slope.

Hope this helps!

Answer:

The first one.

The way I understood it:

m = Rise over Run

Rise: up 1

Run: over 4

1/4=1/4

:-)

I hope it helps!

\(*RosalindCordelia\)

Answer:

The tree was 5 feet when he bought it and it grew one foot every year.

I believe the equation would be h=t+5

Step-by-step explanation:

The answer would be h=t+5 because the height equals the year plus five.

Answer:

$58.50

Step-by-step explanation:

30% of 45 is 13.50 and 13.50 plus 45 is 58.50

Answer:

I think - option c. 54.22kg

Step-by-step explanation:

The linear program is as follows:

T - M ≤ -20,000

P - T ≤ -5,000

N - T ≤ -5,000

S - T ≤ -5,000

G - T - P ≤ 0

L - G ≤ -200

N + S - 2T - 2P ≤ 0

B - P ≤ 0

B - S ≤ 0

B + P ≤ 60,000

L - B - T ≤ 0

Let's define decision variables for each employee's salary as follows:

Let T, P, N, S, G, L, and B represent the salaries of Tom, Peter, Nina, Samir, Gary, Linda, and Bob, respectively.

Our objective is to minimize the salary of the highest paid employee. We can achieve this by introducing another variable, M, that represents the maximum salary among all employees. Therefore, our objective is to minimize M.

Minimize: M

Subject to:

T ≥ 20,000

P ≥ T + 5,000

N ≥ T + 5,000

S ≥ T + 5,000

G ≥ T + P

L ≥ G + 200

N + S ≥ 2(T + P)

B ≥ max(P, S)

B + P ≥ 60,000

L ≤ B + T

Now, we can write the linear program in standard form by moving all variables to the left-hand side of the constraints and adding slack variables:

Minimize: M

Subject to:

T - M ≤ -20,000

P - T ≤ -5,000

N - T ≤ -5,000

S - T ≤ -5,000

G - T - P ≤ 0

L - G ≤ -200

N + S - 2T - 2P ≤ 0

B - P ≤ 0

B - S ≤ 0

B + P ≤ 60,000

L - B - T ≤ 0

All variables are non-negative.

This linear program can be solved using a linear programming solver to find the minimum value of M that satisfies all the constraints. Once we have the optimal solution, we can retrieve the salaries of each employee from the linear program solution.

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Using the law of cosines, the measures of the angles are given as follows:

The law of cosines states that we can find one of the sides or the angle C of a triangle according to the following equation:

c² = a² + b² - 2abcos(C)

In which:

For this problem, the parameters for the triangle are given as follows:

a = b = 12, c = 3.

We want to solve for the smallest angle C, hence:

c² = a² + b² - 2abcos(C)

9 = 288 - 288cos(C)

288cos(C) = 279

cos(C) = 279/288

C = arccos(279/288)

C = 14.36º.

The other two angles are congruent, and the sum of the internal angles of a triangle is of 180º, hence:

14.36 + x + x = 180

2x = 165.64

x = 165.64/2

x = 82.82º.

Then the measures of the angles are given as follows:

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Answer:

14

83

Step-by-step explanation:

i did it on edge

let $p$ and $q$ be the two distinct solutions to the equation$$\frac{4x-12}{x^2 2x-15}=x 2.$$if $p > q$. The value of $p - q$ is 4.

To find the value of $p - q$, we first need to solve the given equation and determine the values of $p$ and $q$.

The equation is:

$$\frac{4x-12}{x^2 - 2x - 15} = x^2.$$

Step 1: Factorize the denominator:

The denominator can be factored as $(x - 5)(x + 3)$.

Step 2: Simplify the equation:

$$\frac{4x-12}{(x - 5)(x + 3)} = x^2.$$

Step 3: Multiply both sides of the equation by $(x - 5)(x + 3)$ to eliminate the denominator:

$$(4x - 12) = x^2(x - 5)(x + 3).$$

Step 4: Expand and rearrange the equation:

$$4x - 12 = x^4 - 2x^3 - 15x^2 + 25x.$$

Step 5: Rearrange the equation and combine like terms:

$$x^4 - 2x^3 - 15x^2 + 21x - 12 = 0.$$

Step 6: Factorize the equation:

$$(x - 3)(x + 1)(x - 2)(x + 2) = 0.$$

From this, we get four possible solutions: $x = 3$, $x = -1$, $x = 2$, and $x = -2$.

However, we are interested in the two distinct solutions $p$ and $q$, where $p > q$. Therefore, the values of $p$ and $q$ are $p = 3$ and $q = -1$.

Finally, we can find the value of $p - q$:

$$p - q = 3 - (-1) = 3 + 1 = 4.$$

Hence, the value of $p - q$ is 4.

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Answer:

A. That he is often blamed for things that are not his fualt.

Step-by-step explanation:

no you dumb

boiiiiiiiiiiii

To prove the relationship between the illumination at two different distances from a lamp, we can use the inverse square law of light propagation. According to this law, the intensity or illumination of light decreases as the distance from the source increases.

The inverse square law states that the intensity of light is inversely proportional to the square of the distance from the source. Mathematically, it can be expressed as:

I1 / I2 = (D2 / D1)^2 where I1 and I2 are the illuminations at distances D1 and D2, respectively. In this case, we are given that the illumination from the lamp at a distance of 1 m is 10 m/m^2 (meters per square meter). Let's assume that the illumination at a distance of 0.5 m is I2.

Using the inverse square law, we can write the equation as:

10 / I2 = (1 / 0.5)^2

Simplifying the equation, we have:

10 / I2 = 4

Cross-multiplying, we get:

I2 = 10 / 4 = 2.5 m/m^2

Therefore, we have proven that the illumination at a point 0.5 m away from the lamp is 2.5 m/m^2, not 40 m/m^2 as stated in the question. It seems there may be an error or inconsistency in the given values.

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Answer:

a or c

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

The rocket better weigh more after it is fueled. So the weight must be 6.1*10^4 after fueling.

6.1 * 10^4 - 4.8*10^4

The easiest way to do this is to take it out of scientific notation.

61000 - 48000 = 13000 kg

If you insist on scientific notation, it is 6.1*10^4 - 4.8*10^4 = 1.3 * 10^4 which makes the answer C

Answer:

49

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

15 is not a prime number, but it is composite.

Daniel's method is incorrect, as the interquartile range is given by the difference between the third quartile and the first quartile.

The interquartile range of a data-set is by the difference of the 75th percentile(Q3) by the 25th percentile(Q1) of the data-set.

The quartiles are described as follows:

From this, we get that the quartiles are related to the median of the set, that is, neither is given by the highest and by the lowest values, hence the interquartile range is given by the difference between the third quartile and the first quartile.

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Answer:

Hypotenuse = 159 ft (nearest integer)

\(\sin(x)=\dfrac{53}{159}\)

\(\cos(x)=\dfrac{150}{159}\)

\(\tan(x)=\dfrac{53}{150}\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}\)

From inspection of the given right triangle:

Substitute these values into Pythagoras Theorem and solve for c (hypotenuse):

\(\implies 53^2+150^2=c^2\)

\(\implies 2809+22500=c^2\)

\(\implies 25309=c^2\)

\(\implies c=\sqrt{25309}\)

\(\implies c=159.0880259...\)

\(\implies c=159\;\; \sf ft\;\;(nearest\;integer)\)

Therefore, the hypotenuse of the given triangle is 159 ft (nearest integer).

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

Trigonometric ratios

\(\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}\)

where:

Given:

Substitute the values into the ratios:

\(\implies \sin(x)=\dfrac{53}{159}\)

\(\implies \cos(x)=\dfrac{150}{159}\)

\(\implies \tan(x)=\dfrac{53}{150}\)

SOHCAHTOA is a mnemonic for the definitions of the trigonometric ratios applicable to right triangles:

(See attachment).

Answer:

niether

Step-by-step explanation:

the answer would be b.

Answer:

The word bisecting is used to describe cutting something into 2 equal slices. That being said, Because we know all the angles are equal (Since we just bisected the other ones we dont know), we can prove that KLM and NLM are congruent.

Answer:

i think its six i haven't done this in a while tho

Step-by-step explanation:

sort them in order from least to greatest and find the middle... i think... that could be medium

Answer:

Step-by-step explanation:

The mean is the average so add them all up and divide the sum by the amount of number there are \(2+9+7+4+6+1=29\) and then divide 29÷6 = 4.8333333333 (3 continued) or 29/6 (fraction) also if that is not the answer round it and it would be 4.8

the third-degree polynomial function with real coefficients, having the zeros 6 + i, 6 - i, and 7, is:

f(x) = (x² - 12x + 37)(x - 7)

To form a third-degree polynomial function with real coefficients such that the complex number 6 + i and the real number 7 are zeros, we can use the fact that complex zeros come in conjugate pairs.

Given that 6 + i is a zero, its conjugate 6 - i will also be a zero. Thus, the zeros of the polynomial are 6 + i, 6 - i, and 7.

To find the polynomial function, we start by forming the factors corresponding to each zero:

(x - (6 + i))   --> This corresponds to the zero 6 + i

(x - (6 - i))   --> This corresponds to the zero 6 - i

(x - 7)        --> This corresponds to the zero 7

To simplify the factors, we multiply them out:

(x - (6 + i))(x - (6 - i))(x - 7)

= ((x - 6) - i)((x - 6) + i)(x - 7)

= ((x - 6)² - i²)(x - 7)

= ((x - 6)² + 1)(x - 7)

Expanding the squared term:

= (x² - 12x + 36 + 1)(x - 7)

= (x² - 12x + 37)(x - 7)

Therefore, the third-degree polynomial function with real coefficients, having the zeros 6 + i, 6 - i, and 7, is:

f(x) = (x² - 12x + 37)(x - 7)

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Answer: 110 yards

Step-by-step explanation:

From the question, the distance from the shovel to the treasure chest is

60 yards while the distance from the treasure chest to the boat is 50 yards. We are to calculate the distance from the boat from the shovel.

The distance from the boat from the shovel will be the addition of the distance from the shovel to the treasure chest which is 60 yards with the distance from the treasure chest to the boat is 50 yards.

= 60 yards + 50 yards

= 110 yards

Given differential equation is y"-9y'+20y=0We can write this equation asy²-9y+20y=0Here, a = 1, b = -9, and c = 20Now, we have to find the roots of this equation.

Now, let us find the value of the discriminant. b²-4ac= (-9)²-4(1)(20)= 81-80= 1Since the value of the discriminant is greater than zero, therefore, we have two real and distinct roots for this equation.Roots are given by the quadratic formula.x= (-b±√(b²-4ac))/2aOn substituting the values of a, b, and c we get,x = (9±√1)/2Now,x1= 5x2= 4/1These roots give two linearly independent solutions as follows: y1=e^5t and y2=e^4tTherefore, the general solution to the differential equation is:y=c1e^5t+c2e^4tWhere c1 and c2 are constants.

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The given differential equation is y"-9y'+20y=0.

Let us use the characteristic equation to solve this differential equation.

The characteristic equation of y"-9y'+20y=0 isr² - 9r + 20 = 0.

Solve for r by factoring the characteristic equation(r - 5)(r - 4) = 0. 

Therefore, r = 5 and r = 4.

Thus, the general solution of the differential equation y"-9y'+20y=0 isy(x) = c₁e⁴x + c₂e⁵x

where c₁, c₂ are constants.

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Answer:

It would cost you approximately R15836.13

Answer:

R = 10 cm

Step-by-step explanation:

The area of a spherical shape is given by :

\(A=4\pi r^2\)

Where

r is the radius of the sphere

ATQ,

One large bubble separates into four small bubbles so that the total area of the small bubbles is equal to the area of the large bubble.

The radius of each small bubble is 5 cm

Using the given condition,

\(4\pi R^2=4\times (4\pi r^2)\\\\R^2=4r^2\\\\R=\sqrt{4r^2} \\\\R=2r\\\\R=2\times 5\\\\R=10\ cm\)

So, the radius of the large bubble is equal to 10 cm.

Answer:

20cm

Step-by-step explanation:

5cm+5cm+5cm+5cm=20cm