In parallelogram EFGH EJ =5x-3 and JG = 3x +9
What is EG?

Answer:

Step-by-step explanation:

diagonal  = 32 cm

Area of square = \(\dfrac{d^{2}}{2}\)

                        \(=\dfrac{32*32}{2}\\\\=512 \ cm^{2}\)

Diagonal separate the square into two equal triangles.

Area of upper triangle that is shaded black = area of lower triangle = 512/2

= 256 cm²

Isosceles triangle:

a = 6 cm  ; b = 6 cm c = 8cm

\(s = \dfrac{a+b+c}{2}\\\\=\dfrac{6+6+8}{2}\\\\=\dfrac{20}{2}\\\\=10\\\\s-a = 10 - 6 = 4 \ cm\\\\s-b = 10-6 = 4 \ cm\\\\c - c = 10 - 8 = 2 \ cm\\\\Area = \sqrt{s*(s-a)(s-b)(s-c)}\\\\=\sqrt{10*4*4*2}\\\\=\sqrt{2 * 2 * 4 * 4 * 5}\\\\=4*2\sqrt{5}\\\\=8\sqrt{5}\\\\=8*2.24\\\\=17.92 \ cm^{2}\)

Area of black shade paper = 256 + 17.92 =  273.92 cm²

Area of white shade paper = 256 cm²

Area of the isosceles triangle = s(s-a)(s-b)(s-c)

The results of the calculations are approximately 7.07 and 3.74, respectively, to the correct number of significant figures.

Performing the calculation:

(10.52)(0.6721) = 7.0671992

Rounding to the correct number of significant figures, we have:

(10.52)(0.6721) ≈ 7.07

Next, let's calculate (19.09 - 15.347):

(19.09 - 15.347) = 3.743

Rounding to the correct number of significant figures, we have:

(19.09 - 15.347) ≈ 3.74

Therefore, the results of the calculations are approximately 7.07 and 3.74, respectively, to the correct number of significant figures.

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Answer:21.50 dollars

Step-by-step explanation:

The customer pays an amount of $26.74 for one pair of binoculars and one bird guide after the mark-up and 8.5% sales tax

The percentage is defined as a ratio expressed as a fraction of 100.

According to the given, the required solution would be as:

Mark up for binoculars = 10 x 1.45 = 14.50

14.5 x 1.085 = 15.7325 in sales tax

The total cost per binocular is $15.73 ($).

Bird Guide Commission = 7 x 1.45 = 10.15

10.15 x 1.085 = 11.01275 Sales Tax

The total cost per Bird Guide is $11.11 ($).

The addition provides one of each.

⇒ 15.73 + 11.01 = 26.74

Thus, the customer pays an amount of $26.74 for one pair of binoculars and one bird guide after the mark-up and 8.5% sales tax

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Answer:

Step-by-step explanation:

Given That,

Earth's mass is 6 × 10^24 kg.

Mass of the Sun = 330,000 times the mass of Earth.

I also present this data as scientific notation.

Mass of the Sun = 3.3 × 10^5 times the mass of the Earth.

From the data and conditions,

Mass of the Sun

\(= 3.3 \times 10^5 \times (6 \times 10^{24} kg)\\\\ = 19.8 \times 10^{29} kg \\\\= 1.98 \times 10 ^{30} kg.\)

The Sun's mass is said to be 330,000 larger than Earth; This in scientific notation represents:

330 * 10³ times.

The mass of the earth is known to be equal to:

6 * 10²⁴ kg

Knowing this, then the mass of the sun is equal to:

Mass of the Sun = 330 * 10³ * mass of the Earth

Mass of the Sun = 330 * 10³ * 6 * 10²⁴ kg

Mass of the Sun = 1.98 * 10³⁰ kg

Answer: 1/5

Step-by-step explanation:

So we have a total of 15 pens and 3 of those pens we know are red. The probability of randomly selecting a red pen would be 3/15 or simplified 1/5

Answer:

1/5

Step-by-step explanation:

** numbers of chances you can pick/total chances of that you can pick anything

--> # of chances you can pick red pens, in this case, is 3, since there are only 3 red pens -->3/total

--> in this case total should be every numbers of pens added --> 3+8+4 = 15

--> 3/15 -->simplify: 1/5

The rule of inference being used here is Modus Tollens. Modus Tollens is a valid deductive argument form that states if a conditional statement "If P, then Q" is true and the consequent Q is false, then the antecedent P must also be false.

In the given scenario, the conditional statement is "If the guard dog doesn't know a person, then it barks."

The observation that the dog didn't bark (Q is false) leads to the conclusion that the dog must have known the person (the antecedent P is false).

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Answer:

This is an obtuse scalene triangle with the length of E measuring around 749 cm.

<D = 54.754° ≈ 55°

<E = 114°

<F = 11.246° ≈ 11°

Side D = 670 cm

Side E = 749.46937 cm ≈ 749 cm

Side F = 160 cm

Explanation:

When given two sides, and an angle, we can use trigonometry to find the missing angles, and sides.

Given the triangle ∆DEF with side D measuring 670 cm, side F measuring 160 cm, and angle E measuring 117°, we can apply the law of sines to identify the missing information. A & a chronologically refers to the first angle, and side. B & b chronologically refers to the second angle, and side. And C & c chronologically refers to the third angle, and side.

a / Sin (A) = b / Sin (B) = c / Sin (C)

[side 1]. [side 2]. [side 3].

↓ ↓ ↓

sideD/sin(<D) SideE/sin(<E) SideF/sin(<F)

______________________________

670cm / Sin(D) = E cm / Sin(114) = 160 / sin(F).

Since we are only given two sides with an angle measure, we can refer to the law of cosines to figure this one out.

It states that A = arccos(b²+c²-a²/2bc) → cos(A) = b²+c²-a²/2bc

B = arccos(a²+c²-b²/2ac) → cos(B) = a²+c²-b²/2ac

and C = arccos(a²+b²-c²/2ab) → cos(C) = a²+b²-c²/2ab

capital A, B, and C are angles A, B, and C.

lowercase a, b, and c are sides a, b, and c.

Therefore c² = a² + b² − 2ab cos(C),

b² = a² + c² - 2ac cos (B), and a² = b²+c² - 2bc.

SOH CAH TOA.

Since we know this, we can solve for pretty much everything as long as we are given at least 3 variables. Chronologically, because we are solving for side e, we must use b² = a² + c² - 2ac cos (B), because the rest are only variables we are given, making it easy to solve. So b² = 670² + 160² - 2(670 × 160) × cos(114°) = 561704.3362754.

Now take the square root of that to get b by itself, so √561704.3362754.... = 749.4693698046.... ≈ 749

Answer:749

Step-by-step explanation:

S.A.S law or Cosines

e=561704.33628= 749.469= 749

Answer: um i think 300

Step-by-step explanation:

Answer: 160

Step-by-step explanation:

first workout the multiplication sums [22 x 28 = 616]

[18 x 28 = 505] then add 2 numbers together [616 + 505 = 1120]

then divide the answer by 2 [1160 / 2 = 160

The girl had (15x) / 2 pennies, where "x" represents the number of dimes in a single stack.

We have,

The girl has 15 stacks of dimes.

There were half as many pennies.

To find the number of pennies, we can start by determining the number of dimes.

Since there are 15 stacks of dimes, we know that there are 15 times the number of dimes in a single stack.

Next,

We are told that there were half as many pennies as there were dimes.

So, to find the number of pennies, we need to divide the number of dimes by 2.

Let's say the number of dimes in a single stack is "x."

Then, the total number of dimes is 15x.

And since there are half as many pennies, the number of pennies would be (15x) / 2.

Thus,

The girl had (15x) / 2 pennies, where "x" represents the number of dimes in a single stack.

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The scale factor of the hen is equal to 3 centimeters / 8 centimeters.

In this question we find an application of scales, a resource to represent figures at affordable size. We have the case of reduction scale, whose formula is shown below:

r = d / D

Where:

If we know that d = 6 cm and D = 16 cm, then the scale factor of the hen is:

r = 6 cm / 16 cm

r = 3 cm / 8 cm

The statement is incomplete, complete form is shown below:

Jaylynn draws a hen on graph paper using 6 centimeter scale. The hen has a heigth of 16 centimeters. Find the scale factor.

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9514 1404 393

Answer:

  see attached

Step-by-step explanation:

Starting with the original function, swap the variables x and y, then solve for y. The resulting function is the inverse of the original function.

Answer: The person that answered at the top is a legend!! The picture below is just proof that he/she is right!! :)

Given that f is a continuous function on R, f(x) > 0 for all x, and \(f(x)^{2}\) = 2f for all x ≥ 0, we need to show that f(x) = x for all x ≥ 0.

Let's assume that there exists a value a ≥ 0 for which f(a) ≠ a. Since f(x) is continuous, the Intermediate Value Theorem can be applied. Consider the function g(x) = f(x) - x. Since g(a) ≠ 0, either g(a) > 0 or g(a) < 0.

If g(a) > 0, it implies that f(a) - a > 0, which leads to f(a) > a. But this contradicts the given condition that f(x) > 0 for all x. Hence, g(a) cannot be greater than 0.

Similarly, if g(a) < 0, it implies that f(a) - a < 0, which leads to f(a) < a. Again, this contradicts the given condition that f(x) > 0 for all x. Therefore, g(a) cannot be less than 0.

Since g(a) cannot be greater than 0 or less than 0, the only possibility is that g(a) = 0, which implies f(a) = a. This holds true for all a ≥ 0. Hence, we can conclude that f(x) = x for all x ≥ 0.

Therefore, based on the given conditions, we have shown that f(x) = x for all x ≥ 0.

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Answer:

8 packages of pasta and 8 jar of sauce which is $32 dollars and 20lbs in total

Step-by-step explanation:

8 pack of pasta is 8$ and 8lbs

8 jars of sauce is 24$ and 12lbs

8 plus 12 is 20 which is the max of lbs Tyler can carry.

Answer:

the answer is

Step-by-step explanation:

....

Answer:l

Step-by-step explanation:

what is even numbers and

Answer:

m angle A = 68deg

Step-by-step explanation:

Since they're complementary, they add up to 90deg

you solve this by first finding x

(4x-28) + (x-2) = 90 >> add the left side

5x-30 = 90              >> add 30 from both sides

5x = 120                    >> divide by 5 on both side to get x alone

x = 24

now you know x is 24, you substitute it in m<A since you're finding the measure of it

(4(24) - 28)

96 - 28

68

you can check by finding the value of m<B (22deg) and adding it to m<A and it will equal to 90deg

The measure of ∠A = 68°.

We have two angles ∠A and ∠B which are complementary of each other.

We have to find the measure of ∠A.

Two angles are said to be complementary if their sum is equal to 90°.

Mathematically -   x + y = 90°

According to the question -

∠A = (4x – 28)°

∠B = (x - 2)°

Now, ∠A and ∠B are Complementary angles. Therefore -

∠A + ∠B = 90°

(4x - 28) + (x - 2) = 90

5x - 30 = 90

5x = 120

x = 24

Therefore →

∠A = (4x – 28)° = (4 x 24 – 28)° = 68°

Hence, the measure of ∠A = 68°.

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Answer:

b

Step-by-step explanation:

Answer:

120.7

Step-by-step explanation:

14.2 x 8.5 = 120.7

Hope that helps!

Answer: 120.7

Step-by-step explanation:  

Answer:

Angle AOB and angle DOC are identical because they share 2 parallels considering it is a bisection

Step-by-step explanation:

Answer:

3( x + 2 ). = 5( x - 2)

3x + 6 = 5x - 10

-2x = - 16

minus,minus cancel

x = 16/2

x = 8

Answer:

8

Step-by-step explanation:

3x+6=5x-10

6=2x-10

2x=16

x=8

The Fourier transform of the function f(t) is given by; F(ω) = ∫∞−∞ f(t) e−jωtdt`   .

Where ω is frequency. Applying the definition of Fourier transform, we get,`F(ω) = ∫∞−∞ f(t) e−jωtdt`              `= ∫∞1 e−t/4 e−jωtdt + ∫1−∞ 0 e−jωtdt`               `= ∫∞1 e−t/4 e−jωtdt`Let's solve the above integral by parts.       `I = ∫∞1 e−t/4 e−jωtdt`         `= e−t/4 (-jω + 1/4) / (jω) | ∞1 − ∫∞1 (−1/4) e−t/4 / (jω) dt`Now,     `e−t/4 (-jω + 1/4) / (jω)` will become zero as t tends to infinity.Therefore,              `I = −(1/4) ∫∞1 e−t/4 / (jω) dt`                 `= (1/4jω) [ e−t/4 ]∞1`                 `= (1/4jω) [0 − e−1/4 ]`Thus, the Fourier transform of the given function is given by     `F(ω) = ∫∞−∞ f(t) e−jωtdt`        `= ∫∞1 e−t/4 e−jωtdt`        `= −(1/4) ∫∞1 e−t/4 / (jω) dt`        `= (1/4jω) [0 − e−1/4 ]`       `= e−1/4 / (4jω)`

Therefore, the Fourier transform of the function is `e−1/4 / (4jω)`.Summary: The Fourier transform of the given function f(t) is `e−1/4 / (4jω)`.

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The correct answer is 200 feet.

To find the width of the sports field, we need to determine the x-coordinate values where the height (y-coordinate) of the field is equal to zero. The given function for the sports field's turf is:

f(x) = -0.00025(x - 100)^2 + 2.5

We will now set f(x) equal to 0 and solve for x:

0 = -0.00025(x - 100)^2 + 2.5

First, let's move the 2.5 to the other side of the equation:

0.00025(x - 100)^2 = 2.5

Next, divide by 0.00025:

(x - 100)^2 = 2.5 / 0.00025 = 10,000

Now, take the square root of both sides:

x - 100 = ±√10,000 = ±100

Finally, solve for x:

x = 100 ± 100

There are two x values: 100 - 100 = 0 and 100 + 100 = 200. These are the leftmost and rightmost edges of the field, respectively.

So, the width of the field is the difference between the rightmost and leftmost edges:

Width = 200 - 0 = 200 feet

Thus, the correct answer is 200 feet.

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the criteria used when deciding upon the inclusion of a variable are A - Theory, B - t-statistic, C - Bias, and D - Adjusted R^2.

When deciding upon the inclusion of a variable, the following criteria are commonly used:

A - Theory: Theoretical justification is often considered to include a variable in a model. It involves assessing whether the variable is relevant and aligns with the underlying theory or conceptual framework.

B - t-statistic: The t-statistic is used to determine the statistical significance of a variable. A variable with a significant t-statistic suggests that it has a meaningful relationship with the dependent variable and may be included in the model.

C - Bias: Bias refers to the presence of systematic errors in the estimation of model parameters. It is important to consider the potential bias introduced by including or excluding a variable and assess whether it aligns with the research objectives.

D - Adjusted R^2: Adjusted R^2 is a measure of the goodness of fit of a regression model. It considers the trade-off between the number of variables included and the overall fit of the model. Adjusted R^2 helps in assessing whether the inclusion of a variable improves the model's explanatory power.

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Answer:

10

Step-by-step explanation:

Equation : 3x + 2 = 32

3x=30

x=10

\(perimeter = 2(3 \frac{1}{10}) + 2 (\frac{3}{4}) \)

\(perimeter = \frac{31}{5} + \frac{3}{2} \)

\(perimeter = \frac{62}{10} + \frac{15}{10} \)

\(perimeter = \frac{77}{10} \)

\(perimeter = 7 \frac{7}{10} \)

The unit is just cm.

//

I might not be right. Double check to make sure. Hope that gives you a general idea of how to do it.

Answer:

Perimeter of rectangle =2(l+b)

=2(3*1/10+3/4)

=2(3/10+3/4) (lcm=40)

=2(12/40+30/40)

=2(42/40)

=42/20

= 21/10

=21/10 cm

Answer:

the answer is 150 days

Step-by-step explanation:

that is the answer