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   x  = 4  is the smaller acute angle of that triangle.

What is the Pythagorean theorem in plain ?

Let x be the length of the shorter leg.

By Pythagorean Theorem

( 5x² ) + x²  = 416

25x²  + x²  = 416

  26x²   = 416

    x  = 4

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The complete question is -

One leg of a right triangle is 5 times as long as the other leg, the length of the hypotenuse is the square root of 416, what is the length of each leg?

The maximum distance Frank can travel would be 10 miles.

What is maximum distance?

For maximum distance that is maximum range of a projectile, the angle of projectile should be 45°.

From given question,

taxicabs charge for first mile = $1.00

for each additional mile = $0.30

The cost for the first mile is $1, and for each additional mile it's $0.30, so for 10 miles it would be $1 + 9 * $0.30 = $4.70. Since Frank has only $3.50, he can travel a maximum of 10 miles.

Therefore, The maximum distance Frank can travel would be 10 miles.

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Answer:

4 is the coefficient of x

Equation of the line which passes through the point (-4,5) and the slope of the line is 0 is equal to y = 0x + 5.

As given in the question,

Line passes through the point ( -4 , 5) and the slope of the line is equal to 0.

Standard equation of the line passes through the point ( x₁ , y₁) and slope m is given by :

( y -y₁ ) / ( x - x₁ ) = m

Substitute the given value of the point ( x₁ , y₁)  = ( -4, 5 ) and slope m = 0 in the standard form we get,

( y - 5 ) / ( x - (-4)) =0

⇒ ( y - 5 ) = 0( x +4)

⇒ y = 0x + 5

Therefore, equation of the line which passes through the point (-4,5) and the slope of the line is 0 is equal to y = 0x + 5.

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Answer:

-14

Step-by-step explanation: 12+(-26)=  -14

You add 12 into -26 and get -14.  OR you can subtract -26 by 12 and still get the same answer but adding is faster and easier.  

Answer: Adding and subtracting polynomials are both arithmetic operations used in algebra. The main difference between the two operations is the sign of the terms being combined.

Adding polynomials involves combining like terms by adding their coefficients. When adding polynomials, the terms being added have the same sign. For example, when adding the polynomials x^2 + 2x + 1 and 3x^2 + 4x + 2, we combine the like terms (x^2 terms, x terms, and constant terms) by adding their coefficients:

(x^2 + 2x + 1) + (3x^2 + 4x + 2) = 4x^2 + 6x + 3

Subtracting polynomials involves subtracting one polynomial from another by changing the sign of each term in the polynomial being subtracted and then adding the resulting polynomials. When subtracting polynomials, the terms being subtracted have opposite signs. For example, when subtracting the polynomial 3x^2 + 4x + 2 from the polynomial x^2 + 2x + 1, we first change the sign of each term in the polynomial being subtracted:

(x^2 + 2x + 1) - (3x^2 + 4x + 2) = x^2 + 2x + 1 - 3x^2 - 4x - 2

Then, we combine the like terms by adding their coefficients:

x^2 -  x - 1

In summary, the main difference between adding and subtracting polynomials is that adding involves combining like terms with the same sign, while subtracting involves changing the sign of one polynomial and then adding the resulting polynomials.

Step-by-step explanation:

Answer:

The area is 260.16 square cm.

Formula:

A=πr2

d=2r

A=1

4πd2=1

4·π·18.22≈260.15529

Answer:

Step-by-step explanation:

18+(-4)= 18 - 4 = 14

-5 + (-18) = - 5 - 18 = - 23  

9 + (-18) = 9 - 18 = - 9  

-18 + 18 = 0

An open sentence p(n) over the domain s = {13, 25, 37, 49} such that p(n) is true for half of the integers in s and false for the other half is -

p(n) = {n : n = x², where x = 5,7}.

A set is a clearly defined group of objects. A capital letter is used to name and represent sets. In set theory, the elements of a set can be anything: people, writing of the letters, numbers, shapes, variables, and so on.

For the given question;

A set is given s = {13, 25, 37, 49}.

We have to write this set in the open sentence form/set builder form such that its  true for half of the integers in s and false for the other half.

Thus,

p(n) = {n : n = x², where x = 5,7}.

Its true for 5,7 and false for other values;

For 5 we have 25 value in set S and for 7 we have its square 49 in the set.

Thus, the set in open sentence p(n) = {n : n = x², where x = 5,7}.

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(a) The values of f(0) = 3 and g(2) = 2.

(b) The values of x for which f(x) = g(x) are -2, 2.

(c) The solutions of the equation f(x) = −1 are x = -3, 4.

(d) The interval on which f is decreasing is [0, 4].

(e) The domain and range of f are:

domain = [-4, 4].

range = [-2, 3].

(f) The domain and range of g are:

domain = [-4, 3].

range = [-0.5, 4].

In Mathematics and Geometry, a function is an equation which defines and represents the relationship that exist between two or more variables.

Part a.

By critically observing the graph of f(x) and g(x) shown in the image attached below, the corresponding output values are as follows:

f(0) = 3.

g(2) = 2.

Part b.

The values of x for which f(x) is equal to g(x) are x = -2 and x = 2;

f(-2) = g(-2) = 1.

f(2) = g(2) = 2.

Part c.

The estimated solutions of the equation f(x) = −1 are as follows;

f(-3) = -1

f(4) = -1

Therefore, x = -3, 4.

Part d.

The function f(x) is decreasing over this interval [0, 4].

Part e.

By critically observing the graph of f(x) shown in the image attached below, we can logically deduce the following domain and range:

domain = [-4, 4].

range = [-2, 3].

Part f.

By critically observing the graph of g(x) shown in the image attached below, we can logically deduce the following domain and range:

domain = [-4, 3].

range = [-0.5, 4].

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The expression which is equivalent to -10 is the option b, -3 - 7.

Explanation:

We can use subtraction and addition of integers to get the value of the given expression. We can write the given expression as;

-3 - 7 = -10 (-3 - 7)

The addition of two negative integers will always give a negative integer. When we subtract a larger negative integer from a smaller negative integer, we will get a negative integer.

If we add -3 and -7 we will get -10. This makes the option b the correct answer.

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This scenario describes a foodborne illness outbreak investigation, where several individuals with similar symptoms of food poisoning have been identified and traced back to a nearby restaurant.

In this situation, the local hospital has encountered multiple cases of individuals exhibiting symptoms consistent with food poisoning. Through interviews, it is discovered that all of them have recently dined at a nearby restaurant, indicating a potential common source of exposure. To further investigate and identify the cause of the illness outbreak, samples from the restaurant's food are collected.

These samples will undergo laboratory testing to check for the presence of pathogens, such as bacteria or viruses, that may be responsible for the foodborne illness. By analyzing the test results, health authorities can pinpoint the specific pathogen and take appropriate measures to prevent further spread and ensure the safety of the community.

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The first four nonzero terms in the series expansion about x = 0 for a solution to the given equation 25x^2y + 15x^2y + By = 0 are y(x) = a₀ + a₂x^2 + a₄x^4 + a₆x^6 = a₀ - (5B/42)x^4 + (25B/112) x^6 - (245B/1728) x^8.

Using the method of Frobenius and the larger indicial root, the first four nonzero terms for the series expansion about x = 0 for a solution to the equation 25x²y + 15x²y + By = 0 are y(x) = a[1 - (3/7)x² + (15/11)x⁴ + O(x⁶)].

For the equation 16x³y'' + 4x²y + 3y = 0, the coefficients a₀, a₁, and a₂ are 1, 0, and -15/224, respectively, and the first four terms for the solution to the differential equation are y(x) = a₀[1 - (3/16)x² + (15/512)x⁴ + O(x⁶)].

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Answer:

it will be 5.04

Step-by-step explanation:

so we know 56=100%

so we want to get what 1% is so we divide both sides by 100 to get 0.56=1%

so know we multiply both sides of 9 to get 5.04=9%

Answer:

=81.64yd

Step-by-step explanation:

c=3.14d

c=(3.14)*(13+13)

=81.64yd

Answer:

4x10 8x5

Step-by-step explanation:

The value changes from 5/4 to 3/8 , then the percent of change from 5/4 to 3/8 is a 60% increase. So, the value change from 5/4 to 3/8 increases in percentage.

To determine whether the percent of change is an increase or a decrease, you need to calculate the difference between the old value and the new value as a percentage of the old value.

The old value is 5/4 and the new value is 3/8. To calculate the difference, you subtract the new value from the old value: 5/4 - 3/8 = 5/4 - 3/8 = 15/32.

Next, you need to express the difference as a percentage of the old value. To do this, you divide the difference by the old value and multiply by 100%. That gives you (15/32) / (5/4) * 100% = 60%.

Since the result is a positive percentage, it means that the percent of change is an increase. So, the percent of change from 5/4 to 3/8 is a 60% increase.

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Answer:

117

Step-by-step explanation:

b1+b2÷2×h is the formula.

Just fill in the formula with the numbers you have.

12+14=26

26÷2=13

13×9=117

The probability that only one bus will arrive within a thirty-minute period is 0.0337

We can model the arrival of shuttle buses as a Poisson process with a rate of λ= 10 buses per hour. Since we want to find the probability of only one bus arriving within a 30-minute period, we need to calculate the Poisson probability mass function for  λ = 5 (since 30 minutes is half an hour):

P(X=k) =  ( λ^k × e^- λ ) / k!

where X is the number of shuttle buses arriving within the 30-minute period

k is the number of buses, which in this case is 1.

Substituting the values, we get:

P(X = 1) = ( 5^1 × e^-5 ) / 1!

≈ 0.0337

Therefore, the probability is 0.0337

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Answer:

The y-intercept is (0,-6), but the way they want it written the answer is y intercept= -6

Step-by-step explanation:

The snail will take approximately 0.43 hours or 25.8 minutes to travel 12 feet at the speed of 8.5 meters per hour.

Given, A snail moves at a speed of 8.5 meters per hour, 1m = 3.28ft. Let's convert meters per hour into feet per hour by multiplying it with 3.28ft/m. So, 8.5 meters per hour = 8.5 × 3.28 feet per hour ≈ 27.88 feet per hour.

Now, to calculate the time taken by a snail to travel 12 feet, we can use the formula: Time = Distance ÷ Speed

Time taken = 12 feet ÷ 27.88 feet per hour ≈ 0.43 hours (rounded to two decimal places)

Now, let's convert 0.43 hours to minutes by multiplying it with 60 minutes per hour: 0.43 hours × 60 minutes per hour ≈ 25.8 minutes (rounded to one decimal place). Therefore, it will take approximately 0.43 hours or 25.8 minutes for the snail to travel 12 feet at the speed of 8.5 meters per hour.

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A monomial is an algebraic expression that consists of a single term. A monomial can contain constants and/or variables, which are multiplied together.

The expression 3x²y is a monomial. It contains the constant 3, the variable x squared, and the variable y. The variables can be raised to an exponent, as in this example; however, the exponent must be a whole number.A monomial can also contain coefficients, which are the numbers that are multiplied with a variable. In the example above, the coefficient is 3. If there is no coefficient stated, then the coefficient is assumed to be 1. Therefore, the expression x²y is also a monomial, with the coefficient being 1.Additionally, a monomial can contain a product of numbers and variables, such as the expression 2xyz. This is also considered a single term, since all of the numbers and variables are multiplied together.

Monomials can be used to calculate polynomials, which are algebraic expressions consisting of multiple terms. By adding, subtracting, and multiplying monomials together, you can create a polynomial. For example, the expression (3x²y) + (2xyz) is a polynomial, since it consists of two terms. The first term is the monomial 3x²y, and the second term is the monomial 2xyz.

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Answer:

In 10 weeks he saved: 87.8-37.8= $50

so each week he saves 50/10= $5  

Step-by-step explanation:

So every week he earns 5*100 / 20= $25

Answer:

4(x - 2 + y) = 4x - 8 + 4y

Step-by-step explanation:

The expression 4(x - 2 + y) is equal to 4 times the sum of x - 2 and y. This can be simplified to:

4(x - 2 + y) = 4x - 8 + 4y

Answer:

8n - 3.9

Step-by-step explanation:

Given

- (- 8n + 3.9 ) ← multiply each term in the parenthesis by - 1

= 8n - 3.9

Answer:

30 sq units

3 + 2 = 5

5 x 6 = 30

Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

Write an algebraic expression for: seven added to five times a number

Answer:

7 + 5x