An animal shelter has 2 cats for every 3 dogs. If there are 45 animals in the shelter, how many dogs are there?

[tex]\displaystyle \boxed{\text{First Attachment, 14}}[/tex]

Answer:

x = 30

y = 60

Step-by-step explanation:

      First, vertical angles are congruent. This helps us fill in more of the angles so we can find x and y.

      Next, supplementary angles add up to 180°, aka a line. We can use this to fill out even more of the diagram given.

      Lastly, corresponding angles on parallel lines are congruent.

      By using the information above, we can decide that x = 30 and y = 60. See the first attachment for all the angle values filled out.

[tex]\displaystyle \boxed{\text{Second Attachment, 12}}[/tex]

Answer:

x = 65

Step-by-step explanation:

      From the above explanation, we will be using vertical angles and supplementary angles to solve this question. See the second attachment.

      We also know there are 180 degrees in a triangle.

      Lastly, we know that alternate interior angles are congruent.

      Using this knowledge, we can decide that x = 65.

[tex]\displaystyle \boxed{\text{Third Attachment, 13}}[/tex]

Answer:

x = 30

Step-by-step explanation:

      Again, we will be using vertical angles, supplementary angles, and corresponding angles to solve this question. See the third attachment.

      After placing vertical angles down from the given information, we can fill in more using corresponding angles.

      Lastly, we know there are 360 degrees in a circle. We can create an equation from this and solve.

      Using this information, we can decide that x = 30.

The relative maxima and relative minima of the function

f(x) = x^5 - 4x^3 + 3x^2 - 8x - 6

The relative minima and maxima is calculated

The procedure is done as follows

x^5 - 4x^3 + 3x^2 - 8x - 6

differentiating gives

5x^4 - 12x^2 + 6x - 8

solving the equation for the critical values are

x₁ = 0.176 + 0.73i

x₂ = 0.176 - 0.73i

x₃ = 1.518

x₄ = -1.871

The second derivative

5x^4 - 12x^2 + 6x - 8

differentiating gives

20x^3 - 24x + 6

substituting x = 1.58

20 * 1.58^3 - 24 * 1.58 + 6

= 46.966 (positive hence minima)

substituting x = -1.871

20 * -1.871^3 - 24 * -1.871 + 6

= -169.9 (negative hence maxima)

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The probability of having at least one dog adopted is 0.6126

It is given that the probability to adopt a dog is 0.1

The adoption of the dog here clearly follows a Binomial distribution

ⁿCₓ  X  pˣ  X  (1 - p)ⁿ⁻ˣ

where,

n = no. os sample

p = probability of success

x = random variable.

Here the success would be the adoption of a dog, We are given here there were 9 visits

Hence,

n = 9

p = 0.1

1 - p = 0.9

we need to find the probability of the adoption of at least one dog

= P(X ≥ 1)

= 1 - P(X = 0)

Hence we get

P(X = 0)

= ⁹C₀  X  0.1⁰  X  0.9⁹

= 0.3874

Hence,

P(X ≥ 1)

= 1 - 0.3874

= 0.6126

Therefore the probability that at least one dog will be adopted is 0.6126

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Step-by-step explanation:

s = 17b

when b  =2:

s = 17b

s = 17(2)

s = 34

when b = 4

s = 17b

s = 17(4)

s = 68

Answer:

A right-angled triangle

Answer:

See below

Step-by-step explanation:

Amount = 100 (1/2)^x

after 3 days

    amount = 100 ( 1/2)^3 = 12.5 gm left

By solving  the equation  x² + 5x - 14 = 0 get the value of x is 2 or -7.

Given,

In the question:

To solve the equation:

x² + 5x - 14 = 0

Now, According to the question:

x² + 5x - 14 = 0

Split the middle term into two terms :

x² - 2x + 7x  - 14 = 0

Factor the first two terms and the last two terms separately

x(x - 2) + 7 (x -2) = 0

Factor out

(x - 2) (x + 7) = 0

Apply Zero Product Property

x - 2 = 0 or x + 7 = 0

x = 2 or x = -7

Hence, By solving  the equation  x² + 5x - 14 = 0 get the value of x is 2 or -7.

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Answer:

the fourth one is the right one

The amount of water after x minutes is equal in both pools.

What is a Linear equation in one variable?

A univariate linear equation is an equation of the form ax + b = 0, where a and b are two integers, x is a variable, and there is only one solution.

For example, 2x+3=8 is a linear equation in one variable.

The given equation is 5000 - 50x = 4800 - 30x.

solving for 'x',

                        5000 - 50x = 4800 - 30x

                        5000 - 4800 = 50x - 30x

                        200 = 20x

                        x = 200/20

                        x = 10

The amount of water after 10 minutes in Pool A will be = 5000 - 50(10)

                                                                                           = 5000 - 500                                                                                                                                              

                                                                                           = 450 liters

The amount of water after 10 minutes in Pool B will be = 4800 - 30(10)

                                                                                           = 4800 - 300                                                                                                                                              

                                                                                           = 450 liters.

Hence, the amount of water will be the same in both pools.

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Answer:

117

Step-by-step explanation:

f(-9)=-9^2-5(-9)-9

f(-9)=81+45-9

f(-9)=126-9

f(-9)=117

hopes this helps please mark brainliest

Step-by-step explanation:

c + 1/2 × a²b = d | - c on both sides

1/2 × a²b = d - c | ×2 on both sides

a²b = 2(d - c) | /b on both sides

a² = (2/b) × (d - c) | sqrt on both sides

a = sqrt(2(d - c)/b)

yes, the given answer is correct.

Answer:

x=-6

Step-by-step explanation:

-18x=108

/-18. /-18

x=-6

Hopes this helps please mark brainliest

Divide both sides by −18.

Divide 108 by −18 to get −6.

Answer:

2:1

Step-by-step explanation:

.5 kg : 250g

the units must be same at both sides

500g : 250g

{as 1 kg = 1000g}

by simplifying both sides

10g : 5g

2g : 1g

2:1

Answer:

Y= -1/3x+11/3

Step-by-step explanation:

Part A: polynomial in Standard form;-

bluef(x) = ax⁴ + bx³ + cx²+ dx + e

Part B: Closure property relates to polynomial;-

The polynomial's closer property for subtraction. When two polynomials of identical degrees with different leading coefficients are subtracted, a polynomial of the same degree is produced.

What is  Polynomial?

A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x.

A.

Any of the following can be the fourth degree polynomial with two terms:

f1(x) = ax⁴ + bx³

f2(x) = ax⁴ + cx²

f3(x) = ax⁴ + dx

f4(x) = ax⁴ + e

a ≠ 0  in all four instances.

Explanation. Because each of the aforementioned polynomials fi(x)-s can be written in the form of f(x) by setting blue0 equal to (c,d,e), (b,d,e), (b,c,e), and (b,c,d), respectively, each of the aforementioned polynomials is in standard form.

B.

The polynomial's closer property for subtraction. When two polynomials of identical degrees with different leading coefficients are subtracted, a polynomial of the same degree is produced.

Example.

Let r(x) be defined as a₁x³ + a₂x² + a₃x + a₄

s(x) is equal to b₁x³ + b₂x² + b₃x + b₄

where a ≠ 0 ≠ b and a ≠ b both belong to a set of real or complex numbers called ai and bi.

If this is how subtraction is defined, then

r(x) - s(x) = [a₁x³ + a₂x² + a₃x + a₄] - [b₁x³ + b₂x² + b₃x + b₄]

r(x) - s(x) = (a₁ - b₁)x³ + (a₂ - b₂)x² + (a₃ - b₃)x + (a₄ - b₄)

Given that (a₁ - b₁) ≠ 0, r(x) - s(x) is similarly a polynomial of fourth degree in this situation.
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Answer:

C) 480

Step-by-step explanation:

[tex]\sf \dfrac{3}{5}*800 = 3 * 160[/tex]

             = 480

Option B is the correct answer, the interval in which the graph of the function is positive is -∞ < x < -1.

What do mean by interval?

In mathematics, a (real) interval is a collection of real numbers that includes all real numbers that fall inside any two of the collection's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 x 1. The set of all real numbers, the set of nonnegative real numbers, the set of positive real numbers, the empty set, and any singleton are additional examples of intervals.

As we can see in the graph provided in the question, the graph of function reach the positive side of the y-axis at x = -1, it means one of the two end point of the interval is going to be -1. And, the graph is constantly and slowing increasing it's value as increase in the x-axis therefore, the other endpoint of the interval cab be considered as negative infinity.

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The proportional relationship that gives the cost of x pounds of rice is given as follows:

y = 3x.

A proportional relationship is a special case of a linear function, with slope represented by k and intercept of 0, hence the output variable y is obtained with the multiplication of the input variable x and the slope k, as follows:

y = kx.

In this problem, the input and the output are given as follows:

You can buy 3 pounds of rice for 9 dollars use, hence the constant representing the cost per pound is given as follows:

k = 9/3 = 3.

Hence the equation is:

y = 3x.

This problem is incomplete but we suppose that it asks for a proportional relationship giving the cost of x pounds of rice.

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Answer:

Find the slope between the points (1,2) and (9,12).

Step-by-step explanation:

If I was going to draw the line of best fit without a calculator, I would draw it including these two points.  Once I had these two points, I would find the slope using these points.

Answer: 1.01% sale tax.

Step-by-step explanation:

First you must take your tax price before and the tax price after and divide them. This gets you 1.01.

To be sure this is your answer you can multiply the 1.01% by 53 and it gives you 53.53$ (If you don't understand I suggest looking at a video from khan academy they explain things much better than I do.)

Hope that helped in some way :)

The cost of 4.5 tonnes of rock is $56.25

Given,

cost of 1 tonne of rock=$12.50

then

to find cost of 4.5 tonnes of rock, multiply 12.50 with 4.5,

cost of 4.5 tonnes of rock = 4.5* 12.50 = $56.25

Thus ,the cost of 4.5 tonnes of rock is $56.25.

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In the expression, 8 + x squared minus 4 x cubed + 5 x + 2 x squared.

2x^2 and x^2 are the like terms

The given expression is 8 + x squared minus 4 x cubed + 5 x + 2 x squared

This is rewritten as

8 + x^2 - 4x^3 + 5x + 2x^2

The terms in the expression are grouped as

constant terms: 8

terms with x variable : 5x

terms with x^2 variables: 2x^2 and x^2

terms with x^3 variables: 4x^3

Like terms refers to terms that are similar either as a constants or have same variables

Hence the like terms in the expression is 2x^2 and x^2

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Using population growth modeling it is concluded that the population of insects after 1 hour will be about 1.05 times.

The method used to calculate the growth and decay of insects or bacteria are called growth and decay modeling.

Let us assume n₀ is the initial population, then the total population n(t) after t time is given by the formula:

n(t) = n₀ [tex]e^{rt}[/tex], where r = the relative rate of growth.

Suppose an initial number of insects is x and after 15 hours it becomes 2x.

2x = x[tex]e^{15r}[/tex]

[tex]e^{15r}[/tex] = 2

Take the log of both sides of the equation

ln [tex]e^{15r}[/tex]= ln 2

15r = ln 2

r = 0.693147/15

Now, population after 1-hour = x [tex]e^{r}[/tex]

= 1.047

≈ 1.05

Hence the population of insects after 1 hour will be about 1.05 times.

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Answer:

I+P=A

Step-by-step explanation:

isolate a on 1 side

I=A—P

+P. +P

I+P=A

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Answer:

A=P+I

Step-by-step explanation:

make A the subject of formula

giving A= P+I

The distance between the x-intercepts of these two line is 10 units.

Given that,

These two lines' x-intercepts are separated by 10 units.

Equation of the line with slope 2 is

y-30/x-40 = 2

For x intercept put y = 0,

then

-30/x-40 =2

x =25

Equation of the line with slope 6 is

y-30/x-40 =6

For x intercept put y = 0,

then

-30/x-40 =6

x =35

Distance between x-intercepts of these two lines is difference of the two intercepts i.e,

D = 35-25 = 10.

Thus, the distance between the x-intercepts of these two line is 10 units.

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Answer:

x=21, m<s=95

Step-by-step explanation:

85+5x-10=180

75+5x=180

5x=105

x=21

m<S= 5(21)-10

m<S= 105-10

m<s=95

24.15 as two significant figures is 24.

All significant figures are those that enhance the overall worth of the number's meaning. Numbers are frequently rounded to avoid repeating quantities that are not significant. When rounding, one must be careful not to lose precision. Sometimes the purpose of rounding numbers is simply to make them simpler.

Use the following guidelines to decide which numbers are important and which are not:

1) A decimal number less than 1 is not affected by the zero to the left of it.

2) The placeholders for all trailing zeros are all insignificant.

3. There should be significance between non-zero numbers.

4) Every non-zero number has meaning.

5) A number is rounded if it has more digits than the necessary number of significant ones. For instance, 432,500 is rounded up to 433,000 to three significant digits using the half-up (regular) method.

6) Zeros at the end of numbers that are not important but are left in because eliminating them would change the number's value. The 000 in 433,000 in the example above cannot be removed without converting the number to scientific notation.

Given the number, 24.15

We have to convert it to two significant figures, so we will consider the only two figures before the decimal point. So, the number up to two significant figures is 24.

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Answer: 60mL per minute

Step-by-step explanation:

300/5=60

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