Jean has 11 trees in her yard and Anita has 8. Write the ratio of trees in Anita's yard to trees in Jean's yard

Answer:

the answer to your question is the slope is 60

The dimensions of triangle ΔDEF can be obtained from ΔABC by applying a scale factor of dilation of \(\displaystyle \frac{1}{2}\).

Reasons:

The given vertices of the triangles are;

ΔABC: A(1, 5), B(3, 9), C(5, 3)

ΔDEF: D(-3, 3), E(-2, 5), and F(-1, 2)

The lengths of the sides of ΔABC are

AB = √((1 - 3)² + (5 - 9)²) = √20 = 2·√5

BC = √((5 - 3)² + (3 - 9)²) = √40 = 2·√10

AC = √((1 - 5)² + (5 - 3)²) = √20 = 2·√10

The lengths of the sides of ΔDEF are;

DE = √((-3 - (-2))² + (3 - 5)²) = √5

EF = FE = √((-1 - (-2))² + (2 - 5)²) = √10

DF = √((-3 - (-1))² + (3 - 2)²) = √5

Therefore;

\(\displaystyle The \ dilation \ that \ gives \ \Delta ABC = \frac{\overline {EF}}{\overline {BC}} = \frac{\overline {DE}}{\overline {AB}} = \frac{\overline {DF}}{\overline {AC}} = \frac{\sqrt{10} }{2\cdot \sqrt{10} } = \frac{1}{2}\)

The ratio of the sides of ΔABC to the corresponding sides of ΔDEF are equal to \(\displaystyle \frac{1}{2}\).

Which gives;

ΔDEF is a dilation of ΔABC, and ΔDEF and ΔABC are similar by the

definition of similarity in terms of a dilation.

Learn more here:

https://brainly.com/question/14380197

Answer:

Step-by-step explanation:

They are congruent by the definition of congruence in terms of rigid motions.

Answer:

25.5 = c

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

17^2 + 19 ^2 = c^2

289+361 = c^2

650 = c^2

Take the square root of each side

sqrt(650) = sqrt(c^2)

25.49509757=c

To the nearest tenth

25.5 = c

Answer:

C = 25.5

Step-by-step explanation:

17² + 19² = x²

289 + 361 = x

289 + 361 = 650

√650 = 25.495097567963924150141120545114

25.495097567963924150141120545114 ≅ 25.5

Answer: answer is a

Step-by-step explanation:

The positive value of x is 6

An index, or power, is the small floating number that appears after a number or letter.

For example, x⁵ is an exponent expression. 5 is the index or power and x is the base. There are some rules that guides Indices.

25^(2x) = 5^(x²-12)

= 5^(4x) = 5^(x²-12

4x = x²-12

x²-4x -12 = 0

x² -6x +2x -12 = 0

(x²-6x) (2x-12) = 0

x( x-6) 2( x-6) = 0

(x+2)(x-6) = 0

x+2 = 0 or x-6 = 0

x = -2 or +6

therefore the positive value of x is 6

learn more about Indices from

https://brainly.com/question/10339517

#SPJ1

The expression b²/b⁻⁷ when simplified with a positive exponent only will become b⁹.

To simplify the expression b²/b⁻⁷, we can use the rules of exponents. The rules of exponents, also known as laws of exponents, are a set of mathematical rules that govern the manipulation of exponential expressions. These rules are essential in simplifying and solving various mathematical problems involving exponents.

Quotient rule of exponent states that when dividing two exponential expressions with the same base, we subtract their exponents, such that:

xᵃ / xᵇ = xᵃ⁻ᵇ.

In this case, we can simplify the expression b²/b⁻⁷ as follows:

b²/b⁻⁷ = b²⁻⁽⁻⁷⁾ = b⁹.

So, the simplified expression is b⁹. This answer is written with a positive exponent only, as requested.

Learn more about rules of exponents here: https://brainly.com/question/11975096.

#SPJ11

Given function:\(f(x) = 3x³ - 3x² - 11x - 1\) We have to find the value of x for which f(x) has a tangent line of slope -3.Tangent to a curve at point P(x₁,y₁) is given by the equation,\(y - y₁ = m(x - x₁)\) where m is the slope of the tangent line.the value of x for which f(x) has a tangent line of slope -3 are\(x = 1 and x = -8/3.\)

So, we have to find the value of x for which the slope\(m = -3, i.e.,f '(x) = 9x² - 6x - 11 = -3\) Let's solve for x using the quadratic formula.\(9x² - 6x - 8 = 0\) Dividing throughout by

\(3,3x² - 2x - 8/3 = 0\)

Using the quadratic formula,\(x = [-(-2) ± √((-2)² - 4(3)(-8/3))]/(2)(3)x = [2 ± 10/3]/6x = 1 or -8/3\)

\(For x = 1,f(x) = 3(1)³ - 3(1)² - 11(1) - 1 = -12For x = -8/3,f(x) = 3(-8/3)³ - 3(-8/3)² - 11(-8/3) - 1 = -14.81\)

To know more about tangent visit:

https://brainly.com/question/27021216

#SPJ11

Answer:

C. He uses the coffers of the ceiling to place Jesus in the mathematical center, and to create an illusion that extends the room beyond what is visible.

Step-by-step explanation:

See attached. We can see that this option is the best as it reflects what we can see in the painting.

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

c

Step-by-step explanation:

Excluding operation of division of nonzero rationals, all other binary operations i.e., subtraction of integers, function composition of polynomials with real coefficients, and multiplication of 2 X 2 matrices with integer entries are all associative.

Thus, option (a), (c), and (d) are associative while option (b) is not associative binary operation.

We have to find out which of the following binary operations are associative.

(a) Subtraction of integers

(b) Division of nonzero rationals

(c) Function composition of polynomials with real coefficients

(d) Multiplication of 2 X 2 matrices with integer entries

Firstly, let us understand what do we mean by the associative property of binary operations. The associative property of binary operations states that in an expression if we restructure the parentheses, then there will be no change in the final answer.

Let us look into each of the binary operations given to us individually.

(a) Subtraction of integers

Let us consider a subtraction operation such as -

a-(b-c) = a-b-c

Now, if we change the parentheses in the above operation like (a-b)-c then also the operation will be given as -

(a-b)-c = a-b-c

So, the subtraction of integers operation is associative.

(b) Division of nonzero rationals

Let us consider a division operation such as -

3/(9/3) = 1

Now, if we change the parentheses in the above operation like (3/9)/3 then the operation will be given as -

(3/9)/3 = (1/3)/3 = 1/9

So, we see that there is change in the final answer when the parentheses is rearranged in the operation of division of nonzero rationals. Thus, the division of nonzero rationals operation is not associative.

(c) Function composition of polynomials with real coefficients

Let us assume that we have polynomials given by -

f, q, s: R→R

This implies that -

(f · (q · s))(x) = f((q · s)(x)) = f(q(s(x)))

Similarly,

((f · q) · s)(x) = (f · q)(s(x)) = f(q(s(x)))

We see that both the final results are same even if the parentheses are rearranged. So, (f · q) · s = f · (q · s)

So, the operations of function composition of polynomials with real coefficients is associative.

(d) Multiplication of 2 X 2 matrices with integer entries

Let us say that P, Q, R are three matrices. This implies that for any entries in the matrices, we can say that -

P(QR) =  ΣP( ΣQR)

=> P(QR) =  ΣΣPQR

Similarly,

(PQ)R = Σ( ΣPQ)R

=>  (PQ)R = ΣΣPQR

So, we see that P(QR) = (PQ)R

Thus, the operation of multiplication of 2 X 2 matrices with integer entries is associative.

Therefore, excepting the operation of division of nonzero rationals, all other binary operations i.e., subtraction of integers, function composition of polynomials with real coefficients, and multiplication of 2 X 2 matrices with integer entries are all associative.

Thus, option (a), (c), and (d) are associative while option (b) is not associative binary operation.

To learn more about associative property visit https://brainly.com/question/5637942

#SPJ4

(a) if 20 cards are defective, then the probability that at least 1 defective card is in the sample is 0.964​

(b) if 5 cards are defective, then the probability that at least 1 defective card appears in the sample is 0.543​

Probability:

In statistics, probability refers the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.

Given,

Here we have a printed circuit cards are placed in a functional test after being populated with semiconductor chips. a lot contains 190 cards, and 20 are selected without replacement for functional testing.

And we need to find the following probability.

Here we have to recall the formula for probability mass function of the hypergeometric random variable X with the parameters

N = 190

n ​= 20​

and the parameter K.

And it is the following expression:

f(x) = [(K x) (140 - k 20 - x)] / (140 20)

Now, we have to Set K=20 and calculate from the probability mass function:

=> P(X≥1)=1−f(0)=0.964​

And then Set K=5 and calculate from the probability mass function:

=> P(X≥1)=1−f(0)=0.543​

To know more about Probability here.

https://brainly.com/question/11234923

#SPJ4

Answer:

5+1=6,2+3=5 6times 5is equal 30

Answer:

7+17i

Step-by-step explanation:

(5+i)(2+3i)

Multiply complex numbers 5+i and 2+3i like you multiply binomials.

By definition, \(i^{2}\) is -1.

5×2+5×(3i)+2i+3(−1)

Do the multiplications.

10+15i+2i−3

Combine the real and imaginary parts.

10−3+(15+2)i

Do the additions.

7+17i

Answer:

D) 51 ft.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

To make wheels of a diameter of 67.5 mm and a width of 29.3 mm, Alfie requires 104891.38 cubic mm volume of plastic.

A cylinder is a 3-Dimensional shape with 3 faces that are one curved face and 2 flat ends. The volume of a cylinder is given by the expression:

V = π\(r^2h\)

r is the radius

h is the height

Given, diameter = 67.5 mm

radius = d ÷ 2 = 67.5 ÷ 2

= 33.75 mm

height = width = 29.3 mm

Volume = \(\frac{22}{7}*33.75*33.75*29.3\)

= 104891.38 cubic mm

Therefore, the volume of the cylindrical wheel that Alfie designed is 104891.38 cubic mm.

Learn more about volume:

https://brainly.com/question/27535498

#SPJ4

The standard deviation of the number of free throws that Chauncey Billups will make in tonight's game is approximately 0.726.

To calculate the standard deviation of free throws that Chauncey Billups will make in tonight's game, we need to use the following formula:

Standard Deviation (σ) = √(n * p * (1 - p))

where n is the number of trials (free throws) and p is the probability of success (making a free throw).

In this case, n = 6 (as Billups shoots six free throws) and p = 0.894 (as his career free-throw percentage is 89.4%).

Substituting the values into the formula, we get:

Standard Deviation (σ) = √(6 * 0.894 * (1 - 0.894))

Calculating this expression, the standard deviation is approximately 0.726.

Therefore, the standard deviation of free throws that Chauncey Billups will make in tonight's game is approximately 0.726.

To learn more about probability visit:

https://brainly.com/question/23417919

#SPJ11

The criteria that we could use to prove the congruency that ΔABC ≅ ΔDEC is;

Vertical Angles are Congruent. We could then use AAS to prove that ΔABC ≅ ΔDEC

There are different triangle congruency postulates namely:

SSS: Side Side Side Congruency Postulate

SAS: Side Angle Side Congruency Postulate

ASA: Angle Side Angle Congruency Postulate

AAS: Angle Angle Side Congruency Postulate

HL: Hypotenuse Leg Congruency Postulate

We want to prove that ΔABC ≅ ΔDEC

Now, from the given image, we see that we are given 2 congruent sides.

However, angle ECD is congruent to angle DCA because they are vertically opposite angles and vertical angles are congruent.

Thus, the triangles are congruent by AAS Congruency postulate.

Read more about Triangle Congruence Postulate at; https://brainly.com/question/29268713

#SPJ1

a. The system of equations is given as follows:

35x = 15 + 32x.

The solution is given as follows:

x = 5.

b. The meaning of the solution is that the cost to purchase 5 jackets in each company is the same.

c. Gabriela should choose Anastasia's Monogram, as the function has a lower numeric value when x = 10.

The cost per jacket for each company is constant, hence a linear function is used to model the situation.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

Hence the functions for each company are given as follows:

The system of equations is used to find when both will have the same cost, as follows:

35x = 32x + 15

3x = 15

x = 5 jackets.

For 10 jackets, the costs are given as follows:

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

Answer:−(5−3m)=7m+10

m+−1(5−3m)=7m+10(Distribute the Negative Sign)

m+(−1)(5)+−1(−3m)=7m+10

m+−5+3m=7m+10

(m+3m)+(−5)=7m+10(Combine Like Terms)

4m+−5=7m+10

4m−5=7m+10

Step 2: Subtract 7m from both sides.

4m−5−7m=7m+10−7m

−3m−5=10

Step 3: Add 5 to both sides.

−3m−5+5=10+5

−3m=15

Step 4: Divide both sides by -3.

−3m

−3

=

15

−3

m=−5

Step-by-step explanation:

brainliest pleaseee

Answer:

The correct option is;

f(x) = 3·sin x/8·π + 2

Step-by-step explanation:

The given parameters for the sinusoidal function are;

Amplitude of oscillation = 3

Frequency of oscillation = 1/8·π

Midline of oscillation= 2

The general form of sinusoidal equation is y = A·sin(B(x - C)) + D

Where;

A = The amplitude

B = The frequency

C = The horizontal shift

D = The midline or vertical shift

Substituting the given values into the general form of sinusoidal equation, we have;

f(x) = y =  3·sin(1/8·π(x - 0)) + 2 = 3·sin(x/8·π) + 2

Which gives;

f(x) = 3·sin(x/8·π) + 2.

Answer:

tttttttttttttttttttttttttttttttttttttttttt

Step-by-step explanation:

tttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttt

Answer:342 meters

Step-by-step explanation:

There are infinitely many solutions and thus infinitely many values for x and y in the first system of equations. There are no solution for the second system of equations.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side

The first system of equations are,

y = 1/2 x + 1

-2x + 4y = 4

Multiplying throughout the first equation by 4, we get

4y = 2x + 4

and the second equation is 4y = 2x + 4

Both the equations are same and so the lines coincide.

They have infinitely many solutions.

The second system of equations are,

y = -x - 3

y + x = 2 ⇒ y = -x + 2

Both are in the form of y = mx +c, which is the equation of the line in slope intercept form.

Here m is the slope.

Given lines have the coefficient of x same, and so slopes are same.

So the lines are parallel.

Two parallel lines does not have a solution.

Hence the first system of equations have infinitely many solutions and second system of equations does not have any solution.

Learn more about System of Equations here :

https://brainly.com/question/24065247

#SPJ1

Answer:

y(x) = 5x+10

Linear relationship between x and y

Step-by-step explanation:

The initial cost, regardless of time, is $10. cost will then increase at a rate of $5 per hour that the boat is rented. Therefore, the cost (y) of renting a paddle boat for 'x' hours is:

\(y(x) = 5x+10\)

There is a linear relationship between x and y, where 5 is the slope of the equation, 10 is the y-intercept, the number of hours is the independent variable, and the cost is the dependent variable.

Therefore, the indicated z-score is 2.45.

To find the indicated z-score, we need to use a standard normal distribution table. From the graph, we can see that the area to the right of the z-score is 0.9850.
Looking at the standard normal distribution table, we find the closest value to 0.9850 in the body of the table is 2.45. This means that the z-score that corresponds to an area of 0.9850 is 2.45.
It's important to note that the standard deviation of the standard normal distribution is always 1. This is because the standard normal distribution is a normalized version of any normal distribution, where we divide the difference between the observed value and the mean by the standard deviation.

To know more about standard deviation visit:

https://brainly.com/question/31516010

#SPJ11

Answer:

Hilda had 35$ before purchase.

Answer:

$35

Step-by-step explanation:

Given:

Spend $35

After Purchase No More Money

So Hilda Had $35 then she Spend $35 at last had no more money so Before purchasing she had $35

Answer:

(3, -3) is correct

Step-by-step explanation:

-4 × 3 = -12. -12 + 9 = -3

Answer:

396

Step-by-step explanation:

circumference of a circle is 2 x pi x r = 2 x 63 x (22/7) = 396

Solution

Experimental Probability:

- The experimental probability is the probability gotten from performing an experiment.

- The formula for finding the experimental probability is similar to theoretical probability, only that it only takes the values of the experiment into consideration. That is,

- In this case, the Event (E) is the event when the student picks the $10 bill. The question tells us the number of times the student selected the $10 bill is 15 out of a total number of trials of 44.

- Thus, we can find the Experimental Probability P(E) as follows:

Theoretical Probability:

- The theoretical probability does not need the values from an experiment. We only consider the hypothetical situation of choosing a particular dollar bill.

- We have 3 bills; $1, $5, and $10. This means that if we are to choose 1 of the bills, the chances of us actually picking one of them is

- This represents the theoretical probability of choosing any of the 3 bills. It is the same for the 3 bills because we have just 1 of each bill in the box and as a result, there should be no reason why one bill should have a greater chance of being selected.

- Thus, the theoretical probability of choosing the $10 bill is

In this triangle, the product of tan A and tan C is `(BC)^2/(AB)^2`.

The given triangle ABC has angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees , Answer: `(BC)^2/(AB)^2`.

We have to find the product of tan A and tan C.

In triangle ABC, tan A and tan C are equal as the opposite and adjacent sides of angles A and C are the same.

So, we have, tan A = tan C

Therefore, the product of tan A and tan C will be equal to (tan A)^2 or (tan C)^2.

Using the formula of tan: tan A = opposite/adjacent=BC/A Band, tan C = opposite/adjacent=AB/BC.

Thus, tan A = BC/AB tan C = AB/BC Taking the ratio of these two equations, we have: tan A/tan C = BC/AB ÷ AB/BC Tan A * tan C = BC^2/AB^2So, the product of tan A and tan C is equal to `(BC)^2/(AB)^2`.

Answer: `(BC)^2/(AB)^2`.

For more questions on adjacent sides, click on:

https://brainly.com/question/28394984

#SPJ8