Given: ABCDis a parallelogram ∠GEC ≅ ∠HFA and AE ≅FC.
Prove △GEC ≅ △HFA.

Answer:

$7

Step-by-step explanation:

$10 - $3 = $7

Answer:

a.\(\bold{log_7(xz) = log_7(x * z) = log_7(x) + log_7(z)}\)

b.\(\bold{log_7(\frac{x}{y}) = log_7(y) - log_7(x)}\)

c.\(\bold{log_7(\sqrt[3]{7} ) = log_7(z^{\frac{1}{3}}) = \frac{1}{3}log_7(z)}\)

Step-by-step explanation:

let me provide an explanation for each of the expressions.

\(\bold{log_7(xz) = log_7(x * z) = log_7(x) + log_7(z)}\)

\(\bold{log_7(\frac{x}{y}) = log_7(y) - log_7(x)}\)

\(\bold{log_7(\sqrt[3]{7} ) = log_7(z^{\frac{1}{3}}) = \frac{1}{3}log_7(z)}\)

Therefore, we can express each of the given expressions in terms of logarithms of x, y, z, or w using the logarithmic properties mentioned above.

Answer:

\(\textsf{a.} \quad \log_7(x) + \log_7(z)\)

\(\textsf{b.} \quad \log_7(y) - \log_7(x)\)

\(\textsf{c.} \quad \dfrac{1}{3}\log_7(z)\)

Step-by-step explanation:

We can express the given logarithmic expressions in terms of x, y, z or w by using the laws of logarithms.

\(\hrulefill\)

\(\boxed{\begin{array}{c}\underline{\textsf{Product law}}\\\\ \log_a(bc)=\log_a(b) + \log_a(c)\\\end{array}}\)

By using the log product law, we can express log₇(xz) as:

\(\log_7(xz) =\log_7(x) + \log_7(z)\)

\(\hrulefill\)

\(\boxed{\begin{array}{c}\underline{\textsf{Quotient law}}\\\\\log_a \left(\dfrac{b}{c}\right)=\log_a(b) - \log_a(c)\end{array}}\)

By using the log quotient law, we can express log₇(y/x) as:

\(\log_7 \left(\dfrac{y}{x}\right)=\log_7(y) - \log_7(x)\)

\(\hrulefill\)

\(\boxed{\begin{array}{c}\underline{\textsf{Power law}}\\\\\log_ax^n=n\log_ax\end{array}}\)

By using the log power law, we can express log₇(∛z) as:

\(\begin{aligned}\log_7 \left(\sqrt[3]{z}\right)&=\log_7 \left(z^{\frac{1}{3}\right) \\&=\dfrac{1}{3}\log_7(z)\end{aligned}\)

Answer:

A

Step-by-step explanation:

Answer:

Ok so i think you can just count it i dont know; edit : i counted, it turns out the answer is 15 :)

Step-by-step explanation:

a.

\(y = kx \\ 21 = k \times 3 \\ 21 \div 3 = \frac{(k \times 3)}{3} \\ 7 = k\)

b.

\(y = kx \\ 24 = k \times 4 \\ \frac{24}{4} = \frac{(k \times 4)}{4} \\ 6 = k\)

The expression that represents the combined inventory of these two stores is given as follows:

A. 7g²/2 - 4g/5 + 15/4.

The combined inventory is obtained adding the inventories for each store, combining the like terms.

The addition of the like terms for g² is given as follows:

1/2 + 3 = 0.5 + 3 = 3.5 = 7/2g².

The term with g is given as follows:

-4g/5.

The constant like terms are combined as follows:

7/2 + 1/4 = 14/4 + 1/4 = 15/4.

Hence the simplified expression is given as follows:

7g²/2 - 4g/5 + 15/4.

Meaning that the correct option is given by option A.

More can be learned about simplification of expressions at https://brainly.com/question/723406

#SPJ1

The value of the constant, c is 4 and the value of the exponent, r is 2.

To find the solution to this initial value problem, we need to solve for c and r.

First, we can divide both sides of the equation by 2t:

y′ = 2y/t

Next, we can separate the variables:

dy/y = 2dt/t

Integrating both sides, we get:

ln|y| = 2ln|t| + C

Exponentiating both sides:

|y| = Ce^(2ln|t|) = \(C(|t|^2)\)

Since y can be negative or positive, we can write:

y = ±C\(|t|^2\)

To find the value of C, we can use the initial condition y(2) = −8:

−8 = ±C(\(2^2\))

Solving for C, we get:

C = −4

The following is the answer to the starting value problem:

y = −\(4|t|^2\)

Note that \(|t|^2\) = \(t^2\) for positive t and \(|t|^2\) = -\(t^2\) for negative t, so we can write:

y = -4\(t^2\) for t > 0

y = 4\(t^2\) for t < 0

So the value of c is 4 and the value of r is 2.

The complete question is:-

Consider the initial value problem 2ty′=4y, y(2)=−8. 2ty′=4y, y(2)=−8. find the value of the constant c and the exponent r so that y=ctry=ctr is the solution to this initial value problem.

To learn more about exponent, refer:-

https://brainly.com/question/30066987

#SPJ4

Given statement solution is :- None of the given options (a, b, c, or d) match the meaning of the slope. The correct interpretation is that the car travels approximately 0.8 miles every minute.

To determine the meaning of the slope of the linear model for the given data, let's analyze the information provided. The table represents the distance traveled by a car at different time intervals.

Minutes | Distance Traveled (in miles)

50 | 20

20 | f

40 | 60

100 | a

125 | 80

100 | 100

To find the slope of the linear model, we need to calculate the change in distance divided by the change in time. Let's consider the intervals where the time changes by a fixed amount:

Between 50 minutes and 20 minutes: The distance changes from 20 miles to 'f' miles. We don't have the exact value of 'f', so we can't calculate the slope for this interval.

Between 20 minutes and 40 minutes: The distance changes from 'f' miles to 60 miles. Again, without knowing the value of 'f', we can't calculate the slope for this interval.

Between 40 minutes and 100 minutes: The distance changes from 60 miles to 'a' miles. We don't have the exact value of 'a', so we can't calculate the slope for this interval.

Between 100 minutes and 125 minutes: The distance changes from 'a' miles to 80 miles. Since we still don't have the exact value of 'a', we can't calculate the slope for this interval.

Between 125 minutes and 100 minutes: The distance changes from 80 miles to 100 miles. The time interval is 25 minutes, and the distance change is 100 - 80 = 20 miles.

Therefore, based on the given data, we can conclude that the car travels 20 miles in 25 minutes. To determine the meaning of the slope, we divide the distance change by the time change:

Slope = Distance Change / Time Change

= 20 miles / 25 minutes

= 0.8 miles per minute

So, none of the given options (a, b, c, or d) match the meaning of the slope. The correct interpretation is that the car travels approximately 0.8 miles every minute.

For such more questions on Car travels

https://brainly.com/question/32301907

#SPJ8

Answer:

B

Step-by-step explanation:

On edge

The probabilities is the greatest for a standard normal distribution is

P(-0.5 ≤ z ≤ 0.5) = 0.382.

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically towards either extreme. The distribution's mean is another name for the centre of the range.

From the diagram attached below, we can write

1. P( -1.55 ≤ z ≤ -0.5)

= 0.092 + 0.15

= 0.242

or, 9.2%+15%=24.2%.

2. P( -0.5 ≤ z ≤ 0.5)

= 0.191 + 0.191

= 0.382

3. P( 0.5 ≤ z ≤ 1.5)

= 0.15 + 0.092

= 0.242

4. P( 1.5 ≤ z ≤ 2.5)

= 0.044 + 0.017

= 0.061

So, the greatest value is P(-0.5 ≤ z ≤ 0.5) = 0.382

Learn more about Normal Distribution here:

https://brainly.com/question/1470443

#SPJ7

\(i) \: \:1 \times \frac{5}{11} \times 12\)

\( = \frac{16}{11} \times 12\)

\( = \frac{192}{11} \)

\(ii) \: \: 1 \times \frac{7}{12} \times 21\)

\( = \frac{19}{12} \times 21\)

\( = \frac{19}{4} \times 7\)

\( = \frac{133}{4} answer\)

The required product of the expression are 17 5/11 and 33 1/4 respectively

Given the following products

1) 1 5/11 * 12

This can also be expressed as:

1) 16/11 * 12

= 192/11

= 17 5/11

For the product 1 7/12 * 21

2) 19/12 * 21

= 399/12

= 33 1/4

Hence the required product of the expression are 17 5/11 and 33 1/4 respectively

Learn more on the product here: https://brainly.com/question/1755985

Answer:

0.3019

Step-by-step explanation:

Null hypothesis: the average age of a groom is now 26.2 years.

Alternative hypothesis: the average age of a groom is not 26.2 years.

We have a sample of 16 so we will use a t-test

Where t score = (x-u)/(sd/√n)

Where x = 26.6, u=26.2, sd= 5.3 and n=16

t score = (26.6-26.2) / (5.3/√16)

t = 0.4/(5.3/4)

t = 0.4/1.325

t = 0.3019

Answer:

42 sea otters per mi2

Step-by-step explanation:

Answer:

y = -5/4x -4

Step-by-step explanation:

slope(m)= -5/4

x1=-4,y1=1

using the formula for one point form

y-y1=m(x-x1)

y-1= -5/4(x-(-4))

y-1 = -5/4x + -5/4 × +4

y - 1 = -5/4x -5

y=-5/4x -5 + 1

y = -5/4x -4.

Don't forget to smash the answer as brainliest if I truly deserve it

Thanks

Answer:

Step-by-step explanation:

Gloss content is same at the input and output.

Let 30% gloss is x gallons, then 15% gloss is (3.75 - x) gallons.

We have the following equation:

Amount of 15% gloss:

30% gloss is 1.25 gallons and 15% gloss is 2.5 gallons

Answer: 54 patterns

Step-by-step explanation:

12+17=19+14=33+21=54

Answer:

y=2/3x+1

Step-by-step explanation:

m= (slope)

b= (y-intercept

Answer:

Step-by-step explanation:

The answer is B

The whole numbers are the + integer set. Since -sqrt(25) = - 5, this number is not included in the whole number set.

The mathematics SAT score representing the top 1% of all scores is approximately 780.

a. The random variable in this case is the mathematics SAT score.

b. To find the probability that a person has a mathematics SAT score over 700, we need to calculate the z-score first.

The z-score is calculated as \(\frac{(X - \mu )}{\sigma}\),

where X is the value we're interested in, μ is the mean, and σ is the standard deviation.

In this case, X = 700, μ = 514, σ = 117.

Using the formula, the z-score is \(\frac{(700 - 514)}{117 } = 1.59\).

To find the probability associated with this z-score, we can consult a standard normal distribution table or use a calculator.

The probability is approximately 0.0564 or 5.64%.

c. To find the probability that a person has a mathematics SAT score of less than 400, we again calculate the z-score using the same formula.

X = 400, μ = 514, and σ = 117.

The z-score is \(\frac{(400 - 514) }{117 } = -0.9744\).

Looking up the probability associated with this z-score, we find approximately 0.1635 or 16.35%.

d. To find the probability that a person has a mathematics SAT score between 500 and 650, we need to calculate the z-scores for both values.

Using the formula, the z-score for 500 is \(\frac{(500 - 514)}{117 } = -0.1197\),

and the z-score for 650 is \(\frac{(650 - 514)}{117 } = 1.1624\).

We can then find the area under the normal curve between these two z-scores using a standard normal distribution table or calculator.

Let's assume the probability is approximately 0.3967 or 39.67%.

e. To find the mathematics SAT score that represents the top 1% of all scores, we need to find the z-score corresponding to the top 1% of the standard normal distribution.

This z-score is approximately 2.33.

We can then use the z-score formula to calculate the corresponding SAT score.

Rearranging the formula,

\(X = (z \times \sigma ) + \mu\),

where X is the SAT score, z is the z-score, μ is the mean, and σ is the standard deviation.

Substituting the values,

\(X = (2.33 \times 117) + 514 = 779.61\).

Rounded to the nearest whole number, the mathematics SAT score representing the top 1% of all scores is approximately 780.

For such more questions on mathematics

https://brainly.com/question/29892643

#SPJ8

The system of equations represented by the graph is:

y = x - 6

y + x = -2

And the solution is (2, -4), then the correct option is the first one.

On the graph, we can see a system of linear equations, we can see a line with a positive slope and a line with a negative slope.

The line with a positive slope intercepts the y-axis at y = -6, then that line is:

y = a*x - 6

with a > 0.

The other line passes through the y-axis at y = -2, then the linear equation is:

y = b*x - 2

Where b < 0.

Also, remember that the solution for the system of equations is the point where the two lines intersect, so we can see that the solution is at (2, -4)

The only option that meets all the criteria is the first option:

y = x - 6

x + y = -2

And the solution is (2, -4)

Learn more about systems of equations:

https://brainly.com/question/13729904

#SPJ1

Step-by-step explanation:

4+(-3)=1

because when you open brackets + and - will be -, so 4-3=1

The distance between the two ship based on the angle of depression is 42 meters.

The distance of each ship can be calculated thus:

TanX = opposite / Adjacent

The first ship:

Tan53 = distance/ 82

distance= 108.82 meters

The second ship:

Tan39 = distance/ 82

distance= 66.40 meters

The Difference between the ships are :

Therefore, the distance between the two ships is 42 meters.

Learn more on angles of depression:https://brainly.com/question/17193804

#SPJ1

Answer:

2¹+3¹ , 2³ -2¹ , 3²

Step-by-step explanation:

to know the magnitude of the value of each expression 3² =9 ,

2³ -2¹ =8-2=6

2¹ +3¹ = 5

Answer:2661615

Step-by-step explanation:

29573.5 is how many millimeters are in an ounce multiply that by 90 and you get 2661615

hope this helps

Answer:

you used two different types of things ounces measure mass and millimeters measure length

but I used google and it said 2.662e+6

Answer:

2x - 3 = 11

x = -21

Step-by-step explanation:

Answer:

200+50x

Step-by-step explanation:

Answer:

The boys' comic books are on the teacher's desk

comically

Step-by-step explanation:

The graph that represents the function y= tanx is Option A.

The graph of y =tan (x) is a periodic function that has vertical asymptotes at x = (n + 1/2)π, where n is an integer.

It oscillates between positive and   negative infinity, creating a wave-  like pattern.

It has a repeating pattern of sharp peaks and valleys, exhibiting both positive and negative slopes.

Thus, option A is the correct answer.

Learn more about graph:
https://brainly.com/question/25184007
#SPJ1

using SOH CAH TOA

Tan 85.144 =h/130

h=tan 85.144*130

h=1530.19 fr

Answer:

C=35x+75

It would cost $425 for 15 people

Step-by-step explanation: