Which equation represents the relationship between the x-and y-values shown in the table?
​

Answer:

  4ab +10b

Step-by-step explanation:

Perhaps you want to simplify the expression.

  \((2.5ab+14b)-(-1.5ab+4b)=2.5ab+14b+1.5ab-4b\\\\=ab(2.5+1.5)+b(14-4)=\boxed{4ab+10b}\)

Answer: 4ab+10

Step-by-step explanation:

2.5ab+14b--1.5ab-4b

4ab+10

Answer:

\(\dfrac{1}{729}\)

Step-by-step explanation:

\(\left(\dfrac{}{}(-3)^2\dfrac{}{}\right)^{-3}\)

First, we should evaluate inside the large parentheses:

\((-3)^2 = (-3)\cdot (-3) = 9\)

We know that a number to a positive exponent is equal to the base number multiplied by itself as many times as the exponent. For example,

\(4^3 = 4 \, \cdot\, 4\, \cdot \,4\)

       ↑1 ↑2 ↑3 times because the exponent is 3

Next, we can put the value 9 into where \((-3)^2\) was originally:

\((9)^{-3}\)

We know that a number to a negative power is equal to 1 divided by that number to the absolute value of that negative power. For example,

\(3^{-2} = \dfrac{1}{3^2} = \dfrac{1}{3\cdot 3} = \dfrac{1}{9}\)

Finally, we can apply this principle to the \(9^{-3}\):

\(9^{-3} = \dfrac{1}{9^3} = \boxed{\dfrac{1}{729}}\)

To have a high credit score, you need to be consistent with your debt repayments since you started taking out loans.

So your friend would be wrong to assume that all those who haven't missed a payment in a single year will have a high credit score because your friend doesn't consider previous years.

Some of these people may have been late or defaulted on previous loans for one reason or another, but were able to keep up with new payments in 2015. While this would improve their credit score, it would still be low due to the previous year's actions that made it decrease.

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Answer:Each pair of alternate interior angles is congruent, and each pair of alternate exterior angles is congruent.

Step-by-step explanation:

Answer:

kitchen scaleuwueieie

Answer:

6 miles in one hour!

Step-by-step explanation:

1, 1/10

2, 6 mph

3, You divide 4 by 24, and you do that to get the answer

4, It means miles per hour, because Adrienne is biking a certain amount of miles in an hour.

5, You can multiply 6 by 4 and it will be 24.

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Triangle ABC with a hypotenuse of 7 units and angle B equal to 70 degrees,

Since triangle ABC is a right triangle and angle B is 70 degrees, it can be deduced that angle C must be 90 - 70 = 20 degrees.

assuming

length of side AC  = a

length of side BC = b.

Using the Pythagorean theorem, we can find the values of a and b.

a^2 + b^2 = 7^2

a^2 = 7^2 - b^2

a = √(7^2 - b^2)

Using the tangent function

tan C = b/a

tan 20 = b/√(7^2 - b^2)

Solving for b, we get:

b = tan(20) * √(7^2 - b^2)

We can use numerical methods to find the approximate value of b. Using a calculator, we can find that b is approximately 4.7. Rounding to the nearest tenth, b is 4.7 units.

Finally, using the Pythagorean theorem again, we can find the value of a:

a^2 + b^2 = 7^2

a^2 = 7^2 - b^2 = 7^2 - 4.7^2

a = √(7^2 - 4.7^2)

a = √(7^2 - 22.09)

Using a calculator, we can find that a is approximately 5.3. Rounding to the nearest tenth, a is 5.3 units.

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Answer:

3/5, 67%, 0.7, 3/4

Answer:

a. 16

Step-by-step explanation:

sin x = cos (90-x)

sin 74 = cos (90-74)

sin 74 = cos 16

The gradient of the function at the point (2, 3) is ∇z(2, 3) = (-5/2) + ln(1), 1.

To find the gradient of the function at the given point (2, 3), we need to calculate the partial derivatives of the function with respect to x and y and evaluate them at the given point.

The gradient of the function z = ln(x^2 - y) * x - 4 is given by the vector (∂z/∂x, ∂z/∂y).

First, we calculate the partial derivative of z with respect to x:
∂z/∂x = (∂/∂x)(ln(x^2 - y) * x - 4)
      = (1/x^2 - y) * x + ln(x^2 - y)

Next, we calculate the partial derivative of z with respect to y:
∂z/∂y = (∂/∂y)(ln(x^2 - y) * x - 4)
      = -1/(x^2 - y) * (-1)
      = 1/(x^2 - y)

Evaluating these partial derivatives at the given point (2, 3), we get:
∇z(2, 3) = (∂z/∂x)(2, 3), (∂z/∂y)(2, 3)
         = (1/4 - 3) * 2 + ln(4 - 3), 1/(4 - 3)
         = (-5/2) + ln(1), 1

Therefore, the gradient of the function at the point (2, 3) is ∇z(2, 3) = (-5/2) + ln(1), 1.

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Answer:

125

Step-by-step explanation:

y = 1k/x^3  I am trying to find the constant k.  I will use the information that I have been given to find k

1 = k/5^3

1 = k/125  Multiply both sides by 125

125 = k

Now, we will find y when x = 1

y = 125/1^3

y = 125

The value of y is 125 when x is 1.

Write the function y as a function of x, i.e., y = f(x), and then solve for x as a function of y, to determine the inverse of a function.

y = 1k/x^3  I am trying to find the constant k.  I will use the information that I have been given to find k

1 = k/5^3

1 = k/125

Multiply both sides by 125

125 = k

Now, we will find y when x = 1

y = 125/1^3

y = 125

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The roots have positive or same signs when c>0.

Note that only real numbers can be positive or negative. This concept does not apply to complex non real numbers. So first we have to make sure that the roots are real which occurs when discriminant is greater or equal to 0.

\(b^{2} -2ac > 0\\2^{2} -2(-1) (c) > 0\\4-2c > 0\\c > -2\)

Roots of quadrant equation have Samsame sign if product of roots >0.

\(\frac{a}{c} > 0\\\frac{c}{-1} > 0\\c < 0\)

Roots of quadratic equation have positive sign if product of roots<0.

c>0.

Combining results, we get:-

roots have positive signs when:-

c>0.

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Step-by-step explanation:

If g(x) = x² + 3x - 6

Then g (-7) can be found by substituting -7 for x in g(x) and solving the equation

⇒ g(-7) = (-7)² + 3(-7) - 6

⇒ g (-7) = 49 - 21 -6

⇒ g (-7) = 22

3√64 × 2^-1

= 4 × 1/2

= 2

The answer is 2.

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Temperature of refrigerators - Cannot determine. Horsepower of race car engines - Ratio. Marital status of school board members - Nominal. Ratings of television programs - Ordinal. Ages of children enrolled in a daycare - Interval

The level of measurement for the temperature of refrigerators cannot be determined based on the given information. The temperature could potentially be measured on a nominal scale if the refrigerators were categorized into different temperature ranges. However, without further context, it is not possible to determine the specific level of measurement.

The horsepower of race car engines can be measured on a ratio scale. Ratio scales have a meaningful zero point and allow for meaningful comparisons of values, such as determining that one engine has twice the horsepower of another.

The marital status of school board members can be measured on a nominal scale. Nominal scales are used for categorical data without any inherent order or ranking. Marital status categories, such as "married," "single," "divorced," etc., can be assigned to school board members.

The ratings of television programs, such as "poor," "fair," "good," and "excellent," can be measured on an ordinal scale. Ordinal scales represent data with ordered categories or ranks, but the differences between categories may not be equal or measurable.

The ages of children enrolled in a daycare can be measured on an interval scale. Interval scales have equal intervals between values, allowing for meaningful differences and comparisons. Age, measured in years or months, can be represented on an interval scale.

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Answer:

the answer is (A) 21-1/2.

Step-by-step explanation:

First, we need to calculate the rate of descent in feet per mile:

750 ft / 3 miles = 250 ft/mile

Next, we can set up a proportion to solve for the distance traveled:

(distance traveled) / (total altitude change) = (distance traveled) / (altitude change due to descent) + (altitude at which descent begins)

Let m be the distance traveled:

m / (32000 ft - 16000 ft) = m / (250 ft/mile * x miles) + 16000 ft

where x is the number of miles traveled when the pilot is 16000 ft above the ground.

Simplifying:

m / 16000 ft = m / (250 ft/mile * x miles) + 1

Multiplying both sides by 16000 ft:

m = m / (250 ft/mile * x miles) * 16000 ft + 16000 ft * 16000 ft

Multiplying both sides by (250 ft/mile * x miles):

m * (250 ft/mile * x miles) = m * 16000 ft + 16000 ft * (250 ft/mile * x miles)

Simplifying:

250 * x * m = 16000 * m + 4000 * x * m

Dividing both sides by m:

250 * x = 16000 + 4000 * x

Subtracting 4000 * x from both sides:

-3750 * x = -16000

Dividing both sides by -3750:

x = 4.266666... miles

Rounding to the nearest half mile gives us:

x ≈ 4.5 miles

Therefore, the answer is (A) 21-1/2.

If we use pi equal to 3, the volume of the sphere is 5,324 cubic inches.

For a sphere of radius R, the volume is given by:

V = (4/3)πR³

Here we can see that π = 3, and the diameter of the sphere is 22 inches, the radius is half the diameter, then:

R = 22in/2 = 11in

REplacing all that in the volume formula we will get:

V = V = (4/3)3(11in)³ = 4(11in)³ = 5,324 in³

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\(8 \times x = 24 \\ x = \frac{24}{8} \\ x = 3\)

Answer:

3

Step-by-step explanation:

24 ÷ 8 = 3

8 × 3 = 24

....................

Answer: perpendicular

Step-by-step explanation:

they make a right angle when graphed

The local maximum and minimum values of the function are as follows: maximum at (smaller x value), minimum at (larger x value), and there are no saddle points.

To find the local maximum and minimum values of the function, we need to analyze its critical points, which occur where the partial derivatives are equal to zero or do not exist.

Let's denote the function as f(x, y) = -8 - 2x + 4y - x^2 - 4y^2. Taking the partial derivatives with respect to x and y, we have:

∂f/∂x = -2 - 2x

∂f/∂y = 4 - 8y

To find critical points, we set both partial derivatives to zero and solve the resulting system of equations. From ∂f/∂x = -2 - 2x = 0, we obtain x = -1. From ∂f/∂y = 4 - 8y = 0, we find y = 1/2.

Substituting these values back into the function, we get f(-1, 1/2) = -9/2. Thus, we have a local minimum at (x, y) = (-1, 1/2).

There are no other critical points, which means there are no local maximums or saddle points. Therefore, the function has a local minimum at (x, y) = (-1, 1/2) but does not have any local maximums or saddle points.

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Answer:

22.5

Step-by-step explanation:

:)

Answer:

Step-by-step explanation:

The goal in scientific notation is to express a value in terms of a number that contains a single unit before the decimal point.  

Examples:

10000:  1.0 x 10^4

23456:  2.3456x10^4

In both cases, the x10^4 is telling us to multiply the first number by 10,000.  10^4 is the same as 10x10x10x10 = 10,000

The justification for scientific notation is that is makes expression large and small numbers much easier, as well as reduces errors due to an incorrectly placed decimal.

An example:  Divide 2500000000 by 5000.  That would normally require setting up a long-hand division problem that not only wastes paper and pencil, but is also prone to decimal point errors.

Do the same problem with scientific notation:

Count the places you want to move the decimal point backwards to just beyond the 5 in 2500000000.  It takes nine steps to move the decimal point to between the 2 and 5:  2.5 followed by 8 zeros.  That's a total of next steps to go in front of the 5.  This is written 2.5 x 10^9

5000 is represented by 5.0x10^4

Now when we divide the same numbers, but in scientific format, it is easier to see the answer:

(2.5x10^9)/(5.0x10^4)

2.5/5 = 0.5

10^9/10^4 = 10^5  [The exponents are subtracted when dividing with exponents:  9-4 = 5]

Put them together to find the final answer:  0.5x10^5

Then move the decimal point one spot to the right and reduce the exponent by 1:

5.0x10^4

------

Add exponents when multiplying:  10^3 x 10^5 = 10^8  (3+5=8)

Subtract when dividing:  10^7/10^2 = 10^5  (7-2=5)

Multiply when there is an exponent raised to another exponent:  (10^4)^3 = 10^12 (4x3 = 12)

Answer: 40

Step-by-step explanation:

Assume Julio's number is x.

The expression would be:

-7 * (x - 15) = -175

x - 15 = -175/-7

x = -175/-7 + 15

x = 40

The average distance that the airplane covered in three flights is 2036 kilometers, time in trip from Hongkong to Manila is 1.468 hours, time in trip from Singapore to Manila is 3.146 hours, time in trip from Korea to Manila is 3.422 hours.

Given the distance that an airplane covered in three different trips:

Hongkong-Manila: 1116 kilometers, Singapore-Manila: 2391 kilometers,

Korea-Manila: 2601 kilometers.

We are required to find the average distance traveled by the airplane in the three trips, the time it took in each trip if the speed of airplane is 760 km/h and the trip that took the longest time to travel.

Average distance that airplane travelled in the three trips=(1116+2391+2601)/3

=6108/3

=2036 kilometers

We know that speed=distance/time.

Time=Distance/speed

Time in trip from Hongkong to Manila=1116/760=1.468 hours

Time in trip from Singapore to Manila=2391/760=3.146 hours

Time in trip from Korea to Manila=2601/760=3.422 hours

We can observe that the trip from Korea to Manila took longest time to travel.

Hence the average distance that the airplane covered in three flights is 2036 kilometers, time in trip from Hongkong to Manila is 1.468 hours, time in trip from Singapore to Manila is 3.146 hours, time in trip from Korea to Manila is 3.422 hours and the trip from Korea to Manila took longest time to travel.

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1. On December 31, 2012, the consolidation worksheet journal entries for Matthews Co. are as follows

:Investment in Jackson account is debited for $55,000Patent account is credited for $18,000Common stock account is credited for $20,000Additional paid-in capital account is credited for $13,000The amount that is shown as the credit for the common stock account is $20,000, which is the result of multiplying the number of shares that Jackson has by the par value of the shares. Matthews Company records the difference between the purchase price and the book value as goodwill. The patent account is credited for $18,000, which is the result of multiplying the $60,000 book value of the patent by 30%.

2. On December 31, 2013, the consolidation worksheet journal entries for Matthews Co. are as follows

:Investment in Jackson account is debited for $48,000Goodwill account is credited for $10,000Retained earnings account is credited for $38,000Matthews Company records the difference between the purchase price and the book value as goodwill. Retained earnings are credited for the amount of Jackson Company's net income for the year.

3. The consolidation worksheet for December 31, 2013, is as follows

: ASSETSCash $45,000Accounts Receivable 60,000Inventory 110,000Equipment 240,000Investment in Jackson 672,000Total Assets $1,127,000LIABILITIESAccounts Payable $85,000Long-term debt 240,000Total Liabilities $325,000OWNERS' EQUITYMatthews Co. Common Stock $400,000Matthews Co. Additional Paid-In Capital 60,000Matthews Co. Retained Earnings 267,000Jackson Co. Common Stock 100,000Jackson Co. Additional Paid-In Capital 300,000Jackson Co. Retained Earnings 75,000Total Owners' Equity $1,202,000Total Liabilities and Owners' Equity $1,527,000

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There are 512 positive integers less than 875 that are multiples of 4, 7, or 3 using principle of inclusion/exclusion.

To solve this problem using the principle of inclusion/exclusion, we need to find the number of integers that are divisible by each of the three given numbers, then subtract the numbers that are divisible by the combination of two of the numbers, and finally add back the numbers that are divisible by all three numbers.

First, we find the number of integers that are divisible by 4, 7, or 3 individually. For 4, the largest multiple less than 875 is 872, and there are 218 multiples of 4. Similarly, for 7, the largest multiple less than 875 is 861, and there are 124 multiples of 7. For 3, the largest multiple less than 875 is 873, and there are 291 multiples of 3.

Next, we find the numbers that are divisible by the combination of two of the numbers. There are three pairs of numbers, and for each pair, we find the largest multiple less than 875 and divide it by the product of the two numbers. The pairs are (4,7), (4,3), and (7,3).

The largest multiples less than 875 for each pair are 868, 870, and 861, respectively. So the numbers that are divisible by (4,7), (4,3), and (7,3) are 31, 58, and 41, respectively.

Finally, we find the numbers that are divisible by all three numbers. The smallest multiple of 4, 7, and 3 is 84, and the largest multiple less than 875 is 864. So there are 9 multiples of all three numbers.

Using the principle of inclusion/exclusion, the number of positive integers less than 875 that are multiples of 4, 7, or 3 is:

218 + 124 + 291 - 31 - 58 - 41 + 9 = 512.

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Answer:

The probability that I will choose a consonant is 62.50%.

Step-by-step explanation:

Given that John has 8 cards that spell the word H O M E W O R K, and he shuffles them and then places them face down, to determine what is the probability he will choose a consonant the following calculation must be performed:

Vowels: 3

Consonants: 5

5/8 = X

0.625 = X

0.625 x 100 = 62.50

Therefore, the probability that I will choose a consonant is 62.50%.

To determine which model best fits the data, we can try  fit each model to the data points and see which one produces the best fit.

Model 1: f(x) = -x^2 + 2x - 3
- When we plug in the x values of the data points, we get the following y values:
 - f(-2) = 1
 - f(0) = -3
 - f(1) = -2
 - f(3) = -12
 - f(5) = -28
- As we can see, this model does not fit the data points very well.

Model 2: f(x) = x + 0.5
- When we plug in the x values of the data points, we get the following y values:
 - f(-2) = -1.5
 - f(0) = 0.5
 - f(1) = 1.5
 - f(3) = 3.5
 - f(5) = 5.5
- This model seems to fit the data points reasonably well, but we can try the other models to see if they fit even better.

Model 3: f(x) = -x^3 + x + 1
- When we plug in the x values of the data points, we get the following y values:
 - f(-2) = -3
 - f(0) = 1
 - f(1) = -1
 - f(3) = -23
 - f(5) = -119
- This model does not fit the data points very well either.

Model 4: f(x) = 2x
- When we plug in the x values of the data points, we get the following y values:
 - f(-2) = -4
 - f(0) = 0
 - f(1) = 2
 - f(3) = 6
 - f(5) = 10
- This model also seems to fit the data points reasonably well.

Based on this analysis, it seems that Model 2 (f(x) = x + 0.5) and Model 4 (f(x) = 2x) are the best models to fit the given data. However, it is important to note that there may be other models that fit the data equally well or even better, depending on the specific criteria for evaluating the goodness of fit.

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