Find the slope of the line

Answer:

here is the, ans hope it helps :)

x = -13 ± (√ 565) / 22 is the solution to the operation

(8x² + 8x - 9) + (3x² + 5x) = 0.

 ∴ (8x² + 8x - 9) + (3x² + 5x) = 0

=> 8x² + 8x - 9 + 3x² + 5x = 0

=> 11x² + 13x -9 = 0

After obtaining the standard form a, b and c are identified from the original equation and are placed into the quadratic formula.

∴ x = (-b±√(b²-4ac))/(2a)

11x² + 13x -9 = 0

where,

a = 11, b = 13, c = -9

=> x = (-13 ± √(13² - 4×11(-9)) )/ (2×11)

=> x =( -13 ± (√ 565) )/ (22).

So, the solution to (8x² + 8x - 9) + (3x² + 5x) = 0 is x = -13 ± (√ 565) / 22.

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The complete question is -

Perform the operation:

(8x² + 8x - 9) + (3x² + 5x) = 0

Answer:

Step-by-step explanation:

The length of x will be 4 cm if is the angle bisector of A.

A straight line that splits an angle in a triangle into two congruent angles is known as the angle bisector.

Given sides;

AB=12

AE=8

BD=6

DE=x

From the triangle angle bisector theorem;

\(\rm \frac{BD}{DE} = \frac{AB}{AE} \\\\ \frac{6}{x} =\frac{12}{8} \\\\ x=4\)

Hence the length of x will be 4 cm.

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Answer:  $26,000

Explanation:

i = simple interest

P = 25,000 = amount loaned

r = interest rate in decimal form = 0.04

t = number of years = 1

So,

i = P*r*t

i = 25000*0.04*1

i = 1000

Howie needs to pay $1,000 in interest on top of the $25,000 loaned to him. In total, he needs to pay back 1,000+25,000 = 26,000 dollars.

Answer:whats the question

Step-by-step explanation:

If we set m = 4 and n = 1, we get a = 15 and c = 17, which means (15, 60, 17) is a primitive Pythagorean triple with b = 4T5. Also, we can find primitive Pythagorean triples with b = 4T6 and b = 4T7 by using the same method. We get (21, 84, 87) for b = 4T6 and (28, 112, 113) for b = 4T7. Therefore, it is clear that for every triangular number Tn, there is a primitive Pythagorean triple (a, b, c) with b = 4Tn

A Pythagorean triple is a set of three integers that satisfy the Pythagorean theorem, which states that the sum of the squares of the lengths of the two shorter sides of a right triangle is equal to the square of the length of the longest side, or hypotenuse. For example, the triple (3, 4, 5) is a Pythagorean triple because 3^2 + 4^2 = 5^2.

Now let's talk about triangular numbers. A triangular number is the sum of the first n positive integers, and it can be represented by the formula Tn = 1 + 2 + 3 + ... + n = (n(n+1))/2. The first few triangular numbers are 1, 3, 6, and 10.

Interestingly, in the list of the first few Pythagorean triples, we can observe a pattern where the value of b is four times a triangular number. For example, in the Pythagorean triple (3, 4, 5), we have b = 4T1. In (5, 12, 13), b = 4T2. In (7, 24, 25), b = 4T3. And in (9, 40, 41), b = 4T4.

So the question is: is this pattern true for all triangular numbers? Let's investigate further.

a) To find a primitive Pythagorean triple (a, b, c) with b = 4T5, we need to find a value of a and c such that a^2 + b^2 = c^2 and b = 4T5. Using the formula for T5, we get T5 = (5(5+1))/2 = 15. Therefore, b = 4T5 = 60. We can use the Euclid's formula for generating Pythagorean triples, which states that for any two positive integers m and n with m > n, a Pythagorean triple (a, b, c) can be generated by a = m^2 - n^2, b = 2mn, and c = m^2 + n^2.

If we set m = 4 and n = 1, we get a = 15 and c = 17, which means (15, 60, 17) is a primitive Pythagorean triple with b = 4T5.

Similarly, we can find primitive Pythagorean triples with b = 4T6 and b = 4T7 by using the same method. We get (21, 84, 87) for b = 4T6 and (28, 112, 113) for b = 4T7.

b) Now, the question is whether there is a primitive Pythagorean triple (a, b, c) with b = 4Tn for any triangular number Tn. Let's assume this is true and try to prove it.

Using the same Euclid's formula, we can generate a primitive Pythagorean triple (a, b, c) with b = 4Tn by setting m = 2Tn+1 and n = Tn. This gives us a = 4Tn^2 + 1 and c = 4Tn^2 + 2Tn + 1, and we can verify that b = 4Tn using the formula for Tn.

Therefore, we have proven that for every triangular number Tn, there is a primitive Pythagorean triple (a, b, c) with b = 4Tn

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A, C, and E are linear transformations.  To justify:  A: T(A) = ASA-I is linear because it satisfies the two properties of linearity:

1. Additivity: T(A+B) = T(A) + T(B) for any matrices A and B in R2x2. This can be shown by plugging in (A+B) for A in T(A) and simplifying.
2. Homogeneity: T(kA) = kT(A) for any scalar k and matrix A in R2x2. This can be shown by plugging in kA for A in T(A) and simplifying.

C: T(A) = A from R to R2x2 is linear because it satisfies the two properties of linearity:
1. Additivity: T(A+B) = T(A) + T(B) for any matrices A and B in R. This can be shown by plugging in (A+B) for A in T(A) and simplifying.
2. Homogeneity: T(kA) = kT(A) for any scalar k and matrix A in R. This can be shown by plugging in kA for A in T(A) and simplifying.

E: T(A) = A from R2x2 to R2x2 is linear because it satisfies the two properties of linearity:
1. Additivity: T(A+B) = T(A) + T(B) for any matrices A and B in R2x2. This can be shown by plugging in (A+B) for A in T(A) and simplifying.
2. Homogeneity: T(kA) = kT(A) for any scalar k and matrix A in R2x2. This can be shown by plugging in kA for A in T(A) and simplifying.

B, D, and J are not linear transformations.

To justify:

B: T(A) = A from R2xs to R2x5 is not linear because it does not satisfy the additivity property of linearity. Specifically, T(A+B) ≠ T(A) + T(B) for some matrices A and B in R2xs.

D: T(A) = 2A from R6x4 to R6x4 is not linear because it does not satisfy the homogeneity property of linearity. Specifically, T(kA) ≠ kT(A) for some scalar k and matrix A in R6x4.

J: T(A) = A+Is from RSx5 to RSx5 is not linear because it does not satisfy either the additivity or homogeneity properties of linearity. Specifically, T(A+B) ≠ T(A) + T(B) and T(kA) ≠ kT(A) for some matrices A and B in RSx5 and scalar k.

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The answer to Math.round(3.6) is D. 4.0. The Math.round() method is used to round a number to the nearest integer.

When we apply Math.round(3.6), it rounds off 3.6 to the nearest integer which is 4.

This method uses the following rules to round the given number:

1. If the fractional part of the number is less than 0.5, the number is rounded down to the nearest integer.

2. If the fractional part of the number is greater than or equal to 0.5, the number is rounded up to the nearest integer.

In the given question, the number 3.6 has a fractional part of 0.6 which is greater than or equal to 0.5, so it is rounded up to the nearest integer which is 4. Therefore, the correct answer to Math.round(3.6) is D. 4.0.

It is important to note that the Math.round() method only rounds off to the nearest integer and not to a specific number of decimal places.

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Answer: 104.65%

Step-by-step explanation: 45/43=1.0465 so you just move the decimal to the right 2 places to make it a percent. It’s over 100% because 45 is higher than the total of 43.

Answer:

280 : 1

Step-by-step explanation:

Diameter of the Sun

\( =1.4\times 10^6\: km\\=1400000 \: km\)

Diameter of Mercury = 5000 km

Ratio of the diameter of the sun to the diameter of mercury

\( = \frac{1400000}{5000} \\ = \frac{1400}{5} \\ = \frac{280}{1} \\ = 280 \: : \: 1\)

The approximate ratio of the diameter of the sun to the diameter of mercury will be 280: 1.

Mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the diameter of the sun is about 1.4x10⁶ km. The diameter of the planet Mercury is about 5000 km.

The ratio will be calculated as:-

Ratio = 1.4x10⁶  / 5000

Ratio = 280 : 1

Therefore, the approximate ratio of the diameter of the sun to the diameter of mercury will be 280: 1.

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Answer:

prime

Step-by-step explanation:

3x^2 + 5x + 1

3x^2  factors in to 3x and x

1 factors into 1 and 1

( 3x   + 1) ( x+1)

We need to verify the middle is 5

3x+1x = 4x

so this is not true

We cannot factor this so it is prime

Answer:

\(\large \boxed{\sf Prime}\)

Step-by-step explanation:

\(3x^2 + 5x + 1\)

We need to find two numbers that add to 5 and multiply to get 1.

There are no real numbers.

The expression cannot be factored. The expression is prime.

The total number of fishes present in the lake on my 1 is 840.

The given data for the question-

September is equivalent to a percentage of tagged fish in May.

3/42 = 60/x

x = 60 *42 / 3

x = 840

Thus, the total number of fishes present in the lake on my 1 is 840.

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To find the critical points in MATLAB, you can use the 'solve' function in combination with symbolic variables.


1. First, define the symbolic variables and the function. For example, let's find the critical points of the function f(x) = x^3 - 6x^2 + 9x.
```MATLAB
syms x;
f = x^3 - 6*x^2 + 9*x;
```
2. Compute the first derivative of the function using the 'diff' function.
```MATLAB
f_derivative = diff(f, x);
```
3. Solve the first derivative for x using the 'solve' function.
```MATLAB
critical_points = solve(f_derivative, x);
```
4. Display the critical points.
```MATLAB
disp(critical_points);
```

By following these steps, you can find the critical points of a function in MATLAB using symbolic variables and the 'solve' function. Remember to define the symbolic variable, the function, compute the first derivative, and then solve the first derivative for x to obtain the critical points.

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Answer:

  375

Step-by-step explanation:

You want to know the number of integers from 1 to 1000 that are multiples of 4 or 6.

Assuming the ends of the range are not multiples of interest, we can find the number of multiples of a given number by dividing the range by that number. Doing this for 4, 6, and (4×6), we find that in [1, 1000], there are ...

The number of multiples of 4 or 6 will be the total of multiples of 4 and multiples of 6, less the number of multiples of both 4 and 6. That is, the first sum counts those multiples of 24 twice.

  250 +166 -41 = 375

There are 375 multiples of 4 or 6 in the range 1 to 1000.

<95141404393>

(a) At least 95.4% of the fish in the lake are between 5 inches and 13 inches long.(b) An interval of (4.34, 13.66) inches will contain fewer than 36% of the fish in terms of length.

(a) To find the proportion of fish between 5 inches and 13 inches long, we can use the standard normal distribution. First, we convert the values to z-scores using the formula \(z = \frac{x - \mu}{\sigma}\), where \(x\) is the length, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.
For 5 inches:
\(z_1 = \frac{5 - 9}{2} = -2\)
For 13 inches:
\(z_2 = \frac{13 - 9}{2} = 2\)
Using the standard normal distribution table or a calculator, we can find the proportion of values between -2 and 2, which is approximately 95.4%. Therefore, at least 95.4% of the fish in the lake are between 5 inches and 13 inches long.
(b) To find an interval where fewer than 36% of the fish have lengths outside the interval, we need to find the z-scores corresponding to the cumulative probabilities of 18% on each tail (36% combined).
Using the standard normal distribution table or a calculator, the z-score corresponding to 18% is approximately -0.94. So, we have:
\(z_{\text{left}} = -0.94\)
To find the z-score corresponding to the upper tail, we use the complement rule: \(1 - 0.18 = 0.82\). The z-score corresponding to 0.82 is approximately 0.92. So, we have:
\(z_{\text{right}} = 0.92\)
Now, we convert the z-scores back to length values using the formula \(x = z \cdot \sigma + \mu\). Substituting the values, we get:
\(x_{\text{left}} = -0.94 \cdot 2 + 9 \approx 4.12\) inches
\(x_{\text{right}} = 0.92 \cdot 2 + 9 \approx 13.84\) inches
Therefore, an interval of (4.12, 13.84) inches will contain fewer than 36% of the fish in terms of length.

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Answer: inverse operation, subtraction

Step-by-step explanation: The key insight here is that we want to solve for x , and in doing so, we need to undo any operation being applied to it. Right now, only 5 is being added to it, so to solve for it, we need to do the inverse operation, subtraction

If you mean this: How to solve multiplication property of equality?

Multiplication Property of Equality

For all real numbers a, b, and c: If a = b, then a • c = b • c (or ab = ac).

I hope this is right :)

Answer:

0.2% of the people had mid allergic reaction.

Step-by-step explanation:

Given that:

Number of people tested for a new shampoo = 9000

Number of people who had allergic reaction = 18

Percent of people = \(\frac{People\ who\ have\ reaction}{Total\ number}*100\)

Percent of people = \(\frac{18}{9000}*100\)

Percent of people = 0.002 * 100

Percent of people = 0.2%

Hence,

0.2% of the people had mid allergic reaction.

Answer:

0

Step-by-step explanation:

if no term exists in an expression this means it has a coefficient of 0

The area of 0.6808 to its left using the Standard Normal Table.

steps: 1. Identify the area: In this case, the area to the left of the z-score is given as 0.6808.

2. Consult the Standard Normal Table: This table shows the area to the left of various z-scores, ranging from negative to positive values.

3. Locate the closest area value: Look for the value in the table that is closest to the given area (0.6808). The table is typically organized into rows and columns, with the row header representing the first two digits of the z-score and the column header representing the third digit.

4. Identify the z-score: Once you've found the closest area value, determine the corresponding z-score by combining the row and column headers where the value is located.

Upon checking the Standard Normal Table, the closest area value to 0.6808 is 0.6800, which corresponds to a z-score of 0.47.

Keep in mind that the Standard Normal Table may not have the exact area value of 0.6808, so you need to find the closest possible value.

In summary, the z-score with an area of 0.6808 to its left using the Standard Normal Table is approximately 0.47.

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The total amount Hailey would spend at the concession stand is $17.55.

The total amount Hailey would spend at the concession stand at the movie theater can be determined by adding the cost of each item she bought together.

Addition is a mathematical operation that involves summing two more more numbers together in order to determine their total value. The other basic operations in maths are subtraction, multiplication and division.

Amount Hailey spent = cost of popcorn + price of soda + price of a bag of candy

7.75 + 5.15 + 4.65 = $17.55

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1.   he ate 1/4 of the bucket

2.   4 of the pool floaties are yellow.

3.   she paid 4$ for the cookies

4 .  3 members of the band play the drums

5.   45 minutes

Answer:

1.  Ansley eats 1/4 of the popcorn bucket

2. He bought 4 yellow floats

3. She pays 4 pounds for the cookies

4. 3 members of the band play the drums

5. They spent 45 minutes jumping on the trampoline

Step-by-step explanation:

If you would like the explanation, I can comment it below (≧∇≦)/ xx

Hope this helps! ♡

First, we want to note two things:

We can describe this with an inequality:  x ≥ -10
Be sure you use ≥ and not >, since -10 is included.

We can describe this with interval notation: [ -10, infty )
Be sure you use [ and not ( on -10, since -10 is included.

You can also use set-builder notation: { x | x ≥ -10 }

Answer: 40

Step-by-step explanation:

38+ 52=90

230-90=40

Answer:

Surface area=114 cm^2

Step-by-step explanation:

Surface area of a cuboid is given be 2(lb+bh+lh). ATQ, l=3, h=3, b=8. Plugging them into the formula, we will get surface area=114 cm^2

Dividing the total ounces of brewed coffee by the size of a medium cup (8 ounces), we can estimate the number of medium cups of coffee:

8,160 ounces (brewed coffee) / 8 ounces (medium cup size) ≈ 1,020 medium cups of coffee.

To determine approximately how many medium cups of coffee 30 lb. of coffee beans will make, we need additional information about the brewing process, the coffee-to-water ratio, and the size of a medium cup of coffee in ounces or milliliters. Without these specific details, it is difficult to provide an accurate estimate.

However, as a general guideline, the coffee-to-water ratio typically used for brewing coffee is around 1:15 to 1:18. This means that for every gram or ounce of coffee, you would use 15 to 18 times the amount of water. Assuming a coffee-to-water ratio of 1:17, we can make an estimate.

Let's assume that a medium cup of coffee is approximately 8 ounces (236.6 milliliters). With a coffee-to-water ratio of 1:17, we would use 1 part coffee to 17 parts water. So, for every ounce of coffee beans, we would need approximately 17 ounces of water.

Now, converting the 30 lb. of coffee beans to ounces (1 lb. = 16 ounces), we have:

30 lb. * 16 ounces/lb. = 480 ounces of coffee beans.

Considering the coffee-to-water ratio and assuming 17 ounces of water for every ounce of coffee beans, we can estimate the total amount of brewed coffee:

480 ounces (coffee beans) * 17 (coffee-to-water ratio) = 8,160 ounces of brewed coffee.

Finally, dividing the total ounces of brewed coffee by the size of a medium cup (8 ounces), we can estimate the number of medium cups of coffee:

8,160 ounces (brewed coffee) / 8 ounces (medium cup size) ≈ 1,020 medium cups of coffee.

Please note that this is a rough estimate and can vary based on specific factors such as brewing method, coffee strength preferences, and cup sizes.

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Answer:

the answer is A 1 thousand 6 hundreds 4 tens 5 ones 2 tenths 9 hundreths

Answer: This is so confusing.... like i think you broke my brain XD

Step-by-step explanation:

To find a differentiable function y(x) that satisfies the initial value problem (IVP) y' = |x| and y(-1) = 2, we can integrate the given differential equation and then apply the initial condition.

Integrating both sides of the differential equation y' = |x| with respect to x, we get:

∫ y' dx = ∫ |x| dx

Integrating ∫ y' dx gives us y(x) + C₁, where C₁ is an arbitrary constant of integration.

Integrating ∫ |x| dx involves considering the different cases for x. Since x > 0 (as given in the problem), we have:

∫ |x| dx = ∫ x dx (for x > 0)

= (x^2)/2 + C₂, where C₂ is another arbitrary constant of integration.

Now, we have:

y(x) + C₁ = (x^2)/2 + C₂

To determine the values of C₁ and C₂, we can use the initial condition y(-1) = 2:

y(-1) + C₁ = ((-1)^2)/2 + C₂

2 + C₁ = 1/2 + C₂

Simplifying further:

C₁ = 1/2 - 2 + C₂

C₁ = C₂ - 3/2

We can rewrite the equation for y(x) by substituting C₁ with C₂ - 3/2:

y(x) = (x^2)/2 + (C₂ - 3/2)

Therefore, a differentiable function that satisfies the given IVP y' = |x| and y(-1) = 2 is:

y(x) = (x^2)/2 + (C₂ - 3/2), where C₂ is an arbitrary constant.

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From the picture we can see that more than half of hger pennies are from Denver Last option is correct

Coins from Philadelphia = 15

Coins from Denver = 22

Coins from San Francisco = 3

The total coin is 40\

40 / 2 = 20

20 is half of the total coin

But Denver has its coins as 22

Hence we say that  More than half of her pennies are from Denver

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