Consider the following system of equations..\( - 2x + 5y = 19\)\(y = - \frac{5}{6} x - \frac{1}{6} \). Use this graph of the system to approximate its solution.

The dot product of vectors a and b is option D. 30.

To find the dot product of two vectors, you need to multiply their corresponding components and then sum the results.

Let's calculate the dot product of vectors a = <5, 2> and b = <4, 5>:

a • b = (5 x 4) + (2 x 5)

= 20 + 10

= 30

Therefore, the dot product of vectors a and b is 30.

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The equation X^2/2 - 8 = 2X - 2 has two solutions, X = 6 and X = -2. These are the values of X that satisfy the equation and make both equations Y = X^2/2 - 8 and Y = 2X - 2 intersect on the graph.

To find the solutions to the equation X^2/2 - 8 = 2X - 2, we need to set the two equations equal to each other and solve for X.

The equation is:

X^2/2 - 8 = 2X - 2

To simplify the equation, let's multiply both sides by 2 to eliminate the fraction:

X^2 - 16 = 4X - 4

Next, we rearrange the equation to have all terms on one side:

X^2 - 4X - 12 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use factoring in this case:

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

Setting each factor equal to zero gives us two possible solutions:

X - 6 = 0 --> X = 6

X + 2 = 0 --> X = -2

So the solutions to the equation X^2/2 - 8 = 2X - 2 are X = 6 and X = -2.

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Answer:

y=4x+9

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(1-(-11))/(-2-(-5))

m=(1+11)/(-2+5)

m=12/3

m=4

y-y1=m(x-x1)

y-(-11)=4(x-(-5))

y+11=4(x+5)

y=4x+20-11

y=4x+9

The length of side AD is,

⇒ AD = 16

We have to given that;

The given figure is a right triangular prism.

In the prism:

• DF = 22 in.

• EG = 11 in.

• Volume of the prism = 1936 cubic in.

Since, Volume of right triangular prism is,

V = 1/2 (bh) x L

Substitute all the values we get;

V = 1/2 (22 × 11) × AD

1936 = 121 × AD

AD = 16

Thus, The length of side AD is, 16

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Answer:

The new point would be (-5,-5)

Step-by-step explanation:

i have big brain

Answer: (-5, -5)

Step-by-step explanation:

-4 + -1

-3 + -2

-5, -5

Answer:

I added the answer as a screenshot, using math solvers is helpful for math problems, I haven't learned this yet but I found the answer. Also, I only need one more person to mark me brainliest to move onto the next level which is expert.

Hope I helped :)

Answer:

or,180=3x

or,x=180+3

or,x=183 answer

Answer:

54

Step-by-step explanation:

there are 2 ways

(180 - 18) ÷ 3 = 54

(360-18-18) ÷ 6 = 54

same answer

The area of the smaller rectangle (KLMN) is 16.

Since rectangles ABCD and KLMN are similar, their corresponding sides are proportional.

Let's assume the length of side AB in rectangle ABCD is x, and the length of side KL in rectangle KLMN is y.

We can set up the proportion:

(x/y) = (20/16)

To find the area of the smaller rectangle, we need to determine the ratio of their areas.

Since the area of a rectangle is given by the product of its length and width, the ratio of the areas will be equal to the square of the ratio of their sides:

(Area of ABCD)/(Area of KLMN) = (x²)/(y²)

We are given that the area of ABCD is 25, so we have:

25/(Area of KLMN) = (x²)/(y²)

To find the area of KLMN, we need to substitute the values of x and y from the proportion:

25/(Area of KLMN) = (20/16)²

Simplifying the right side:

25/(Area of KLMN) = (5/4)²

25/(Area of KLMN) = 25/16

Cross-multiplying:

25 × 16 = 25 × (Area of KLMN)

400 = 25 × (Area of KLMN)

Dividing both sides by 25:

16 = Area of KLMN

Therefore, the area of the smaller rectangle (KLMN) is 16.

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The properties of the functions are added below

The function is given s

f(x) = -4(x + 7)³

The function has no restriction on the input and output

So, the domain and the range are (-∝, +∝)

The +7 in f(x) = -4(x + 7)³ implies that the horizontal shift is

Horizontal shift = 7

However, the function has no vertical shift

The 4 in f(x) = -4(x + 7)³ implies that the vertical stretch is

Vertical stretch = 4

However, the function is no compressed vetrically

The axis of reflection of the function is the x-axis

This is represented by the minus sign in -4

To calculate the inflection point, we set the expression in bracket to 0

So, we have

x + 7 = 0

This gives

x = -7

So, we have

Inflection point = (-7, 0)

Using graphing tools, we have

Intervals: \(\mathrm{Decreasing}:-\infty \: < x < -7,\:\mathrm{Decreasing}:-7 < x < \infty \:\)

End behaviors: As x approaches +∝, f(x) approaches -∝ and as x approaches -∝, f(x) approaches +∝

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To find the value of k that makes the system of linear equations have a unique solution, we need to find the determinant of the coefficient matrix and check if it is non-zero. The coefficient matrix is:

| k   1   1 |

| 1   k   1 |

| 1   1   k |

The determinant of this matrix is:

det = k(k^2 - 1) - (k - 1) + (1 - k)

   = k^3 - k - k + 1 - k + 1

   = k^3 - 3k + 2

For the system to have a unique solution, the determinant must be non-zero. So we need to solve the equation k^3 - 3k + 2 = 0:

(k - 1)(k^2 + k - 2) = 0

The solutions are k = 1 and k = -2. Since we are looking for the value of k that makes the system have a unique solution, we choose k = 1.

To find the value of k that makes the system have more than one solution, we can use the same approach but this time we need the determinant to be zero. So we need to solve the equation k^3 - 3k + 2 = 0 and find any repeated roots. However, we already solved this equation and found that the only real solution is k = 1. Therefore, the system has no repeated roots and has a unique solution for k = 1.

To find the value of k that makes the system have no solution, we can use the same approach but this time we need the determinant to be zero and at least one of the minor determinants to be non-zero. The minor determinants are:

| k  1 |

| 1  k | = k^2 - 1

| 1  k |

| 1  1 | = k - 1

| k  1 |

| 1  1 | = k - 1

So we need to solve the equation k^3 - 3k + 2 = 0 and check if any of these minors are non-zero. We already solved this equation and found that the only real solution is k = 1. For k = 1, all three minors are non-zero. Therefore, the system has no solution for k = 1.

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Answer:

(4, 1)

Step-by-step explanation:

Where the 2 lines intercept is where the solution is.

Answer:

Step-by-step explanation:

y=-x+5

y=x-3

I put the atachment .

The solution is, the product is 9.25* 10^83.2.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

2.5\times 10^22.5×10^2 and 3.7 \times 10^53.7×10^5

=2.5* 10^22.5×10^2 × 3.7 * 10^53.7×10^5

=9.25* 10^24.5*10^58.7

=9.25* 10^83.2

Hence, The solution is, the product is 9.25* 10^83.2.

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Answer: Around 1.33 Cups per batch

Step-by-step explanation:

4 / 3 ≈ 1.33

Answer:

1 1/3

Step-by-step explanation:

Math

Answer:

\(y=6(x-8)-2\qquad\text{point-slope form}\)

\(y=6x-50\qquad\text{slope-intercept form}\)

Step-by-step explanation:

The equation of a line can be written in several forms. Two of the most-used forms are the point-slope and the slope-intercept forms.

The point-slope form requires to have one point (xo, yo) through which the line passes and the slope m. The equation expressed in this form is:

\(y=m(x-xo)+yo\)

The slope-intercept form requires to have the slope m and the y-intercept b, or the y-coordinate of the point where the line crosses the y-axis. The equation is:

\(y=mx+b\)

The line considered in the question has a slope m=6 and passes through the point (8,-2). These data is enough to find the point-slope form of the line:

\(\boxed{y=6(x-8)-2\qquad\text{point-slope form}}\)

To find the slope-intercept form, we operate the above equation:

\(y=6x-48-2\)

\(\boxed{y=6x-50\qquad\text{slope-intercept form}}\)

Answer:

Darlene will get there first

Step-by-step explanation:

I have uploaded the work

To solve the expression 1 - (1 + 0.04/12)^(-12x10), you can follow these steps: Step 1: Simplify the exponent. In this case, -12x10 simplifies to -120.

Step 2: Evaluate the term within the parentheses first. 0.04/12 simplifies to 0.0033333 (approximately).

Step 3: Add 1 to 0.0033333 to get 1.0033333.

Step 4: Raise 1.0033333 to the power of -120.

Step 5: Calculate the value inside the parentheses using a calculator or software. The result is approximately 0.742657.

Step 6: Subtract the value obtained in Step 5 from 1.

1 - 0.742657 = 0.257343 (approximately).

Hence, the value of the expression 1 - (1 + 0.04/12)^(-12x10) is approximately 0.257343.

It's important to follow the order of operations (PEMDAS/BODMAS) when solving mathematical expressions. In this case, the exponent is evaluated first, followed by addition and subtraction. Utilizing a calculator or software that supports exponentiation and parentheses can help simplify complex expressions and obtain accurate results efficiently.

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Hi how u doin ?

\( {x}^{2} + 4 = 4\)

Subtract both sides 4

\( {x}^{2} + 4 - 4 = 4 - 4\)

\( {x}^{2} = 0\)

\(x = 0\)

There's just one solution .

Have a great day ❤

the answer is E.) none of the above

\(\dfrac{7!4!}{5!3!}=6\cdot7\cdot4=168\)

The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

The complete question is attached in the diagram.

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Answer:

Step-by-step explanation:

13 and 36 have no common factor except 1.

Perhaps you meant that the 13 should be 12. In that case

GCF

The greatest common factor is 2 * 2 * 3

If there is a number that is not bolded, it is what is left behind inside the backets the distributive property creates.

Answer: 12(1 + 3)

Note: the 1 is part of the answer inside the brackets when one of the numbers inside the brackets and the GCF are the same

These are a legitimate probability distribution:

To have a legitimate probability distribution, the probabilities for all possible values of X must satisfy two conditions:

Each probability value must be between 0 and 1, inclusive.

The sum of all probability values must equal 1.

Check if the given probabilities satisfy these conditions:

P(X=-3) = 0.14 (valid)

P(X=1) = 0.1 (valid)

P(X=3) = 0.135 (valid)

P(X=5) = 0.306 (valid)

Now, calculate the remaining probability to check if it satisfies the second condition:

P(X=6) = 1 - (P(X=-3) + P(X=1) + P(X=3) + P(X=5))

P(X=6) = 1 - (0.14 + 0.1 + 0.135 + 0.306)

P(X=6) = 1 - 0.681

P(X=6) = 0.319

Since the calculated probability is valid (between 0 and 1), There is a legitimate probability distribution for the discrete random variable X:

P(X=-3) = 0.14

P(X=1) = 0.1

P(X=3) = 0.135

P(X=5) = 0.306

P(X=6) = 0.319

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Answer: its 5 and -1  so D

Step-by-step explanation: In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or any expression; it is usually a number, but may be any expression. In the latter case, the variables appearing in the coefficients are often called parameters, and must be clearly distinguished from the other variables

Answer:

\(Area = 4x^2 - 14x + 10\)

Step-by-step explanation:

See Attachment for Complete Question

Given

\(Width = 5mi\) --- For the forest

\(Length = 2mi\) -- --- For the forest

Required

Determine the area of the habitat

Since the distance between the animal's habitat is x mi on both sides;

The length and width of the habitat is:

\(Width = 5 - (x + x)\)

\(Width = 5 - 2x\)

\(Height = 2 - (x +x)\)

\(Height = 2 - 2x\)

The area is then calculated as follows;

\(Area = Width * Height\)

\(Area = (5 - 2x) * (2 - 2x)\)

Expand

\(Area = 5(2 - 2x) -2x(2 - 2x)\)

Open Brackets

\(Area = 10 - 10x - 4x + 4x^2\)

\(Area = 10 - 14x + 4x^2\)

Reorder

\(Area = 4x^2 - 14x + 10\)

Hence; the required polynomial for the habitat area is:

\(Area = 4x^2 - 14x + 10\)

The height of the roof will be 10.75 units.

Given is to find the height of the roof.

The upward motion is modelled by the equation -

S = - t² + 3t + 4

The height of the roof is equal to maximum height attained. For the maximum height attained -

dS/dt = 0

d/dt (- t² + 3t + 4) = 0

- 2t + 3 = 0

2t = 3

t = 3/2                                                    .... Eq(1)

The  height of the roof will be -

S(max) = - t² + 3t + 4

S(3/2) = - (3/2)² +(3 x 3/2) + 4

S(3/2) = 9/4 + 9/2 + 4

S(3/2) = 2.25 + 4.5 + 4

S(3/2) = 10.75 units.

Therefore, the height of the roof will be 10.75 units.

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Answer:

hjgkulihjoj;l

Step-by-step explanation:

Answer: 10+4y=20

4y= 10

y= 10/4

y= 5/2

Step-by-step explanation: above