What is the solution to the system of equations below?

y = -5x - 1
4x - 7y = 7

Answer:

D,xy=-12

Step-by-step explanation:

y=x²+x-2

x+y=1

or x+x²+x-2=1

x²+2x-3=0

x²+3x-x-3=0

x(x+3)-1(x+3)=0

(x+3)(x-1)=0

either x=-3

or x=1

when x=-3

x+y=1

-3+y=1

y=1+3=4

one solution is (-3,4)

xy=-3×4=-12

if x=1

1+y=1

y=0

second solution is (1,0)

xy=1×0=0

When the cosine of an angle (0) is 3/5 and the angle lies in quadrant 4, the exact value of the sine of that angle is -4/5.

To find the exact value of sin(0), we can utilize the Pythagorean identity, which states that \(sin^2(x) + cos^2(x) = 1,\) where x is an angle in a right triangle. Since the terminal side of the angle (0) is in quadrant 4, we know that the cosine value will be positive, and the sine value will be negative.

Given that cos(0) = 3/5, we can determine the value of sin(0) using the Pythagorean identity as follows:

\(sin^2(0) + cos^2(0) = 1\\sin^2(0) + (3/5)^2 = 1\\sin^2(0) + 9/25 = 1\\sin^2(0) = 1 - 9/25\\sin^2(0) = 25/25 - 9/25\\sin^2(0) = 16/25\)

Taking the square root of both sides to find sin(0), we have:

sin(0) = ±√(16/25)

Since the terminal side of (0) is in quadrant 4, the y-coordinate, which represents sin(0), will be negative. Therefore, we can conclude:

sin(0) = -√(16/25)

Simplifying further, we get:

sin(0) = -4/5

Hence, the exact value of sin(0) when cos(0) = 3/5 and the terminal side of (0) is in quadrant 4 is -4/5.

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Note the correct and the complete question is

Q- Find the exact value of sin(0) when cos(0) =3/5 and the terminal side of (0) is in quadrant 4​ ?

Possible answer: 9

Step-by-step explanation:

9 doubled is 18, and that is 9 more than the original number itself.

Unless I'm wrong.

Answer:

C. 360

Step-by-step explanation:

Plugging it into a calculator.

n = 6 , r = 4

\(nPr=\frac{n!}{(n-r)!}\)

\(6P4=\frac{6!}{(6-4)!}=360\)

By applying the maximum modulus principle, we found that the maximum value of 2i(z²) + 3 on the set of complex numbers whose modulus is less than or equal to 1 is √13.

Let's start by expressing the given function in terms of z. We have:

f(z) = 2i(z²) + 3

Now, let's consider the modulus of f(z):

|f(z)| = |2i(z²) + 3|

According to the maximum modulus principle, the maximum value of |f(z)| occurs on the boundary of the given domain, which is the circle of radius 1 centered at the origin in the complex plane.

In order to find the maximum value, we need to evaluate |f(z)| on the boundary of the circle |z| = 1.

Let's substitute z = 1 into f(z):

f(1) = 2i(1²) + 3

= 2i + 3

Taking the modulus of f(1):

|f(1)| = |2i + 3|

To find the maximum value, we need to determine the magnitude of the complex number 2i + 3. The modulus (or magnitude) of a complex number a + bi, denoted as |a + bi|, is given by:

|a + bi| = √(a² + b²)

For the complex number 2i + 3, we have:

|2i + 3| = √(2² + 3²)

= √(4 + 9)

= √13

Therefore, the maximum value of |f(z)| occurs at |z| = 1 and is equal to √13.

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Step-by-step explanation:

send the question compeletly .

Answer:

Step-by-step explanation:

There are 26 letters in the alphabet and 10 digits that you can use (0,1,2,3,4,5,6,7,8,9)

As a result, we can find the number of combinations by doing the following:

26 x 26 x 10 x 10 x 10

since the first two symbols are alphabets and the last three are digits. After doing the math you get

26 x 26 x 10 x 10 x 10 = 676000 => You can make a total of 676,000 PIN codes

The statements that are not true with respect to the indicated sets of vectors in R are A. If a set contains the zero vector, the set is linearly independent, and E. If the number of vectors in a set exceeds the number of entries in each vector, the set is linearly dependent.

For statement A. If a set contains the zero vector, the set is linearly independent.

To have a zero vector in a set makes the set linearly dependent. This is because the zero vector can be shown as a linear combination of the other vectors in the set when a coefficient of zero is assigned to the zero vector.

On statement E. If the number of vectors in a set exceeds the number of entries in each vector, the set is linearly dependent.

On statement E. If the number of vectors in a set exceeds the number of entries in each vector, the set is linearly dependent.

This statement is also not true because Having more vectors than the number of entries in each vector doesn't necessarily mean they are linearly dependent.

Whether a set is linearly dependent or not relies on the relationships between the vectors and not on their dimensions only.

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Answer: 192

Step-by-step explanation:

Use algebra

x + 3x + x + 3x = 64 (perimeter)

Combine Like Terms

8x = 64

x = 8

8 + 24 + 8 + 24 = 64

24/8 = 3

Answer:

B

Step-by-step explanation:

You simplify it using radicals.

Answer:

y=4x

Step-by-step explanation:

Write the equation of linear function

Substitute:  

Multiply the monomials:  

Rearrange unknown terms to the left side of the equation:  

Reduce the greatest common factor on both sides of the equation:  

Rearrange unknown terms to the left side of the equation:  

Divide both sides of the equation by the coefficient of variable:  

Substitute one unknown quantity into the elimination:  

Solve the equation: m=4

Write the solution set of the equations:  

Substitute: y=4x

Answer: y=4x

Answer:

-14m - 18

Step-by-step explanation:

Hi there!

To find the answer, we will first have to merge the expressions.

-18m - 4 + 4m - 14

To simplify this, we have to combine like terms.

-18m and 4m can be added together to create -14m

-4 and -14 can be added together to make -18.

Now that our terms are simplified, the expression becomes -14m - 18.

Hope this helped!

The equation of the line that passes through (-3, 5) and is perpendicular to the line passing through (-6, 1/2) and (-4, 2/3) is y = -12x - 31.

To find the equation of the line that passes through (-3, 5) and is perpendicular to the line passing through (-6, 1/2) and (-4, 2/3), we need to follow these steps:

1. Find the slope of the given line.

2. Determine the negative reciprocal of the slope to find the slope of the perpendicular line.

3. Use the slope and the point (-3, 5) to find the equation of the perpendicular line using the point-slope form.

Let's begin by finding the slope of the given line:

Slope of the given line = (y2 - y1) / (x2 - x1)

                       = ((2/3) - (1/2)) / (-4 - (-6))

                       = ((4/6) - (3/6)) / (-4 + 6)

                       = (1/6) / 2

                       = 1/12

The slope of the given line is 1/12.

To find the slope of the perpendicular line, we take the negative reciprocal:

Slope of perpendicular line = -1 / (1/12)

                          = -12

The slope of the perpendicular line is -12.

Now, using the slope (-12) and the point (-3, 5), we can find the equation of the perpendicular line using the point-slope form:

y - y1 = m(x - x1)

Substituting the values, we get:

y - 5 = -12(x - (-3))

y - 5 = -12(x + 3)

y - 5 = -12x - 36

y = -12x - 36 + 5

y = -12x - 31

Therefore, the equation of the line that passes through (-3, 5) and is perpendicular to the line passing through (-6, 1/2) and (-4, 2/3) is y = -12x - 31.

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The required area of the parallelogram and pentagon is 91 unit² and 75 unit².

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

A parallelogram in is shown in figure 1 with the dimensions height = 7 and base = 13,
Area of the parallelogram  = 13 × 7 = 91 unit²

Now,
A pentagon is shown in figure 2,
Area of the pentagon = 5 [1/2 × height × side]
                                 = 5 [1/2 × 5 × 6]

                                 = 75 suqare units.

Thus, the required area of the parallelogram and pentagon is 91 unit² and 75 unit².

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The effective interest rate of the loan would be

In this case, we are given 4 options:

The formula of compounded interest rate is:

\(A = P (1+\frac{r}{n})^{nt}\)

Where:

A = amount, P = principal amount, r = interest rate, n = number of times interest rate compounded, t = time

Let’s assume the principal amount is $100 for 1 year

Loan L =

\(A = 100 (1+\frac{0.08254}{356})^{356x1}\)

A = $108.603

Loan M =

\(A = 100 (1+\frac{0.08474}{52})^{52x1}\)

A = $108.834

Loan N =

\(A = 100 (1+\frac{0.08533}{12})^{12x1}\)

A = $108.875

Loan O =

\(A = 100 (1+\frac{0.08604}{1})^{1x1}\)

A = $108.604

Therefore, the best effective interest rate for Craig is Loan L with nominal rate of 8.254% compounded daily.

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\(y = {x}^{2} + 4x - 12\)

Answer:

It is 40

Step-by-step explanation:

The highest common factor of 200 and 240 is 40

The level of significance, typically set at 0.05, is used to determine whether the observed difference is statistically significant or simply due to chance

To determine whether the difference between groups is statistically significant, you would typically use a hypothesis test such as a t-test, ANOVA (analysis of variance), or a chi-square test. These tests are used to compare the means or proportions of different groups and calculate the probability of obtaining the observed difference by chance. The level of significance, typically set at 0.05, is used to determine whether the observed difference is statistically significant or simply due to chance. To determine if the difference between groups is statistically significant, you can use a hypothesis test called the t-test. The t-test compares the means of two groups and takes into account the sample size and variance within each group. This test helps you determine if there is a significant difference between the groups or if the observed difference is due to random chance.

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Yes, the ratios form a proportion.

Given that, Steve plants 64 bulbs in which 48 are tulips.

So the ratio of tulips to total bulbs of Steve is = 48:64 = 3:4

Again, Dawn plants 96 bulbs in which 72 are tulips.

So the ratio of tulips to total bulbs of Dawn is = 72:96 = 3:4

Since the ratio are same so the ratios form a proportion.

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The volume of the simplex is 1^n. So , the volume of the simplex with vertices at the origin and the standard basis vectors in nn dimensions is simply 1.

In nn dimensions, the simplex is a geometric shape formed by connecting the origin and the standard basis vectors.

The volume of this simplex can be determined by finding the determinant of the matrix formed by these basis vectors. Since the standard basis vectors are orthogonal, the determinant of this matrix will be equal to the product of their magnitudes.

In nn dimensions, each standard basis vector has a magnitude of 1. Therefore, the volume of the simplex is 1^n.

To simplify, any number raised to the power of 1 is equal to the number itself.

So, the volume of the simplex with vertices at the origin and the standard basis vectors in nn dimensions is simply 1.

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Answer:

I will assume you mean 0.015 out of 1.

It is 0.985

Step-by-step explanation:

Answer:

0.985

Step-by-step explanation:

The probability that a new fridge does not have a fault = 1 - 0.015

                                                = 0.985

Answer:

y=17 x=14

Step-by-step explanation:

see my attached picture

The results of the expressions involving logarithms are listed below:

Case 1: 1 / 2

Case 2:

Subcase a: 0

Subcase b: 11 / 2

Subcase c: - 11 / 2

In this problem we have a case of an expression involving logarithms that must be simplified and three cases of expressions involving logarithms that must be evaluated. Each case can be solved by means of the following logarithm properties:

㏒ₐ (b · c) = ㏒ₐ b + ㏒ₐ c

㏒ₐ (b / c) = ㏒ₐ b - ㏒ₐ c

㏒ₐ cᵇ = b · ㏒ₐ c

Now we proceed to determine the result of each case:

Case 1

㏒ ∛8 / ㏒ 4

(1 / 3) · ㏒ 8 / ㏒ 2²

(1 / 3) · ㏒ 2³ / (2 · ㏒ 2)

㏒ 2 / (2 · ㏒ 2)

1 / 2

Case 2:

Subcase a

㏒ [b / (100 · a · c)]

㏒ b - ㏒ (100 · a · c)

㏒ b - ㏒ 100 - ㏒ a - ㏒ c

3 - 2 - 2 + 1

0

Subcase b

㏒√[(a³ · b) / c²]

(1 / 2) · ㏒ [(a³ · b) / c²]

(1 / 2) · ㏒ (a³ · b) - (1 / 2) · ㏒ c²

(1 / 2) · ㏒ a³ + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · ㏒ a + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · 2 + (1 / 2) · 3 + 1

3 + 3 / 2 + 1

11 / 2

Subcase c

㏒ [(2 · a · √b) / (5 · c)]⁻¹

- ㏒ [(2 · a · √b) / (5 · c)]

- ㏒ (2 · a · √b) + ㏒ (5 · c)

- ㏒ 2 - ㏒ a - ㏒ √b + ㏒ 5 + ㏒ c

- ㏒ (2 · 5) - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- ㏒ 10 - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- 1 - 2 - (1 / 2) · 3 - 1

- 4 - 3 / 2

- 11 / 2

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Answer: 104

Step-by-step explanation: Based on the given conditions, formulate:: 12x5+4x11

Calculate the product or quotient: 60+40

Calculate the sum or difference: 104

Answer:

The coach spent $104 in total

Step-by-step explanation:

Each baseball costs $4 and there are 11 of them. the eqaution is 11 x 4 = 44

Each hat costs $12 and there are 5 of them. the equation is 12 x 5 = 60

Add them together in the equation 60 + 44 and you get 104.

Answer:

Below

Step-by-step explanation:

Equivalent interest rate in decimal form will be   ( 1+i)^n - 1    

   where i = periodic interest in decimal = .05/4     n = periods = 4  per year  

(1+ .05/4)^4 -1 = 5.09 % equivalent interest per year

.05 / 4 = .0125    or    1.25%   16 times   ( 4 times per year x 4 years)  

Answer:

209 cubic mm.

Step-by-step explanation:

Formula for volume of cone:

\(V=\frac{1}{3} \pi r^2 h\)
Now let's plug in the values.
\(V=\frac{1}{3} \pi 5^2 8\)
\(V=\frac{1}{3} \pi 200\)
\(V=\frac{200}{3} \pi\)
\(V=209.4395...\)
Round to the nearest cubic mm and the volume is 209 cubic mm.

Answer:

209.333

Step-by-step explanation:

→ State the area for the volume for a cone

1/3 × π × r² × h

→ Substitute in the numbers

1/3 × 3.14 × 5² × 8

→ Evaluate

209.333