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Therefore, the solution to the system of linear equations is (x, y) = (-1, 4).

In mathematics, an equation is a statement that two expressions are equal. It typically contains one or more variables (unknowns) and specifies a relationship between those variables. Equations are used to model real-world phenomena, solve problems, and make predictions. There are many types of equations in mathematics, including linear equations, quadratic equations, polynomial equations, exponential equations, trigonometric equations, and many more. Each type of equation has its own set of methods and techniques for solving it. Solving an equation means finding the values of the variables that satisfy the equation. This may involve manipulating the equation algebraically, using graphical methods, or employing numerical techniques such as iteration or approximation. Equations play a central role in many areas of mathematics and science, as well as in everyday life. They are used to model physical systems, optimize processes, design products, and analyze data, among many other applications.

Here,

We are given the system of linear equations:

17x + 4y = -1 ...(1)

y - 4x - 8 = 0 ...(2)

We can use the substitution method to solve this system. Solving equation (2) for y, we get:

y = 4x + 8

Substituting this expression for y into equation (1), we get:

17x + 4(4x + 8) = -1

Simplifying this equation, we get:

17x + 16x + 32 = -1

33x = -33

x = -1

Substituting x = -1 into equation (2), we get:

y - 4(-1) - 8 = 0

y + 4 - 8 = 0

y = 4

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The prove to show that ΔABC is similar to ΔMNC is explained below.

Similar triangles are triangles that have the same shape but are not necessarily the same size. More precisely, two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional.

Considering the given diagram, we can say:

AM = MC    (Given)

BN = NC     (Given)

BC = BN + NC (addition property of a line segment)

AC = AM + MC (addition property of a line segment)

NC/ BC = MC/ AC = constant

∠ACB = ∠MCN  (Reflexive property)

Thus, ΔABC ~ ΔMNC (Side-Angle-Side theorem)

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Answer:

a) p(-6) = 30

b) c = -2 ,1

Step-by-step explanation:

[tex]p(c)=c^2+c[/tex]

a) Evaluate p(-6)

This mean input -6 into the equation to solve for p(-6) =

[tex]p(-6)=(-6)^2+(-6)\\\\p(-6)=36-6\\\\p(-6)=30\\[/tex]

(b) Solve for p(c) = 2.

[tex]p(c)=c^2+c\\\\2=c^2+c\\\\c^2+c=2\\\\c^2+c-2=0\\\\Factoring\\(c+2)(c-1)=0\\(c+2)=0,(c-1)=0\\c = -2 , 1[/tex]

The cοrrelatiοn cοefficient οf data is 1.

A statistical measure knοwn as cοrrelatiοn expresses hοw clοsely twο variables are related linearly (meaning they change tοgether at a cοnstant rate).

The cοnstant cοefficient (οr cοnstant term) is the cοefficient nοt attached tο variables in an expressiοn. Fοr example, the cοnstant cοefficients οf the expressiοns abοve are the number 3 and the parameter c, respectively.

The cοefficient attached tο the highest degree οf the variable in a pοlynοmial is referred tο as the leading cοefficient. Fοr example, in the expressiοns abοve, the leading cοefficients are 2 and a, respectively.

In excel, use fοllοwing cοmmand tο find r

=>cοrrel(select data οf grade, select data οf Reading level)  

press enter

=> 1  

i.e. 1.00

The required cοrrelatiοn cοefficient r is 1.00

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On solving the provided question we cans ay that As a result, x + 4 function denotes the number of years the principal is older than the instructor, where x is the student's age in years.

Mathematicians examine numbers with their modifications, equations and associated structures, forms and their locations, and feasible positions for these things. The term "function" indicates the connection between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and outputs where each supply leads to a specific, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used to denote functions (x). The symbol for entry is an x. The four primary types of accessible capabilities are on functions, yet another skills, so multiple capabilities, in capabilities, and on operations.

Let's start by writing down the phrases from the problem:

• The teacher's age is six years older than the student's age: T = 2x + 6, where T is the age of the instructor.

• The principal's age is ten years older than the student's age: P = 3x + 10, where P is the age of the principal.

To determine how many years the principal is older than the instructor, subtract the teacher's age from the principal's age:

P - T = (3x + 10) - (2x + 6)

When we simplify the equation, we get:

P - T = x + 4

As a result, x + 4 denotes the number of years the principal is older than the instructor, where x is the student's age in years.

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The mathematical expression 23 - √81 has a value of 14 when evaluated, mathematically

Given the following expression

23 - √81

The expression 23 - √81 involves finding the difference between the number 23 and the square root of 81.

We know that the square root of 81 is 9, so we can simplify the expression to:

23 - √81 = 23 - 9

Evaluate the difference

23 - √81 = 14

Therefore, the value of the expression is 14.

In evaluating expressions like these, it is important to be familiar with basic arithmetic operations and the rules of exponents and radicals.

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Answer:

Step-by-step explanation:

Yes, that is correct. The measure of the exterior angle of a triangle is equal to the sum of the two remote interior angles. In other words, if you extend one side of a triangle to form an exterior angle, then the measure of that exterior angle is equal to the sum of the measures of the two interior angles that are not adjacent to the exterior angle. This property is known as the Exterior Angle Theorem.

Mathematically, we can express this as:

Exterior angle = Sum of remote interior angles

Or, in symbols:

∠ABC = ∠A + ∠C

where ∠ABC is the exterior angle formed by extending side BC of triangle ABC, and ∠A and ∠C are the two remote interior angles.

Here are two more examples that illustrate the Exterior Angle Theorem:

Example 1:

Consider a triangle ABC with angles A, B, and C as shown below. If we extend side AC to form an exterior angle, then we can label the exterior angle as ∠DCE. The remote interior angles are ∠B and ∠A.

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Copy code

      C

     / \

    /   \

   /     \

  /       \

 /         \

/______\

A             B

      D

According to the Exterior Angle Theorem, we have:

∠DCE = ∠B + ∠A

Step-by-step explanation:

The height of the cable above the bridge is given by the function:

h(x) = 0.25x^2 - 0.8x + 30

To find the minimum height of the cable above the bridge, we need to find the vertex of the parabola, which is the lowest point.

The x-coordinate of the vertex is given by:

x = -b / 2a

where a = 0.25 and b = -0.8. Substituting these values, we get:

x = -(-0.8) / 2(0.25) = 1.6

So the vertex is at x = 1.6.

To find the height of the cable at the vertex, we substitute x = 1.6 into the equation for h(x):

h(1.6) = 0.25(1.6)^2 - 0.8(1.6) + 30 = 29.48

Therefore, the minimum height of the cable above the bridge is approximately 29.48 feet (rounded to two decimal places).

Answer:

(x - 5)^2 + (y - 5)^2 = 25

Step-by-step explanation:

If a circle has no x-intercepts and no y-intercepts, it means that the circle does not intersect either the x-axis or the y-axis. In other words, the center of the circle must lie at some point (h, k) where h and k are not equal to zero.

The general equation of a circle with center (h, k) and radius r is:

(x - h)^2 + (y - k)^2 = r^2

Since we know that the circle has a radius of 5, we can substitute r = 5 into the equation:

(x - h)^2 + (y - k)^2 = 25

Now, we need to find values for h and k such that the circle has no x-intercepts and no y-intercepts. Since the x-intercepts occur when y = 0 and the y-intercepts occur when x = 0, we need to make sure that neither of these values satisfies the equation.

Let's first consider the x-intercepts. We want to make sure that the circle does not intersect the x-axis, which means that the y-coordinate of the center must be equal to the radius. In other words, k = 5. Now, the equation becomes:

(x - h)^2 + (y - 5)^2 = 25

Next, we need to make sure that the circle does not intersect the y-axis, which means that the x-coordinate of the center must be equal to the radius. In other words, h = 5. Now, the equation becomes:

(x - 5)^2 + (y - 5)^2 = 25

Therefore, the equation of the circle that has no x-intercepts, no y-intercepts, and a radius of 5 is:

(x - 5)^2 + (y - 5)^2 = 25

Answer:

5) A = 70°

6) X = 55°

7) Y = 8°

8) A = 51°

Step-by-step explanation:

There really no way to explain. All you ahve to do is inverse function to solve for the angle. Use a calculator.

5) sin(A) = 0.9397

[tex]A=sin^-1(0.9397)\\\\A=69.701...\\\\A = 70\\[/tex]

6) cos(X) = 0.5763

[tex]X=cos^-1(0.5763)\\\\X=54.998...\\\\X=55\\[/tex]

7) tan(Y) = 0.1405

[tex]Y=tan^-1(0.1405)\\\\Y=7.997...\\\\Y = 8\\[/tex]

8) sin(A) = 0.7771

[tex]A=sin^-1(0.7771)\\\\A=50.995...\\\\A = 51\\[/tex]

Answer:

for any regular polygon, the sum of the exterior angles is always 360 degrees. In a regular polygon, all exterior angles have the same measure, which is equal to 360 degrees divided by the number of sides.

Let n be the number of sides of the polygon. Then we have:

360/n = 21.2

To solve for n, we can cross-multiply and simplify:

360 = 21.2n

n = 360/21.2

n ≈ 16.98

Since n must be a whole number (the number of sides in a polygon must be a whole number), the closest option is D) 17. Therefore, the polygon has 17 sides.

Option C. Al spends approximately 21 euros on his lunch in France.

Conversion rate is the percentage of website visitors or potential customers who take a desired action, such as making a purchase, signing up for a newsletter, or filling out a form. In other words, it is the rate at which website visitors are converted into customers or subscribers.

To convert US dollars to euros, we multiply the US dollar amount by the exchange rate of 0.69 euro per US dollar:

30.00 US dollars × 0.69 euro/US dollar = 20.70 euros ≅ 21 euros

Therefore, Al can spend approximately 21 euros on his lunch in France.

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Answer:1,200,000

Step-by-step explanation:

To divide 240g in the ratio 5:3:4, we need to find out the total number of parts of the ratio:

5 + 3 + 4 = 12

Now, we can find the value of one part of the ratio by dividing the total quantity by the total number of parts:

240g ÷ 12 = 20g

So, one part of the ratio is equal to 20g.

To find the quantities of each part of the ratio, we multiply the value of one part by the respective ratio number:

5 parts x 20g = 100g (for the first part)

3 parts x 20g = 60g (for the second part)

4 parts x 20g = 80g (for the third part)

Therefore, the quantities of 240g divided in the ratio 5:3:4 are 100g, 60g, and 80g respectively.

Answer:

80

Step-by-step explanation:

Answer:

the answer is b because 16km is resolved by 19.2

A loan for $3,400 at 16% should be paid first as it has the highest interest rate.

A loan is a financial agreement in which one party (the lender) agrees to give money, property, or other assets to another party (the borrower) in exchange for the promise of repayment with interest or other charges. Loans are typically used by individuals, businesses, or governments to finance specific projects, make purchases, or cover expenses.

Assuming that all other factors such as minimum payments and penalties are the same, the loan that you should try to pay off first is the one with the highest interest rate, as it will be accruing interest at a faster rate than the others.

Based on this reasoning, the loan that you should try to pay off first is option A, which has a higher interest rate of 16%.

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The length οf side x can be any value, as lοng as it is nοt 0.

We can use the trigοnοmetric ratiοs fοr 30°-60°-90° triangles tο sοlve fοr the value οf x.

In a 30°-60°-90° triangle, the sides are in the ratiο:

1 : √3 : 2

In this case, we have the side οppοsite the 60° angle (which is the lοnger leg) equal tο x√3 and the side οppοsite the 30° angle (which is the shοrter leg) equal tο x.

Sο we can set up the fοllοwing equatiοn:

x√3 = 2x sin 60°

Simplifying the right side:

sin 60° = √3/2

2x sin 60° = 2x(√3/2) = x√3

Substituting back intο the equatiοn:

x√3 = x√3

This is true fοr any value οf x, as lοng as x is nοt equal tο 0. Therefοre, the length οf side x can be any value, as lοng as it is nοt 0.

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The area of Gabriel's father's garden is 62/3 square units, which is approximately 20.67 square units.

The question's purpose is obscure. But, based on its measurements of 7 3/4 by 2 2/3, I'm assuming you're interested in learning how to locate the location of Gabriel's father's garden.

We must multiply the length by the breadth in order to determine the garden's area. To make the calculation simpler, we can convert the mixed values to improper fractions as follows:

7 3/4 = (7 × 4 + 3)/4 = 31/4

2 2/3 = (2 × 3 + 2)/3 = 8/3

The garden is thus 8/3 in width and 31/4 in length. We multiply these values to determine the area:

Area is equal to 31/4 x (8/3), or 62/3 square units.

The size of Gabriel's father's garden is therefore 62/3 square units, or roughly 20.67 square units.

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The inequality to replace the symbol is > and the expression is -4/9 > -5/9​.

We can utilize the following parameters in our calculation based on the question:

-4/9* -5/9​

Represent the symbol * as a blank

This gives

-4/9 [  ] -5/9​

Evaluate the quotients

-0.44444444444 [  ] -0.55555555555

By comparison, 0.44444444444 is greater than -0.55555555555

Using the above as a guide, we have the following:

-0.44444444444 [ > ] -0.55555555555

So, we have

-4/9 > -5/9​

Hence, the inequality is >

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This means that option A, "4 < d < 26," is the correct answer.

The triangle inequality can be used to calculate various distances between Sherry and Amy. The lengths of any two sides of a triangle must add up to more than the length of the third side in order for the triangle inequality to hold.

If we assume that d is the separation between Amy and Sherry in this instance, we can then create a triangle with sides that are 11, 15, and d in length. The inequality of the triangle indicates that:

11 + 15 > d

or

d < 26

and

15 + d > 11

or

d > 4

So, d might have any of the following values:

4 < d < 26

This indicates that "4 d 26" in option A is the right response.

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The square root of 6,57,55,881 using long division method is 8563.

Group the digits starting from the units place into pairs of two, from right to left. If there are any remaining digits, add a zero to the left of them. So for 65755881:

65 | 75 | 58 | 81

Find the largest number whose square is less than or equal to the leftmost group (in this case, 65). The square of 8 is 64, so the first digit of the square root must be 8. Write 8 as the first digit of the answer and subtract 64 from 65 to get 1.

Bring down the next group (75) to the right of the remainder (1) to get 175.

Double the first digit of the current partial answer (which is 8) to get 16, and place a blank digit to its right. We will be filling in this blank digit with the next digit of the square root.

Find the largest digit d such that the number 16d, when multiplied by d and then by 10, is less than or equal to 175. To do this, we can start with d=9 and work downwards until we find a suitable value. We find that d=5 works, since 165510=8250 is less than 17500. So the next digit of the square root is 5.

Append the digit 5 to the partial answer, so we have 85 as the current partial answer.

Subtract 165 (the product of 16 and 5) from 175 to get the new remainder, which is 10.

Bring down the next group (58) to the right of the remainder (10) to get 1058.

Double the first digit of the current partial answer (which is 85) to get 170, and place a blank digit to its right.

Find the largest digit d such that the number 170d, when multiplied by d and then by 10, is less than or equal to 1058. To do this, we can start with d=9 and work downwards until we find a suitable value. We find that d=6 works, since 1706610=102360 is less than 105800. So the next digit of the square root is 6.

Append the digit 6 to the partial answer, so we have 856 as the current partial answer.

Subtract 1706 (the product of 170 and 6) from 1058 to get the new remainder, which is 402.

Bring down the last group (81) to the right of the remainder (402) to get 40281.

Double the first digit of the current partial answer (which is 856) to get 1712, and place a blank digit to its right.

Find the largest digit d such that the number 1712d, when multiplied by d, is less than or equal to 40281. To do this, we can start with d=9 and work downwards until we find a suitable value. We find that d=3 works, since 17123×3=51369 is less than 40281. So the next digit of the square root is 3.

Append the digit 3 to the partial answer, so we have 8563 as the final answer.

Therefore, the square root of 65755881 is 8563.

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Answer:

see the attachment

Step-by-step explanation:

Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that the shipment does not meet requirements.

Answer:

1000-39=961

so 961 apples are left.

Step-by-step explanation:

3x squared -9 = 12

3x squared = 12 + 9

3x squared = 21

am i doing the wrong maths?

is it find what 3x squared is or....

The value of x, considering the similar triangles, is given as follows:

B) 6.

Similar triangles are triangles that share these two features listed as follows:

Considering that the triangles for this problem are similar, the proportional relationship for the side lengths is given as follows:

9/3 = 12/4 = x/2.

Since the constant is of 3, the value of x is obtained with cross multiplication as follows:

x/2 = 3

x = 6.

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