How do you define the range Mcq?.

So, the y-coordinate of the solution of the system of equations 3x + 2y = 7 and y - 3x = 11 is 6.

To find the y-coordinate of the solution of a system of equations, we can use one of the methods for solving systems of equations, such as substitution, elimination, or graphing. In this case, we will use substitution method.

The system of equations is:

3x + 2y = 7

y - 3x = 11

We can solve for y in the second equation and get:

y = 3x + 11

Now we can substitute this expression of y into the first equation:

3x + 2(3x + 11) = 7

3x + 6x + 22 = 7

9x + 22 = 7

9x = -15

x = -5/3

Now we can substitute this value of x into the second equation:

y = 3(-5/3) + 11

y = -5 + 11

y = 6

So, the y-coordinate of the solution of the system of equations 3x + 2y = 7 and y - 3x = 11 is 6.

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The three (3) statements which are true include the following:

A. The radius of the circle is 3 units.

B. The center of the circle lies on the x-axis.

D. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²   ....equation 1.

Where:

From the information provided above, we have the following equation of a circle:

x² + y² – 2x – 8 = 0      ......equation 2.

In order to determine the true statements, we would rewrite the equation in standard form and then factorize by using completing the square method:

x² – 2x + y² = 8 = 0

x² – 2x + (2/2)² + y² = 8 + (2/2)²

x² – 2x + 1 + y² = 8 + 1

(x – 1)² + (y - 0)² = 9         .......equation 3.

Comparing equation 1 and equation 3, we have the following:

Center (h, k) = (1, 0)

Radius (r) = 3

Additionally, this line and the center of the given circle lies on the x-axis (x-coordinate) because the y-value is equal to zero (0).

(x – 0)² + (y - 0)² = 3²

x² + y² = 9.

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Answer:

371 meters

Step-by-step explanation:

This is a triangle trigonometry problem. The phase "angle of depression" means the angle looking down to the boat instead of looking straight out from the top of the tower. See image. You can then find the rest of the angle is 70°. Looking at the boat creates one line, the tower is another side, 135m, and the distance to the boat is the third side of a triangle. See image.

Tangent is a trig ratio. It compares the side opposite from the angle to the side next to (adjacent) the angle. We can then write an equation. Unless the teacher/program/text gives you tan 70°, you need a calculator to find it.

tan 70° = x/135

Multiply both sides by 135.

135 tan 70° = x

Put this in a calculator.

135 × tan70°

it comes out a long decimal. But the directions said to round to the nearest meter.

The boat is about 371 meters away from the foot of the tower.

Answer:

Simon's age is 18.

Step-by-step explanation:

Let Simons age be s and the age of each twin be t.

s + 2t = 48

s - t = 3

Subtract the second equation from the first:

s - s + 2t - (-t) = 45

2t + t = 45

3t = 45

t = 45/3 = 15.

Now we find Simon's age by plugging t = 15 in the second equation:

s - t = 3

s - 15 = 3

s = 3 + 15 = 18.

Answer:

To calculate the volume of a triangular pyramid, we can use the formula:

V = (1/3) * B * h

where V is the volume, B is the area of the base, and h is the height of the pyramid.

Since the base of the pyramid is a right-angled triangle, we can use the Pythagorean theorem to find the length of the other two sides, which are the legs of the triangle. The hypotenuse is 6 cm and the angle opposite to the hypotenuse is 30°, so we can use the sine function to find the length of the other leg:

sin(30) = opposite / hypotenuse

opposite = (sin(30) * hypotenuse) = (1/2 * 6) = 3

Now we can use the area formula for a right-angled triangle:

B = (1/2) * base * height = (1/2) * 3 * 6 = 9

To find the height of the pyramid, we can use the fact that all side faces form an angle of 60° with the base. We can use the sine function to find the height of the pyramid:

sin(60) = opposite / hypotenuse

opposite = (sin(60) * hypotenuse) = (√3/2 * 6) = 3√3 cm

Now we can substitute the values of B and h into the volume formula:

V = (1/3) * B * h = (1/3) * 9 * 3√3 = 3√3 cm³

So the exact volume of the triangular pyramid is 3√3 cm³.

Step-by-step explanation:

The scatter plot is the type of graph that is most frequently used to show the relationship between two numerical variables.

The graphs that show the association between two variables in a data set are called scatter plots. It shows data points on a two-dimensional plane or a Cartesian system.

The independent variable or attribute is represented by the X-axis, and the dependent variable is plotted using the Y-axis. To describe these charts, diagrams or graphs are usually employed. An XY graph, scatter chart, or scattergram are other names for a scatter plot. The scatter diagram plots numerical data pairings with one variable on each axis to show the relationship between them.

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Answer:

8 ft

Step-by-step explanation:

Area of a circle is given by πr² where r is the radius

Here we are given the area A and asked to find the radius

We have Area :
πr² = 64π

Dividing by π on both sides we get
r² = 64

r = ±√64

r = ±8

We can ignore negative values for radius and state that

r = 8 ft

The values of composite functions are,

(w о u)(2) = √7 + 2

(u о w)(2) = 9 + 4√2

Function composition is an operation о used in mathematics that takes two functions, f and g, and creates a function, h = g о f, such that h(x) = g. The function g is applied in this operation to the outcome of applying the function f to x.

Given:

u(x) = x^2 + 3

w(x) = √x+2

We have to find (w о u)(2) and (u о w)(2).

First to find (w о u)(x)

(w о u) = w(u(x))

         = w(x^2 + 3)

(w о u) = √(x^2 + 3) + 2

(w о u)(2) = √(2^2 + 3) + 2

 (w о u)(2) = √7 + 2

Now to find (u о w).

(u о w)(x) = u(w(x))

= u(√x+2)

= (√x+2)^2 + 3

= x + 4√x + 4 + 3

(u о w)(x) = x +  4√x + 7

(u о w)(2)  = 2 + 4√2 + 7

 (u о w)(2)  = 9 + 4√2

Hence,

The values of composite functions are,

(w о u)(2) = √7 + 2

(u о w)(2)  = 9 + 4√2

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Answer:

Lauren has 44 watermelons

Step-by-step explanation:

Let us use W to denote the number of watermelons and O to denote the number of oranges

We have

W:O = 88:14

This can be represented as a fraction:

[tex]\dfrac{W}{O} = \dfrac{88}{14}[/tex]

Divide numerator and denominator of  [tex]\dfrac{88}{14}[/tex]  by 2

[tex]\dfrac{88 \div 2}{14 \div 2} = \dfrac{44}{7}\\\\\\\\\mathrm{So\; \dfrac{W}{O} = \dfrac{44}{7}}\\\\[/tex]

This means for every 7 oranges there are 44 times that number of watermelons

Since we are given that there are 7 oranges she should have 44 watermelons

Another way of looking at this is from the relation

[tex]\dfrac{W}{O} = \dfrac{44}{7}}\\\\[/tex]

Putting in O = 7 we get

[tex]\dfrac{W}{7} = \dfrac{44}{7}\\\\[/tex]

Since the denominators are the same the numerators must be the same i.e. W = 44

Lauren has 44 watermelons

Considering triangle HRC, the equations that can be used to solve for the value of w are

The triangle HRC is a right triangle and can be solved by various methods such as: Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

m² = s² + w²

(√125)² = 9² + w²

Applying SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

solving for w using cos, CAH

cos y = w / m

cos y = w / √125

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The distance between the given set of points is 7.8 units.

To find the distance between two points in a coordinate plane, we can use the distance formula.

The distance formula states that the distance between two points (x1, y1) and (x2, y2) is given by the square root of ((x2 - x1)^2 + (y2 - y1)^2).

In this case, we are given the points p(8, 2) and q(3, 8). Therefore, we can plug in the coordinates of these points into the distance formula:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Distance = √((3 - 8)^2 + (8 - 2)^2)

Distance = √((-5)^2 + 6^2)

Distance = √(25 + 36)

Distance = √61

The square root of 61 is approximately 7.8 which rounded to the nearest tenth is 7.8.

Therefore, The distance between the given set of points is 7.8 units.

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The substance having half-life of 6 seconds and quantity of 50 gm initially will remain 1.5625gm after 30seconds.

What is half-life of a substance?

When we talk about half life, we are talking about the time taken for exactly half of the mass of the radioactive mass in question to have disintegrated.

More like, the amount of time it takes for the radioactive mass to have lost exactly half of its mass.

Now,

Since it is just 5 half lives, we can proceed manually

In the first, we shall have 25g left

in the second, we shall have 12.5g left

In the third, we shall have 6.25g left

In fourth, we shall have have 3.125g left

and finally, in the fifth, we shall have 1.5625g.

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The mirror image of the coordinates is (4, - 20)

The term coordinates is defined are ordered pairs of points that help us locate any point in a 2D plane or 3D space.

Here we have given the coordinates (4, 20).

And we need to find the mirror image of given coordinates.

As per the definition of coordinates the rule of Mirror image of (x , y ) in the x - axis is  written ( x , -y).

Here we have the value of x as 4 and the value of y as 20.

When we apply the rule on the given coordinates then we get the resulting points,

=> (4, 20) = (4, - 20)

Complete Question:

What is the mirror image of the coordinate (4,20)?

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The additive inverse of 3/7 is -3/7, and the multiplicative inverse of 3/7 is 7/3.

A number that gives 0 after adding with its is called an Additive inverse and it gives 1 after multiplication with its is called a multiplicative inverse.

Here, the given number is: 3/7

Let, x be the additive inverse of the number:

3/7+x=0

x=-3/7

Thus, the additive inverse of 3/7 is -3/7.

Now, let y be the multiplicative inverse of 3/7,

⇒3/7*y

⇒1*y=7/3

Thus, the multiplicative inverse of 3/7 is 7/3.

Hence, the product of additive inverse and multiplicative inverse of minus 3 upon 7

⇒-3/7*7/3

⇒-1

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Answer:

170 and 130

Step-by-step explanation:

Answer:0 on his road trip playlist

Step-by-step explanation:

Answer:

87cm²

Step-by-step explanation:

surface area =l×w all round since there is no square, we begin with the first part

6×3×2=36

3×2×2=12

6×2×2=24

4×1×2=

3×1×2=

1×1=1

Then add them all =87cm²

The zeros, y-intercept and vertex for the given quadratic equation f(x)=       (x + 1)² + 4 are respectively,

Zeros-  (-1 + 2i)

Y-intercept- 5

Vertex- (-1, 4)

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

f(x) = y = (x + 1)² + 4

y = (x + 1)² + 4

y - 4 =  (x + 1)²

So, for vertex

x + 1 = 0

x = -1

y-4 = 0

y = 4

For Zeros, y = 0

y-4 = (x +1)²

(x +1)² = -4

x = -1 + 2i,   -1-2i

the zeros are imaginary

For y intercept, x = 0

y-4 = (x +1)²

y   = 4 + (1)²

y   = 5

Hence,  vertex, zeros, and y-int. are respectively (-1, 4), (-1 + 2i), 5

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Answer: -3/2

Step-by-step explanation:

To find the slope of the line perpendicular to the given one, we first need to change the equation to y=mx+b to find the original slope.

[tex]6x-9y=216[/tex]             [subtract both sides by -6x]
[tex]-9y=-6x+216[/tex]        [divide both sides by -9]
[tex]y=\frac{2}{3} x-24[/tex]

Now we know slope is 2/3. The slope of the perpendicular line is the opposite sign and reciprocal of the slope.

Opposite would make it -2/3.

Reciprocal would be -3/2.
So the slope is -3/2.

The assumption we would make to start the indirect proof of AB is congruent to BC is AB + BC.

Indirect Proof: 

Step 1 Suppose a right triangle's hypotenuse is not the longest side. That is BC > AB and AC > AB.

Step 2 If BC > AB, then ∠C < ∠A. Since m C = 90, ∠A > 90. So, ∠C + ∠A > 180. By the same

reasoning, ∠C + ∠B > 180.

Step 3 Both connections counter the fact that the sum of the measures of the angles of a triangle equals 180.

Thus, the hypotenuse must be the longest side of a right triangle.

Hence, the correct option is C.

--The given question is incorrect; the correct question is

"What assumption would you make to start the indirect proof that AB is

congruent to BC?

A. A ≠ B

B. B ≠ C

C. AB + BC

D. BA < CB​"--

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The answer of 10 more than 99 is 109.

The answer of 10 more than 99 is 109 which can be derived using simple mathematical calculations.

To find 10 more than 99, you can add 1 to the original number 99.

10 + 99 = 109

It's a simple arithmetic operation where you add a specific number, in this case, 10, to the original number.

An arithmetic operation is a mathematical process that combines two or more numbers to produce a new number. The most basic arithmetic operations are addition, subtraction, multiplication, and division.

Addition: It is the process of combining two or more numbers to find their sum. For example, 2 + 3 = 5 is an addition operation.

Subtraction: It is the process of finding the difference between two numbers. For example, 5 - 3 = 2 is a subtraction operation.

Multiplication: It is the process of finding the product of two or more numbers. For example, 3 x 4 = 12 is a multiplication operation.

Division: It is the process of finding the quotient of two numbers. For example, 12 ÷ 3 = 4 is a division operation.

Therefore, The answer of 10 more than 99 is 109.

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Evaluating the exponential equation:

y = (1/3)*4^x

on x = 3/2 gives y = 8/3.

Here we have the following exponential equation:

y = (1/3)*4^x

And we want to evaluate it on x = 3/2, to do so, we just need to replace the variable on the equation by the given number.

We will get:

y = (1/3)*4^(3/2)

The power part can be rewrite as:

y = (1/3)*√4^3

y = (1/3)*2^3

y = (1/3)*8 = 8/3

That is the value of the equation when evaluated on x = 3/2.

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The inverse of a function in vertex form can be determined by substituting the function in the standard form of a quadratic function

The various steps to find the inverse of a function in vertex form can be noted as -

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Account B has more money than account A. Then account that has the greater principal will be account B.

Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.

The formula for interest is written as,

I = (PRT)/100

Where P is the principal, R is the rate of interest, and T is the time.

Dakota procured $10.50 in revenue in Record An and $35.00 in revenue in Record B following 21 months. In the event that the straightforward financing cost is 3% for Record An and 5% for Record B.

Then the account has the greater principal will be given as,

10.50 = [P₁ x 3 x (21/12)] / 100

1050 = 5.25P₁

P₁ = $200

35 = [P₂ x 5 x (21/12)] / 100

3500 = 8.75P₂

P₂ = $400

Account B has more money than account A. Then account that has the greater principal will be account B.

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Answer:

2x - 7 = x + 14

By drawing every diagonal from one vertex in a convex, n-sided polygon, the polygon can be decomposed into n - 2 triangles.

The sum of a the internal angle measures of a polygon of n sides is given by the equation presented as follows:

S(n) = 180(n - 2).

Hence the sum of the internal angle measures of a triangle, composed of three sides, is given as follows:

180.

Thus the number of triangles on a polygon of n sides is given as follows:

180(n - 2)/180 = n - 2.

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The inequality statement will be x-5 ≤ 6.

Inequalities are mathematical expressions that contain variables and numerical terms that are separated by the inequality symbol.

An inequality can be derived from a statement of words, which must be correctly interpreted in order to yield the appropriate inequality.

When there are more than and fewer than values in the inequality, we know that the variable must be in the middle.

The inequality symbols are greater than, less than, greater than or equal, and less than, or equal.

There are two conditions given in the question as mentioned below:

1. Five less than a number

2. the number is less than or equal to 6

Let x be the number,

x-5 ≤ 6

So, the inequality statement will be x-5 ≤ 6

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Graph behavior as x approaches is referred to be the end behavior of a polynomial function.

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The error interval for the area of the shaded region is given as follows:

56.6 < a < 56.8.

The area of the circle is of 78.1 cm², rounded to one decimal place, hence the interval for the area of the circle is of:

78.05 <= area circle < 78.15.

The area of the square is of 21.4 cm², rounded to one decimal place, hence the interval for the area of the circle is of:

21.35 <= area square < 21.45.

The error formula is:

Area circle - Area square.

The minimum error is when the area of the circle is the greatest and the square is the least, hence:

m = 78.15 - 21.35

m = 56.8.

The maximum error is when the area of the circle is the least and the square is the greatest, hence:

n = 78.05 - 21.45

n = 56.6.

Meaning that the error interval is of:

56.6 < a < 56.8.

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The commutative property applies only to addition and multiplication of real numbers.

What is commutative property in math?

This law simply states that with addition and multiplication of numbers, you can change the order of the numbers in the problem and it will not affect the answer. Subtraction and division are NOT commutative.

so as ask in question that, does the commutative property apply to all real numbers?

The commutative property applies to addition and multiplication of real numbers, meaning that a + b = b + a and a * b = b * a for any real numbers a and b.

However, it does not apply to subtraction or division, meaning that a - b ≠ b - a and a / b ≠ b / a for all real numbers a and b.

Therefore, the commutative property applies only to addition and multiplication of real numbers.

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