What is the solution of the system?
4g + h = -4
12g + 2h = -4

Enter the coordinate pair in the boxes in alphabetical order (_, _)

The solution of the system of linear equations is (-1,3) and thus has unique solution as shown in the graph attached.

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

Given here: The linear equations here as y = -x + 2 & y = 3x + 6

For a system of two linear equations and two variables, there can be no solution, exactly one solution, or infinitely many solutions (just like for one linear equation in one variable). An equation can have infinitely many solutions when it should satisfy some conditions. The system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept. If the two lines have the same y-intercept and the slope, they are actually in the same exact line.

But clearly the two equations are not coincident and also not parallel

Thus the system of equations must have exactly one unique solution.

Therefore solving for the equations

y = -x + 2

y = 3x + 6

Substracting the two equations we get -4x-4=0 or x=-1

∴ y=1+2

     =3

Hence, The solution of the system of linear equations is (-1,3) and thus has unique solution as shown in the graph attached.

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Step-by-step explanation:

3×4(5)-10

12(5)-10

60-10

50

if pp is sufficient for q  is not equivalent to P <-> q for p and q conditional statement

The true statements for the conditional statement p → q are;

If p then q

p, therefore q

q, if p

p is enough condition for q

Reason for the above selection

The conditional statement p → q is read as If p then q

The deductive validity of the conditional statement is; p, therefore q

The conditional statemen, p → q also means;

1) q, if p

2) q, provided p

3) p, only of q

4) p implies q

5) q whenever, p

6) p is enough condition for q

7) q is a necessary condition for p

Therefore, the correct statements are;

If p then q

p, therefore q

q, if p

p is enough condition for q

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A. The radius of the sun in scientific notation is 9.66 x 10^8 kilometers and the radius of Earth is 6.37 x 10^3 kilometers.

B. To find the surface area of a sphere with a given radius, we can use the formula S = 4πr^2.

The surface area of the sun is 4π(9.66 x 10^8)^2 = 1.4 x 10^18 square kilometers.

The surface area of Earth is 4π(6.37 x 10^3)^2 = 5.1 x 10^10 square kilometers.

C. To find the ratio of the surface area of the sun to the surface area of Earth, we can divide the surface area of the sun by the surface area of Earth.

The ratio of the surface area of the sun to the surface area of Earth is: 1.4 x 10^18 / 5.1 x 10^10 = 2.7 x 10^7.

This ratio tells us that the surface area of the sun is 2.7 x 10^7 times larger than the surface area of Earth.

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Answer:34.5

Step-by-step explanation:

An expression to find the perimeter of this triangle is P = 3x + 10.

Mathematically, the perimeter of a triangle can be calculated by using this mathematical expression:

P = a + b + c

Where:

Given the following parameters:

Substituting the given parameters into the perimeter of a triangle  formula, we have the following;

Perimeter of triangle, P = x + 4 + x + 6 + x

Perimeter of triangle, P = 3x + 10

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The product of the operation -1.2 x (-1.2) is 1. 44

Multiplication is simply described as one of the four primary mathematical operations of arithmetic, other are;

The result of any multiplication operation is called a product.

Also, to multiply simply means to add equal group of numbers or variables.

It is also important to note the following multiplication of mathematical signs, we have;

From the information given, we have that;

-1.2 x (-1.2)

To find the product, expand the bracket, we get;

- 1.2 × - 1.2

Multiply the values, we get;

1. 44

Hence, the value is 1.44

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The equation can be used to find the number of pie he need to sell to break event.

c. 5x + 30 = 12x

Given :Mrs. Ramirez is making pies to sell at the local farmer’s market. It costs her $5 to make each pie, plus a one-time cost of $30 for baking supplies. She plans to sell the pies for $12 each.

To Find: Which equation can be used to find the number of pies she needs to sell to break even.

Solution:

Let no. of pies be x

It cost her $5 to make each pie

So, cost of making x pies = 5x

Since there is a one-time cost of $30 for baking supplies.

So, total cost for her is 5x+30

If she sells each pie for $12

Then cost of pies = 12x

Now,

The equation can be used to find the number of pies she needs to sell to break even:

c) 5x+30=12x

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This means that the solution to the triangle issue is ABC, which is equivalent to XYZ.

Any shape with 3 sides and three points is a polygon. The fundamental form of geometry is this. The corners of the triangular Triangle ABC are A, B, and C. When four parts are not collinear in a geometric shape, a single plane plus triangle are produced. As triangles have three sides as well as a top right corner, they are included in polygons.

Here.

Thus,

To prove : ABC and XYZ are similar

hence ∠A =  ∠X.

The definition of  ∠B and  ∠Y is the same.

Because  ∠Z =  ∠C,

Similar to xy, line ab shares the same value.

There is no difference between lines bc and yz.

XZ corresponds to line ac.

To come up with a solution, Cpct was used.

Triangle segments that match each other are congruent.

The solution to the triangle problem is ABC is proportional with XYZ as a result.

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Answer: it's Y  because i took the test, also when doing this type of math  problem you wouldn't start from X or Z because they are starting points

Step-by-step explanation:   I TOOK the test

The value of the integration of the expression [tex]$$\int x^3+\frac{1}{x^{0.5}} d x$$[/tex] will be  [tex]\frac{1}{4} x^4+2 x^{0.5}+C[/tex]

[tex]$$\int x^3+\frac{1}{x^{0.5}} d x$$[/tex]

Split the single integral into multiple integrals.

We will get: [tex]$$\int x^3 d x+\int \frac{1}{x^{0.5}} d x$$[/tex]

By the Power Rule, the integral of x^3 with respect to x is (1/4)x^4.

[tex]\frac{1}{4} x^4+C+\int \frac{1}{x^{0.5}} d x[/tex]

Let u=x^{0.5}.

Then [tex]d u=\frac{0.5}{x^{0.5}} d x[/tex],

So [tex]$\frac{x^{0.5}}{0.5} d u=d x$[/tex].

Now, we will rewrite the above using u and du.

Let u=x^{0.5}.

Finding the value of (du/dx)

Differentiate x^{0.5}.

[tex]\frac{d}{d x}\left[x^{0.5}\right][/tex]

Differentiate using the Power Rule which states that [tex]$\frac{d}{d x}\left[x^n\right]$[/tex] is n x^{n-1} where n=0.5.

We will get: 0.5 x^{-0.5}

Simplify.

Rewrite the expression using the negative exponent rule

[tex]b^{-n}=\frac{1}{b^n}\\0.5 \frac{1}{x^{0.5}}[/tex]

Combine 0.5 and [tex]\frac{1}{x^{0.5}}[/tex] we will get [tex]\frac{0.5}{x^{0.5}}[/tex]

Rewrite the problem using u and du.

We will get it as:

[tex]\frac{1}{4} x^4+C+\int 2 d u[/tex]

Apply the constant rule, we will get: [tex]\frac{1}{4} x^4+C+2 u+C[/tex]

Simplifying we will get it as: [tex]\frac{1}{4} x^4+2 u+C[/tex]

Replace all occurrences of u with x^{0.5}.

We will get it as: [tex]\frac{1}{4} x^4+2 x^{0.5}+C[/tex]

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The approximate annual cost of raising a child born in 2013 at age 17 is 15230.

Scatter plots are used to observe and plot relationships between two numeric variables graphically with the help of dots. The dots in a scatter plot shows the values of individual data points.

a) Plot (2, 12,940), (5, 12,970), (8, 12,800), (11, 13,600) 1nd (14, 14420) on graph.

b) (8, 12800) and (14, 14420)

Here, slope m=(14420-12800)/(14-8)

= 1,620/6

= 270

Substitute m=270 and (x, y)=(8, 12800) in y=mx+c, we get

12800=270(8)+c

12800=2160+c

c=10640

Substitute m=270 and c=10640 in y=mx+c, we get

y=270x+10640

c) Now, substitute x=17 in y=270x+10640, we get

y=270×17+10640

y=15230

Therefore, the approximate annual cost of raising a child born in 2013 at age 17 is 15230.

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To multiply two mixed numbers, you can convert them to improper fractions and then multiply the numerators and denominators separately.

2 1/5 can be written as (2 x 5 + 1) / 5 = 11/5

2 2/3 can be written as (2 x 3 + 2) / 3 = 8/3

So the product of 2 1/5 x 2 2/3 is (11/5) * (8/3) = 88/15 which is equivalent to 5 8/15 or 5.533 repeating (if you want to express it as decimal)

You can simplify 88/15 by dividing both numerator and denominator by the greatest common divisor (GCD) which is 1 in this case, so the final result is 88/15.

No, they are not similar. There is no postulate or theorem that can prove these two triangles are similar since they are not similar.

Similar triangles are triangles that have the same angle measures and the same side lengths. In order to determine if two triangles are similar, it is necessary to compare the sides and angles of the triangles.

In this case, the sides and angles of △fhk and △ghj are not the same, so they are not similar. Therefore, there is no postulate or theorem that can prove these two triangles are similar. No, they are not similar. There is no postulate or theorem that can prove these two triangles are similar since they are not similar.

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Triangle ABC and Triangle DEF are congruent, as stated, of 7:3 with scale factor of isocellus triangle.

Find scale factor?

According to the scale factor, the ratio obtained by dividing the equivalent side lengths of like figures.

Triangle ABC and Triangle DEF are congruent, as stated.

Similar figures have equivalent angles and sides that are equal.

To determine the scale factor,

You must ascertain the ratio between the triangle's corresponding sides.

In order to obtain the sides of the other triangle, multiply each side of the first triangle by the same number.

What we're looking for is the scale factor, which is represented by the number.

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y = x^2 represents a nonlinear function.

A linear function has the form of y = mx+b where m and b are constants and x is variable, the graph of a linear function is always a straight line. A nonlinear function is any function that is not linear, the graph of a nonlinear function is not a straight line.

y = x^2 is nonlinear because the variable x is squared, a quadratic function and its graph is a parabola.

y=2x is a linear function and its graph is a straight line, increasing linearly with x.

y = x is also a linear function and its graph is also a straight line, increasing linearly with x.

y = x+2 is a linear function and its graph is also a straight line with a y-intercept of 2, increasing linearly with x

So, y = x^2 represents a nonlinear function, and it is the correct answer.

The time period of fm wave is found to be  1.13 x 10⁻⁸ sec.

The quantity of waves that pass a fixed point in a unit of time is referred to as frequency in physics.

For the given frequency of a fm wave =  8.85 × 10⁷ hertz.

Time period = 1 / frequency

T = 1 / 8.85 × 10⁷

T = 0.112 x 10⁻⁷ sec

T = 1.13 x 10⁻⁸ sec

Thus, the period of the fm wave is found to be  1.13 x 10⁻⁸ sec.

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No, not all the multiples of 2 are not prime numbers  only 2 itself is prime number other multiples of 2 are composite numbers.

As given in the question,

Given number is equal to :

2

Prime numbers are defined as the number which represents only two factors one and the number itself.

Multiples are defined as the given number when multiply by any integer.

Multiples of 2 are as follow :

2 × 1 = 2

2 × 2 = 4

2 × 3 = 6

2 × 4 = 8

2 × 5 = 10 ................ so on.

2 × n = 2n where 'n' belongs to any integer.

Only 2 has two factors.

other multiples of two has more than two factors.

Minimum number of factors of other multiples are :

One, two , and the number itself.

Other multiples represents composite number.

Only 2 is representing the prime number.

Therefore, in the multiple of 2 only 2 is the prime number other are composite number.

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Answer:

Step-by-step explanation:

show picture

Therefore , the solution to the given problem of mean comes out to be  the sample size yields the equivalent number of households is 30.

Regardless of whether many elements are discrete or continuous, averages can only be calculated for numeric variables. You may find this by dividing the total number of values in the dataset by the total number of values in the dataset. It is possible to perform computations using either raw data or data that has been compiled into frequency tables. The average value in mathematics is obtained by adding up all the numbers in a set of data and dividing the total by the total number of numbers.

Mean = 2 Four pets are two standard deviations away from the mean, and one standard deviation equals one pet.

We can determine that at least

100 (1-1k2)% = 100 (1-1/4)% = 75%

is within 2 standard deviations of the mean using Chebyshev's Rule with

k = 2. The percentage times the sample size yields the equivalent number of households:

75% x 40 = 30 Therefore , the solution to the given problem of mean comes out to be  the sample size yields the equivalent number of households is 30.

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On solving the provided question, we can say that the expression, we have here is 4 7. |10|= 470 or -470

In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.

the expression, we have here is

4 7. |10|= 470 or -470

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Therefore , the solution of the given problem of equation comes out to be 3.69x = y.

Equ is the translation of the Latin word for equivalent. Latin roots can be found in the base words of many English language words that are subject to modification, such as adequate, moderate, and equality. As both sides of either an equation are, in essence, "same" to one another, the Latin root term equ enters our variable quite easily.

Here,

Given :  Jimmy spends $3.69 per gallon of fuel he puts in his vehicle.

Thus,

To find the equation for the amount of money:

Let x be the number of times he refuel his gallon of fuel:

So,

Here y represents the total amount of  money.

3.69x = y

Therefore , the solution of the given problem of equation comes out to be 3.69x = y.

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Let angle D be an acute angle such that  D=0. 33. The measure of angle D is 70.7 degree.

Acute Angle:

An angle is formed when two rays meet at a vertex. If this angle is less than 90°, it is called an acute angle. In the image below, the angle formed between "Ray 1" and "Ray 2" is acute. Bisecting a right angle also creates two acute angles.

Inverse Cosine :

Inverse cosine is the important inverse trigonometric function. Mathematically, it is written cos-1(x) and is the inverse of the trigonometric cosine cos(x). Note that arc cosine is not the reciprocal of cos x. There are six inverse trigonometric functions like sin-1x, cos-1x, tan-1x, csc-1x, sec-1x, cot-1x. The arc cosine is used to determine angular measurements from the trigonometric ratio cos x values.

According to the question:

To approximate the measure of angle D, we will need to use the inverse cosine function on our calculator. All calculators vary, so I am not sure where you would find the button for it on your calculator. However, I know many calculators have it so you click the second button, then cos

 cos(D) = 0.33

⇒ D = cos^-1 (0.33)

⇒ D = 70.7 degrees

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According to our answer to the given question of ratio, Holly earns 4 share at $5 every, for a maximum of $20, and Jasmin receives just as, or

$ten (2 x $5).

An ordered combination of numbers “ a ” and “ b that is stated as just a / b, where b not greater than zero, is referred to as a ratio. A ratio is the result of equation two ratios. If there were one boy and three girls, the ratio could be shown as 1:3.   1/4 are boys, and 3/4 are girls. A part is a number, a proportion of size, or a difference among two or more things.

Here,

There is a total of $30.

Gertie shares out $30 in such a 2:4 proportion.

The maximum number of outstanding shares is 6, which is 2 plus 4.

$5 per share is the result of dividing $30 by six.

Two parts, or $ten (2 x $5), go to Jasmine.

Holly will receive four $5 shares, for a totaling of $20.

According to our answer to the given question, Holly earns 4 share at $5 every, for a maximum of $20, and Jasmin receives just as, or $ten (2 x $5).

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Answer: -21x-8

Step-by-step explanation:

Combine the like terms

Comparing the provided equations in the options with the slope-intercept form y = mx + c and with the intercept value given , The answer is option A and B.

An equation is a statement of equality between two expressions. It typically includes numbers and mathematical operations such as addition, subtraction, multiplication, and division. For example, the equation 2x + 3 = 7 is a statement that the value of the expression 2x + 3 is equal to the value of 7. Equations can also include variables, which represent unknown values that can be solved for.

In a linear equation, the slope (also called the gradient) is a measure of the steepness of the line, and the y-intercept is the point at which the line crosses the y-axis. The slope of a linear equation can be represented as m in the form of y = mx + b, where m is the coefficient of x, and b is y-intercept. The y-intercept is the point where the line crosses the y-axis, which can be represented by the value of b in the form of y = mx + b.

intercept (c) = 3units

option A also has 3 as c

option B also has 3 as c

when compared with y= mx + c

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Therefore ,consider that the divided congruent triangle corresponding bases are equivalent as proof.

Given that it contains three sides & three vertices, a triangle qualifies as a polygon. It is a fundamental characteristic in geometry. Triangle ABC is the name given to a triangle with vertices A, B, & C. When the three components are not collinear, Euclidean geometry reveals an unique plane and triangle. The polygonal shape of a triangle has 3 components and three corners. The points where three sides touch each other end to end are referred to as the triangle's corners. The sum of the three triangle angles is 180 degrees.

Here,

Given :

This RHS theorem can be employed to demonstrate the equality of the respective.

bases of all those split congruents as well as the congruency of two independents that are produced by the altitude of such an isosceles from every given vertex.

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Answer:

3

Step-by-step explanation:

trust lil bru

The equation of the perpendicular line is y = -7/2(x + 5) + 2

From the question, we have the following parameters that can be used in our computation:

y=2/7x-8

Also, from the question;

We have the following points

Point = (-4, 2) i.e.  (x, y) = (-4, 2)

The equation of a line can be represented as

y = mx + c

Where

Slope = m

By comparing the equations, we have the following

m = 2/7

This means that the slope is 2/7

The slopes of perpendicular lines are opposite reciprocals

This means that the slope of the other line is -7/2

The equation of the line is then calculated as

y = m(x - x₁) +y₁

Where

m = -7/2

(x₁, y₁) = (-4, 2)

So, we have

y = -7/2(x + 5) + 2

Hence, the line has an equation of y = -7/2(x + 5) + 2

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The 3-4-5 rule is a rule that states that in any right triangle, the ratio of the length of the two shorter sides will be 3:4 if the length of the hypotenuse is 5.

To determine if a triangle is a 3-4-5 triangle, you can use the following steps:

Divide the length of the hypotenuse by 5: 10 / 5 = 2

Multiply the result by 4: 2 x 4 = 8

Multiply the result by 3: 2 x 3 = 6

So, the triangle has sides of 6, 8, and 10 units, which is a multiple of 3-4-5 triangle and it is a right triangle.

Note that not all triangles that have sides in the ratio 3:4:5 will be a right triangle, only those that have a 90-degree angle are considered as a right triangle.

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