Solve the system of equations using the substitution method. Show your work and be sure to include the solution to the system y=x-1 2x+y=8

Answer:x-int=4 1/4   y-int=-5 1/3

Step-by-step explanation:[tex]4x-3y=17\\ +3y =+3y\\ 4x=3y+17\\4x/4=3y/4 +17/4\\x=\frac{3}{4}x+ 4 \frac{1}{4} \\\\4x-3y=17\\-4x=-4x\\-3y=-4x+17\\-3y/-3=-4x/-3+17/-3\\y=\frac{4}{3}x -5\frac{1}{3}[/tex]

Answer:

1) x = 29; m∠3 = 6º

2a) scalene

2b) acute

Step-by-step explanation:

1) We can first solve for m∠3, as it is supplementary to 174º.

174º + m∠3 = 180º

m∠3 = (180 - 174)º

m∠3 = 6º

Then, we can solve for x by setting the sum of the measures of the interior angles of the triangle to 180º.

m∠1 + m∠2 + m∠3 = 180º

↓ substitute in given and solved values

(3x + 2)º + (5x - 60)º + 6º = 180º

↓ combine like terms

8xº - 52º = 180º

↓ add 52 to both sides

8xº = 232º

↓ divide both sides by 8º

x = 29

2a) We know that this triangle is not equilateral, as the measure of one of its interior angles (m∠3) is 6º. However, the triangle may be isosceles if m∠1 = m∠2. We can check for that by substituting x into each angle measure expression.

m∠1 ≟ m∠2

(3x + 2)º ≟ (5x - 60)º

↓ substitute in x-value

3(29)º + 2º ≟ 5(29)º - 60º

↓ simplify

(87 + 2)º ≟ (145 - 60)º

89º ≠ 85º

m∠1 ≠ m∠2; the triangle is not isosceles. Therefore, it must be scalene.

2b) All of the triangle's angles are less than 90º. Hence, it is an acute triangle.

The evaluated value of the expression b² - 4ac when a = -2, b = -4 and c = 1 is 24.

To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.

To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations.

Therefore, let's evaluate b² - 4ac when a = -2, b = -4 and c = 1.

Hence,

b² - 4ac = (-4)² - 4(-2)(1) = 16 + 8 = 24

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The Costa Rican coffee should be used is 160 pound.

What is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Given that the cost of Costa Rican coffee that sells for $7 per pound and Kenyan coffee that sells for $10.

The cost of the mixture is $8.5 per pound.

Assume that the manager mixed 80 pounds of the Kenyan coffee with the x pound of the Costa Rican coffee to get a mixture.

The cost of 80 pound Kenyan coffee is $(80×10) = $800.

The cost of x pound Costa Rican coffee is 7x.

The cost of mixture coffee is (80 + x)8.5

According to the question:

800 + 7x = (80 + x)8

800 + 7x = 640 + 8.x

640 + 8x = 800 + 7x

x = 800 - 640

x = 160

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He will have to mix 3 pounds of cashews and 7 pounds of peanuts .

What is equation ?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Let c be denoted as cashew and p be denoted as peanuts

c + p = 10  ⇒ (1)

5.6c + 2.3p = 3.29*10 ⇒ (2)

Multiply eq(1) by 560

Multiply eq(2) by 100

560c + 560p = 5600

560c + 230p = 3290

Subtract and solve for "p":

330p = 2310

p = 7  (amt. of peanuts needed)

substitute  the value of p in eq(1)

c + 7 = 10

c = 3  (amt. of cashews needed)

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Answer:

Therefore x is either 6 or 5.

The temperature in a town is 12°C, then the temperature in degrees Fahrenheit is 53.6°F.

The Fahrenheit temperature scale, named after German physicist Daniel Gabriel Fahrenheit, is the most commonly used temperature measurement in the United States (and its associated territories) and several Caribbean nations. Water freezes at 32°F and boils at 212°F on a Fahrenheit scale (at sea level).

The Celsius temperature scale—originally known as centigrade before being renamed after Swedish astronomer Anders Celsius—is used almost everywhere else in the world. Water freezes at 0 degrees Celsius and boils at 100 degrees Celsius on the Celsius scale (at sea level).

To convert degrees Celsius to Fahrenheit, multiply by 1.8 (or 9/5) and add 32.

In the question, the temperature in a town in 12°C .

by applying the equation F=1.8C+32

                                            =1.8×12+32

                                            =53.6°F

Hence, The temperature in a town is 12°C, then the temperature in degrees Fahrenheit is 53.6°F.

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-2 is the zero of the polynomial 3x²+ 4x + 2k for the value of k equals to -2.

As given in the question,

Given polynomial is equal to :

3x²+ 4x + 2k

-2 is the zero of the given polynomial 3x²+ 4x + 2k

Compare with the standard quadratic equation ax² + bx + c

Let 'α' be the zero whose value is equal to -2.

And 'β' be the another zero.

Sum of the zeros of the polynomial = -b/ a

⇒ α + β = -4 / (3)

⇒α + β = -4/3 ___(1)

Product of the zeros = c/a

⇒αβ = 2k / 3

⇒(-2)β = 2k/3

⇒β = -k/3

Substitute the value of α and β in (1)

-2 + -k/3 = -4/3

⇒-k/3 = -4/3 + 2

⇒ -k/3 =2/3

⇒ k = -2

Therefore , the value of k for the given polynomial with the given condition is equal to -2.

The above question is incomplete , the complete question is :

For what value of k , - 2 is a zero of the polynomial 3x²+ 4x + 2k?

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Answer:

∠ ADC = 122°

Step-by-step explanation:

ABCD is a cyclic quadrilateral.

opposite angles in a cyclic quadrilateral sum to 180° , that is

∠ ADC + ∠ ABC = 180∠

∠ ADC + 58° = 180° ( subtract 58° from both sides )

∠ ADC = 122°

Step-by-step explanation:

To solve a system of equations by substitution, you can solve one of the equations for one of the variables and substitute this expression into the other equation. This will give you an equation with only one variable, which you can then solve to find the value of that variable. You can then substitute this value back into one of the original equations to find the value of the other variable.

In this case, the given system of equations is:

y = -4

y = -2x - 20

Since the second equation is already in the form y = ..., we can substitute the expression for y from the second equation into the first equation:

-4 = -2x - 20

Solving this equation for x, we get:

x = -12

Substituting this value of x back into the second equation, we get:

y = -2(-12) - 20

= 24 - 20

= 4

Therefore, the solution to the system of equations is (x, y) = (-12, 4).

Answer:

x = -8

Step-by-step explanation:

-2x - 20 = -4

-2x = 16

x = -8

The z-score of the sample research is calculated as; -3.32

We are given the formula for z-score as;

z = (x-bar - μ)/(σ/√n)

where;

x-bar is sample mean

μ is population mean

σ is population standard deviation

We are given;

Population mean; μ = 7.5 hours

Sample mean; x-bar = 7.2 hours

population standard deviation; σ = 0.7 hours

sample size; n = 60

Thus;

z-score = (7.2 - 7.5)/(0.7/√60)

z-score = -0.3/0.0903696

z-score = -3.32

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There are many common idioms. Following are the 20 idioms that is mostly used.

An idiom is a collection of words with a figurative, extraneous meaning that cannot be understood from the individual words alone. Idioms frequently began with literal meanings but lost them when they strayed from their original context.

Rome was not build in a day is my favorite idiom

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Answer: 5

Step-by-step explanation: if you do something to one side of the equation, it has to be done to the other side.

in this case, they divided the left side (3x+5y) by 5

so so make both sides equal, you'd have to divide the right side (25) by 5 as well which would give you 5

The expression given in question can be written in an equation form and hence, we determine the unknown variable x.

An expression is a combination of terms and operator. The terms contain two or more numbers or both numbers and variables. An expression describes a mathematical concept or system of mathematical operation in a symbolic form. The expression which has an equal sign to express the equality among the terms is called equation. So, the only difference between equation and expression is the equal sign =.

The above is a mathematical expression that contains two numbers 1,3 and one variable x along with a subtraction sign, -.

The number 1 is called constant number and number 3 is called the coefficient of x.

In order to do the problem, we can put any real value of x such as x= 0, 1, 2, 3, 4, 5, 6, 7 or -1, -2, -3, -4, 5 and so on.

For each value of x, we get a result either positive or negative.

3×0 -1, when x=0

-1

3×1 -1, when x=1

the result is 2

We can also write the expression in the form of equation by putting an equal sign such as 3x-1 = 0

from the equation, we can easily get the value of x.

3x -1 =0

3x = 1

x =1/3

this is the result.

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Answer: x = 3/4

Step-by-step explanation:

1/3x + 3 = 4 - x

Subtract 3 from both sides

1/3x = 1 - x

Then times 3 from both sides

x = 3 - 3x

Add 3x on both sides

4x = 3

Divided by 4, both side

x = 3/4

12 students like science the most and can draw a model having 18 things out of which 12 are circled.

What is model in mathematics?

Consider the provided information.

Your class has 18 students. Exactly 2/3 of them say that, out of all their subjects, they like science the most.

First calculate 2/3 of 18.

= (2/3) * 18

= 2 * 6

= 12

Hence, 12 students like science the most.

We can draw a model having 18 things out of which 12 are circled.

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The probability of making exactly 4 shots is 4/5, in where 4 is outcomes Favour to me and 5 is total possible outcomes.

The probability is measured as the ratio of favorable outcomes of a particular event to the total possible outcomes of that event. The value of probability should be lies between 0 to 1.

The term favorable outcome uses to determine the probability in mathematics. It is the possibility of happening expected incident of a particular event.

the ways in how i can make exactly 4 shots in the game = my favorable outcomes/total possible outcomes

                                                             =4/5

hence, the result is 4/5.

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We find the mean grade 7 by using formula Mean = ∑x / n

Where, ∑ represents the summation

x represents observations

n represents the number of observations .

In addition to the mode and median, the mean is one of the measurements of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally.

The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean.

By dividing the sum of the given numbers by the entire number of numbers, the mean (the average of the given numbers) is determined.

Mean = (Sum of all the observations/Total number of observations)

The mean in grade 7 is calculated by using formula Mean = ∑x / n

Where, ∑ represents the summation

x represents observations

n represents the number of observations .

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The above quadratic equation has two solutions, as shown by the question Yes.

A second-order polynomial equation with a single variable, x, is known as a quadratic equation.

ax2 + bx + c = 0 is a quadratic equation in standard form.

x stands for an unknown (an variable)

With respect to known numbers, a, b, and c, where a 0

The polynomial's number of solutions is influenced by the equation's highest possible power given in the question.

The roots or zeros of the expression on the left-hand side of the equation are the values of x that fulfill the equation.

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Answer:

Number of muffins= 18

Number of beverages= 14

Amount spent on muffins= $63

Amount spent on beverages= $24.50

Step-by-step explanation:

To find the number of muffins sold, we can first assume that all the 32 items purchased were beverages.

If the class bought 32 beverages,

Total spending

= 32($1.75)

= $56

Difference in total spending

= $87.50 -$56

= $31.50

The difference in the total spending is due to the number of muffins purchased that we had assumed they were beverages.

Difference in cost for each muffin vs beverage

= $3.50 -$1.75

= $1.75

Thus, for every incorrect assumption we made, the total spending will be $1.75 lesser than the actual amount.

Sets of wrong assumption

= $31.50 ÷$1.75

= 18

This means that out of the 32 items we previously assumed to be beverages, 18 were actually muffins. The remaining number of items were indeed beverages.

Number of muffins= 18

Number of beverages

= 32 -18

= 14

Amount spent on muffins

= 18($3.50)

= $63

Amount spent on beverages

= 14($1.75)

= $24.50

Total spending

= $63 +$24.50

= $87.50

Por propiedades algebraicas, la ecuación de la variable n es función de la variable S es igual a n = - 1 / 2 ± (1 / 2) · √(1 + 8 · S).

En esta pregunta tenemos un ecuación donde la variable S en función de la variable n y debemos reescribir la expresión como una de la variable n en función de la variable S. Esto es posible mediante el uso de propiedades algebraicas. Primero, escriba la ecuación:

S = n · (n + 1) / 2

Segundo, utiliza la propiedad distributiva:

S = (n² + n) / 2

Tercero, aplica compatibilidad con la multiplicación, existencia del inverso multiplicativo y propiedad modulativa:

2 · S = n² + n

Tercero, construya una ecuación cuadrática:

n² + n - 2 · S = 0

Cuarto, utilice la fórmula cuadrática:

n = - 1 / 2 ± (1 / 2) · √[1² - 4 · (- 2 · S)]

n = - 1 / 2 ± (1 / 2) · √(1 + 8 · S)

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SSS Stands on Side - Side - Side

SAS Stands on Side - Angle - Side

ASA Stands for Angle - Side - Angle.

There are three theorems that may be used to determine whether two triangles are similar: Angle - Side - Angle (ASA), Side - Angle - Side (SAS), and Side - Side - Side (SSS).

SSS, which stands for "side, side, side," denotes that there are two triangles with identical angles on all three sides. The triangles are congruent if their third sides are the same as those of another triangle.

That is what the SAS regulation says. The triangles are congruent if the two sides and included angle of one triangle are the same as the two sides and included angle of another triangle. Any angle that is created by two specified sides is an included angle.

According to the ASA postulate of Euclidean geometry, two triangles are similar if their two corresponding angles are congruent and one side is equal to the corresponding side of the other triangles.

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Answer:

60

Step-by-step explanation:

Adding [tex]72[/tex] to both sides yields [tex]t=72-12=60[/tex].

Answer:

[tex] \sf \: a) \: 60[/tex]

Step-by-step explanation:

Now we have to,

→ find the required value of t.

The equation is,

→ t - 72 = -12

Then the value of t will be,

→ t - 72 = -12

→ t = -12 + 72

→ [ t = 60 ]

Hence, the value of t is 60.

Sets are the term used in mathematics which means the collection of any objects or collection.

Now, According to the question:

Let's know:

What is sets?

Any collection of objects (elements), which may be mathematical (e.g., numbers and functions) or not. A set is commonly represented as a list of all its members enclosed in braces. The intuitive idea of a set is probably even older than that of number.

What is sets in real life?

We all have a group of some objects, collection of our favorite things, sets of books, a list of cities and countries in our life. These all are sets, and we come to their usage in our daily life.

Examples of sets in daily life:-

1. Kitchen is the most relevant example of sets. Our mother always keeps the kitchen well arranged. The plates are kept separate from bowls and cups. Sets of similar utensils are kept separately.

2.School bags of children is also an example. There are usually divisions in the school bags, where the sets of notebooks and textbooks are kept separately.

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Answer:

8% of 575 is 46

8% of 575 is 46

8% of 575 is 46

8% of 575 is 46

8% of 575 is 46

8% of 575 is 46

8% of 575 is 46

8% of 575 is 46

8% of 575 is 46

Answer:

2 / 27

Step-by-step explanation:

2/9 * 1/3   =  (2*1) / (9*3) = 2/27

The factor of 6x² 11x 3 is 6x(x + 3).

The factor is a number that can be multiplied by itself to produce a specific result. It is used in mathematics and science to determine the relationship between two or more variables. For example, the factor of 4 is 2 because 2 multiplied by 2 is 4. Factors can also be used to determine the probability of an event occurring or the likelihood of a given outcome. In these cases, the factor is a measure of the degree of influence that one variable has on the other.

The factor of 6x² 11x 3 is 6x(x + 3).

This can be determined by factoring out the greatest common factor (GCF) of the expression.

The GCF of 6x² 11x 3 is 6x, and the remaining factors are x + 3.

Therefore, the factor of 6x² 11x 3 is 6x(x + 3).

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Complete questions as follows-

Factorise: 6x 2+11x+3

Answer:

62.5%

Step-by-step explanation:

Split the time up into 5 minute slots. That gives us 24 slots of 5 minutes.

20/5=4 of the 5 minute slots playing outside

25/5=5 of the 5 minute slots on his phone

5+4=9 out of 24 slots spent

24-9=15 slots remaining to play his instrument

15/24x100=62.5% time playing instrument

Answer:62.5%

Step-by-step explanation:

The surface area of any particular thing is the area or region that the object's surface occupies. Volume, on the other hand, is the quantity of space accessible in an object. There are several forms and sizes in geometry, such as the sphere, cube, cuboid, cone, cylinder, and so on. Each form has both a surface area and a volume.

The area amount denotes the size of a region on a flat or curved surface. The area of an open surface or the boundary of a three-dimensional object is referred to as surface area, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina. The area is the region determined by the shape of an item. The area of a form is the space in a plane covered by a figure or other two-dimensional geometric object.

Here,

The surface area of any given thing is the area or region occupied by the object's surface. Volume, on the other hand, refers to the quantity of space accessible in an object. Shapes and sizes in geometry include the sphere, cube, cuboid, cone, cylinder, and so on. Each form has a surface area as well as a volume.

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