21x+7y=42 and -5x+5y=10
Find the solution to the system of equations​

Answer:

The answer is x = 5.

Step-by-step explanation:

Given:

Δ ABC is an Isosceles triangle with AB = CA

   m∠ ABC = ( 6x + 4 )°

   m∠ BAC = 73°

   m∠ BCA = ( 8y - 7 )°

To Find:

x = ?

Solution:

Properties of an Isosceles Triangle.

Here , Δ ABC is an Isosceles triangle with AB = CA

∴  m∠ BAC = m∠ BCA

[tex]73= 8y-7\\8y=73+7\\8y=80\\y=\frac{80}{10} \\y=10[/tex]

∴      m∠ BCA = ( 8y - 7 )°

                       = 8 × 10 - 7

       m∠ BCA  = 73  Which is same as ∠ CAB

Property of a Triangle is Sum of the measures of the angle of a triangle is 180°.

[tex]\angle ACB + \angle CAB + \angle CBA = 180[/tex]

Substituting the values we get,

[tex]73 + 73 + (6x+4) = 180\\6x+4=180-146\\6x=34-4\\6x=30\\x=\frac{30}{6} \\x=5\\[/tex]

The answer is x = 5.

Answer:

[tex]\displaystyle 2[/tex]

Step-by-step explanation:

Starting from the y-intercept of [tex]\displaystyle [1, 1],[/tex]you do [tex]\displaystyle \frac{rise}{run}[/tex]by either moving two blocks south over one block west or two blocks north over one block east [west and south are negatives]. Doing this will give you the equation below:

[tex]\displaystyle y = 2x + 1[/tex]

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Answer:

52

Step-by-step explanation:

2200 / 42 = 52.381

You cannot bring a section of a carton, and 53 cartons is too much

53 * 42 = 2226. This goes over the weight limit.

52 * 42 = 2184. 2184 is less than 2200, so 52 is the greatest number you can bring

By dividing the elevator's weight capacity of 2200 pounds by the weight of one 42-pound carton, we find it can carry a maximum of 52 whole cartons simultaneously without exceeding the weight limit.

To solve this problem, we can use simple mathematical analysis. We need to calculate how many 42-pound cartons can fit into an elevator that has a maximum capacity of 2200 pounds without exceeding this limit.

We start with the equation:

Therefore, the elevator can safely carry 52 cartons at once, without any people in it.

The rectangle can be divided into  6 ways as, 1 × 56 or 56 × 1,  2 × 28 or 28 × 2, and 4 × 14 or 14 × 4.

An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel, opposite sides. Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The rectangle's longer side is its length, while its shorter side is its breadth.

Given:

Darren has a piece of wood that is 7 in by 8 in

The area of the rectangle can be given by,

[tex]Area = Length\times width[/tex]

Area = 7 × 8

Area = 56

You can now divide the length and width as shown below,

Rectangle =   1 × 56 or 56 × 1

Rectangle =   2 × 28 or 28 × 2

Rectangle =   4 × 14 or 14 × 4

Therefore, the rectangle can be divided into  6 ways as   1 × 56 or 56 × 1,  2 × 28 or 28 × 2, and 4 × 14 or 14 × 4.

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Answer:

Step-by-step explanation:

12:32 am

Answer:

1:32 AM

Step-by-step explanation:

Arriving in Oklahoma City, the time is already 12:32 AM since it is past midnight. From Mountains to Central, time moves forward by 1 hour. 12:32 + 1 hour is 13:32 or 1:32 AM. Since the time is still past midnight, the time is AM.

To find the depth of the swimming pool, use the formula for the volume of a rectangular solid and substitute the given values to calculate the depth as 2.5 meters.

The depth of the Olympic-size swimming pool can be calculated using its volume, length, and width.

First, use the formula for the volume of a rectangular solid:

Volume = Length x Width x Depth

4000 = 80 x 20 x Depth

Depth = 4000 / (80 x 20) = 2.5 meters

Depth = 2.5 meters

How much money did he have

Answer:

His profit would be $37 of the money he got back.

Step-by-step explanation:

Answer:

Smaller number = 8 (x)

Larger number = 24  (y)

Step-by-step explanation:

x+y=32

7x+3y=128

Solving by Elimination

-3x-3y= -96

7x+3y=128

4x=32

4x/4=32/4

x=8

-7x-7y= -224

7x+3y=128

-4y= -96

-4y/-4= -96/-4

y=24

Check answer

x+y=32

8+24=32

7x+3y=128

7(8)=3(24)=138

56+72=128

128=128

Answer:

a. .3

b. .7

c. The car is fairly reliable because there is more people with no mechanical issues than there is people with mechanical issues

Step-by-step explanation:

Answer:

A. 3

B. .7

C. The car is fairly reliable, their is more people with no mechanical issues than their is people with mechanical issues

Step-by-step explanation:

Answer:

The equivalents are 1/6¹⁰ and  1/6⁸

Step-by-step explanation:

1. Let's recall the rule about the negative exponents to find the equivalents to the expressions provided:

The rule says that any number different than zero, raised to a negative power equals its reciprocal raised to the opposite positive power.

Thus, x ⁻ⁿ = 1/x ⁿ

2. Now, let's find the equivalents after following the rule:

6 ⁻ ¹⁰ = 1 ÷ 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 = 1/6 ¹⁰

6 ⁻ ⁸ = 1 ÷ 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6  = 1/6 ⁸

Answer:

5,841 divided by 62 is 94.2

Answer:

An equation is a statement that maintains the equal value of two mathematical expressions. If the statement is true for all variable values, it is called an identity. ... An equation shows the equality of two variables while an inequality shows the inequality of two variables

An equation with a variable expresses a precise equality between expressions, while an inequality with a variable represents a range of possible values expressing that one value is greater or less than another. Equations typically have a definitive set of solutions, whereas inequalities signify a continuum of solutions that satisfy the relational condition.

The difference between an equation with a variable and an inequality with a variable lies in the relationship they describe between the variables. An equation states that two expressions are equal by means of the equal sign (=), implying a specific value or set of values for the variables involved. For example, in the equation of a line y = mx + b, where x and y are the variables on the horizontal and vertical axis respectively, and b and m represent the y-intercept and the slope, we can see a direct relationship between x and y that determines the position of a point on a Cartesian plane. Conversely, an inequality such as x > y or x < 10 indicates a range of possible values rather than a single specific value, expressing a relationship where one value is either greater than or less than another value, but not equal to it.

In the context of a graph, the independent variable typically plotted on the x-axis is assumed to be the cause or input which then determines the value of the dependent variable, depicted on the y-axis. The dependent variable changes in response to the independent variable, thereby showing their relationship. This is often represented by inequalities when a range of outcomes is possible, extending beyond the linear relationship that might be depicted with an equation.

confused as to what you want but if you want to see the number then its 200,025

Answer:

200,025

Step-by-step explanation:

200 1000s so 200,0000 and add 25

54 54 54

54 54 54

54 54 54

Answer:

√(4/5)

Step-by-step explanation:

First, let's use reflection property to find tan θ.

tan(-θ) = 1/2

-tan θ = 1/2

tan θ = -1/2

Since tan θ < 0 and sec θ > 0, θ must be in the fourth quadrant.

Now let's look at the problem we need to solve:

sin(5π/2 + θ)

Use angle sum formula:

sin(5π/2) cos θ + sin θ cos(5π/2)

Sine and cosine have periods of 2π, so:

sin(π/2) cos θ + sin θ cos(π/2)

Evaluate:

(1) cos θ + sin θ (0)

cos θ

We need to write this in terms of tan θ.  We can use Pythagorean identity:

1 + tan² θ = sec² θ

1 + tan² θ = (1 / cos θ)²

±√(1 + tan² θ) = 1 / cos θ

cos θ = ±1 / √(1 + tan² θ)

Plugging in:

cos θ = ±1 / √(1 + (-1/2)²)

cos θ = ±1 / √(1 + 1/4)

cos θ = ±1 / √(5/4)

cos θ = ±√(4/5)

Since θ is in the fourth quadrant, cos θ > 0.  So:

cos θ = √(4/5)

Or, written in proper form:

cos θ = (2√5) / 5

Answer:

x=-6

Step-by-step explanation:

Follow along:

1. Distribute the -3 to those within the parenthesis.

-3x-6=12

2. Move the whole numbers to one sides, isolate the variable.

-3x=18

3. Divide both sides by -3

x=-6

Answer:

An independent clause is a group of words that contains both a subject and a predicate. It expresses a complete thought and can stand alone as a sentence. It can also be joined to other dependent or independent clauses to make a more interesting and complex sentence.Step-by-step explanation:

Answer:

We rewrite the statement correctly:

 "A linear function has an y-intercept of 12 and a slope of 3/8"

 Therefore, the linear function is:

 y = (3/8) x + 12

 We look for the linear function of the table:

 y-yo = m (x-xo)

 Where,

 m = (y2-y1) / (x2-x1)

 m = ((- 3/8) - (- 3/4)) / ((1/3) - (- 2/3))

 m = ((- 3/8) - (- 6/8)) / (3/3)

 m = ((- 3 + 6) / 8) / (1)

 m = 3/8

 (xo, yo) = (- 2/3, -3/4)

 Substituting:

 y + 3/4 = (3/8) (x + 2/3)

 y = (3/8) x + 2/8 - 3/4

 y = (3/8) x + 1/4 - 3/4

 y = (3/8) x + -2/4

 y = (3/8) x + -1/2

 The lines are:

 y = (3/8) x + 12

 y = (3/8) x + -1/2

 Answer:

 It has the same slope and a different y-intercept

Step-by-step explanation:

Answer:

B same slope but different y intercept

Step-by-step explanation:

Answer:

The area  of the cover for the hot tub must be:

Step-by-step explanation:

First, you must understand that since a hydromassage tub is mentioned and the diameter, it is assimilated that it is round in its upper part, which is why the formula is used to find the area of a circle:

Since the diameter is mentioned, it can be replaced in the formula:

Answer:

I believe it is 38

Step-by-step explanation:

HAVE A GOOD DAY AND GOD BLESS YOU

Answer:

[tex]z^2-5z+4=(z-4)(z-1)[/tex]

Step-by-step explanation:

Answer:

28 oz can is the better deal.

Step-by-step explanation:

In order to compare the two, we need to find the unit rate for each can. In this case, the unit rate will be in dollars per oz.

For the 28 oz can,

unit rate = $1.89 ÷ 28 = $0.675 / oz

For the 32 oz can

unit rate = $2.95 ÷ 32 = $0.922 / oz

comparing the unit rates, we can see that the unit rate for the 28 oz can is lower (i.e it costs less per oz for the 28 oz can compared to the 32 oz can)

Hence the 28 oz can is the better deal.

Good evening ,

Answer:

Vertex (-4 , 0)

axis x = -4

It’s a parabola.

Min = 0

Step-by-step explanation:

x2 + 8x + 16 = (x + 4)².

Answer:

The graphs of the functions are both straight lines and parallel to x-axis

Step-by-step explanation:

The graph of f(x) is the line y = 16 which is parallel to x-axis.

This is because for every value of x the function f(x) only takes the value 16

Similarly the graph of g(x) is also a straight line but is characterized by y = 3/64. This line is also parallel to the x-axis.

For every value of x the function g(x) only takes the value 3/64

To graph 2/5 on a number line, divide the number line into equal segments and locate the point that represents 2/5.

To graph 2/5 on a number line, divide the number line into equal segments and find the point that represents 2/5. Start by labeling the endpoints of the number line with the corresponding values. In this case, you can label 0 on the left and 1 on the right. Since the number line is divided into 5 equal segments, mark the points that correspond to 1/5, 2/5, 3/5, and 4/5 between 0 and 1. Then, locate the point that corresponds to 2/5 and mark it on the number line. Remember to place a dot to represent the point.

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In the context of the question, the Y-intercept represents the cost of the tablet that Mio purchased before counting the ongoing costs per month for internet service.

In the context of this problem, the Y-intercept in the graph represents the cost of buying the tablet. Using the algebraic equation for a line, which is y = b + mx, the 'b' term is the Y-intercept. When x (in this case, the number of months) equals zero, y is the initial cost, which serves as our Y-intercept. This is the starting point on the Y-axis, and in the context of Mio's spending, this would be her initial expenditure which is the cost of the tablet itself.

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The value of x in 984 ÷ x = 3 remainder: 84 is 300

Step-by-step explanation:

In the division problem A ÷ B = Q [tex]\frac{R}{B}[/tex], where

If A is divisible by B, then R = 0

Examples:

The rule of the dividend is ⇒dividend = (divisor × quotient) + reminder

Let us use this rule to find x

984 ÷ x = 4, remainder 84

∵ Dividend = 984

∵ Divisor = x

∵ Quotient is 3

∵ Remainder = 84

- Substitute these values in the rule of dividend above

∵ 984 = (x × 3) + 84

∴ 984 = 3x + 84

- Subtract 84 from both sides

∴ 900 = 3x

- Divide both sides by 3

∴ 300 = x

∴ The value of x = 300

The value of x in 984 ÷ x = 3 remainder: 84 is 300

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Answer:

Step-by-step explanation:

if y = 1/2x - 1 is the function

y = 1/2(-4) - 1

y = -2 - 1

y = -3

(-4, -3)

y = 1/2(2) -1

y = 1 - 1

y = 0

(2, 0)

y = 1/2(6) - 1

y = 3 - 1

y = 2

(6, 2)

the pictures should be in order

Answer:

[tex]\displaystyle 2 = f(6), 0 = f(2), -3 = f(-4)[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{1}{2}[6] - 1 = 3 - 1 = 2 \\ \\ \frac{1}{2}[2] = 1 - 1 = 0 \\ \\ \frac{1}{2}[-4] - 1 = -2 - 1 = -3[/tex]

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Answer:

x equals plus or minus square root of 5 minus 1

Step-by-step explanation:

we have

[tex]x^{2} +2x=4[/tex]

Divide by 2 the coefficient of the x-term

[tex]2/2=1[/tex]

squared the number

[tex]1^2=1[/tex]

Adds both sides

[tex]x^{2} +2x+1=4+1[/tex]

[tex]x^{2} +2x+1=5[/tex]

Rewrite as perfect squares

[tex](x+1)^{2}=5[/tex]

take the square root both sides

[tex]x+1=(+/-)\sqrt{5}[/tex]

[tex]x=(+/-)\sqrt{5}-1[/tex]

therefore

x equals plus or minus square root of 5 minus 1

Answer - B. x = ± [tex]\sqrt{5[/tex] - 1