Solve for x when lines are parallel

Answer:

see explanation

Step-by-step explanation:

[tex]\frac{3\pi }{4}[/tex] is an angle in the second quadrant where sin > 0 and cos < 0

cos([tex]\frac{3\pi }{4}[/tex] )

= cos (π - [tex]\frac{3\pi }{4}[/tex] )

= - cos ([tex]\frac{\pi }{4}[/tex] )

= - [tex]\frac{\sqrt{2} }{2}[/tex]

and similarly

sin ([tex]\frac{3\pi }{4}[/tex] )

= sin ([tex]\frac{\pi }{4}[/tex] )

= [tex]\frac{\sqrt{2} }{2}[/tex]

The total area of the regular pentagon prism is 485 square units

The given parameters are:

Base area = 50

Height = 11

Base = 7

Start by calculating the total area of the 5 sides using

Sides = n * Height * Base

Sides = 5 * 11 * 7

Sides = 385

The total surface area is

Total = 2 * Base area + Sides

This gives

Total = 2 * 50 + 385

Evaluate

Total = 485

Hence, the total area of the regular pentagon prism is 485 square units

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The solution for the system of linear inequalities 7x+2y > 3 and x-2y < 2 are x = 5/8 and y = -11/16

Linear inequalities are inequalities that have constant average rates of change, slope or gradient

A system of linear inequalities is a collection of at least two linear inequalities.

In this case, the system of linear inequalities is given as

7x+2y > 3

x-2y < 2

Rewrite the inequalities as equations

7x+2y = 3

x-2y = 2

Make x the subject in the second equation, by adding 2y to both sides of the equation

x - 2y +2y = 2 + 2y

This gives

x = 2 + 2y

Substitute x = 2 + 2y in 7x+2y = 3

7(2 + 2y) +2y = 3

Expand the brackets

14 + 14y + 2y = 3

Evaluate the like terms

16y = -11

Divide both sides by 16

y = -11/16

Substitute y = -11/16 in x = 2 + 2y

x = 2 - 2 * 11/16

Evaluate the product

x = 2 - 11/8

Evaluate the difference

x = 5/8

Hence, the solution for the system of linear inequalities 7x+2y > 3 and x-2y < 2 are x = 5/8 and y = -11/16

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Answer:

Step-by-step explanation:

hello

calculate x : 3x+2 =5

means : 3x+2-2 =5-2

3x = 3

so : x = 3/3 =1

1 is the  element in domain has the image 5 under function f(x)= 3x+ 2

Q1

Nominal - D

Ordinal-  B, G

Ratio - A, C, E, F

Q2

Quantitative- A, C, D, G

Qualitative -B, E, F, G

Q3

Simple Random - A, C

Systematic Sample - B

Nominal measures are the most accurate and meaningless, as they only show the "characteristics" or "identities" that we are interested in. In other words, in a nominal variable, a number just gives the attribute a unique "name". In this case, the number is just a label.

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Here, Given

Area of Equilateral triangle = 3cm2

therefore, we know;

Area of Equilateral triangle =( [tex]\sqrt{3}[/tex]÷4)×[tex]a^{2}[/tex]

so,

3 =( [tex]\sqrt{3}[/tex]÷4)×[tex]a^{2}[/tex]

3÷( [tex]\sqrt{3}[/tex]÷4) = [tex]a^{2}[/tex]

2.63 cm = a .

The area of ​​an equilateral triangle is the area covered by an equilateral triangle on a two-dimensional plane. An equilateral triangle is a triangle with all sides equal and all angles at 60 degrees. The area of ​​the shape is the number of unit squares that fit inside.

Here, "unit" refers to 1, and a unit square is a square with one side. Alternatively, the area of ​​an equilateral triangle is the total amount of space it surrounds in a two-dimensional plane.

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The statement indicates that the interval 12​%±5​% is likely to contain the true population percentage of people that prefer chocolate pie.

According to the statement

we have a given that the Among the 1000 respondents,

12​% chose chocolate​ pie, and the margin of error was given as

±5 percentage points.

and we have to explain the statement that the margin of error was given as ±5 percentage​ points.

We know that the interval is a set of real numbers that contains all real numbers lying between any two numbers of the set.

And this statements also indicates the interval between the like and unlike respondents of chocolate pie.

So, this statement indicates that the interval 12​%±5​% is likely to contain the true population percentage of people that prefer chocolate pie.

So, The statement indicates that the interval 12​%±5​% is likely to contain the true population percentage of people that prefer chocolate pie.

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Answer:

A and B

Step-by-step explanation:

A : (a²+b²=c²) 11²+13²=290 (c²); c=√290

B : 7²+24²=625; c=√625=25

C : 2²+5²=29≠7²

According to the Pythagorean triple, the side lengths that will form a right triangle are:

A. 11, 13, √290

B. 7, 24, 25

The Pythagorean triple are three set of sides that can form a right triangle if the square of the longest side equals the sum of the squares of the other two smaller sides.

11² + 13² = (√290)²

290 = 290 [correct]

7² + 24² = 25²

625 = 625 [correct]

2² + 5² = 7²

29 ≠ 49 [correct]

Therefore, the side lengths that will form a right triangle are:

A. 11, 13, √290

B. 7, 24, 25

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Answer:

Creditable

Step-by-step explanation:

Could also be:
up-to-date

The data-set that places 22.6 as an outlier is given as follows:

2.4, 5.3, 3.5, 22.6, 1.8, 2.1, 4.6, 1.9

A measure is considered an outlier in a data-set if it is very far from other measures, especially in these two cases:

In this problem, he data-set that places 22.6 as an outlier is given as follows:

2.4, 5.3, 3.5, 22.6, 1.8, 2.1, 4.6, 1.9.

The second highest value is 5.3, which is considerably less than 22.6, hence 22.6 is an outlier in the data-set.

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Y=4x+5 and y=4x-5 has no solution

What are Linear Equations in two Variables?

The formula for a two-variable linear equation is Ax + By + C = 0, where A and B are the coefficients, C is a constant term, and x and y are the two variables, each with a degree of 1. A linear equation with two variables, for instance, is 7x + 9y + 4 = 0. These two linear equations are referred to be simultaneous linear equations if we take them into consideration.

Steps

[tex]Y=4x+5\\ Y=4x-5[/tex]

Substitute y=4x+5

[tex][4x+5=4x-5][/tex]

Refine [tex][4x+5=4x-5][/tex]

-10=0

-10=0 is a false ,therefore the system of a equation have no solution

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imagine the cd/cd as 1 which is a whole number. then, add the denominators (d+c-cd)/cd

Answer: 21 units²

Step-by-step explanation:

Since there is a pair of parallel sides, this figures is a trapezoid. The formula for the area of a trapezoid is [tex]\frac{1}{2}(a+b)h[/tex], where a and b are the parallel sides and h is the height.

Here, a and b are 5 and 9, while 3 is the height. Let's put all 3 values into the formula.

[tex]A=\frac{1}{2}(5+9)*3[/tex]

[tex]A=\frac{1}{2}(14)*3[/tex] [Adding in the parentheses]

[tex]A=7*3[/tex] [Multiplying one-half by 14]

[tex]A=21[/tex] [Multiplying 7 and 3]

The area is 21 units².

The x-intercepts from the graph are -3.646 and 1.646 with the parabolic curve facing upwards

Quadratic functions are functions that has a leading coefficient of 2.

According to the question, we are to graph the quadratic function f(x) = x^2 + 2x - 6. The curve will be parabolic in nature and facing upwards since it is a quadratic function.

The x-intercepts from the graph are -3.646 and 1.646 as shown in the attached graph.

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Using proportions to find the radius of figure 2, we have that:

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The rule of three to find the radius of figure 2 is given as follows:

[tex]\frac{5}{9} = \frac{r}{4.5}[/tex]

Applying cross multiplication:

9r = 4 x 4.5

r = 4 x 4.5/9

r = 2 in

The circumference of a circle of radius r is given by:

[tex]C = 2\pi r[/tex]

In this problem, we have that r = 2 inches, hence:

[tex]C = 2\pi \times 2 = 4\pi[/tex]

The area of a circle of radius r is given by pi multiplied by the radius squared, as follows:

[tex]A = \pi r^2[/tex]

Hence:

[tex]A = 4\pi[/tex]

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Answer: First one is 5, Second is 6.25

Step-by-step explanation: Correct on Edmentum/Plato

Answer:

A

Step-by-step explanation:

His commision was 0.06(160000-20000) = $8400.

His salary was $10,000.

His bonus was $500.

Adding these together, we get $18,900.

The polynomial expression that represents the profit of selling x tablets is 10x - 100

profit = revenue – cost

= (100 + 30x) - (20x + 200)

= 100 + 30x - 20x - 200

Profit = 10x - 100

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The 95% confidence interval of the statistics is (7.795, 8.243).

Based on the information given, the 95% confidence interval will be:

= 8.019 + (1.962 × 3.183/✓1114)

= 8.243 and

= 8.019 - (1.962 × 3.183/✓1114)

= 7.795

In conclusion, the 95% confidence interval of the statistics is (7.795, 8.243).

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From statement equation, the number of correct answers will result in a passing grade is 9.3

Given that each question on the quiz is worth 8 points.

Also given a score of 75 is a passing grade.

Let the number of correct answered questions be x

Thus the total score of the correct answers is 8x

The statement equation is -

⇒ 8x = 75

⇒ x = 75/8 = 9.3

∴  x ≈ 9

Therefore, from statement equation, the number of correct answers will result in a passing grade is 9.3

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Answer:

Step-by-step explanation:

AC=DC. (Given in figure)

AB=BD. (Given in figure

BC=BC. (Common)

that means triangle BAC is congruent to triangle BDC by SSS criterion.

The total surface area of the composite figure is calculated as 444 m².

Total surface area = surface area of the bottom rectangular prism + surface area of the top triangular prism - area of the shared surface.

Surface area of the triangular prism = (S1 + S2+ S3)L + bh = (16 + 10 + 10)5 + (6)(16) = 276 m²

Rectangular prism surface area = 2(wl + hl + hw) = 2(5×16 + 4×16 + 4×5) = 328 m²

Area of shared surface = 2(16)(5) = 160 m²

Total surface area = 328 + 276 - 160 = 444 m².

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Answer:

-1

Step-by-step explanation:

Expanding (x² − x + 2)(x − 1) we get [tex]x^{3} -x^{2} -x^{2} +x+2x-2[/tex]. When we simplify that, we get [tex]x^{3} -2x^{2} +3x-2[/tex] which fits the form Ax³ + Bx² + Cx + D.

We can see that A = 1, B = -2, C = 3, D = -2. Thus A + D = 1 - 2 = -1.

Therefore your answer is -1

Answer:

A + D = -1

Step-by-step explanation:

Given: (x² − x + 2)(x − 1) = Ax³ + Bx² + Cx + D

Step 1: Simplify using the Distributive Property.

[tex]\\\implies (x^2 - x + 2)(x - 1) \\\\\implies x(x^2 - x + 2) + -1(x^2 - x + 2)\\\\\implies x^3 - x^2 + 2x - x^2 + x - 2\\\\\implies \bold{1}x^3 -\bold{2}x^2 + \bold{3}x - \bold{2}[/tex]

Step 2: Determine the value of the coefficients.

[tex]\implies {\sf A} = 1, {\sf B} = -2, {\sf C} = 3, {\sf D} = -2[/tex]

Step 3: Find the value of A + D.

[tex]\implies {\sf A} + {\sf D} \Rightarrow 1 - 2 = \boxed{-1}[/tex]

Answer: 156 degrees

Step-by-step explanation:

Answer:

Step-by-step explanation:

cos A = √( 1 - (5/13)²) = √( 1 - 25/169) = √(144/169) = - 12 /13

in 2 A = 2 sin A cos A

sin 2 A = 2 *5/13 ( - 12/13 ) = - 120 / 169

the answer is -120/169

Answer:

x=17

Step-by-step explanation:

Since they are intersecting lines, 3x=51

x=17

Answer:

x = 17

Step-by-step explanation:

When two lines intersect each other, the opposite angles are identical. Therefore, you can set both angles equal to each other to find the value of "x".

3x = 51

x = 17

The student with the correct list of steps is student B

The list of steps is to create a line parallel to line AB

Both students are correct in step (1).

However, the step (2) of student A is incorrect.

This is so because, the student did not provide how points C and G are created

Hence, the student with the correct list of steps is student B

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Answer:

C.  (x,y) ⇒ (x + 8, y − 3)

Step-by-step explanation:

See attached image.

Answer:

we have

6x+2y > -106x+2y>−10

Isolate the variable y

Subtract 6x6x both sides

2y > -6x-102y>−6x−10

Divide by 22 both sides

y > -3x-5y>−3x−5

The equation of the line of this inequality is

y=-3x-5y=−3x−5

The slope is negative and is equal to m=-3m=−3

The y-intercept is the point (0,-5)(0,−5) ----> value of y when the value of x is equal to zero

The x-intercept is the point (-5/3,0)(−5/3,0) ----> value of x when the value of y is equal to zero

The solution of the inequality is the shaded area above the dotted line

Using a graphing tool

see the attached figure

Answer:

Step-by-step explanation:

The height of the pyramid (h) = 3.6m

The perimeter of the base = 4.1m

Volume of a pyramid = ?

Formula:-

[tex]\boxed{\sf Volume =\cfrac{1}{3} \: a^2h}[/tex]

So,

Perimeter = 4a

[tex]\sf 4.1=4a[/tex]

[tex]\sf a=1.025[/tex]

Now, let's put the value of a in the formula:-

[tex]\sf V=\cfrac{1}{3} \:(1.025)^{2} (3.6)[/tex]

[tex]\sf 1.26075m^2[/tex]

[tex]\sf \thickapprox 1.3m^3[/tex]

Therefore, the volume of the pyramid is 1.3m³.