Solve x please explain

Answer:

5/12

Step-by-step explanation:

A ratio of 3:4 means that red counters make up 3/7 of the sum of red and blue counters and blue counters make up 4/7 of the total sum of red and blue counters.

If there is 20 blue counters, then 20 is 4/7 of the sum of the total red and blue counters.

So we need to solve for the total sum.

[tex] \frac{4}{7} x = 20[/tex]

[tex]4x = 140[/tex]

[tex]x = 35[/tex]

So the total amount of red and blue counters are 35,

So this means the amount of red counters is 15.

The amount of yellow counters is 25.

So the total number of counters are 60.

So P(Yellow counters)= 25/60= 5/12

The distance between the initial position and the final position is 72.1ft

The initial position is (0ft, 0ft). Where the notation used is:

(horizontal position, vertical position).

Martha climbs 40 steps, then the final position is:

(40*1ft, 40*1.5ft) = (40ft, 60ft)

The distance between the initial position and the final position is:

[tex]d = \sqrt{(40ft - 0ft)^2 + (60ft - 0ft)^2} = 72.1ft[/tex]

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Answer: 4

Step-by-step explanation:

The ratio of the areas of similar figures is the square of the side length.

Since the ratio of the areas is 16:4 = 4:1, the ratio of the side lengths is 2:1.

So, the length of the corresponding side is 2(2) = 4.

The drug will decay to 82% of the initial dosage after 7.18 hours.

Finding the Decay constant(λ):

λ = 0.693 / (half-life)

we are given that the half-life is 47 hours

λ = 0.693 / (47)

λ = 0.01925 /hour

Time is taken for 82% decay:

Since decay is first-order, we will use the formula:

[tex]t = \frac{2.303}{0.0192} log\frac{100}{82}[/tex]

Final amount = 100*82/100 = 82 mg

Replacing the values in the equation:

t = 2.303/ 0.0192 x 0.06

t = 7.18 hours

Therefore, the drug will decay to 82% of the initial dosage after 7.18 hours.

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The expression that represents the area of the rectangle is 2x² + 6x − 20. Thus, the correct option is C.

A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but reverse statement may or may not be true.

The area of the rectangle is the product of its length and its width. Therefore, the area of the given rectangle is,

Area = (2x-4)(x+5)

       = 2x² + 10x - 4x - 20

       = 2x² +6x - 20

Hence, the expression that represents the area of the rectangle is 2x² + 6x − 20. Thus, the correct option is C.

The complete question is:

Write a simplified polynomial expression in standard form to represent the area of the rectangle below.

The image of the rectangle is given below.

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Factoring polynomials is breaking them down to the products of other smaller polynomials. Identifying the greatest common divisor (GCF) is an important first step because it will reduce the number of factors in each term and thus make factoring easier. In addition to polynomials, it can be factored by decomposition of the intermediate term or by difference of squares. Then, the Zero Product Property can be applied to solve the equation.

Use the sum-product pattern.

Extract the common factors.

Rewrite factored

Answer:

(x+2)(x+8)

Step-by-step explanation:

two numbers that multiply to 16 and add up to 10 is 2 and 8. You just plug both numbers in this factored form (x+ n1)(x+n2). if you chech the answer by multiplying the binomials, you will find out that the answer is the original question (x^3 +10x+16).

⊱________________________________________________________⊰

Answer:

Step-by-step explanation:

Points with both negative co-ordinates are found in the third quadrant.

[tex]\boxed{\begin{tabular}{c | 1} \sf{~~Quadrant 2 (-x,y)~~& Quadrant 1~ (x,y)~~} \\ \\\\\\\\\\\\ \cline{1-2} \sf{Quadrant \ 3 (-x,-y) \ & Quadrant \ 4 (x,-y)} \\\\\\\ \\\\\\\\\\\end{tabular}}[/tex]

done !!

⊱_____________________________________________________⊰

The area of a 2D form is the amount of space within its perimeter. The area of the garden is 72 feet² and the perimeter of the garden is 36 feet.

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

The diagram for the given garden is given below.

1.) The area of the garden is,

The area of the garden = Area of rectangle + Area of triangle

                                       = (6 x 8) + (0.5 x 6 x 8)

                                       = 48 + 24

                                       = 72 feet²

2.) The perimeter of the garden is,

The perimeter of the triangle = 12 + 8 + 6 + 10 = 36 feet

Hence, the area of the garden is 72 feet² and the perimeter of the garden is 36 feet.

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The probability that the person uses exactly one of the facilities is 0.64

Probability is the likelihood of an event happening or an event not happening.

When it is certain an event would happen the probability is 1.

Probability can be independent or mutually exclusive.

Analysis:

Find analysis in the attached file.

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Answer:

9000000001

Step-by-step explanation:

.....................

Answer:

6210001000

Hope This Helps!!!

Answer:

Step-by-step explanation:

Arithmetic sequence:

   a = first term = 4

   d = common difference =  second term - first term

       = 9 - 4

   d  = 5

[tex]\sf t_n =a +(n -1)*d[/tex]

   = 4 + (n - 1) *5

   = 4 + 5n - 5

    = 5n -1

Check; n= 1 ,  first term = 5*1 - 1 = 5 - 1 = 4

           n = 2,  second term = 5*2 - 1 = 10 -1 = 9

           n = 3, third term = 5*3 - 1 = 15 - 1 = 1

The next term, fifth term  = 5*5 - 1

                                          = 25 - 1

                                          = 24

The figure will have a triangle and a rectangle. The area of a triangle is 10 in² and the rectangle is 80 in². Therefore, the total area is 90 in².

This question requires your knowledge about the area of compound shapes. For solving this, you should:

The figure is composed of a triangle and a rectangle.

Therefore, you should sum the area of these geometric figures for determining the area of the irregular figure.

Area of the triangle= [tex]\frac{b*h}{2}[/tex]. The figure shows that: the base = 10 in and the height =2 in

Thus,  A_triangle=[tex]\frac{b*h}{2}=\frac{10*2}{2} =10 in^{2}[/tex]

Area of the rectangle = bh . The figure shows that:  the base = 10 in and the height =8 in

Thus,  A_rectangle=bh= 10*8=80 in²

A_total= A_triangle + A_rectangle

A_total= 10+80=90 in²

A_total= 90 in²

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Using translation concepts, it is found that the equation of the blue graph is given by:

C. G(x) = (x - 1)³.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the function G(x) is a shift of one unit right of F(x) = x³, hence it's equation is:

G(x) = F(x - 1) = (x - 1)³.

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The volume of the cone is 1, 139. 49 cm³

Height of cone = 17cm

Base of cone = 16cm

Diameter = 16cm

Radius = diameter/2 = 16/2 = 8cm

Formula for volume of a cone = [tex]\pi r^{2} \frac{h}{3}[/tex]

Substitute the values

Volume = [tex]3. 142[/tex] × [tex]8[/tex] × [tex]8[/tex] × [tex]\frac{17}{3}[/tex]

Volume = [tex]201. 088[/tex] × [tex]5. 67[/tex]

Volume = 1, 139. 49 cm³

Thus, the volume of the cone is 1, 139. 49 cm³

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Point Y is the centre of the circle that passes through points D, E, and F.So option A is correct.

If we draw a circle through all the vertices of a triangle then the circle obtained is the circumcircle of the given triangle.

And the circumcenter is the centre point of the circumcircle which is obtained by the point of intersection of the perpendicular bisector of all the sides of the triangle.

Therefore, since Y is the circumcenter of the triangle DEF, so, point Y is the centre of the circle that passes through points D, E, and F.

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Answer:

A

Step-by-step explanation:

Last option. The sequence that can be used to to get the figure A'B'C'D' is Reflection about the y-axis followed by a translation to the right by 1 unit.

We have an opposite orientation in this question. This based on the fact that (ABCD)' is counterclockwise. While its reflection ABCD is clockwise.

The reflection has to go over a vertical line given that (CD)' and CD are at the bottom. Hence this reflection has to go over  a vertical line.

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Answer:

B = 1.875

Step-by-step explanation:

given that A varies directly as B and inversely as C then the equation relating them is

A = [tex]\frac{kB}{C}[/tex] ← k is the constant of variation

to find k use the condition A = 12 when B = 3 and C = 2 , then

12 = [tex]\frac{3k}{2}[/tex] ( multiply both sides by 2 to clear the fraction )

24 = 3k ( divide both sides by 3 )

8 = k

A = [tex]\frac{8B}{C}[/tex] ← equation of variation

when A = 10 and C = 1.5 , then

10 = [tex]\frac{8B}{1.5}[/tex] ( multiply both sides by 1.5 )

15 = 8B ( divide both sides by 8 )

1.875 = B

Answer:

2/3

Step-by-step explanation:

Since there are 4 circles and 6 triangles, and they are asking for the ratio of circles to triangles, the fraction would be 4/6

4/6 when divided by two = 2/3 which is the simplest form of the fraction 4/6

The simplest ratio of circles to triangles would be; 2/3

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that there are 4 circles and 6 triangles.

Since there are 4 circles and 6 triangles, and they are asking for the ratio of circles to triangles, the fraction would be as given;

4/6

when divided by two we get;

2/3

This is the simplest form of the fraction 4/6

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Answer: y = 3/5x + 7

What we know:

How to solve:

By substituting the point the slope passes through into slope-intercept form, we can calculate the y-intercept (b.) From here, we can use our slope and y-intercept values to set up the final equation.

Finding the y-intercept

Set up equation                                                         y = mx + b

Substitute                                                                   4 = 3/5(-5) + b

Simplify                                                                       4 = -3 + b

Simplify                                                                     +3    +3

Solve                                                                           7 = b

Creating final equation

Set up equation                                                         y = mx + b

Substitute                                                                   y = (3/5)x + 7

Check:

If you graph this equation (a good tool to use is desmos graphing calculator,) then this equation creates a line that has a slope of 3/5 and passes through the point (-5,4)

The polynomial in its simplest form is 3x³ + x² + 6x-9 , Option D is the correct answer.

The algebraic expression that consists of variables and coefficients are called Polynomials.

It is given that

The variables A, B, and C represent polynomials

where

A = x²

B = 3x + 2

C = x - 3

The Polynomial AB -C² = ?

From the value given

AB -C² = x² (3x + 2) - (x - 3)²

= 3x³  + 2x² - x² - 9 + 6x

= 3x³ + x² + 6x-9

Therefore the polynomial in its simplest form is 3x³ + x² + 6x-9 , Option D is the correct answer.

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Answer:

A. Because it passed the y axis

Answer: its 7

Step-by-step explanation: hope it helps

Answer:

x=3

Step-by-step explanation:

Isolate x.

[tex]4(5)^x=500[/tex] Divide both sides by four

[tex]5^x=125[/tex] Take [tex]log_{5}[/tex] of both sides. In other words, what power must you raise 5 to in order to get 125? ([tex]5^3=125[/tex])

x=3

a. Distance moved by effort = 1 meter

b. Work done by effort = 80 Joules

c. Losses in energy = 18 Joules

a. Note that velocity ratio is defined as the ratio of a distance through which any part of a machine moves to the distance moved by its parts

Velocity ratio = distance moved by the effort/distance moved by the body

Where velocity ratio = 5

vertical distance = 20cm

Distance moved by effort = 5 × 0. 20 = 1 meter

b. Formula for work done is given as ;

Work done = Effort × distance moved by effort

Work done = 80 × 1

Work done = 80 Newtons

c. First, let's find the work output

Work output = m g h

Work output = 50 × 9.8 × 0. 20

Work output = 98 Joules

Losses in energy = Work output - work done

Losses in energy = 98 - 80

Losses in energy = 18 Joules

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Answer: [tex]46^{\circ}[/tex]

Step-by-step explanation:

[tex]m\angle CDE=m\angle UDE+m\angle CDU\\\\154^{\circ}=108^{\circ}+m\anlge CDU\\\\m\angle CDU=46^{\circ}[/tex]

Hello,

We have A(3, 5) and B(5, 6)

[tex]m=\frac{y_{B}-y_{A}}{x_{B}-x_{A}} =\frac{6-5}{5-3} =\frac{1}{2}[/tex]  

We know the line contain the point (3, 5)

    y = 1/2x + b

⇔ 5 = 1/2 × 3 + b

⇔ 5 = 3/2 + b

⇔ 5 - 3/2 = b

⇔ b = 10/2 - 3/2

⇔ b = (10 - 3)/2

⇔ b = 7/2

[tex]\boxed{y = \frac{1}{2}x + \frac{7}{2} }[/tex]

Answer:

140%

Step-by-step explanation:

So a fraction can be expressed as: [tex]\frac{a}{b}[/tex] and if a number decreases by x%, the new number is (100-x)% the original value. So since the numerator decreases by 30%, it's not 70% the original value, and it's very similar with the denominator, with it only retaining 50% of it's original value. This gives you the formula: [tex]\frac{0.70a}{0.50b}[/tex]. You can rewrite the fraction as: [tex]\frac{1.4 * 0.5 * a}{0.5 * b}[/tex] in doing so it's easy to see that you can cancel out the 0.5 and get: [tex]1.4\frac{a}{b}[/tex]. This means the value is increasing by 1.4 or 140%

Answer:

140%

Step-by-step explanation:

since the numerator decreases by 30%, it isnt 70% the original value, This gives a formula: . You can rewrite the fraction as so, in doing so it's easy to see that you can cancel out the 0.5 and get: . This means the value is increasing by 1.4 or 140%.

Answer: X = 5.0

Step-by-step explanation:

- since these are right triangles you can use trigonometry to solve this pretty easily

- for this situation, you only have to use sine/sin

__________________________________________________________

- to start you just need to identify which side is which:

- so, for this problem the equation is: [tex]10xSin(45) = 7.071067812[/tex]

__________________________________________________________

- so 7.071067812 is the hypotenuse of the smaller triangle so you just do the same thing again

- start with identifying which side is which:

- so for this part, the equation is: [tex]7.071067812xSin(45) = 5.0[/tex]

- so X = 5.0

__________________________________________________________

hope this helps :)

Answer:

x = 5

Step-by-step explanation:

Check the file for detailed solution.

This involves SOH-CAH-TOA method, always remember that the opposite of the 90 degree mark is always the hypotenuse. Meanwhile, the position of the given angle (theta) is dependent on which side it is placed. It give either an adjacent or opposite side.

Answer:

The correct option is OPTION (A) .