Given: 5(2x-4)=10
Prove: x=3

Drag the correct reason to the box.

Marissa will have $720 in 7 years when she has $48 in her saving account that earns 2% simple interest per year.

where

Calculation

From, A = P(1 + RT)

where, p = $48

R = 2%

T= 7 years

A = 48(1 + 2*7)

A = $720

Hence, Marissa will have $720 in her bank account after 7 years.

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Answer:

(A∩B)={1,15}

Step-by-step explanation:

The Required Factors   (x + 1) (x - 3 ) (x + 2) (x - 2).

Given equation.
x^4 - 2x^3 - 7x^2+8x+12 = 0

Factors : factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.

polynomial : an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable

Now, factorize the polynomial of degree 4 as follows.

= (x + 1) (x - 3) (x^2 - 4)

Then, again factorize polynomial of degree 2.

Therefore  (x + 1) (x - 3 ) (x + 2) (x - 2)

This is the required factors.

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In the given picture the polygon ABCD is the formed polygon (in red color) and the reflection of the polygon is A'B'C'D' (in green color).

Graphing the polygon and reflection in a graph:

A polygon is a 2 - dimensional shape, that is formed by three or more straight edges. To graph, a polygon, plot the given points on the plane and connect the vertices using straight lines, without crossing any lines.

To reflect the image in the line y = x, switch the values of x to y and y to x. After switching the points, join the formed points and draw the reflected image.

Here we have

A(2, -1),  B(-1, 2),  C(2, 3),  D(4,2)

After switching the values of x to y and y to x the resultant points are

A'(-1, 2),  B'(2, -1),  C'(3, 2),  D'(2,4)

In the given picture the polygon ABCD is the formed polygon (in red color) and the reflection of the polygon is A'B'C'D' (in green color).

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Answer:

13/3

Step-by-step explanation:

3 [tex]\frac{12}{9}[/tex]

[tex]\frac{12}{9}[/tex]= 1 [tex]\frac{1}{3}[/tex]

3+1 1/3

4 [tex]\frac{1}{3}[/tex]

13/3

Answer:

Step-by-step explanation:

step one just add 5/9 +7/9 since they have the same denominator then that will equal 4/3

2nd step add the 1 and 2 together since they are both whole numbers. which equals 3

3rd step 4/3 + 3/1 which equals 13/3 maybe or if the answers wants a mixed number than the answer might be 4 1/3!

I'm not quite sure but try and see if its correct! :)

If Midland is 20 miles from Odessa, and Lubbock is 113 miles from Midland. Then 111.22 miles is Odessa from Lubbock.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given,

The cities of Midland, Lubbock, and Odessa form a triangle.

The distance between Midland and Odessa is 20 miles.

The distance between Lubock and Odessa is unknown, we need to find this.

This can be find by using Pythagorean theorem

Odessa  from Lubbock=20²+x²

113²=20²+x²

12769=400+x²

12369=x²

x=111.22

Hence, 111.22 miles, Odessa could possibly be from Lubbock.

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The dimension of the rectangular room in the actual building are 55 feet by 30 feet.

Scale is used to represent the relationship between a measurement on a model and the corresponding measurement on the actual object.

A blueprint for a building includes a rectangular room that measures 3 inches long and 5.5 inches wide. The scale for the blueprint says that 1 inch on the blueprint is equivalent to 10 feet in the actual building.

The dimensions of this rectangular room in the actual building can be found as follows:

let's find the length of the actual room

1 inches = 10 feet

3 inches  = ?

cross multiply

length = 30 ft

Let's find the width of the room

1 inches = 10 feet

5.5 inches  = ?

cross multiply

width = 55 ft

Therefore, the width and length of the room are 55 feet and 30 ft respectively.

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A factor is a number that divides another number, leaving no remainder

The distance and direction of the ship from the starting point is found using vectors as follows;

The ship is 48.03 nautical miles from the starting point at a directional bearing of N 18.53° E

A vector is a quantity that has a property of magnitude or size and direction.

The ship's speed = 36 nautical miles per hour

Direction of the ship = Due east

The duration the ship continues in the direction = 1 hour

The new direction of the ship = N32°E

The duration in which the ship continues in the new direction = Half an hour

The vector of the distances traveled by the ship are;

[tex]\overrightarrow{d_1}[/tex] = 36·i

[tex]\overrightarrow{d_2}[/tex] = 0.5 × 36×sin(32°)·i + 0.5 × 36×cos(32°)·j = 18×sin(32°)·i + 18×cos(32°)·j

The sum of the distances traveled by the ship is therefore;

36·i + 18×sin(32°)·i + 18×cos(32°)·j = (36 + 18×sin(32°))·i + 18×cos(32°)·j

(36 + 18×sin(32°))·i + 18×cos(32°)·j = 45.54·i + 15.26·j

The distance of the ship from the starting point, d, is therefore;

d ≈ √(45.54² + 15.26²) ≈ 48.03

The distance of the ship from the starting point is approximately 48.03 miles.

The direction from the North of the ship from its starting point, θ, is therefore;

[tex]\theta = arctan\left(\dfrac{15.26}{45.54} \right) \approx 18.53^{\circ}[/tex]

Then direction of the ship is N 18.53° E

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Considering the given figure we have that

< BAC = < CAD         definition of angle bisection

< BAC = < BCA         base angles of isosceles triangle

This refers to when angles are being shared or divided into two equal parts.

In the given problem, line AC is the bisector of < BAC. creating wo equal angles in the process. hence

< BAC = < CAD         definition of angle bisection

Triangle BAC is an isosceles triangle, since the sides BA and BC are equal. the angles are also equal therefore

< BAC = < BCA         base angles of isosceles triangle

Line AC is also a transversal line, connecting the two parallel lines BC and AD. This creates opportunity for alternate angle theorem

< BCA = < CAD        alternate internal angle theorem

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The fraction is equivalent to the [tex]\sqrt{x+2}-\sqrt{x}[/tex].

The correct option is (C).

Given,

The fraction is given as:

[tex]\frac{2}{\sqrt{x} -\sqrt{x+2} }[/tex]

To find the above fraction which choice is equivalent to the fraction?

Now, According to the question:

Simplify or expand

[tex]\frac{2}{\sqrt{x} -\sqrt{x+2} }[/tex]

Rationalize the denominator:

[tex]\frac{2(\sqrt{x} -\sqrt{x+2} )}{(\sqrt{x} -\sqrt{x+2})(\sqrt{x} -\sqrt{x+2} ) }[/tex]

Expand the expression:

[tex]\frac{2(\sqrt{x} +\sqrt{x+2} )}{(\sqrt{x})^2-(\sqrt{x+2} )^2 }[/tex]

[tex]\frac{2(\sqrt{x} +\sqrt{x+2} )}{x-(x+2)}[/tex]

[tex]\frac{2(\sqrt{x} +\sqrt{x+2} )}{-2}[/tex]

Determine the sign and cross out the common factor:

[tex]\sqrt{x+2}-\sqrt{x}[/tex]

Hence, The fraction is equivalent to the [tex]\sqrt{x+2}-\sqrt{x}[/tex].

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The capital is £430,600.

Define capital.

The money that a company has on hand to support both its current operations and potential expansion is known as capital. One source of funding for it is the earnings from its operations. When calculating a company's capital worth, all of the company's physical assets and financial assets would be included (minus its liabilities).

The capital account—also referred to as the capital and financial account—records the net flow of investment transactions into an economy and is used in macroeconomics and international finance.

Solution Explained:

Given, Assets = £451,100 and liabilities = £20,500

Capital = Assets - Liabilities

            = 451100 - 20500
            = £430,600

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The mean is xbar = Σxf/Σf = 64,950/43 = 1510.47

acc to our question-

hence,The mean is xbar = Σxf/Σf = 64,950/43 = 1510.47

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The dimensions of the playground are;

Width = 60 feet

Length = 160 feet

The formula for calculating perimeter of a rectangle is expressed as;

Perimeter = 2( l + w)

Where;

We have the values as;

Perimeter = 440 feet

Length = 3w - 20

Width = w

Now, substitute the values into the formula, we have;

440 = 2( 3w - 20 + w)

expand the bracket

440 = 2( 4w - 20)

440 = 8w - 40

collect like terms

8w = 480

Make 'w' the subject of formula

w = 60 feet

Length = 3(60) - 20

Length = 180 - 20

Length = 160 feet

Hence, the values are 60feet and 160 feet

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The  Weight  of Mary is 80. Students who are having trouble solving a problem can use the "draw a picture" method to create a visual representation of the issue.

Students who are having trouble solving a problem can use the "draw a picture" method to create a visual representation of the issue.

the justifications.

Inquiry 1.

Formula: w = 10 8 pound

Answer: x = 80 lb

Inquiry 2:

Formula: d = 108 lb - 8 pound

d = 72 lb

Explanation:

First of all

When Mary was born, she weighed 8 pounds.

Statement 2: Mary weight 10 times as much when she was 10 years old.

w = 10 8 pounds, or 80 pounds.

Description of the illustration:

She was born weighing 8 pounds, which is represented by each cell. The 10 cells indicate that the number 8 lbs. has been repeated 10 times.

Next, the sum of the multiplication is shortened:

8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 = 10 × 8 = 80.

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The range of market return is 15.9% and the mean of market return is 2.94%

Productive Investments Limited provided the returns for Laska stocks for 2017 to 2021.

Year         Laska return

2017         -2.2%

2018          -3.4%

2019         12.5%

2020         -0.8%

2021          8.6%

The range of market return = Highest return - lowest return

= 12.5 - (-3.4)

= 15.9%

mean market return = (-2.2 +(-3.4) + 12.5 +(-0.8) + 8.6)/5

mean market return = 2.94%

Therefore, the range of market return is 15.9% and the mean of market return is 2.94%

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The numbers that are correctly written in scientific notation are:

Scientific notation is a shorthand (approximate) manner of writing long or short numbers using decimal forms raised to 10 power a baseline.

The rules for correctly writing a scientific notation include the following:

Thus, the scientific notation rules are correctly satisfied by Options B and D, unlike Options A, C, and E.

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A) 42 x 10⁵

B) 1.1 x 10⁴

C) 7.0 x 20⁴

D) 6.01 x 10⁻⁴

E) 18.0 x 10³

Answer: -6

Step-by-step explanation:

The ratio of the areas of these two photos is equal to 9:16.

In Mathematics, a ratio simply refers to a mathematical expression that is typically used for denoting the proportion of two (2) or more quantities with respect to one another and the total quantities.

This ultimately implies that, a ratio is generally expressed as a quotient of two numerical quantities or variables.

Generally speaking, the corresponding ratio of the areas of two geometric figures (shapes) is equal to the square of the ratio of their corresponding side length:

Area of photos = (a:b)²

Substituting the given parameters into the formula, we have;

Area of photos = (3:4)²

Area of photos = 9:16

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Answer:

answer should be d

Step-by-step explanation:

it's d because if u fraction 6 u will get d

Answer:

Step 1: Simplify both sides of the equation.

1/3(6y+3)−24 = 3(1/3y−6)

1/3(6y) + 1/3(3) -24 = 3(1/3y) + 3(-6)

2y +1 −24 = y−18

2y −23 = y −18

Subtract y from both sides.

2y−23−y=y−18−y

y−23=−18

Step 3: Add 23 to both sides.

y−23+23 = −18+23

y = 5

Step-by-step explanation:

The correct option regarding the price is C. no; The packs of socks are marked up to $7 and then discounted to $4.20.

In this situation, a shoe store buys packs of socks wholesale for $5 each and marks them up by 40%. The price will be:

= Original price + Markup

= 5 + (40% × 5)

= 5 + 2

= $7

Then, the store decides to discount the packs of socks by 40%. This will give a price of:

= 7 - (40% × 7)

= 7 - 2.8

= $4.2

The price isn't discounted to $5.

In conclusion, the correct option is C.

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Answer:

.7 kg

Step-by-step explanation:

1. Convert answers in grams into kilograms

1000g = 1 kg

750g = .75kg

705g = .705 kg

2. Find smallest number of kg

= .7 kg

Answer:

36

Step-by-step explanation:

substitute m = - 3 into the expression

m² - 7m + 6

= (- 3)² - 7(- 3) + 6

= 9 + 21 + 6

= 36

If each has the same probability of performance. If the system is to have a .92 probability of performing, The minimum probability of performing needed by each of the individual components is: 0.97126.

Given data:

Number of identical component = 3

Probability of performing = .92

Now let determine the probability

Probability =  0.92 ^(1/3)

Probability = 0.92^0.3333

Probability =.9726

Therefore the probability is .9726.

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The slope intercept form equation of the straight line is y = -1/2x + 6

Slope intercept form

Slope intercept form of the equation used to calculate the equation of a straight line by using the slope and intercept value.

And the general form of slope intercept equation is

y = mx + c

where

m refers the slope

c refers the y - intercept

Given,

Here we have the graph of straight line.

Through the given graph we have to identify the equation of slope intercept form.

In order to find the slope intercept form equation we need two values they are slope and the y intercept.

So, to find these two values, we need two points,

So we have selected the points from the given graph. They are (2,5) and (4,4).

Now we have to use the slope formula to find the value of the slope,

m = (4 - 5) / (4 - 2)

m = -1/2

Now, we have to use the slope and one of the point (4,4), to find the value of y intercept,

4 = -1/2 (4) + c

4 = -2 + c

c = 6

Now, we have identified the values of slope and the intercept.

Then the slope intercept form equation of these straight line is written as,

y = -1/2x + 6

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Given graph represent the graph of  g(x) = [tex]-x^{2} (x -2)[/tex]

Given,

In the question;

The equation is:

g(x) = - [tex]x^{2} (x -2)[/tex] or h(x) = [tex]x^{2} (x -2)[/tex]

To find the is this the graph of g(x) or h(x).

Graph is given in the figure.

Now, According to the question;

g(x) = [tex]-x^{2} (x -2)[/tex]        and      h(x) = [tex]x^{2} (x -2)[/tex]

g(x) = 0                                    h(x) = 0

[tex]-x^{2} (x -2) = 0[/tex]                         [tex]x^{2} (x -2)[/tex] = 0

x = 0, 2                                    x = 0, 2

If we put x = 1 then,

g(1) = [tex]-(-1)^2(1-2)[/tex]     and   h(1) = [tex](1)^2(1-2)[/tex]

g(1)  =  -1 (-1)                          h(1) = 1(-1)

g(1)   = 1                                 h(1) = -1

But as shown in graph, graph take positive value at x = 1

∴Given graph is the graph of g(x) = [tex]-x^{2} (x -2)[/tex]

Hence, Given graph represent the graph of  g(x) = [tex]-x^{2} (x -2)[/tex]

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If Abigail Henderson has $3400.00 budgeted for spending money on an upcoming trip .The currency needed is 200 euro and 500 pounds.

Formulate an equation

1.30x + 1.60y = 3400

Hence,

x =4y Equation 1

1.30x + 1.60y = 3400 Equation 2

Substitute eq1 into eq2

1.30(4y) + 1.60y = 3400

5.2y +1.60y =3400

6.8y =3400

Divide both side by 6.8y

y =3400/6.8

y = 500

Number of euro

4y where y = 500

4(500)

=2000

Therefore  the answer in practical terms is : 2000 euro of European currency and 500 pounds of Britain currency are needed.

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