Factor 64+56. Write your answer in the form a(b+c) where a is the GCF of 64 and 56.

Completing the equation below by writing an expression equivalent to the length of a, the leg of a right triangle is given below

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.

According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Hence, the complete equation according to this theorem is given above.

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nonononononononnnono

Answer: look at the image for the solution and the answer

Step-by-step explanation:

Just multiply each side by side

Step-by-step explanation:1.Times one side by another

2. Times your answer by the third side

The two-column table that can be used to prove the congruence relationships between the segments of the triangles are presented as follows;

             Statement    [tex]{}[/tex]                                   Reasons

1. [tex]\overline{KN}[/tex] ≅ [tex]\overline{MN}[/tex]                     [tex]{}[/tex]                            Given

 [tex]\overline{NL}[/tex] bisects ∠KNM           [tex]{}[/tex]                          

2. ∠KNL ≅ ∠MNL [tex]{}[/tex]                                        Definition of bisected angle

3. [tex]\overline{NL}[/tex] ≅ [tex]\overline{NL}[/tex]                   [tex]{}[/tex]                               Reflexive property

4. ΔKNL ≅ ΔMNL [tex]{}[/tex]                                         SAS congruence rule

5. [tex]\overline{KL}[/tex] ≅ [tex]\overline{ML}[/tex]         [tex]{}[/tex]                                        CPCTC

6. KL = ML [tex]{}[/tex]                                                    Definition of congruence

C.  

[tex]{}[/tex]               Statement [tex]{}[/tex]                                   Reasons

1.  [tex]\overline{BE}[/tex] ≅ [tex]\overline{CE}[/tex], [tex]\overline{AE}[/tex] ≅ [tex]\overline{DE}[/tex]                               Given

2. ∠AEB ≅ ∠CED [tex]{}[/tex]                                        Vertical angles theorem

3. ΔABE ≅ ΔCED [tex]{}[/tex]                                        SAS congruence rule

4. [tex]\overline{AB}[/tex] ≅ [tex]\overline{CD}[/tex]                                         [tex]{}[/tex]        CPCTC

Congruent segments are segments that have the same lengths.

The details of the reasons used to prove the equivalence of sides KL and ML and the congruence of the segments [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are presented as follows;

Definition of bisected angles

Bisected angles are angles that are split in two angles of the same measure by a segment passing through their vertex.

Reflexive property

The reflexive property of congruence states that a segment is congruent to itself.

SAS congruence rule

The SAS, Side-Angle-Side congruence rule states that if two sides and an included angle of a triangle are congruent to two sides and an included angle in another triangle, then the two triangles are congruent.

CPCTC

CPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent.

Definition of congruence

Geometric figures, such as segment, angles and shapes are congruent when their sizes and measurements are the same.

Vertical angles theorem

The vertical angles theorem states that vertical angles formed by the intersection of two lines are congruent

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A general formula to describe is F = 1.6×d² will be correct answer.

A relationship is considered proportional if the ratio remains constant. For instance, the average number of apples produced per tree is a measure of proportionality, and the number of trees in an orchard is inversely related to the number of apples produced in a harvest. When two quantities are proportionate with one another, then expand and contract at the same pace, keeping the relationship constant.

Finding the general formula we obtain:

F=kd²

40=k×5²

k=1.6

so, F =1.6×d².

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The formula possible formula for the trigonometric function whose values are in the following table is  y = 6 x sin(π/2 * x) - 4.

Trigonometric functions are described as the periodic functions which denote the relationship between angle and sides of a right-angled triangle.

The formula for a trigonometric function is typically written as :

y = a sin (bx + c) + d

where a, b, c, and d are constants which tells us  the amplitude, frequency, phase shift, and vertical shift of the function, respectively.

From the above table,  the amplitude = 6,

the frequency is 2π/4 = π/2

the phase shift = 0, and

the vertical shift = -4.

Therefore, we can write  the formula for the function as Y = 6 * sin(π/2 * x) - 4.

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The correct option is B, the system of equations has infinitely many solutions.

When we graph a system of equations, the points where the graphs of the equations intercept are the solutions.

In this case we can see a single line graphed, which only can happen when both equations of the system represent the exact same line.

Then the graphs intercept at infinite points, thus, the system of equatios has infininitely many solutions.

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Answer: The answer is x²+2x-8

Step-by-step explanation:

Answer:

hope this helps!!! That’s the answer!

Step-by-step explanation:

Answer:

9.43 units.

Step-by-step explanation:

To find the distance between two points in a 2D plane, you can use the Pythagorean theorem. The formula for finding the distance between two points (x1, y1) and (x2, y2) is:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the values for W and Z:

d = √((8 - 3)^2 + (-2 - 6)^2)

d = √(5^2 + (-8)^2)

d = √(25 + 64)

d = √89

The distance between the points W and Z is approximately 9.43 units.

The value for  x-5(x - 1)=x- (2x-3) which gives x = 2/3.

An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.

Given:

x-5(x - 1)=x- (2x-3)

Now, solving the Equation for x we get

x -5x + 5 = x - 2x + 3

-4x + 5 = -x + 3

-4x + x = 3 -5

-3x = -2

x= 2/3

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The number of machines used in order to get to the number 450 from the number 900 is 9.

An expression contains more than one term with addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

900 to 450

We need a number of machines such that 450 is the last output starting from 900.

Now,

If we subtract 50 from each consecutive number we get,

900, 850, 800, 750, 700, 650, 600, 550, 500, 450

So,

We use 9 machines to get 450 from 900.

Thus,

9 machines should be used in order to get to the number 450 from the number 900.

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Jane would take 5 hours painting the window so both of them could end up charging the same amount

An equation is an expression that shows the relationship between numbers and variables using mathematical operators like addition, subtraction, multiplication and division. Equations can be linear, quadratic.

Let y represent the total charge for working x hours.

Suzie has quoted a flat rate of $250 for the job. For Suzie:

y = 250

Jane's quote is $40 per hour, plus $50 to cover the cost of materials. For Jane:

y = 40x + 50

For the two to charge the same amount:

250 = 40x + 50

40x = 200

x = 5 hours

Jane would spend 5 hours painting the window.

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The greatest common factor of the 24x³ + 36x² is 12x².

It is the greatest factor common to all the numbers given such that there are no greater factors common other than that.

Example:

4 is the gcd of 12, 8, 16.

We have,

24x³ + 36x²

Taking out the common factor.

= 12x² (2x + 3)

Thus,

GCF of the expression is 12x².

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Answer:

The amount that will be in Heidi’s account after 15 years is option A. $164,146.52.What is  Future Value?It can be calculated using the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:FV = M  (((1 + r)^n - 1) / r)Where;FV = Future value of the amount need to findM = total monthly contribution which is Heidi’s monthly contribution of 11% of her monthly salary + Employer monthly contribution of 6% of Heidi’s monthly salary can be calculated as;= (11% of Heidi’s monthly salary + 6.25% of Heidi’s monthly salary) = (11% of $3,250) + (6.25% x $3,250) = $552.50r = Monthly interest rate= Annual interest rate of 401(k) / 12 = 6.25% / 12 = 0.0625 / 12 r = 0.00520833333333333n = number of months = Number of years x 12 = 15 x 12 n= 180Substituting all the values into equation (1), we have;FV = $552.50  (((1 + 0.00520833333333333)^180 - 1) / 0.00520833333333333)FV = $552.50 x 297.097770863934FV = $164,146.518402324Rounding to the nearest cent, we get;FV = $164,146.52Therefore, the amount that will be in Heidi’s account after 15 years is option A. $164,146.52.

Step-by-step explanation:

.

The circumference of a circle with a diameter of 26 feet is approximately 81.64 feet.

What is the circumference?

The circumference is the length of any great circle, the intersection of the sphere with any plane passing through its center. A meridian is any great circle passing through a point designated as a pole.

The formula for the circumference of a circle is 2 * π * r, where r is the radius of the circle.

To find the circumference, we first need to find the radius of the circle.

The diameter of the circle is 26 feet, so the radius can be calculated by dividing the diameter by 2:

r = 26 feet / 2 = 13 feet

Now that we know the radius, we can find the circumference:

C = 2 * π * r = 2 * 3.14 * 13 = 81.64 feet

Therefore, the circumference of a circle with a diameter of 26 feet is approximately 81.64 feet.

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The marked-up price of the discounted tablet computer is $298.35.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, During a sale, a store offered a 35% discount.

So, The discounted price of the computer tablet is,

= [(100 - 35)/100]×340.

= (65/100)×340.

= $221.

Now, The price is marked up by 35% which is,

= [(100 = 35)/100]×221.

= (135/100)×221.

= $298.35.

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The probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

The number of possible subcommittees that contain only undergraduate students can be calculated by choosing 3 members from the 4 undergraduate students. This can be done in

(4 choose 3) = 4 ways.

The total number of possible subcommittees of three students that can be formed from the 6 members of the committee can be calculated by choosing 3 members from the 6 students. This can be done in

(6 choose 3) = 20 ways.

Therefore, the probability that there will be no graduate students on the subcommittee is:

Number of subcommittees with only undergraduate students / Total number of possible subcommittees

= 4 / 20

= 1/5

= 0.2

So, the probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

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The graph states that there are 2 number of gallons of lemonade in a container, y, after drinking 12 glasses of lemonade.

How to interpret a graph?

The horizontal scale across the bottom and the vertical scale along the side tell us how much or how many. The points or dots on the graph show us the facts. The lines connecting the points give estimates of the values between the points.

since , it is a decreasing graph because it has a negative slope . Therefore , as no of glasses increases the gallons numbers decreases.

Hence , the graph states that there are 2 number of gallons of lemonade in a container, y, after drinking 12 glasses of lemonade.

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Answer:

no run hide

Step-by-step explanation:

hide run boo

Answer:

Step-by-step explanation:

o find the solution of a system of linear equations, we can find the point where the two lines intersect. The point of intersection represents the solution to the system of equations.

The first linear equation can be determined by finding its slope and y-intercept using the given points:

m = (7 - 6) / (3 - 1) = 1

b = 6 - m * 1 = 6 - 1 * 1 = 5

y = mx + b

y = x + 5

The second linear equation can be found similarly:

m = (8 - 6) / (5 - 3) = 1

b = 6 - m * 3 = 6 - 1 * 3 = 3

y = mx + b

y = x + 3

Since the two lines have the same slope, they are coincident and represent the same line. The solution to the system of equations is therefore any point on this line, but since we were asked for a specific point, we can choose (3,6) as the solution.

The given statement is transitive property.

Transitive property is also called transitive property of equality when we have two equal values and either of this value is equal to third value.

DE≅XY AND [tex]\hat{DE}$$\approx\hat{XY} and \hat{XY}$$\approx$$\YZ, then\hat{DE}$$\approx$$\hat{YZ}[/tex]

This is a transitive property.

Here we have three values, initially first two values are equal and second & third values are equal.

Which gives any one of the value of first and second equals third value.

This is the transitive property.

Hence, the given statement is transitive property.

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Yes, Sage and Tom have the same number of talk minutes left in their cell phones. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

The term "arithmetic operations" refers to the four basic mathematical operations that can be used to express any real number. Multiplication, division, addition, and subtraction are the four operations.

We are given that Sage and Tom both started the month with the same number of talk minutes on their cell phones.

So, let 'x' be the number of talk minutes on their cell phones.

Sage talked for 7 minutes with her dad.

So, talk minutes left in Sage's phone = x-7

Tom talked for 4 minutes with a friend and 3 more minutes with his mom.

So, talk minutes left in Tom's phone = x - (4 +3) = x -7

Hence, Sage and Tom have the same number of talk minutes left in their cell phones.

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The speed at which Ken should run to overtake Joe by 7.30 is 9mi/h.

What is meant by the speed of an object?

The size of a change in an object's position over time is measured by its speed. The rate at which an object travels a distance can be thought of as its speed. A fast-moving object travels at a high speed and completes a significant distance in a brief period of time. This is in contrast to an object travelling slowly, which travels a relatively short distance in the same length of time. It is a scalar value.

Given,

Time at which Joe starts jogging  = 7 am

Time at which Ken starts jogging = 7.10 am

Speed of Joe = 6mi/h

Let Speed of Ken required to overtake Joe = x mi/h

Since Ken has to overtake Joe by 7.30, both will have travelled the same distance by 7.30.

Time taken by Ken to cover the distance = 7.30 - 7.10  20 minutes = 20/60=1/3 h

Time taken by Joe to cover the distance = 7.30 - 7 = 30 minutes = 1/2 h

Distance = speed * time

Both cover the same distance.

6 * 1/2 = x * 1/3

x = 9 mi/h

Therefore the speed at which Ken should run to overtake Joe by 7.30 is 9mi/h.

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The statement that correctly compares the two functions is

They have the same x-intercept and the same end behavior as x approaches ∞.

A function's final behaviour is represented by the value of f(x) as x approaches infinity. Both functions in this scenario have the same final behaviour because they both have unbounded growth, or they both go to positive infinity.

To find y-intercept of a function we have to put x= 0

So, The y-intercept of f(x) is y = -3.

and, The y-intercept of g(x) is y = -4.

To  find x -intercept of a function put y = 0

So, The x-intercept of f(x) is x = 1.

and, The x-intercept of g(x) is x = 1.

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If you were to  graph a sine function from the data listed in the table the days since Jan 8 is an independent variable and amount of moon visible is dependent variable

Given that, we have to graph a sine function from the data listed in the table

From the table we can see that there a two types of variables, The days since the Jan 8 and the amount of moon visible

The independent variable is defined as the variables that does not depends on any other variables

The dependent variable is defined as the variables that depends on other variables

Here the days since the Jan 8 does not depends on any other variables, so it is an independent variable. similarly the amount of moon visible depends on the days since Jan 8 value, so it is a dependent variable

Therefore, the days since Jan 8 is an independent variable and amount of moon light visible is dependent variable

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The given question is incomplete, the complete question is :

if you were to graph a sine function from the data listed in the table above, what values would be represented by the dependent variable and what would be represented by the independent variable?

Answer:

13 or 17

-------------------

Given numbers:

Put them in the ascending order:

Let the possible number to be added be x.

Since x is the median, it should be between 13 and 17:

Also x is the mode. As we see all 6 number are unique, x should be repeat of 13 or 17 in order to be a mode. Therefore the possible number that can be written on the blank card is either 13 or 17.

Answer:

Step-by-step explanation: A congruence statement expresses that two figures have the same size and shape. Here's how you can write a congruence statement step by step:

Write the two figures you want to compare. For example, you could write "Triangle ABC" and "Triangle DEF".

Use the symbol "≅" to indicate congruence. Place the symbol between the two figures, like this: "Triangle ABC ≅ Triangle DEF".

Label the corresponding parts of the two figures to show that they are congruent. For example, you could write "AB = DE", "BC = EF", and "AC = DF".

The final congruence statement would look like this: "Triangle ABC ≅ Triangle DEF, with AB = DE, BC = EF, and AC = DF". This statement says that Triangle ABC is congruent to Triangle DEF, and that the lengths of their corresponding sides are equal.

The actual dimensions of the figure is 3.9 x 2.1

Scale factor is a mathematical term, which we use to scale 2-dimensional and 3-dimensional shapes. Scale factor is a measure of similar figures. Those figures who look the same but are in different sizes.

For example, Two spheres look similar but could have different radii.

For the first dimension of 7.8 cm, we can set up a proportion using the scale factor:

2 cm : 1 m = 7.8 cm : x

where x is the actual length we want to find.

Solving for x, we get:

x = (7.8 cm x 1 m) / 2 cm

x = 3.9 m

Therefore, the first actual dimension is 3.9 meters.

For the second dimension of 4.2 cm, we can use the same method:

2 cm : 1 m = 4.2 cm : y

where y is the actual width we want to find. Solving for y, we get:

y = (4.2 cm x 1 m) / 2 cm

y = 2.1 m

Therefore, the second actual dimension is 2.1 meters.

So the actual dimensions of the figure are 3.9 meters by 2.1 meters.

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Answer:

22ft

Step-by-step explanation:

Always good to try and draw out the scenario, it can make it more easily understandable.

Have a look at the pic.

Hope its clear.

Answer: 1.08g

Step-by-step explanation:

Concentration = Moles/ Volume

Moles = Concentration x Volume

Moles = 0.048 x 250/1000

Moles= 0.012

Moles= Mass / Relative Formula Mass

Mass = Moles x Relative Formula Mass

Mass = 0.012 x 90

= 1.08g