Chapter 3 Lesson 4 Arithmetic Sequence

Yes, A triangle has sides of lengths 10, 24, and 26 is a right triangle.

A right-angled triangle is a triangle with one of the angles at 90 degrees. A 90-degree angle is called a right angle.

The formula states that in a right triangle:

The square of the hypotenuse is equal to the sum of the square of the base and the square of the altitude.

(Hypotenuse)² = (Base)² + (Altitude)²

c²=a²+b²

The three numbers which satisfy the above formula are the Pythagorean triplets

Properties of right angle:

consider c=26 a=10, b=24 substitute in above formula:

26²=10²+24²

⇒676=100+576

⇒676=676

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Answer:

Hope the picture helps you draw.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given that Angie can mow her lawn 4 times using 1/3 gallon of gas, you want to know how much gas is required for each mowing, and how many times Angie can mow on one gallon of gas.

To find the number of gallons required for each mowing of the lawn, divide the number of gallons by the number of mowings:

  (1/3 gal)/(4 mowings) = 1/(3·4) gal/mowing = 1/12 gal/mowing

It takes 1/12 gallon to mow the lawn once.

The reciprocal of this value has the reciprocal units.

  1/(1/12 gal/mowing) = 12 mowings/gal

Angie can mow the lawn 12 times with one gallon of gas.

__

Additional comment

It often proves useful to keep the units with the numbers when working rate problems. This can eliminate a lot of mistakes. The units are treated as you would treat a variable.

Answer:

Step-by-step explanation:Its actually 102, not 110

I would choose both I and II for accomplishing the task of "When you want to Add or Remove Filters, you select Data in the ribbon, and then Filter. You would prefer to do this with one click, so you decide to add Filters to the Quick Access Toolbar."

Click the Commands Not in the Ribbon option in the Customize Quick Access Toolbar dialog box. Click Filter in the list of commands. Select the Add option. Press the OK button. You may use the FILTER function to filter a set of data depending on criteria you provide. The Filter option makes it simple to narrow down your search field.

Here,

I would choose both I and II to complete the task of "When you wish to Add or Remove Filters, go to the Data ribbon, then Filter. You'd prefer to do this with a single click, so you add Filters to the Quick Access Toolbar."

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Answer:

55555555546776546567

An equation that can be used to find the value of,x=$700.0 - $176.95.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

The statement is not an equation if there is no "equal to" sign in it.

According to our question-

x= $700.0 - $176.95

523.05

Hence, An equation that can be used to find the value of,x=$700.0 - $176.95.

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The slope and the y-intercept of the linear function in this problem are given as follows:

The equation of the linear function in this problem is given as follows:

y = -2x + 6.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the parameters are given as follows:

From the table, we have that when x = 0, y = 6, hence the intercept b is given as follows:

b = 6.

When x increases by one, y decays by two, hence the slope m of the linear function is given as follows:

m = -2.

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By using properties for angles we can find and solve some linear equations, there we can see that x = 30°.

Remember that the sum of the interior angles of a triangle must give 180°, and we also know that the angle defined by a line is 180°.

Let's define N as the angle located at vertex N of the right triangle in the left side, we then can write:

2x + 90° + N = 180°

And we also can write the linear equation:

105° + 45° + N = 180°

Solving this one, we can find the value of N.

N = 180° - 45° - 105°  =30°

N = 30°

Replacing that in the equation with x we will get:

2x + 90° + 30°  =180°

2x = 180° - 90° - 30°

2x = 60°

x = 60°/2 = 30°

The value of x is 30°.

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Answer:

Draw a vertical line that goes through the point given.  This will make the two lines perpendicular.  The line given is horizontal, a vertical like would be 90° o the horizontal line.

Step-by-step explanation:

So the only boundary point of [0,∞) and (0,∞) is 0 itself. It is in [0,∞), so that set is closed. It is not in (0,∞), so that set is open.

In mathematics, a (real) interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0, 1, and all numbers in between. Other examples of intervals are the set of numbers such that 0 < x < 1, the set of all real numbers

the set of nonnegative real numbers, the set of positive real numbers, the empty set, and any singleton (set of one element).

Real intervals play an important role in the theory of integration, because they are the simplest sets whose "length" (or "measure" or "size") is easy to define. The concept of measure can then be extended to more complicated sets of real numbers, leading to the Borel measure and eventually to the Lebesgue measure.

Intervals are central to interval arithmetic, a general numerical computing technique that automatically provides guaranteed enclosures for arbitrary formulas, even in the presence of uncertainties, mathematical approximations, and arithmetic roundoff.

So the only boundary point of [0,∞) and (0,∞) is 0 itself. It is in [0,∞), so that set is closed. It is not in (0,∞), so that set is open.

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[tex]x^2[/tex] - (b+c)x +bc=0  is the quadratic equation whose roots are b,c.

If the roots of a quadratic equation are given, the equation can be written by factoring the equation using the roots.

Given the roots, let's say r1 and r2, the quadratic equation can be written as (x - r1)(x - r2) = 0.

Expanding the above equation x^2 - (r1 + r2)x + r1r2 = 0

Therefore, if the roots of a quadratic equation are given as r1 and r2, the quadratic equation can be written as:

x^2 - (r1 + r2)x + r1r2 = 0

since we are given that the root of the equation are b,c;

so r1=b,r2=c;

putting the value in the above equation we get the equation with b and c as root:

[tex]x^2[/tex] - (b+c)x +bc=0

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Complete question :

The coefficient b and c in the equation [tex]x^2+bx+c[/tex] is also root of another equation where c≠0 .

please write the equation

Answer:

It can't add a plot for those numbers-

Step-by-step explanation:

The ordered pair that would be needed by the company for shipment can be loaded in the trailer as the pair will take only 3200ft³ of the volume of the trailer which is 3800 cubic feet.

The total volume of the trailer = 3800 cubic feet

The volume of each recliner = 40 cubic feet

The volume of each sofa = 80 cubic feet

The number of recliner needed = 30

The number of sofas needed = 25

The volume that the sofa will cover = 25 × 80 = 2000

The volume that the recliner will cover= 30 × 40 = 1200

Therefore the total volume both will take = 3200 cubic feet.

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Answer:

Step-by-step explanation:

good

Given that,

Perimeter of kite -  38 cm

Let "x" be the one side of kite

Both of the top sides are equal

Therefore, other side = x

One side of a kite is 2 cm less than 2 times the length of another

Therefore,

One of bottom side = 2x - 2

Bottom sides are also equal

Thus, other bottom side = 2x - 5

We know that,

Perimeter = sum of all sides

38 = x + x + 2x - 2 + 2x - 2

38 = 6x - 4

6x = 38 + 4

6x = 42

x = [tex]\frac{42}{6}[/tex]

x = 7

Thus length of each side of kite is:

x = 7

2x - 2 = 2(7) - 2 = 14 - 2 = 12

Thus length of each side of kite is 7 cm , 7 cm , 12cm , 12cm

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Answer:

Step-by-step explanation:

91

As you can see 91 is the largest 2 digit multiple of 13 as the next multiple is 104 which is a 3 digit number.

Answer:

Step-by-step explanation:

there is 1 dime and 12 quarters

A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. All angles are congruent, and the diagonals bisect each other and are congruent. It does not, however, have the property that all angles are equal.

A parallelogram is a four-sided shape with two pairs of parallel lines. The opposite sides of the parallelogram must be congruent, meaning that they have the same length. All angles are congruent, which means that they all have the same measure. The diagonals of the parallelogram bisect each other, meaning that they divide each other into two equal parts, and they must also be congruent. All of these properties are true for a parallelogram, except that the angles do not have to be equal. The angles can be either acute, obtuse, or right angles, but they must all have the same measure. So, in conclusion, the property that is not true for a parallelogram is that all angles are equal.

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The compound inequality that shows the possible heights of the third tree is 8 ≤ x ≤ 18

An equation shows how two or more numbers and variables are related to each other.

The height of two of the trees are 8 feet and 16 feet. If the height of the third tree is x feet, hence:

Sum of three palm tree heights = x + 8 + 16 = x + 24

The sum of three palm tree heights range from 32 to 42 feet. Hence:

32 ≤ x + 24 ≤ 42

32 - 24 ≤ x ≤ 42 - 24

8 ≤ x ≤ 18

The solution to the compound inequality is 8 ≤ x ≤ 18

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The linear equations would be
4x + 5y = 62 (the equation representing the total cost of Kent)

6x + 2y = 60 (the equation representing the total cost of Rew)

and the solution would be x = 8, y = 6.

What is a system of linear equations?

A system of linear equations is a set of two or more linear equations that describe a relationship between multiple variables. The variables in each equation are related to each other, and the solution of a system of linear equations is the set of values that satisfy all of the equations in the system.

In this case, since Kent and Rew each bought the same amount of boondins and hopts, we can use the same variable names (x for boondins and y for hopts) for both of them. We can use this information to write two equations to model the relationship between the amounts of boondins and hopts that Kent and Rew bought:

4x + 5y = 62 (the equation representing the total cost of Kent)

6x + 2y = 60 (the equation representing the total cost of Rew)

This system of linear equations is called a system of two equations in two variables.

Hence, the linear equations would be
4x + 5y = 62 (the equation representing the total cost of Kent)

6x + 2y = 60 (the equation representing the total cost of Rew)

and the solution would be x = 8, y = 6.

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Four hemispheres are present in the shaded area. One large hemisphere and three smaller hemispheres each have a radius of 18 cm.

Consequently, the hemisphere's total surface area is 3(pi)R2. A semicircle has a curved line and a straight line that are both equal to the circle's diameter. The curving line is 2R in length while the straight line is (pi)R in length. So, 2R + (pi)R is the semicircle's total perimeter.

The shaded regions' area is calculated as follows:

initially, area of a hemisphere = 2r2 square units

the area of three small hemispheres

(2*3.14*6 r).3 = 226.08 cm2

Area of the larger hemisphere

2*3.14*18^2 = 2034.72cm^2

Total area of the shaded regions = 226.08 + 2034.72 = 2260.8cm^2

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Bag A as required by the task content has 31.25 percent fewer marbles than Bag B.

It follows from the task content that the percent fewer marbles which Bag A has relative to Bag B is to be determined.

As given in the task content; Bag A contains 110 marbles, while Bag B contains 160 marbles.

On this note, the difference between the number of marbles is; 160 - 110 = 50 marbles.

Hence, the percent of fewer marbles in Bag A relative to Bag B is;

= ( 50 / 160 ) × 100%

= 31.25%.

Therefore, Bag A has 31.25% fewer marbles than Bag B.

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The word used to remember the 3 trigonometric ratios sine, cosine, and tangent is SOH-CAH-TOA

We know that in right triangle for an angle θ, the trigonmetric ratios are:

sin(θ) = opposite side of θ/ hypotenuse

cos(θ) = adjacent side of θ / hypotenuse

tan(θ) = opposide side of θ / adjacent side of θ

cot(θ) = 1/tan(θ)

sec(θ) = 1/cos(θ)

cosec(θ) = 1/sin(θ)

The word 'SOH-CAH-TOA' is used to remember the sine, cosine, and tangent ratios in a right triangle.  

SOH means, Sine = Opposite side / Hypotenuse.

CAH means, Cosine = Adjacent side / Hypotenuse.

TOA means, Tangent = Opposite side / Adjacent side

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The length of the ramp is 161.62 inches when the barrel turns 47 times in being rolled up the ramp.

The Circumference of a circle is defined as the product of the diameter of the circle and pi.

C = πd

where 'd' is the diameter of the circle

The circumference of the circular base of the barrel is given by the formula C = πd, where C is the circumference and d is the diameter of the base.

In this case, d = 1.1 inches, so C = π1.1 inches = 3.46 inches.

Since the barrel turns 47 times, the distance it travels is 47 times the circumference of the base,

47 × 3.46 inches = 161.62 inches

Therefore, the length of the ramp is 161.62 inches.

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Answer:

10

Step-by-step explanation:

no explanation just math-way

After H hours of coaching, let E indicate her profits (in dollars). She receives $20 for every hour she tutors. This indicates that her total earnings in H hours would be  E = 20H.

After H hours of coaching, let E indicate her profits (in dollars). She receives $20 for every hour she tutors. This indicates that her total earnings in H hours would be

E = 20H.

We would enter H = 17

into the formula to get Mai's pay after 17 hours of tutoring.

E = 20 × 17 E = $340 is the result.

The complete question is:

Mai tutors history. For each hour that she tutors, she earns 20 dollars. Let E be her earnings (in dollars) after tutoring for H hours. Write an equation relating E to H . Then use this equation to find Mai's earnings after tutoring for 17 hours.

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The regular price of a ticket to the game was $204.00.

We can use algebra to solve the problem. Let x be the regular price of a ticket to the game.

We know that the group rate saved Mason $5.75 per ticket, so the regular price of a ticket is x + $5.75.

We know that Mason bought 16 tickets and paid a total of $296.00, so we can set up the following equation:

x + $5.75 = (x + $5.75) * 16 = 16x + $92

So the regular price of a ticket is x = $296.00 - $92 = $204.00

Therefore, the regular price of a ticket to the game was $204.00.

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Answer:

x + 5 = 10

Step-by-step explanation:

Answer: -14

Step-by-step explanation:   When you have a problem like this all you do in multiply the answer and the number your given.

 7x-2 that would by -14

You want to check your answer by changing X for -14 and you solve from there. Plus 2 negatives equal a positive.

Hope this helps!

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{x}{-2} = 7}[/tex]

[tex]\text{Multiply } \rm{ -2}\text{ to both sides}[/tex]

[tex]\mathsf{\dfrac{x}{-2}\times -2 = 7\times -2}[/tex]

[tex]\text{Simplify it}[/tex]

[tex]\mathsf{x = 7\times -2}[/tex]

[tex]\mathsf{x = -14}[/tex]

[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x = -14}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]