Determine whether the statement below is true or false boxy is rectangle

The integers ranging from 5n to 5n + 10, with 5n as a positive odd integer, in each case, the range contains three even integers.

When n = 1:

The range is 5(1) to 5(1) + 10

= 5 to 15.

There are three even integers in this range: 6, 8, and 10.

When n = 3:

The range is 5(3) to 5(3) + 10

= 15 to 25.

There are three even integers in this range: 16, 18, and 20.

When n = 5:

The range is 5(5) to 5(5) + 10

= 25 to 35.

There are three even integers in this range: 26, 28, and 30.

In each case, the range contains three even integers.

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AB = AD and BC = DC are given. Furthermore, we can see that AC = AC by the reflexive property. We have three pairs of congruent corresponding sides, which allows us to use the SSS congruence theorem. From that, we would use CPCTC to conclude that angle B is congruent to angle D.

CPCTC = corresponding parts of congruent triangles are congruent.

Answer:

See explanation

Step-by-step explanation:

The question is incomplete, as the total orders is not given.

To solve this question, I will assume a value for the total number of order.

Let

[tex]x \to 12-cup[/tex]

[tex]n_x = 18[/tex] ---- number of 12-cup

[tex]y \to 36-cup[/tex]

[tex]n_y = ??[/tex] ---- number of 36-cup

[tex]n \to[/tex] Total order

Required

Calculate [tex]n_y[/tex]

To do this, we make use of the following equation:

[tex]n_x * x + n_y * y = n[/tex]

Substitute known values

[tex]18 * 12 + n_y * 36 = n[/tex]

[tex]216 + 36n_y= n[/tex]

Collect like terms

[tex]36n_y= n - 216[/tex]

Divide both sides by 36

[tex]n_y= \frac{n - 216}{36}[/tex]

Assume the number of orders is: 540 cups

The equation becomes

[tex]n_y= \frac{540 - 216}{36}[/tex]

[tex]n_y= \frac{324}{36}[/tex]

[tex]n_y= 9[/tex]

Answer:

hope it helps plz mark me brainliest ;)

Step-by-step explanation:

A.P. -9,-14,-19,-24

first term (a) = -9

common difference of the A.P. (d) = -14 - (-9)

                                                        = -14 + 9

                                                        = -5

an = a + (n-1) d

here we find a30 and a20

so for 30th term

a30 = a+ (20-1) d

= -9 + (19) (-5)

= -9 -95

= -104

so

a30 - a20 = -154 - (-104)

= -154 + 104

= -50

therefore for the given A.P a30 - a20 = -50

Answer:

Different sequence but just in-case anyone needs it

d=-20

Explicit

Recursive

Step-by-step explanation:

Instructions: For the following sequence, state the common difference, identify which is the explicit form and which is the recursive form of the rule, and find the term listed.

Sequence: 5,−15,−35,−55,…

Common Difference:

Answer -20

an=25−20n

Answer Explicit

an=an−1−20

a1=5

Answer Recursive

Answer:

32.61° is the answer

Step-by-step explanation:

Tanx=17.6/27.5

Answer:

32.8 mi²

Step-by-step explanation:

Hi there!

Area of a triangle when given two sides, a and b, and the angle that conjoins them, C:

[tex]A=\frac{1}{2} ab*sinC[/tex]

Plug in the known information:

a=11, b=6, C=97°

[tex]A=\frac{1}{2} (11)(6)*sin(97)\\A=33sin(97)\\A=32.8[/tex]

Therefore, the area of the triangle is approximately 32.8 mi².

I hope this helps!

Answer:

B

Step-by-step explanation:

The trick here is to find the height. The answer is

height = sin(180 - 97) * 11

The height is found by finding the supplement of 97, taking the sin of that angle and multiplying by 11.

There is a drawing required. You need to extend ZY until a line from x meets ZY (extended) at right angles. When that happens you find the sine of the supplement.

height = sin(83)*11

height = 10.92

Now use the standard area formula.

Area = base (ZY) * height / 2

base = 6

height = 10.92

Area = 6 * 10.92 /2

Area = 32.75

Answer:

the answer is c

Step-by-step explanation:

when solving for theta, we are given the side length adjacent to it (5) and the length of the hypotenuse ( 14).

the trigonometric function that deals with adjacent and hypotenuse values is cosine.

you can use SOH CAH TOA

stands for :

sin = opposite/hypotenuse

cos = adjacent/ hypotenuse

tan = opposite/adjacent

we dont know theta so :

cos(theta) = 5/14

cos = about 69

check :

cos(69) = 5/14

                   cos(69) = 0.35836794954

                   5/14 = 0.35714285714

Answer:

acute triangle

Step-by-step explanation:

We have 3 angles that are not equal to each other

They are all smaller than 90 degrees which means they are acute angles

Answer:

Acute

Step-by-step explanation:

Acute=less than 90 degrees

Obtuse=more than 90 degrees

Right=1 side has 90 degrees

Equiangular=every side has the same degree

Therefore, it would be Acute

Answer:

m∠1 = 103

m∠2 = 103

Step-by-step explanation:

by definition, the opposite angles of a kite are congruent.

we know that a quadrilateral's angles add up to 360.

117 º+ 37º + 2xº = 360º

2xº = 206º

xº=103º

Answer:

for 3644 produced books the costs will be the same.

Step-by-step explanation:

x = number of books

f(x) = production method 1 costs

g(x) = production method 2 costs

f(x) = 11.75x + 57077

g(x) = 21.25x + 22459

for what number of books (x) will that be the same ?

11.75x + 57077 = 21.25x + 22459

34618 = 9.5x

x = 34618 / 9.5 = 3644

Given:

The preimage and image of a triangle in the given figure.

To find:

The dilation scale factor.

Solution:

From the given figure it is clear that the vertices of the triangle ABC are A(-2,-2), B(-1,2) and C(2,1).

The vertices of the triangle A'B'C' are A'(-4,-4), B'(-2,4) and C'(4,2).

If a figure is dilated by factor K with (0,0) as the center of dilation, then

[tex](x,y)\to (kx,ky)[/tex]

Let the scale factor be K, then the image of point A is:

[tex]A(-2,-2)\to A'(k(-2),k(-2))[/tex]

[tex]A(-2,-2)\to A'(-2k,-2k)[/tex]

From the given figure it is clear that the image of point A is A'(-4,-4).

[tex]A'(-2k,-2k)=A'(-4,-4)[/tex]

On comparing both sides, we get

[tex]-2k=-4[/tex]

[tex]k=\dfrac{-4}{-2}[/tex]

[tex]k=2[/tex]

Therefore, the dilation scale factor is 2.

Step-by-step explanation:

in this situation

A+B =D

Answer:11/20

Step-by-step explanation:

Don: 1/4 of $300 = 300x.25 = $75

Ron:1/5 of $300 = 300x.20 = $60

75 + 60 = $135

300-135 = $165

165/300 = .55 = 55% = 55/100 = 11/20

OR

take 1/4 and 1/5 and make denominators equal

D: 5/20 and R: 4/20 = D+R:9/20 so C:11/20

The increase in the amount of wages of Gabriela is $ 41,400

What is an Equation?

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.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total amount after increase in wages be = A

Now , the initial amount of Gabriela be = $ 36,000

And , the percentage increase in the wages = 15 %

So , the equation will be

Total amount after increase in wages A = initial amount + ( percentage increase x initial amount )

Total amount after increase in wages A = 36,000 + ( 15/100 x 36,000 )

Total amount after increase in wages A = 36000 + ( 15 x 360 )

Total amount after increase in wages A = 36000 + 5400

Total amount after increase in wages A = $ 41,400

Therefore , the value of A is $ 41,400

Hence , The increase in the amount of wages of Gabriela is $ 41,400

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Answer:

x = 8

Step-by-step explanation:

The angles shown are vertical angles

Vertical angles are congruent hence 8x + 36 = 5x + 60

( Notice that we just created an equation that we can use to solve for x )

We now solve for x algebraically

8x + 36 = 5x + 60

Step 1: Subtract 5x from both sides

8x - 5x + 36 = 5x - 5x + 60

Outcome: 3x + 36 = 60

Step 2: Subtract 36 from both sides

3x + 36 - 36 = 60 - 36

Outcome: 3x = 24

Step 3: Divide both sides by 3

3x/3 = 24/3

Outcome: x = 8

Answer:

[tex]x=4\sqrt{2}\\y=7[/tex]

Step-by-step explanation:

In order to solve this problem, the easiest approach is to draw a line connecting the vertex between the side with a measure of (y) and (3) to the side with the length (x). This side should be parallel to the side with a length of (4).

Since the new side constructed (call this side (b)), is parallel to the side with a length of (4) and is intersected by segments that are perpendicular to the side with a length of (4), the side (b) and (4) must have the same measure. Therefore (b = 4).

The triangle formed with sides (x) and (b) is a (45 - 45 - 90) triangle. Meaning that its angles have the following measure, (45 - 45- 90). This means that its sides follow the following ratio:

angle : side opposite

[tex]45:x\\45:x\\90:x\sqrt{2}[/tex]

Apply this logic to the given situation.

[tex]x=b*\sqrt{2}\\x = 4\sqrt{2}[/tex]

The side (b) divides the side (y) into two parts. Call the part that is a side of the triangle ([tex]y_1[/tex]) the side that is a part of the rectangle is called ([tex]y_2[/tex]). As per the logic used to find the lengths of side (b), one can use similar logic to find the length of side ([tex]y_2[/tex]). The sides ([tex]y_2[/tex]) and (3) are parallel and are intersected by the sides with a measure of (4) and (b), therefore  ([tex]y_2[/tex]) and (3) are cognrunet. Thus ([tex]y_2[/tex] = 3).

The base angles converse theorem states that when two angles in a triangle are congruent, the triangle is isosceles, and the sides opposite the congruent angles are also congruent. Thus, one can state the following:

[tex]y_1=b\\y_1=4[/tex]

Now add up the measurement of ([tex]y_2[/tex]) and ([tex]y_1[/tex]) to find the measure of (y):

[tex]y_2+y_1=y\\4+3=y\\7=y[/tex]

Answer:

f(n) = f(n - 1) - 5

Step-by-step explanation:

The recursive formula allows a term in the sequence to be found by adding the constant difference to the previous term.

Here d = 1 - 6 = - 4 - 1 = - 9 - (- 4) = - 14 - (- 9) = - 5 , then

f(n) = f(n - 1) - 5 with n ≥ 1 and f(1) = 6

Answer:

[tex]3\frac{5}{7}[/tex]

Step-by-step explanation:

13 ÷ 3.5

[tex]3.5=3\frac{5}{10}[/tex]

Answer:

[tex] MN= \boxed{15}[/tex]

Step-by-step explanation:

refer the attachment

therefore Let,

according to the question

[tex] \displaystyle (x - 3 ) (x + 13) =( x + 3 {)}^{2} [/tex]

simplify square and Multiplication:

[tex] \displaystyle {x}^{2} + 10x - 39 = {x}^{2} + 6x + 9[/tex]

cancel x² from both sides:

[tex] \displaystyle 10x - 39 = 6x + 9[/tex]

cancel 6x from both sides:

[tex] \displaystyle 4x - 39 = 9[/tex]

add 39 to both sides:

[tex] \displaystyle 4x = 48[/tex]

divide both sides by 4:

[tex] \displaystyle \boxed{x = 12}[/tex]

given that,

[tex] MN= x + 3[/tex]

substitute the got value of x:

[tex] MN= 12 + 3[/tex]

simplify addition hence,

[tex] MN= \boxed{15}[/tex]

Answer:

Using a calculator;

A is approximately 51.34°

G is approximately 28.36°

Step-by-step explanation:

Part 1

The given trigonometric ratio is presented as follows;

tan A = 5/4

Therefore, the angle, A = arctan(5/4)

Using a calculator,  the value of A is found as follows;

1. Ensure the angle mode of the calculator is set to the correct value (the selected mode here is degrees)

2. Entering 5/4 into the calculator, using the keypad

3 . Selecting the arctan button to give, A ≈ 51.34°

Part 2

The given trigonometric ratio is cos G = 0.88

Therefore, G = arccos(0.88)

1. Ensure the angle mode of the calculator is set to the correct value (the selected mode here is degrees)

2. Enter 0.88 into the calculator by typing

3. Select arccos from the function menu, to give

arcos(0.88) = G ≈ 28.36°.

Answer:

7. 35-(2*3+5*4.5)

8. 6.5

Answer:

11

Step-by-step explanation:

Vicky used 462 beads to make 11 necklaces, she would have left 38 beads.

Answer:

He make seven necklaces

Answer:

5

Step-by-step explanation:

A function

[tex]a \times {b}^{x} [/tex]

where a is the initial value and b is the multiplicative rate of change.

In the function,

[tex]f(x) = 2 \times {5}^{x} [/tex]

5 is the value of b so

5 is the multipicative rate of change

Answer:

Yes

Step-by-step explanation:

Statistics can perdict cyclones for example lets say that somewhere a cyclone happens almost every February then its statistically likely to happen this February too.

First find the gradient of L.

-6÷3=-2

gradients of perpendicular lines multiply together to give -1.

(-2)×1/2=-1

m=1/2 or 0.5

y=0.5x-1.5

Answer: QF = 5

Step-by-step explanation:

We know that if a triangle has a centroid, the ratio of the longer segment to shorter segment is 2:1. We can set up a proportion [tex]\frac{2}{1} = \frac{10}{x}[/tex], where x is the length of QF. By cross multiplying and dividing, you get x = 5 or QF = 5.

Answer:

5

Step-by-step explanation:

Answer:

5 calories per gram

Step-by-step explanation:

Take the number of calories and divide by the number of grams

225/45

5 calories per gram

Answer:

The angle between two nonzero vectors u and v is given by

Cos Θ=u*v/║u║║v║

1) If u*v=0, then CosΘ=0

arccos 0=90°

2) If u*v > 0, then CosΘ >0

If (cos Θ > 0, then Θ is less than 90°

3) If u*v < 0, then Cos Θ < 0

If Cos Θ < 0, then Θ is greater than 90°

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