Find m/_1 and m/_2. Justify each answer​

The sequence is an arithmetic sequence with d = 25 and the next two terms are 125, 150.

Suppose we are given a sequence: a1, a2, a3, a4, ...

To determine whether the sequence is an arithmetic, geometric, or uncategorized one, we need to check the relation between its consecutive terms.

Arithmetic sequence.

If:

a2 - a1 = a3 - a2 = a4 - a3 = constant

then the given sequence is an arithmetic sequence. Furthermore, the constant d = a2 - a1  is usually called the common difference.

Geometric sequence.

If:

a2/a1 = a3/a2 = a4/a3 = constant

then the given sequence is a geometric sequence. Furthermore, the constant r = a2/a1  is usually called the common ratio.

The given sequence is:

25,50,75,100, ........

Let us check the difference:

50 - 25 = 75 - 50 = 100 - 75 = 25.

We can, then, conclude that the sequence is an arithmetic sequence with d = 25.

To find the next two terms, add 25 to every last terms.

100 + 25 = 125

125 + 25 = 150

Hence the next two terms are: 125, 150.

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By SSS (Side, side, side) congruency;

⇒ ΔA B C ≅ ΔX Y Z .

Given that;

The vertices of ΔA B C are;

A (3, -1) , B (3, 7) and C (7, 7)

The vertices of  ΔX Y Z  are;

X (-7, 0), Y (-7, 4), Z (1, 4)

We have to prove that ΔA B C ≅ ΔX Y Z .

What is congruency in triangle?

If all three corresponding sides are equal and all the three corresponding angles are equal in measure, then Two triangles are said to be congruent.

Now,

The vertices of ΔA B C are;

A (3, -1) , B (3, 7) and C (7, 7)

The vertices of  ΔX Y Z  are;

X (-7, 0), Y (-7, 4), and Z (1, 4)

To prove ΔA B C ≅ ΔX Y Z we use distance formula and prove all sides are equal.

In ΔA B C;

Distance between A and B;

[tex]D_{AB} = \sqrt{(3-3)^2 + (7 -(-1))^2} = \sqrt{64} = 8[/tex]

Distance between B and C;

[tex]D_{BC} = \sqrt{(7-3)^2 + (7 -7)^2} = \sqrt{16} = 4[/tex]

Distance between C and A;

[tex]D_{CA} = \sqrt{(7-3)^2 + (7 -(-1))^2} = \sqrt{80}[/tex]

In ΔX Y Z;

Distance between X and Y;

[tex]D_{XY} = \sqrt{(-7-(-7))^2 + (4 -0)^2} = \sqrt{16} = 4[/tex]

Distance between Y and Z;

[tex]D_{YZ} = \sqrt{(-7-1)^2 + (4 -4)^2} = \sqrt{64}= 8[/tex]

Distance between Z and X;

Clearly, Distance between sides of  ΔA B C and  ΔX Y Z are;

[tex]D_{AB} = D_{YZ} \\\\D_{BC} = D_{XY}\\\\D_{CA} = D_{XZ}[/tex]

Hence, By SSS congruency;

⇒ ΔA B C ≅ ΔX Y Z .

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Answer:

Step-by-step explanation:Given f(x)=x-5

f(-1)= -1-5

    = -6

f(0)=0-5

   = -5

f(1)=1-5

  = -4

f(2)=2-5

   = -3

f(5)=5-5  

    =0

f(8)=8-5

    = 3

Answer:

Step-by

You have to determine how much more would $10,000 earn in 3 years compounded daily at 1.33% than compounded semiannually at 4.33%.

The first step is to calculate the final amount for both options. To do so, you have to use the following formula:

Where

A is the accrued amount

P is the principal amount

r is the interest rate expressed as a decimal value

t is the time in years

n is the number of compounding periods per year.

→ First, find the accrued amount for P=$10,000, R=1.33%, and t=3 years.

The account compounds daily,

The graph of the equation is showing that we are walking towards our home. If the equation d = 4 - (1/15)t represents your distance from home d for each minute you walk t .

A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.

The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.  

Therefore,

m =  y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.

Be aware that tan ∅ = y/x

We also refer to this tan as the line's slope

We have given d = 4 - (1/15)t

We will use the graph tool and determine the coordinates

(see the attached image)

When t = 0, d = 4                     (y-intercept)

This provide the info that at the time t = 0 the house was four units away.

When t = 60 min,  d = 0           (x-intercept)

This provide the info that he was already at home at the time t = 60 minutes.

Thus, this slope proves that he was walking towards the house.

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Answer:

-291.462

Step-by-step explanation:

My mom is a teacher lol and I have a calculator haha

Answer:

0.07874506561 or 0.07875

Step-by-step explanation:

cubed root of 2 = 1.25992104989

or 1.260

The slope - intercept form of the equation x-2 y+3=1 is  y = x/2 + 1 .

Simply said, the slope-intercept form is the technique to write a line's equation so that the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) are instantly visible. This form is frequently known as the y = mx + b form.

The slope - intercept form is y = mx + c

The given equation is

x-2 y+3=1

Subtract 3 from both sides,

x - 2y = -2

Divide the whole equation by 2

x/2 - y = -1

Rearrange the equation -

y = x/2 + 1

So the equation in slope-intercept form is y = x/2 + 1 , where slope is 1/2 and c = 1.

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Answer:

Line 1 and Line 2 are parallel.

Answer:

3 because you always know your answer by the smalest number which has a digit of 3

Step-by-step explanation:

Answer:

28 units

Step-by-step explanation:

• the diagonals of a rectangle are congruent , then

AC = BD , that is

4x - 8 = 2x + 10 ( subtract 2x from both sides )

2x - 8 = 10 ( add 8 to both sides )

2x = 18 ( divide both sides by 2 )

x = 9

Then

BD = 2x + 10 = 2(9) + 10 = 18 + 10 = 28

the diagonals are 28 units long

Answer:

[tex] {7}^{ \frac{1}{4} } = \sqrt[4]{7} [/tex]

The correct answer is A.

The constant of variation in y = (12) x is (12)

y = kx            (Where k is the constant)

Here,

⇒ y = (12) x

So, k = (12)

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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The unit is 2.5 Pounds per week.

So, this is a fraction of 25 Pounds in 10 Weeks.

We want a unit rate with a denominator of one, so we divide the top and bottom by ten.

Therefore, the unit is 2.5 Pounds per week.

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The cube with he greater side length is: cube B.

Volume of a cube = a³

Surface area of a cube = 6a²

Therefore:

Volume of cube A = 125 in.³

125 = a³

√125 = a

a = 5 in.

Side length of Cube A = 5 in.

Surface area of Cube B = 121 in.²

121 = 6a²

√(121/6) = a

√(121/6) = a

10.7 = a

a = 10.7

Side length of cube B = 10.7 in.

Therefore, the cube with he greater side length is: cube B.

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Answer:

It will take you nearly 11 weeks

Step-by-step explanation:

80+6x = 145

6x = 145-80

6x = 65

x = 65/6 (weeks)

Answer:

Question:

Sunil has 40 counters. 9 of Sunil's counters are red. (c) What fraction of Sunil's counters are not red?

Answer: 0.775 or 77.5%

Step-by-step explanation:

Based on the given conditions, formulate: (40 - 9) / 40

Calculate the sum or difference: 31/40

= 31/40 = 77.5% or 0.775

If Ana owns a lot that contains 27 acres and is 972' wide and if she buys an adjacent lot that has the same depth but is only 648' wide then the total acres of land she will own is c.45

First of all, we convert the acres into square feet.

As 1 acre = 43560 square feet

27 × 43560 = 1176120 square feet

Dividing it with 972' to find the depth of the lot she already owns:

1176120 / 972 = 1210 depth

As the adjacent lot has the same depth, therefore;

1210 × 648 = 784080 square feet

Converting square feet into acres by division;

784080 / 43560 = 18 acres

Now we can calculate the total acres of land she will own by addition;

total acres = 27 acres + 18 acres

total acres = 45 acres

Therefore, the total acres of land she will own is calculated to be 45.

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Answer:

[tex]x \leq \dfrac{13}{4}[/tex]

Step-by-step explanation:

Given inequality:

[tex]2x-6(x-3)\geq 5[/tex]

Expand -6(x - 3):

[tex]\implies 2x-6(x)-6(-3)\geq 5[/tex]

[tex]\implies 2x-6x+18\geq 5[/tex]

Combine like terms  2x - 6x = -4x:

[tex]\implies -4x+18\geq 5[/tex]

Subtract 18 from both sides:

[tex]\implies -4x+18-18\geq 5-18[/tex]

[tex]\implies -4x\geq -13[/tex]

Divide both sides by -1, remembering to reverse the inequality:

[tex]\implies\dfrac{ -4x}{-1}\geq \dfrac{-13}{-1}[/tex]

[tex]\implies 4x\leq 13[/tex]

Divide both sides by 4:

[tex]\implies \dfrac{4x}{4}\leq \dfrac{13}{4}[/tex]

[tex]\implies x \leq \dfrac{13}{4}[/tex]

Answer:

[tex]{ \tt{average \: \triangle = \frac{y _{2} - y _{1} }{x _{2} - x _{1} } }} \\ [/tex]

[tex]{ \tt{ = \frac{5 - ( - 3)}{3 - ( - 1)} }} \\ \\ = { \tt{ \frac{8}{4} }} \\ \\ = 2[/tex]

The change in price of the inline skates for the month  of July is $153, August is $141 and September is $129 and using the mathematical operations we conclude that we cannot buy the inline skates after savings in the month of August

As per the question statement, we are supposed to find the change in  price of the inline skates when price of the inline skates for the month of June is $165.

Using mathematical operations,

Price In July =165+(-12)=153 dollars

Price In August =165+2(-12)=165-24=141 dollars

Price In September =165+3(-12)=165-36=129 dollars

Also in the second part of question asks that whether we will be able to buy the skates in the month of August if we save $[tex]35[/tex] in June, $[tex]55[/tex] in July,  $[tex]45[/tex] in August and $[tex]18[/tex] in September.

Price of Skates in August = $141

Using mathematical operations,

Total savings tlll August =35+55+45=135$dollars

As the savings is less than the price of Skates in August, we CANNOT buy the inline skates in the month of August.

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Using proportions, it is found that:

a) You would find 36 kg of carbon is a 300 kg piece of marvel.

b) 40% of marble is Calcium.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

For this problem, the ratio 10:3:12 of calcium, carbon and oxygen means that:

Hence for item a, the amount is given as follows:

300 x 3/25 = 36.

You would find 36 kg of carbon is a 300 kg piece of marvel.

For item b, the percentage is found as follows:

10/25 = 40%.

40% of marble is Calcium.

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Answer: 22425

Step-by-step explanation: hope this helps!!

Answer:

22425

Step-by-step explanation:

Answer:

-27

there is a pattern of x3 every time :)

Answer:

A. 70>5g+61

Step-by-step explanation:

$5 per gigabyte means $5g

$61 + 5g

he keeps his budget lower than $70 so,

5g + 61 < 70

Answer:

(0,1)

Step-by-step explanation:

|x| is minimized when x=0, meaning the vertex is at (0,1).

The measure of the major arc JLK will be 206°. Then the correct option is B.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

The measure of the minor arc JK will be 154°.

Then the sum of the major arc and minor arc in a circle is 360°.

Then the major arc JLK will be given as,

JLK + JK = 360°

JLK + 154° = 360°

JLK = 206°

The measure of the major arc JLK will be 206°. Then the correct option is B.

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The equation of the line passing through the point (4 , -3)  and has a slope of 1/2 is H. y = (1/2)x - 5.

The equation of a line can be expressed in different forms: standard form, slope-intercept form, and point-slope form

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Given the slope of 1/2 and a point (4 , -3), use the point-slope form to generate the equation of the line by plugging in the values in the equation.

(y - y1) = m(x - x1)

y - -3 = 1/2(x - 4)

y + 3 = (1/2)x - 2

Isolating the variable y in the left side,

y + 3 = (1/2)x - 2

y = (1/2)x - 2 - 3

y = (1/2)x - 5

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