Complete the following sentences.

Angle e= Angle , as they are alternate angles.

Angle f= Angle , as they are alternate angles.

Angles a, b and c add up to °, as they are on a straight line.

Therefore, angles e, f and b also add up to

**Answer:**

Angle e = Angle **a**, as they are alternate angles.

Angle f = Angle **c**, as they are alternate angles.

Angles a, b, and c add up to **180°**, as they are on a straight line.

Therefore, angles e, f and b also add up to **180°**.

Easy question, pls explain:

In a particular class, 72% of the students have black hair. Five black-haired students leave the class, so that now 65% of the students have black hair. How many students were originally in the class?

**Answer:**

72% are black haired - 5 students becomes 65% students are black haired.

meaning 7% are 5 students

Base = Percentage/Rate

Base = 5/0.07

Base = 71 students

CHECKING71 (students) * 0.72 (rate of black haired) = 51

There are 51 black hair students51 - 5 (leave the class) = 46 students

71 (students) * 0.65 (rest of black hair) = 46 students

Therefore, we checked our answers and its correctThere are total of 71 students in the class. 51 are black hair, but since 5 left, there will be 46 black hair students left**Step-by-step explanation:**

An object moving with a speed of 21 m/s and has a kinetic energy of 140 J, what is the mass of the object?

**Answer:**

0.63 kg

**Step-by-step explanation:**

KE = 1/2mv²

solve for m:

m = 2(KE)/v²

m = 2(140J) / (21m/s)²

m = 280J / 441 = 0.63 kg

When solving the following equations, multiply the first and second equation by a constant in order to eliminate the y terms.

2x + 2y = 7

6x + 3y = -2

What are the constants of both equations?

**Answer:**

**Step-by-step explanation:**

You want to **solve** the **given system of equations** by **eliminating** the **y-term**. You also want to know **what constants** are used in the process.

The y-term can be eliminated from these equations by combining them in such a way as to may the coefficient of y be zero. This can be done an infinite number of ways.

One way that works reasonably well is to identify the coefficients of y, and multiply each equation by the y-coefficient in the other equation. The resulting equations can be *subtracted* one from the other to eliminate the y-terms, which now have *identical coefficients*. You can choose the equation with the smaller x-coefficient to subtract from the other one.

The y-term coefficients are 2 and 3.

**Multiply the first equation by 3, and the second by 2**.

3 × (2x +2y) = 3 × 7 ⇒ 6x +**6y** = 21

2 × (6x +3y) = 2 × (-2) ⇒ 12x +**6y** = -4

The x-coefficients are 6 and 12. We choose to subtract the first equation (with x-coefficient 6) from the second equation:

(12x +6y) -(6x +6y) = (-4) -(21)

6x = -25 . . . . . . . . simplified

** x =** -25/6 **= -4 1/6** . . . . . divide by 6

Substituting for x in the first equation, we have ...

2(-25/6) +2y = 7

2y = 7 +25/3 . . . . . add 25/3

2y = 46/3 . . . . . . . .combine terms

** y =** 23/3 **= 7 2/3** . . . . divide by 2

**The solution to the equations is (x, y) = (-4 1/6, 7 2/3)**.

Since these numbers are not integers, we choose to check them in the original equations. We used the first equation to find y, so we'll use the second equation for checking.

6(-4 1/6) +3(7 2/3) = -25 +23 = -2 . . . . . . as required

__

*Additional comment*

If you solve these by *addition*, rather than *subtraction*, you want to choose multipliers that result in opposite coefficients, so they add to zero. Essentially, you use the opposite coefficients, as described above, but you *negate one of them*.

Above, we chose the subtraction in a way that resulted in the x-coefficient being positive. If you arbitrarily choose the signs of the multipliers (always negating the second one, for example), the combined equations may make the x-coefficient negative. That works, too, but may require more mental effort to deal with the minus sign.

Of course, you can use the x-coefficients and eliminate the x-terms.

Or, you can use a single multiplier that corresponds to the ratio of the coefficients. For example the ratio of the 2nd y-coefficient to the first one is 3/2. Multiplying the first equation by this will give the y-term a coefficient of 3, matching the y-coefficient in the 2nd equation. Then the subtraction can proceed as already described.

(6x +3y) -3/2(2x +2y) = (-2) -3/2(7)

3x = -25/2 . . . . . simplified; y is gone.

Anna has 7,209 cans of soup that need to be boxed. If she puts 9 cans of soup in 1 box, how many boxes will she need.

**Answer:**

801 boxes

**Step-by-step explanation:**

[tex]\frac{7209}{9}[/tex] = 801

Set up a proportion first.

If 9 cans in 1 box, then x boxes will be need for 7209 cans.

9x= 7209

9x/9= 7209/9

x= 801

801 boxes will be needed for 7209 cans

If 9 cans in 1 box, then x boxes will be need for 7209 cans.

9x= 7209

9x/9= 7209/9

x= 801

801 boxes will be needed for 7209 cans

What is the equation for the hyperbola shown?

The **hyperbola's** standard equation is [(x2/a2) - (y2/b2)] = 1, where X denotes the transverse axis and Y denotes the conjugate axis.

A **hyperbola** is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set. A hyperbola is made up of two mirror images of one another that resemble two infinite bows. These two sections are known as connected components or branches. A hyperbola is a geometric shape in mathematics where the difference between the lengths from any point on the figure to two fixed locations is a constant (the Greek letter o literally means "overshooting" or "excess"). We refer to the two fixed spots as foci (plural of focus).

Given

The equation for the **hyperbola**

The hyperbola's standard **equation** is [(x2/a2) - (y2/b2)] = 1, where X denotes the **transverse** axis and Y denotes the **conjugate** axis.

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Which can be proven? Select all that apply.

A. ∠ C E D ≅ ∠ A H J

B. A B ≅C B

C. C B ≅D B

D. ∠ D A G ≅ ∠ J C F

The Option that can be **proven **is:

Definitions, assertions, and methods are linked in a proper fashion to get the desired outcome in **mathematical proof**.

This procedure helps pupils understand the rationale behind the statement. This is also true of counterexamples and their important significance in **mathematics**.

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10) Find the missing angle measure. Round answers to the

nearest tenth.

37

24

**Answer:**

Θ = 49.6°

**Step-by-step explanation:**

cos Θ = adj/hyp

cos Θ = 24/37

cos Θ = 0.64864

Θ = cos^-1 0.64864

Θ = 49.6°

Suppose you have the following three student loans: $12,000 with an APR of 7.5% for 17 years, $18,000 with an APR

of 8% for 22 years, and $13,500 with an APR of 9% for 12 years.

a. Calculate the monthly payment for each loan individually.

b. Calculate the total you'll pay in payments during the life of all three loans.

c. A bank offers to consolidate your three loans into a single loan with an APR of 8% and a loan term of 22 years.

What will your monthly payments be in that case? What will your total payments be over the 22 years?

a) The **monthly payment** for each loan individually is as follows:

Loan A Loan B Loan C Total

Monthly payments $133.82 $188.18 $195.00 $517.00

b) The **total payments** during the life of all three loans is $105,060, classified as follows:

Loan A Loan B Loan C Total

Total amount $27,300 $49,680 $28,080 $105,060

c) The **monthly payments** after consolidating the three loans are $350.69.

d) The **total payments** over the 22 years period will be $92,581.47.

Note that student loans attract **simple interest** and not **compound interest.**

After the bank consolidates it, the **interest system** changes to **compounding**.

The total **interest** is computed by applying the **annual percentage rate** (APR) to the **principal** and the loan **term**. The result is added to the principal to obtain the total payment for each loan.

The **total payment** is divided by the loan **period** to get the monthly payments.

But for the consolidated loan by the bank, we can use an **online finance calculator** to determine the monthly payments and total payment over the loan term as follows.

Loan A Loan B Loan C Total

Student loan $12,000 $18,000 $13,500 $43,500

APR 7.5% 8% 9%

Loan term 17 years 22 years 12 years

Period in months 204 264 144

Total interests $15,300 $31,680 $14,580 $61,560

Total amount $27,300 $49,680 $28,080 $105,060

Monthly payments $133.82 $188.18 $195.00 $517.00

Consolidated Loans:Total amount of loans = $43,500 ($12,000 + $18,000 + $13,500)

Bank APR = 8%

Loan term = 22 years

N (# of periods) = 264 months (22 years x 12)

I/Y (Interest per year) = 8%

PV (Present Value) = $43,500

FV (Future Value) = $0

Results:

PMT = $350.69

Sum of all periodic payments = $92,581.47

Total Interest = $49,081.47

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The graph below represents a system of equations.

-9 8 7 6

3

-10

Which of the following statements is true?

A. The system has infinite solutions

B. The solutions to the system are (0,1) and (0,-3)

C. The solution to the system is (-4,3)

D. The system has no solution

**Answer:**

C. The solution to the system is (-4,3) where the 2 lines MEET

**Step-by-step explanation:**

D. The system has no solution only if the lines are PARALLEL

A. The system has infinite solutions only if both equations give ONE and the same line

minute math

Noah has 5 m of rope how many pieces of rope of length 1/2 meter can he cut from it

**Answer: 10 pieces**

**Step-by-step explanation:**

**Answer:**

10 ropes

**Step-by-step explanation:**

5 divided by 1/2 is 10

How much would you need to deposit in an account now in order to have $5,000.00 in the account in 27

months?

Assume the account earns 2.01% simple interest.

You would need to deposit ______ in your account now?

The **amount **needed to be deposited in an account in order to have $5000 in 27 month is **$4997.74.**

**Simple interest **is based on the **principal **amount of a loan or the first deposit in a savings account.

To calculate the **amount** that needed to be deposited, we use the formula below.

Formula:

P = 100A/(RT+100)................. Equation 1Where:

P =From the question,

Given:

A = $5000R = 2.01% = 0.0201T = 27 months = 2.25 yearsSubstitute these values into equation 1

P = (100×5000)/(0.0201×2.25+100)P = 500000/100.045225P = $4997.74Hence, the amount needed to be deposited is $4997.74.

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HELP PLSS ILL MARK BRAINLIEST!!!

Select the correct images on the graph.

Identify which shapes on the graph are congruent to shape I by performing these sequences of transformations on shape I:

a reflection across the y-axis, followed by a 90° counterclockwise rotation about the origin, and then a translation 3 units down

. a 90° counterclockwise rotation about the origin and then a translation 2 units up and 2 units left

a 180° rotation about the origin and then a translation 1 unit right

Look down below

Mark me Brainly

Mark me Brainly

let x be the set of 2000 correct: your answer is correct. people (the pigeons) and y the set of all 1825 incorrect: your answer is incorrect. possible birthdays (the pigeonholes).

**Yes**, in a group of 2,000 people,** at least 5** must have the same **birthday**.

This is due to the **Pigeonhole Principle**, which states that if there are more pigeons than pigeonholes, then at least one pigeonhole must contain more than one pigeon.

In this case, there are 2,000 people (the pigeons) and 365 possible **birthdays **(the pigeonholes). This means that, since 2,000 is greater than **365**, at least 5 people must share the same birthday.

The Pigeonhole Principle states that if you have more items than boxes, then at **least **one box must contain **more **than **one** item. It can also be used to prove that certain problems have **no solution**.

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Complete Question:

In a group of 2,000 people, must at least 5 have the same birthday? Why? Let X be the set of 2000 people (the pigeons) and Y the set of all possible birthdays (the pigeonholes). Define a function B: X - Y by specifying th B(x) = x's birthday. Now 2,000 > 4.366 = 1,464, and so by the generalized pigeonhole principle, there must be some birthday y such that B-1(y) has --Select- 4 + 1 = 5 elements. Hence at -Select- 5 people must share the same birthday.

Use what you know about multiplying integers to explain why this equation is true:

20 ÷ (−5) = (−4).

Here, in the given **equation** it is true because two different sign, and the result is negative.

To multiply or divide **signed integers**, always multiply or divide the absolute values and use these rules to determine the sign of the answer.

When multiply two integers with the same signs, the result is always positive. Just multiply the **absolute values **and make the answer positive.

When multiply two integers with the different signs, the result is negative.

Here in this equation,

20 ÷ (-5)

= - 4

So, it is true.

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Find the interest rate for a principal of $5305 and charged $39534 in interest for 20 years

**Answer:**

37.237%

**Step-by-step explanation:**

Use the Formula I = P x R x T

P = Principal amount (the beginning balance).

R = Interest rate (usually per year, expressed as a decimal).

T = Number of time periods (generally one-year time periods).

Plug in the values

I = 5305 x R x 20

Solve for R by dividing 20 by 5305

I=5305 x R x 20

20 / 5305 = 0.0037

**Answer: 10.56 or 10.6 %**

**Step-by-step explanation: **

5305 x x^20 = 39534

39534/5305 = x^20

20√39534/5305 = x

x = 1.1056

1.1056 x 100 = 110.56

110.56 - 100 = 10.56 or 10.6

Algebraically find the x-coordinates where the line y=2x+3 intersects the circle (x-3)^2 + (y+6)= 50

The **x-coordinates** where the **line** y = 2x + 3 intersects the circle is equal to -2 and -4.

Mathematically, the standard form of the **equation** of a **circle** is represented by this mathematical expression;

(x - h)² + (y - k)² = r²

Where:

h and k represents the coordinates at the center of aFrom the information provided, we have the following system of **equations**:

(x - 3)² + (y + 6)² = 50 ......equation 1.

y = 2x + 3 .............equation 2.

In order to determine the x-coordinates at the point of intersection, we would substitute the **equation** 2 into equation 1:

(x - 3)² + (2x + 3 + 6)² = 50

(x - 3)² + (2x + 9)² = 50

x² - 6x + 9 + 4x² + 36x + 81 - 50 = 0

5x² + 30x + 40 = 0

x² + 6x + 8 = 0

x² + 6x + 9 = 1

(x + 3)² = 1

Taking the square of both sides of the **equation**, we have;

x + 3 = ±1

x = ±1 - 3

x = -2 and -4

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Find the exact area (in units2) of the region bounded by the given equations if possible. If you are unable to determine the intersection points analytically, use a calculator to approximate the intersection points with three decimal places and determine the approximate area (in units2) of the region, then round your answer to three decimal places.x^2 = y^3 and x = 2y

The region bounded by the equations has a **precise area** of 21.33 units.

A boundary or some set of constraints are imposed on a bounded region. To put it another way, the size of a bounded shape cannot be infinite. Anything that is bound must be able to be contained within certain **parameters**.

x2 = 4y2 from equation (1), y3 = 4y2 y3 - 4y2 = 0 y2(y - 4) = 0 y2 = 0 or y-4 = 0 or y = 4 These will be our **integration bounds**. We have given that x2 = y3 --------- (1) and x = 2y --------- (2).

Therefore, we will **express area** as A = [- 4]04 = [- 4 - 0] = 64 - 85.33 A = -21.33, or A = 21.33. This indicates that the area of the bounded region is 21.33 units.

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K

Determine whether the following statement is true or false, and explain why.

If a function is concave upward on an interval, it must be increasing on the interval.

Is the statement true or false?

A. The statement is true. Functions that are concave upward are always increasing.

B. The statement is false. Functions that are concave upward are always decreasing.

C. The statement is false. Functions that are concave upward are constant and do not increase or decrease.

D. The statement is false. Functions that are concave upward can be either increasing or decreasing.

11

The statement is **true**. Functions that are **concave** **upward** are always **increasing**.

**What is Concave Upward Function?**

Where the **derivative** f′ is **growing**, a function f is **concave** **up** (or upwards). This is **equivalent** to the derivative of f′, which is represented by the **notation** f′′f, start **superscript**, **prime**, end **superscript**, **positive**.

Explanation:

If a function is **concave** **upward** on an **interval**, it must be **increasing** on the **interval**. Given statement is **true**. Functions that are **concave** **upward** are **always** **increasing**.

A **function** is said to be **concave** **upward** on an interval if f″(x) > 0 at each point in the interval and **concave** **downward** on an interval if f″(x) < 0 at each point in the **interval**.

At interval if function is **increasing** then f**unctions** that are **concave** **upward** are always **increasing**.

Hence, The statement is **true**. Functions that are **concave** **upward** are always **increasing**.

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what is the rate of change (slope) of the distance in feet below sea level with respect to time that the submarine traveled? place your answer in the box:

The **rate of change** (slope) of the **distance **in **feet below sea level** with **respect **to **time** that the **submarine traveled** is 11 feet .

Slope and rate of change are the same thing. The difference is just **semantics **of the situation.

Typically we use the word “slope” when we are referring to a graph, and we use the phrase** “rate of change”** when we are referring to a table or a situation in real life.

But that’s not** absolute.** We can count the slope on a graph, but there’s also a **“slope formula”** for use when you have two coordinate points or two data points — even though you are not creating a graph.

It is the derivative of of the slope, or the** second derivative **of the original function.

For example, if you plot position **verses time,** the slope between two points(change in position per change in time) is the velocity. This is the first derivative.

Take any** two points** ( 0 , 380 ) and ( 15 , 545 )

slope m = 545 - 380 / 15 - 0

= 165 / 15

= 33 / 3

= 11 / 1

= 11 feet

Hence the **slope** m is 11 feet .

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Graph TU with endpoints T(1,2) and U(4,6) and its image after the composition

TU with endpoints T(1,2) and U(4,6) and its images after the **composition **are T' = (-1, -1) and U' = (2,3) and T'' = (-3, 7) and U'' = (0,11).

Tradition holds that the reflection of point P across the line, denoted by the word P', is the "**image**" of point P. (pronounced "P prime").

Given, line TU with **endpoints **T(1,2) and U(4,6).

To find the **translation**:

In 1:

Translate TU 2 units **left **and 3 units down.

That means,

T' = (-1, -1) and U' = (2,3)

In 2:

**Translate **TU 4 units left and 5 units up.

That means,

T'' = (-3, 7) and U'' = (0,11)

Therefore, the **image **points are T' = (-1, -1) and U' = (2,3) and T'' = (-3, 7) and U'' = (0,11)

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Find the value of x

**Answer:**

x is equal to 87

**Step-by-step explanation:**

42 +51=93

93-180=x

x=87

x is equal to 87

42+51+x=180

42+51=93

180-93=87

42+51+x=180

42+51=93

180-93=87

y = 4x - 9

y=x - 3

HELP WILL GIVE BRAINLIEST

The **solution** to the **system of equations**, y = 4x - 9 and y = x - 3, is: (2, -1)

The coordinates of the ordered pair that will make both **equations** true is the solution to the **system**.

Given the **linear equations** as:

y = 4x - 9 --> equation 1

y = x - 3 --> equation 2

Make both **linear equations** equal to each other and find the value of x. Thus:

4x - 9 = x - 3

Combine like terms

4x - x = 9 - 3

3x = 6

Divide both sides by 3

3x/3 = 6/3

x = 2

To find the value of y, substitute x = 2 into equation 1:

y = 4(2) - 9

y = 8 - 9

y = -1

The **solution** is, (2, -1).

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Grace is going to invest $140 and leave it in an account for 13 years. Assuming the interest is compounded continuously, what interest rate, to the nearest hundredth of a percent, would be required in order for Grace to end up with $190?

The **interest rate**, to the nearest hundredth of a **percent**, which would be required in order for Grace to end up with $190 is 2.38%.

Mathematically, **compound interest **can be calculated by using this formula:

A(t) = P(1 + r)^{t}

Where:

A represents the future value.P represents theSubstituting the given parameters into the **compound interest **formula, we have;

190 = 140(1 + r)^{13}

190/140 = (1 + r)^{13}

1.3571 = (1 + r)^{13}

Taking the 13th root of both sides of the equation, we have:

[tex]\sqrt[13]{1.3571} = \sqrt[13]{(1 + r )^{13} }[/tex]

1.0238 = 1 + r

r = 1.02378 - 1

Interest rate, r = 0.0238

Interest rate, r = 2.38%

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Given that A,O & B lie on a straight line segment, evaluate the size of the smallest angle.

The diagram is not drawn to scale.

Based on the definition of the **angles of a straight line**, the measure of the smallest **angle** is: are: 40°.

The sum of all the angles on a **straight line** is equal to 180 degrees.

To find the size of the smallest **angle**, find the value of a by creating the equation below:

(2a + 62) + (54 - a) + (5a - 20) = 180

Open the parentheses:

2a + 62 + 54 - a + 5a - 20 = 180

Combine like terms

6a + 96 = 180

6a = 180 - 96

6a = 84

6a/6 = 84/6

a = 14

Find the measure of each **angles**:

2a + 62 = 2(14) + 62 = 90°

54 - a = 54 - 14 = 40°

5a - 20 = 5(14) - 20 = 50°

The size of the smallest **angle** is 40°.

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Which of the following is equivalent to

16^3/4

**Answer:**

B. 8

**Step-by-step explanation:**

I’m glad to help you

What is 1 1/2 + 5/7?

A. 2 1/14

B. 2 2/7

C.11/14

D 2 3/14

The **fraction** 1¹/₂ + ⁵/₇ = 2³/₁₄

**Fractions **are numbers written in the form a/b where a and b are integers and b ≠ 0.

Since we have the** fractions ** 1¹/₂ and ⁵/₇ and we want to compute the sum

1¹/₂ + ⁵/₇, we re-write the first fraction as an **improper fraction.**

So, 1¹/₂ = ³/₂

Now, re-writting the equation, we have

³/₂ + ⁵/₇

To find the sum, wetake the L.C.M of both numbers which 2 × 7 = 14.

So, we make both denominators equal to the L.C.M.

So,

³/₂ × ⁷/₇ + ⁵/₇ × ²/₂ = ²¹/₁₄ + ¹⁰/₁₄

= (21 + 10)/14

= 31/14

= (28 + 3)/14

= 28/14 + 3/14

= 2 + 3/14

= 2³/₁₄

So, 1¹/₂ + ⁵/₇ = 2³/₁₄

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Solve g(x) = 10, if g(x) = 2/x+1

**Answer:**

x = -0.8.

**Step-by-step explanation:**

To solve for x in the equation g(x) = 10, we need to find the value of x that makes g(x) equal to 10. Since we are given that g(x) = 2/x+1, we can substitute this expression for g(x) in the equation g(x) = 10 to get:

2/x+1 = 10

Next, we can multiply both sides of the equation by x+1 to get rid of the fraction on the left side:

2 = 10 * (x+1)

This simplifies to 2 = 10x + 10, which we can rearrange to get 2 - 10 = 10x. Subtracting 10 from both sides gives us -8 = 10x. Finally, dividing both sides by 10 gives us the solution: x = -0.8.

Therefore, the value of x that makes g(x) equal to 10 is x = -0.8.

I’m how many ways can 25 be expressed as the sum of three prime numbers

**Answer:**

Below

**Step-by-step explanation:**

Primes under 25 2 3 5 7 11 13 17 19 23

5 7 13

7 7 11 ( can we use numbers twice?)

you can look for more....but that may be it ....

Last year, Reagan grew 9/10 of an inch and her brother grew 2/5 of an inch. How much more did Reagan grow than her brother?

Reagan will grow 1/2 inch than her brother if Reagan grew 9/10 of an inch and her brother grew 2/5 of an inch by using ratio and** proportion **concept,

When b does not equal 0, an **ordered pair **of numbers a and b, represented as a / b, is said to be a ratio. Two ratios are set to be equal in an equation called a proportion. For instance, if there is 1 boy and 3 girls, the ratio would be written as 1: 3 (there are 3 girls for every boy), meaning that there are 1 in 4 boys and 3 in 4 girls.

A: b a/b is the ratio formula, which may be used to calculate any two values. A:b::c:da:b::c:da, on the other hand, is how the **percentage **formula is written.

Given,

The height grown by Reagan=9/10 inch

The height grown by Reagan brother=2/5 inch

(9/10)-(2/5)

=1/2 inch

Therefore, Reagan will grow 1/2 inch than her brother.

Therefore,

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From her eye, which stands 1.75 meters above the ground, Myesha measures the angle of elevation to the top of a prominent skyscraper to be 19^{\circ}

∘

. If she is standing at a horizontal distance of 337 meters from the base of the skyscraper, what is the height of the skyscraper? Round your answer to the nearest hundredth of a meter if necessary

**Answer:**

117.79 m

**Step-by-step explanation:**

You have an observer **337 m from a skyscraper** who measures the angle of **elevation** from a point **1.75 m above the ground** to be **19°**. You want to know the **height of the skyscraper**.

The tangent relation tells you ...

Tan = Opposite/Adjacent

Solving for the side opposite the angle, we get ...

Opposite = Adjacent · Tan

ApplicationIn this scenario, the height of the building above the eye height is ...

height above eyes = (337 m)(tan 19°) = 116.038 m

Then the height of the building is ...

skyscraper height = eye height + height above eyes

skyscraper height = 1.75 m + 116.038 m = 117.788 m

**The height of the skyscraper is about 117.79 meters**.

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