If 2 ½ teaspoons of vanilla are needed for a recipe for 18 people, how many
teaspoons of vanilla are needed for 27 people?

a) In midday there is no change in the height of the water.

b) At 19.00 hours the height of water will decrease 1.5

Given,

The height of the water = h

Equation, h = 3sin(30t)°

t is the time in hours

a) We have to find the height of water in midday;

Midday = 12 noon

Now,

h = 3sin(30t)²

t = 12

Then,

h = 3sin(30 x 12)°

h = 3sin360°

h = 0

That is,

In midday there is no change in the height of the water.

b) We have to find the height of the water at 19.00

Now,

h = 3sin(30t)²

t = 19

Then,

h = 3sin(30 x 19)°

h = 3sin570°

h = -1.5°

That is,

At 19.00 hours the height of water will decrease 1.5

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T is the midpoint of RS and V lies between Rand T is RV+VT =TS

The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the endpoints, and it is equally distant from both of them. It cuts the section in half.

Divide the measurement of the distance between the two end locations by 2. The middle of that line is located at this separation from either end. Alternately, combine the two endpoint x coordinates and divide by 2. similarly for the y coordinates.

The midpoint rule substitutes the midpoints, mi, of each subinterval for xi in a Remain sum with subintervals of equal width to estimate definite integrals.

T is the midpoint of RS so RT =TS

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T is the midpoint of RS and V lies between Rand T is RV+VT =TS

RT = TS because T is the midpoint of RS.

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We can use the distance formula to determine the side lengths of DEF.

D (3, -1)

E (7, -4)

F (4, -4)

DE --> √((7 - 3)^2 + (-4 - (-1))^2) = √(4^2 + (-3)^2) = √(16 + 9) = √25 = 5

DF --> √((4 - 3)^2 + (-4 - (-1))^2) = √(1^2 + (-3)^2) = √(1 + 9) = √10 ≈ 3.2

EF --> √((7 - 4)^2 + (-4 - (-4)^2) = √(3^2 + 0^2) = √9 = 3

Notice DEF is congruent to ABC because due to SSS (side-side-side) congruency; DE = AB, DF = AC, EF = BC. Because DEF and ABC are congruent, DEF and ABC must have congruent angles.

angleBAC = angleEDF = 34.7 degrees

angleACB = angleDFE = 108.4 degrees

angleCBA = angleFED = 36.9 degrees

Answer:

x=4

Step-by-step explanation:

x=4 would go through 4,3 and 4,8 as 4 is a vertical line

Yes! they can afford an $85,000 house with a $65,000 mortgage requiring payments of $720 per month.

What is in a mortgage?

Principal, interest, taxes, and insurance make up the majority of mortgage payments. Your outstanding loan balance is reduced by the amount of the principal part. Borrowing money has a cost, which is interest.

Given data:

Annual Salary =$42,000

Cost =$85,000

Mortgage = $65000

Monthly Payment = $720

First Criterian : - Never Spend more than 2.5 times of your Annual Income.

2.5 * 42,000

= 105,000

it can be afforded.

Second Criterian : - Monthly Payment should not exceed Weekly Income

Monthly Payment = 720

Weekly earnings = 42000 / 52 weeks = 807

it can afforded.

Third Criterian : - monthly payment should not exceed 28% of monthly earnings.

Monthly payment = 720

Monthly earnings = 42,000 / 12 = 3500

28% * 3500

= 980

it can be afforded.

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Answer:

You do it as solving by substitution.So first make x the subject of the formula in eqn1

substitute eqn1 into eqn two and solve After getting y substitute in the equation* and get x

The value of x and y in the system of equations are 8 and -5 respectively.

Given,

2x + 5y = -9

3x + 4y = 4

Now,

To solve the system of equation,

Let us make the coefficient of x same in both the equations to eliminate x.

2x +5y = -9

3x + 4y = 4

Multiply equation 1 with 3 and equation 2 with 2.

6x + 15y = -27

6x + 8y = 8

Now subtract both the equations,

7y = -35

y = -5

Now substitute y in equation,

2x + 5(-5) = -9

2x - 25 = -9

x = 8

Thus the system of equation solutions are x = 8 and y = -5.

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Answer:

x - y = 3

Step-by-step explanation:

Answer:

2x - 5y = 20

Step-by-step explanation:

Standard form should look like:

Ax + By = C

and the numbers A,B, and C have to be whole numbers (actually integers, because negative is okay too except A has to be positive)

You have been given a point and the slope. There is a shortcut, fill-in-the-blank equation called point-slope that you can just fill in a point and the slope. Then we can change that equation into standard form.

Point-slope equation:

y - Y = m(x - X)

Fill in (5, -2), which is the (X, Y). 5 in place of X and -2 in place of Y. Fill in 2/5 for the m which is slope.

y - Y = m(x - X)

y - -2 = 2/5(x - 5)

simplify, and distribute.

y + 2 = 2/5x - 2

Multiply through by 5 to get rid of the fraction.

5y + 10 = 2x - 10

Subtract 10.

5y = 2x -20

Subtract 2x.

5y - 2x = -20

Rearrange the terms.

-2x + 5y = -20

Multiply through by -1 (because that A has to be positive)

2x - 5y = 20

The equation in standard form is:

2x - 5y = 20

Answer:

'e'

Step-by-step explanation:

number of letter in his name: 7

number of times his name is written at the 1000th letter

= 1000/7 = 142 R 6

since there is a remainder of 6 letters after the previous complete set of his name, therefore the 1000th letter is the 6th letter of his name, and that is e

Answer:

x log (7) -2

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

1) Substitute d into the question

We can see that the question says that is d is 2 what would 6d be.

Another way of writing 6d would be 6 x d

If we put d into the equation we would be left with 6 x 2

2) Solve

6 x 2 = 12

Hope this helps, have a great day!!

Answer:

12

Step-by-step explanation:

6d=6(2)

6*2=12

HOPE IT HELPS

Answer:

Step-by-step explanation:Le quedo +10$

Ya que

-65 y le regalaron +10

Answer:

Linear

Step-by-step explanation:

because it is in the form y=mx+c if rearranged

The roots of the Quadratic Equation are

(2 + i√26)/3 and (2 - i√26)/3

Given, a quadratic equation i.e. 3x² + 10 = 4x

On simplifying, we get

3x² - 4x + 10 = 0

while checking the discriminant of the given quadratic equation, we get

D = b² - 4ac

D = (-4)² - 4(3)(10)

D = 16 -120

D = -104

i.e. D < 0.

So, the quadratic equation has imaginary roots

On applying quadratic formula, we get

x = (4 ± √(-104))/6

x = (4 ± i2√26)/6

x = (2 ± i√26)/3

Hence, the roots of the Quadratic Equation are

(2 + i√26)/3 and (2 - i√26)/3

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Answer:

yes, because 130 + 50 = 180 .

Step-by-step explanation:

If the degrees on the inside adds up to 180 then the lines are parallel.

After solving thie expression using BODMAS rule we get the result equal to  [tex]\frac{67}{24}[/tex].

To solve arithmetic expressions of several operators, the BODMAS rule is a mathematics is a technique. We will solve an equation with several operators with the use of BODMAS. It provides the decoding of the mathematical phrase in the proper sequence.

B= Bracket

O= Of

D= Divide

M= Multiply

A= Addition

S= Subtraction

To solve this numerical expression,

[tex]\frac{2}{3}[/tex] ÷ 2⁴ + ([tex]\frac{3}{4}[/tex] + [tex]\frac{1}{6}[/tex]) ÷ [tex]\frac{1}{3}[/tex]

Use BODMAS method

[tex]\frac{2}{3}[/tex] ÷ 16 + ([tex]\frac{9+2}{12}[/tex]) ÷ [tex]\frac{1}{3}[/tex]

[tex]\frac{2}{3}[/tex] ÷ 16 + ([tex]\frac{11}{12}[/tex]) ÷ [tex]\frac{1}{3}[/tex]

[tex]\frac{2}{3}[/tex]  × [tex]\frac{1}{16}[/tex] + ([tex]\frac{11}{12}[/tex]) × 3

[tex]\frac{1}{24}[/tex] + [tex]\frac{33}{12}[/tex]

[tex]\frac{67}{24}[/tex]

The expression has a value equal to [tex]\frac{67}{24}[/tex].

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The value of the given expression in the question, -[4.1-3(2.2)] / (0.2)² + 2       is 64.5.

What do you mean by expression?

An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)

You can think of expressions as being similar to phrases. A phrase in language may contain an action on its own, but it does not constitute a complete sentence.

-[4.1-3(2.2)] / (0.2)² + 2

Using the BODMAS rule to simplify the given expression.

Given expression can be written as:

= -[4.1-6.6] / 0.04 + 2

= -[-2.5]/0.04+2

=2.5/0.04+2

=62.5+2

=64.5

Therefore, 64.5 is answer for expression  -[4.1-3(2.2)]/(0.2)^2+2.

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(7, 14)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

   Brackets

   Parenthesis

   Exponents

   Multiplication

   Division

   Addition

   Subtraction

   Left to Right

Equality Properties

Algebra I

   Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define Systems

4x + y = 42

y = x + 7

Step 2: Solve for x

Substitution

   Substitute in y:                    4x + (x + 7) = 42

   Combine like terms:           5x + 7 = 42

   Isolate x term:                     5x = 35

   Isolate x:                              x = 7

Step 3: Solve for y

   Define equation:                    y = x + 7

   Substitute in x:                       y = 7 + 7

   Add:                                        y = 14

Measure of angle YLA in the given figure is 32°.

Given,

∠LYA = 21°

∠GLA = 32°

A is the incentre of the ΔPQR.

Therefore,

∠YLA = ∠GLA

∠LYA = ∠GYA

=> ∠YLA = 32

Hence, Measure of angle YLA in the given figure is 32°.

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The amplitude, midline and period of the function are 3 units, 4units and 5 units respectively

The amplitude is half the full height of the periodic function. That is:

Amplitude = (maximum - minimum)/2

Check the image attached, the maximum and minimum are labeled max and min respectively

Amplitude = (-1 - (-7))/2  = 6/2 = 3 units

The midline is the middle of the periodic graph or halfway between the minimum and maximum of the graph

Midline = (maximum + minimum)/2

Midline = (-1 + (-7))/2 = -8/2 = -4 units

The period is the distance between two peaks or (maximums) on the graph.

Period = 1-(-4) = 5 units

Therefore, the amplitude, midline and period are 3 units, 4units and 5 units respectively

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Answer:

lmfa you answer my questions i recently posted ill answer yours.

Step-by-step explanation:

please tho

The correct solution is x=(+11 , +3)

Step-by-step solution:

2(x-7)²=32

⇒2(x-7)(x-7)=32

⇒(x-7)(x-7)=(32/2)

⇒(x-7)(x-7)=16

⇒(x-7)²=16

⇒[tex](x-7)=\sqrt{16}[/tex]

⇒(x-7) = ±4

⇒(x-7) = +4   or   ⇒(x-7) = -4

⇒x = +4+7   or   ⇒x = -4+7

⇒x = +11  or   ⇒x = +3

Therefore, the correct solution is x = (+11 , +3)

Answer:

1. 2,772

2.1,071

3.4,641

4. 36,610

5. 4,096

6. 36,270

7. 2,403

8. 3,320

Answer: x = 85° ,   y =45°

Step-by-step explanation:

x + 95 = 180°

x = 180° - 95°

x = 85°

In a triangle,

50° + x + y = 180°

50° + 85° + y = 180°

135° + y = 180°

y = 45°

From the above given expression

x = 35°

y = 95°

In a straight line, the angle is 180°

given angles are  50° internal angle and 95° external angle

then   x + 50° + 95° = 180°

          x + 145° =  180°

          x = 180° - 145°

          x = 35°

so in a triangle total angle is 180°

then  50° + x + y = 180°

         50° + 35° + y 180°

         y = 180° - 85°

         y = 95°

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Answer:

- 7

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

Answer:

Step-by-step explanation:

5

The equation of line passes through the point (-4, -2) will be;

⇒ 3x - 4y = - 4

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point on the line are (-4, -2).

And, The parallel line is,

⇒ 3x - 4y = 7

⇒ y = 3/4x - 7/4

Now,

Since, The equation of line passes through the point (- 4, -2).

So, We need to find the slope of the line.

Since, The slope of the parallel line is same.

Hence, Slope of the line is,

⇒ y = 3/4x - 7/4

m = dy/dx = 3/4

m = 3/4

Thus, The equation of line with slope 3/4 is,

⇒ y - (-2) = 3/4 (x - (-4))

⇒ y + 2 = 3/4 (x + 4)

⇒ y + 2 = 3/4x + 3

⇒ y = 3/4x + 3 - 2

⇒ y = 3/4x + 1

⇒ 4y = 3x + 4

⇒ 3x - 4y = - 4

Therefore, The equation of line passes through the point (-4, -2) will be;

⇒ 3x - 4y = - 4

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The largest place value of the numeric part of this quantity is 10 million.

Our entire number system is built around place value. This is the system in which the value of a number is determined by the position of its digits. The numbers 42,316 and 61,432 differ because the digits are in different positions.

Every digit in a number has a place value in mathematics. Place value is the value represented by a digit in a number based on its position in the number. For example, 7 hundreds or 700 is the place value of 7 in 3,743. The place value of 7 in 7,432 is, however, 7 thousands or 7,000.

In the number, 12,345,000, the highest place value is 1 and it denotes 10 million.

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Answer:

Parallel: Lines a and b

Perpendicular: none

Step-by-step explanation:

Both lines a and b have a slope of 1/3.

This means they are parallel, so they'll never intersect.

Perpendicular lines form a right angle, and none seem to do see here.

The sum z1 + z2 gives the point with coordinates (1, - 4), so option A is the correct one.

We know that these two points have the coordinates:

z1 = (3, 1)

z2 = (-2, - 5)

And we want to find the addition of the two points.

To add them, we just need to add the correspondent coordinates:

(3, 1) + (-2, -5) = (3 - 2, 1 - 5) = (1, - 4)

That point is the sum of z1 and z2, and we know that it is the point A, so point A is the correct option.

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The solution to each of the equations are matched together as:

1. 4 = 6/a*x + 5 → x = -a/6

2. 7 + 2ax = 13 → x = 3/a

3. -ax - 20 = -14 → x = -6/a

To solve an equation, apply the properties of equality in order to isolate the variable solved for to one side of the equation, which gives us the solution to the problem.

1. 4 = 6/a*x + 5

4 = 6x/a + 5

Combine like terms

-6x/a = -4 + 5

-6x/a = 1

-6x/a(a) = 1(a) [multiplication property of equality]

-6x = a

-6x/-6 = a/-6 [division property of equality]

x = -a/6

2. 7 + 2ax = 13

2ax = 13 - 7

2ax = 6

Divide both sides of the equation by 2a

x = 6/2a

x = 3/a

3. -ax - 20 = -14

-ax = -14 + 20

-ax = 6

x = 6/-a

x = -6/a

Therefore, the solutions are:

1. x = -a/6

2. x = 3/a

3. x = -6/a

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Answer:

C

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

To obtain either equation we require to know both the slope and one ordered pair that lies on the line.

As per the rule of round off, the nearest ten thousand to the numbers are

a.12,456 = 10,000

b.60,792 = 60,000

c.93,245​ = 90,000

Round off

Round off defines a change a number into an approximation having fewer significant digits.

Given,

Here we need to round off the following numbers to the nearest ten thousand.

a.12,456

b.60,792

c.93,245​

a. 12,456

If you rounded to the nearest ten thousands place. The 1 in the ten thousands place rounds down to 1, or stays the same, because the digit to the right in the thousands place is 2.

If the digit to the right is less than 5 we round toward 0.

Therefore, 12,456 was rounded down toward zero to 10,000

b. 60,792

If you rounded to the nearest ten thousands place. The 6 in the ten thousands place rounds down to 6, or stays the same, because the digit to the right in the thousands place is 0.

So, if the digit to the right is less than 5 we round toward 0.

Then 60,792 was rounded down toward zero to 60,000

c. 93, 245

Similar to the previous one, if rounded to the nearest ten thousands place. The 9 in the ten thousands place rounds down to 9, or stays the same, because the digit to the right in the thousands place is 3.

When the digit to the right is less than 5 we round toward 0.

93245 was rounded down toward zero to 90,000

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