Sierra has a recipe she wants to make. She has to use eggs and sticks of butter. The ratio for these ingredients is 12 to 4 to make 4 batches. What will the equivalent ratio be if she wants to make 8 batches?

The exact height of the triangle is 20.8ft

The area of the right tringle in radical form is 72√3 ft²

The area of the triangle in decimal form is 124.7 ft²

The side XY or height of the triangle can be found as follows:

Using trigonometric ratios,

tan 60° = XY / 12

XY = 12 tan 60°

XY = 12 × 1.73205080757

XY = 20.7846096908

height = 20.8ft

The area of XYZ = 1 / 2 bh

where

Therefore,

The area of XYZ = 1 / 2 × 12 × 20.8 = 124.707658145  = 124.7 ft²

The area in radical form = 1 / 2 × 12 × 12 tan 60°

The area in radical form =  1 / 2 × 12 × 12 × √3 = 144√3 / 2 = 72√3 ft²

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Answer:

6 Ways

Step-by-step explanation:

Given: 3 students, Madeline, Austin, and Aubree

To Find: How many different ways can they stand in line?

Solution: 3 students, can line up in 3 so 6 ways.

Answer:

Add the exponents and keep the same base. Then find the reciprocal and change the sign of the exponent.

Step-by-step explanation:

your welcome

Answer:

Es el acronimo de la (Contraloría General de la República

Step-by-step explanation:

Espero ayudarte suerte

Significado de SGR. El significado de la sigla SGR es el acrónimo de Sociedades de Garantía Recíproca. El significado de la sigla SGR es el acrónimo de sociedad de garantía recíproca y pertenece a la categoría Europa. El significado de la sigla SGR es el acrónimo de Sociedad de Garantías Recíprocas.

The expression is equivalent to the expression (12 + 3) ÷ 5 is (3 + 12) ÷ 5

From the question, we have the following parameters that can be used in our computation:

(12 + 3) ÷ 5

The above expression is a quotient expression

However, we can apply some algebraic properties

Take for instance;

12 + 3 can be expressed as 3 + 12

So, we have

(12 + 3) ÷ 5 = (3 + 12) ÷ 5

Hence, the expression is equivalent to the expression is (3 + 12) ÷ 5

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The ropes should be staked 12 ft away from 16 ft pole and 18 ft away from 24 ft pole.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. If two or more figures have the same shape, but their sizes are different, then such objects are called similar figures.

Given that, two vertical poles, one 16 ft high and the other 24 ft high, stand 30 feet apart on a flat field. A worker wants to support both poles by running rope from the ground to the top of each post, we need to find where should the stake be laced to use the least amount of rope,

Let rope of the 16 ft high pole be at x ft and that of 24 ft high pole at (30-x)

The structure of rope and poles are making a set of similar triangles, (refer to figure attached)

We know that, the corresponding sides of the similar triangle are in same ratio,

Therefore,

16 / x = 24 / (30-x)

2 / x = 3 / (30-x)

60 - 2x = 3x

5x = 60

x = 12

30-12 = 18

Hence, the ropes should be staked 12 ft away from 16 ft pole and 18 ft away from 24 ft pole.

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Question 4

The sketch of the isosceles right triangle is given below

For an isosceles right triangle, the two legs are equal

So we will get the value x as follow

The perimeter of the triangle can be obtained as follow

The perimeter is simply the sum of all the sides of the triangle

To get the area of the triangle

we will use the formula

The area of the triangle is 16 square units

Answer:

\(x = y = 3\sqrt{ 2\)

Step-by-step explanation:

Given

The attached triangle

Required

Find x and y

The given triangle has 45 degrees as one of its angles, and it is also a right angle triangle.

For this kind of parameter, the opposite = the adjacent

i.e. x = y

Apply Pythagoras theorem

\(x^2 + y^2= 6^2\)

Substitute x for y

\(y^2 + y^2= 6^2\)

\(2y^2= 36\)

Divide by 2

\(y^2 = 18\)

Take square root

\(y = \sqrt{18\)

\(y = \sqrt{9 * 2\)

Split

\(y = \sqrt{9} *\sqrt{ 2\)

\(y = 3*\sqrt{ 2\)

\(y = 3\sqrt{ 2\)

\(x = y = 3\sqrt{ 2\)

Answer:

y=-2(3)^x.

Step-by-step explanation:

Based on the information given, the price of the zero coupon bond is $692.04.

To calculate the price of a zero coupon bond, we need to use the following formula:

\(\sf P =\dfrac{F}{1+r\div n}^{(nt)\)

Where:

Also, the annual interest rate is 7.50%, which is the market interest rate, and the compounding is semiannual, which means n = 2. Finally, the time to maturity is 5 years.

Plugging in the values into the formula, we get:

\(\sf P = \dfrac{1000}{(1+0.075\div2)^{(2\times5)}}\)

\(\sf P = \dfrac{1000}{(1.0375)^{10}}\)

\(\sf P = \dfrac{1000}{1.4450}\)

\(\sf P = \$692.04 \ \ (rounded \ to \ the \ nearest \ cent)\)

Therefore, the price of the zero coupon bond is $692.04.

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Answer:

a) 0.15 / 0.09

b) 0.15 / 1

c) 0.15 / 0.23

Answer:

h = 231 feet

Step-by-step explanation:

Given that,

A person standing 248 feet from the base of a church, x = 248 feet

The angle of elevation to the church's steeple to be 43°.

We need to find the tall of the church. Let the length of the church is h. Using trigonometry to find it.

\(\tan\theta=\dfrac{P}{B}\\\\\tan\theta=\dfrac{h}{x}\\\\h=x\tan\theta\\\\h=248\times \tan(43)\\\\=231.26\ \text{feet}\)

or

h = 231 feet

So, the height of the church is 231 feet.

Answer:

Each population must be at least 10 times as large as its corresponding sample.

Step-by-step explanation:

The 10 percent rule checks that the sample is small relative to the population (that is, that the population is at least 10 times as large as the sample size) so that independence of observations within a sample is reasonable to assume.

The check that must be made is (b)  Both population must be approximately normal

From the question, we have the following highlights

When the above highlights are true, then the population where the samples are to be selected must be approximately normal

Hence, the check that must be made is (b)  Both population must be approximately normal

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Answer:

The answer is

Step-by-step explanation:

In order to solve this question we use ratio and proportion

From the question

Day Drive 270 miles in 6 hours

So in order to find the distance drove in 13 hours, we compare the distance drove in 6 hours to the distance drove in 13 hours and solve

That's

if in 6 hours Day drove 270 miles

Then in 13 hours the person will drive

\( \frac{13 \times 270}{6} = \frac{3510}{6} \)

We have the final answer as

Hope this helps you

Take a look at the attachments...

Hope this helps! :)

Answer:

The answer is y = -1/3

Step-by-step explanation:

Hope this helps

Answer:

x = - 1

Step-by-step explanation:

- 9(1 + 6x) = 42 - 3x ← distribute parenthesis on left side by - 9

- 9 - 54x = 42 - 3x ( add 3x to both sides )

- 9 - 51x = 42 ( add 9 to both sides )

- 51x = 51 ( divide both sides by - 51 )

x = - 1

Answer:-1=x

Step-by-step explanation:

-9(1+6x)=42-3x

-9-54x=42-3x

+54x          +54x

-9=42+51x

-42     -42

-51/51=51x/51

-1=x

Answer:

14

Step-by-step explanation:

(segment piece) x (segment piece) =   (segment piece) x (segment piece)

12*x = 8 * (x+2)

Distribute

12x = 8x+16

Subtract 8x

12x-8x = 8x+16-8x

4x = 16

Divide by 4

4x/4 = 16/4

x = 4

We want NT

NT = 8+x+2

     = 10 +x

    = 10 +4

    = 14

The value of x will be 2. So, Option B is correct for the equation \(3^{2x} = 9^{3x - 4}\)

In the given question, the equation is \(3^{2x} = 9^{3x + 4}\), we have to find out the value of x. First, we need to re-arrange the equation in order to apply the property of exponents. So,

           => \(3^{2x} = 9^{3x -4}\)  => \(3^{2x} = 3^{2(3x - 4)}\)

We know according to the property of exponents if \(x^{m} = x^{n}\), then m = n.

Similarly, in this equation the base of both RHS and LHS are the same, We get

           => 2x = 2(3x - 4)

           => 2x = 6x - 8   =>  4x = 8

           =>  x = 2

We get value of x = 2.

Hence the value of x for this equation will be 2 and option B is correct.

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The absolute value function that matches the graph is given as follows:

y = -|x + 1| + 1.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

In which a is the leading coefficient.

The coordinates of the vertex in this problem are given as follows:

(-1, 1).

Hence:

y = a|x + 1| + 1.

The function is reflected over the x-axis with a slope of -1, hence the leading coefficient a is given as follows:

a = -1.

Thus the function is:

y = -|x + 1| + 1.

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Answer:

The answer is 4y

Step-by-step explanation:

6×2y-6×1-2×2y=6y

Answer: There are two ways to find maximum profit: with a graph, or with calculus.

Graphically, you’re looking for a global maximum.

A global maximum is the maximum over the entire range of the what is a function. On a graph, that’s the highest peak.

Local maximums happen at inflection points (where the graph changes direction).

At the maximum of a function, the gradient or slope of the function is zero. With calculus, you can find the derivative of the function to find points where the gradient (slope) is zero, but these could be either maxima or minima.

If the slope is increasing at the turning point, it is a minimum.

If the slope is decreasing at the turning point, then you have found a maximum of the function.

Step-by-step explanation: i juat told what i know :)

the sum of the circumferences of the two circles is π(1 + √2).

Let the side length of the square be s, and let the radius of each circle be r.

Since the circles are externally tangent to each other, their centers are separated by a distance of 2r. Since the circles are also tangent to the sides of the square, the distance from each circle's center to a corner of the square is equal to r.

Using the Pythagorean theorem, we can find the side length of the square:

s^2 + s^2 = (2r + 2r)^2 = 16r^2

2s^2 = 16r^2

s^2 = 8r^2

The perimeter of the square is 2s + 2s = 4s, which we know to be equal to 2 + √2:

4s = 2 + √2

s = (1 + √2)/2

Substituting this value for s into the equation we derived for s^2 in terms of r^2, we get:

(1 + √2)^2/8 = r^2

Simplifying, we get:

r = (1 + √2)/4

The circumference of each circle is 2πr, so the sum of their circumferences is:

2πr + 2πr = 4πr

Substituting the value we found for r, we get:

4π[(1 + √2)/4] = π(1 + √2)

Therefore, the sum of the circumferences of the two circles is π(1 + √2).

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Answer:

\((-2,6)\)

Step-by-step explanation:

Given

\(Elena = (10,-4)\)

\(Midpoint = (4,1)\)

Required

Determine the coordinates of Naya's

Midpoint is calculated as:

\(M(x,y) = \frac{1}{2}(x_1+x_2,y_1+y_2)\)

In this case:

\((x_1,y_1) = (10,-4)\)

\((x,y) = (4,1)\)

So, we have:

\((4,1) = \frac{1}{2}(10+x_2,-4+y_2)\)

Multiply through by 2

\(2 * (4,1) = \frac{1}{2}(10+x_2,-4+y_2) * 2\)

\((8,2) = (10+x_2,-4+y_2)\)

By comparison:

\(8 = 10 + x_2\)

\(2 = -4 + y_2\)

So:

\(8 = 10 + x_2\)

\(x_2 = 8 - 10\)

\(x_2 = -2\)

\(2 = -4 + y_2\)

\(y_2 =2+4\)

\(y_2 =6\)

So, the coordinate is: \((-2,6)\)

Answer:

its option D......im 100 percent sure

Answer:

d

Step-by-step explanation:

Answer:

Step-by-step explanation:

let assume the no. - x

x*94/5=42

x=42*5/94

x=21*5/47

x=105/47

Sorry if I’m wrong

Let the number should be multiplied be X

Given number = 9 4/5

⇛ (9×5+4)/5

⇛ (45+4)/5

⇛ 49/5

On multiplying 49/5 with X then the result

= (49/5)×X

= 49X/5

According to the given problem

The result = 42

⇛ 49X/5 = 42

⇛ 49X = 42×5

⇛ 49X = 210

⇛ X = 210/49

⇛ X = 30/7

⇛ X = 4 2/7

Answer↓

The required number is 30/7 or 4 2/7

Check↓

On multiplying 4 9/5 with 4 2/7

⇛ 4 9/5 × 4 2/7

⇛ (49/5)×(30/7)

⇛ (49×30)/(5×7)

⇛ 7×6

⇛ 42

Verified.

Answer:

x = -4

Step-by-step explanation:

The two points have the same x-coordinate, -4.

That means the line is a vertical line.

Answer: x = -4

Answer:

0.012*3400=40.80

D

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