what is the simplified ratio of 32:24

Answer:

1) B = 88°, a = 13.1, b = 26.9

2) C = 73°, a = 20.9, b = 12.6

Step-by-step explanation:

To solve for the remaining sides and angles of the triangle, given two sides and an adjacent angle, use the Law of Sines formula:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Given values:

As the interior angles of a triangle sum to 180°:

\(\implies A+B+C=180^{\circ}\)

\(\implies B=180^{\circ}-A-C\)

\(\implies B=180^{\circ}-29^{\circ}-63^{\circ}\)

\(\implies B=88^{\circ}\)

Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:

\(\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)

\(\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)

Solve for a:

\(\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)

\(\implies a=\dfrac{24\sin 29^{\circ}}{\sin 63^{\circ}}\)

\(\implies a=13.0876493...\)

\(\implies a=13.1\)

Solve for b:

\(\implies \dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)

\(\implies b=\dfrac{24\sin 88^{\circ}}{\sin 63^{\circ}}\)

\(\implies b=26.9194211...\)

\(\implies b=26.9\)

\(\hrulefill\)

Given values:

As the interior angles of a triangle sum to 180°:

\(\implies A+B+C=180^{\circ}\)

\(\implies C=180^{\circ}-A-B\)

\(\implies C=180^{\circ}-72^{\circ}-35^{\circ}\)

\(\implies C=73^{\circ}\)

Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:

\(\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)

\(\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)

Solve for a:

\(\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)

\(\implies a=\dfrac{21\sin 72^{\circ}}{\sin 73^{\circ}}\)

\(\implies a=20.8847511...\)

\(\implies a=20.9\)

Solve for b:

\(\implies \dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)

\(\implies b=\dfrac{21\sin 35^{\circ}}{\sin 73^{\circ}}\)

\(\implies b=12.5954671...\)

\(\implies b=12.6\)

Answer:

\(21.7 x 10^5\)

Step-by-step explanation:

(6.2 x 10²) x (3.5 x 10³)

First, multiply the coefficients: 6.2 x 3.5 = 21.7.

Then, add the exponents: 10² x 10³ = 10^(2+3) = 10^5.

Therefore, the result is 21.7 x 10^5.

Answer:

3286000

Step-by-step explanation:

(x,y) --> (x, y-2)

=======================================================

Explanation:

Choice A can be ruled out because of the jump from x to 2x, and from y to 2y. This is a dilation with a scale factor 2. Meaning the preimage enlarges to a bigger image. Specifically the larger image has side lengths twice as long as the smaller preimage. The larger image of course cannot possibly be congruent to the smaller preimage. Congruent figures must have the same corresponding side lengths.

We'll come back to choice B.

Choice C and choice D are ruled out for similar reasoning as choice A was eliminated.

-------------

To summarize the previous section: We ruled out choices A, C, and D. The only thing left is choice B.

Choice B is a translation. The jump from y to y-2 means we shift the point 2 units down. There is no left or right shifting because x stays the same.

For example, the point (5,12) moves to (5,10).

Notice that dilation is not being applied for choice B.

With any geometric translation, aka shifting, the side lengths will remain intact. Something that is 5 units long will stay 5 units long. No amount of shifting will change the distance.

Therefore, a translation preserves distances and lengths. We consider it a rigid transformation. This is why choice B will have the preimage congruent to the image.

Answer:B) (x, y) → (x, y − 2)

Step-by-step explanation:

Step-by-step explanation:

1) (3x)^2 = (3x)*(3x)

2) (3x)^2 = 3x * 3x = 9 x^2

Answer:

            4  to  1

Step-by-step explanation:

                                                Tablespoon of cocoa   to Tablespoon of sugar

                                                                          8             :                2

                                                                          \(\frac{8}{2}\)              :                \(\frac{2}{2}\)

                                                                          4             to                1

When recipe is doubled:                             ( 8 x 2)         to        (2 x 2)

                                                                         16             :              4

                                                                         \(\frac{16}{4}\)             :               \(\frac{4}{4}\)

                                                                          4           to              1

It can be observed that the ratio remains the same

Answer:

Step-by-step explanation:

(x-2)(x+4)=x^2+4x-2x-8=0=> x =2, x=0

Answer:

A

Step-by-step explanation:

Answer:

put it into slope intercept form. which is y=mx+b

Step-by-step explanation:

This shows that 76 cookies will be made with the total pounds of cookies

Fractions are written as a ratio of two integers. Given the following parameters

Total pounds of cookies made = 4 3/4 pounds

Total pounds of cookies made = 19/4 pounds

If he uses 1/16 pound of dough for each cookie, the total amount of cookies made is given;

Number of cookies = 19/4 ÷ 1/16

Number of cookies = 19/4 * 16/1

Number of cookies = 19 * 4

Number of cookies = 76

This shows that 76 cookies will be made with the total pounds of cookies

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Mean and IQR (Interquartile Range) give the best tools for measuring the center and spread. So, the correct option is C.

The mean is a measure of central tendency that is calculated by adding up all the values in a dataset and dividing by the number of values. The mean is sensitive to extreme values, also known as outliers, and can be affected by skewed data.

The IQR is a measure of spread that gives the range of the middle 50% of the data. It is calculated by finding the difference between the 75th percentile (Q3) and the 25th percentile (Q1) of the data. The IQR is less sensitive to outliers than the standard deviation, which is a measure of spread that gives the average distance of the data points from the mean.

The median is a measure of central tendency that is the middle value in a dataset when the values are arranged in order. It is less sensitive to extreme values than the mean and is useful when the data is skewed.

While mean and standard deviation are commonly used measures of center and spread, they may not be appropriate for all datasets, especially those that are skewed or contain outliers. Therefore, mean and IQR are often preferred for summarizing the center and spread of such data.

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The determinant of the given elementary matrices is  20 .

What is a Matrix ?

The matrix is defined as an arrangement of set of numbers arranged in rows and columns to form a rectangular array.

In the matrix the horizontal elements are called as Rows and

the vertical elements are called as Columns .

In the question ,

it is given that ,

the matrix is  \(\left[\begin{array}{ccc}8&5\\4&5\end{array}\right]\)  ,

the determinant of the matrix is represented as ⇒ (8×5 - 5×4)

Simplifying the given expression further ,

we get ,

= 40 - 20

= 20 .

Therefore , the determinant is 20 .

The given question is incomplete, the complete question is

Compute the determinants of the elementary matrices given as \(\left[\begin{array}{ccc}8&5\\4&5\end{array}\right]\) .

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Answer:

About 8.49

Step-by-step explanation:

Find the square root of each and just add them up

Answer:

8.48

Step-by-step explanation:

Square root of 50: 7.07

Square root of 2: 1.41

7.07 + 1.41 = 8.48

Hope this helps :)

The size of angle ACB to the nearest degree is 88 degree.

Construction Steps:

Create a line segment BC with the property AC = 4 cm.

Draw two arcs that meet at point A by using B as the centre and a radius of 4 cm, and C as the centre and a radius of 7 cm.

Join AB and AC now. Consequently, the necessary triangle is ABC.

With the use of a compass, draw a line segment AB = 7 cm from A, cutting an arc AC = 4 cm.

Cut an arc of 3 cm from point B.

Embrace BC and AC

Triangle with  angle ABC is necessary.

< ACB = 88 degree

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Answer:

Hey

Step-by-step explanation:

 -4x + 16= -2×2x -2×(-8)= -2(2x-8)

Answer C

The exponential function will be equal to y = 20ˣ.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Carter shared his post with 10 friends, who each share with only 2 people each day.

The exponential function will be written as,

y = abˣ

y = 10(2)ˣ

y = 20ˣ

Therefore, the exponential function will be equal to y = 20ˣ.

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Answer:

f(x) = 10(2)^x

Step-by-step explanation:

Rule for solving: The first number is the first part of the equation, and the second number is in parenthesis.

Answer:

what's are the graphs??

Step-by-step explanation:

here's the answer to your question

Answer:

a) 263,158

b) $164,500

c) Ethical issues companies face when deciding to move operations: job loss for employees, poor working conditions and exploitation of workers, negative environmental impact,...

Step-by-step explanation:

a)

Total cost = (0.25 + 0.02 + 0.03 + 0.15) x + 250,000

Total revenue = 1.40x

Setting the two equations equal to each other and solving for x, we get:

(0.45)x + 250,000 = 1.40x

0.95x = 250,000

x ≈ 263,158

b)

If the company sells 270,000 candy bars at $1.40 each, the total revenue generated is:

270,000 * $1.40 = $378,000

The total cost of producing 270,000 candy bars is:

(0.25 + 0.02 + 0.03 + 0.15) * 270,000 + $250,000 = $213,500

Therefore, the company's profit is:

$378,000 - $213,500 = $164,500

c)

Ethical issues companies face when presented with the decision to move operations: job loss for employees, poor working conditions and exploitation of workers, negative environmental impact,...

Answer:

-36

Step-by-step explanation:

-1/2x<18

multiply each term by LCM=2

-1/2x×2<18×2

the 2on the left hand side will cancel each other leaving

-x <36

divide both sides by -1

-x/-1>36/-1

(note the equality sign changes because following the laws when you divide by a negative number the sign will change

X>-36

Answer:

Step-by-step explanation:

x>-36 is the anwser brainlist whould be aprecited and verifed

The allusion in this statement is "Sasquatch," referencing a legendary creature known for its large size and used humorously to imply the person's abnormally large shoe size.

The allusion in the given statement is "Sasquatch." Sasquatch, also known as Bigfoot, is a legendary creature often depicted as a large, hairy, and elusive humanoid. In this context, the reference to Sasquatch is used metaphorically to humorously imply that the person's shoe size is abnormally large.

The mention of Sasquatch adds a playful and exaggerated tone to the conversation about shopping for shoes. It serves as a lighthearted way for the dad to comment on the frequency of buying new shoes, suggesting that the person's feet grow rapidly or that they have a high shoe consumption rate.

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Answer:

4 pounds and 1/4 ounces

Step-by-step explanation:

8 and 1 half pounds = 8.5 Ibs

One half of 8.5 = 8.5/2 = 4. 25 Ibs or 4 & 1/4  or 4Ibs 4 ounces.

Correct option is A

Independent variable

Independent variable is manipulated by the researcher to determine the effect of its change relative to a change in dependent variable.

Independent Variables

An independent variable is exactly what it sounds like. It is a variable that stands alone and isn't changed by the other variables you are trying to measure. For example, someone's age might be an independent variable.

In an experiment the independent variable is the variable that is varied or manipulated by the researcher. The dependent variable is the response that is measured. One way to think about it is that the dependent variable depends on the change in the independent variable.

Qualitative research consist in observing some variables and obtaining information. Usually the qualitative research does not involve the manipulation of independent variables, these types of researches focuses more in collecting answers in groups of people, and making statistics with those answers or information. So the variables are not manipulated.

Correct option is A

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Answer:

s

Step-by-step explanation:

s

The price for apples is cheaper at quick market.

From the question, we have

Quick market:

\(\dfrac{1.52}{6} = \text{0.25 per apple}\)

Walmart:

\(\dfrac{1.32}{5} = \text{0.26 per apple}\)

The price for apples is cheaper at quick market.

Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups. When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers. One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping.

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The value of y is 18

Similar triangles have the same corresponding angle measures and proportional side lengths. The angles of the two triangle must be equal and it not necessary they have equal sides.

Therefore the corresponding angles of similar triangles are congruent and the ratio of corresponding sides of similar triangles are equal.

Therefore;

14/21 = 12/y

14y = 21 × 12

14y = 252

divide both sides by 14

y = 252/14

y = 18

Therefore the value of y is 18.

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The fraction of the area of the tray occupied by the blondies is 1/9.

To find the fraction of the area of the tray occupied by blondies, we need to determine the area occupied by the blondies and compare it to the total area of the tray.

Let's calculate the area of each individual blondie:

The blondies are squares with 3-inch sides, so the area of each blondie is 3 inches × 3 inches = 9 square inches.

Now, let's calculate the area occupied by the blondies in each row:

Since there are 4 rows of blondies and each row contains 4 blondies, the total number of blondies is 4 rows × 4 blondies per row = 16 blondies.

So, the total area occupied by the blondies is 16 blondies × 9 square inches per blondie = 144 square inches.

Next, let's determine the area occupied by the brownies:

The brownies are squares with 6-inch sides, so the area of each brownie is 6 inches × 6 inches = 36 square inches.

Since there are also 4 rows of brownies and each row contains 4 brownies, the total number of brownies is 4 rows × 4 brownies per row = 16 brownies.

Therefore, the total area occupied by the brownies is 16 brownies × 36 square inches per brownie = 576 square inches.

Now, let's calculate the total area of the tray:

Given that the tray is completely full and has an area of 648 square inches, we can subtract the area occupied by the brownies from the total area to find the remaining area occupied by the blondies:

Total area of the tray - Area occupied by the brownies = Area occupied by the blondies

648 square inches - 576 square inches = 72 square inches.

So, the fraction of the area of the tray occupied by the blondies is:

Area occupied by the blondies / Total area of the tray = 72 square inches / 648 square inches.

To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 72 in this case:

72 square inches / 648 square inches = 1/9.

Therefore, the blondies' percentage of the tray's surface area is 1/9.

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Answer:

It is a rate,

A rate is the ratio between two related quantities in different units.

Miles and hours are two different units and its 50 miles per 2 hours.

Answer:

angle ced is a right ange

so the m angels debate =135 m angle aeb =35

so the answer is 135+35 =170

180 is a all side sim

=180-170=10 answer

Answer:

∠CED is a right angle.

∠CEA is a right angle.

m∠CEB = m∠BEA

m∠DEB = 135°