i need help on this equation

The measure of side a given the characteristics of the oblique triangle as discussed is; 34.02.

As evident in the task content, A = 151° C = 9° b = 24. Therefore, the measure of angle B = 180° - 151° - 9° = 20°.

Ultimately, the length of side a can be determined using sine rule as follows;

a / sin 151° = b / sin 20°

a = 24 sin 151° / sin 20°

a = 34.02.

Ultimately, the length of side a is; 34.02.

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The conversion of 275 mm to inches is 10.8268 inches.

Millimeter (mm) and inch are both units of measurement used to express length or distance. Millimeter is a metric unit of length commonly used in the International System of Units (SI) and is equivalent to one-thousandth of a meter.

To convert 275 mm to inches, we can use the conversion factor of 1 inch = 25.4 mm.

So, we can divide 275 mm by 25.4 mm/inch to get the equivalent measurement in inches:

275 mm ÷ 25.4 mm/inch = 10.8268 inches (rounded to four decimal places)

Therefore, 275 mm is approximately equal to 10.8268 inches.

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The single natural logarithm expression is ln(2). Therefore, correct answer is (a)

The expression in the form [tex]e^a=b[/tex] can also be written as In b = a  which is called as logarithmic expression.

Properties of Logarithms:

1. In (mn) = In m + In n

2. In [tex]a^m =[/tex] m In a

3. In [tex]e^a[/tex] = a.

The natural logarithm expression is:

4 + ln 2 - ln 4

Apply the product and quotient rule of natural logarithm:

4 + ln 2 - ln 4  = In (4 × 2/4)

Evaluate the quotient:

4 + ln 2 - ln 4  = In (2)

Hence, the single natural logarithm expression is ln(2).

The correct option is (a)

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Answer:

B: ln 4.

Step-by-step explanation:

The missing sides of each pair of similar triangles are listed below:

Case 15: w = 5, x = 25 / 12, y = 65 / 12, z = 169 / 12

Case 16: x = 12, y = 6√3, z = 3√5

Case 17: x = 40 / 3, y = 32 / 3

Case 18: x = 5, y = 20, z = 10√3

In this problem we find four cases of pairs of similar triangles, whose missing sides can be found by means of proportion formulas and Pythagorean theorem. Now we proceed to determine the missing lengths for each length:

Case 15

w = √(13² - 12²)

w = 5

12 / w = w / x

w² = 12 · x

x = w² / 12

x = 5² / 12

x = 25 / 12

y = √[(25 / 12)² + 5²]

y = 65 / 12

z = 12 + x

z = 169 / 12

Case 16

6 / 3 = x / 6

x = 36 / 3

x = 12

y = √(x² - 6²)

y = √(12² - 6²)

y = 6√3

z = √(3² + 6²)

z = 3√5

Case 17

y / 8 = 8 / 6

y = 8² / 6

y = 64 / 6

y = 32 / 3

x = √(8² + y²)

x = √[8² + (32 / 3)²]

x = 40 / 3

Case 18

x = √[10² - (5√3)²]

x = 5

y = x + 15

y = 20

z = √[15² + (5√3)²]

z = 10√3

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a) The value of a from the equation is a = 7.9

b) The cost of each pair of shorts is given by y = $ 11.50

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

2.25 ( a + 1.3 ) = 20.7

Divide by 2.25 on both sides , we get

a + 1.3 = 9.2

Subtracting 1.3 on both sides , we get

a = 7.9

b)

The cost of each pair of shorts be y

The cost of shirt be x = $ 10

The number of outfits = 3

The total cost of outfits = $ 64.50

So , the equation will be

3 ( x + y ) = 64.50

On simplifying the equation , we get

3 ( 10 + y ) = 64.50

Divide by 3 on both sides , we get

10 + y = 21.50

Subtracting 10 on both sides , we get

y = $ 11.50

Hence , the cost of each shorts is $ 11.50

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A cheetah could run 630 miles in 6 hours

Answer:

It can run 630 miles in 6 hours.

Step-by-step explanation:

If the cheetah can run 105 miles per hour

then,

in 6 hours, it can run 105*6 miles.

105*6= 630

Hope this helps.

The ordered pairs in f(x)=x^2-2x+3 and f(x)=-2x+19 are (√21, 24 - 2√21) and (-√21, 24 + 2√21)

To find the ordered pairs of the two functions, we need to solve the system of equations:

f(x) = x^2 - 2x + 3

f(x) = -2x + 19

We can set the two expressions for f(x) equal to each other:

x^2 - 2x + 3 = -2x + 19

Simplifying and rearranging, we get:

x^2 = 21

Taking the square root of both sides, we get:

x = ± √21

Therefore, there are two ordered pairs that satisfy both equations:

(√21, f(√21)) and (-√21, f(-√21))

To find the values of f(√21) and f(-√21), we can substitute the values of x into either equation. Let's use the first equation:

f(√21) = (√21)^2 - 2(√21) + 3 = 21 - 2√21 + 3 = 24 - 2√21

f(-√21) = (-√21)^2 - 2(-√21) + 3 = 21 + 2√21 + 3 = 24 + 2√21

Therefore, the two ordered pairs are:

(√21, 24 - 2√21) and (-√21, 24 + 2√21)

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The capital letter H has 2 reflectional symmetry and 2 rotational symmetry.

A figure has reflectional symmetry if it can be reflected across a line and still look the same. For the capital letter H, there is two lines of symmetry, which is the vertical line and horizontal line that divides the letter into two equal halves. Reflecting the letter across this line produces the same letter. So, the H has only 2 reflectional symmetries.

A figure has rotational symmetry if it can be rotated by some angle and still look the same. For the capital letter H, if we rotate it 180 degrees and 360 degrees about the center point of the letter, it will look the same. There is no other angle of rotation that produces the same letter. Therefore, the H has only 2 rotational symmetries.

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--The question is incomplete, answering to the question below--

"How many reflectional symmetries does this figure have?

Enter your answer

___ reflectional symmetries

How many rotational symmetries does this figure have?

Enter your answer

___ rotational symmetries"

The value of x such that  the angles LFDE and LFDB are supplementary is:

17º

If LFDE and LFDB are supplementary, then their sum is 180°. Therefore, we can write an equation using this information:

m∡FDE + m∡LFDB = 180°

Substituting the given expressions for m∡FDE and m∡LFDB, we get:

(3x - 15)° + (5x + 59)° = 180°

Combining like terms and simplifying, we get:

8x + 44 = 180

Subtracting 44 from both sides of the equation, we get:

8x = 136

Dividing both sides of the equation by 8, we get:

x = 17

Therefore, the value of x that makes LFDE and LFDB supplementary is 17.

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The interpretation of the slope in the context of the problem is: For every hour the electrician works, her pay will increase $28.

The slope of any function is the unit rate or average rate of change of the given function for that situation.

here, we have,

Given the function, E(x) = 130 + 28x, where:

E(x) is the amount an electrician charges per job

130 is the flat rate service which is the starting value or y-intercept

28 is the unit rate or slope, which is the fee charged per hour by the electrician to complete a job.

Thus, the interpretation of the slope in the context of the problem is: For every hour the electrician works, her pay will increase $28.

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To convert between pounds and kilogrammes, multiply the number of pounds by 0.45359237, and to do the opposite, multiply the number of kilogrammes by 2.20462.

65 kg is equal to 143.3003 lbs.

The fundamental mass unit in the metric system is the kilogramme (kg). A kilogramme and 1,000 cubic centimetres of water have fairly similar masses.

One pound is approximately equal to 454 grams. One kilogram is the same as 2.20462 lbs.

One pound is equal to 0.45359237 kilograms.

To convert kilograms (kg) to pounds (lbs), you can use the following formula:

To convert kilograms to pounds, multiply your figure by 2.20462

To convert 65 kg to lbs, you can multiply 65 by 2.20462:

65 kg X 2.20462 lbs/kg

= 143.3003 lbs

Therefore, 65 kg is approximately equal to 143.3003 lbs.

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One inches is equal to 2.54 cm

To convert 1 inches to cm, we can use the following formula:

1 inch = 2.54 cm

The conversion factor is 2.54

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

Therefore,

The length in cm = conversion factor × The length in inches

Substitute the values in the equation

1 inches = 1 × 2.54 cm

Multiply the numbers

= 2.54 ( rounded to two decimal places )

Therefore, one inch is 2.54 cm

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To convert 1km into other measurements: 1) 1000 meter, 2) 3280.84, 3) 1e+6 millimeter, 4) 100000 centimeter, 5) 39370.1 inch, 6) 1093.61 yard1 km, 7) 0.621371 mile.

It is necessary to measure these quantities using units of measurement. Sometimes the units of measurement chosen don't match the standards needed for a specific procedure or application, as well as the measurement preference and ease of use.

It's essential to convert these units in a way that enables proper comprehension and use. When converting between different units in the metric system, a decimal point must typically be moved. If you remember what the prefixes mean, you can convert between different units of measurement within the metric system fairly quickly by simply multiplying or dividing the number by the prefix's value.

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The value 0.5625 as a fraction is 9/16 .

In mathematics, fractions are defined as part of a whole. A whole can be an object or a group of objects. In real life, if you cut a pie out of the whole pie, that piece becomes part of the pie. Fractions are words of Latin origin. "Fractus" means "broken" in Latin. In ancient times, rest was expressed in words. Later it was introduced in numerical form.

Fractions are also called parts or sections of any quantity. Represented by the symbol '/'. Bachelor/Bachelor For example, 2/4 is the numerator above and the fraction below the denominator. In this article, you will learn the definition of fractions in mathematics, types of fractions, how to convert fractions to decimals, and many solved examples and full explanations

to convert in fraction we will muliply and devide by 100.

.5625*100/100 = 9/16

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Answer:

Step-by-step explanation:

(a) If you face south and turn anti-clockwise to east, you'd have turned a right angle ( one 90° turn).

(b) If you turn clockwise from east to east again, you'd have completed a revolution or 360° (or 4 right angles)

(c) From west clockwise to south, you'd have turned 90° to north, another 90° to east and 90° to south making 3 right angles or 270°.

Hope these help! :)

1 milligram equals 0.001 grams. 1 gram is equal to 1000 milligrams.

So, 500 milligrams is equivalent to 0.5 grams.

The International System of Units uses the unit of mass known as the gramme (symbol: g) (SI).

The kilogramme serves as the basis for the definition of the gramme.

The SI base unit of mass is the gramme, which is one thousandth of a kilogramme.

The kilogramme, the foundation unit of mass in the SI (International System of Units), serves as the basis for the weight and mass unit known as the milligramme.

It is equivalent to 1/1,000,000 kilos or 1/1,000 gramme.

500 milligrammes equal 0.5 grammes.

grammes (g) from milligrammes (mg) (g),

You can divide the number of milligrams by 1000:

500 mg ÷ 1000 = 0.5 g

So,

500 milligrams is equivalent to 0.5 grams.

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The sum to infinity of the sequence is 96/13

Every term in a geometric sequence is obtained by multiplying the term before it by the same number. [tex]\mathrm{a_n= a_1 r^{n -1 }}[/tex] is the general term for it. The common ratio is denoted by the number r. Any term in the sequence can be used to find it by dividing it by the term before it.

Given the nth term of a geometric sequence expressed as:

Tn = Σ12(-5/8)ⁿ

The sum to infinity of the sequence is expressed as;

S∞ = a/1-r

where

a is the first term = 12

r is the common ratio = -5/8

Substitute

S∞ =  12/1-(-5/8)

S∞ = 12/1+5/8

S∞ = 12/(13/8)

S∞ =12 *8/13

S∞ = 96/13

Hence, the sum to infinity of the sequence is 96/13

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The equation of line passes through the points (0, -3) and (4, -1) will be;

⇒ y = 1/2x - 3

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;

Two points on the line are (0, -3) and (4, -1)

Now,

Since, The equation of line passes through the points (0, -3) and (4, -1).

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

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 1 - (-3)) / (4 - 0)

m = 2 / 4

m = 1/2

Thus, The equation of line with slope 1/2 is,

⇒ y - (-3) = 1/2 (x - 0)

⇒ y + 3 = 1/2x

⇒ y = 1/2x - 3

Therefore, The equation of line passes through the points ((0, -3) and

(4, -1) will be;

⇒ y = 1/2x - 3

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Answer: The fact of being correct and without any mistakes:

Step-by-step explanation: Hope this helps!

Answer:

514.2857142857

Step-by-step explanation:

14cm=0.14m

so,

no. of planks=72/0.14=514.2857142857

Answer: 8x^3 - 18x^2 + 11x - 3

Distribute and combine like terms

Option A. The dealer has 17 cars for sale. The problem provides us with a ratio of cars to trucks on the lot, which is 11 to 33. This means that for every 11 cars, there are 33 trucks.

We are given that there are currently 51 trucks for sale. We can use this information along with the ratio of cars to trucks to determine how many cars are for sale.

We can start by setting up a proportion with the ratio of cars to trucks:

cars/trucks = 11/33

We can then substitute the given value for trucks:

cars/51 = 11/33

To solve for cars, we can cross-multiply and simplify:

[tex]cars = (11/33) * 51[/tex]

cars = 17

Therefore, the dealer has 17 cars for sale.

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Answer: x x x x x x x

Step-by-step explanation:

xxxxxxxxxxxxxxxxxx

The sample mean symbol is X bar, representing the average value of a sample, calculated by summing values and dividing by observations.

The sample mean image is addressed by (articulated "x-bar"). It is utilized to address the typical worth of an example of information, and is determined by adding every one of the qualities in the example and separating by the quantity of perceptions.

For instance, in the event that we have an example of 10 numbers {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, we can compute the example mean by including the entirety of the qualities and isolating by the all out number of perceptions:

X bar = (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10)/10

X bar = 5.5

The sample mean is a normally involved measurement in inferential insights, where it is utilized to gauge the populace mean. It is likewise utilized in speculation testing, certainty stretches, and other measurable examinations.

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The, 9 kilograms is equal to approximately 19.84 pounds (rounded to two decimal places).

To convert 9 kilograms (kg) to pounds (lbs), you can use the following formula:

1 kg = 2.20462 lbs

So, to convert 9 kg to lbs, you can multiply 9 by 2.20462:

9 kg * 2.20462 lbs/kg = 19.84158 lbs

Therefore, 9 kilograms is equal to approximately 19.84 pounds (rounded to two decimal places).

"Kilograms" (kg) and "pounds" (lbs) are mass or weight measuring units.

The International System of Units' base unit of mass is the kilogramme (kg) (SI). The mass of a specific platinum-iridium alloy cylinder stored at the International Bureau of Weights and Measures in France is defined.

The pound (lb or lbs) is a popular measure of mass in the United States and other nations. One pound equals 0.45359237 kilos. The pound is often used to weigh objects such as humans, animals, and food.

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Answer:

Add parentheses ( ) to make the equation true:

11 x 6 ÷ (8 + 3) = 6

Solve for y

4y + (16 - 7) = 25

y = 4

9 x (8 - 5)

= 27

3. {[3 x (9 + 7)] - 8}

Sorry, can't figure this one out.

5. Mable saved $10 of her lemonade stand money. She then made 7 times as much as the money she had saved. Mable's friend gave her $12. How much money does Mable now have in all?

Mable has $82 all together.

Step-by-step explanation:

You're welcome.

Answer:

1 fluid oz = 29.5735 milliliters

Step-by-step explanation:

A unit can be used for measurement, and is commonly found in mathematics to describe length, size, etc.

Converting these units:

Therefore, for every 1 fluid ounce, it is equivalent to 29.5735 milliliters.

The area of the trapezoid given is 160 cm².

We can write the area of the trapezoid as -

A = {1/2} x {sum of parallel sides} x {distance between them}

A = {1/2} x {P₁ + P₂} x {h}

Given is that a trapezoid with 24 cm length and 10 cm height. One side of the trapezoid is 8 cm.

We can write the area of the trapezoid as -

A = {1/2} x {P₁ + P₂} x {h}

A = {1/2} x {24 + 8} x 10

A = 1/2 x 10 x 32

A = 160 cm²

Therefore, the area of the trapezoid given is 160 cm².

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