In a triangle, the second angle measures two times the first. The measure of the third angle is 170° more than the measure of the second. Find the measures of the three angles

Answer:

Let's use the formula:

distance = rate × time

Let's assume Latasha's rate of travel as "r". Then, Nathan's rate of travel would be "r + 8".

For Latasha:

distance = r × 9

For Nathan:

distance = (r + 8) × 9

According to the problem, the combined distance they traveled is 288 miles. So:

r × 9 + (r + 8) × 9 = 288

Simplifying the equation:

18r + 72 = 288

18r = 216

r = 12

So, Latasha's rate of travel is 12 mph, and Nathan's rate of travel is 20 mph (12 + 8).

Therefore, Latasha is traveling at 12 mph and Nathan is traveling at 20 mph.

The value of x is 8 when GH is 3x-2, HI is 7x-4 and GI is 8x+10. It forms a straight line.

Segment addition is a concept in geometry that states that given three collinear points A, B, and C, with B between A and C, the length of AB added to the length of BC will give the length of AC. This can be expressed algebraically as:

AB + BC = AC

We can use the fact that GH + HI = GI (by the segment addition postulate) and substitute the given expressions to get:

(3x - 2) + (7x - 4) = 8x + 10

Simplifying the left side by combining like terms, we get:

10x - 6 = 8x + 10

Subtracting 8x from both sides, we get:

2x - 6 = 10

Adding 6 to both sides, we get:

2x = 16

Dividing by 2, we get:

x = 8

Therefore, x = 8.

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Answer:

7) S=6.28 yd  A=12.57 [tex]yd^{2}[/tex]

8) S=99.48 ft A=945.1 [tex]ft^{2}[/tex]

9) S=21.99 in  A=43.98 [tex]in^{2}[/tex]

Step-by-step explanation:

7)

S=r θ

S=4([tex]\frac{90\pi }{180}[/tex])........................................plug in values

S=4([tex]\frac{\pi }{2}[/tex])...........................................simplify

S=6.28 yd...................................solve and round

A=[tex]\frac{1}{2}[/tex]([tex]r^{2}[/tex]) θ

A=[tex]\frac{1}{2}[/tex]([tex]4^{2}[/tex])([tex]\frac{90\pi }{180}[/tex]) ....................................plug in values

A=[tex]\frac{1}{2}[/tex](16)([tex]\frac{\pi }{2}[/tex])  .....................................simplify

A=12.57 [tex]yd^{2}[/tex]...................................solve and round.

8)

S=r θ

S=19([tex]\frac{300\pi }{180}[/tex]).........................................plug in values

S=19([tex]\frac{5\pi }{3}[/tex]).............................................simplify

S=99.48 ft........................................solve and round

A=[tex]\frac{1}{2}[/tex]([tex]r^{2}[/tex]) θ

A=[tex]\frac{1}{2}[/tex]([tex]19^{2}[/tex])([tex]\frac{300\pi }{180}[/tex]) ....................................plug in values

A=[tex]\frac{1}{2}[/tex](361)([tex]\frac{5\pi }{3}[/tex])  .....................................simplify

A=945.1 [tex]ft^{2}[/tex].......................................solve and round.

9)

S=r θ

S=4([tex]\frac{315\pi }{180}[/tex]) ............................................plug in values

S= 4( [tex]\frac{7\pi }{4}[/tex])..............................................simplify

S=21.99 in..........................................solve and round

A=[tex]\frac{1}{2}[/tex]([tex]r^{2}[/tex])θ

A=[tex]\frac{1}{2}[/tex]([tex]4^{2}[/tex])([tex]\frac{315\pi }{180}[/tex]) ....................................plug in values

A=[tex]\frac{1}{2}[/tex](16)( [tex]\frac{7\pi }{4}[/tex])......................................simplify

A=43.98 [tex]in^{2}[/tex]....................................solve and round.

Answer:

1,610,000

Step-by-step explanation:

To round to the nearest hundred, we need to go to the hundreds place. In 683, we can round this to the nearest hundred by using this rule:

5 or more, let it sore

4 or less, let it rest

683 rounded to the nearest hundred is 700

2329 rounded to the nearest hundred is 2300

Now we just need to multiply both of them to get the product

[tex]2300\times 700=1,610,000[/tex]

The sοlutiοns tο the inequality are x values greater than 5.

A number line frοm negative 3 tο 3 in increments οf 1. An οpen circle is at 5 and a bοld line starts at 5 and is pοinting tο the right.

-6x - 5 < 10 - x and -6x + 15 < 10 - 5x are cοrrect representatiοns οf the inequality –3(2x – 5) < 5(2 – x).

Tο sοlve the inequality -3(2x - 5) < 5(2 - x), we can start by distributing the negative 3 and the pοsitive 5 οn the right side:

-6x + 15 < 10 - 5x

Then, we can simplify by mοving all the x terms tο οne side and all the cοnstant terms tο the οther side:

-x < -5

Finally, we can divide bοth sides by -1, remembering tο reverse the inequality sign:

x > 5

Therefοre, the sοlutiοns tο the inequality are x values greater than 5. The representatiοns οf this sοlutiοn οn a number line are:

A number line frοm negative 3 tο 3 in increments οf 1. An οpen circle is at 5 and a bοld line starts at 5 and is pοinting tο the right.

A number line frοm negative 3 tο 3 in increments οf 1. An οpen circle is at negative 5 and a bοld line starts at negative 5 and is pοinting tο the left.

Hοwever, οnly the first representatiοn is cοrrect, since the secοnd representatiοn shοws the sοlutiοns tο x < -5, which is the οppοsite inequality tο the οne we fοund.

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Answer:

50ml of water should be added

Answer:

Gary would have 45 and Mary would have 75

Approximately 9.42 units of paint would be required to paint the outside of a cylinder with a radius of 3 meters and a height of 5 meters, without the top.

To calculate the amount of paint required to paint the outside of a cylinder, you will need to find the surface area of the cylinder. Since the cylinder is without a top, we only need to find the lateral surface area.

formula of surface area

Lateral Surface Area = 2πrh

when r is the cylinder's radius, h is its height, and is a constant value roughly equivalent to 3.14.

Once you have calculated the lateral surface area of the cylinder, you can use the following formula to find the amount of paint required:

Amount of Paint = Lateral Surface Area / Coverage per unit of paint

where coverage per unit of paint refers to the area that can be covered by one unit of paint. This will depend on the type of paint you are using and its thickness.

For example, if the cylinder has a radius of 3 meters and a height of 5 meters, the lateral surface area would be:

Lateral Surface Area = 2πrh

Lateral Surface Area = 2 x 3.14 x 3 x 5

Lateral Surface Area = 94.2 square meters

If the coverage per unit of paint is 10 square meters, the amount of paint required would be:

Amount of Paint = Lateral Surface Area / Coverage per unit of paint

Amount of Paint = 94.2 / 10

Amount of Paint = 9.42 units of paint

Therefore, approximately 9.42 units of paint would be required to paint the outside of a cylinder with a radius of 3 meters and a height of 5 meters, without the top.

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The three coordinates that satisfy the system of inequalities include the following:

(0, -2)

(-7, - 5)

(-2, -8).

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.

By critically observing the graph of the given system of inequalities y < -2x + 4 and 2x - 4y ≥ 3, the three required solutions that satisfies it include following;

Ordered pair = (0, -2).

Ordered pair = (-7, - 5).

Ordered pair = (-2, -8).

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Answer:

honestly don't know but you got this bro {=•=}

We can say that after answering the offered question Therefore, the proportionality constant of proportionality in this scenario is 11.25.

Proportionate relationships are those that have the same ratio every time. For example, the average number of apples per tree defines how many trees are in an orchard and how many apples are in an apple harvest. Proportional refers to a linear relationship between two numbers or variables in mathematics. When the first quantity doubles, the second quantity doubles as well. When one of the variables decreases to 1/100th of its previous value, the other falls as well. When two quantities are proportional, it means that when one rises, the other rises as well, and the ratio between the two remains constant at all values. The diameter and circumference of a circle serve as an example.

In this case, we may use the following formula to calculate the proportionality constant:

proportionality constant = output/input

where the output is John's pay and the input is the number of hours he worked.

As a result, the proportionality constant is:

Paycheck/hours worked = proportionality constant

proportionality constant = 450/40

proportionality constant = 11.25

As a result, the proportionality constant in this scenario is 11.25.

In this case, we may use the following formula to calculate the proportionality constant:

proportionality constant = output/input

where the output is John's pay and the input is the number of hours he worked.

As a result, the proportionality constant is:

Paycheck/hours worked = proportionality constant

proportionality constant = 450/40

proportionality constant = 11.25

Therefore, the constant of proportionality in this scenario is 11.25.

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Therefore, approximately 110,294 ball bearings of radius 4mm can be made from the steel rod.

Volume is the amount of space that a three-dimensional object occupies. It is typically measured in cubic units, such as cubic meters, cubic centimeters, or cubic feet. The volume of an object can be calculated by multiplying its length, width, and height, or by using a specific formula for the shape of the object, such as the formula for the volume of a sphere, cylinder, or cone. Volume is an important concept in mathematics, physics, engineering, and many other fields, and it is used to describe the size and shape of objects, as well as their capacity, density, and other properties.

Here,

To solve this problem, we need to determine the total volume of the steel rod and then calculate how many ball bearings of radius 4mm can be made from this volume. First, we need to calculate the volume of the steel rod. We are given that one kilogram of the steel has a volume of 150 cm³. Therefore, the total volume of the steel rod is:

25 kg * 150 cm³/kg = 3750 cm³

Next, we need to calculate the volume of one ball bearing of radius 4mm. The formula for the volume of a sphere is:

V = (4/3)πr³

Substituting r = 4mm = 0.4cm, we get:

V = (4/3)π(0.4)³ = 0.034 cm³ (rounded to three decimal places)

To find the number of ball bearings that can be made from the steel rod, we divide the total volume of the steel rod by the volume of one ball bearing:

3750 cm³ / 0.034 cm³ ≈ 110,294

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Answer:

To find the percentage decrease, we need to find the difference between the original price and the new price, divide that difference by the original price, and then multiply by 100 to get the percentage.

The difference between the original price and the new price is:

80 - 44 = 36

To find the percentage decrease, we divide this difference by the original price:

36 / 80 = 0.45

Finally, we multiply by 100 to get the percentage:

0.45 * 100 = 45%

Therefore, the percentage decrease from $80 to $44 is 45%.

Answer:  The percentage decrease is 45%.

Step-by-step explanation:

Percentage decrease = [tex](\frac{Oringinal Value-NewValue}{Oringinal Value} )*100[/tex]

                                    = [tex](\frac{80-44}{80} )*100[/tex]

                                    = 45%

Answer:

-25

Step-by-step explanation:

= 2*(2) - 28 - 1

= 4 - 29

= -25

Given:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━

hope it helps! :)

Answer:

[tex]\huge\boxed{\sf x = -24}[/tex]

Step-by-step explanation:

[tex]\displaystyle -\frac{1}{2} x - 4 =8\\\\Add \ 4 \ to \ both \ sides\\\\-\frac{1}{2} x = 8+4\\\\-\frac{1}{2} x = 12\\\\Multiply \ both \ sides \ by \ -2\\\\-\frac{1}{2} x \times \ -2 = 12 \times -2\\\\\boxed{x = -24}\\\\\rule[225]{225}{2}[/tex]

Answer:

[tex]\boxed{\mathtt{1) \ x=4}}[/tex]

[tex]\boxed{\mathtt{2) \ x=2}}[/tex]

[tex]\boxed{\mathtt{3) \ x=-24}}[/tex]

Step-by-step explanation:

[tex]\textsf{For these problems, we are asked to solve for x in each equation.}[/tex]

[tex]\textsf{We should use similar steps for each of them.}[/tex]

[tex]\large\underline{\textsf{For Number 1:}}[/tex]

[tex]\textsf{We should first begin by adding 2 to both sides of the equation.}[/tex]

[tex]\mathtt{8x=32}[/tex]

[tex]\textsf{Now, divide by 8.}[/tex]

[tex]\boxed{\mathtt{1) \ x=4}}[/tex]

[tex]\large\underline{\textsf{For Number 2:}}[/tex]

[tex]\textsf{Let's begin by subtracting 5 from both sides of the equation.}[/tex]

[tex]\mathtt{-x=-2}[/tex]

[tex]\textsf{Now, divide by -1.}[/tex]

[tex]\boxed{\mathtt{2) \ x=2}}[/tex]

[tex]\large\underline{\textsf{For Number 3:}}[/tex]

[tex]\textsf{Beginning Number 3, let's multiply by -2 to both sides of the equation.}[/tex]

[tex]\mathtt{x+8=-16}[/tex]

[tex]\textsf{Now, subtract 8 from both sides of the equation.}[/tex]

[tex]\boxed{\mathtt{3) \ x=-24}}[/tex]

Answer:

To find the price of 3 tons of concrete, we need to use a proportion:

If 2/3 ton of concrete costs $42, then 1 ton of concrete costs:

$42 ÷ (2/3) ton = $42 × (3/2) = $63

Therefore, 3 tons of concrete will cost:

$63 × 3 = $189

So Trey would need to pay $189 for 3 tons of concrete.

According to the given information, the approximate temperature of the Sun's core is [tex]1.485*10^{7}[/tex]degrees Celsius.

The Sun is a massive ball of gas that generates heat and light through nuclear fusion at its core. The temperature of the Sun's core is much hotter than its surface temperature, and this difference in temperature is responsible for the Sun's energy output.

The temperature of the Sun's surface is approximately [tex](5.5*10^{3})[/tex] degrees Celsius, which is also known as the photosphere. However, the temperature at the Sun's core is estimated to be about [tex](2.7*10^{3})[/tex] times hotter than the surface temperature. This is because the core is the site of intense nuclear fusion reactions that convert hydrogen into helium and release huge amounts of energy in the form of heat and light.

To find the approximate temperature of the Sun's core, we can start with the temperature of the Sun's surface, which is given as [tex](5.5*10^{3})[/tex] degrees Celsius. We need to multiply this by the factor of  [tex](2.7*10^{3})[/tex]  to get the temperature of the core.

The approximate temperature of the Sun's core

= [tex](5.5*10^{3}) * (2.7*10^{3})[/tex]

=[tex]14.85*10^{6}[/tex]degrees Celsius

= [tex]1.485*10^{7}[/tex] degrees Celsius (in scientific notation)

Therefore, the approximate temperature of the Sun's core is [tex]1.485*10^{7}[/tex]degrees Celsius.

This extremely high temperature is necessary to sustain the nuclear reactions that power the Sun's energy output. The high temperature and pressure in the core create the ideal conditions for nuclear fusion to occur, which releases energy that eventually makes its way to the surface of the Sun and out into space in the form of light and heat.

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The distance between the two points N(-3, -11) and P(-3, -2) is 9 units.

Given the points

N(-3,-11) and P(-3,-2)

To find the distance between two points, we can use the distance formula:

d = √((x2 - x1)²+ (y2 - y1)²)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Using this formula, we can find the distance between the two points N(-3, -11) and P(-3, -2) as follows:

d = √((-2 + 11)²+ (-3 + 3)²)

This gives

d = √9²+ 0²)

So, we have

d = √81

Evaluate

d = 9

Therefore, the distance between the two points N(-3, -11) and P(-3, -2) is 9 units.

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Step-by-step explanation:

Since the number of bacteria in the petri dish doubles every two hours, after 2 hours, Harriet will have 103 x 2 = 206 bacteria.

After another 2 hours (i.e., 4 hours from the beginning), the number of bacteria will double again to become 206 x 2 = 412 bacteria.

After another 2 hours (i.e., 6 hours from the beginning), the number of bacteria will double once more to become 412 x 2 = 824 bacteria.

Therefore, Harriet will have 824 bacteria in the dish at the end of 6 hours. Answer: A. 1024 (rounded to the nearest whole number).

Answer:

The answer is Ahope this helps

Since line GF = line JK and < G = <J ; the minor arcs, the major arcs of the both circle are also similar and equal.

The minor arc of the given circle above can be defined as the part of the circle that is less than 180°. This is represented by <HGF in the first circle( with a red ink).

The major arc of the given circle above can be defined as the part of a circle that is greater than 180°. Thus is represented by <IJK in the second circle (with black ink).

Therefore in conclusion, there is a established similarity between the two circles since line GF = line JK and < G = <J, thus making their minor and major acre to be equal too.

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7x³ +3y³ +4y

Simplify the expression by Removing parentheses and brackets by multiplying factors, use the exponent rule to remove grouping if the term contains exponents, combine like terms by adding or subtracting coefficients and combine the constants.

Answer: The answer is  7x^3 + 3y^3 + 4y. Or in simpler terms choice A is correct

Step-by-step explanation:

Therefore, the total cost price of the goods is #5400.

Cost price refers to the amount of money that is spent by a business or individual to acquire or produce a product or service. It includes all the costs involved in the production or acquisition of the product or service, such as raw materials, labor costs, transportation costs, and other expenses. The cost price is usually used as a starting point for calculating the selling price of a product or service and is an important factor in determining the profitability of a business.

by the question.

Let's assume the cost price of the goods to be "x".

According to the problem, the trader sold the goods at a price of #5184 and incurred a loss of 4%.

we know that,

selling price = cost price - loss

Substituting the given values in the above formula, we get:

#5184 = x - 0.04x

Simplifying the equation, we get:

#5184 = 0.96x

Dividing both sides by 0.96, we get:

x = #5400

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We can solve this problem using the standard equation of a circle:

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle and r is the radius.

Since Noa is at the origin, the center of the circle is the midpoint between the object and the point where the drone passes:

h = (210 - 170)/2 = 20

k = (190 - 150)/2 = 20

The radius is the distance between the center and the point where the drone passes:

r = √((170 - 20)² + (190 - 20)²) = √(150² + 170²) = √(62500) = 250

So the equation of the drone's path is:

(x - 20)² + (y - 20)² = 250²

When the drone passes due north of Noa's position, its x-coordinate is 20, so we can substitute that into the equation:

(20 - 20)² + (y - 20)² = 250²

y - 20 = ±√(250²)

y = 20 ± 250

y ≈ -230 or y ≈ 270

So the drone will be approximately 230 feet north of Noa's position.

Answer:

B (A rectangular prism in which BA = 30 and h = 5 has a volume of 150 units3; therefore, Shannon is correct)

Step-by-step explanation:

I took the test!

The solution is,: A rectangular prism in which BA = 30 and h = 5 has a volume of 150 units^3; therefore, Shannon is correct

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

step 1

Find the area of the base of the rectangular pyramid

we know that:

The volume of the rectangular pyramid is equal to:

V = 1/3 * bh

where

B is the area of the base

H is the height of the pyramid

we have

V= 50

h = 5

substitute and solve for B

we get,

b= 30

step 2

Find the volume of the rectangular prism with the same base area and height

we know that

The volume of the rectangular prism is equal to

V = bh

we have

b = 30

h = 5

substitute

V = 30 * 5 = 150 unit^3

therefore

The rectangular prism has a volume that is three times the size of the given rectangular pyramid. Shannon is correct

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Answer:

22 cakculator is write answer

Answer:

QR & ST = 37

Step-by-step explanation:

Because this is a regular hexagon, all the sides are equal.

Thus, since the length of QR = the length of ST, we can set the equations for both sides equal to each other and solve for y:

[tex]3y+19=6y+1\\3y+18=6y\\18=3y\\6=y[/tex]

Now, we can plug in 6 for y into any of the two equations to find the length of both QR and ST:

[tex]QR=3(6)+19\\QR=18+19\\QR=37[/tex]