a 10-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 8feet from the base of the building. How high up does the ladder reach?

Answer:

1. 15

2. 15

3. 13

4. 11

5. 14

6. 11

7. 18

8. 19

9. 18

10. 14

Step-by-step explanation:

The measures of the angles of the triangles are

The measure of ∠B = 80.3°

The measure of ∠C = 59.7°

The length of side AB = 20.2 units

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

Now , the measure of side AC = 23

The measure of side BC = 15

The measure of ∠A = 40°

From the law of sines , we get

( sin A ) / a = ( sin B ) / b = ( sin C ) / c

Substitute the value of A and a in the equation , we get

sin ( 40 )° / 15 = sin B / 23

On simplifying the equation , we get

sin B = ( 23/15 ) x sin ( 40 )°

Now , m∠B = 80.27°

So , the measure of angle ∠B = 80.3°

And ,

The interior angles of a triangle is 180°

So , The measure of angle ∠C = 180° - ( 80.3° + 40° )

On simplifying the equation , we get

The measure of angle ∠C = 59.7°

Now ,

From the law of cosines , c² = a² + b² - 2ab ( cos C )

Substitute the value of a , b and cos C in the equation , we get

c² = 15² + 23² - 2 ( 15 ) ( 23 ) cos ( 59.7 )°

On simplifying the equation , we get

c² = 225 + 529 - 348.12363

c² = 405.87

Taking square roots on both sides of the equation , we get

c = 20.156

c = 20.2 units

Therefore, the measure of side AB = 20.2 units

Hence , the measures angles of triangle is solved

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The number of miles the taxicab traveled is 12.

The area of mathematics known as algebra aids in the representation of circumstances or problems into mathematical expressions. To create a meaningful mathematical expression, it takes variables like x, y, and z together with mathematical operations like addition, subtraction, multiplication, and division.

Given that,

The fixed charges = $ 2.30

Additional charges per miles = $ 0.80,

Thus, the additional charges for x number of miles = $ 0.80x

So, the total charges for x number of miles = Fixed charges + additional charges

=> 2.30 + 0.80x

According to the question,

2.30 + 0.80x = 11.90 (this is the required equation)

Subtracting 2.30 from both sides,

0.80x = 9.6

Dividing both sides by 0.80

x = 12

Hence, the taxicab traveled 12 miles.

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Answer:

y = - 3

Step-by-step explanation:

Call the line y = a + bx (d)

Since d go through (-7;-3) so -7 = a - 3b (1)

Since d go through (8;-3) so 8 = a - 3b (2)

From (1) and (2), we have equations: [tex]\left \{ {{a - 3b = -7} \atop {a - 3b = 8}} \right.[/tex]

Solve the equations, we have [tex]\left \{ {{a = 0} \atop {b = -3}} \right.[/tex]

When two inner angles are stated as 61° and 52° in the sixth figure, x and y are both set to 67°.

A circle is created in the plane by each point that is a specific distance from another point (center). Thus, it is a curve made up of points that are separated from one another by a defined distance in the plane. Additionally, it is rotationally symmetric about the center at every angle. Every pair of points in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle. Additionally, it is rotationally symmetric about the center at every angle.

given

in 6th figure

61° + 52° + x = 180° ( sum of exterior angle )

113° + x = 180°

x = 67°

y = 67°

When two inner angles are stated as 61° and 52° in the sixth figure, x and y are both set to 67°.

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Answer:

11√12

Step-by-step explanation:

√12 = 2√3

2√12

= 2 * 2√3

= 4√3

√48 = 4√3

3√48

= 3 * 4√12

= 12√12

√75 = 5√3

2√12 + 3√48 - √75

= 4√3 + 12√12 - 5√12

= 16√12 - 5√12

= 11√12

Answer: My answer is 11√3

Step-by-step explanation:

Pull terms out from under the radical, assuming positive real numbers.

Exact Form:

11√3

Decimal Form:

19.05255888…

The system of equations is inconsistent for any value of k.

If we subtract the first equation from the second one, we get 0 = 12x, which is inconsistent no matter what value k is. This means that the system of equations has no solution and is therefore inconsistent.

The system of equations KX + 3y = K + 2 and 12x + Ky = K is inconsistent for any value of k. This is because when we subtract the first equation from the second one, we get 0 = 12x, which is an inconsistent equation no matter what value k is. This means that the system of equations has no solution and is therefore inconsistent. No matter what value we assign to k, the equations cannot be solved simultaneously and so the system of equations is inconsistent.

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The third side of a triangle, the following formula can be used c² = a² + b² - 2abcos(C)

To calculate the third side of a triangle, first find the lengths of the other two sides and the angle opposite the third side. Then plug these values into the formula above and solve for c.

Where c is the third side of the triangle, a and b are the other two sides, and C is the angle between them.

For example, for a triangle with two sides of length 4 and 6, and an angle between them of 75 degrees, the formula would look like this:

c² = 42 + 62 - 2(4)(6)cos(75)

Solving for c yields a third side length of 8.4.

To solve for c, first square the two side lengths: 42 = 16 and 62 = 36. Then, multiply the two side lengths together and multiply by the cosine of the angle between them: 2(4)(6)cos(75) = 43.9. Finally, add the two squared values together and subtract the result of the multiplication: 16 + 36 - 43.9 = 8.1. Then, take the square root of this result to get the length of the third side: √8.1 = 8.4.

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According to the compound interest formula, the population is 5 years is 422,385.

The term compound interest in math is defined as the interest calculated on the principal and the interest accumulated over the previous period.

Here we have given that the population of 210,000 people is increasing by 15% each year.

And then while looking into the given question, we have identified that the value of

interest rate = 15%

principal count = 210,000

time period = 5

Here we have to convert R as a percent to r as a decimal, then we get

=> r = R/100

=> r = 15/100

=> r = 0.15 rate per year,

Now, we have to solve the equation for A

[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]

Apply the values on it , then we get,

[tex]A = 210,000.00(1 + \frac{0.15}{1} )^{(1)(5)}[/tex]

When we simplify this one then we get

[tex]A = 210,000.00(1 + 0.15)^5[/tex]

Therefore, the value of A is 422,385.

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Answer: 7 13/15

Step-by-step explanation:

First of, you have to get your common denominator, as it's impossible without one.

The closest common denominator is 15, and it will ask you for a simplified version.

Multiply the 2/3 in 5 2/3 by 5 on both sides to get 5 10/15

Multiply the 1/5 in 2 1/5 by 3 on both sides to get 2 3/15

Then add up your sum.

5 10/15+2 3/15=7 13/15

Answer:

7 13/15

Step-by-step explanation:

5 2/3+2 1/5

We need to get a common denominator for the fraction

3*5 = 15

2/3 *5/5 = 10/15

1/5 * 3/3 = 3/15

5 10/15 + 2 3/15 = 7 13/15

Yes, a triangle whose sides have lengths 10.2 cm, 5.8 cm and 4.5 cm is possible.

As we know if these sides form a triangle, then

the sum of two sides > the third side

Now, the sum of 10.2 cm and 5.8 cm = 16 cm > 4.5 cm

The sum of 5.8 cm and 4.5 cm = 10.3 cm > 10.2 cm

The sum of 10.2 cm and 4.5 cm = 14.7 cm > 5.8 cm

Here the sum of the two sides is greater than the third side in all three cases.

Therefore a triangle whose sides are 10.2 cm, 5.8 cm and 4.5 cm is possible.

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Answer: The answer is $1,317.50

Step-by-step explanation:

First, Find how much they earn in the goods sale.

Make $1,700, their goal to earn, into 1,700/1 and set it to multiply that by 2/5, the fractional amount of money earnt at the goods sale proportional to how much they have to earn.

Simplify that by crossing 1,700 and 5 into a 340 and 1.

Multiply 340/1 by 2/1 to get 680/1.

Make that into a whole number ($680) to show how much money earnt from the goods sale.

Secondly, find how much money they earn by the Bingo Night

Make 1,700, like last time, into 1,700/1 and set it to multiply 3/8, the fractional amount of money earnt from the Bingo Night proportional to how much they have to earn

You can't simplify, so just multiply the amount.

If you multiply, you will get 5,100/8.

Divide 5,100 by 8 (the divisor by the dividend).

Make sure to also add the 0 after the tenths place after you get your quotient, which is supposed to be 637.5 (or $637.50)

Lastly, You have to add them up.

Add $637.50+$680.

You shall get $1,317.50

It divides by three. According to the law of divisibility for three, a number is fully divisible by three if its digit sum is likewise divisible by three.

The divisibility rule is a clear and useful method for determining if an integer is divisible by a given set of divisors without actually doing division, sometimes simply looking at the integer's digits. The divisibility test allows you to rapidly determine if a given integer can be divided by a specified divisor without actually doing the division process. The quotient must be an integer and the remainder must be zero when dividing two numbers precisely.

here  

add all the numbers,

326 = 3+2+6 = 11

so it is not divisible by 3

327 = 3+ 2 + 7 = 12

so it is divisible by 3

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Answer:

Step-by-step explanation:

9 - 3 = 6

6/10 = 3/5

Answer:

6/10 and/or 3/5(this is the answer simplified

Step-by-step explanation:

Subtract: 9/10 - 3/10

= 9 - 3/10

= 6/10

= 2 · 3/ 2 · 5

= 3/5

It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(10, 10) = 10. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 10 × 10 = 100. In the following intermediate step, cancel by a common factor of 2 gives 3/5. In other words - nine tenths minus three tenths is three fifths.

Answer:

NEED:

WANT:

Step-by-step explanation:

Right on Plato! <3

Have a wonderful day!

The needs listed are tuition and fees and staple foods, while the wants are a vacation, a Lamborghini, and a lavish wedding.

The listed needs and wants reflect different aspects of a person's life and priorities. "Tuition and Fees" and "Staple Foods" are necessities that are essential for a person's survival and well-being.

On the other hand, "Vacation," "Lamborghini," and "Lavish Wedding" are desires that are often seen as luxury items or experiences. While having wants is normal and human, it is important to understand that not all wants can be fulfilled, and it is equally important to prioritize needs over wants. Having a balanced approach to spending, budgeting, and financial planning can help ensure that both needs and wants can be met in a sustainable manner.

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Answer:

Step-by-step explanation:

analyze the graph, we found ∠1=∠5,∠2=∠6,

one.because ∠5+∠6=180, so ∠2=∠6=180-∠5=180-55=125

two.∠3=∠2=125

three.∠8=∠5=55

four.∠12=∠9=80

five.∠14=∠10=180-∠9=100

so, the three options are ∠2,∠8,∠14

Answer:

D)  (6.6, 7.4)

Step-by-step explanation:

Begin by finding the margin of error based on the given information.

[tex]\boxed{\begin{minipage}{7.3cm}\underline{Margin of Error formula}\\\\$\textsf{Margin of Error}= Z \times \dfrac{S}{\sqrt{n}}$\\\\where:\\\phantom{ww} $\bullet$ $Z =$ $Z$ score\\\phantom{ww} $\bullet$ $S =$ Standard Deviation of a population\\\phantom{ww} $\bullet$ $n =$ Sample Size\\\end{minipage}}[/tex]

Given:

The z-score for 95% confidence level is 1.96.

Therefore, to find the margin of error, substitute the values into the formula:

[tex]\implies \textsf{Margin of Error}= 1.96 \times \dfrac{1.3}{\sqrt{50}}[/tex]

[tex]\implies \textsf{Margin of Error}=0.360341...[/tex]

To find a reasonable range for the true mean number of hours a teenage spend on their phone, subtract and add the margin of error to the given mean of 7 hours:

[tex]\begin{aligned}\implies \textsf{Lower bound}&=7-0.360341...\\&=6.63965...\\&=6.6\;\; \sf (1\;d.p.)\end{aligned}[/tex]

[tex]\begin{aligned}\implies \textsf{Upper bound}&=7+0.360341...\\&=7.360341...\\&=7.4\;\; \sf (1\;d.p.)\end{aligned}[/tex]

Therefore, the reasonable range for the true mean is:

1. The Riemann Hypothesis Equation

The formula for a directed line segment is A = (x2 - x1, y2 - y1). It is a vector equation, meaning that it describes the direction and magnitude of a line segment, rather than its endpoint coordinates.  

A directed line segment is a line segment with a starting point and an ending point, where the direction of the line can be described in terms of its magnitude and direction. To calculate the directed line segment, first calculate the difference between the x-coordinates of the start and end points, and then calculate the difference between the y-coordinates of the start and end points. The result is the vector A, which describes the magnitude and direction of the line segment.

For example, consider a line segment with start point (1, 2) and end point (4, 6). To calculate the directed line segment, first calculate the difference between the x-coordinates of the start and end points (4 - 1 = 3). Then, calculate the difference between the y-coordinates of the start and end points (6 - 2 = 4). The result is the vector A = (3, 4). This vector describes the magnitude and direction of the line segment, with the magnitude being the length of the line segment, and the direction being the direction from the start point to the end point.

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[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{-4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~-8 - 1~~)^2 + (~~-4 - (-6)~~)^2} \implies d=\sqrt{(-8 -1)^2 + (-4 +6)^2} \\\\\\ d=\sqrt{( -9 )^2 + ( 2 )^2} \implies d=\sqrt{ 81 + 4 } \implies d=\sqrt{ 85 }\implies d\approx 9.22[/tex]

Answer:

tree = 8

snowman = 1

deer = 4

snowflake = 4

Step-by-step explanation:

say t = tree, s = snowman, d = deer, f = snowflake

1. For 2d + f, since you know d is equal to f, replace the snowflake with a deer, turning the equation into 3d = 12. To find the value of d divide by 3 on both sides. This will result in 4. So, the value of deer = 4.

2. Now, find the value of the snowman using the value of the deer.

4-3 = 1. This means the value of the snowman = 1.

3. Plug in the value of the snowman into 2t + s = 17.

     2t + 1 = 17

  Subtract on both sides to get 2t by itself and then simplify

      2t = 17 -1 --> 2t = 16

  Divide by 2 on both sides to find the value of the tree

      2t/2 = 16/2 --> t = 8

Answer:

One way is to make a factor tree. She below for examples.

Step-by-step explanation:

Answer:

You basically just count jumps of that number

An equation in slope-intercept form of the amount of money saved after x weeks is y=21x+213.

The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.

The standard form of the slope intercept form is y=mx+c.

Given that, after 17 weeks, you have $570, and after 29 weeks, you have $822.

Here, (17, 570) and (29, 822)

Substitute (x₁, y₁)=(17, 570) and (x₂, y₂)=(29, 822) in m=(y₂-y₁)/(x₂-x₁)

= (822-570)/(29-17)

= 252/12

= 21

Substitute, m=21 and (x, y)=(17, 570) in y=mx+c, we get

570=21×17+c

570=357+c

c=213

Substitute, m=21 and c=213 in y=mx+c, we get

y=21x+213

Therefore, an equation in slope-intercept form of the amount of money saved after x weeks is y=21x+213.

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The equations which show direct proportion between a and b are:

a=2b and a=b/2.

Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value. It is represented by the proportional symbol, ∝. In fact, the same symbol is used to represent inversely proportional, the matter of the fact that the other quantity is inverted here.

Example: x and y are two quantities or variables which are linked with each other directly, then we can say x ∝ y. When we remove the proportionality symbol, the ratio of x and y becomes equal to a constant, such as x/y = C, where C is a constant.

Given, two variables a and b

If two variables a and b are in direct proportion

then,

a/b = constant.

1. a = b²

a/b = b

which is not constant

⇒ a is not in direct proportion with b.

2. a = 2b

a/b = 2

which is constant

⇒a is in direct proportion with b.

3. a = b/2

a/b = 1/2

which is constant

⇒ a is in direct proportion with b.

4. a=b+2

a/b = 1+2/b

which is not constant

⇒ a is not in direct proportion with b.

5. a = 2/b

ab = 2

⇒a is inversely proportional to b.

Hence, In equation a=2b and a=b/2, a is directly proportional to b.

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According to a recent study of 35 students,Population-wide, there was a 2.8-hour standard deviation. 16.60 is the population mean's 95% confidence interval.

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Answer:

6 tubes of lip balm

Step-by-step explanation:

We can start solving this problem by isolating the variable x.

Given the equation 1.5x + 2.5y = 9, and we know that y = 0 (because we're not buying any bottles of hand sanitizer), we can substitute this into the equation:

1.5x + 2.5(0) = 9

Simplifying this, we get:

1.5x = 9

To solve for x, we can divide both sides of the equation by 1.5:

x = 9/1.5

x = 6

So we can buy 6 tubes of lip balm if we do not buy any bottles of hand sanitizer

Answer:

[tex]108\pi[/tex] or approx. [tex]339.3 m^{2}[/tex]

Step-by-step explanation:

The question asks us to find the total surface area of the given hemisphere. The question gave us the formula for total surface area of a sphere, [tex]SA_{tot} =4\pi r^2[/tex]. But we need it for a hemisphere, so multiply the equation by [tex]\frac{1}{2}[/tex].

[tex]SA} = (\frac{1}{2}) 4\pi r^2[/tex] => [tex]SA} =2\pi r^{2}[/tex]

We also need the area of the base, which is circle. [tex]A_{circle}=\pi r^{2}[/tex].

Now add these equations together to get our equation.

[tex]SA_{tot} =2\pi r^2 +\pi r^{2}[/tex] => [tex]SA_{tot} =3\pi r^2[/tex]

Now we have the proper equation for total surface area of a hemisphere, [tex]SA_{tot} =3\pi r^{2}[/tex]. Plug in the value of [tex]r[/tex] which is given in the problem, [tex]r=6m[/tex].

=> [tex]SA_{tot} =3\pi (6)^{2}[/tex] => [tex]SA_{tot} =3\pi (36)[/tex] => [tex]SA_{tot} =108\pi m^{2}[/tex] or approx. [tex]339.3 m^{2}[/tex]

Answer: 12 cups of applesauce

Step-by-step explanation:

Let l be the length of the classroom in feet, and w be the width of the classroom in feet. We know that l + 5 = w and l * w = 84.

We can use these two equations to solve for the length and width of the classroom.

First, we can solve the second equation for l:

l = 84 / w

Substituting this expression for l into the first equation gives us:

84 / w + 5 = w

Expanding the left side of the equation gives us:

84 / w + 5 = w

84 / w = w - 5

84 = w^2 - 5w

w^2 - 5w - 84 = 0

This is a quadratic equation that we can solve using the quadratic formula:

w = (5 + sqrt(5^2 - 4 * 1 * -84)) / 2 * 1

= (5 + sqrt(25 + 336)) / 2

= (5 + sqrt(361)) / 2

= (5 + 19) / 2

= 24 / 2

= 12

Now that we know the value of w, we can substitute it back into the equation l = 84 / w to find the value of l:

l = 84 / 12

= 7

Therefore, the dimensions of the classroom are 7 feet by 12 feet.