A ladder is leaning against a building so that the distance from the ground to the top of the ladder is 9 feet less than the length of the ladder. Find the length of the ladder if the distance from the bottom of the ladder to the building is 15 feet.

Answer:

4x+1

Step-by-step explanation:

Please see attached image.

Answer:

linear and lateral

Step-by-step explanation:

thsts it

Final answer:

A coordinate grid, also known as a Cartesian coordinate system, is a mechanism used in mathematics to define every point in a plane with a pair of numerical values indicating horizontal and vertical positions from an origin. Systems like UTM and SPC are derived from this concept, using a grid to simplify plotting and calculations on a plane surface.

Explanation:

A coordinate grid, or a Cartesian coordinate system, is a tool used in mathematics to specify each point uniquely in a plane by a pair of numerical coordinates. These are typically written as an ordered pair (x, y) where 'x' represents the horizontal displacement and 'y' represents the vertical displacement, both measured from a specific origin point. This system of geometry was developed by René Descartes, hence the name Cartesian.

For example, the origin of a coordinate system is the starting point where both x and y are zero, designated as (0,0). If we move to the right, x increases, and if we move up, y increases. Conversely, moving to the left decreases x and moving down decreases y. So, for instance, the point (3,4) is located 3 units to the right of the origin and 4 units above it.

Plane coordinate systems, like the Universal Transverse Mercator (UTM) and the State Plane Coordinate (SPC) systems, simplify calculations by using a grid pattern superimposed on a flattened representation of the Earth's surface, facilitating easier and more precise location plotting than spherical coordinate systems like latitude and longitude.

9514 1404 393

Answer:

  216 J

Step-by-step explanation:

The kinetic energy is given by ...

  KE = 1/2mv^2

  KE = (1/2)(3 kg)(12 m/s)^2 = 216 kg·m²/s² = 216 J

The kinetic energy of the toy is 216 joules.

__

Its potential energy depends on its height.

Answer:216 J Is the answer I just checked

Step-by-step explanation:

Answer:

90°

Step-by-step explanation:

By inscribed angle theorem:

[tex]m\angle STU = \frac{1}{2} \times 180 \degree = 90 \degree[/tex]

Answer:

See below.

Step-by-step explanation:

The 3 angles in a triangle add up to 180 degrees, so the sum of the other 2 angles is 180 - 35 = 145 degrees.

So, for example the other 2 angles could be 60 and 85 degrees.

Answer:

75° and 70°

25° and 120°

90° and 55°

Step-by-step explanation:

I got it right

Answer:

F. Jenny earned 492 points on 6 tests.

Jenny has the same average

math test score as Alisha i.e. 82.

Step-by-step explanation:

Points earned by Jenny = 492

no. of maths tests attempted by Jenny = 6

average maths test score = 492/6

=82

Answer:

110.000

Step-by-step explanation:

Selling at a loss of 5% means it was sold for 95% of its purchase value.

If 120.175 equals to 95% then 100%(the purchase value) is 126.500.

120.175/95*100 = 126.500 (plenty of other ways to calculate this, but this is one of the easiest)

So now we change to the dealer's perspective, he sold the car for 126.500 and for him that meant a 15% profit. If the purchase value is 100%, then the sale value is 115% (purchase value+15% profit)

Calculate the purchase value:

126.500/115*100 = 110.000

The dealer bought the car for 110.000, sold it for 126.500, so he made a profit of 16.500 (126.500-110.000) which is a 15% profit (15% of 110.000 is 16.500).

Answer:

n=7/3

Step-by-step explanation:

1 (n – 4) – 3 = 3 - (2n+3)

1. distribute the 1 on the left side and distribute the -1 on the right side

1n-4-3=3-2n-3

2. add like terms

1n-7=-2n

3. move n to one side and by itself

-7=-3n

4. divide -3 to get n alone. Both negatives cancel out each other

7/3=n

Step-by-step explanation:

[tex]1(n-4)-3=3-(2n+3)[/tex]

[tex]n-4-3=3-2n-3\\n+2n=3-3+3+4\\3n=7\\n=\frac{7}{3}[/tex]

Proof

[tex]1(n-4)-3=3-(2n+3)[/tex]

[tex]1(\frac{7}{3} -4)-3=3-[2(\frac{7}{3}) +3]\\1(\frac{7-12}{3} )-3=3-(\frac{14}{3} +3)\\1(\frac{-5}{3} )-3=3-(\frac{14+9}{3})\\\frac{-5}{3} -3=3-(\frac{23}{3})[/tex]

[tex]\frac{-5-9}{3} =\frac{9-23}{3} \\\frac{-14}{3} =\frac{-14}{3}[/tex]

A quadratic function whose zeros are 2 and 7 is [tex]f(x) = x^2 - 9x+14[/tex]

If the zeros of a quadratic function are a and b, the quadratic function will be given as:

f(x)  =  (x  -  a)(x  -  b)

For the function f(x) whose zeros are 2 and 7:

f(x)  =  (x  -  2)(x  -  7)

Expand the equation

[tex]f(x)=x^2-7x-2x+14\\\\f(x) = x^2 - 9x+14[/tex]

Therefore, a quadratic function whose zeros are 2 and 7 is [tex]f(x) = x^2 - 9x+14[/tex]

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Final answer:

A quadratic function with zeros at 2 and 7 can be constructed by multiplying (x - 2) and (x - 7), leading to the function f(x) = (x - 2)(x - 7). A constant 'a' scales the function, which, if not specified, can be assumed to be 1 for simplicity.

Explanation:

The question asks about constructing a quadratic function f with zeros at 2 and 7. In mathematics, a quadratic function is of the form f(x) = ax2 + bx + c, where a, b, and c are constants and a ≠ 0.

To construct a quadratic function with zeros 2 and 7, we utilize the fact that if 2 and 7 are zeros, the function must be divisible by (x - 2) and (x - 7).

Hence, f(x) can be written as f(x) = a(x - 2)(x - 7), where a is a non-zero constant that scales the function.

To determine a, more information about the function is needed, such as a specific value f(x) takes at a certain point.

In the absence of additional information, we can assume a = 1 for simplicity, which gives us the specific quadratic function f(x) = (x - 2)(x - 7).

This function will cross the x-axis at x = 2 and x = 7, making them its zeros.

Answer:

The bus travelled 60 miles in 1 hour.

Step-by-step explanation:

To solve this problem we need to calculate the average speed at which the bus travelled. This is given by the distance travelled divided by the time that they took to get there. So we have:

average speed = distance/time

average speed = 360/6

average speed = 60 miles/h

Therefore in 1 hour they travelled 60 miles.

Answer:

1) (a/3) - (b/2)

2) (m/3) + (5n/12)

3) (-5m/3) + (4x/3)

4) (4x/9) + (8y/9) - (z/3)

5) (-5a/8) + (-3b/8) + (-3c/2)

Step-by-step explanation:

1) 2a-3b divided by 6

(2a-3b)/6 = (2a/6) - (3b)/6 = (a/3) - (b/2)

2) 4m+5n divided by 12

(4m+5n)/12 = (4m/12) + (5n/12) = (m/3) + (5n/12)

3) 5m-4x divided by -3

(5m-4x)/(-3) = (-5m/3) + (4x/3)

4) 4x+8y-3z divided by 9

(4x+8y-3z)/9 = (4x/9) + (8y/9) - (3z/9) = (4x/9) + (8y/9) - (z/3)

5) 5a+3b+12c divided by -8

(5a+3b+12c)/(-8) = (-5a/8) + (-3b/8) + (-12c/8) = (-5a/8) + (-3b/8) + (-3c/2)

Answer:

D.) Step 6: student needed to add the b value.

Step-by-step explanation:

I got it wrong and it gave me the right answer, which is what i provided, D.

Answer: Step6

Step-by-step explanation:

Step-by-step explanation:

40° + 90° + 90° + angle ACB = 360°

220° + angle ACB = 360°

angle ACB = 360° - 220°

Therefore angle ACB = 140°

Hope it will help :)

Final answer:

To find angle ACB, determine angle AOB by subtracting the tangents' right angles and angle APB from 360 degrees, which results in 140 degrees. Then, using the Inscribed Angle Theorem, angle ACB is half the measure of angle AOB, yielding 70 degrees.

Explanation:

The student is asking how to find the angle ACB when given that PA and PB are tangents to a circle with centre O, and angle APB is 40 degrees. To find angle ACB, which is the angle at the circle subtended by the chord AB, we first determine the measure of angle AOB, which is central and subtended by AB as well. Since the tangents from a point outside a circle form a right angle with the radius at the point of contact, we have two right triangles OAP and OBP, each with an angle of 90 degrees. These right angles add to the given angle APB to form a full angle around point P which is 360 degrees. Knowing angle APB is 40 degrees, we can find angle AOB by subtracting the sum of the two right angles and angle APB from 360 degrees.

Angle AOB = 360 degrees - (90 degrees + 90 degrees + 40 degrees) = 360 degrees - 220 degrees = 140 degrees

Finally, since angle ACB is inscribed and angle AOB is central, both subtended by the same chord AB, angle ACB is half the measure of angle AOB by the Inscribed Angle Theorem. Therefore, angle ACB is 70 degrees.

Angle ACB = ½ * Angle AOB = ½ * 140 degrees = 70 degrees

Answer:

B. 3

Step-by-step explanation:

Answery

y= 2x+2

Step-by-step explanation:

Answer: you would expect it to flip about 150 times heads.

Step-by-step explanation: A coin has two sides. There's an equal chance for each side. So 50-50 chance.

300 divided by 2 is 150

(Sorry if it's not the best mathematical way to say it)

Answer:

738 cans.

Step-by-step explanation:

To calculate 82% of 900, take 0.82 *900. Your answer will be 738.

Answer:

738 cans

Step-by-step explanation:

900 x .82=738

To find the speed of the truck, start by assigning the speed of the train as 'x', then the truck's speed is 'x + 20'. Set up an equation based on the principle of time = distance/speed, make them equal to each other then solve for 'x'. The truck's speed will be 'x + 20'.

Let's call the speed of the freight train 'x' (in mph). We know from the question, that the loaded truck is traveling 20 mph faster than the train, so the truck's speed is 'x + 20' mph.

Given that the time it takes for the train to travel 160 miles is the same time it takes the truck to travel 240 miles, we can write an equation based on the principle that time equals distance divided by speed.

For the train, time = 160/x and for the truck, time = 240/(x+20). As both times are equal, we can write the equation as:

160/x = 240/(x + 20).

Solving this equation for 'x' will give us the speed of the freight train in mph. Then, by adding 20 to 'x', we can find the speed of the truck.

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Find the volume of the candle using the formula for volume of a cylinder:

V = PI x r^2 x h = 3.14 x 3.4^2 x 6 = 217.79 cubic cm. Round to 217.8

Find the volume of the block: V = l x w x h = 15 x 12 x 18 = 3,240 cubic cm.

Now divide the volume of the block by the volume of a candle:

3240 / 217.8 = 14.88

Round to the nearest tenth = 14.9 candles.

Number of cylindrical candles after melting the rectangular block  is 14.9.

" Cylinder is a three dimensional surface formed by two parallel lines and two parallel circular base."

" Volume is the total amount of space occupied by any 3 dimensional body."

Formula used

Volume of a cylinder = π r²h

Volume of a rectangular block = length × width ×height

According to the question,

Height of a cylinder = 6cm

radius of cylinder = 3.4cm

Length of a block = 15cm

width of a block = 12cm

height of a block = 18cm

Volume of a cylinder = [tex]3.14[/tex]× [tex](3.4)^{2}[/tex]×[tex]6[/tex]

                                  =217.8 cubic cm

Volume of rectangular block = [tex]15[/tex] × [tex]12[/tex] × [tex]18[/tex]

                                                 = 3240 cubic cm

Number of candles = Volume of rectangular block / volume of cylinder

                                 = [tex]\frac{3240}{217.8}[/tex]

                                 = 14.88

                                 = 14.9 (nearest tenth)

Hence the Number of cylindrical candles after melting the rectangular block  is 14.9.

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Answer:

The car was moving approximately at a speed of 37.74 miles per hour.

Step-by-step explanation:

We are given the following in the question:

The stopping distance of a car is given by

[tex]d = 0.05r(r + 2)[/tex]

where d is the stopping distance in feet and r is speed of the car in miles per hour.

The stopping distance is 75 feet, we have to find the speed of the car,

Putting d = 75 in the equation, we get,

[tex]75 = 0.05r(r + 2)\\r^2 + 2r = 1500\\r^2 + 2r-1500 = 0\\\\r =\dfrac{-2\pm \sqrt{4-(4)(1)(-1500)}}{2}\\\\r\approx -39.74,37.74[/tex]

Thus, the car was moving approximately at a speed of 37.74 miles per hour.

Answer:

7

Step-by-step explanation:

Answer:

[tex]\sin 253.740^{\textdegree} = -\frac{24}{25} = -0.960[/tex]

[tex]\cos 253.740^{\textdegree} = -\frac{7}{25} = -0.280[/tex]

[tex]\tan 253.340^{\textdegree} = \frac{24}{7} = 3.429[/tex]

Step-by-step explanation:

The point is in the 3rd Quadrant of the Cartesian Plane. Therefore, angle must be between 180° and 270° with respect to the horizontal.

The angle is:

[tex]\theta = 180^{\textdegree}+\tan^{-1}\left(\frac{24}{7} \right)[/tex]

[tex]\theta \approx 253.740^{\textdegree}[/tex]

The values of the trigonometrical functions are computed below:

[tex]\sin 253.740^{\textdegree} = -\frac{24}{25} = -0.960[/tex]

[tex]\cos 253.740^{\textdegree} = -\frac{7}{25} = -0.280[/tex]

[tex]\tan 253.340^{\textdegree} = \frac{24}{7} = 3.429[/tex]

Answer:

-18

Step-by-step explanation:

b is where the line crosses the y-axis, or where x=0. Since it starts at -18, then that would be the b.

Answer:

a radius

x-h

y-k

x-h, y-k

Step-by-step explanation:

The standard form of the circle is given by ( x - h )² + ( y - k )² = r²

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

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

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the equation of circle be C

Let the center of the circle be represented as A ( h , k )

Now , the radius of the circle is = r units

And , standard form of a circle is

( x - h )² + ( y - k )² = r²

when it is a unit circle , the center is at ( 0 , 0 )

S0 , the equation of circle is x² + y² = r²

Hence , the standard form of circle is ( x - h )² + ( y - k )² = r²

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Answer:

15 m

Step-by-step explanation:

25² = 20² + b²

625 = 400 + b²

b² = 225

b = 15

it is 15 hope this helped and good luck...

Answer:

65%

Step-by-step explanation:

Divide 13 by 20:

0.65

Times 100:

65

So 65%

Answer:

rate of motorboat: b

rate of current: c

So the rate the boat travels upstream is $b - c$, and the rate it travels downstream is $b + c$

Step-by-step explanation:

d = rt

200 = (b - c)\cdot 5

200 = (b + c)\cdot 4

b - c = 40

b + c = 50

Adding these equations, we get:

2b = 90

b = 45

So

c = 50 - 45 = 5

Therefore the rate of the boat is 45kph, and the rate of the current is 5kph

Hope this helps :)

Final answer:

The boat has a speed of 45 mph in still water, and the current runs at 5 mph. By using the given times and distances for upstream and downstream travel, we can set up equations to solve for the boat's speed and the current's speed.

Explanation:

To find the rate of the boat in still water and the rate of the current, let's denote the boat's speed in still water as b and the speed of the current as c. When the boat goes upstream, its effective speed is b - c, and when it goes downstream, its effective speed is b + c. We can translate this into two equations based on the information given:

(b - c) × 5 hours = 200 miles (upstream)

(b + c) × 4 hours = 200 miles (downstream)

By dividing the distance by the time, we can solve for the effective speeds upstream and downstream.

b - c = 200 miles / 5 hours = 40 mph

b + c = 200 miles / 4 hours = 50 mph

Add these two equations:

2b = 90 mph

b = 45 mph (boat's speed in still water)

Next, subtract the first equation from the second:

2c = 10 mph

c = 5 mph (current's speed)

So, the boat has a speed of 45 mph in still water, and the current has a speed of 5 mph.

Answer:

2

Step-by-step explanation:

There are 120 different ways to assign 6 weapons to 3 soldiers, each receiving one weapon, calculated using permutations.

Calculating Permutations for Weapons Assignment

To determine how many different ways 3 soldiers can be assigned weapons from a selection of 6, we need to calculate the permutations of 6 objects taken 3 at a time. We use the permutation formula, which is expressed as P(n, k) = n! / (n-k)!, where n is the total number of items, and k is the number of items to choose. In this case, n is 6 (the total number of weapons), and k is 3 (the total number of soldiers).

We calculate the permutations as follows:

6! / (6-3)! = (6  * 5 * 4) / (3 * 2 * 1) = 120 ways.

Therefore, there are 120 different ways to assign the weapons to the soldiers, with each soldier getting one weapon.

Answer:

By dividing the top number by the bottom.

Step-by-step explanation:

ummmmm

To convert a fraction into a decimal, divide the fraction's numerator by its denominator. Multiplying a decimal by 100 converts it to a percent, and dividing a percent by 100 converts it back into a decimal. This process is used to manipulate numerical values for various mathematical applications.

Converting a Fraction to a Decimal

To convert a fraction into a decimal, you simply divide the numerator (the top number) by the denominator (the bottom number). For example, to convert 3/4 to a decimal, you divide 3 by 4, which equals 0.75. If the fraction is not in simplest form, you may first simplify it before dividing. This is a basic mathematical skill that you will use in many areas of math.

To convert a decimal to a percent, you multiply the decimal by 100. For instance, 0.75 multiplied by 100 equals 75%, because you are essentially finding how many 'parts out of 100' are present in the decimal.

In the case of converting percents, to turn a percent into a decimal, you divide by 100. So, taking 75% and dividing by 100 would give you 0.75, which is the original decimal we started with.

Another example is converting 0.0479 into a decimal that's a number between 1 and 10. To do this, we would move the decimal point to the right two places to get 4.79, as specified by the conversion factor which helps in adjusting units or scaling numbers without changing the value.

Answer:

ST = 12 units

Step-by-step explanation:

Δ RAS and Δ TES are similar triangles, thus the ratios of corresponding sides are equal, that is, noting that SR = 21 - ST, thus

[tex]\frac{ST}{SR}[/tex] = [tex]\frac{TE}{AR}[/tex] substitute values

[tex]\frac{ST}{21-ST}[/tex] = [tex]\frac{8}{6}[/tex] ( cross- multiply )

6ST = 8(21 - ST)

6ST = 168 - 8ST ( add 8ST to both sides )

14ST = 168 ( divide both sides by 14 )

ST = 12