Find x. Is the triangle equilateral, isosceles, or scalene

The required percentage of the new punch is 62.5. Option C is correct.

Given that,
Four cups of pure water are added to a 20-cup bowl of punch that is 75% juice.

here,
The quantity of water added = 4 cups
The initial quantity of water = 20 * 25/100 = 5 cups
Now, quantity of punch = 4 + 20 = 24 cups
The initial composition of juice is 75% intially
Quantity of juice initally = 20 * 75/100 = 15 cups
Now, the composition of juice after adding 4 cups of water,
= 15 / 24*100
= 62.5%

Thus. the required percentage of the new punch is 62.5. Option C is correct.

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Answer:

The correct option is "C" or 62.5%

Answer:

draw a line trough (2,3) and (0, 2)

Step-by-step explanation:

f(x)=(3/2)x+2

so 3/2 is your slope  and 2 is your y coordinate of y-intercept

pick any point to start for example (0, 0) and go slope=rise/run=3/2 and you will end-up at (2,3)

now you have a point (2,3) and a second the y-intercept (0,2)

draw a line trough those points

Step-by-step explanation:

The cube have 6 sides.

The 2 sides are base surface and the other 4 are lateral surface.

A=4L

4A=4❨4L)

4A=16L

4A=16(2 3/4)

4A=16(11/4)

4A=4(11)

4A=44

so the lateral surface is 44

Answer:

D) AAA

Step-by-step explanation:

Answer:

C: ratio of the horizontal change to the vertical change of a line

Step-by-step explanation:

A and B are correct.

C is incorrect.

Answer:

x^2 - 10x + 9

Step-by-step explanation:

Zeros would be 9 and 1, so the equation would be (x-9)(x-1), and multiplying with FOIL gives us x squared -10x+9

Answer: x= 1.20833

The way it was written was a little confusing but hope this helps, This may be wrong just re write it for me and it should be correct next time.

Step-by-step explanation:

Step 1: Make parentheses

( 3x - 2 ) 4 ( -2x - 5 ) 3 = ( 1 + x ) 6

Step 2: Solve parentheses ( Multiplication and division first )

(4 * 3x = 12x) - (4 * 2 = 8) -> 12x - 8

(-2x * 3 = -6x) - (3 * 5 = 15) -> -6x - 15

(6 * 1 = 6) + (6 * x = 6x) -> 6 + 6x

New and improved equation:

-12x - 8 - 6x  - 15 = 6 + 6x

Step 3: add like terms

-12x - 6x = -18x

-8 - 15 = -23 so...

-18x - 23 = 6 + 6x

Step 4: solve it

-18x - 23 = 6 + 6x

               + 23

-18x = 29 + 6x

-6x

-24x = 29

x= 1.20833

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Answer:

dumb dumb

Step-by-step explanation:

Answer:

HURRY

Step-by-step explanation:

The value of the other angle will be 40°.

It should be noted that the value of the angle on a straight line equals to 180°.

In this case, the adjacent angles (two angles that share a common side and vertex) form a straight

angle and one of the angles measures 140°.

The value of the other angle will be:

= 180° - 140°

= 40°

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Answer:

Step-by-step explanation:

-Start by distributing the 2, -2(3m+1/2).

-Getting -6m-1, your equation should look like -40-6m-1=7m-2

-Combine -40 and -1 to get -41, and then add the -6m to the other side.

-The equation should look like -41=13m-2. Add the 2 to the -41 to get -39.

-Now, we have -39=13m. divide both sides by 13 to get m=-3.

Answer:

$30

Step-by-step explanation:

To find the cost, plug in 10 for x, then simplify

1.5x + 15

1.5(10) + 15

= 30

So, it will cost Johnny $30 to download 10 songs

The total amount of money that Johnny will have to pay is f(10) = 30.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Given is that it costs Johnny $15 a month plus $1.50 per song to download music. This situation is represented by the expression →

1.5(x) + 15.

The expression is given by -

f(x) = 1.5(x) + 15

where [x] is the number of songs downloaded.

For [x] = 10 songs, the total amount of money that Johnny will have to pay is -

f(10) = 1.5 x 10 + 15

f(10) = 15 + 15

f(10) = 30

Therefore, the total amount of money that Johnny will have to pay is f(10) = 30.

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Answer:

80 degrees

Step-by-step explanation:

angle c=50

this is an isoceles triangle in which both base angles are same

so, angle e=50

now we will use angle sum.property which states that the sum of all the interior angles of a triangle is equal to 180

so, 50+50+angle d=180

100 + angle d = 180

angle d =180-100

angle d = 80 degrees

To determine the percentage of times the machine will dispense more than 7.1 oz of coffee, we need to calculate the z-score and find the corresponding area under the normal distribution curve.

The z-score is calculated using the formula:

z = (x - μ) / σ

where x is the value we're interested in (7.1 oz), μ is the mean (7.6 oz), and σ is the standard deviation (0.5 oz).

Let's calculate the z-score:

z = (7.1 - 7.6) / 0.5

z = -0.5 / 0.5

z = -1

Now we need to find the area under the normal distribution curve for a z-score of -1. We can use a standard normal distribution table or a statistical calculator to find this area.

The area corresponds to the probability that the machine will dispense more than 7.1 oz.

Using a standard normal distribution table, we can find that the area to the left of z = -1 is approximately 0.1587. Since we're interested in the area to the right (more than 7.1 oz), we subtract this value from 1:

P(X > 7.1) = 1 - 0.1587

P(X > 7.1) ≈ 0.8413

Therefore, the vending machine will dispense more than 7.1 oz approximately 84.13% of the time.

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Answer:

$38.97

Step-by-step explanation:

100% - 10% = 90% = 0.9

$40 × 0.9 = $36

100% + 8.25% = 108.25% = 1.0825

$36 × 1.0825 = $38.97

On solving the provided question, we can say that from the graphs three of the four vertices of a quadrilateral the vertex will be (-5, -1), (-3,1), (-3. 2) and (5,5).

Mathematicians utilize graphs to visually express or chart data or values in a rational order. Usually, a graph point will show the link between two or more objects. A graph is a non-linear database structure composed of nodes, also known as vertices, and edges. The nodes, sometimes referred to as vertices, should be joined. In this graph, the vertex numbers are 1, 2, 3, and 5, while the edge numbers are 1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Graphical depictions of exponential development in statistics charts, such as bar charts, pie charts, and line graphs. Three of the four vertices of a quadrilateral on a logarithmic graph will be (-5, -1), (-3, 1), (-3. 2), and (-3. 3) respectively (5,5).

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The function that represents the total cost f(x) to send a letter that is x ounces can be calculated as follows:

$$f(x) = \begin{cases} 0.5 & \text{if } x = 1\\ 0.5 + 0.42(x-1) & \text{if } x > 1\end{cases}$$

Therefore, the correct options are:a) $f(x) = 0.5 + 0.42(x-1)$b) $f(x) = 0.5$

The total cost to send a letter that is 1 ounce is $0.50, and the total cost to send a letter that is 3 ounces is $0.92. Since the postal service calculates the weight to the whole ounce, if we send a 2-ounce letter, we can consider it as sending two 1-ounce letters.

Therefore, the total cost of sending a 2-ounce letter will be twice the cost of sending a 1-ounce letter.

Let f(x) be the total cost to send a letter that is x ounces.

Then,f(1) = 0.50f(2) = 2f(1) = 2(0.50) = 1.00f(3) = f(2) + 0.42 = 1.00 + 0.42 = 1.42

Hence, we can represent the function as follows:

$$f(x) = \begin{cases} 0.5 & \text{if } x = 1\\ 0.5 + 0.42(x-1) & \text{if } x > 1\end{cases}$$

Therefore, the correct options are:a) $f(x) = 0.5 + 0.42(x-1)$b) $f(x) = 0.5$

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Original price: x

36% of the original price: $223.20

Then, taking the percentage of the original price:

The minimum cost of the container is $576, and the dimensions that minimize the cost are a width of 2 meters, length of 4 meters, and height of 2 meters.

To minimize the cost, we need to find the dimensions of the container that minimize the total cost, taking into account the cost of the base, sides, and lid.

Let's start by defining the dimensions of the rectangular container:

Let the width of the base be "w" meters.

The length of the base will be twice the width, so the length is "2w" meters.

The height of the container is "h" meters.

The volume of the container is given as 16 m³, so we can write the equation:

Volume = Length × Width × Height

16 = 2w × w × h

16 = 2w²h

w²h = 8 ----(Equation 1)

Now, let's find the cost of the base, sides, and lid.

Cost of the base:

The base is a rectangle with dimensions of length = 2w and width = w.

Area of the base = length × width

Area of the base = (2w) × w = 2w²

Cost of the base = Area of the base × Cost per m² = 2w² × $8 = 16w²

Cost of the sides and lid:

The container has two sides with dimensions of length = 2w and height = h.

The container has two sides with dimensions of width = w and height = h.

The container has a lid with dimensions of length = 2w and width = w.

Area of each side = length × height = 2w × h = 2wh

Area of each side = width × height = w × h

Area of the lid = length × width = 2w × w = 2w²

Total area of the sides and lid = 2(2wh) + 2(wh) + 2w² = 4wh + 2wh + 2w² = 6wh + 2w²

Cost of the sides and lid = Total area × Cost per m² = (6wh + 2w²) × $16 = 96wh + 32w²

Now, we need to express the cost in terms of one variable, either w or h, so we can find the minimum value. Since Equation 1 relates w, h, and the volume, we can express h in terms of w.

From Equation 1:

w²h = 8

h = 8/w²

Now, substitute h in the cost equation:

Cost = 16w² (cost of the base) + (96wh + 32w²) (cost of the sides and lid)

Cost = 16w² + 96w(8/w²) + 32w²

Cost = 16w² + 768/w + 32w²

Cost = 48w² + 768/w ----(Equation 2)

To find the minimum cost, we differentiate Equation 2 with respect to w and set it equal to zero:

d(Cost)/dw = 96w - 768/w² = 0

96w = 768/w²

w³ = 8

Taking the cube root of both sides:

w = 2

Substituting w = 2 back into Equation 1:

w²h = 8

(2)²h = 8

4h = 8

h = 2

Therefore, the dimensions of the container that minimize the cost are:

Width (w) = 2 meters

Length = 2w = 4 meters

Height (h) = 2 meters

The minimum cost can be found by substituting the values of w and h into Equation 2:

Cost = 48w² + 768/w

Cost = 48(2)² + 768/2

Cost = 48(4) + 384

Cost = 192 + 384

Cost = $576

So, the minimum cost of the container is $576, and the dimensions that minimize the cost are a width of 2 meters, length of 4 meters, and height of 2 meters.

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Answer:

Here is the fruit pie....chart lol

Step-by-step explanation:

Hope this helps and have a great day!

The parachutist will reach the ground after 13.54 seconds.

To solve this problem, we can divide the parachutist's motion into two phases: free fall (before the chute opens) and descent with a parachute (after the chute opens).

Phase 1: Free Fall

Given:

Mass of the parachutist (m) = 85 kg

Initial velocity (v₀) = 0 m/s

Acceleration due to gravity (g) = 9.81 m/s²

Air resistance constant when chute is closed (b₁) = -30 N·s/m

Threshold velocity for chute opening (v_threshold) = 20 m/s

We can use the equation of motion to calculate the time taken for the parachutist to reach the threshold velocity:

v = v₀ + gt

v_threshold = v₀ + gt_threshold

20 m/s = 0 m/s + (9.81 m/s²) * t_threshold

Solving for t_threshold:

20 m/s = 9.81 m/s² * t_threshold

t_threshold = 20 m/s / 9.81 m/s²

                 = 2.038 s

Phase 2: Descent with Parachute

Given:

Air resistance constant when chute is open (b₂) = 100 N·s/m

We need to calculate the time taken for the parachutist to descend from the threshold velocity (20 m/s) to the ground velocity (0 m/s). Since air resistance is now acting on the parachutist, we can use the equation of motion for motion with air resistance:

m * dv/dt = -b₂ * v - m * g

Separating variables and integrating, we get:

∫ (1 / (-b₂ * v - m * g)) dv = ∫ dt

Integrating both sides:

-ln|b₂ * v + m * g| / b₂ = t + C

Applying initial conditions:

At v = 20 m/s, t = t_threshold

-ln|b₂ * 20 + m * g| / b₂ = t_threshold + C

To solve for C, substitute the values of t_threshold, b₂, m, and g:

-ln|100 * 20 + 85 * 9.81| / 100 = t_threshold + C

Simplifying:

-ln|2000 + 833.85| / 100 = t_threshold + C

Now, we can substitute the initial conditions for the time at the chute opening (t_threshold) and solve for C:

-ln|2000 + 833.85| / 100 = (20 m/s / 9.81 m/s²) + C

Solving for C:

C = -ln|2000 + 833.85| / 100 - (20 m/s / 9.81 m/s²)

Finally, we can substitute C back into the equation to find the time taken for the parachutist to reach the ground:

-ln|b₂ * v + m * g| / b₂ = t + C

-ln|b₂ * 0 + m * g| / b₂ = t + C

Simplifying:

-ln|85 * 9.81| / 100 = t + C

Calculating the result:

t = -ln|85 * 9.81| / 100 - (-ln|2000 + 833.85| / 100 - (20 m/s / 9.81 m/s²))

t = -ln(833.85) / 100 - (-ln(2833.85) / 100 - (20 / 9.81))

t ≈ 11.502 seconds

Therefore, the parachutist will reach the ground 2.038+11.50.2 = 13.54 seconds.

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Answer:

ps and qr is parellel so the 70°and x is co interior angles.

so, our equation will be look like .

70°+x=180°

x=180°-70°

x=110°

The sides PS and QR are parallel for x = 110°

Option 4 is correct.

The pair of non-adjacent interior angles that are on the same side of the transversal are referred to as consecutive internal angles.The term "consecutive" describes events that take place side by side.

As per the given data:

PQRS is a quadrilateral with sides PS and QR parallel.

∠P = 70°

∠Q = x°

∠S = 112°

For sides PS and QR to be parallel:

∠Q + ∠P = 180° {Co-interior angles on the same side of the transversal}

x° + 70° = 180°

x = 110°

Hence, sides PS and QR are parallel for x = 110°

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Answer:

b) \(x^2 + 6x + 8\)

Step-by-step explanation:

Para ampliar la habitación cuadrada, se agregaron 4 metros de largo y 2 metros de ancho, como se muestra en la figura.

Deje que la longitud y el ancho de la habitación antes de la expansión sean x.

La nueva longitud de la sala es (x + 4).

El nuevo ancho de la sala es (x + 2).

La nueva área de la sala será:

\((x + 4)(x + 2)\\x^2 + 2x + 4x + 8\\x^2 + 6x + 8\\\\\)

Esa es la nueva área de la habitación.

The limit exists and is finite, the series is convergent. The sum of the convergent series is 1/2.

To determine if the series is convergent or divergent, we need to express the series Sn as a telescoping sum. Based on the given information, the series can be written as:

Sn = Σ(1/n - 1/(n+1)), where n starts from 2.

Now, let's rewrite the series:

Sn = (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + ... + [1/n - 1/(n+1)]

Notice that the series is telescoping, as most terms cancel out:

Sn = 1/2 - 1/(n+1)

Now, let's analyze the series as n approaches infinity:

lim (n -> ∞) Sn = lim (n -> ∞) [1/2 - 1/(n+1)]

As n goes to infinity, 1/(n+1) goes to 0, so the limit becomes:

lim (n -> ∞) Sn = 1/2

Since the limit exists and is finite, the series is convergent. The sum of the convergent series is 1/2.

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The distance across the lake is approximately 25.78 meters. The law of cosines: cos(B) = (a^2 + c^2 - b^2) / (2ac) is used to get this result.

where B is the angle at point B, a is the distance AE, b is the distance BC, and c is the distance CE.

First, let's find angle B:

cos(B) = (AE^2 + CE^2 - DE^2) / (2AE * CE)
cos(B) = (15^2 + 21^2 - 18^2) / (2 * 15 * 21)
cos(B) = 0.8772
B = 29.7 degrees (rounded to the nearest tenth)

Next, we can use the law of cosines again to find BC:

b^2 = a^2 + c^2 - 2ac * cos(B)
b^2 = 15^2 + 21^2 - 2 * 15 * 21 * cos(29.7)
b^2 = 664.16
b = 25.78 meters (rounded to the nearest hundredth)

Therefore, the distance across the lake is approximately 25.78 meters.

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Answer: 61 degrees

Step-by-step explanation:

\(\\ \sf\longmapsto \dfrac{20}{3x-18}=\dfrac{15}{9}\)

\(\\ \sf\longmapsto 300=15(3x-18)\)

\(\\ \sf\longmapsto 300=45x-270\)

\(\\ \sf\longmapsto 45x=570\)

\(\\ \sf\longmapsto x\approx 13\)

Answer:

• from scale factors, big triangle : small triangle

\(\dashrightarrow \: { \tt{ \frac{24}{(24 - 9)} = \frac{(3x - 18) + 20}{20} }} \\ \\\dashrightarrow \: { \tt{20 \times 24 = (3x + 2) \times 15}} \\ \\ \dashrightarrow \: { \tt{480 = 45x + 30}} \\ \\ \dashrightarrow \: { \tt{45x = 450}} \\ \\ \dashrightarrow \: { \boxed{ \tt{x = 10}}}\)

• The missing length:

\( = { \tt{3x - 18}} \\ \\ = { \tt{3(10) - 18}} \\ \\ = { \tt{30 - 18}} \\ \\ \dashrightarrow \: { \boxed{ \boxed{ \tt{ \: \: missing \: length = 12 \: \: }}}}\)

Answer: A

Step-by-step explanation:

The linear equation for their total combined age in 5 years is 2x + 17 = 31.

Let the age of Alex be x years old.

Let the age of June be 'y'.

June is exactly 7 years older than Alex.

y = x+7

In next 5 years, combined  total age will be of 31 years.

(x+5) + (y+5) = 31

Now, the linear equation that models total combined age in 5 years

Replace y with (x+7)

x + 5 + (x+7) + 5 = 31

2x + 17 = 31

Thus, linear equation for their total combined age in 5 years is 2x + 17 = 31.

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