I know the answers but don’t know how to get them!!!☹️

Answer:

One side - 15 feet

Second side - 4 feet

Third side - 13 feet

Step-by-step explanation:

Let's call the sides A B and C, respectively.

We know that:

A = B + 11

C = B + 9

and that

A + B + C = 32

Please note that we have 3 equations and 3 unknowns. We can solve this, we'll use substitution.

A + B + C = (B + 11) + B + (B + 9) = 32

3B + 20 = 32

3B = 12

B = 4

The sides have lengths of 4+11 = 15, 4 and 4+9 = 13. This is in fact a proper triangle (because the shorter sides add up to more than the longer side).

The values of a and b in the given triangle are;

a = 59° and b = 6

From the given image, it is clear that in Triangle YVW that we have;

YV = WV

Now, a triangle that has two sides equal  is referred to as an Isosceles triangle which means that the two base angles are equal. Thus;

∠Y = ∠W = 31°

Now, the sum of angles in a triangle is 180° and as such;

∠YVW = 180 - 2(31)

∠YVW = 118°

Since VX is perpendicular to YW and so;

a = 180 - (90 + 31)

a = 59°

Thus; ∠WVX = 59°

This means that WX = YX = 6

Thus, b = 6

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The dimensions of the rectangle are 4 ft by 5 ft.

Given that the length of a rectangle is 3 ft less than twice the width, and the area of the rectangle is 44 sq.ft. We have to find the dimensions of the rectangle. Let's consider the width of the rectangle as x ft.Length of the rectangle = (2x - 3) ftArea of the rectangle = Length x Width44 = (2x - 3) x x44 = 2x^2 - 3x44 = x (2x - 3)2x^2 - 3x - 44 = 0To solve for x, we will factorize the equation by splitting the middle term.2x^2 - 8x + 5x - 20 = 0Factorize2x(x - 4) + 5(x - 4) = 0(x - 4) (2x + 5) = 0x = 4 ft (since the width of a rectangle can't be negative)or 2x = -5This gives us an invalid value, so x = 4 ftNow that we have the width of the rectangle, we can calculate the length as follows:Length of the rectangle = (2x - 3) ftLength of the rectangle = (2 * 4) - 3Length of the rectangle = 8 - 3Length of the rectangle = 5 ft.

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Based on the percent of red paint, Casho's purple paint will be redder than Isaiah's.

To determine whose purple paint will be redder based on the percent of red paint, we need to compare the ratios of red paint to the total paint used by Isaiah and Casho.

Isaiah's Ratio:

Isaiah mixes 3 cups of blue paint and 7 cups of red paint, making a total of 3 + 7 = 10 cups of paint.

To calculate the percent of red paint, we divide the amount of red paint (7 cups) by the total amount of paint (10 cups) and multiply by 100 to get the percentage:

Red paint percentage for Isaiah = (7 cups / 10 cups) * 100 = 70%

Casho's Ratio:

Casho mixes 4 cups of blue paint and 13 cups of red paint, making a total of 4 + 13 = 17 cups of paint.

To calculate the percent of red paint, we divide the amount of red paint (13 cups) by the total amount of paint (17 cups) and multiply by 100 to get the percentage:

Red paint percentage for Casho = (13 cups / 17 cups) * 100 = 76.47% (rounded to two decimal places)

Comparing the percentages, we can see that Casho's purple paint will be redder because Casho's paint has a higher percentage of red paint (76.47%) compared to Isaiah's paint (70%).

Therefore, based on the percent of red paint, Casho's purple paint will be redder than Isaiah's.

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Answer:

He has 2 lbs. left over for cookies.

Step-by-step explanation:

I got this answer by first adding 1/2 + 1  1/2 = 2. Then subtracting 2 from 4 witch would be 2 lbs. left over.

Answer:

1309.10

Step-by-step explanation:

1200 = 110%

(1200/110)*120 = 1309.10

Answer:

5m

Step-by-step explanation:

regla de 3:

1m = 3ft

15 pies ÷ 3 = 5m

The Nearest tenth of a second, the flag is in the air for approximately 0.1 seconds before Zack catches it.

To determine the time the flag is in the air before Zack catches it, we can use the kinematic equation for vertical motion:

h = 16t^2 + vt + s

Where:

h is the height of the flag,

t is the time in seconds,

v is the initial vertical velocity of the flag,

s is the initial height of the flag.

In this case, the flag is thrown into the air from a height of 5 feet (s = 5) with an initial vertical velocity of 30 feet per second (v = 30). Zack catches it at a height of 7 feet (h = 7).

We can rewrite the equation as:

7 = 16t^2 + 30t + 5

To find the time (t) when the flag is at a height of 7 feet, we can rearrange the equation and solve for t. However, since this is a quadratic equation, we can also use the quadratic formula.

The quadratic equation in this case is:

16t^2 + 30t + 5 - 7 = 0

16t^2 + 30t - 2 = 0

Now, we can use the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Applying the values from the quadratic equation, we have:

t = (-30 ± √(30^2 - 4 * 16 * (-2))) / (2 * 16)

Simplifying further:

t = (-30 ± √(900 + 128)) / 32

t = (-30 ± √1028) / 32

Using a calculator, we find two solutions:

t ≈ -1.08 seconds or t ≈ 0.06 seconds

Since time cannot be negative in this context, we discard the negative solution.

Therefore, to the nearest tenth of a second, the flag is in the air for approximately 0.1 seconds before Zack catches it.

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Answer:

0.0071% or 1/14000

Step-by-step explanation:

5/70,000 is approximately 0.00007142857 which is approximately 0.000071 which is 0.0071%

Answer:

7,115.6

Step-by-step explanation:

6700+410+5.6=7,115.6

Answer:

Step-by-step explanation:

The equation for the height h of the object after t seconds is given by:

h = -16t^2 + 145t + 2

To find when the height will be 230 feet, we can set h = 230 and solve for t:

230 = -16t^2 + 145t + 2

We can simplify this equation by moving all the terms to one side:

16t^2 - 145t + 228 = 0

To solve for t, we can use the quadratic formula:

t = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 16, b = -145, and c = 228. Plugging in these values, we get:

t = (-(-145) ± sqrt((-145)^2 - 4(16)(228))) / 2(16)

t = (145 ± sqrt(21025 - 14592)) / 32

t = (145 ± sqrt(6433)) / 32

t ≈ 0.56 seconds or t ≈ 9.17 seconds

Therefore, the height of the object will be 230 feet at approximately 0.56 seconds or 9.17 seconds after it is thrown.

To find when the object will reach the ground, we can set h = 0 and solve for t:

0 = -16t^2 + 145t + 2

Again, we can simplify this equation by moving all the terms to one side:

16t^2 - 145t - 2 = 0

Using the quadratic formula again, we get:

t = (-(-145) ± sqrt((-145)^2 - 4(16)(-2))) / 2(16)

t = (145 ± sqrt(21249)) / 32

t ≈ 9.51 seconds or t ≈ 0.15 seconds

Therefore, the object will reach the ground at approximately 0.15 seconds or 9.51 seconds after it is thrown. However, since the negative solution does not make physical sense in this context, the object will reach the ground after approximately 9.51 seconds.

~~~Harsha~~~

Answer:

2/299

Step-by-step explanation:

there were 300 tickets and 1 is out .    299 tickets left

There were 3 prizes and 1 is out.  2 prizes left.

The probability of winning ANY prize when next ticket is drawn   is

P(prize) =2/299

Answer:

A. \(\frac{24}{25}\)

Answer:

it will take them 1.71 hours to finish cutting the lawn if they work together.

Step-by-step explanation:

If Marsha cuts the lawn by herself it will take her 3 hours, this mean that in one hour she cuts 1/3 of the lawn.

On the other hand Bob needs one more hour to finish the lawn, this means it takes him 4 hours to cut it and therefore he cuts 1/4 of the lawn per hour.

Now, to know how much they cut by working together we need to sum up the amount of lawn they cut per hour:

Working together in one hour: Marsha's one hour + Bob's one hour

Working together in one hour: \(\frac{1}{3}+ \frac{1}{4}=\frac{4+3}{12}=\frac{7}{12}\)

Therefore, working together they will cut 7/12 in one hour.

Now, to know how long will it take it to cut the entire lawn (which is equivalent to 12/12), we can write this in terms of proportions

Time        Total amount of lawn

1 hour               7/12

x hours             12/12

Solving for x (to know the amount of hours it will take them) we have:

\(x=\frac{12}{12}\)÷\(\frac{7}{12}\)=\(1\)×\(\frac{12}{7}=\frac{12}{7}=1.714\)

Rounded to the nearest hundredth, we have that working together it will take them 1.71 hours to finish cutting the lawn.

Answer:

4sqrt(15)

Step-by-step explanation:

a² + b² = c²

x² + 7² = 17²

x² + 49 = 289

x² = 240

\(\sqrt{x^2} =\sqrt{240}\)

\(x=4\sqrt{15}\)

Answer:

I helped you last time so I'll help you again.

Step-by-step explanation:

We can find the average rate of change of f(x) over the interval [10, 20] using the formula:

average rate of change = (f(b) - f(a))/(b - a)

where a = 10 and b = 20.

So, we have:

f(a) = f(10) = 1.85(10)^2 = 185

f(b) = f(20) = 1.85(20)^2 = 740

average rate of change = (740 - 185)/(20 - 10) ≈ 55.5

Therefore, the average rate of change of f(x) over the interval [10, 20] is approximately 55.5.

Answer:

Step-by-step explanation:

This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.

Answer:

Find the components of the line (x,y)

And then use Tan ^-1(y/x)= Theta or angle

I hope you understand, and I go explain further.

Step-by-step explanation: In "simple terms". Slope is rise/run. Rise is the change in y value, which will equal the length of the opposite side of the right triangle. Run is the change in x value, which is the length of the adjacent side. The trigonometric function Tangent is opposite/adjacent. Use the inverse tangent of the slope to find the angle.

The only catch is that sometimes inverse tangent will give you a negative angle. It is generally not acceptable to provide the angle in a triangle as the negative angle. If you get a negative angle, use the absolute value of the angle.

The length of leg is equal to 100 based on the length of hypotenuse and angle.

The length of leg will be calculated using Pythagoras theorem as the stated triangle is right angled triangle. Based on the theorem, se have side A is hypotenuse. So, sin theta = perpendicular/hypotenuse, where theta will be 90 degree and perpendicular is leg. Let us represent the leg as x.

sin 90 = x/ A

Keep the value of sin 90, which is 1

1 = x/100

Rearrange the equation in terms of x along with performing multiplication

x = 100

Hence, the length of leg is 100.

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The members in Jasmine's dance troupe is an illustration equivalent expressions.

The number of members in Jasmine's dance troupe is 62

Assume the number of dancers is n.

One third of the rest is:

\(\mathbf{x = \frac{1}{3}(n - 2)}\)

When she called three more, we have:

\(\mathbf{x = \frac{1}{3}(n - 2) + 3}\)

Expand

\(\mathbf{x = \frac{n}{3} - \frac{2}{3} + 3}\)

\(\mathbf{x = \frac{n}{3} + \frac{-2 + 9}{3}}\)

\(\mathbf{x = \frac{n}{3} + \frac{7}{3}}\)

The remaining dancers (r) are:

\(\mathbf{r = n- \frac{n}{3} - \frac{7}{3}}\)

\(\mathbf{r = \frac{3n - n}{3} - \frac{7}{3}}\)

\(\mathbf{r = \frac{2n}{3} - \frac{7}{3}}\)

\(\mathbf{r = \frac{2n - 7}{3}}\)

When two-fifth of the remaining dancers are added, we have:

\(\mathbf{x = \frac{n}{3} + \frac{7}{3} + \frac{2}{5}(\frac{2n - 7}{3})}\)

\(\mathbf{x = \frac{n+7}{3} + \frac{2}{5}(\frac{2n - 7}{3})}\)

\(\mathbf{x = \frac{n+7}{3} + \frac{4n - 14}{15}}\)

Take LCM

\(\mathbf{x = \frac{5n + 35 + 4n - 14}{15}}\)

\(\mathbf{x = \frac{9n + 21}{15}}\)

\(\mathbf{x = \frac{3n + 7}{5}}\)

When she called one more dancer, we have:

\(\mathbf{x = \frac{3n + 7}{5} + 1}\)

\(\mathbf{x = \frac{3n + 7+5}{5}}\)

\(\mathbf{x = \frac{3n + 12}{5}}\)

The remaining of the dancer is:

\(\mathbf{r = n - \frac{3n + 12}{5}}\)

\(\mathbf{r = \frac{5n - 3n + 12}{5}}\)

\(\mathbf{r = \frac{2n + 12}{5}}\)

When three-fourth are added, we have:

\(\mathbf{x = \frac{3n + 12}{5} +\frac{3}{4} \times \frac{2n + 12}{5}}\)

\(\mathbf{x = \frac{3n + 12}{5} + \frac{6n + 36}{20}}\)

Take LCM

\(\mathbf{x = \frac{12n + 48+6n + 36}{20}}\)

\(\mathbf{x = \frac{18n +84}{20}}\)

When the last two members are added, we have:

\(\mathbf{n = \frac{18n +84}{20} + 2}\)

\(\mathbf{n = \frac{18n +84+40}{20} }\)

\(\mathbf{n = \frac{18n +124}{20} }\)

Multiply through by 20

\(\mathbf{20n = 18n +124}\)

Collect like terms

\(\mathbf{20n - 18n =124}\)

\(\mathbf{2n =124}\\\)

Divide both sides by 2

\(\mathbf{n =62}\)

Hence, the number of members in Jasmine's dance troupe is 62

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The value of y is 18

Similar triangles have the same corresponding angle measures and proportional side lengths. The angles of the two triangle must be equal and it not necessary they have equal sides.

Therefore the corresponding angles of similar triangles are congruent and the ratio of corresponding sides of similar triangles are equal.

Therefore;

14/21 = 12/y

14y = 21 × 12

14y = 252

divide both sides by 14

y = 252/14

y = 18

Therefore the value of y is 18.

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Answer:

Converting into metre (1m=100cm)= 5/100=0.05m.. Converting into km. (1km=100000cm). so 5 cm=5/100000=0.00005km.

Answer:

5cm in meters = 0.05 metre

5cm in kilometres = 0.00005km

Answer:

The fourth number is 13

Step-by-step explanation:

7+9+11+13 = 40 it's the only one that works

The explicit rule for nth term is 60-30n .

An arithmetic sequence is the sequence of numbers following a pattern and have a certain common difference .

The nth term for a sequence is given by

\(\rm a_n = a_1 + (n-1)d\\\)

In the given question the sequence is

30 , 0 , -30 , - 60

Here the first term is 30

the difference is -30

\(\rm a_n = 30 + (n-1)(-30)\\\\\\\rm a_n = 30 -30n +30\\\\\\\rm a_n =60-30n\\\)

Therefore, the explicit rule for nth term is 60-30n .

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Answer:

$47.70

Step-by-step explanation:

45 × 0.06 = $2.70

the tax is $2.70 add tax with price of shoes

45+ 2.7= $47.70

Answer:

the tax is $7.50 :)

10 units squared. Hope this helped.

The area of the triangle is 10 square units.

The given coordinates are A(2,0), B(6,0), and C(8,5).

The formula of area of triangle formula in coordinate geometry is the area of the triangle in the coordinate geometry is:  \(A=\frac{1}{2} |x_{1} (y_{2}-y_{3})+x_{2} (y_{3}-y_{1})+x_{3} (y_{1}-y_{2})|\)

Now, Area=1/2|2(0-5)+6(5-0)+8(0-0)|=0.5|20|

=10 square units

Therefore, the area of the triangle is 10 square units.

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Answer:

\(\textsf{A.} \quad (2+x)^x\left[\dfrac{x}{2+x}+\ln(2+x)\right]\)

Step-by-step explanation:

Replace f(x) with y in the given function:

\(y=(x+2)^x\)

Take natural logs of both sides of the equation:

\(\ln y=\ln (x+2)^x\)

\(\textsf{Apply the log power law to the right side of the equation:} \quad \ln a^n=n \ln a\)

\(\ln y=x\ln (x+2)\)

Differentiate using implicit differentiation.

Place d/dx in front of each term of the equation:

\(\dfrac{\text{d}}{\text{d}x}\ln y=\dfrac{\text{d}}{\text{d}x}x\ln (x+2)\)

First, use the chain rule to differentiate terms in y only.

In practice, this means differentiate with respect to y, and place dy/dx at the end:

\(\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}}{\text{d}x}x\ln (x+2)\)

Now use the product rule to differentiate the terms in x (the right side of the equation).

\(\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}\)

\(\textsf{Let}\; u=x \implies \dfrac{\text{d}u}{\text{d}x}=1\)

\(\textsf{Let}\; v=\ln(x+2) \implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{1}{x+2}\)

Therefore:

\(\begin{aligned}\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}&=x\cdot \dfrac{1}{x+2}+\ln(x+2) \cdot 1\\\\\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}&= \dfrac{x}{x+2}+\ln(x+2)\end{aligned}\)

Multiply both sides of the equation by y:

\(\dfrac{\text{d}y}{\text{d}x}&=y\left( \dfrac{x}{x+2}+\ln(x+2)\right)\)

Substitute back in the expression for y:

\(\dfrac{\text{d}y}{\text{d}x}&=(x+2)^x\left( \dfrac{x}{x+2}+\ln(x+2)\right)\)

Therefore, the differentiated function is:

\(f'(x)=(x+2)^x\left[\dfrac{x}{x+2}+\ln(x+2)\right]\)

\(f'(x)=(2+x)^x\left[\dfrac{x}{2+x}+\ln(2+x)\right]\)