The length of a rectangle is 20 units more than its width. The area of the rectangle is x4−100.

Which expression represents the width of the rectangle?

1. x2−10 because the area expression can be rewritten as (x2−10)(x2+10) which equals (x2−10)((x2−10)+20).

2. x2+10 because the area expression can be rewritten as (x2+10)(x2−10) which equals (x2+10)((x2+10)−20).

3. x2−30 because the area expression can be rewritten as (x2+10)(x2−10) which equals (x2+10)((x2−30)+20).

4. x2+30 because the area expression can be rewritten as (x2−10)(x2+10) which equals (x2−10)((x2+30)−20).

Answer:

7425

Step-by-step explanation:

First let's make the last two fractions improper.

-4  1/2 = -9/2    -2  1/5 = -11/5

Now we have to find the least common denominator.

\(\frac{5}{6} *\frac{-9}{2}*\frac{-11}{5}\)

The least common denominator is 30 because all the denominators can be multiplied by something to get 30.

\((\frac{5}{5})*\frac{5}{6}* (\frac{15}{15})*\frac{-9}{2}* (\frac{6}{6})*\frac{-11}{5}\) Simplify

\(\frac{25}{30}*\frac{-135}{30}*\frac{-66}{30}\) simply

\(\frac{-3375}{30}*\frac{-66}{30}\)

\(\frac{222750}{30}\) simply

7425

The dy/dx of the equation  x⁴ * xy - y⁴ = x * y² is (y² - 4x³ * xy) / (x⁴ - 4y³ + 2xy).

To find dy/dx of the given equation x⁴ * xy - y⁴ = x * y², we'll first differentiate both sides of the equation with respect to x.

Using the product rule for differentiation (uv)' = u'v + uv', we have:

d/dx (x⁴ * xy) - d/dx (y⁴) = d/dx (x * y²)

Differentiating each term, we get:

(x⁴)'(xy) + (x⁴)(xy)' - (y⁴)' = (x)'(y²) + (x)(y²)'

Now, we'll find the derivatives:

4x^3 * xy + x⁴ * (y + x(dy/dx)) - 4y³(dy/dx) = y² + x * (2y * (dy/dx))

Now, we'll solve for dy/dx. First, let's collect the terms containing dy/dx on one side:

x⁴(dy/dx) - 4y³dy/dx) + 2xy(dy/dx) = y² - 4x³ * xy

Next, we factor out dy/dx:

dy/dx (x⁴ - 4y³ + 2xy) = y² - 4x³ * xy

Finally, we'll divide both sides by the expression in parentheses to isolate dy/dx:

dy/dx = (y² - 4x³ * xy) / (x⁴ - 4y³ + 2xy)

This is the expression for dy/dx.

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The length of the diagonal and the shorter base are 17. 24 feet and 18. 7 feet long respectively.

The cosine rule is given as;

\(c = \sqrt{a^2 + b^2 - 2ab cos \alpha }\)

c = length of the diagonal

a = base length = 22 feet

b = 7 feet

\(c = \sqrt{7^2 + 22^2 - 2 * 7 * 22 cos 40}\)

\(c = \sqrt{533 - 308 * 0. 7660}\)

\(c = \sqrt{533 - 235. 93}\)

\(c = \sqrt{297. 072}\)

\(c = 17. 24\) feet

Using sine rule

\(\frac{a}{sin A } = \frac{c}{sin C}\)

\(\frac{a}{sin 70} = \frac{17. 24}{sin 40}\)

Cross multiply

\(a\) × \(sin 60\) = \(c\) × \(sin 70\)

\(a\) × \(0. 8660\) = \(17. 24\) × \(0. 9397\)

\(a = \frac{16. 20}{0. 8660}\)

a = 18. 7 feet long

Thus, the length of the diagonal and the shorter base are 17. 24 feet and 18. 7 feet long respectively.

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Answer:

I think C sorry if im worng <3

Answer:

=3

Step-by-step explanation:

log5 125= log5 5^3 (125=5^3)

=3 log5 5. (logx^y=ylogx)

=3x1=3. (Loga a=1)

=3

Answer:

A. 29.93 grams

B. 29.925 grams

C. 0.005 grams

D. 5.985 grams per dose

Step-by-step explanation:

Chemical A = 10.357 grams

Chemical B = 12.062 grams

Chemical C = 7.506 grams

Number of doses of drugs = 5

A. About how much medicine in grams

Round each chemical to the nearest tenth

Chemical A = 10.36 grams

Chemical B = 12.06 grams

Chemical C = 7.51 grams

Total medicine in grams = chemical A + chemical B + chemical C

= 10.36 + 12.06 + 7.51

= 29.93 grams

B. Find the exact amount of medicine mixed by Dr. Stevens.

Total medicine in grams = chemical A + chemical B + chemical C

= 10.357 + 12.062 + 7.506

= 29.925 grams

C. What is the difference between the exact amount and the estimated amount of medicine

Difference = Estimated amount - Exact amount

= 29.93 grams - 29.925 grams

= 0.005 grams

D. How many grams are in one dose of medicine?

Grams in a dose = exact amount of chemicals / 5 doses

= 29.925 grams / 5

= 5.985 grams per dose

Approximately 5.99 grams per dose

The solution to the equation is x = 15.

To rewrite the exponential equation using the same base, we need to express both 8 and 32 as powers of the same base. Since both 8 and 32 are powers of 2, we can rewrite the equation as:

\((2^3)^(2x) = (2^5)^(x+3)\)

Here, we used the fact that\((a^b)^c = a^(b*c)\)to simplify the exponents. We also used the property that 8 is equal to 2 raised to the power of 3, and 32 is equal to 2 raised to the power of 5.

Now that we have rewritten the equation with the same base, we can equate the exponents on both sides of the equation to solve for x:

\(2^(6x) = 2^(5x + 15)\)

Since the bases on both sides of the equation are equal, we can equate the exponents and solve for x:

6x = 5x + 15

Subtracting 5x from both sides, we get:

x = 15

Therefore, the solution to the equation is x = 15.

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The area of the tile is 58 cm²

We have the following information from the question is:

A quadrilateral the bottom vertex and perpendicular to the top that is 7 centimeters.

The right vertical side is labeled 3 centimeters.

The portion of the top from the left vertex to the perpendicular segment is 4 centimeters.

The perpendicular vertical line segment and is labeled 6 centimeters.

We have to find the area of the tile .

Now, According to the question:

Let us assign the name of the sides of quadrilateral.

BC = 3 cm and CD = 7 cm.

We also know that AD = 4 cm and BD = 6 cm.

To find the length of AB,

So, we can use the Pythagorean theorem:

\(AB^2 = AD^2 + BD^2AB^2 = 4^2 + 6^2AB^2= 52AB = \sqrt{52}\)

AB = 2 ×√(13) cm

Area = (1/2) x (sum of parallel sides) x (distance)

The sum of the parallel sides is AB + BC = \(2\sqrt{13} + 3 cm\),

and the distance between them is CD = 7 cm.

Area = (1/2) x (2 ×√(13) cm + 3) x 7

Area = (√(52) + 3/2) x 7

Area ≈ 58 cm²

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A and B are mutually exclusive, with P(A) is 0.7 and P(B) is 0.2, the probability of event B given event A (P(B|A)) and the probability of event B given event A (P(BIA)) are both 0.2.

To find the probability of B given A, we can use the formula:

P(B|A) = P(A and B) / P(A)

Given:

P(A) = 0.5

P(B) = 0.1

P(A and B) = 0.3

P(B|A) = 0.3 / 0.5

= 0.6

Therefore, the probability that B will occur if A occurs is 0.6.

Given:

P(A) = 0.3

P(B) = 0.4

Since A happening guarantees that B must also happen, the events A and B are not independent. In this case, we can use the formula:

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 0.3 + 0.4 - 0.3

= 0.4

Therefore, the probability of A or B occurring is 0.4.

Given:

P(A) = 0.7

P(B) = 0.2

Since A and B are mutually exclusive events, they cannot occur together. In this case, we have:

P(A and B) = 0

Therefore, P(B|A) = P(BIA)

= 0.

P(BIA) = P(B)

= 0.2.

So, P(BIA) < P(B) is true.

When events A and B are mutually exclusive, with P(A) = 0.7 and P(B)

= 0.2, the probability of event B given event A (P(B|A)) and the probability of event B given event A (P(BIA)) are both 0.2.

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Check the picture below.

we know the LA is 9 and 1/2 or namely 19/2 and the height is 5, so

\(\stackrel{slant~height}{\cfrac{19}{2}}~~ = ~~\stackrel{slant~height}{\sqrt{r^2+h^2}}\implies \left( \cfrac{19}{2} \right)^2~~ = ~~r^2+5^2\implies \cfrac{361}{4}~~ = ~~r^2+25 \\\\\\ \cfrac{361}{4} - 25~~ = ~~r^2\implies \cfrac{261}{4}=r^2\implies \sqrt{\cfrac{261}{4}}=r\implies \boxed{\cfrac{3\sqrt{29}}{2}=r} \\\\[-0.35em] ~\dotfill\\\\ LA=\pi r\stackrel{slant~height}{\sqrt{r^2+h^2}}\implies LA=\pi \left( \cfrac{3\sqrt{29}}{2} \right)\cfrac{19}{2}\implies \boxed{LA=\cfrac{57\pi \sqrt{29}}{4}}\)

\(~\dotfill\\\\ SA=\pi r\sqrt{r^2+h^2}~~ + ~~\pi r^2\implies SA=LA~~ + ~~\pi r^2 \\\\\\ SA=\cfrac{57\pi \sqrt{29}}{4}~~ + ~~\cfrac{3\pi \sqrt{29}}{2}\implies \boxed{SA=\cfrac{63\pi \sqrt{29}}{4}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill LA\approx 241.1\qquad SA\approx 266.5~\hfill\)

The solution to the inequality are the region in the shaded area and the graph is attached

From the question, we have the following parameters that can be used in our computation:

y ≥3(0.8)^x

y ≥ x² - 5

Represent properly

y ≥ 3(0.8)^x

y ≥ x² - 5

Next, we make a plot of the system to determine the solution

The shaded area in the plot represent the solution to the inequality

In this case, one of the coordinates in the shaded area has a coordinate of (0, 5)

None of the options represent the shaded area (see attachment)

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Answer:

- 4

Step-by-step explanation:

If the equation of a function is y=x2-5, the output when the input is -1 is

y = (-1)² - 5

= - 4

Hope it will help :)

Answer:7.585 g

Step-by-step explanation: i took the test trust me

Comparing the values by subtraction, the mass of the pencil is greater than the mass of the crayon by 3.295 g.

Using subtraction, two values can be compared by getting how much one exceeds the other.

If the mass of a pencil is 5.44 g and the mass of a crayon is 2.145 g, subtract the mass of the crayon from the mass of the pencil to know how much greater is the mass of the pencil compared to the mass of the crayon.

5.44 g - 2.145 g = 3.295 g

Hence, the mass of the pencil is greater than the mass of the crayon by 3.295 g.

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According to the information given, the number of SUVs sold would be x + 50.

Since the total number of vehicles sold is 120, we can set up the equation:\(x + (x + 50) = 120\)

Combining like terms, we have: \(2x + 50 = 120\)

Subtracting 50 from both sides: 2x = 70

Dividing both sides by 2: x = 35

Therefore, the number of passenger cars sold is 35, and the number of SUVs sold is \(35 + 50 = 85.\)

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Answer:

4.2L=4200^3<this one Is a I think

0.35km=350m<This one ik

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

The formula for D in terms of t is D=0.01875t²

The value of D is 76.8

Step-by-step explanation:

See above for an image

Hope I helped!

After calculating by definition of proportionality, the value of D is 76.8

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

The distance, D, travelled by a particle is directly proportional to the square of the time, t.

So, We can defined as;

⇒ D = k × t²

Where, 'k' is constant of proportion.

Here, When t = 40, D = 30,

⇒ D = k × t²

⇒ 30 = k × 40²

⇒ 30 = k × 1600

⇒ k = 30 / 1600

⇒ k = 3/160

So, When t = 64, the value of D is,

⇒ D = 3/160 × 64²

⇒ D = 76.8

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Answer: 3/4 of a cup is 0.75

Step-by-step explanation:

Given:

A figure of a triangle.

To find:

The measure of angle A.

Solution:

Label the points in the figure as shown below.

In the below figure,

\(\angle ACB\cong \angle DCE\)            (Vertically opposite angles)

\(m\angle ACB=m\angle DCE\)              (Congregant angles)

\(m\angle ACB=8x+4\)

Using exterior angle theorem in triangle ABC, we get

\(m\angle A+m\angle C=\text{Exterior }m\angle B\)

\(m\angle BAC+m\angle ACB=130^\circ\)

\((3x-6)+(8x+4)=130^\circ\)

\(11x-2=130^\circ\)

Isolate the variable term x.

\(11x=130^\circ+2\)

\(11x=132^\circ\)

\(x=\dfrac{132^\circ}{11}\)

\(x=12^\circ\)

Now, the measure of angle A is:

\(m\angle A=3x-6\)

\(m\angle A=3(12^\circ)-6\)

\(m\angle A=36^\circ-6\)

\(m\angle A=30^\circ\)

Therefore, the correct option is B.

Answer:

85km/ h

Step-by-step explanation:

\(\frac{2380}{28} \\\\= 85km/hour\)

Answer:

10/20 for green, then 4/19 for blue. 10/20 * 4/19 = 2/19

Step-by-step explanation:

Explanation is above. If you need any more help let me know.

When these conditions are met, you can use the dependent samples t-test to compare the mean of the difference between the two populations.

Paired samples

Random sampling.

Normal distribution

Independence of pairs.

To use the dependent samples t-test for the mean of the difference of two populations, the following conditions are necessary:
Paired samples:

The data must consist of pairs of observations (e.g., pre- and post-test scores) that are related or dependent on each other.
Random sampling:

The paired samples must be randomly selected from the populations.
Normal distribution:

The distribution of the differences between the paired samples should be approximately normally distributed.

This condition can be evaluated using a normality test, such as the Shapiro-Wilk test, or by visually inspecting a histogram or Q-Q plot of the differences.
Interval or ratio data:

The data should be measured on an interval or ratio scale (e.g., weight, height, test scores), rather than on an ordinal or nominal scale.
Independence of pairs:

The differences within each pair of observations should be independent of the differences in other pairs.

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If these conditions are met, then the dependent samples t-test can be used to test the null hypothesis that the mean difference between the two populations is zero.

The dependent samples t-test is used to compare the means of two related or dependent populations, where the samples are paired or matched. In order to use the dependent samples t-test for the mean of the difference of two populations, the following conditions should be met:

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Answer:

I believe the answer would be x<=-4

The equal sign next to the < sign just stand for the line underneath since my keyboard cannot type that

Step-by-step explanation:

Brainliest?!? PLEASE?

Answer:

a) 3x² + 7x + 2

b) 4x² + 2x - 12

c) x² + 8x + 12

d) π (16x² + 144)

Step-by-step explanation:

a) Rectangle

A = bh

A = 3x + 1 (x + 2)

A = 3x² + 6x + 1x + 2

A = 3x² + 7x + 2

b) Parallelogram

A = bh

A = 2x + 4 (2x - 3)

A = 4x² + (-6x) + 8x + (-12)

A = 4x² + 2x - 12

c) Trapezoid

A = a + b/2 (h)

A = [(x + 3) + (x + 9)]/2 (x + 2)

A = (2x + 12)/2 (x + 2)

A = x + 6 (x + 2)

A = x² + 2x + 6x + 12

A = x² + 8x + 12

d) Circle

A = πr²

A = π (4x + 12)²

A = π (16x² + 144)

This will be you're simplest answer unless you multiple 16x² + 144 times pi (π) and round.

Answer:

17.0

Step-by-step explanation:

right angle with angles 45, 45 and 90

SOHCAHTOA

cos 45 = A/H

Cos 45 = 12/r

r= 12/cos 45

r= 16.97

The four angles of a quadrilateral are  30°, 60°, 150°, and 120°  if the four vertices of an inscribed quadrilateral divide a circle in the ratio 1:2:5:4.

It is defined as the four-sided polygon in geometry having four edges and four corners.

We have the four vertices of an inscribed quadrilateral divide a circle in the ratio:

1:2:5:4

Let the sides of the quadrilateral be x, 2x, 5x, 4x.

We know the sum of all angles of quadrilateral = 360°

x+2x+5x+4x=360

12x = 360

First angle, x = 30°

Seconds angle, 2x = 2×30 ⇒ 60°

Third angle, 5x = 5×30 ⇒ 150°

Fourth angle, 4x = 4×30 ⇒ 120°

Thus, the four angles of a quadrilateral are  30°, 60°, 150°, and 120°

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The four angles of a quadrilateral are  30°, 60°, 150°, and 120°

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(\frac{2}{3}\)(y + 57) = 178

distribute \(\frac{2}{3}\) into the parentheses

\(\frac{2}{3}\)y + 38 = 178

      -38    -38

\(\frac{2}{3}\)y = 140

multiply both sides by the reciprocal of \(\frac{2}{3}\) which is \(\frac{3}{2}\)

( \(\frac{3}{2}\) ) \(\frac{2}{3}\)y = 140(     \(\frac{3}{2}\) )

\(\frac{2}{3}\) is cancelled out with only y remaining on the left side

y = 210

The upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

To determine the upper and lower control limits for the sample means, we can use the formula:

Upper Control Limit (UCL) = Mean + (Z * Standard Deviation / sqrt(n))

Lower Control Limit (LCL) = Mean - (Z * Standard Deviation / sqrt(n))

In this case, we want to include roughly 95.5 percent of the sample means, which corresponds to a two-sided confidence level of 0.955. To find the appropriate Z-value for this confidence level, we can refer to the standard normal distribution table or use a calculator.

For a two-sided confidence level of 0.955, the Z-value is approximately 1.96.

Given:

Mean = 2.0 litres

Standard Deviation = 0.01 litres

Sample size (n) = 5

Using the formula, we can calculate the upper and lower control limits:

UCL = 2.0 + (1.96 * 0.01 / sqrt(5))

LCL = 2.0 - (1.96 * 0.01 / sqrt(5))

Calculating the values:

UCL ≈ 2.0018 litres

LCL ≈ 1.9982 litres

Therefore, the upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

Mean of the sample means = (2.005 + 2.001 + 1.998 + 2.002 + 1.995 + 1.999) / 6 ≈ 1.9997

Since the mean of the sample means falls within the control limits (between UCL and LCL), we can conclude that the process is in control.

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