Don't know where to start.... please help!

Answer: x² + 3x - 10

Step-by-step explanation:

(x + 5)(x - 2)

Distribute:

x² - 2x + 5x - 10

Combine like terms:

x² + 3x - 10

Hope this helps!

Answer:

Function I

Step-by-step explanation:

Differentiate each function.

Function I

\(f(x)=e^{4-x}\)

\(\boxed{\begin{minipage}{5.5 cm}\underline{Differentiating $e^{f(x)}$}\\\\If $y=e^{f(x)}$, then $\dfrac{\text{d}y}{\text{d}x}=f\:'(x)e^{f(x)}$\\\end{minipage}}\)

\(f'(x)=-e^{4-x}\)

The domain of f'(x) is all real numbers:  (-∞, ∞)

Therefore f(x) is differentiable for all values of x over the interval (-5, 5).

Function II

\(f(x)=|4-x|\)

\(\boxed{\begin{minipage}{6.5 cm}\underline{Differentiating an absolute value function}\\\\$|f(x)|'=\dfrac{f(x)}{|f(x)|}f'(x)$\\\end{minipage}}\)

\(f'(x)=-\dfrac{4-x}{|4-x|}\)

The domain of f'(x) is all real numbers except x = 4:  (-∞, 4) ∪ (4, ∞)

Therefore, f(x) is not differentiable for all values of x over the interval (-5, 5).

Function III

\(\begin{aligned}f(x)&=\sqrt[3]{4-x}\\&=(4-x)^{\frac{1}{3}}\end{aligned}\)

\(\boxed{\begin{minipage}{7 cm}\underline{Differentiating $[f(x)]^n$}\\\\If $y=[f(x)]^n$, then $\dfrac{\text{d}y}{\text{d}x}=n[f(x)]^{n-1} f'(x)$\\\end{minipage}}\)

Therefore:

\(\begin{aligned}f'(x)&=\dfrac{1}{3}(4-x)^{\frac{1}{3}-1} \cdot -1\\&=-\dfrac{1}{3}(4-x)^{-\frac{2}{3}}\\&=-\dfrac{1}{3(4-x)^{\frac{2}{3}}}\end{aligned}\)

The domain of f'(x) is all real numbers except x = 4:  (-∞, 4) ∪ (4, ∞)

Therefore, f(x) is not differentiable for all values of x over the interval (-5, 5).

Function 4

\(f(x)=(4-x)^{\frac{2}{3}}\)

\(\boxed{\begin{minipage}{7 cm}\underline{Differentiating $[f(x)]^n$}\\\\If $y=[f(x)]^n$, then $\dfrac{\text{d}y}{\text{d}x}=n[f(x)]^{n-1} f'(x)$\\\end{minipage}}\)

Therefore:

\(\begin{aligned}f'(x)&=\dfrac{2}{3}(4-x)^{\frac{2}{3}-1} \cdot -1\\&=-\dfrac{2}{3}(4-x)^{-\frac{1}{3}}\\&=-\dfrac{2}{3(4-x)^{\frac{1}{3}}}\end{aligned}\)

The domain of f'(x) is all real numbers except x = 4:  (-∞, 4) ∪ (4, ∞)

Therefore, f(x) is not differentiable for all values of x over the interval (-5, 5).

In the class, Lucy's score is 6.

In statistics, the median is the middle value in a sorted, ascending or descending list of numbers. Thus, it represents the midpoint of the data.

The median is often compared with other descriptive statistics such as the mean (average), mode, and standard deviation.

Since Lucy is one of the 29 students in the class and her score was the same as the median score for her class.

Thus, the median score will be 15th score (i.e. the midpoint of 29). Using the frequency in of each score from the figure, let's keep adding the frequency until we reach 15 and we will then check the corresponding score at the 15th position:

2 + 2 + 4 + 7 = 15

Thus, the the corresponding score at the 15th position is 6.

Therefore, the median score is 6 and consequently Lucy's score is 6.

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The expression representing the perimeter of the polygon is given as follows:

7mn³/3 + 4m² + 3mn².

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

Hence the perimeter for the polygon in this problem is given as follows:

mn³(1/3 + 2) + m²(1 + 3) + mn²(1 + 2) = 7mn³/3 + 4m² + 3mn².

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Answer:

-3x+1/4

Step-by-step explanation:

hope this helps!

Answer:

-3x+1/4

Step-by-step explanation:

i got it right on k12

Answer:

a = 0.9

Step-by-step explanation:

For the quadratic equation \(\boxed{ax^2 + bx + c = 0}\) to have exactly one real root, the value of its discriminant, \(\boxed{b^2 - 4ac}\), must be zero.

For the given equation:

\(y = ax^2 - 6x + 10\),

• a = a

• b = -6

• c = 10.

Substituting these values into the formula for discriminant, we get:

\((-6)^2 - 4(a)(10) = 0\)

⇒ \(36 - 40a = 0\)

⇒ \(36 = 40a\)

⇒ \(a = \frac{36}{40}\)

⇒ \(a = \bf 0.9\)

Therefore the value of a is 0.9 when the given quadratic has exactly one root.

Total depth of the bottom of the plate is 4 + 1 = 5

Force = limit(5,1) 62.5 *7* x * dx

= 437.5. Lim(5,1) x*dx

= 437.5(x^2/2)^5 , 1

= 437.5 x (5^2/2 - 1/2)

= 437.5 x 12

= 5,250 pounds

The hydrostatic force against one side of the plate will be 5250 pounds.

The force exerted by the water of surface is known as hydrostatic force.

A 4-ft-high and 7-ft-wide rectangular plate is submerged vertically in water so that the top is 1 ft below the surface.

\(\rm Force = \int^5_1 62.5 *7* x * dx\\\\\\ Force = 437.5 \left [ \dfrac{x^2}{2} \right]^5_1\\\\\\Force = 218.75 \left [ x^2 \right]^5_1\\\\\)

Solve the equation further, we have

Force = 218.75 x (5² – 1²)

Force = 218.75 x 24

Force = 5,250 pounds

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The solution of the expression is,

a) 3,724

b) 2,784

We have to given that,

a) Divide 70,756 by 19.

b) Subtract 940 from your answer to part a).​

Now, We can simplify as,

a) Divide 70,756 by 19.

⇒ 70,756 ÷ 19

⇒ 3,724

And, Subtract 940 from your answer to part a).​ that is, 3724

⇒ 3724 - 940

⇒ 2,784

Therefore, The solution of the expression is,

a) 3,724

b) 2,784

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The radius of the semicircle having an arc of length equal to 8.5 \(\pi\) in a right-angle triangle ABC is equal to 7.5 cm.

Given:

Angle ABC of triangle ABC is a right angle. The sides of ABC are the diameters of semicircles.

The area of the semicircle on AB equals 8\(\pi\).

Area of a semicircle = \(\pi r^2/2\)

Therefore:

\(\pi r^2/2\) =  8\(\pi\)

\(r^2 = 16\)

\(r = 4\)

Next, the arc of the semicircle on AC has a length of 8.5\(\pi\).

Length of the arc of a semicircle = \(\pi r\)

\(\pi r\) = 8.5\(\pi\)

\(r = 8.5\)

Using Pythagoras theorem

\(8.5^{2} = 4^{2} + x^{2}\)

\(x^{2} = 8.5^2 - 4^2\\\)

\(x^{2} = 56.25\)

\(x = \sqrt{56.25}\)

\(x = 7.5\)

The radius of the semicircle of BC = 7.5 Units.

Refer to this complete question for this:

Angle ABC of triangle ABC is a Right angle. The sides of ABC are the diameters of semicircles as shown. The area of the semicircle on AB equals 8pi and the arc of the semicircle on AC has a length of 8.5pi. What is the radius of the semicircle of BC?

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Answer:

15

Step-by-step explanation:

10+(8-3)=15

................

Answer:

Vertical angles are congruent so x=145°

Answer:

x= 145° ( Corresponding angles)

Answer:

Y = theta = 32.68

Step-by-step explanation:

Formula

y^2 = x^2 + z^2  - 2*x*z * cos(theta)

Givens

y = 55

theta = ?

z = 50

x = 90

Solution

55^2 = 90^2 + 50^2 - 2*90*50 cos(theta)

3025 = 8100 + 2500 - 9000 cos(theta)      Combine the right

3025 = 10600 - 9000 Cos(theta)                Subtract 10600

3025 - 10600 = -9000 Cos(theta)

-7575 = - 9000 Cos(theta)                            Divide by - 9000

-7575/-9000 = cos(theta)

0.8417 = cos(theta)

cos-1(0.8417) = theta

theta = 32.68

(a) only A occurs: A − B − C

(b) A and B occur but C does not occur: (A ∪ B) − C

(c) exactly one of the events occurs: (A − B − C) ∪ (B − A −C) ∪ (C − A − B)

(d) at least one of the events occurs: A ∪ B ∪ C

(e) at most one of the events occurs: S − (A ∩ B) − (A ∩ C) − (B ∩ C)

(f) exactly two of the events occur: (A ∩ B − C) ∪ (A ∩ C − B) ∪ (B ∩ C − A)

(g) at least two of the events occur: (A∩B)∪(A∩C)∪(B∩C)

(h) at most two of the events occur: S − (A ∩ B ∩ C)

(i) all three events occur: A ∩ B ∩ C

(j) none of the events occur: S − A − B − C

(a) If only event A occurs, then the event A is said to be the difference of the universal set (S) and the events B and C (S − B − C).

(b) If events A and B occur but event C does not occur, then the union of events A and B (A ∪ B) is the difference of the universal set (S) and the event C (S − C).

(c) If exactly one of the events occurs, then it can be represented as the union of the differences of the universal set (S) and the other two events for each of the three events (A − B − C) ∪ (B − A −C) ∪ (C − A − B).

(d) If at least one of the events occurs, then it can be represented as the union of all three events (A ∪ B ∪ C).

(e) If at most one of the events occurs, then it can be represented as the difference of the universal set (S) and the intersection of any two events (S − (A ∩ B) − (A ∩ C) − (B ∩ C)).

(f) If exactly two of the events occur, then it can be represented as the union of the intersections of two events and the difference of the third event (A ∩ B − C) ∪ (A ∩ C − B) ∪ (B ∩ C − A).

(g) If at least two of the events occur, then it can be represented as the union of the intersections of any two events (A∩B)∪(A∩C)∪(B∩C).

(h) If at most two of the events occur, then it can be represented as the difference of the universal set (S) and the intersection of all three events (S − (A ∩ B ∩ C)).

(i) If all three events occur, then it can be represented as the intersection of all three events (A ∩ B ∩ C).

(j) If none of the events occur, then it can be represented as the difference of the universal set (S) and all three events (S − A − B − C).

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Answer:

Step-by-step explanation:

Well, since the length of a month can vary in the number of days, this answer can also vary.

For example, February is only 28 days long, while December is 31 days long.

That being said, the average length of all 12 months is 30.436875 days, so if Denny left to another country on June 20th, he would most likely be back   July 19th of July 20th.

I hope this helps!

Answer:

The answer is

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

\(m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\ \)

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(10, 8) and (1, 9)

The slope is

\(m = \frac{9 - 8}{1 - 10} = \frac{1}{ - 9} \\ = - \frac{1}{9} \)

We have the final answer as

\( - \frac{1}{9} \\ \)

Hope this helps you

We can use the given points to solve.

Slope formula: y2-y1/x2-x1

9-8/1-10

1/-9

-1/9

Best of Luck!

Answer:

5cm^2

Step-by-step explanation:

l=5 w=2

Area= 5×2

=10cm^2

Area of triangle= 10/2

=5cm^2

Answer: The answer to your question is C. Brainliest?

Step-by-step explanation:

For the first square, we can multiply both the numerator and denominator by 5 to get an equivalent fraction with a denominator of 60:

2/12 = (2 x 5) / (12 x 5) = 10/60

For the second square, we can multiply both the numerator and denominator by 4 to get an equivalent fraction with a denominator of 60:

2/15 = (2 x 4) / (15 x 4) = 8/60

Now, we can add the two fractions:

10/60 + 8/60 = 18/60

Simplifying this fraction by dividing both numerator and denominator by 6, we get:

18/60 = 3/10

Therefore, the total shaded area in the diagram is 3/10 or 0.3 in decimal form.

The answer is C. 0.3.

Answer:

Step-by-step explanation:

x₁ = 0   ; y₁=0  &

x₂ = 1    ; y₂=2

Slope =\(\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

         \(=\dfrac{2-0}{1-0}\\\\\\=\dfrac{2}{1}\\\\\\= 2\)

Slope = 2

Answer:

Starting with:

-15 > -11 + w

Add 11 to both sides:

-15 + 11 > w

Simplifying:

-4 > w

Therefore, the solution for the inequality -15 > -11 + w, when solved for w, is:

w < -4

Then 1 - 3/5 = 2/5. This means that 2/5 of the frogs in that particular part of the rainforest are not poisonous. This fraction can also be expressed as 40/100 or 0.4 in decimal form.

In the given scenario, we know that 3/5 of the frogs in a particular part of the rainforest are poisonous. This means that the remaining fraction of the frogs are not poisonous.

To find this fraction, we need to subtract 3/5 from 1 (since the sum of the fractions of poisonous and non-poisonous frogs is equal to 1).

It's important to note that just because a frog is not poisonous, it doesn't mean it's safe to touch or handle them. It's always best to admire these beautiful creatures from a safe distance and leave them alone in their natural habitat.

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Answer:

y = -8/3x + 8

Step-by-step explanation:

Step 1:  Identify which values we have and need to find in the slope-intercept form:

The general equation of the slope-intercept form of a line is given by:

y = mx + b, where

Since we're told that the y-intercept is 8, this is our b value in the slope-intercept form.

Step 2:  Find m, the slope of the line:

Thus, we can find m, the slope of the line by plugging in (3, 0) for (x, y) and 8 for b:

0 = m(3) + 8

0 = 3m + 8

-8 = 3m

-8/3 = m

Thus, the slope is -8/3.

Therefore, the the equation of the line in slope-intercept form whose x-intercept is 3 and whose y-intercept is 8 is y = -8/3x + 8.

Optional Step 3:  Check the validity of the answer:

Thus, we can check that we've found the correct equation in slope-intercept form by plugging in (3, 0) and (0, 8) for (x, y), -8/3 for m, and 8 for b and seeing if we get the same answer on both sides of the equation when simplifying:

Plugging in (3, 0) for (x, y) along with -8/3 for m and 8 for b:

0 = -8/3(3) + 8

0 = -24/3 + 8

0 = -8 = 8

0 = 0

Plugging in (0, 8) for (x, y) along with -8/3 for m and 8 for b;

8 = -8/3(0) + 8

8 = 0 + 8

8 = 8

Thus, the equation we've found is correct as it contains the points (3, 0) and (0, 8), which are the x and y intercepts.

Using trigonometric function the length to the nearest foot of the shortest ladder that will safely reach a roof that is 23 feet high is calculated as 25 feet.

What are trigonometric functions?

Simply put, trigonometric functions—also called circular functions—are the functions of a triangle's angle. This means that these trigonometric functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

Given the angle a ladder makes with the ground should be no greater than 67°.

So the angle θ ≤ 67°.

Let us assume the angle to be equal to 67°

The height of the roof from the ground is 23 feet.

The ladder and wall form the right triangle where the ladder works as hypotenuse and the wall as perpendicular.

With the sine function, find the length of the ladder -

sin θ = perpendicular/hypotenuse

Let the length of ladder be x.

sin 67° = 23/x

x = 23/sin 67°

x = 23/0.920

x = 25 feet

Therefore, the length of the ladder is 25 feet.

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The probability that it weighs more than 51 pounds exactly 53 pounds.

Given that, mean weight of 50 pounds and a standard deviation of 0.5 pounds.

We need to find the probability that it weighs more than 51 pounds,

P(X = 53) = 0

z = (51 - 50) / 0.5 = 2.00

P(X > 51) = P(z > 2.00) = 0.0228

z1 = (49 - 50) / 0.5 = -2.00

z2 = (51 - 50) / 0.5 = 2.00

P(49 < X < 51) = P(-2.00 < z < 2.00) = P(z < 2.00) - P(z < -2.00) = 0.9772 - 0.0228 = 0.9544

Hence, the probability that it weighs more than 51 pounds exactly 53 pounds.

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Answer: the answer would be a-y=0.25x+6.5

Hello!

The distance, d, is less than 200 miles.

B. d > 200

Answer: 375

Step-by-step explanation:

Ruling out each number:

6: In the first two rows, the 6's placement did not change but the clue did, meaning that it is talking about a different number. Otherwise, it would say it's in the right place twice or in the wrong place twice.

3 & 5: Since we know 6 is already ruled out, both 5 & 3 would have to be correct.

2 & 4 & 8: Is proven wrong in the 4th clue.

7: 7 would have to be in the middle since the second clue says it's in the wrong place. If it was 1, it would say it's in the right space.

1: Is proven wrong after 7 is proven true.

Figuring out placement:

5: For the first clue, it says that it's in the correct place meaning that 5 is the last digit.

3: For both of the times 3 appears, it is in the wrong spot, revealing that it's the first digit.

7: In the second clue, it could either be 1 or 7. However, since 3 took the first spot and 5 took the last spot, 7 would have to be in the middle since the clue says it's in the wrong place. If it was 1, it would say it's in the right space.