Gabriella drove to her friend's house and
back. The trip there took six hours and the
trip back took five hours. She averaged
60 km/h on the return trip. Find the
average speed of the trip there.

Factored form of an expression is writing it in the terms of multiplication of factors. The factors of given expression are: \((7x+4)\)  and \((x-1)\)

If the given quadratic expression is of the form \(ax^2 + bx + c\),

then its factored form is obtained by two numbers alpha( α ) and beta( β) such that:

\(b = \alpha + \beta \\ ac =\alpha - \beta\)

The given expression is \(7x^2 - 3x - 4\)

Comparing it with the standard form of quadratic expression \(ax^2 + bx + c\), we get: a = 7, b = -3, c = -4

ac = -28

-28 = -2 times 14

-28 = -7 times 4 (-7 + 4 = -3 = b)

Thus, \(\alpha = -7, \beta = 4\)

Thus, we get:

\(7x^2 - 3x - 4 = 7x^2 - 7x + 4x - 4 = 7x(x-1) + 4(x-1) = (7x+4)(x-1)\\7x^2 - 3x - 4 = (7x+4)(x-1)\)

Thus, The factors of given expression are: \((7x+4)\)  and \((x-1)\)

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Answer:

Step-by-step explanation:

In general, the Divergence Test (nth term test) only allows us to determine whether a series diverges or not. It does not help us to determine the convergence of a series. Therefore, none of the other tests apply to this series.

The Divergence Test (nth term test) states that if the limit of the nth term of a series is not equal to zero, then the series diverges.

The series [infinity] 12 n n=1 is defined as follows:

[infinity] 12 n n=1 = 12¹ + 12² + 12³ + ...

The nth term of this series is given by:

aₙ = 12ⁿ As n → ∞, aₙ → ∞,

which means the limit of the nth term of the series does not exist.

Therefore, the series [infinity] 12 n n=1 diverges by the Divergence Test (nth term test).

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The object was dropped from approximately 42.402 meters above the ground.

To find the object's average velocity in the x-direction between t = 1.35 s and t = 2.45 s, we need to calculate the displacement and divide it by the time interval.

The expression for the object's position in the x-direction is x(t) = 5t^2 + 2t.

Let's find the displacement between t = 1.35 s and t = 2.45 s:

x(2.45) - x(1.35) = (5(2.45)² + 2(2.45)) - (5(1.35)² + 2(1.35))

Calculating the values:

x(2.45) - x(1.35) = (29.4125 + 4.9) - (9.16875 + 2.43)

x(2.45) - x(1.35) = 34.3125 - 11.59875

x(2.45) - x(1.35) ≈ 22.71375

The time interval is t = 2.45 s - t = 1.35 s = 1.10 s.

Now, let's calculate the average velocity:

Average velocity = Displacement / Time interval

Average velocity = 22.71375 / 1.10 ≈ 20.649 m/s

Therefore, the object's average velocity in the x-direction between t = 1.35 s and t = 2.45 s is approximately 20.649 m/s.

For the second question, if an object is dropped from rest and takes 2.94 seconds to reach the ground, we can use the equation of motion for free fall:

h = (1/2) * g * t²

where h is the height, g is the acceleration due to gravity (approximately 9.8 m/s²), and t is the time taken.

Plugging in the values:

h = (1/2) * 9.8 * (2.94)²

h = 1/2 * 9.8 * 8.6436

h ≈ 42.402 m

Therefore, the object was dropped from approximately 42.402 meters above the ground.

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Answer:

the slope would be -1

Step-by-step explanation:

slope is determined by the sign + or - and the number before x

Answer:

The answer is option B.

Step-by-step explanation:

Before the regulations were applied to the field of chemistry, the elements, their characteristics and other information related to them were so disorganized that this was causing the progress in the field to slow down.

So the committees decided to regulate things such as the names of any newly discovered elements, any properties it had so that it could be put to use in a more effective way.

The correct answer for this question is option B.

I hope this answer helps.

The early committees regulated how the newly discovered elements were named.

Around the  mid-1800s to the early 1900s, chemical discoveries soared rapidly due to the invention of new equipment that made research a lot more easier.

Around 1919, the international union of pure and applied chemistry set up committees to regulate the naming of new elements and compounds hence strict rules were set up for the naming of newly discovered elements and compounds.

Hence, the early committees regulated how the newly discovered elements were named.

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Answer

x=5 y=2

Step-by-step explanation:

The probability of the coin showing heads is 1/2.

The probability of the spinner landing on purple is 1/4.

The probability of the cube showing a 1, 2, 3, or 5 is 2/3.

The probability of all three events happening is = 1/12.

Therefore, the probability that Jennifer will flip a heads, spin the spinner on purple, and roll a 1, 2, 3, or 5 is 1/12.

Here is a breakdown of the calculation:

Probability of coin showing heads: 1/2

Probability of spinner landing on purple: 1/4

Probability of cube showing 1, 2, 3, or 5: 2/3

Probability of all three events happening: 1/2 * 1/4 * 2/3 = 1/12

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Answer:

yes

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

c = (1/2) * ln[(1/3) * (e^(8) - e^(2) + 2)]

To find a value c in [1, 4] such that f(c) is equal to the average value of f(x) = e^(2x) + 1 on [1, 4], we need to use the Mean Value Theorem. The Mean Value Theorem states that if f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a number c in (a,b) such that f'(c) = (f(b) - f(a))/(b-a).

First, we need to find the average value of f(x) on [1, 4]. The average value of a function on an interval [a,b] is given by:

Average value = (1/(b-a)) * ∫[a,b] f(x) dx

In this case, a = 1, b = 4, and f(x) = e^(2x) + 1. So the average value is:

Average value = (1/(4-1)) * ∫[1,4] (e^(2x) + 1) dx

= (1/3) * (e^(8) - e^(2) + 3)

Next, we need to find a value c in [1, 4] such that f(c) = average value. So we need to solve the equation:

e^(2c) + 1 = (1/3) * (e^(8) - e^(2) + 3)

Simplifying and rearranging terms gives us:

e^(2c) = (1/3) * (e^(8) - e^(2) + 2)

Taking the natural logarithm of both sides gives us:

2c = ln[(1/3) * (e^(8) - e^(2) + 2)]

Finally, we can solve for c:

c = (1/2) * ln[(1/3) * (e^(8) - e^(2) + 2)]

This is the value of c in [1, 4] such that f(c) is equal to the average value of f(x) on [1, 4].

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Answer:

Step-by-step explanation:

4th

The A 5 gallons of water will pour through the hose in 8 minutes.

The formula to be used for calculation of amount of water pouring through hose :

Total amount of water = amount of water pouring per minute × amount of time (in minutes)

Keep the values in formula to find the total amount of water

Total amount of water = 2.5 × 8

Performing multiplication on Right Hand Side of the equation

Total amount of water = 20 quarts

Now performing unit conversion

Amount of water in gallon = amount of water in quarts × 0.25

Amount of water in gallon = 20 × 0.25

Amount of water = 5 gallon

Hence, the correct answer is A 5.

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For each of the equations;

a) Two solutions

b) Two solutions

c) Two solutions

d) Two solutions

In mathematics, the number of solutions that the equation would have has a lot to do with the kind of equation that we are dealing with. If the equation that we are dealing with is a linear equation then it would have only one solution.

In the same way, if what we have is a quadratic equation of a system of linear equations that have two variables then we are going to have two solutions for the equation.

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The resulting integral of \(\int\limits^{-\sqrt6}_\sqrt6\) ∫ 0 √6-\(y^2\) cos (\(x^2 + y^2\)) dx dy is ∫ 0 π ∫ 0 √6 cos(\(r^2\)) r dr dθ.

To transform the integral to polar coordinates, we substitute x = r cosθ and y = r sinθ. We also need to find the limits of integration in terms of r and θ.

\(\int\limits^{-\sqrt6}_\sqrt6\) ∫ 0 √6-\(y^2 cos (x^2 + y^2)\) dx dy

Using the substitutions, we get:

\(\int\limits^{\theta=0}_{\pi/2\) ∫ r=0 to √(6-\(sin^2\)θ) \(cos(r^2)\) r dr dθ

To evaluate the resulting integral, we first integrate with respect to r from 0 to √(6-\(sin^2\)θ):

\(\int\limits^{\theta=0}_{\pi/2\) ∫ r=0 to √(6-\(sin^2\)θ) \(cos(r^2)\) r dr dθ

= \(\int\limits^{\theta=0}_{\pi/2\) [sin((6-\(sin^2\)θ)/2) * cos((6-\(sin^2\)θ)/2)] dθ

= \(\int\limits^{\theta=0}_{\pi/2\) [sin((6\(cos^2\)θ)/2) * cos((6\(cos^2\)θ)/2)] dθ (using \(sin^2\)θ + \(cos^2\)θ = 1 and substituting cosθ for sinθ)

= \(\int\limits^{\theta=0}_{\pi/2\) 1/2 sin(3θ) dθ

Now we can integrate with respect to θ from 0 to π/2:

\(\int\limits^{\theta=0}_{\pi/2\) 1/2 sin(3θ) dθ

= [-1/6 cos(3θ)] θ=0 to π/2

= 1/6

Therefore, the value of the integral is 1/6.

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Answer:

The scientific notation is  2.622 × 10^14

Step-by-step explanation:

Answer: -12

Step-by-step explanation:

1. Write out the problem

4x+1=-47

2. Subtract 1 from both sides to get rid of the number without a variable, so the equation only has the number with the variable on one side and the number without the variable on the other side.

4x+1=-47

   -1     -1

4x=-48

3. Divide both sides by 4 to isolate x.

4x/4=-48/4

x=-12

\(a^3 \cdot a^4 = a^{3 + 4} = a^7\)

Option B is correct

Answer:

m ZC = 71 degrees. Option C.

Step-by-step explanation:

Triangles always measure a total of 180 degrees.

47 + 62 + c = 180

109 + c = 180

c = 71

Answer:

71°

Step-by-step explanation:

The total angles in a triangle should equal 180°

a + b + c = 180

47 + 62 + c = 180

109 + c = 180

180 - 109 = 71

c = 71°

Hope this helped!

Answer:

x=-6 and x=1

Step-by-step explanation:

Given that:

\(3x^2+15x-18\)

Now,

\(3x^2+15x-18=0\\\)

Using the quadratic formula where a=3, b=15, and C=-18

x=-b±\(\sqrt{b^2-4ac} /2a\)

x=-15±\({\sqrt{15^2-4(3)(-18} } /2(3)\)

x=-15±\(\sqrt{441} /6\)

the discriminant \(b^2-4ac>0\)

So, there are two real roots

x=-15±21/6

\(x=\frac{6}{6} \\x=1\\x=\frac{-36}{6} \\x=-6\)

Therefore, x=-6 and x=1

The p-value for the test of the claims is roughly 0.004.

To test the claim of the bulb patron, we can use a thesis test with the following null and indispensable suppositions.

We can use the binomial distribution to calculate the probability of observing 1050 or further imperfect bulbs out of,000 if the imperfect rate is 0.01 or lower. This probability is the p-value of the test.

To calculate the p-value, we need to use the binomial distribution and find the probability of observing 1050 or further imperfect bulbs out of,000 if the imperfect rate is 0.01 or lower. Using a binomial calculator or statistical software, we can find that the probability of observing 1050 or further imperfect bulbs is roughly 0.004.

Since this p-value is lower than the significant position of 0.05, we can reject the null thesis and conclude that the imperfect rate of the bulbs is more advanced than 0.01.

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The line integral is zero: ∫C 4sin(y)dx + 4xcos(y)dy = 0.

To apply Green's Theorem, we need to find the curl of the vector field F = (4sin(y), 4xcos(y)). We have:

∂F2/∂x = 4cos(y)

∂F1/∂y = 4cos(y)

So the curl of F is:

curl(F) = ∂F2/∂x - ∂F1/∂y = 0

Since the curl of F is zero, we can apply Green's Theorem to find the line integral along the ellipse C:

∫C F · dr = ∬R curl(F) dA = 0

where R is the region enclosed by C, and dA is an infinitesimal area element.

Therefore, the line integral is zero:

∫C 4sin(y)dx + 4xcos(y)dy = 0

So the answer is 0.

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Answer:

A: The line is a dotted line and the shaded part is on the right side of the line

B: Yes it is correct because if u put in the x value and the y value and calculate it the statement is true.

The coefficients a, b, and c depend on the values of k1, k2, and k3, and both Joel and Eve's quadratics yield the same values for these ki when evaluated for x=1, x=2, and x=3, their quadratics are necessarily the same.

Joel and Eve are thinking of quadratics using x as their variable.

When they evaluate their quadratics for x=1, x=2, and x=3, they both get the same results (k1, k2, and k3, respectively).

To determine if their quadratics are necessarily the same, we can set up three equations using ax^2 + bx + c = ki:
1. a + b + c = k1
2. 4a + 2b + c = k2
3. 9a + 3b + c = k3

We can then solve for the quadratic coefficients (a, b, and c) in terms of ki:
a = (k1 - 2k2 + k3) / 2
b = (-5k1 + 8k2 - 3k3) / 2
c = (3k1 - 3k2 + k3)

Since the coefficients a, b, and c depend on the values of k1, k2, and k3, and both Joel and Eve's quadratics yield the same values for this ki when evaluated for x=1, x=2, and x=3, their quadratics are necessarily the same.

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Step-by-step explanation:

Vertical length of the smaller  triangle is:

Horizontal length of the smaller triangle is:

The fraction:

This fraction is same for the larger triangle, which is 4/6 = 2/3.

It means the slopes are same.

Since the slopes are same, the segments are part of same red line.

The given argument is invalid. It says that if one person has more gray hair in their beard than another person, then they have a higher percentage of gray hair in their beard.

The argument is invalid because it is possible for one person to have a higher percentage of gray hair in their beard but a lower number of gray hairs in total.One possible counterexample by model is:Suppose Plato has 200 hairs in his beard and 50 of them are gray. So, 1/4 of his hairs are gray. Now, let's suppose Aristotle has 400 hairs in his beard, and 300 of them are gray. So, 3/4 of his hairs are gray. Even though Plato has fewer gray hairs than Aristotle, his percentage of gray hairs is more significant (1/4) than Aristotle's (3/4).

Therefore, the given argument is invalid since Aristotle's beard contains more gray hairs in quantity, but Plato has a higher percentage of gray hair in his beard.

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Answer:

1500 grams

Step-by-step explanation:

The area of the circle with circumference 19cm is 6.42cm²( nearest hundredth).

Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr2. Where r is the radius.

The circumference of a circle is given as ;

C = 2πr

C = 9cm

therefore, 9 = 2× 3.14 × r

9 = 6.28r

r = 9/6.28

r = 1.43 cm

Area of circle = πr²

= 3.14 × 1.43²

= 6.42cm²( nearest hundredth)

therefore the area of the circle is 6.42cm²

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Answer:

Yep I got that to! 20480

Step-by-step explanation:

I multiplyed them together

Answer:

$1.83

Step-by-step explanation:

$2.15 (original price of cookies) - 15% (discount) = $1.83 (rounded since the original total was: 1.8275)

Answer:

D. for the first one and B. for the second one i think

The phrases that could be represented by the algebraic expression would be as " the sum of  1/5 of m and 4"

Usually, simplification involves proceeding with the pending operations in the expression. Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form. here Simplification usually involves making the expression simple and easy to use later.

We need to write phrases that could be represented by the algebraic expression;

m/5 + 4.

The 1/5 of m means m/5

Then 'the addition of  1/5 of m and 4"

Therefore the phrases that could be represented by the algebraic expression would be as " the sum of  1/5 of m and 4"

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