How to solve logarithmic equations as such

V=1728m³

Hope this answer helps!!

Answer:  [tex]\bold{f(x)=2\bigg(x+\dfrac{3}{4}\bigg)^2+\dfrac{-25}{8} }[/tex]

Step-by-step explanation:

f(x) = 2x² + 3x - 2

[tex]\text{Add 2 to both sides:}\\f(x) + 2 = 2x^2+3x\\\\\\\text{Factor out 2 on the right side:}\\f(x) + 2 = 2\bigg(x^2+\dfrac{3}{2}x\bigg)\\\\\\\text{Add the value that creates a perfect square on the right side:}\\f(x) + 2 + 2\bigg(\dfrac{3}{2\cdot2}\bigg)^2=2\bigg[x^2+\dfrac{3}{2}x+\bigg(\dfrac{3}{2\cdot2}\bigg)^2\bigg]\\\\\\\text{Simplify:}\\f(x)+2+\dfrac{9}{8}=2\bigg(x+\dfrac{3}{4}\bigg)^2\\\\\\\text{Isolate f(x):}\\f(x)=2\bigg(x+\dfrac{3}{4}\bigg)^2+\dfrac{-25}{8}\\[/tex]

Answer: OPTION A

Step-by-step explanation:

To find the zeros of the quadratic equation given in the exercise, you need to apply the proccedure shown below:

- You must rewrite it as following:

[tex]2x^2+9x+4=0[/tex]

-You can apply the Quadratic formula, which is shown below:

[tex]x=\frac{-b\±\sqrt{b^2-4c}}{2a}[/tex]

In this case:

[tex]a=2\\b=9\\c=4[/tex]

- Therefore, when you substitute values, you obtain:

[tex]x=\frac{-9\±\sqrt{(9)^2-4(2)(4)}}{2(2)}[/tex]

[tex]x_1=-4\\\\x_2=-\frac{1}{2}[/tex]

The zeroes of the function y = 2x² + 9x + 4 is x = -1/2 and x = -4.

Given a function,

y = 2x² + 9x + 4

We have to find the zeroes of the function.

Zeroes of the function are the values of x or the input values when the values of y or the output values become 0.

Here the zeroes are the x values when y = 0.

Consider,

y = 2x² + 9x + 4

Let y = 0

2x² + 9x + 4 = 0

Using the quadratic formula,

Discriminant = √(9² - (4×2×4)) = √49 = 7

x values are,

x = (-9 ± 7) / 4

x = -1/2 and x = -4

Hence the correct option is A.

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The division of 5,945 by 612 yields a quotient of 9 with a remainder of 437, which corresponds to option C: 9 R437.

To solve the division problem 5,945 \/ 612, we'll use long division:

First, see how many times 612 fits into 5,945.

Starting from the left, 612 does not fit into 5. We extend it to 59, but 612 doesn't fit into 59 either.

When we take the first three digits, 612 fits into 594 exactly 0 times. So we take one more digit. 612 fits into 5,945 around 9 times because 612 * 9 = 5,508 which is less than 5,945.

Subtract 5,508 from 5,945 to get the remainder. 5,945 - 5,508 = 437.

The quotient is 9 with a remainder of 437, which matches option C: 9 R437.

Answer:

Step-by-step explanation:

1, 16

2, 75

3, 28

4, 9

5, 48

6, 2

7, 24

Answer:

1.) 16 apples total

2.) 75 cupcakes

3.) $28

Step-by-step explanation:

1.) 5 bags = 2 apples 2*5 = 10 apples for 5 bags 6 from the pervious bags ->

10 +6 = 16 total apples

2.) 45 - 3 = 42 cupcakes.. then she makes 33 more, so add 42 + 33 = 75 cupcakes

3.) each bar is $4 -> 15 bars per box -> sold 7 bars.. she made $28

hope this helps!!

Final answer:

Francisco's water bottle volume can be calculated using the volume formula for a cylinder. With the given height of 20 cm and radius of 4 cm, the volume comes out to approximately 1.005 liters.

Explanation:

Francisco wants to achieve his daily water intake goal of 2 liters and is curious about the volume of his water bottle with dimensions of a 20 cm height and 4 cm radius. To find the volume of a cylindrical object like a water bottle, we use the formula for the volume of a cylinder, V = πr2h, where V is the volume, r is the radius, and h is the height of the cylinder.

Substituting the given values into the formula:

V = π(4 cm)2(20 cm) = π(16 cm2)(20 cm) = 320π cm3

Since 1 liter is equivalent to 1,000 cubic centimeters (cm3), we convert the volume from cubic centimeters to liters:

V = 320π cm3 × (1 liter/1,000 cm3) ≈ 1.005 liters

Therefore, Francisco's water bottle has a volume of approximately 1.005 liters.

Answer: The correct answer is the one on the lower left.

Step-by-step explanation: You are looking for the equation that is five times the quotient of a number and 10.

Since it is five times the quotient, you are looking for an expression that has 5 outside of the parentheses, and a quotient means that there is division taking place. The only option that has 5 outside parentheses with division inside the parentheses is the lower left.

Answer: The answer is lower left: C. 5(z/10).

Step-by-step explanation:

In simple terms, an adjacent angle shares a common vertex and one side with the given angle. From the choices given, Angle BGE is adjacent to Angle BGC since it shares the vertex G and side BG.

In geometry, an adjacent angle shares a common vertex and a common side but do not overlap. If we consider the Angle BGC, the angle that shares its vertex at G and one of its sides (the side GB or GC) would be the adjacent angle. Based on the options provided and the definition of adjacent angles, the angle adjacent to Angle BGC would be Angle BGE as it fulfills the criteria of sharing a common vertex (G) and a side (BG) with Angle BGC.

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Your smallest angle is 26°

Angles in a triangle add up to 180°. This means:

Angle1 + Angle2 + Angle3 = 180°

The second angle of a triangle is 3 times as large as the first.

Angle2 = 3 * Angle1

The third angle is 50° more than the first.

Angle3 = Angle1 + 50°

Substitute these into the first formula, in terms of Angle1.

Angle1 + (3 * Angle1) + (Angle1 + 50°) = 180°

Expand and simplify.

5 * Angle1 + 50° = 180°

Put it into the formula Ax = B. You will have all the variables on one side and the integers on the other.

5 * Angle1 + 50° = 180°

5 * Angle1 + 50° - 50° = 180° - 50°

5 * Angle1 = 130°

Put it into the formula x = b. Solve to find 1 of the variable.

5 * Angle1 = 130°

5 * Angle1 / 5 = 130° / 5

Angle1 = 26°

Check this is right by substituting into the given formulas.

Angle2 = 3 * Angle1

Angle2 = 3 * 26

78 = 3 * 26

Angle3 = Angle1 + 50°

Angle3 = 26 + 50°

76 = 26 + 50°

Angle1 + Angle2 + Angle3 = 180°

26 + 78 + 76 = 180°

The smallest angle of the triangle is 26 degrees.

The question is referring to a triangle, and the sum of the angles in a triangle is always 180°. Let's denote the first angle as 'x'. According to the question, the second angle is 3x and the third angle is x + 50°. Therefore, we set up the equation x + 3x + x + 50 = 180. This simplifies to 5x + 50 = 180. After subtracting 50 on both sides of the equation, we get 5x = 130, and hence, x = 130 / 5 = 26. Therefore, the smallest angle is 26°.

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Answer:

I believe it's P- 3250 (2.5) t

Step-by-step explanation:

If the framework is k= yx, P is the population total. 3250 is the number after 200 and 2.5t is the rate it increases by 2.5% every year, t

Answer:

Option D. [tex]40\°[/tex]

Step-by-step explanation:

we know that

The inscribed angle measures half that of the arc comprising

so

[tex]m<QPS=\frac{1}{2}(minor\ arc\ QS)[/tex]

we have

[tex]m<QPS=20\°[/tex] ----> given problem

substitute

[tex]20\°=\frac{1}{2}(minor\ arc\ QS)[/tex]

[tex]40\°=(minor\ arc\ QS)[/tex]

Rewrite

[tex]minor\ arc\ QS=40\°[/tex]

Numbers on dice: 1,2,3,4,5,6= 6 numbers

Odd numbers: 1,3,5 = 3 number

P=3/6= 1/2

To find the weight of a cylindrical oak tree stump with a diameter of 3 feet and a height of 2 feet, calculate its volume and multiply by the average weight of oak per cubic foot, resulting in approximately 834.1 pounds.

The question is asking us to calculate the weight of a cylindrical oak tree stump, given its dimensions and the average weight of oak per cubic foot. To do this, we will first find the volume of the stump and then multiply it by the average weight of oak to find the total weight.

Round to the nearest tenth, the stump weighs approximately 834.1 pounds.

Answer:d

Step-by-step explanation:because of you add 500 and 3%

Answer:

Mean: 4, Median: 4, Mode: 4, Range: 5

Step-by-step explanation:

First Put the numbers in order from least to greatest:

2, 2.5, 3.1, 3.7, 4.3, 4.3, 5.1, 7

MEAN: The mean of a group of numbers is the the average so we'll add up all the numbers then divide them by the amount of numbers total. In this case: the um of all the numbers is 32. We are going to now dived 32 by 8, because there are 8 numbers. Using my multiplication facts, I know that 8*4 equals 32, therefore, 32/8 equals 4. So your mean is 4

MEDIAN: Your median is the middle number. This is why it was helpful to put the numbers in alphabetical order. In this one, you will cross off numbers from each end to find the one in the middle. Here is where it would be good to  have a piece of paper and a pencil to cross out the numbers as you go. If you don't have paper, you can use your fingers, which is what I did. Take your finger and put it in front of the end numbers and from there keep going until you have a final middle number. In this case, there are 2 numbers in the middle, so you take the average of those 2 numbers. The two numbers in this problem are 3.7 and 4.3. You ad those together, and you get 8, now you divide 8 by 2 because you have 2 numbers. 8/2 is 4. So your median is 4.

MODE: is the easiest. It's simply the number that appears the most times in the sequence of numbers. so the mode here is 4.3.  

RANGE: Range is the difference between the number with the highest value and the number with the lowest value. The highest value is 7 and the lowest is 2. 7-2 equals 5. So your range is 5

I hope this was helpful!

To calculate the mean, add all numbers together and divide by the count: the mean is 4. Order the numbers to find the median, which is the average of the two middle numbers: the median is also 4. The mode is the most frequent number: in this case, 4.3. Lastly, the range is the difference between the largest and smallest numbers: the range is 5.

To find the mean, median, mode, and range of the given set of numbers (5.1, 3.7, 3.1, 4.3, 7, 2, 4.3, 2.5), let's calculate each one step-by-step.

Mean: Add up all the numbers and divide by the total count:

Mean = (5.1 + 3.7 + 3.1 + 4.3 + 7 + 2 + 4.3 + 2.5) / 8

Mean = 32 / 8 = 4. The mean is 4.

Median: Order the numbers from least to greatest and find the middle number. If there is an even number of data points, take the average of the two middle numbers: 2, 2.5, 3.1, 3.7, 4.3, 4.3, 5.1, 7.

Median is (3.7 + 4.3) / 2 = 4.

Mode: The number that appears most often. In this set, 4.3 appears twice, so the mode is 4.3.

Range: Subtract the smallest number from the largest number in the set: 7 - 2 = 5. The range is 5.

Therefore, the mean is 4, the median is 4, the mode is 4.3, and the range is 5.

Answer:

a)105

Step-by-step explanation:

first we plug in 12 for where the x is.

then we simplify the expression and get 105

~~bangtanboys7

the parallelogram in the image is a rectangle. There are two ways to tell this from the information given: The diagonals of a rectangle bisect each other, but the diagonals in the image do not bisect each other. The opposite sides of a rectangle are congruent, and the sides of the parallelogram in the image appear to be congruent.

The diagonals are perpendicular. In the image, one of the answer choices states that the diagonals are perpendicular, and this is the key giveaway. Diagonals of a rectangle are always perpendicular, so if a parallelogram has perpendicular diagonals, it must be a rectangle.

The diagonals are congruent. Another answer choice states that the diagonals are congruent. While this is also true for rectangles, it is not true for all parallelograms. So, while not all parallelograms with congruent diagonals are rectangles, all rectangles do have congruent diagonals.

Therefore, based on the information given in the image, we can conclude that the parallelogram is a rectangle.

Here are some additional properties of rectangles that you may find helpful:

Opposite sides of a rectangle are equal and parallel.

Opposite angles of a rectangle are equal.

All angles of a rectangle are right angles.

The diagonals of a rectangle bisect each other.

Answer:

180

Step-by-step explanation:

We can use the central angle theorem to understand this problem.

The Central Angle Theorem states that the inscribed angle that fall on the opposite side of the circumference is half of the arc subtended by it.

The angle that is on the opposite side of the circumference is a right angle and thus it measures 90°. This is half of the arc labeled x. So x is twice that of 90.

So, x = 180 degrees

Answer:

180°

Step-by-step explanation:

The angle subtended by the arc is calculated as follows. The angle made at the center by an arc is twice the angle subtended at the circumference.

In the figure the angle subtended at the circumference by the arc is a right angle, that is, 90°  thus the angle that subtends the arc is 2×90=180°

Answer: C. (-7x+9)(x-2)

Step-by-step explanation:

1. Factor out the negative sign.

−(7x^2+5x−18)

2. Split the second term in 7x2+5x−18 into two terms.

−(7x^​2​​+14x−9x−18)

3, Factor out common terms in the first two terms, then in the last two terms.

−(7x(x+2)−9(x+2))

4.  Factor out the common term x+2x+2x+2.

−(x+2)(7x−9) or (-7x+9)(x-2)

The correct factorization of the trinomial [tex]-7x^{2} - 5x + 18[/tex] is Option (B) [tex]-1(7x - 9)(x + 2)[/tex]

The given expression is - [tex]-7x^{2} - 5x + 18[/tex]

Factorizing the given expression -

=  [tex]-7x^{2} - 5x + 18[/tex]

=  [tex]-(7x^{2} + 5x - 18)[/tex]

=  [tex]-(7x^{2} + 14x - 9x - 18)[/tex]

=  [tex]-[7x(x + 2) - 9(x + 2)][/tex]

=  [tex]-1(7x - 9)(x + 2)[/tex]

Thus the factorization of the equation is Option (B) [tex]-1(7x - 9)(x + 2)[/tex]

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Answer:3,000.000+800.000+90.000,7.000+0.003

Step-by-step explanation:

you would write these with each of the positions separate and add them as listed above

Answer:

Where it says "add attachment" with the paper clip, select your picture from there. If you don't know how to do that, take a picture of it with your phone, email it to yourself, and download it on your computer. It should then be in a folder called "downloads" or something similar. Feel free to ask further questions if you're still stuck!

Step-by-step explanation:

if you could take a screenshot, take it and then use the paper clip to clip it to the question.

Answer:

The measure of the smallest angle is 77°

Step-by-step explanation:

* Lats study some facts about the circle

* In any circle; If the vertices of a quadrilateral lie on its

 circumference then the quadrilateral is called a cyclic quadrilateral

- In any cyclic quadrilateral each two opposite angles are supplementary

 that means their sum = 180°

* In any circle; if the vertex of an angle lies on the circumference

 is called an inscribed angle

- The inscribed angle subtended by the opposite arc

- The measure of the inscribed angle = 1/2 the measure of

  the subtended arc

* Now we can solve our question

∵ R , A , T , E all on the the circumference of the circle

∴ RATE is a cyclic quadrilateral

∵ Angle RAT is an inscribed angle subtended by arc RET

∵ The measure of arc RE = 121°

∵ The measure of arc ET = 51°

∴ The measure of arc RET = 121 + 51 = 172°

∵ m∠RAT = (1/2) measure of arc RET

∴ m∠RAT = (1/2) × 172 = 86°

∵ Angle ATE is an inscribed angle subtended by arc ARE

∵ The measure of arc AR = 85°

∵ The measure of arc RE = 121°

∴ The measure of arc ARE = 85 + 121 = 206°

∵ m∠ATE = (1/2) measure of arc ARE

∴ m∠ATE = (1/2) × 206 = 103°

* Now lets find the remainder angles by using cyclic quadrilateral

∵ RATE is a cyclic quadrilateral

∴ m∠RAT + m∠RET = 180°

∵ m∠RAT = 86°

∴ m∠RET = 180 - 86 = 94°

* Similar;

∵ RATE is a cyclic quadrilateral

∴ m∠ATE + m∠ARE = 180°

∵ m∠ATE = 103°

∴ m∠ARE = 180 - 103 = 77°

* The measure of the smallest angle is 77°

Answer:

77

Step-by-step explanation:

Answer:   [tex]\bold{8\sqrt[5]{8} }[/tex]

Step-by-step explanation:

[tex]64^{\frac{3}{5}}\\\\=2^{6(\frac{3}{5})}\\\\=2^{\frac{18}{5}}\\\\=2^{\frac{15}{5}}\cdot 2^{\frac{3}{5}}\\\\=2^3\cdot \sqrt[5]{2^3} \\\\=\boxed{8\sqrt[5]{8} }[/tex]

Answer:

i think maybe A.

Step-by-step explanation:

Answer:

48m^6

Step-by-step explanation:

=(6m^4 )(8m^2 )

The constants are multiplied and the exponents of same variables are added in polynomial multiplication.

=(6*8)(m^(4+2))

=48m^6

rise over run

you can remember it doing the vertical over horizontal

Answer:

Step-by-step explanation:

It’s rise over run

Answer:2.6363 so if you estimate it it is 2.64

Answer:

2.6̅3

Step-by-step explanation:

Everything is on this file, enjoy!!!

Answer:

15 yd = 45 ft because :

Step-by-step explanation:

You have to multiply the length by 3.

1 yd = 3 ft.

15 x 3 = 45.

Hope this helps,

Davinia.

Answer:

They all have equal sides.

Step-by-step explanation:

All angles are 60◦, thus all corresponding angles are equal. Since all the sides are equal in each triangle, the ratio of corresponding sides will all be equal.

Answer: OPTION D

Step-by-step explanation:

Solve for x in each inequality given in the problem, as you can see below:

[tex]-2x+11>31[/tex]

[tex]-2x+11>31\\-2x>31-11\\-2x>20\\x<-10[/tex]

[tex]7x-4\geq17\\7x\geq17+4\\7x\geq21\\x\geq3[/tex]

Finally you must make the union of both solutions obtained above.

Then for the first inequality you have:

[tex]x<-10[/tex]

and for the second inequality you have:

[tex]x\geq3[/tex]

Therefore, the solution is:

[tex]x<-10\ or\ x\geq3[/tex]

Answer:

The correct answer option is D. x < -10 or x ≥ 3.

Step-by-step explanation:

We are given the following compound inequality and we are to solve it:

[tex]-2x + 11 > 31[/tex] or [tex]7x- 4 \geq  17[/tex]

Solving them to get:

[tex]-2x+11>31[/tex]

[tex]-2x>31-11[/tex]

[tex]-2x>20[/tex]

[tex]x<-\frac{20}{2}[/tex]

x < -10

[tex]7x-4\geq 17[/tex]

[tex]7x\geq 17+4[/tex]

[tex]x\geq \frac{21}{7}[/tex]

x ≥ 3

Therefore, the correct answer option is D. x < -10 or x ≥ 3.