log based question, i just need help with parts b and c

Answer:

[tex]\large\boxed{x=\dfrac{-9\pm\sqrt{41}}{2}}[/tex]

Step-by-step explanation:

[tex]\text{The quadratic formula of}[/tex]

[tex]ax^2+bx+c=0[/tex]

[tex]\text{If}\ b^2-4a<0,\ \text{then the equation has no solution}\\\\\text{If}\ b^2-4ac=0,\ \text{then the equation has one solution}\ x=\dfrac{-b}{2a}\\\\\text{If}\ b^2-4ac>0,\ \text{then the equation has two solutions}\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\=========================================[/tex]

[tex]\text{We have}\ x^2+9x+10=0\\\\a=1,\ b=9,\ c=10\\\\\text{substitute:}\\\\b^2-4ac=9^2-4(1)(10)=81-40=41>0\qquad _{\text{two solutions}}\\\\\sqrt{b^2-4ac}=\sqrt{41}\\\\x=\dfrac{-9\pm\sqrt{41}}{2(1)}=\dfrac{-9\pm\sqrt{41}}{2}[/tex]

Answer:

Step-by-step explanation:

Points to remember

solution of a quadratic equation ax² + bx + c = 0

x = [-b ± √(b² - 4ac)]/2a

It is given that, x² + 9x + 10 = 0.

To find the solution

Here a = 1, b= 9 and c = 10

x = [-b ± √(b² - 4ac)]/2a

 = [-9 ± √(9² - 4*1*10)]/2*1

 = [-9 ± √(81 - 40)]/2

 =  [-9 ± √(41)]/2

 = [-9 ± √41]/2

Therefore the solution of given quadratic equation  =  [-9 ± √41]/2

Answer:

Step-by-step explanation:

Put z = 5 to the expression (10 + 25) ÷ z:

(10 + 25) ÷ 5 = 35 ÷ 5 = 7

A. -3/8

B. -2/5, -1/2

The formula for area of a sector is...

A = [tex]\frac{1}{2} r^{2}[/tex]θ

NOTE θ is converted from degree to radian

θ = 167 × [tex]\frac{\pi }{180}[/tex]

θ = [tex]\frac{167\pi }{180}[/tex]

so...

A = [tex]\frac{1}{2}(17.8)^{2} (\frac{167\pi }{180})[/tex]

A = (1/2)(316.84)(2.9146)

A = 158.42 * 2.9146

A = 461.7

Hope this helped!

The area of the shaded sector is A = 461.7

The formula for area of a sector is...

[tex]A = (1)/(2) r^(2)θ[/tex]

θ is converted from degree to radian

[tex]θ = 167 × (\pi )/(180)[/tex]

[tex]θ = (167\pi )/(180)[/tex]

so...

[tex]A = (1)/(2)(17.8)^(2) ((167\pi )/(180))[/tex]

A = (1/2)(316.84)(2.9146)

A = 158.42 x  2.9146

A = 461.7

Answer:

Step-by-step explanation:

38. b. the mode would decrease

39. 4 since it is the middle point by count of x

Answer:

1)   the mean would basically decrease so its B

2) the balanced point would be 4 as the two numbers 4 and 4 come in the middle.

~batmans wife dun dun dun....

Answer:

0.22

Step-by-step explanation:

If 58% of the students play neither tennis nor baseball, then;

100 - 58 = 42% play tennis, baseball or both sports. Now,

Pr ( tennis ∪ baseball) = Pr ( tennis) + Pr ( baseball) - Pr ( tennis ∩ baseball)

42% = 40% + 24% -  Pr ( tennis ∩ baseball)

Pr ( tennis ∩ baseball) = 40 + 24 - 42

Pr ( tennis ∩ baseball) = 22%

Therefore, If you pick a student at random the probability that the student plays both tennis and baseball is 0.22

The radius of the circle with a circumference of 12.56 inches is 2 inches, calculated using the formula C = 2πr and rearranging it to find the radius.

The circumference of a circle is given by the formula C = 2πr, where C stands for the circumference and r stands for the radius of the circle. The value of π (pi) is approximately 3.14159. Given the circumference of the circle as 12.56 inches, you can find the radius by rearranging the equation to r = C / (2π).

Now, let's calculate the radius using the given circumference:

r = 12.56 inches / (2 × 3.14159)

r = 12.56 inches / 6.28318

r = 2 inches

Therefore, the measure of the radius of the circle is 2 inches, which corresponds to option A.

To find the measure of the radius of the circle given its circumference, we can use the circumference formula of a circle, which is:
\[ C = 2 \pi r \]
Where \( C \) is the circumference, \( \pi \approx 3.14159 \), and \( r \) is the radius of the circle.
Now, we know the circumference (\( C \)) is 12.56 inches. We can solve for the radius (\( r \)) by rearranging the formula:
\[ r = \frac{C}{2 \pi} \]
Plugging the given circumference into the equation, we get:
\[ r = \frac{12.56}{2 \times \pi} \]
\[ r = \frac{12.56}{2 \times 3.14159} \]
\[ r = \frac{12.56}{6.28318} \]
\[ r = 2 \]
Rounding the result to two decimal places as may be required for some comparisons, we still get \( r = 2.00 \) inches.
Therefore, the measure of the radius of the circle is 2 inches, which corresponds to option A.

Answer:

D. The last one

Step-by-step explanation:

When you convert measures into m³ the measurement is the SAME but it changed from cm to m. That's it.

Answer:

1:3

Step-by-step explanation:

if a + b = 4a then b has to be 3a

(1) + (3) = 4(1)

(2) + (6) = 4(2)

it works no matter what you plug in for a

To find the ratio a:b given that a+b=4a, we rearrange the equation to find b=3a, and then simplify the ratio to get 1:3.

To find the ratio a:b, given that a+b=4a, we first need to express b in terms of a. This can be done by subtracting a from both sides of the equation:

a + b - a = 4a - a

b = 3a

Now that we have b expressed as 3a, we can find the ratio of a to b:

a : b = a : 3a

As we can simplify the ratio by dividing both terms by a (assuming a is not zero):

a : b = 1 : 3

Therefore, the ratio of a to b is 1:3.

Answer: 25

Form a proportion. Let x be the missing term.

[tex]\frac{60}{144} = \frac{x}{60}[/tex]

Solve for x by cross-multiplying.

[tex]144x = 60(60)\\144x = 3600\\x = 25[/tex]

Answer:

Step-by-step explanation:

Use FOIL: (a + b)(c + d) = ac + ad + bc + bd

and i² = -1

[tex](3+i)(4+2i)\\\\=(3)(4)+(3)(2i)+(i)(4)+(i)(2i)\\\\=12+6i+4i+2i^2\qquad\text{combine like terms}\\\\=(12-2)+(6i+4i)\\\\=10+10i[/tex]

Answer:

11 + 10i

Step-by-step explanation:

Note that we're multiplying two binomials here, and thus may use the FOIL method.  This requires four multiplications, as follows:

3*4 + 3*2i + 4i - 1               (The last term is 1 because i(i) = i^2 = -1.)

Simplifying, we get:

12 + 6i + 4i -1, or:

11 + 10i

Answer:

Quotient: y^2 -2y +3

Remainder = 0

Step-by-step explanation:

We need to solve he equation:

y^3-4y^2+7y-6 ÷ y -2

It is solved in the figure attached below:

After solving we get

Quotient: y^2 -2y +3

Remainder = 0

ANSWER

y=(x+3)(x-1)(x-5)

EXPLANATION

The given polynomial has x-intercepts at x=-3,x=1,x=5

These are called the zeros of this polynomial.

We can use the factor theorem to obtain the polynomial in factored form.

The polynomial in factored form is of the form

y=a(x+3)(x-1)(x-5)

The polynomial rises on the left and keep rising on the right.

This implies that, the 'a' is positive.

Therefore

y=(x+3)(x-1)(x-5)

The correct choice is the first option.

Answer: y = (x + 3)(x - 1)(x - 5)

So in your case, it would be C.

Answer:

C ≈ 56.55

Step-by-step explanation:

First I translated this into English.

"Find the circumference of a circle whose diameter is 18 cm."

Formula:

C = 2πr

Translated in Spanish:

Primero tienes que dividir la circunferencia por dos. Luego lo enchufas en la fórmula para "R" y resuelves.

English Translation:

First you have to divide the circumference by two. Then you plug it into the formula for "R" and solve.

How much money you will make is included in a financial plan to protect assets. Hence, option A is correct.

Financial plan is the compressive study and understanding of the financial goals with looking the current situation or current financial condition. Financial plan is the best way to achieve the targeted goal in life, as it give a map and blueprint to the person to go with.

Some of the strategies to make the financial plan -

Thus, option A is correct.

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Answer:

Step-by-step explanation:

4,3

Answer:

C.

Step-by-step explanation:

(m^2-m-3) + (m-4)

there is no like terms for m^2 so it stays the stay.

next you add -m to m because the first m is negative they cancel out leaving nothing. lastly we add -4+-3 these added together give you -7.

so you are left with m^2 +0 -7

which simplifies to m^2 - 7

Answer:

1st option because those angles are a linear pair.

Answer:

b I think

Step-by-step explanation:

hope that's helped

Answer:

Step-by-step explanation:

its A

Answer:

13.6

Step-by-step explanation:

I gave the same explanation on your previous question.

Answer:

The value of c is 10.9 ⇒ 3rd answer

Step-by-step explanation:

* Lets study the problem

* In ΔABC

- a, b, c are the lengths of its 3 sides, where

# a is opposite to angle A  ⇒ BC

# b is opposite to angle B  ⇒ AC

# c is opposite to angle C  ⇒ AB

- m∠C = 68°  

- a = 8 ⇒ side BC

- b = 11 ⇒ side AC

- Find the value of c ⇒ side AB

* We have the length of two sides and the measure of the

  including angle between them and we want to find the

  length of the side opposite to this angle then the cosine

  rule is the perfect way

∵ c² = a² + b² - 2ab cos(C)

∵ a = 8 , b = 11 and m∠C = 68°

∴ c² = (8)² + (11)² -2(8)(11) cos(68°)

∴ c² = 119.069 ⇒ take √ for both sides

∴ c = 10.9 units

* The value of c is 10.9

To find the two numbers, we set up a system of equations and solve it to find the values of x and y.

To solve this problem, we can set up a system of equations. Let's represent the two numbers as x and y. Since the sum of the two numbers is 24, we can write the equation:

x + y = 24

Twice the smaller number, which is 2x, is 3 less than the larger number, so we can write the equation:

2x = y - 3

Now we can solve this system of equations using substitution or elimination method. Let's start with substitution method:

Therefore, the two numbers are 7 and 17.

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the two numbers are 7 and 17.

The problem states that the sum of two numbers is 24 and that twice the smaller number is 3 less than the larger number. Let's denote the smaller number as 'x' and the larger number as 'y'. According to the first condition, we have:

x + y = 24 ... (1)

For the second condition, twice the smaller number (2x) is 3 less than the larger number (y), so we have:

2x = y - 3 ... (2)

To find the two numbers, we solve these equations simultaneously. By rearranging equation (2), we get y = 2x + 3. Substituting this into equation (1), we have:

x + (2x + 3) = 24

3x + 3 = 24

3x = 24 - 3

3x = 21

x = 7

Now that we have the smaller number, we substitute x back into equation (1) to find the larger number:

7 + y = 24

y = 24 - 7

y = 17

Thus, the two numbers are 7 and 17.

Answer:

x=35

Step-by-step explanation:

These are alternate interior angles.  Since a and b are parallel, they are equal

5x - 54 = 3x+16

Subtract 3x from each side

5x-3x -54 = 3x -3x +16

2x -54 = 16

Add 54 to each side

2x-54+54 = 16+54

2x = 70

Divide each side by 2

2x/2 = 70/2

x = 35

Answer:

[tex]y=256e^{-0.288x}[/tex]

where y is in thousands

Step-by-step explanation:

The equation in two variables that can be used to represent the situation given can be determined using computer software such Stat-Crunch or Ms. Excel or advanced calculators.

I shall use Ms. Excel for this question.

In Ms. Excel, enter the data into any two adjacent columns. Next, highlight the data, then click the insert ribbon and select the scatter-plot option.

Excel returns a scatter-plot chart as shown in the attachment below.

After obtaining the scatter-plot, we shall need to add a trend line in order to determine the mathematical equation that best fits the scenario given.

Click anywhere inside the chart, then select the design tab under chart tools. Click on the Add Chart element in the upper left corner of the excel workbook and select more trend-line options. This feature will enable us to fit any trend-line to our data.

Select the exponential option, since we were informed that he number of flip cell phones is in exponential decline,ensuring you check the box; Display Equation on chart.

Find the attached.

The equation in two variables is thus;

[tex]y=256e^{-0.288x}[/tex]

Answer:

x = -2

Step-by-step explanation:

In order to find the axis of symmetry, we will have to find the x-value of the vertex.

Vertex = (-b/2a, f(-b/2a))

In x² + 4x + 6,

a = 1 , b = 4 , c = 6

Vertex = (-4/2,f(-4/2))

Vertex = (-2,f(-2))

We have found the x-value of the vertex which is -2.

Hence, line/axis of symmetry is x = -2

The axis of symmetry for f(x) = [tex]x^2 + 4x + 6[/tex]  is -2.

Given that,

Based on the above information, the calculation is as follows:

Here we have to determine the x-value of the vertex.

[tex]Vertex = (-b\div 2a, f(-b\div 2a))[/tex]

Now as per the given equation i.e [tex]x^2 + 4x + 6[/tex]

Here,

a = 1 , b = 4 , c = 6

Now  

[tex]Vertex = (-4\div 2,f(-4\div 2))[/tex]

 = (-2,f(-2))

= -2

Therefore we can conclude that the axis of symmetry for f(x) = [tex]x^2 + 4x + 6[/tex]  is -2.

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Answer:

A. he held the tube iver the flame too long

Final answer:

The cracking of the test tube could have been caused by thermal shock due to overheating one side of the test tube by holding it over the flame for too long, or by heating an empty test tube meant for containing liquids.

Explanation:

When heating substances in a test tube, such as in a chemistry lab, it's important to take certain precautions to prevent accidents, such as the cracking of the test tube. One potential cause for a test tube to crack is thermal shock, which can occur if the test tube is heated too quickly or unevenly. This brings us to option A: 'He held the test tube directly over the flame for too long'. Holding a test tube directly in the flame can cause one side to expand more rapidly than the other due to the heat, leading to stress and cracking, particularly if the glass isn't designed to withstand rapid temperature changes. To avoid this, the test tube should be moved in and out of the flame to heat it gently and evenly, and a boiling chip can be used to prevent superheating and ensure smooth boiling.

Option B suggests another possibility: 'He did not add water to the test tube'. While not adding water to a test tube might not directly cause it to crack, if the test tube was meant to contain a liquid and was instead heated while empty, the glass could become too hot and weaken, increasing the chance of breaking. It's always important to follow specific instructions for each experiment, including whether or not to add substances to the test tube.

Both scenarios emphasize the importance of careful temperature control when heating glassware to avoid breakage from thermal stress.

Answer:

x=5

Step-by-step explanation:

4x-7(x+3)=-36

Distribute

4x-7x-21=-36

Combine like terms

-3x-21 = -36

Add 21 to each side

-3x+21 = -36+21

-3x = -15

Divide by -3

-3x/-3 = -15/-3

x = 5

Answer: use photomath

Step-by-step explanation:

Answer:

This is the exact answer

Sample response: A triangular prism has a 3-sided base and 3 lateral faces. A rectangular prism has a 4-sided base and 4 lateral faces. The number of sides of the base of a prism is equal to the number of lateral faces of the prism.

Step-by-step explanation:

Answer:

A triangular prism has a 3-sided base and 3 lateral faces. A rectangular prism has a 4-sided base and 4 lateral faces. The number of sides of the base of a prism is equal to the number of lateral faces of the prism.

Step-by-step explanation:

creds to the other person

Answer:

(-15)/3 = -5  

Step-by-step explanation:

(-15)/3

Assume that your positive tiles are yellow, and your negative tiles are red.

The question is asking, "if you take 15 red tiles and split them into three equal groups, how many will you have in each group?"

How can you model the first value of -15?  With 15 red tiles.

Let’s model how to divide the tiles into three equal groups by moving one tile at a time into three separate groups until all 15 tiles have been moved.

Step 1.

Start with 15 red tiles, as in the first picture.

Step 2.

Start by moving tiles one at a time to begin creating three new groups.

The middle picture shows the situation after you have moved the first three tiles.

Step 3.  

Continue moving tiles one at a time from the original group and stacking them evenly in the three new groups until you have no more tiles to move.  

The third picture shows the situation when you have finished.

How many red tiles are in each group?  There are five.

Is the answer positive or negative?  The answer is negative, because there are five red negative tiles in each group.

Conclusion? (-15)/3 = -5

Integers are expressions without decimals.

The result of the quotient of -15 and 3 is: -5

The expression is given as:

[tex]\mathbf{\frac{-15}{3}}[/tex]

To do this using integer tiles, we start by isolating the negative sign

[tex]\mathbf{\frac{-15}{3} = (-)\frac{15}{3}}[/tex]

Then divide 15 by 3 (see attachment for illustration of the division)

From the attached figure, we have:

[tex]\mathbf{\frac{15}{3} = 5}[/tex]

Substitute 5 for 15/3 in [tex]\mathbf{\frac{-15}{3} = (-)\frac{15}{3}}[/tex]

So, we have:

[tex]\mathbf{\frac{-15}{3} = (-)5}[/tex]

Remove bracket

[tex]\mathbf{\frac{-15}{3} = -5}[/tex]

Hence, the result of the expression is: -5

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Answer:

the solution is (5, 6)

Step-by-step explanation:

Please reserve " × " for representing multiplication, and " x " as a variable name.

Starting with the system

6x-5y= 0  

4×-5y = -10​

multiply the 2nd equation by -1.  This results in the system

6x - 5y  = 0  

-4x + 5y = 10

and combining these two equations results in

​ 6x - 5y  = 0  

-4x + 5y = 10

------------------

2x         = 10, or x = 5.

Substituting 5 for x in the first equation, we get

6(5) - 5y = 0, or 5y = 30.  Then y = 6, and the solution is (5, 6).