PLEASE HELP
OFFERING 10 POINTS

Answer:

  (d)  b = 7

Step-by-step explanation:

You want the solution to b³ = 343.

The equation can be written in standard form and factored according to the factoring of the difference of cubes:

  b³ -343 = 0

  (b -7)(b² +7b +49) = 0

The solutions to this are the values of b that make the factors 0.

  b -7 = 0   ⇒   b = 7

  b² +7b +49 = 0   ⇒   b = -3.5 ± i√36.75 . . . . . complex solutions

The one real solution to the equation is b = 7.

__

Additional comment

Every cubic has 3 solutions. Here, two of them are complex. When the only terms in the equation are the cubic term and the constant, there will always be only one real root.

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The equation b^3 = 343 has two valid real solutions: b = 7 and b = -7. Both values satisfy the equation and meet the given condition. Option B.

To determine the value of b, we can solve the equation b^3 = 343.

Taking the cube root of both sides, we get:

b = ∛343

The cube root of 343 is 7, since 7 * 7 * 7 = 343. Therefore, one solution to the equation is b = 7.

However, it's important to note that the cube root function has a real and complex solution. In this case, b = 7 is the real solution, but there are two additional complex solutions.

Using complex numbers, we can express the other two solutions as follows:

b = -∛343

b = -7

So the complete set of solutions for b is b = 7, -7.

In summary, the equation b^3 = 343 has two real solutions: b = 7 and b = -7. These solutions satisfy the equation and fulfill the condition. So Option B is correct.

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a.

Noah put marbles on a bag, each color marble represents that the battery of the toy died before 15 hours (red marbles) or that the battery lasted after 15 hours (green marbles)

There are 4 batteries on the toy, for each battery there are two possible outcomes, each one represented by a red and green marble.

So, for each battery, he has to put two marbles. There will be 4 red marbles and 4 green marbles in the bag.

b.

To estimate the probability that at least one battery will die within 15 hours, you have to calculate the expected value.

1. The value of 34% of 850 is 289.

3. The amount that Kepley paid for the tool is $120.

From the information, we want to calculate 34% of 850. This will be calculated thus:

= 34% ×850

= 34/100 × 850

= 0.34 × 850

= 289

The amount paid for the tool will be:

= Price or tool - Discount

= $200 - (40% × $200)

= $200 - $80

= $120

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A lollypop have a circular shape

Diameter D is the line in a circumference that divides it in half

then calculate directly π• D

to the nearest tenth

π•D = 3.14 x 2 = 6.28

then nearest number is 6.3 , or 6.30. Option C)

Answer:

draw a line from the top left to the bottom right going through the centre

Step-by-step explanation:

because m=-1 (gradient)

and b=0 (y intercept)

the sum of the internal angles of a triangle is equal to 180, then

so

answer:

angle 1 = 2x + 7 = 2(23) + 7 = 46 + 7 = 53°

angle 2 = 5x = 5(23) = 115°

angle 3 = 12°

4a)

Looking at the figure,

AD and BE are parallel lines

AE and BD are transversals

Thus,

angle DAE is congruent to angle BEA because they are alternate angles(They lie in similar positions but on alternate sides of the transversal

Also,

angle ADB is congruent to angle EBD because they are alternate angles(They lie in similar positions but on alternate sides of the transversal.

Angle ACD is congruent to angle BCE

Recall, 2 triangles are similar if at least, 2 of their corresponding angles are congruent. In this case, 3 corresponding triangles are congruent. Thus,

triangle ADC is similar to triangle EBC by AA(angle angle) postulate

4b) If 2 triangles are similar, it means that the ratio of their corresponding sides is equal. Thus,

AD/EB = DC/BC = AC/ CE

From the information given,

AD = 2

AC = 4

EB = 5

Thus,

2/5 = 4/CE

By cross multiplying,

2 * CE = 5 * 4

2CE = 20

CE = 20/2

CE = 10

Use the elimination method to solve the given system of equations.

To do so, multiply the first equation by -3 so that the coefficient of x in the first equation becomes the additive inverse of the coefficient of x in the second equation:

Then, the system is equivalent to:

Add both equations to eliminate the variable x and to obtain an equation in terms of the variable y only:

Replace y=2 into the first equation to find the value of x:

Replace y=2 and x=5 into the second equation to confirm the answer:

Therefore, the solution to the system of equations is x=5, y=2.

ANSWER:

EXPLANATION:

Given:

To find:

The area of the training field

We can see that the two semicircles will form a circle with a diameter(d) of 60 m, so the radius(r) of the circle will be;

r = d/2 = 60/2 = 30 m

Given pi as 3.14, we can go ahead and determine the area of the circle as seen below;

The fraction for the amount of honey each jar holds is 2/3.

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

From the information, Daniel fills 24 equal sized jars with honey and he brings a total of 16 cups of honey to sell at the farmers' market.

The amount of honey will be:

= Number of cups / Number of jars

= 16 / 24

= 2/3

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Given:

The eqution is given as, x^2 + 4x + 1 = 0​.

The objective is to solve the equation by compleing the square.

Consider the middle of the equation.

Here, the value of a is x. Then, the value of b can be calculated as,

To complete the equation add +b^2 and -b^2 to the equation.

Take square root on both sides, to solve the value of x,

Hence, the value of x are +√3-2 and -√3-2.

Given,

The coordinates of the points shown in the graph is:

Here, the given mapping is:

On comparing the coordinates then x = 6.

Hence, the value of x is 6.

Answer

Option C is correct.

The area of the triangle = 18 square units

Explanation

The area of a triangle is given as

Area of the triangle = ½ × B × H

where

B = Base of the triangle = 6 units (From -3 t

Part A:

Let:

T(h)= Total Number of bacterias as a function of time

h = Number of hours

B = Initial number of bacterias

Since the number of bacteria increases by 25 every hour, we can defined the equation as:

Part B:

B = 5

h = 6

Evaluate the previous equation for those values:

there will be 155 baterias after 6 hours

Part C

Let's graph the equation:

From the given side lengths, let's find the measures that will form a right triangle.

Apply Pythagorean Theorem:

Where:

• a ,and ,b, are lengths of the legs

• c is the length of the hypotenuse.

Now, let's start from the first measures in option a.

• 48m, 64m, and 85m

The measures in option a will NOT form a right triangle since the left side of the equation does not equal the right side.

• 27 yd, 36 yd, 45 yd

The measures in option B will form a right triangle because the Equation is true.

ANSWE

The probability of a 6 being drawn in one pick is

For 4 drawings, the probability would be

We were given a principal to invest ($14,000) in a timespan of 2 years, and we need to choose between applying it on an account that is compounded montlhy at a rate of 6%, and one that is compounded continuously at a rate of 5.88%. To solve this problem, we need to calculate the final amount on both situations, and compare them.

The expression used to calculate the amount compounded monthly is shown below:

Where A is the final amount, P is the invested principal, r is the interest rate and t is the elapsed time.

The expression used to calculate the amount compounded continuously is shown below:

Where A is the final amount, P is the invested principal, r is the interest rate, t is the elapsed time, and "e" is the euler's number.

With the two expressions we can calculated the final amount on both situations, this is done below:

The first account, that is compounded monthly yields a return of $15780.24, while the second one that is compounded continuously yields a return of $15747.12, therefore the first account is the one that yield the larger amount in 2 years.

Solution

For this case we can do the following:

We can understand 7/2 as the reciprocal of 2/7 and we can create the following diagram

Area of a circle is

If a square foot cost $ 1.25

The perimeter is the sum of all sides, therefore:

The factors of 3 that sum to 4 are 3 and 1. So:

The correct list is

This is option F

a) We have a number X that is twice the difference of a number c and 40.

We can write this as:

b) Four times the sum of a number f and fifty.

Then, X is:

The number of quarts of each constituent she needs to produce 16 quarts of punch is; 12 quarts of fruit juice and 4 quarts of citrus soda.

It follows from the task content that the quantity of each constituent that is required to make 16 quarts of punch are to be determined.

Since it follows that 3 quarts of fruit juice are required to mix with every quart of citrus soda, it follows that the amount of punch made in this scenario is; 4 quarts of punch.

Hence, since there are 4 partitions of 4 quarts punch is 16 quarts punch, the amount of.each constituent needed by proportion are as follows;

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The discount rate of the digital player is 22%

From the question, we have the given parameters:

List price = $249.99

Sales price = $194.99

Start by calculating the change in the price.

This is calculated as follows

Change = List price - Sales price

So, we have

Change = $249.99 - $194.99

Evaluate the difference

Change = $55

The discount rate of the digital player is then calculated as

Discount = Change/List price x 100%

This gives

Discount = 55/249.99 x 100%

Evaluate

Discount = 22%

Hence, the discount rate is 22%

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Answers:

Line A is parallel to line D.

Line A is perpendicular to line C.

Line C is perpendicular to line D.

=====================================================

Explanation:

Let's use the slope formula to calculate the slope of the line through (-1,-17) and (3,11)

[tex](x_1,y_1) = (-1,-17) \text{ and } (x_2,y_2) = (3,11)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{11 - (-17)}{3 - (-1)}\\\\m = \frac{11 + 17}{3 + 1}\\\\m = \frac{28}{4}\\\\m = 7\\\\[/tex]

The slope of line A is 7

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Now let's find the slope of line B.

[tex](x_1,y_1) = (0,4) \text{ and } (x_2,y_2) = (7,-5)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-5 - 4}{7 - 0}\\\\m = -\frac{9}{7}\\\\[/tex]

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Now onto line C.

[tex](x_1,y_1) = (7,1) \text{ and } (x_2,y_2) = (0,2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{2 - 1}{0 - 7}\\\\m = \frac{1}{-7}\\\\m = -\frac{1}{7}\\\\[/tex]

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

Lastly we have line D.

[tex](x_1,y_1) = (-1,-6) \text{ and } (x_2,y_2) = (1,8)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{8 - (-6)}{1 - (-1)}\\\\m = \frac{8 + 6}{1 + 1}\\\\m = \frac{14}{2}\\\\m = 7\\\\[/tex]

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Here's a summary of the slopes we found

[tex]\begin{array}{|c|c|} \cline{1-2}\text{Line} & \text{Slope}\\\cline{1-2}\text{A} & 7\\\cline{1-2}\text{B} & -9/7\\\cline{1-2}\text{C} & -1/7\\\cline{1-2}\text{D} & 7\\\cline{1-2}\end{array}[/tex]

Recall that parallel lines have equal slopes, but different y intercepts. This fact makes Line A parallel to line D.

Lines A and C are perpendicular to one another, because the slopes 7 and -1/7 multiply to -1. In other words, -1/7 is the negative reciprocal of 7, and vice versa. These two lines form a 90 degree angle.

Lines C and D are perpendicular for the same reasoning as the previous paragraph.

Line B unfortunately is neither parallel nor perpendicular to any of the other lines mentioned.

You can use a graphing tool like Desmos or GeoGebra to verify these answers.

(x - h)^2 = 4p(y - k)

(-1 - 3)^2 = 4p(8 - 0.5)

(-4)^2 = 4p(7.5)

16 = 30p

p = 16/30

p = 8/15

(x - 3)^2 = 16/15(y - 0.5)

15(x^2 - 6x + 9) = 16y - 8

15x^2 - 90x + 135 = 16y - 8

16y = 15x^2 - 90x + 135 + 8

y = 15/16 x^2 - 90/16 x + 143/16

f(x) = 15/16 x^2 - 90/16x + 143/16

Leah investment is:

Where M is the ammount of money that she has, and y the number of years.

We want to know the number of years that must elapse for her investment to triple, so we want to know the value of y such that:

It will take 73.79 years to triple her investment.

Lauren investment is:

Where M is the ammount of money that she has, and m the number of months, and y is the number of years.

We want to know the number of years that must elapse for her investment to triple, so we want to know the value of y such that:

Those are similar triangles, which means, they are related by a ratio

For example in this case,

7: 10

to find x

10 / 7 = x/3

x= 10*3 /7

x= 30/ 7

x= 4.29

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