Solve x2 + 5x + 3 = 0.

Answer: C. 17

Step-by-step explanation:

Given : An investment is currently worth [tex]2.125\times10^4[/tex] dollars . Ten years ago, the investment was worth [tex]1.25\times10^3[/tex] dollars.

Then, the number of times the value of the investment today is greater than the value of the investment ten years ago is given by :-

[tex]\dfrac{\text{Current investment}}{\text{\text{Yen years ago investment}}}\\\\=\dfrac{2.125\times10^4}{1.25\times10^3}\\\\=\dfrac{2.125}{1.25}\times10^{4-3}\ \ [\because a^m\times a^n=a^{m+n}]\\\\=1.7\times10=17[/tex]

Hence, the value of the investment today is 17 times greater than the value of the investment ten years ago .

The solution value of b in the equation 2/3b + 5 = 20 - b is: b = 9.

Here, we have,

given that,

the equation is:

2/3b + 5 = 20 - b

so with these equations, you collect 'like terms.'

like terms are basically grouping things that are the same together,

so for example a+a-b+2b would be 2a+b.

with this equation you want to do the same.

2/3b + 5 = 20 - b

first, make all the numbers integers (whole numbers).

we want to make 2/3b a whole number,

so we multiply the whole equation by 3 to keep everything in proportion with each other,

thus ending up with

2b + 15 = 60 - 3b

now we collect 'like terms.'

add 3b to both sides gives

5b + 15 = 60

subtract 15 from both sides

5b = 45

divide by 5 to leave the value of b

b = 9

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Answer

6 and 10

Step by step explanation

a distance of 2 units from 8 on a number line

we need to find out the numbers that are 2 units from 8 on the number line

To find out the numbers we need to subtract and add 2 from 8

[tex]8+2=10[/tex]

[tex]8-2=6[/tex]

10 is 2 units from 8 on the right side

6 is 2 units from 8 on the left side

So, 6 and 10 are 2 units away from 8 on the number line.

To meet their goal of saving $8,000 for their wedding, Mike and Kate need to adjust their plan. Increasing the amount they save each month by $80 (Option B) will allow them to reach their goal.

To determine which option will allow Mike and Kate to meet their goal of saving $8,000 for their wedding, we need to analyze the information given. They saved $4,000 in the first year, which means they saved $4,000 in 12 months. To reach their goal, they need to save an additional $4,000 in 8 months.

Option A: If they stay with saving the same amount they've been saving each month, they will save the same amount each month for the remaining 8 months. Therefore, they will not reach their goal of $8,000.

Option B: If they increase the amount they save each month by $80, they will be saving $80 more each month for the remaining 8 months. This will result in them saving an additional $640 ($80 x 8 months) and reaching their goal of $8,000.

Therefore, the correct answer is Option B - Only option B will allow them to meet their goal.

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Answer:

x=7

Step-by-step explanation:

[tex]x^2 - 14x + 49 = 0[/tex]

Factor the left hand side of the equation

product is 49 and sum is -14

-7 times -7 is 49

-7 plus -7 is -14

so two factors are -7 and -7

[tex]x^2 - 14x + 49 = 0[/tex]

[tex](x-7)(x-7)= 0[/tex]

Now we apply zero factor property

SEt each factor =0 and solve for x

x-7 =0 , x=7

The correct solution for the equation [tex]x^{2}- 14x+49 = 0[/tex]  is [tex]x = 7[/tex].

Given equation,

[tex]x^{2}- 14x+49 = 0[/tex]

The equation is a quadratic equation. A polynomial equation of second degree is known as quadratic equation.

The standard form of a quadratic equation is:

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

Find the solution of given equation for x, Use the standard formula:

x = (-b ± √(b² - 4ac)) / (2a)

From the question,

a = 1, b =-4 , c = 49.

Put the value of a, b ,c in the formula to find x.

x = (-(-14) ± √((-14)² - 4(1)(49))) / 2(1)

= (14 ± √(196 - 196)) / 2

= (14 ± √(0)) / 2

= [tex]\dfrac{14}{2}[/tex]

= 7

The value of the discriminant [tex]\sqrt{b^{2} - 4ac }[/tex] is 0. this indicates that their will be only one value of x.

The equation [tex]x^{2}- 14x+49 = 0[/tex] has a single solution which is x =7.

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If the mass is represented as m and acceleration as the net force f acting on the particle will be f =ma.

Force is defined as the product of mass and change in velocity.The objects interactions with one another are what cause push and pull. Force may also be expressed using words like stretch and squeeze.

The force is in mathematical form is,

Force = mass × acceleration

If m is the mass in kilogram and a is the acceleration in m/s² is,

F = m × a

F = (1 kg) × (1 m/s²)

F = 1 kg.m/s²

As we know, 1 kg.m/s² = 1 N

F = 1 N

The measures mentioned above are taken into account by the Newton unit (N). As a result, one newton is defined as the force needed to accelerate 1 kilogram of mass 1 meter per second squared in a certain direction. 1N = 1kg (m/s²) is the way to express force.

Thus, if the mass is represented as m, acceleration as the net force f acting on the particle will be f =ma.

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Answer:

C.Yes, because every x-value corresponds to exactly one y-value.

Step-by-step explanation:

A function is a relation in which each element of the domain (x) is mapped to one element of the range (y).  This means that no x can be mapped to more than one y; basically it means that no x can repeat.

In this table, no x repeats; each x is mapped to only 1 y.  This means that it is a function.

Answer:

The correct option is C) Yes, because every x-value corresponds to exactly one y-value.

Step-by-step explanation:

Consider the provided table:

x     y

2    1

4    3

6    3

8    4

10   6

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Or we can say that, a function is a set of ordered pairs in which x element has only one y-element associated with it.

Now observe the table for each x element we have only one y element.

Therefore, the table represent a function.

The correct option is C) Yes, because every x-value corresponds to exactly one y-value.

Answer:

|v| = 10.06 units

Step-by-step explanation:

It is given that,

The x component of the vector is, [tex]v_x=7.6\ units[/tex]

The y component of the vector is, [tex]v_y=-6.6\ units[/tex]

We need to find the magnitude of vector v. The magnitude of any vector is calculated as :

[tex]|v|=\sqrt{v_x^2+v_y^2}[/tex]

[tex]|v|=\sqrt{(7.6)^2+(-6.6)^2}[/tex]

|v| = 10.06 units

So, the magnitude of vector v is 10.06 units. Hence, this is the required solution.

1st question - answer is #2

line P & Q = x=3, Y=5

 triangle question, x = 17

Rick, Maya, and Tom worked a total of 1086 minutes.

To calculate this:

1. Convert Rick's hours to minutes: 5 hours and ½ hour = [tex]\( 5 \times 60 + 30 = 330 \) minutes.[/tex]

2. Convert Maya's hours to minutes: 6 hours and 1/10 hour = [tex]c\( 6 \times 60 + 6 = 366 \) minutes.[/tex]

3. Convert Tom's hours to minutes: 6 hours and 30 minutes = [tex]\( 6 \times 60 + 30 = 390 \) minutes.[/tex]

Now, add up all the minutes worked:

[tex]\[ 330 + 366 + 390 = 1086 \] minutes.[/tex]

Therefore, Rick, Maya, and Tom worked a total of 1086 minutes.

- Rick worked for 5 hours and ½ hour, which is 330 minutes.

- Maya worked for 6 hours and 1/10 hour, which is 366 minutes.

- Tom worked for 6 hours and 30 minutes, which is 390 minutes.

Adding these minutes together gives a total of 1086 minutes.

complete question

Rick, Maya, and Tom work in a call center. On a particular day, Rick worked 5 and ½ hours, Maya worked 6.1 hours, and Tom worked 6 hours and 30 minutes. What is the total number of minutes that they worked?

Final answer:

The equation representing a direct variation where y varies directly as x with a constant of variation of -3 is y = -3x. It is a linear equation without a y-intercept.

Explanation:

If y varies directly as x, and the constant of variation is -3, the equation that represents this relationship can be written as y = kx, where k is the constant of variation. Since the constant of variation is given as -3, the equation becomes y = -3x. This is a linear equation similar to the form y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, since the constant of variation is -3, the slope of the line is -3 and the y-intercept is 0 because there is no addition or subtraction of a constant in the equation.

The  amount of interest earned is $990 when we deposit of $5,500 at 6% for 3 years

percentage, a relative value indicating hundredth parts of any quantity.

We have to find the  amount of interest earned

The deposited amount or principal amount us 5500

Rate of interest is 6% and time is 3 years

The formula for simple interest is I=PRT

I = interest, P = principal, R = rate, T = time in years.

Let us convert 6% to decimal form

Divide 6 by 100

6%=0.06

I = 5500(0.06)(3)

I = $990

Hence, the  amount of interest earned is $990 when we deposit of $5,500 at 6% for 3 years

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Two segments are always coplanar. The correct option is A.

A line segment in geometry is a section of a line that has two clearly defined endpoints and contains every point on the line that lies within its confines.

An adjacent line to another line in the same plane. Any two intersecting lines must be coplanar, that is, they must be on the same plane. Two line segments are always in the same plane.

Straight lines that are parallel and do not intersect at any point are called parallel lines. In the same three-dimensional space, parallel planes are any planes that never cross.

Therefore, the segments are always coplanar. The correct option is A.

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The student's calculations for mean and standard deviation are correct, although the standard deviation was slightly misunderstood. The calculation for the z-score was correct, but the student failed to convert this z-score into a probability.

The question discusses certain calculations about the distribution of gypsy moths in traps placed by a state agriculture department. Your calculation for (a), the

mean

number of moths in 30 traps, is correct. We multiply the mean number of moths in one trap (0.6) by the number of traps (30) to obtain 18. However, for (b), the

standard deviation

of the distribution is incorrectly calculated. In fact, as we apply the formula for standard deviation of sample means σ/√n, where σ is the population standard deviation (0.4) and n is the sample size (30), it comes out to be 0.073 (rounded to ±0.001). Lastly, for (c), using the given values in the

central limit theorem

, the z-score calculator gives us a value of 1.37, but remember, this is a z-score, not a probability. To convert the z-score to a probability, you need to consult a standard normal distribution table or use a calculator with a built-in z-score to probability converter.

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Answer: Third option is correct.

Step-by-step explanation:

Since we have given that

X/0.4= 10

We need to find the value of x .

For this, we will multiply by 0.4 on both sides, we get that

X= 0.4 × 10

X = 4

Hence, third option is correct.

The slope of a line drawn through the points are zero.

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points have the same Y-coordinates but different X-coordinates.

Now,

Since, Two points have the same Y-coordinates but different X-coordinates.

Hence, Take two points as;

(x, y) = (3, 4) , (5, 4)

Thus, The slope of line passing through the points (3, 4) and (5, 4) is,

⇒ m = (4 - 4) / (5 - 3)

⇒ m = 0

Thus, The slope of a line drawn through the points are zero.

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To find the cost of an adult ticket, we can set up an equation using the given information and then solve for the variable.

To solve this problem, let's start by defining some variables. Let the cost of an adult ticket be x dollars. Since children's tickets are sold for half the price of adult tickets, the cost of a children's ticket is (1/2)x dollars.

Given that 5 adult tickets and 8 children's tickets cost a total of $27, we can set up the following equation to represent the total cost:

5x + 8(1/2)x = 27

To solve for x, we can simplify the equation:

5x + 4x = 27

9x = 27

Dividing both sides by 9, we find that x = 3.

Therefore, the cost of an adult ticket is $3.

~~~~~~~~~~The answer is 366 m/min~~~~~~~~~~~~~~~~~~ First, convert the turtles speed to meters per minute. 27 km/h * 1000 m/km = 27000 m/h / 60 min/h = 450 m/min Now convert the girls speed to meters per minute. 14 dm/s / 10 dm/m * 60 s/min = 84 m/min Now subtract the girl's speed from the turtle's speed. 450 m/min = 84 m/min = 366 m/min