III. Write each quadratic equation in standard form

1. 3x-2x² = 7

2.5-2x² = 6x

3.(x+3)(x+4)=0

4.(2x + 7)(x-1)=0

5,2x(x-3) = 15
ax²+bx+c=0

Answer: 4 side faces and one base faces I believe im sorry times a 100 if its wrong

Step-by-step explanation:

Answer:

-3.39 is your answer

Step-by-step explanation:

Answer:

A) 120 ft^2

Step-by-step explanation:

The total surface area is the sum of the areas of the 4 congruent triangular sides and the area of the square base.

TA = 4 * area of triangle + area of square

TA = 4 * bh/2 + s^2

TA = 4 * 6 ft * 7 ft/2 + (6 ft)^2

TA = 84 ft^2 + 36 ft^2

TA = 120 ft^2

Answer:

A) 120 ft^2

Step-by-step explanation:

Part One: The vector representing the path to the object is <30, 20>.

Part Two: The object is approximately 36.06 meters away from the human character.

Part Three: The angle of rotation needed for the first human character to face the second human character is approximately 45 degrees.

Part One: To represent the path to the object using a vector, we can consider the displacement from the human character to the object.

Since the object is 30 meters to the right and 20 meters in front of the human character, the vector representing this displacement is <30, 20>.

The first component of the vector represents the displacement in the x-direction (horizontal), and the second component represents the displacement in the y-direction (vertical).

Part Two: To find the distance between the object and the human character, we can use the Pythagorean theorem.

The distance is given by the magnitude of the vector representing the displacement.

Using the formula for magnitude (or length) of a vector, the distance is approximately √(30^2 + 20^2) = √(900 + 400) = √1300 ≈ 36.06 meters.

Part Three: To determine the angle of rotation needed for the first human character to face the second human character, we can create a vector between the two humans by subtracting the position vector of the first human from the position vector of the second human.

Let's assume the position vector of the second human is <-40, 50>. Then, the vector between the two humans is given by <(-40 - 30), (50 - 20)> = <-70, 30>.

Next, we can calculate the angle between the vectors <30, 20> and <-70, 30> using the dot product formula and trigonometry.

The dot product of two vectors A and B is defined as A · B = |A| |B| cos(theta), where |A| and |B| are the magnitudes of the vectors and theta is the angle between them.

Solving for theta, we have cos(theta) = (A · B) / (|A| |B|). Plugging in the values, cos(theta) = ((30)(-70) + (20)(30)) / (√(30^2 + 20^2) √((-70)^2 + 30^2)). Calculating this expression gives us cos(theta) ≈ -0.916.

Finally, taking the inverse cosine (arccos) of -0.916, we find the angle of rotation needed is approximately 22.91 degrees.

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The number of degrees of freedom for the chi-square goodness-of-fit test is of:

2.

The number of degrees of freedom for a chi-square goodness-of-fit test is obtained according to the multiplication presented as follows;

df = (r - 1) x (c - 1).

In which the variables are listed as follows:

The table in this problem has three rows, given as follows:

The table has two columns, which are given as follows:

Hence the number of degrees of freedom of the test is given as follows:

df = (3 - 1) x (2 - 1) = 2 x 1 = 2.

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We must calculate the standard deviation of the differences between the values in the matched pairs in order to build a confidence interval using those values.

The 95% confidence interval is another frequently used measure of accuracy. In order to calculate it, a range of values that is 95% likely to contain the true population mean must be created using the standard deviation.

According to the 68-95-99.7 Rule, 95% of values are within two standard deviations of the mean, so to calculate the 95% confidence interval, one need only add and deduct two standard deviations from the mean.

Data dispersion in relation to the mean is quantified by a standard deviation, or σ. Data are said to be more closely clustered around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

The difference between the values in the matched pairs' standard deviation is calculated.

The complete question is:

To construct a confidence interval using matched pairs, we must compute the standard deviation of the ___ between the values in the matched pairs.

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We must calculate the standard deviation of the differences between the values in the matched pairs in order to build a confidence interval using those values.

What is the difference between standard deviation and confidence interval?

The 95% confidence interval is another frequently used measure of accuracy. In order to calculate it, a range of values that is 95% likely to contain the true population mean must be created using the standard deviation.

According to the 68-95-99.7 Rule, 95% of values are within two standard deviations of the mean, so to calculate the 95% confidence interval, one need only add and deduct two standard deviations from the mean.

Data dispersion in relation to the mean is quantified by a standard deviation, or σ. Data are said to be more closely clustered around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

The difference between the values in the matched pairs' standard deviation is calculated

To construct a confidence interval using matched pairs, we must compute the standard deviation of the ___ between the values in the matched pairs.

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Answer:

u=47

Step-by-step explanation:

...................

The measure of angle U is 74 degrees.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

here, we have,

to determine the measure of angle U:

From the question, we have the following parameters that can be used in our computation:

△PQR ≅ △STU

If m ∠P = 62 degrees and m ∠Q = 45 degrees

The above parameters mean that

P  = S Q = T and R = U

So, we have

U = R = 180 - P - Q -- by the angles in a triangle theorem

So, we have

U = 180 - 61 - 45

   = 74

Evaluate

U = 74

Hence, the value of m ∠U is 74 degrees

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The corresponding angles and sides of the two triangles need to be given in order to prove congruence by side-angle-side.

In order to prove congruence by side-angle-side, the corresponding angles and sides of the two triangles must be given. The sides must be proportional, which means that two sides of one triangle must be equal to two sides of the other triangle, and the angles between these two sides must also be equal. In other words, if two sides of one triangle are equal to two sides of the other triangle, and the angle between those two sides is also equal, then the two triangles are congruent. This can be expressed as “If two sides and the included angle of one triangle are equal to the corresponding sides and angle of a second triangle, then the two triangles are congruent.” In order to prove congruence by side-angle-side, all of the corresponding sides and angles must be given in order to show that they are equal.

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The additional information that is needed to prove the triangles are congruent by Side-Angle -Side us that the corresponding angles and sides of the two triangles need to be given .

What is Side-Angle-Side Congruence ?

The Two Triangles can be called as  Congruent by Side-Angle-Side rule  if any 2 sides and angle included between sides of one triangle is equivalent to corresponding 2 sides and angle between sides of second triangle .

In order to prove the Congruence by Side-Angle-Side, the corresponding angles and the sides of the 2 triangles must be given.

The sides must also be in proportional, that means that the two sides of one triangle must be equal to two sides of other triangle, and

the angles between these two sides of the triangle must  be equal.

So , In order to prove a triangle congruent by Side-Angle-Side, all of the corresponding sides and angles must be given in order to prove  that they are equal.

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Answer: (2) Square root of 90

Step-by-step explanation:

After you rotate it counterclockwise around the origin by 90 degrees, the point would be (-2,7). Since you translate it down by 2, it would then be (-2,5). The points (-2,5) and the original point (7,2) would form the hypotenuse of a right triangle and you can use the Pythagorean Theorem to find the length of the hypotenuse. The length is 9 units, the height is 3 units.

\(3^2+9^2=c^2\\ 9+81=c^2\\ 90=c^2\\ \sqrt{90}=c\)

Answer:

Step-by-step explanation:

3x = f

2x = e

x is how many batches you want to make.

Answer:11

Step-by-step explanation:

=8x5=40-29 =11

hope this helps

Answer:

11 is the final result

Step-by-step explanation:

=8x5=40-29=11

Answer:

Either C or D

Step-by-step explanation:

Hi there!

Let the equation be

\(y = kx + b\)

When x = 0, y = 2

And

when x = 3, y = 1.25

So, b = 2

3k + b = 1.25

=> k = -0.25

b = 2

Therefore, y = -0.25x + 2 (Substituting the two points)

Hope this helps !

Reasoning:

'a' is less than 0, so we write a < 0

Since a < 0, this means a^4 > 0. Raising a negative to an even exponent will make the result positive. Example: (-2)^4 = 16

Applying the cube root to some positive number leads to some other positive number.

So far we see that the expression    a^(4/3)   is positive

The final result however is negative because the negative out front flips things from positive to negative.

It turns out it doesn't matter if 'a' is positive or negative. As long as 'a' is nonzero, then   -a^(4/3)   is negative. If a = 0, then the whole thing is 0.

To determine if two lines are parallel, you can compare their equations and examine the coefficients of their variables.

In general, the equation of a line can be written in slope-intercept form as y = mx + b, where m represents the slope of the line.

If two lines have the same slope (m1 = m2), then they are parallel. This is because parallel lines have equal slopes and will never intersect.

On the other hand, if the slopes of the two lines are different (m1 ≠ m2), then they are not parallel. In this case, the lines may intersect at some point.

Therefore, to determine if two lines are parallel, you need to compare their slopes. If the slopes are equal, the lines are parallel; if the slopes are not equal, the lines are not parallel.

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Answer:

24

Step-by-step explanation:

a circle is 360

we can divide 360 by 15

360 divided by 15 =

24

Answer:

x = 23

Step-by-step explanation:

if line j is parallel to line k then

5x + 9 + 33 + x = 180 add like terms

6x + 42 = 180 subtract 42 from both sides

6x = 138 divide both sides by 6

x = 23

Thus, it is important to interpret the F-ratio in the context of the research question and to consider other factors, such as effect size and practical significance, when drawing conclusions from an ANOVA analysis.

When conducting an analysis of variance (ANOVA), we are interested in comparing the means of two or more groups.

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(11) The measure of angle IGJ is  46⁰.

(12) The measure of arc JH is determined as 138⁰.

The measure of the arc or central angle indicated is calculated as follows;

(11) The measure of angle IGJ is calculated as follows;

m∠LGK =  arc angle LK (interior angle of intersecting secants)

m∠LGK = 48⁰

m∠HGI = m∠LGK = 48⁰ (vertical opposite angles are equal)

m∠IGJ + m∠HGI + m∠JGK = 180⁰  (sum of angles in a straight line)

m∠IGJ + 48⁰ + 86⁰ = 180

m∠IGJ = 180 - 134

m∠IGJ = 46⁰

(12) The measure of arc JH is calculated as follows;

arc JH = arc JI + arc IH

arc JI = arc FG

arc FG = 180 - 137⁰ (sum of angle in a straight line)

arc FG = 43⁰

arc FG = arc JI (vertical opposite angles are equal)

arc JH = arc JI + arc IH

arc JH = 43⁰ + 95⁰

arc JH = 138⁰

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Answer:

420

Step-by-step explanation:

its correct trust me you can try it on a calculator

Answer:

how many bags are there?

Step-by-step explanation:

Expression for the number of tiles Bruce used: 5x+2

Expression for the number of tiles Felicia used: 5x+5

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

The first want you'll want to do is translate the question into something easily understood. So for Bruce, we know that he bought three boxes with the same number of tiles in each, so 3, then he had to buy three more, another 3 but didn't finish the last box only using two, 2. So, we know he completely used the first 3 he bought then 2 of the 3 more boxes he bought.

For boxes completely used we can show it like this: 3+2=5 or 5x to represent the not known number of tiles in each box. Now we have to include the last box he bought, but he only used two tiles out of the whole box so it wouldn't be added to the same number as the other five (so not 6x).

To represent those last two tiles we can simply add +2.

Now putting it all together we get 5x+2

5x is the number of boxes multiplied by an unknown number of tiles. so 5x=tiles in 5 boxes. and the 2 are those two tiles that were taken out of the last box.

For Felicia, we go through the same process. We know she bought five boxes with the same number of tiles that Bruce had, 5, then bought five more individual tiles (not in a box), 5.

Not too much to do, so we know she got 5 boxes, so now we add our variable to represent the tiles in the boxes. so that 5 becomes 5x. Now with like we did with the two tiles Bruce only used, we do not add the 5 additional tiles into that number (so not 10x).

Because those were individual tiles they are simply 5.

Putting the whole thing together we get 5x+5

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Ralph received his June flash card bill, which includes a previous balance and a finance charge because he did not pay his May bill in full.

Ralph's June flash card bill reflects the consequences of not paying his May bill in full. When a credit card balance is not paid in full by the due date, the remaining amount is carried over to the next billing cycle, resulting in a previous balance. This previous balance represents the unpaid amount from the previous month, which is still owed.

Additionally, credit card companies apply finance charges to outstanding balances that are not paid in full. A finance charge is the cost of borrowing money from the credit card issuer. It is typically calculated based on the outstanding balance and the applicable interest rate.

Therefore, Ralph's June bill includes a previous balance, which represents the unpaid amount from May, and a finance charge, which is the cost incurred for carrying that balance. These charges serve as a reminder for Ralph to pay his credit card bills in full to avoid accumulating additional costs and interest charges in the future.

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For the simple harmonic motion equation d=2 sin(pi/3t), the period is 6 seconds.

The period of a simple harmonic motion is the time taken for one complete cycle of the motion. In this equation, d represents the displacement or position of the object at time t. The equation is in the form of sin function with the argument (pi/3)t. The general form of the equation for simple harmonic motion is d=A sin(ωt+φ), where A is the amplitude, ω is the angular frequency, and φ is the phase angle. To determine the period of this motion, we can use the formula T=2π/ω, where T is the period and ω is the angular frequency. In this case, ω=pi/3, so the period is T=2π/(pi/3)=6 seconds (rounded to the nearest second). Therefore, the object completes one full cycle of motion every 6 seconds.

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Given: Radius of the wheel = 30 inches, Revolutions per minute = 401 rpmThe linear speed of the car in miles per hour can be calculated as follows:

Step 1: Convert the radius from inches to miles by multiplying it by 1/63360 (1 mile = 63360 inches).30 inches × 1/63360 miles/inch = 0.0004734848 milesStep 2: Calculate the distance traveled in one minute by the wheel using the circumference formula.Circumference = 2πr = 2 × π × 30 inches = 188.496 inchesDistance traveled in one minute = 188.496 inches/rev × 401 rev/min = 75507.696 inches/minStep 3: Convert the distance traveled in one minute from inches to miles by multiplying by 1/63360.75507.696 inches/min × 1/63360 miles/inch = 1.18786732 miles/minStep

4: Convert the distance traveled in one minute to miles per hour by multiplying by 60 (there are 60 minutes in one hour).1.18786732 miles/min × 60 min/hour = 71.2720392 miles/hour Therefore, the linear speed of the car is 71.3 miles per hour (rounded to the nearest tenth).Answer: 71.3

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The radius of the wheel on a car is 30 inches. If the wheel is revolving at 401 revolutions per minute, The linear speed of the car is approximately 19.2 miles per hour.

To find the linear speed of the car in miles per hour, we need to calculate the distance traveled in one minute and then convert it to miles per hour. Here's how we can do it step by step:

Calculate the circumference of the wheel:

The circumference of a circle is given by the formula

C = 2πr

where r is the radius of the wheel.

In this case, the radius is 30 inches, so the circumference is

C = 2π(30)

   = 60π inches.

Calculate the distance traveled in one revolution:

Since the circumference represents the distance traveled in one revolution, the distance traveled in inches per revolution is 60π inches.

Calculate the distance traveled in one minute:

Multiply the distance traveled in one revolution by the number of revolutions per minute.

In this case, it is 60π inches/rev * 401 rev/min = 24060π inches/min.

Convert the distance to miles per hour:

There are 12 inches in a foot, 5280 feet in a mile, and 60 minutes in an hour.

Divide the distance traveled in inches per minute by (12 * 5280) to convert it to miles per hour.

The final calculation is (24060π inches/min) / (12 * 5280) = (401π/66) miles/hour.

Approximating π to 3.14, the linear speed of the car is approximately (401 * 3.14 / 66) miles per hour, which is approximately 19.2 miles per hour.

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The limit of (2x+1)/(x-14) as x approaches 14 is A. lim (2x+1) = 29. To find the limit, we can directly substitute the value 14 into the expression (2x+1)/(x-14).

However, this leads to an indeterminate form of 0/0. To resolve this, we can factor the numerator as 2x+1 = 2(x-14) + 29.

Now, we can rewrite the expression as (2(x-14) + 29)/(x-14). Notice that the term (x-14) in the numerator and denominator cancels out, resulting in 2 + 29/(x-14).

As x approaches 14, the value of (x-14) approaches 0. Therefore, the limit of (2(x-14) + 29)/(x-14) is equal to 2 + 29/0, which is undefined.

Hence, the correct choice is B. The limit does not exist, as the expression approaches an undefined value as x approaches 14.

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Answer:

(5x-2)

Step-by-step explanation:

first factor the quadratic equation

10x²+26x-12 by factoring out the gcf of 2

2(5x²+13x-6)    to factor the quadratic, first multiply ac (5)(-6)

find factors of -30 that multiply to give you -30 and add to give you the middle term 13.

factors -2, 15

take your leading term 5x and put it over the 2 factors, then reduce when necessary.  it is not necessary to use the 5x² because the x in the denominator cancels one out)

5x/-2 and 5x/15 (this one can be reduced to x/3

(5x-2)(x+3) are the factors.

the shared factor is (5x-2)

Answer:

they share 5x-2 as common factor

Step-by-step explanation:

10x² + 26x – 12 and 2(5x – 2)(x – 3)

10x² + 26x – 12  take 2 as common factor

2(5x²+13x-6)     factorize

2(5x-2)(x+3)

they share 5x-2 as common factor

The probability of drawing a club can be expressed as:Number of club cards / Total number of cards Since there are 13 club cards in the pack, the probability of drawing a club is: 13/52 = 1/4 Therefore, the probability of drawing a club as a fraction is 1/4.

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. The probability of an event A occurring is denoted as P(A) and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

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Answer:

x  <  0  or     x  >  3

Explanation:

The solution to the given system of inequality is x > 0 and x> 3

Inequalities are equation noe separated by an equal sign

Given the inequality expression

5 + 1/x > 16/x
5 > 16/x - 1/x
5 > 15/x

Cross multiply

5x^2 > 15x
5x^2 - 15x > 0

5x(x-3)>0
5x > 0 and x - 3>0

x > 0 and x> 3

Hence the solution to the given system of inequality is x > 0 and x> 3

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Answer:

(-4,-1)

Step-by-step explanation:

The solution to a system of linear equations is simply where the two lines intersect.

From the graph, we can see that they intersect at (-4,-1).

Therefore, the solution to the system graphed below is (-4,-1).

And we're done!