Select the correct answer. Solve for x. x2 + 4x - 21 = 0 A. -3, -7 B. -3, 7 C. 3, -7 D. 3, 7

The value of x is equal to; A. 5.

In Mathematics, the basic proportionality theorem states that when any of the two (2) sides of a triangle is intersected by a straight line which is parallel to the third (3rd) side of the triangle, then, the two (2) sides that are intersected would be divided proportionally and in the same ratio.

By applying the basic proportionality theorem to the given triangle, we have the following:

x/(x + 5) = (x - 2)/(x + 1)

By cross-multiplying, we have the following:

x(x + 1) = (x - 2)(x + 5)

x² + x = x² + 5x - 2x - 10

By rearranging and collecting like-terms, the value of x is given by:

2x - 10 = 0

2x = 10

x = 10/2

x = 5.

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the best rule to describe this rotation is:

(x, y) → (-y, x)

Why it is?

The given rotation is a 270 degree clockwise rotation about the origin. This means that each point in Triangle ABC is rotated 270 degrees in a clockwise direction around the origin to produce the corresponding point in Triangle A'B'C'.

One possible rule to describe this rotation is:

(x, y) → (-y, x)

This rule represents a 90 degree clockwise rotation about the origin, which can be applied three times to achieve a 270 degree clockwise rotation.

So, if we apply this rule to each vertex of Triangle ABC, we get the corresponding vertices of Triangle A'B'C':

A = (a, b) → A' = (-b, a)

B = (c, d) → B' = (-d, c)

C = (e, f) → C' = (-f, e)

Therefore, the best rule to describe this rotation is:

(x, y) → (-y, x)

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Answer:

Step-by-step explanation:

ur mom

Florian has to pay $2,013.3, then he own on his car for 3 months

"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."

We always count the unit or amount value first and then calculate the more or less amount value. For this reason, this procedure is called a unified procedure.

Many set values ​​are found by multiplying the set value by the number of sets.

A set value is obtained by dividing many set values ​​by the number of sets.

According to our question-

6040 is the total amount

he has to repay in 3 months

dividing the total amount/3

6040/3

$2,013.3

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The measures of central tendency include mean and mode, which include a third measure called median.

The three measures for determining central tendency are mean, median, and mode. The mean, also known as average, is the result of dividing the total number of observations by the number of observations. The mode is the value that occurs the most frequently, whereas the median is the midpoint value in the ordered set of observations.

The average or middle of a dataset can be discovered with the aid of central tendency measures. The most frequent value is the mode. The median is the midpoint of an ordered dataset. Mean: the product of the total number of values and their sum.

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Correct question is:

The measures of _________ include mean and mode. The third of those measures is ________.

Dividing the sum of all data values by the total frequency will give us the_____.

the exponent of the product of 8.9 x 10¹² and 4.7 x 10⁻² in scientific notation is 11.

Exponential refers to a mathematical function or relationship in which a variable (such as x) is raised to a constant power (such as 2, 3, or e) to produce a result. The term "exponential" can also be used more broadly to describe any situation in which something grows or changes at an increasingly rapid rate over time, often with a compounding effect.

First, we multiply the two numbers:

(8.9 x 10¹²) x (4.7 x 10⁻²) = 41.83 x 10¹⁰

41.83 x 10¹⁰ = 4.183 x 10¹¹

Therefore, the exponent of the product of 8.9 x 10¹²and 4.7 x 10⁻² in scientific notation is 11.

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Answer:

same

Step-by-step explanation:

They are the same since

1/2÷4=1/2×1/4(reciprocal)

Answer:

dfgdfvdfvthtybg f cv v  

Step-by-step explanation:

The equation of Line 1 in the form y=-12x+28

A measurable path between two places is referred to as a line segment. Line segments may make up the sides of any polygon since they have a set length.

Coordinates of Line 2 M(4,5) and N(6,-19)

Slope of Line 2 is =(-19-5)/(6-4)

=-24/2=-12

Slope of line 1 and line 2 are same

Cordinate of Line 1 is D(2,4)

D(2,4) must pass through line 1, so it must satisfy the equation

y=mx+b

4=2(-12)+b

4+24=b

b=28

the equation of Line 1 in the form y=-12x+28

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Using trigonometric functions, the value of the side AC = 2.85 units.

The right triangle's angle serves as the domain input value for the six fundamental trigonometric operations, and the output is a range of numbers.

The angle, given in degrees or radians, is the domain of the trigonometric function, sometimes referred to as the "trig function," of  f(x) = sin, and the range is [-1, 1]. The other functions have a similar domain and scope. Trigonometric functions are widely used in algebra, geometry, and calculus.

Now in the given figure,

The angle is a right-angled triangle.

Now as per the trigonometric functions,

Sin 35° = AC/AB

⇒ 0.57 = x/5

⇒ x = 0.57 × 5

= 2.85.

The length of the opposite side AC is 2.85 units.

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If the probability an American will die from falling is 0.41%, the probability a American will not die from falling is 100% - 0.41% = 99.59%.

Answer: 99.59%.

Answer: $8

Step-by-step explanation:

To find how much he saved over the course of 6 weeks, subtract 62 from 110.

110 - 62 = 48

To find how much he saved each week, divide 48 by 6.

48 ÷ 6 = 8

Liam saved $8 each week.

They can present in 96 different orders. Given, there are five student groups to present in class and one group cannot go first because they need additional set-up time.

Permutation is to select an object then arrange it and it cares about the orders while Combination is about only selecting an object without caring the orders.

We have 5 positions to fill here.

First position: 4 ways (one of the rest 4 groups will present first)

Second position: 4 ways (one of the rest 3 groups and the group which could not present first, will present second)

Third position: 3 ways (one of the rest 3 groups will present third)

Fourth position: 2 ways (one of the rest 2 groups will present fourth)

Fifth position: 1 way (rest group will present last)

Total ways in which they can present = 4*4*3*2*1 = 96

Hence, the answer is 96.

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The compass directions that are given to A, B and C. are East, South-East and North-west respectively.

North, South, East, and West are the four cardinal directions. The sun's rising and setting serve as a point of reference for these instructions.

Thus, the compass directions that are given to A, B and C. are East, South-East and North-west respectively.

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As Masons backyard deck is rectangular, the length of the deck is 22 feet.

Let's start by using algebra to solve for the length of the rectangular deck.

Let L be the length of the deck.

Then, the width of the deck is L - 12.

The perimeter is the sum of all four sides, so we have:

Perimeter = 2L + 2(L - 12) = 64

Simplifying the equation, we get:

2L + 2L - 24 = 64

Combining like terms, we get:

4L - 24 = 64

Adding 24 to both sides, we get:

4L = 88

Dividing both sides by 4, we get:

L = 22

Therefore, the length of the deck is 22 feet.

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Step-by-step explanation:

since we can officially use only one point (the given point), we need to start with the point-slope form :

y - y1 = m(x - x1)

with m being the slope, (x1, y1) being the point.

sadly, to get the slope, we need a second point anyway, because the slope is the ratio

y coordinate difference / x coordinate difference

when going from one point on the line to another.

I recommend to use (0, 50) for the "other" point, as there seems to be the smallest error in the coordinates.

so, when going from (0, 50) to the given point (6, -40) :

x changes by +6 (from 0 to 6).

y changes by -90 (from 50 to -40).

the slope m = -90/+6 = -15/1 = -15

y - -40 = -15(x - 6) = -15x + 90

y + 40 = -15x + 90

y = -15x + 50

that is the slope-intercept form.

m = -15

b = 50

y = -242

-242 = -15x + 50

-292 = -15x

x = -292/-15 = 292/15 = 19.46666666... ≈ 19

a. the mean is 200.31 cm. b. The height of the new player is 210 cm.

The mean, commonly referred to as the average, is a statistic that depicts the usual value of a group of data and measures central tendency. It is calculated by adding up all of the data set's values and dividing the result by the total number of values. Since it offers a single value that summarises the complete set of data, the mean is an effective statistical tool. It may, however, be vulnerable to outliers or extremely high or low values that affect the mean's value. As a result, while examining data, it is crucial to take additional measures of central tendency into account, such as the median or mode.

The mean or average is given as:

mean = (sum of all heights) / (number of players)

The total number of players are:

1 + 3 + 2 + 5 + 2 = 13

Sum of heights is:

(198 x 1) + (199 x 3) + (200 x 2) + (201 x 5) + (202 x 2) = 198 + 597 + 400 + 1005 + 404 = 2604

Thus,

mean = 2604 / 13 = 200.31 cm

b. For the new player the number of players are 14:

201 = (2604 + height of new player) / 14

201 x 14 = 2604 + height of new player

2814 = 2604 + height of new player

height of new player = 2814 - 2604 = 210 cm

Hence, a. the mean is 200.31 cm. b. The height of the new player is 210 cm.

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A The amount of money in a savings account with an annual interest rate of 1.5%

Answer:

the numbers are

[tex] \sqrt{10} + 5 \\ - \sqrt{10} + 5[/tex]

Step-by-step explanation:

then there difference is

square root of 10 + 5 -(- square root of 10 +5)

=

[tex]2 \sqrt{10} [/tex]

and the cube of there sum is 15^3 = 15* 15* 15

= 3375

(a) The present value of an annuity formula can be used to calculate the monthly payment: Payment is equal to (PV x I / (1 - (1 + i)(-n)).

Where PV is the loan's present value, I is its monthly interest rate (0.035 / 12), and n is the number of payments (15 years multiplied by 12 months every year = 180 months).

Applying the values provided, we obtain:

(136,000 x 0.002917) / (1 - (1 + 0.002917)(-180)) is the amount to be paid.

Amount paid: $1,054.63

Hence, the installment will be $1,054.63 per month.

(b) By deducting the loan amount (PV) from the total amount paid over the loan's lifetime, it is possible to get the total interest payment:

Total interest equals PV minus (Payment x n)

Applying the values provided, we obtain:

$1,054.63 multiplied by 180 equals $136,000 in interest.

Interest totaled $88,833.40.

The total interest payment will therefore be $88,833.40.

(c) The Turners will have paid 120 times over the course of 10 years (10 years x 12 months/year). To determine their equity, we can apply the formula for calculating a loan's remaining balance:

The remaining balance is calculated as follows: PV x (1 + i)n - Payment x (1 + i)n - 1)/i

Where n denotes how many payments are still due (180 - 120 = 60).

Applying the values provided, we obtain:

The remaining balance is calculated as follows: $136,000 x (1 + 0.002917)60 - $1,054.63 x (1 + 0.002917)60 - 0.002917

Balance remaining: $71,587.90

As a result, their equity will be $170,000 (the original purchase price) less $71,587.90 (the outstanding balance) = $98,412.10 after ten years.

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(a) The probability that exactly two cars finish the race is 0.0512.

(b) The probability that at most two cars finish the race is 0.05792.

(c) The probability that at least three cars finish the race is 0.94208.

(a) To determine the probability that exactly two cars finish the race, we have to use binomial distribution. In this case, we have n = 5 trials, and p = 0.8 is the probability that a car finishes the race (1 - 0.2). Using the binomial distribution formula:

P(X = k) = (nCk)(p^k)(1 - p)^(n - k)

Where X is the number of cars that finish the race, we get:

P(X = 2) = (5C2)(0.8²)(0.2)³= (10)(0.64)(0.008)= 0.0512

Therefore, the probability that exactly two cars finish the race is 0.0512.

(b) To determine the probability that at most two cars finish the race, we have to calculate the probabilities of 0, 1, and 2 cars finishing the race and add them up.

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)= (5C0)(0.8⁰)(0.2)⁵ + (5C1)(0.8¹)(0.2)⁴ + (5C2)(0.8²)(0.2)³= 0.00032 + 0.0064 + 0.0512= 0.05792

Therefore, the probability that at most two cars finish the race is 0.05792.

(c) To determine the probability that at least three cars finish the race, we can calculate the probability of 0, 1, and 2 cars finishing the race and subtract it from 1, which gives us the probability of at least three cars finishing the race.

P(X ≥ 3) = 1 - [P(X = 0) + P(X = 1) + P(X = 2)]= 1 - (0.00032 + 0.0064 + 0.0512)= 0.94208

Therefore, the probability that at least three cars finish the race is 0.94208.

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Answer:

Yes, we can use the given information to prove that $\triangle ABC\cong\triangle DEF$ by the Angle-Side-Angle (ASA) congruence criterion.

We are given that $\angle A\cong\angle D$ and $\angle C\cong\angle F$, which satisfies the Angle-Angle (AA) criterion. Furthermore, we are given that $\overline{AC}\cong\overline{DF}$, which satisfies the Side-Side-Side (SSS) criterion. Therefore, by combining the AA and SSS criteria, we can conclude that $\triangle ABC\cong\triangle DEF$ by the ASA criterion.

In summary, the given information satisfies the necessary conditions for the ASA congruence criterion, and therefore we can prove that $\triangle ABC\cong\triangle DEF$.

Answer:

CP of computer = 27000 rs.

Step-by-step explanation:

D% = Dis/MP*100

We know, Dis = MP-SP

Given Profit= 1160 rs.

So,CP = 27000 rs.

The given example of f(1011) = 1110 illustrates how a one-to-one function operates, in that the same bitstring is not mapped to multiple elements in the range.

For the given functions f: A -> A and g: A -> A which are one-to-one functions, the following statements are true:

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Probabilities (at least 13 graduates) = 0.29858

The variable is binomial, which means that it can only have two possible outcomes (in this case, either a student will graduate or they will drop out). The probability of at least 13 students out of 15 graduating is calculated by adding the probability of exactly 13 students graduating and the probability of exactly 14 students graduating:

P(at least 13 graduate) = P(exactly 13 graduate) + P(exactly 14 graduate)

To calculate the probability of exactly 13 students graduating, use the binomial formula:
P(X = 13) = (15 choose 13) * (0.105)13 * (0.895)2

The calculation for P(X = 13) is: (15 choose 13) * (0.105)13 * (0.895)2 = (15!/13!(15-13)!) * (0.105)13 * (0.895)2 = (15 * 14 / 1 * 1) * (0.00155) * (0.80505) = 0.16437

Similarly, to calculate the probability of exactly 14 students graduating, use the binomial formula:
P(X = 14) = (15 choose 14) * (0.105)14 * (0.895)1

The calculation for P(X = 14) is: (15 choose 14) * (0.105)14 * (0.895)1 = (15!/14!(15-14)!) * (0.105)14 * (0.895)1 = (15 / 1) * (0.01462) * (0.895) = 0.13421

Finally, add the probabilities together to find the probability of at least 13 students graduating.
P(at least 13 graduates) = P(exactly 13 graduate) + P(exactly 14 graduate)
P(at least 13 graduates) 0.16437 + 0.13421 = 0.29858, rounded to three decimal places.

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Answer:

$2.235

Step-by-step explanation:

15% = 0.15

We Take

15.50 x 0.15 = $2.235

So, the tip for this bill is $2.235

Answer:

x = 4

Step-by-step explanation:

6x + 21  =  5x + 25

Then, subtract 5x from both sides:

x + 21  = 25

Then, subtract 21 from both sides.

x = 4

Therefore, x is equal to 4 degrees