The base of a triangle is 6 inches more than 3 times the height. If the area of the triangle is 120 square inches.
find the base and height.

The matrix M is: M = [2/9 -8/27 , 4/9 -8/27 ]

Let's say that M is a 2 x 2 matrix that satisfies M × [3 -2 , 6 -8 ] = [-2 16]. This means that the product of matrix M and matrix [3 -2 , 6 -8 ] will give us the result matrix [-2 16].  We know that the product of two matrices is equal to the sum of the products of their corresponding elements.  We can use this knowledge to solve for the unknown elements in matrix M. Let us assume that M = [a b , c d] so that we can solve for its elements.

a(3) + b(6) = -2 ... (1) c(3) + d(6) = 16 ... (2) a(-2) + b(-8) = -2 ... (3) c(-2) + d(-8) = 16 ...

(4)Simplifying equations (1) to (4),  we get:

3a + 6b = -2 ... (5) 3c + 6d = 16 ... (6) -2a - 8b = -2 ... (7) -2c - 8d = 16 ... (8)

Solving for a, b, c, and d, we get:a = 2/9 b = -8/27 c = 4/9 d = -8/27.

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9514 1404 393

Answer:

  f(x) = (x +4)(x +1)(x -6)(x -2)^4

Step-by-step explanation:

Each root p will contribute a factor of (x -p) to the function. Repeated factors can be written using an exponent.

  f(x) = (x +4)(x +1)(x -6)(x -2)^4

Answer:

The answer is "1:2"

Step-by-step explanation:

Let 96 car sales are X and 96 truck sales are Y  And income from 97 cars is 0.89X, income from 97 trucks is 1.07Y

\(\to \frac{(0.89X+1.07Y)}{(X+Y)}=1.01\\\\\frac{X}{Y}=?\\\\\to \frac{(0.89X+1.07Y)}{(X+Y)}\ \ \text{Divide by Y and get}\ \ \frac{( \frac{0.89X}{Y}+1.07)}{(\frac{X}{Y}+1)} =1.01\\\\\)

Then

\(\to \frac{X}{Y}=1:2\)

Answer:

To solve the given system of equations using the substitution method, we need to solve one equation for one variable and then substitute that expression into the other equation for that same variable. Let's solve the second equation for y.

-x + y = 4

y = x + 4

Now we can substitute this expression for y into the first equation and solve for x.

-2x + 2(x + 4) = 7

-2x + 2x + 8 = 7

8 = 7

The equation 8 = 7 is not true, which means the system of equations has no solution. We can see this visually by graphing the two lines. They are parallel and will never intersect, which means there is no point that satisfies both equations.

Therefore, the solution to the system of equations is "No solution."

Note: Please be sure to double-check your work to avoid mistakes.

Step-by-step explanation:

Hope this helps you!! Have a wonderful day/night!!

Answer:

x  ⪯ 7

Step-by-step explanation:

5 + 2 = 7

Answer:

Concept: Statistics

Answer:

u will try urself ......okay ...

...

Answer $2,295.60:

Step-by-step explanation: i just did this assignment and got it right, hope this helps

There are several methods for factoring expressions, including factoring out the greatest common factor (GCF), by grouping, using the difference of squares or sum/difference of cubes, using the FOIL method or the reverse FOIL method or using special cases such as perfect square trinomials or difference of squares.

Factoring out the GCF: This method involves finding the greatest common factor of all the terms in an expression and then dividing it out of each term. For example, if we have the expression 12x^2 + 8x^2, the GCF is 4x^2, so we can factor it out and write the expression as 4x^2(3 + 2).

Factoring by grouping: This method involves grouping the terms of an expression into pairs and factoring out a common factor. For example, if we have the expression x^2 + 3x + 2x + 6, we can group the first two terms and the last two terms and factor out a common factor of x from the first group and 2 from the second group. This gives us x(x + 3) + 2(x + 3)

Factoring quadratics: There are a few methods to factor quadratics, such as factoring a difference of squares, or factoring a sum or difference of cubes. For example, if we have the expression x^2 - y^2, we can factor it as (x-y)(x+y) using difference of squares.

Factoring trinomials: There are a few methods to factor trinomials, such as FOIL method or reverse FOIL method. The FOIL method is a mnemonic acronym for first, outer, inner, and last, which is used to multiply two binomials. Reverse FOIL is used to factor a trinomial that is the product of two binomials. For example, if we have the expression x^2 + 5x + 6, we can factor it as (x+2)(x+3) using reverse FOIL method.

Factoring special cases: There are some special cases of factoring that have specific methods. For example, factoring perfect square trinomials such as x^2 + 2x + 1 is factored as (x+1)^2 and factoring difference of squares such as x^2 - y^2 is factored as (x-y)(x+y)

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There is no solution for the system of equations because the determinant of A is zero.

A matrix is an array of rows and columns containing numbers, symbols, or expressions that is rectangular in shape.

In linear algebra, matrices describe linear mappings and enable explicit computations. As a result, a significant portion of linear algebra involves the study of matrices, and the majority of the characteristics and operations of abstract linear algebra may be described in terms of matrices.

Given the equations,

9x + 4y + 6z = -8

9x + 4y + 6z = -5

x - 8y + 8z = -6

solving by matrix method,

A = \(\left[\begin{array}{ccc}9&4&6\\9&4&6\\1&-8&8\end{array}\right]\)

B = \(\left[\begin{array}{ccc}-8\\-5\\-6\end{array}\right]\)

X = \(\left[\begin{array}{ccc}x\\y\\z\end{array}\right]\)

X = A⁻¹B

for A⁻¹, calculate the determinant of A

|A| = \(\left|\begin{array}{ccc}9&4&6\\9&4&6\\1&-8&8\end{array}\right|\)

|A| = 9(32 + 48) - 4(72 - 6) + 6(-72 - 4)

|A| = 720 - 264 - -456

|A| = 0

since |A| is zero there are no solutions for the equation.

Hence there are no solutions for a system of equations.

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The satellite should be insured for 98 months (rounded up to the nearest month) to be 96% confident that the microchip will last beyond the insurance date.

To answer this question, we need to find the number of months for which we can be 96% confident that the microchip will not malfunction. This means we want to find the value of x such that P(X > x) = 0.04, where X is the random variable representing the life expectancy of the microchip.

We know that X follows a normal distribution with mean μ = 92 months and standard deviation σ = 3.6 months. Therefore, we can standardize X to the standard normal distribution Z ~ N(0, 1) using the formula

Z = (X - μ) / σ

We can then rewrite the probability P(X > x) as

P(X > x) = P(Z > (x - μ) / σ)

1.75 = (x - 92) / 3.6

Solving for x, we get

x = 98 months

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The given question is incomplete, the complete question is:

A relay microchip in a telecommunications satellite has a life expectancy that follows a normal distribution with a mean of 92 months and a standard deviation of 3.6 months. when this computer-relay microchip malfunctions, the entire satellite is useless. a large london insurance company is going to insure the satellite for 50 million dollars. assume that the only part of the satellite in question is the microchip. all other components will work indefinitely. a button hyperlink to the salt program that reads: use salt.for how many months should the satellite be insured to be 96% confident that it will last beyond the insurance date?

Answer:

Step-by-step explanation:

The vertex form of an equation of the parabola:  

                                                        f(x) = a(x - h)² + k

the vertex is (3, -7)  ⇒   h = 3,  k = -7

so:

     f(x) = a(x - 3)² - 7

The parabola goes through the point (2, -6) ⇒   x=2,  f(x)=-6

-6 = a(2 - 3)²  - 7

-6 = a(-1)²  - 7

+7           +7

1  = a

It means the equation of the parabola in vertex form:

                               f(x) = (x - 3)² - 7

Sample size of 385 should be taken. Rounding up to the next whole number, the required sample size would be 385. So, in order to provide a 95% confidence interval with a margin of error of 0.1 for the population proportion of 0.25, a sample size of 385 should be taken.

We can use the formula:

n = (Z^2 * p * (1-p)) / E^2

where:

Z is the z-score corresponding to the desired confidence level (for 95% confidence, Z = 1.96)

p is the estimated population proportion (p = 0.25)

E is the desired margin of error (E = 0.1)

Plugging in the values:

n = (1.96^2 * 0.25 * (1 - 0.25)) / 0.1^2

n = 384.16

we are attempting to gauge the populace extent with a room for mistakes of 0.1 and a certainty level of 95%.

To find the example size we want, we utilize an equation that considers the assessed populace extent (0.25), the ideal safety buffer (0.1), and the certainty level (95%). The recipe gives us a number that we gather together to the closest entire number. For this situation, the recipe lets us know that we want to test 385 individuals.

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Answer:

3/5

Step-by-step explanation:

4/10 are left. We can reduce it and get 2/5.

Hope it helps you!

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The value of p in the given equation is -1.

Given is an equation p-3 = -4, we need to find the value of p,

So,

p-3 = -4

p = -4+3

p = -1

Hence, the value of p in the given equation is -1.

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The factors of 5x as calculated from the data given is found to be as 5, x and  1 .

On factorizing 5x we can write it as ,

5 x 1 x x .

Therefore the factors are 5 , 1 and x.

There are some integers which are positive and can divide a number completely leaving no remainders. Such integers are known as factors for a number. If we want to get a product by multiplying two numbers , we will have to multiply two factors. Each number is a multiplier of itself.

The prime factor is the factor of a given number that is also a prime number. Factors are numbers that are multiplied together to produce another number.

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The probability that a person chooses a new car with an Automatic Transmission and no other option is 83%.

P(A and not(B or C)) = P(A) - P(A and (B or C))

                   = P(A) - P(A and B) - P(A and C) + P(A and B and C)

                   = 0.70 - 0.85 + 0.98

                   = 0.83

Therefore, the probability is 83%.

Mutually exclusive events are events that cannot occur at the same time. If two events are mutually exclusive, the occurrence of one event means that the other event cannot occur. In this case, the events A, B, and C are not mutually exclusive since the probabilities of A or B, A or C, and B or C are not zero. If two events are mutually exclusive, they cannot be independent because the occurrence of one event affects the probability of the other event. Independence means that the occurrence of one event does not affect the probability of the other event. Therefore, the answer is No, mutually exclusive events are not independent.

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Once you have the distance covered in the first 6.5 hours, you can divide it by 6.5 to calculate your average speed during that time interval.

To estimate your speed at 6.5 hours into the trip, you would need to know the distance covered during that time interval. The speed is calculated by dividing the distance traveled by the time taken.

To make an accurate estimate, you would need the following information:

Distance covered: You would need to know how far you have traveled in the first 6.5 hours of the trip. This could be obtained from a GPS device, odometer, or by referencing a map.

Time taken: You already know that it has been 6.5 hours into the trip.

Consistency of speed: It is assumed that your speed has remained relatively constant throughout the trip. If there were significant variations in speed, the estimate would be less accurate.

This estimate assumes that your speed has been consistent, without any major fluctuations. Keep in mind that this estimate represents your average speed over the given time period, and your actual speed at any specific moment during the trip could have been different.

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Answer:

Step-by-step explanation:

Lets start with 13

-2(13 + 3) = -4(13) + 20

-32 = -52 + 20

-32 = -32

x = 1 basically

now 19

-2(19 + 3) = -4(19) +20

-44 = -76 + 20

-44 = -56

so divide those

-2(31 + 3) = -4(31) + 20

-68 = -124 + 20

-68 = -104

divide them

-2(37 + 3) = -4(37) + 20

-80 = -148 + 20

-80 = -128

Similar triangles are those with the same form but different sizes. The expression's measure for the value of x is 32.5.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects.

In other words, if two triangles are identical, their respective sides are equal in number and their corresponding angles are congruent.

From the given diagram, since the triangle ABC is similar to DCE, hence the measure of the angle CDE is equal to ABC that is;

<CDE = <ABC

2x = 65

x = 65/2

x = 32.5

Hence the measure of the value of x from the expression is 32.5

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his loan will be $37,234 in the year 2022.

ax2+bx+c=0, with a not equal to 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

Given, David took out a 20-year $70,000 loan from his bank in 2010.

The quadratic equation that approximates the year/loan balance relationship is y = -98*x^2 - 1,531x + 69,718,

where x is the number of years and

y is the balance

Since the Loan balance is given $37,234.

Thus to calculate the year

$37,234 = -98*x^2 - 1,531x + 69,718,

98 x² + 1534x - 32484 = 0

Comparing with the general form of the quadratic equation.

ax² + bx + c = 0

The discriminant b² - 4ac > 0 thus it has Two real roots.

using the Quadratic Formula

x = \(\frac{-b +- \sqrt{b^{2} - 4ac } }{2a}\)

x = -27.62

and

x = 12

Thus year = 2010 + 12 = 2022

Therefore, In the year 2022, his loan will be $37,234.

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TRUE

The fatal accident rate for young drivers aged 16 to 19 is about four times higher than at night. Two or more passengers of the same age triple the risk of a fatal accident driving a teenager.

An accident in which someone dies. Synonyms: Accident. Type: Collateral damage.

Of the collisions between cars, angled collisions are the most deadly (about 8,000 in 2020). The interactive chart also shows the estimated number of fatalities, injuries, casualties, and all accidents in different types of car accidents.

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Answer:

None. Both the amount of sugar and the amount of flour would be equal.

The recipe has more flour than sugar.

Answer:

g(4) = - 16

Step-by-step explanation:

Substitute x = 4 into g(x) , that is

g(4) = - 7(4) + 12 = - 28 + 12 = - 16

we know:  g(x) = -7x + 12

=> g(4) = -7.(4) + 12 = -28 +12 = -16

Ok done. Thank to me:>

Answer:

pic?

Step-by-step explanation:

The correct option: b. Reaction times were the longest when people had to read words presented in colored ink.

A seemingly unimportant phenomena called the Stroop effect explains a great deal about how the brain functions.

Thus, the stroop experiment's findings most accurately represent when respondents used to have to read words given in colorful ink, reaction times tended to be the longest.

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The complete question is-

This following question refers to the outcome of the actual experiment (described on the conclusions slides), not the data generated from your performance in particular (which may or may not have matched the real experimental results).

a. Reaction times were the longest when people had to read words presented in black ink.

b. Reaction times were the longest when people had to read words presented in colored ink.

c. Reaction times were the longest when people had to name the color of colored chips/shapes.

d. Reaction times were the longest when people had to name the color of words presented in colored ink.

Therefore , the solution to this problem of fraction comes out to be as quotient 4-i.

a rational number written in the classic "display" notation form ab or in the in-line notation form a/b, with a standing for the numerator and b for the denominator. A fraction is a piece of the entire.In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction.In the numerator or denominator of a complex fraction is a fraction.

Here,

Given :  22 + 3 i / 5 + 2 i

which can be written as :

=> 22+ 3i / 5+2i

Further dividing 22+ 3i by 5+ 2i

We get remainder as 0

The quotient comes out to  be 4-i

Therefore , the solution to this problem of fraction comes out to be as quotient 4-i.

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Answer:

The answer is

\( - 9 \frac{1}{4} \)

Answer:

90

Step-by-step explanation: