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3 years ago

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12. Given the following conditional: “If two angles are complementary, then the two angles add up to 90°.” a) Write the converse

of this conditional. b) Rewrite the information as a biconditional.

1 answer:

Dimas [21]3 years ago

6 0

I love this okay so with angles it’s weird because sometimes 5*[3/4] and take the spot where it’s 5(2/3 but hope this helps

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Express the sum of 3x³ - 7x² +2 and -x³ +9x² - 5<br> as a trinomial

saw5 [17]

2x³ + 2x² - 3 is the cubic trinomial that is expressed as the sum of 3x³ - 7x² +2 and -x³ +9x² - 5.

Given: To express the sum 3x³ - 7x² +2 and -x³ +9x² - 5 of as a trinomial.

What are algebraic equations?

Algebraic equations are a sequence or combination of characters containing variables, alphabets, numbers, symbols, etc. which are equated to some value.

What are polynomials?

Polynomials are algebraic expressions that consist of variables, coefficients, and operators. A polynomial is usually depicted as the sum of m terms for some unknown variable x, raised to the power of n with some constants.

For example: Let us consider p(x) to be a polynomial of degree n. The p(x) can be represented as

p(x) = Cₙ xⁿ + Cₙ₋₁xⁿ⁻¹ . . . . . . . + m terms . . . . . + K (where K is some constant and C's are coefficients of x)

What are trinomials?

Trinomials are algebraic expressions that consist of three non-zero terms or monomials.

For example: f(x) = x + y + z is a linear trinomial of 3 variables x, y, and z.

f(x) = x² + 4x + 1 is a quadratic trinomial of 1 variable x and so on.

Let's solve the problem:

Consider f(x) = 3x³ - 7x² +2 and g(x) = -x³ +9x² - 5

We have to express it as a sum of trinomials.

We can see both f(x) and g(x) are Cubic trinomials of one variable x and the lower degrees of x are the same.

So f(x) + g(x) will also given a cubic trinomial of one variable x

f(x) + g(x) = (3x³ - 7x² +2) + (-x³ +9x² - 5)

Grouping similar terms

f(x) + g(x) = (3x³ - x³) + (-7x² + 9x²) + (2 - 5)

f(x) + g(x) = 2x³ + 2x² - 3

Therefore, the required trinomial is 2x³ + 2x² - 3.

Hence 2x³ + 2x² - 3 is the cubic trinomial that is expressed as the sum of 3x³ - 7x² +2 and -x³ +9x² - 5.

Know more about "trinomials" here: brainly.com/question/16347049

#SPJ9

6 0

1 year ago

State whether each expression is meaningful. If not, explain why. If so, state whether it is a vector or a scalar.a. a. (bxc)i.

Artemon [7]

Answer:

ii

iii

i

iv

iii

ii

Step-by-step explanation:

a) For the first vector expression a. (bxc)

Yes, the expression is meaningful because the expression is in form of an associative rule, here we have a dot and a cross, the cross is evaluated first, thereafter the dot and eventually the results gives a scalar. the expression can also be written as a. (bxc) = (a.b) x (a.c)

correct option is (ii)

b) for the expression a x(b.c)

Yes, the expression has no meaning, because a cross product can only be expressed for two terms i.e a cross and then a dot as such it is neither a vector nor a scalar and hence the correct option is (iii)

c) for the expression a x (bxc)

Yes, the expression is meaningful because of the dominance of the cross product which can also be written as a x (bxc) = (axb) x(axc) as such it is a vector, correct option is (i)

d) for the expression a.(b.c)

the expression here has no meaning because the dot product can only be expressed for two term as such it is neither vector nor scalar hence the correct option is (iv)

e) for the expression (a.b)x(c.d)

The expression is meaningless because the cross product is only defined for two terms as such the expression can not be written in another way, it is neither scalar nor vector. the correct option is (iii)

f) for the expression (axb) . (cxd)

the expression here is meaningful because if the cross product terms are evaluated first before the dot product, a unique solution will be gotten which will be in terms of a scalar. correct option is (ii)

6 0

4 years ago

I want to bring my grade up so if anyone knows tell me

olga2289 [7]

Answer:

no

Step-by-step explanation:

You will have more time to do it, but no, try extra credit

Sorry mate hope this helps<3

5 0

3 years ago

What is the greatest two-digit whole number, the product of whose digits is 8?

Sergio039 [100]

Possible two digit pairings:
1*8 = 8(The two digit number being 18)
2*4 = 8 (The number being 24)
4*2 = 8 (Or, 42)
8*1=8 (81)

81 is the largest of the possible numbers.

8 0

4 years ago

1. A magazine reported 66% of all dog owners usually greet their dog before greeting their

NISA [10]

Answer:

(a) There is 95% confidence that the true proportion of dog owners who greet their dogs first is between 0.475 and 0.775.

(b) The point estimate is 0.625. The margin of error is 0.15.

(c) It is plausible that the true proportion of all owners who greet their dog first is 66%.

Step-by-step explanation:

The (1 - α)% confidence interval for population parameter implies that there is a (1 - α) probability that the true value of the parameter is included in the interval. Or, the (1 - α)% confidence interval for the parameter implies that there is (1 - α)% confidence or certainty that the true parameter value is contained in the interval.

In statistic, point estimation comprises of the use of sample data to estimate a distinct data value (known as a point estimate) which is to function as a "best guess" or "best estimate" of an unidentified population parameter. The point estimate of the population mean (µ) is the sample mean ( $\bar x$ ).

The (1 - α)% confidence interval for population proportion is:

$CI=\hat p\pm z_{\alpha/2}\times \sqrt{\frac{\hat p(1-\hat p)}{n}}$

The margin of error for this interval is:

$MOE=\frac{UL-LL}{2}$

For the hypothesis test, if the confidence interval consist of the null value of the parameter then the null hypothesis is accepted or else rejected.

The 95% confidence interval for the population proportion of owners who greet their dog first is,

CI = (0.475, 0.775)

(a)

The 95% confidence interval for the population proportion, (0.475, 0.775), implies that there is a 0.95 probability that the true proportion of dog owners who greet their dogs first is between 0.475 and 0.775.

Or, there is 95% confidence that the true proportion of dog owners who greet their dogs first is between 0.475 and 0.775.

(b)

The point estimate of the population proportion (<em>p</em>) is the sample mean ( $\hat p$ ).

Compute the point estimate from the 95% confidence interval as follows:

Point estimate = (UL + LL)/2

$=\frac{0.775+0.475}{2}\\=0.625$

The point estimate is 0.625.

Compute the margin of error as follows:

$MOE=\frac{UL-LL}{2}=\frac{0.775-0.475}{2}=0.15$

The margin of error is 0.15.

(c)

The hypothesis to test whether the proportion of all owners who greet their dog first is 66% is:

<em>H₀</em>: The proportion of all owners who greet their dog first is 66%, i.e. <em>p</em> = 0.66

<em>Hₐ</em>: The proportion of all owners who greet their dog first is not 66%, i.e. <em>p</em> ≠ 0.66.

The 95% confidence interval for the population proportion of owners who greet their dog first is,

CI = (0.475, 0.775)

The 95% confidence interval consists of the null value, i.e. <em>p</em> = 0.66.

The null hypothesis was failed to rejected.

Thus, it is plausible that the true proportion of all owners who greet their dog first is 66%.

6 0

3 years ago