Write each expression as the product of two binomials x2 - 5x + 6

Answer: The answer is (A) -5.

Step-by-step explanation:  We are given to find the element [tex]a_{23}[/tex] in the following matrix:

[tex]A=\begin{bmatrix}8 & -4 & -3\\ 3 & -9 & -5\\ -8 & 8 & 8\end{bmatrix}[/tex]

We know that [tex]a_{mn}[/tex] is an element of a matrix present in the m-th row and n-th column.

So, [tex]a_{23}[/tex]  will be the element present in the second row and third column.

Since the element in the second row and third column is - 5, so we have

[tex]a_{23}=-5.[/tex]

Thus, (A) -5 is the correct option.

The cost that's necessary to pay the loan will be $31,616.16.

First, we need to calculate the effective monthly interest rate. This will be:

i = 0.053/12

= 0.0044

The effective annual interest rate will then be:

i = (1 + 0.0044)^12 - 1

I = 0.0543

Next thing will be to calculate the present worth of all the loans which will be:

P = 6125 + 6125 (1 + 0.0543) + 6125 (1 + 0.0543)² + 6125(1 + 0.0543)³

P = $22,671.40

The worth of the loans after four years will be:

P = 22671.40 (1 + 0.0543)⁴

= $31,616.16

In conclusion, the correct option is $31,616.16.

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To calculate the total cost of Toby's 4 Stafford loans, the monthly amount for one loan is first calculated and then multiplied by four and by the number of months. The correct total lifetime cost is approximately $31,569.60.

To determine the total lifetime cost that Toby will pay to pay off his 4 Stafford loans, each with a principal of $6,125, an interest rate of 5.3% compounded monthly, and a loan duration of ten years, we need to calculate the monthly payment for a single loan and then multiply by the number of loans and the duration. The formula for the monthly payment on an installment loan is:

P = P[r(1+r)^n] / [(1+r)^n - 1]

where:

Using the data given:

P = $6,125 * [0.004417(1 + 0.004417)^120] / [(1 + 0.004417)^120 - 1]

Calculating this gives us a monthly payment of approximately $65.77 for each loan. Toby took out 4 loans, so his total monthly payment is 4 * $65.77 = $263.08.

The total lifetime cost for a single loan is the monthly payment * number of payments (120), which is:

Total cost for one loan = $65.77 * 120 = $7,892.40

And the total lifetime cost to pay off all 4 loans:

Total cost for all loans = $7,892.40 * 4 ≈ $31,569.60

Therefore, rounding each loan's payment to the nearest cent, the total lifetime cost to pay off all 4 of Toby's loans is roughly $31,569.60, making the answer option b the correct one.

The simplified product of 3/7 multiplied by 14 is 6.

To multiply 3/7 by 14, you can follow these steps:

Multiply the numerators: 3 x 14 = 42.

Multiply the denominators: 7 x 1 = 7.

Therefore, the product of 3/7 multiplied by 14 is 42/7.

However, we can simplify this fraction further by dividing both the numerator and denominator by their greatest common divisor, which is 7.

= 42/7

= 6/1

= 6.

So, the simplified product of 3/7 multiplied by 14 is 6.

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To solve this problem, we have to find the multiples of 3 and then find the probability of selecting them. The probability of having a multiple of 3 is 1/3.

The probability of tossing a six-sided dice and a eight-sided dice.

When we toss them together, the maximum value will be

[tex]6 * 8 = 48[/tex]

The multiplies of 3 will be

Data;

The probability of having a multiple of 3 will be

[tex]P(multiple of 3) = \frac{16}{48} = \frac{1}{3}[/tex]

The probability of having a multiple of 3 is 1/3

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In the given two column proof two sides and included angles are equal.

Triangles are congruent if any pair of corresponding sides and their included angles are equal in both triangles .In the figure sides BD≅BD , AB≅ BC and <ABD ≅,BDD Therefore triangle ABD and triangle CBD are congruent by SAS property of congruence.

The correct  option for missing statement is D. ΔABD ≅ ΔCBD .

Answer:

ΔABD ≅ ΔCBD

Step-by-step explanation:

Guys this is the right answer,  ΔABD ≅ ΔCBD. I got it right on my test!

The number of sodas sold is 145, and the number of hot dogs sold is 112. (145 sodas, 112 hot dogs)

Let's denote:

-  s  as the number of sodas sold.

- h  as the number of hot dogs sold.

Given that the total number of sodas sold is 145, we have:

[tex]\[ s = 145 \][/tex]

And we know that the number of hot dogs sold is 33 less than the number of sodas sold:

[tex]\[ h = s - 33 \][/tex]

Now, substitute the value of  s  into the equation for h :

[tex]\[ h = 145 - 33 \]\[ h = 112 \][/tex]

So, the number of hot dogs sold is 112, and the number of sodas sold is 145.

The solution of equation 9x + 7 = 7x - 5 is -6.

The equation 9x + 7 = 7x - 5 can be solved by first isolating x on one side. To do this, we subtract 7x from both sides of the equation, which gives us 2x + 7 = -5. Next, we subtract 7 from both sides to get 2x = -12. Finally, we divide both sides by 2 to find that x = -6. This single solution can be checked by substituting x back into the original equation to verify that both sides equal out, confirming it is an identity. Therefore, the correct solution is x=-6.

To validate the result, we substitute -6 back into the original equation:
9(-6) + 7 = 7(-6) - 5
-54 + 7 = -42 - 5
-47 = -47, which is indeed an identity.

The additional information needed to prove that ΔABC ≅ ΔDEF by ASA is two pairs of congruent angles and the included side between the two pairs of congruent angles.

We are given that;

The two triangles ΔABC and ΔDEF

Now,

To prove that ΔABC ≅ ΔDEF by ASA (Angle-Side-Angle) congruence criterion, we need the following information:

Two pairs of congruent angles.

The included side between the two pairs of congruent angles.

If two angles and one side of one triangle are equal to two angles and one side of another triangle, then they are congruent. For example, in ΔABC and ΔDEF, ∠A = ∠D, ∠B = ∠E and BC= EF then ΔABC ≅ ΔDEF by AAS criteria

Therefore, by congruent triangles answer will be two pairs of congruent angles and the included side between the two pairs of congruent angles.

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Arc DB measure less than 180 degrees,  is called a minor arc.

Option (b) is correct

A minor arc is an arc whose angle is less than 180 degrees.

From given figure, It is observed that, arc DB measure less than 180 degrees is called a minor arc.

Hence, option (b) is correct.

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Answer:

-17 - (-8)

Option 3 is correct.

Step-by-step explanation:

Phrase: "the difference between -17 and -8"

Expression: To write the phrase into algebraic form with a variable or constant.

Difference: write two number using subtraction between them.

"the difference between -17 and -8"

First number is -17 and second number is -8

Expression: -17 difference -8

Now using minus sign write as expression.

[tex]\Rightarrow -17-(-8)[/tex]

Hence, The correct expression is -17-(-8)