In the equation x^2 + 10x + 24 = (x + a)(x + b), b is an integer. Find algebraically all possiblevalues of b.

Answers

Answer 1

Answer: To factor (x² +10x+24); you first have to ask yourself, what 2 numbers will multiply and give me positive 24, but add and give me positive 10? After listing your factors, (1,24)(2,12)(3,8)and (4,6); you decide that (4*6)=24 & adds to get you 10. Meaning that (x²+10x+24) factors are (x+4)(x+6).
Now algebraically, there wouldn't be any other possible value of b, 6, because if you put (-6) & (4), those numbers will multiply and give you (-24) and add & give you (-2); & that is not what you're looking for.

I hope I explained this enough for you to understand. (:

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What is the converse of the following conditional?If a point is in the first quadrant, then its coordinates are positive

a. If a point is in the first quadrant, then its coordinates are positive
b. If the coordinates of a point are positive, then the point is in the first quadrant
c. If the coordinates of a point are not positive, then then the point is not in the first quadrant
d. If a point is not in the first quadrant, then the coordinates of the point are not positive.

Answers

The answer is B because the converse just flips the two phrases within the statement.

Answer:

b. If the coordinates of a point are positive, then the point is in the first quadrant

Step-by-step explanation:

P = 2(w + h)W = 12 correct to the nearest whole number

h = 4 correct to the nearest whole number

Work out the upper bound for the value P

(urgent please)

Answers

After substituting W = 12, h = 4, in the equation P = 2(w + h), P = 32

What is upper bound?

"An element greater than or equal to all the elements in a given set."

What is equation?

"It is an expression which contains an equal symbol."

For given question,

Given equation: P = 2(w + h)

W = 12, h = 4

After substituting these values in given equation,

⇒ P = 2 × (12 + 4)

⇒ P = 2 × 16

⇒ P = 32

Learn more about upper bound here:

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Answer:

p=32

Step-by-step explanation:

4+12=16

16×2=32

p=32

Can you please solve this problem for me? Thank you :)___ in. = 5 ½ ft.
36 in. = ____ yd.
6 yd = ____ in.
90 ft. = ____ yd.

Thanks :)

Answers

One foot is 12 inches, so 5 1/2 feet are 66 inches.

There are 36 inches in a yard, so 36 inches is 1 yard and 6 yards is 216 inches.

There are three feet in a yard, so 90 feet will be 30 yards.

12 in= 1 ftratio and proportion1/12= x/5.5cross multiply66in= 5.5 ft36= 1 yd36/1= x/6x= 210 inches3/1= 90/xx= 30 ydshope this helps

7 is 70% of what number

Answers

seven is 70% of the number ten 7/10 = 70%

$x-searched\ number\n\n70\%x=7\n\n0.7x=7\ \ \ \ \ \ |:0.7\n\nx=10\n\n7\ is\ 70%\ of\ 10$

The balance in Alex's bank account is $675. The accountearns 6% simple interest calculated twice per year. If Alex
makes no deposits or withdrawals for 2 full years, the
balance in his account (rounded to the nearest dollar) will
be -
Select one:
O
$852
$715
$837
$756

Answers

Answer:

$852

Step-by-step explanation:

From the given question, the following are given:

Present value, PV = $675

Rate, r = 6% = 0.06

Number of years, n = 2 years

Number of times per year, m = 2

The balance in his account is the future value (FV), so that;

Future value = PV $(1+r)^(nm)$

= 675 $(1+0.06)^((2*2))$

= 675 x 1.26248

= 852.174

Future value = $852

Thus, the balance in Alex's account would be $852.

Find the surface area of the following figures 16 ft 13 ft 12ft 19ftPlease help me solve number 3! And if i got #2 incorrect, please help me fix that one too.

Answers

Answer:

1192 ft²

Step-by-step explanation:

Figure 3 is a trapezoidal prism.

The total surface area of a trapezoidal prism is made up of 2 congruent trapezoid bases and 4 rectangular faces connecting the bases.

The formula for the area of a trapezoid is:

$\boxed{S.A.=(1)/(2)(a+b)h}$

where a and b are the bases, and h is the height.

From observation of the given diagram, the bases are 16 ft and 19 ft, and the height is 12 ft. Therefore, the area of each trapezoid base is:

$\begin{aligned}\textsf{Area of trapezoid base}&=(1)/(2)(16+19)\cdot 12\n\n&=(1)/(2)(35)\cdot 12\n\n&=17.5\cdot 12\n\n&=210\; \sf ft^2\end{aligned}$

To calculate the areas of all the rectangular faces, we first need to calculate the slant (s) of the trapezoid base by using the Pythagoras Theorem:

$\begin{aligned}s^2&=(19-16)^2+12^2\ns^2&=3^2+12^2\ns^2&=9+144\ns^2&=153\ns&=√(153)\end{aligned}$

The area of a rectangle is the product of its width and length.

Therefore, the sum of the areas of the rectangular faces is:

$\begin{aligned}\textsf{Area of rectangular faces}&=16\cdot13+12\cdot13+19\cdot13+√(153)\cdot13\n&=208+156+247+13√(153)\n&=771.801119...\n&=772\; \sf ft^2\;(nearest\;foot)\end{aligned}$

To find the total surface area of the given trapezoidal prism, sum the area of the two trapezoid bases and the area of the rectangular faces:

$\begin{aligned}\textsf{Total S.A.}&=2 \cdot 210+772\n&=420+772\n&=1192\; \sf ft^2\end{aligned}$

Therefore, the total surface area of the given trapezoidal prism is 1192 ft², rounded to the nearest foot.

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