If 12(x - a)(x - b) = 12x² - 7x - 12 , then ab =

Answer choices :

1
-1
7
12
-12​

Answer:

[tex] {k}^{2} + 2k + \frac{15}{2} = 0 \\ {k}^{2} + 2k + 1 = - \frac {15}{2} + 1 \\ {k + 1}^{2} = - \frac{13}{2} \\ k + 1 = - \sqrt{ \frac{13}{2} } \\ k = 1 + or - - \sqrt{ \frac{13}{2} } [/tex]

Answer:

Not factarable, all terms must be in x. or y

Step-by-step explanation:

Step-by-step explanation:

-9x+15=3(2-x)

6-6x

2. collect like terms

-9x+15= 6-6x

15-6 = 6x+9x

11= 15x

3. divide both sides by the coefficient of X which is 15

x= 11/15

Answer:

[tex]{ \sf{ {(x - 2)}^{2} + {(y + 8)}^{2} = 4}}[/tex]

Answer:

Center is (2, -8) and radius =2

h = 2 and k = -8

Filling in this equation:

(x -h)² + (y -k)² = radius²  we get:

(x - 2)^2 + (y--8)^2 = 2^2 which equals

(x-2)^2 + (y +8)^2 = 4

Source: http://www.1728.org/circleqn.htm

Step-by-step explanation:

Compute the quotient and remainder,

[tex]\dfrac{2x^4+x^3-14x^2+5x+6}{x^2+2x+k} \\\\ = 2x^2 - 3x - (8+2k) + \dfrac{(21+7k)x+(6+8k+2k^2)}{x^2+2x+k}[/tex]

The remainder upon dividing [tex]2x^4+x^3-14x^2+5x+6[/tex] by [tex]x^2+2x+k[/tex] should leave no remainder, which means

[tex]21+7k = 0 \implies 21 = -7k \implies k=-3[/tex]

and

[tex]6+8k+2k^2 = 0 \implies 2(k+3)(k+1)=0 \implies k=-3\text{ or }k=-1[/tex]

Only k = -3 makes both remainder terms vanish.

Then the previous result reduces to

[tex]\dfrac{2x^4+x^3-14x^2+5x+6}{x^2+2x-3} = 2x^2 - 3x - 2[/tex]

so that

[tex]2x^4+x^3-14x^2+5x+6 = (x^2+2x-3) (2x^2 - 3x - 2) \\\\ 2x^4+x^3-14x^2+5x+6 = (x+3)(x-1)(2x + 1)(x-2)[/tex]

and so the zeroes of the quartic polynomial are x = -3, x = 1, x = -1/2, and x = 2.

Answer:

x = 41°, y = 139°

Step-by-step explanation:

The given parameters are;

Line m is parallel to line n and lines m and n have a common transversal

The corresponding angles formed by the common transversal to the two parallel lines are 41° on line m and x° on line n

Therefore, x° = 41° by corresponding angles formed between on two parallel lines by a common transversal are equal

x° and y° are linear pair angles and they are, supplementary

∴ x° + y° = 180°

∴ x° + y° = 41° + y° = 180°

y° = 180° - 41° = 139°

y° = 139°.

Answer:

Anna is right in her meaning concerning on triangle solvability.

Step-by-step explanation:

The side [tex]c[/tex] represents the hypotenuse of a right triangle as [tex]C = 90^{\circ}[/tex] and is opposite to that angle. There are two ways to solve this triangle trigonometrically:

i) Law of Sine

[tex]\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}[/tex] (1)

ii) Law of Cosine

[tex]c^{2} = a^{2} + b^{2} - 2\cdot a\cdot b \cdot \cos C[/tex] (2)

The Pythagorean Theorem is a particular case of the Law of Cosine for [tex]C = 90^{\circ}[/tex]

The triangle cannot be solved as there is an input missing, either another side or another angle. If [tex]C = 90^{\circ}[/tex], then (2) is reduced into this form:

[tex]c^{2} = a^{2}+b^{2}[/tex] (2b)

In this case we need to know the measure of either [tex]a[/tex] or [tex]b[/tex] to determine its counterpart and the values of the missing angles by (1). In nutshell, Anna is right.

Answer:

B

Step-by-step explanation:

The decimal number 0.00897 written in scientific notation is 8.97 ×10^3 and it has significant figures

Answer:

8.97 * 10⁻³

Step-by-step explanation:

0.00897 = [tex]\frac{8.97}{1000}=8.97 * 10^{-3}[/tex]

Place the decimal point after the first nonzero number.

Write the power of 10,

(i) If we move the decimal to the right, the power of 10 decrease by number of moves.

(ii) If we move the decimal to the left, the power of 10 increase by the number of moves

Answer:

9 times 20 is equally to 180 minutes

Answer:

f=-1/20t+12

Step-by-step explanation:

khan

Answer:

20

Step-by-step explanation:

it is 20

Answer:

1

Step-by-step explanation:

-2(x-4)+1=7

First Distribute the -2.

-2x+8+1=7

Subtract the 8 and 1 from the whole equation.

-2x=-2

Divide both sides of the equation by -2.

x=1

I hope this helps!

Answer:

x = 1

Step-by-step explanation:

-2(x − 4) + 1 = 7

-2x  + 8 + 1 = 7

-2x + 9 = 7

-2x = -2

x = 1

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Explanation:

This figure is a kite since we have two pairs of adjacent sides that are congruent, but not all sides are the same length.

One property of kites is that the diagonals are always perpendicular (this applies to rhombuses as well). This means angle 3 is 90 degrees.

The measure of ∠3 is 90°

Because in a kite the diagonals bisects at 90°

Therefore ∠3 is 90°

Answered by Gauthmath must click thanks and mark brainliest

Answer:

x^2+(y-1)^2=25

Step-by-step explanation:

eqn of circle : (x-h)^2+(y-k)^2=r^2

center of circle = (h,k)

hence, the center of the current circle is (2,3)

moving 2 units to the left would make the center (0,1)

the radius would remain the same (5) , hence the new eqn would be

(x-0)^2+(y-1)^2=25

x^2+(y-1)^2=25

Answer:

Slope = -2

Step-by-step explanation:

The coefficient next to x is indicative of the equation's slope.

Answer:

slope = gradient

straight line equation is y = mx + c

where m is gradient therefore answer is -2

Answer:

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

Step-by-step explanation:

To find the value of sin 45° we divide the opposite side length with hypotenuse

[tex]\frac{1}{\sqrt{2} }[/tex]  we then multiply this by [tex]\sqrt{2}[/tex] because denominator cannot be irrational

[tex]\frac{1}{\sqrt{2} }[/tex]  x [tex]\sqrt{2}[/tex]  = [tex]\frac{\sqrt{2} }{2}[/tex] gg

Answer:

148°

Step-by-step explanation:

The central angle is twice the angle at the circumference, subtended on the same arc.

shaded angle = 2 × 74° = 148°

Answer:

The locus of the midpoints of the radii of the sphere is a sphere half the radii M of the given sphere and having the same center as of the given sphere.

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

[tex]\frac{10}{x} = \frac{4x}{10}[/tex]

[tex]4x^{2} =100\\x^{2} =25\\x=5[/tex]

Distributive property

screenshot if you need more words. seems to be a well illustrated and compact explanation right there

Answer: Ssh=1323π

Step-by-step explanation:

Answer:

[tex]7\frac{5}{9}[/tex]

Step-by-step explanation:

Hi there!

We are given this expression:

34÷(14-5)×2

And we want to evaluate it

We'll be using the order of operations

Depending on the country you're in, the acronym can be different, but in the US, the typical acronym used for the order of operations is PEMDAS, or Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

The order of operations states that we should start with any expressions in parentheses

In this case, it's (14-5), which is equal to 9

The expression now becomes

34÷9×2

There are no exponents, so let's skip that

Now this is where it gets tricky:

Based on the acronym alone, we should be doing 9*2 next, however, we should always work left to right, even if in a case like this, we'll be doing division instead of multiplication

Divide 34 by 9

[tex]\frac{34}{9}[/tex]×2

Now multiply [tex]\frac{34}{9}[/tex] by 2

[tex]\frac{68}{9}[/tex]

(as a mixed fraction, it's 7[tex]\frac{5}{9}[/tex])

Hope this helps!

Answer:

B

Step-by-step explanation:

each of the numbers is just adding 1.25 on to it

Answer: Choice B

16.00, 17.25, 18.50, 19.75, ...

==========================================================

Explanation:

We start with $16.00 as the first term, as this is the amount the boss pays him initially. Then we add on 1.25 to get 16+1.25 = 17.25 to represent the next wage after that first raise.

Then after the second raise he gets, he'll then earn 17.25+1.25 = 18.50 an hour. This process theoretically can go on forever, but realistically the boss will likely set some kind of limit.

We say that this sequence { 16.00, 17.25, 18.50, 19.75, ... } is arithmetic with the first term of 16.00 and common difference 1.25

The common difference is the gap width between any two neighboring terms, and it's the amount the wage goes up each time he gets a raise.

Step-by-step explanation:

Answer:

39

Step-by-step explanation:

4x+7=9x-33

4x-9x=-33-7

-5x=-40

x=8

4×8+7=39

Answer:

Part A:

c = .86*p

c =1.72 for 2 lbs

Part B:

c =.81p

Step-by-step explanation:

Part A:

Total cost = cost per pound * number of pounds

c = .86*p

Let p = 2

c = .86*2

c =1.72

Part B:

Total cost = cost per pound * number of pounds

c = .(.86-.05)*p

c =.81p

Answer:

112 m

Step-by-step explanation:

The area (A) of a square is

A = s² ( s is the length of side )

Here A = 784 , then

s² = 784 ( take the square root of both sides )

s = [tex]\sqrt{784}[/tex] = 28

Then

perimeter = 4s = 4 × 28 = 112 m

Answer:

112m

Step-by-step explanation:

the area of the square is 784m^2 so the square root of 784 would give us the length of the sides(since it's a square the length of each sides are equal). √784 would give 28m. 28 m is the length of each sides..so now the perimeter would be the addition of each sides which in case would be 4 times 28 because it's a square. 4 times 28 gives 112m.

Answer:

The graph shifts 5 units left

Step-by-step explanation:

The given functions are;

f(x) = [tex]2^{x - 2}[/tex], g(x) = [tex]2^{x + 3}[/tex]

Therefore, we have;

When x = 2, f(2) = [tex]2^{2 - 2}[/tex] = 1  and g(2) = [tex]2^{2 + 3}[/tex] = 32

When x = 3, f(3) = [tex]2^{3 - 2}[/tex] = 2  and g(3) = [tex]2^{3 + 3}[/tex] = 64

When x = 6, f(6) = [tex]2^{6 - 2}[/tex] = 16  and g(6) = [tex]2^{6 + 3}[/tex] = 512

When x = 7, f(7) = [tex]2^{7 - 2}[/tex] = 32 and g(7) = [tex]2^{7 + 3}[/tex] = 1024

When x = 8, f(8) = [tex]2^{8 - 2}[/tex] = 64  and g(8) = [tex]2^{8 + 3}[/tex] = 2,048

Therefore, the y-value of f(x) obtained at x = 8, is obtained by g(x) at x = 3, and the graph is shifts(ed) 5 units left.

This question is solved using the central limit theorem, giving an answer of:

Fourth option, approximately normal with mean of 140 seconds and standard deviation of 10 seconds.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 140, standard deviation of 20, sample of 4:

By the Central Limit Theorem, the distribution is approximately normal.

Mean is the same, of 140.

[tex]n = 4, \sigma = 20[/tex], thus:

[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{20}{\sqrt{4}} = 10[/tex]

Thus, the correct answer is:

Fourth option, approximately normal with mean of 140 seconds and standard deviation of 10 seconds.

For another example of the Central Limit Theorem, you can check https://brainly.com/question/15519207