.simplify
(2a+5)²-(a+3)(a-3)​

9514 1404 393

Answer:

  (a)  42.3°

Step-by-step explanation:

Side 'a' is the shortest of three unequal sides, so angle A will be the smallest angle in the triangle. Its measure can be found from the Law of Cosines.

  a² = b² +c² -2bc·cos(A)

  cos(A) = (b² +c² -a²)/(2bc) = (21² +25² -17²)/(2·21·25) = 777/1050

  A = arccos(777/1050) ≈ 42.3°

The measure of angle A is about 42.3°.

_____

Additional comment

The smallest angle in a triangle can never be greater than 60°. This lets you eliminate choices that exceed that value.

Answer:

 (a)  42.3°

Step-by-step explanation:

Answer:

Roots is a fancy word for zero, which is also another fancy word for the x intercept.

You can factor a quad or use the quadratic equation to get zeros.

In this case, its non-factorable. So you gotta use the quadratic.

Using the quadratic equation you get : x = -2 ± √-1 (√5),

which can be rewritten as x = -2 ± i(√5)

Function was : x^2 + 4x + 9

For quad, I identified the following:

A = 1

B = 4

C = 9

I also added a picture of the formula in the attached.

Answer:

f (x) = x2 - 3x + 2

Step-by-step explanation:

Answer:

f(x)=-3x+2

Step-by-step explanation:

The first one is a quadtratic function because it is in quadtratic form.

The second one is also not linear because it looks like a squiggly line. Sorry I forgot what they are called but I know it is not linear.

That leaves the last one is is linear and should be going down because there is a negative in front of the coefficient. It also has so exponent to prove why it is linear even further.

Hope this helps!

Answer:

6 mm and 9 mm are the dimensions of the piece of plastic.

Step-by-step explanation:

Keep in mind the formulas for the area and perimeter of a rectangle:

A = lw

P = 2 (l + w)

List the factors of 54:

1, 2, 3, 6, 9, 18, 27, 54

POSSIBLE DIMENSIONS of the piece of plastic:

1 mm and 54 mm:

Area - 54 mm^2

Perimeter - 110 mm

2 mm and 27 mm

Area - 54 mm^2

Perimeter - 58 mm

3 mm and 18 mm

Area - 54 mm^2

Perimeter - 42 mm

6 mm and 9 mm

Area - 54 mm^2

Perimeter - 30 mm

The rectangular piece of plastic with the dimensions 6mm and 9 mm corresponds with the area and perimeter of the piece of plastic mentioned. So these are the correct dimensions.

Hope this helps!

Answer: Circumference of circle = 27.004 inches

              Area of circle = 58.0586 inches²

Step-by-step explanation:

Diameter of circle = 8.6 inches

Pi ([tex]\pi[/tex]) = 3.14

Circumference of circle (With diameter) = [tex]\pi \\[/tex]d ([tex]\pi[/tex]×diameter)

                                                                = 3.14 × 8.6

                                                                = 27.004 inches

Area of circle (With diameter) = [tex]\pi[/tex][tex]d^{2}[/tex]/4

                                                 = 3.14 × 8.6 × 8.6 / 4

                                                 = 3.14 × 73.96 / 4

                                                 = 58.0586 inches²

Answer:

3b (3a - 4b)

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

9ab - 12b² ← factor out 3b from each term

= 3b(3a - 4b) → C

Answer:

B

Step-by-step explanation:

half × base × height

height × length

Answer: B

Step-by-step explanation:

Triangle)

25 - 7 = 18

[tex]A=\frac{1}{2}(b)(h)\\A=\frac{1}{2}(18)(17)\\A=153cm^2[/tex]

Rectangle)

[tex]A=b(h)\\A=7(17) = 119cm^2[/tex]

Total)

[tex]153+119=272 cm^2[/tex]

Step-by-step explanation:

-6>t-(-13)

= -6>t+13

= -6-13>t

= -19>t

= t<-19

Answer:

t < - 19

Step-by-step explanation:

Given

- 6 > t - (- 13) , that is

- 6 > t + 13 ( subtract 13 from both sides )

- 19 > t , then

t < - 19

Answer:

hes going 10 miles an hour,

Step-by-step explanation:

if it took you 3.5 hrs and you went 35 miles, you can do 35/3.5=10, which is 10 miles an hour

Answer:

10 miles per hour

Step-by-step explanation:

We know that distance = rate * time

35 miles = rate * 3.5 hours

Divide each side by 3.5 hours

35 miles / 3.5 hours = rate

10 miles per hour = rate

Answer:

The angles that are congruent to 4 are: 3, 8, and 7.

3 and 4 are vertical angles, 8 and 3 are opposite interior angles, 8 and 7 are vertical angles.

Hope this helps!

Answer:

your slope would be 4.5.... so go up 4 and to the right 5. the y-intercept is 650 so that is where your line would start instead of at 0... hope this helped :)

Step-by-step explanation:

The exponential function gotten from the table is given by y = 650(1.045)ˣ

An exponential function is in the form:

y = abˣ

where y, x are variables, a is the initial value of y and b is the multipliers.

Let y represent the bacteria population after x hours.

The class started out with 650 bacteria cells.

Growth rate = 4.5%

The exponential function gotten from the table is given by y = 650(1.045)ˣ

After 30 hours:

Find out more on exponential function at: https://brainly.com/question/12940982

Answer:

[tex]x = 34^\circ[/tex]

Step-by-step explanation:

Note that ∠TSU and ∠PSR are vertical angles. Hence:

[tex]m\angle TSU = m\angle PSR[/tex]

∠PSR is the sum of ∠PSQ and ∠QSR. Hence:

[tex]\displaystyle m\angle TSU = m\angle PSQ + m\angle QSR[/tex]

We know that ∠TSU measures 4x and ∠QSR measures 3x. Thus:

[tex](4x) = m\angle PSQ + (3x)[/tex]

Solve for ∠PSQ:

[tex]m\angle PSQ = x[/tex]

Next, ∠PQS and ∠RQS form a linear pair. Thus:

[tex]m\angle PQS + m\angle RQS = 180^\circ[/tex]

∠RQS measures 68°. Thus:

[tex]m\angle PQS +(68^\circ) = 180^\circ[/tex]

Solve for ∠PQS:

[tex]m\angle PQS = 112^\circ[/tex]

The interior angles of a triangle must total 180°. So, for ΔPQS:

[tex]\displaystyle m\angle SPQ + m\angle PQS + m\angle PSQ = 180^\circ[/tex]

Substitute in the known values:

[tex](x) + (112^\circ) + (x) = 180^\circ[/tex]

Simplify:

[tex]2x = 68^\circ[/tex]

And divide. Hence:

[tex]x = 34^\circ[/tex]

Answer:

y = 3x+6

Step-by-step explanation:

refer to the picture

Answer:

y = 3x + 6

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x + 2 ← is in slope- intercept form

with slope m = 3

Parallel lines have equal slopes, so slope of parallel line is 3

Expressing the equation in point- slope form with m = 3 , (x₁, y₁ ) = (1, 9)

y - 9 = 3(x - 1)

y - 9 = 3x - 3 ( add 9 to both sides )

y = 3x + 6 ← in slope- intercept form

Answer:

(3.5, - 3.5)

Step-by-step explanation:

Using the Midpoint theorem, we have

x=(9-2)/2=7/2=3.5

y=(-8+1)/2=-7/2=-3.5

Answer:

3−42+7+16

Step-by-step explanation:

if its simplify

Answer:

Step-by-step explanation:

f(x) = 2x - 4

g(x) = 1/2x - 4

6)

f(4) means that wherever you see an x on the right, you put a 4.

f(4) = 2x - 4

f(4) = 2*4 - 4

f(4) = 8  - 4

f(4) = 4

7)

g(x) = 1/2x - 4

g(2) = 1/2(2) - 4

g(2) = 1 - 4

g(2) = - 3

8)

f(-5) = 2*-5  - 4

f(-5) = -10 - 4

f(-5) = -14

9)

g(-6) = 1/2 ( - 6) - 4

g(-6) = -3 - 4

g(-6) = - 7

Answer:

1 [tex]\frac{1}{6}[/tex] pounds of candy

Step-by-step explanation:

Add together the fractions by creating a common denominator of 6:

[tex]\frac{5}{6} + \frac{1}{3}[/tex]

[tex]\frac{5}{6} + \frac{2}{6}[/tex]

= [tex]\frac{7}{6}[/tex]

Simplify into a mixed fraction:

= 1 [tex]\frac{1}{6}[/tex]

So, the girls had 1 [tex]\frac{1}{6}[/tex] pounds of candy

Answer:

The answer is X=28.

Answer:

40 coats don't have hoods

Answer:

Hello,

answer 22

Step-by-step explanation:

[tex]\dfrac{1}{j} +\dfrac{1}{k} =\dfrac{1}{3} \\\\\dfrac{k+j}{j*k} =\dfrac{1}{3} \\\\\\3k+3j=j*k\\\\k(3-j)=-3j\\\\k=\dfrac{3j}{j-3} \\\\k=\dfrac{3j-9+9}{j-3} \\\\k=3+\dfrac{9}{j-3} \\\\\\j-3\ must\ be \ a divisor\ of\ 9 ==> 1,3,9\\\\j-3=1 ==> j=4 , k=3+\dfrac{9}{1} =12\\\\j-3=3 ==> j=6 , k=3+\dfrac{9}{3} =6\\\\j-3=9 ==> j=12 , k=3+\dfrac{9}{9} =4\\\\\sum\ k=12+6+4=22\\[/tex]

The sum of all possible values for k is 22.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

1/j + 1/k= 1/3

Simplifying the fraction

(k+ j)/ kj= 1/3

3k + 3j = kj

k(3- j) = -3j

k = -3j/ (3- j)

k= 3j/ (j-3)

k = 3j + 9 - 9 / (j-3)

k = 3 + 9/ (j-3)

Since (j-3) must be divisor of 9.

j- 3 = 1---> j=4, k= 3 +9 = 12

j- 3 = 3---> j=6, k= 3 +9/3 = 6

j- 3 = 9---> j=12, k= 3 +9/9 = 4

So, The sum is = 12+ 6 + 4 = 22

Learn more about Fraction here:

https://brainly.com/question/10354322

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Step-by-step explanation:

From both the cases we can say that √n is either a natural number or an irrational number. Hence the correct option is (d)Either a natural number or an irrational number. Note: Before solving this type of question we should have proper knowledge of natural numbers, rational numbers and irrational numbers.

Answer:

A. (2,5), (3,6), (6,9)

Step-by-step explanation:

In order to be a function, all inputs (x values) must go to only one output (y value). List A is the only list that obeys this rule. Therefore, List A is a function.

Answer:

if Im correct it should be $8.40

Step-by-step explanation:

why well if you think of breaking down by say 1/4 of 168 all you do is divide 4 which is the whole amount by 0.2 which is the amount the father gave her so 4/0.2= 20 the you take your whole 168 and divide by 20 which the whole number for 0.2 the your answer should be this 168/20= 8.4 which then i assumed it was $8.40 hopefully that is correct hehe

Answer:

F.  m/10.

Step-by-step explanation:

10 miles = 1 inch

1 mile = 1/10 of an inch so

m miles = m/10 inches.

Answer:

Option C,

y² = 18x, since the graph opens right

Answered by GAUTHMATH

Answer:

55 Gallons

Step-by-step explanation:

143 - (8)(11)

143 - 88

143 -  88

55 gallons

Answer:

Step-by-step explanation:

If you drew out the bell curve and put the values where they go, this would be a no-brainer that doesn't even need math to solve. However, we will use the formula and then the table for z-scores to find this answer.

We are looking for the probability that the number of calls falls between 19 and 67. The standard deviation is 8 and the mean is 43. The probability we are looking for is P(19 < x < 67), therefore we look for the probability first that number of calls is greater than 19:

[tex]z=\frac{19-43}{8}=-3[/tex] and from the table and to the right of the z-score, the probability that the number of calls is greater than 19 is .99865 (or 99.8%). Likewise,

[tex]z=\frac{67-43}{8}=3[/tex] and from the table and to the right of the z-score, the probability that the number of calls is greater than 67 is .00315.

Take the difference of these to get the probability that the number of calls falls between these 2:

.99865 - .00135 = .9973 or 99.7%

Replace x with -11 and solve:

Y = (-11)^2 + 11

(-11)^2 = 121

Y = 121 + 11

Y = 132

Answer: 132

Answer:

132

Step-by-step explanation:

y = x^2 +11

Let x = -11

y = (-11)^2 +11

  = 121+11

  = 132