If f(x) = -2x + 7 and g(x) = x2 – 2, then f(g(3)) is
equal to

Answer:

32

Step-by-step explanation:

The base angles of the triangle are the same since the sides are the same

<C = 74

A+B+C = 180 since the sum of the angles of a triangle = 180

74+B+74=180

Combine like terms

148+B =180

B = 180-148

B = 32

Answer:

[tex]\text{A. }32^{\circ}[/tex]

Step-by-step explanation:

From the Isosceles Base Theorem, the two base angles of a isosceles triangle are equal. Therefore, [tex]\angle A=\angle C=74^{\circ}[/tex].

Since the sum of the interior angles of a triangle is always equal to 180 degrees, we can write the following equation:

[tex]\angle A+\angle B+\angle C=180[/tex]

Substitute [tex]\angle A=\angle C=74^{\circ}[/tex] into this equation to solve for [tex]\angle B[/tex]:

[tex]74+\angle B+74=180,\\\angle B=180-74-74=\boxed{32^{\circ}}[/tex]

Answer:

60.2 grams

Step-by-step explanation:

a = 510(1 - .263)⁷

a = 60.2341229517

rounded

a = 60.2 grams

Answer:

P = 0, -5

Step-by-step explanation:

Answer:

p = 0

p = - 5

Step-by-step explanation:

3p(p + 4) = p(p + 2)​

3p² + 12p - (p² + 2p) = 0

3p² + 12p - p² - 2p = 0

3p² + 10p - p² = 0

2p² + 10p = 0

2p(p + 5) = 0

p = 0

p + 5 = 0

p + 5 - 5 = 0 - 5

p = - 5

For initial 100 milligrams of a radioactive substance was if decreased by 2% in 8 hours, then half-life of the radioactive substance is 108.3 hours.

Rate of change is the change in one variable due to change in other.

Given the following:

Amount of a radioactive substance initially present=100mg

After 8 hours, mass decreased by 2%

Mass after 8 hours= 100-(2% of 100)

=100-(2*100/100)

=100-2

=98

The rate of decay is proportional to the amount of the substance present at time t.

Mathematically,

Let the amount of radioactive substance is A and at time t,

[tex]\dfrac d{dt}A\ \alpha\ A\\\\[/tex]

[tex]\dfrac d{dt}A= kA\\\\\\dA=kAdt[/tex]

On integrating both sides,

[tex]\int \frac {1}{kA}dA=\int dt\\\\[/tex]

[tex]\dfrac {ln A}{k}=t +ln \ c_1\\ln A =kt+k\ ln \ c_1\\[/tex]

On taking antilogarithm both sides,

[tex]e^{ln A} =e^{kt+k\ ln \ c_1\\A=e^{kt}e^{k\ ln \ c_1}\\A=e^{kt}e^{\ ln \ c_1^k}\\A=e^{kt}c_1^k \\[/tex]

Let, [tex]c_1^k=c[/tex]

[tex]A =e^{kt}c[/tex].................................1

At t=0, A=100

Substituting values in 1

[tex]100= e^0c\\c=100[/tex]

At t= 8, A=98

[tex]98=e^{k8}100\\0.98=e^{8k}\\8k=ln0.98[/tex]

k=-0.0064.

To determine the half time of the decay.

At half time A became A/2=50 mg

Substituting in 1.

[tex]50=e^{-0.0064t}100\\ln 0.5=-0.0064t\\t=\frac{ln 0.5}{-0.0064}\\t=108.3042\\t=108.3[/tex]....................................rounded to one decimal place.

Thus, The half-life of the radioactive substance is 108.3 hr.

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Answer:

(k+11)/2

Step-by-step explanation:

2x-11=k

2x=k+11

x=(k+11)/2

Answer:

6

Step-by-step explanation:

Answer:

[tex]10\\[/tex]

Step-by-step explanation:

[tex]7\frac{1}{2} =\frac{15}{2}[/tex]

[tex]\frac{15}{2}[/tex] ÷ [tex]\frac{3}{4}=[/tex]

[tex]\frac{15}{2} *\frac{4}{3}=[/tex]

you don't have to, but cross simplifying is better to do right now so that the answer you get will be simplified.

[tex]\frac{5}{1} *\frac{2}{1}=[/tex]

[tex]=\frac{10}{1}[/tex]

[tex]=10[/tex]

Hope this helps

Answer:

50%

Step-by-step explanation:

There are 12 months in a year.In the problem there are six months the number of cars his team sells more than 40%.=6/12x100%=0.5x100%=50%.Therefore his team sold 50%.

Hope this helped!

First let's understand the discriminant. Discriminant is an equation of D = b²-4ac. Discriminant is to find how many solutions do the equation have. In case for Quadratic Equation, there are 3 types of solutions which are:

To find discriminant graphically, we need to know that the x-axis plane represents the solutions to the equations. All equations can be drawn as a graph. Some graphs do not intersect x-axis while some graph do.

You may also notice that some graphs intersect x-axis more than one point. Like I said that the x-axis represents the roots or the solutions. Intersecting x-axis "n" times means that the equation has "n" roots.

For example, if a graph intersects x-axis 8 points - the equation has 8 roots or solutions.

From the graph, the parabola intersects on x-axis just only one point. That means there is only one solution. The question asks to find the discriminant of the function. Recall that if D = 0, there's only one real root. Therefore the discriminant for the function is zero.

Answer

Let me know if you have any doubts!

Answer:

28.26

Step-by-step explanation:

The formula for calculating diameter is πd (pi times the diameter), so 3.14 times 9 is 28.26.

Answer:

x = 20

Step-by-step explanation:

For the lines to be parallel, the angles have to be equal

2x+15 = 55

Subtract 15 from each side

2x+15-15 = 55-15

2x = 40

2x/2 = 40/2

x = 20

Answer:

14+28

Step-by-step explanation:

Answer:

6x^{2}-54x=0

6x2−54x=0

Step-by-step explanation:

Answer:

fraction- 1/2

decimal- .5

percent 50%

Step-by-step explanation:

Answer:

-x+y+6z=? You did not spcify so I just made it 0

x = -22/5, y = -4/5, z = -3/5

Step-by-step explanation:

Solve the following system:

{-x - 3 y - 2 z = 8 | (equation 1)

-x + y + 6 z = 0 | (equation 2)

x - 9 y - 2 z = 4 | (equation 3)

Subtract equation 1 from equation 2:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x+4 y + 8 z = -8 | (equation 2)

x - 9 y - 2 z = 4 | (equation 3)

Divide equation 2 by 4:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x+y + 2 z = -2 | (equation 2)

x - 9 y - 2 z = 4 | (equation 3)

Add equation 1 to equation 3:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x+y + 2 z = -2 | (equation 2)

0 x - 12 y - 4 z = 12 | (equation 3)

Divide equation 3 by 4:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x+y + 2 z = -2 | (equation 2)

0 x - 3 y - z = 3 | (equation 3)

Swap equation 2 with equation 3:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x - 3 y - z = 3 | (equation 2)

0 x+y + 2 z = -2 | (equation 3)

Add 1/3 × (equation 2) to equation 3:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x - 3 y - z = 3 | (equation 2)

0 x+0 y+(5 z)/3 = -1 | (equation 3)

Multiply equation 3 by 3:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x - 3 y - z = 3 | (equation 2)

0 x+0 y+5 z = -3 | (equation 3)

Divide equation 3 by 5:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x - 3 y - z = 3 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Add equation 3 to equation 2:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x - 3 y+0 z = 12/5 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Divide equation 2 by -3:

{-x - 3 y - 2 z = 8 | (equation 1)

0 x+y+0 z = -4/5 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Add 3 × (equation 2) to equation 1:

{-x + 0 y - 2 z = 28/5 | (equation 1)

0 x+y+0 z = -4/5 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Add 2 × (equation 3) to equation 1:

{-x+0 y+0 z = 22/5 | (equation 1)

0 x+y+0 z = -4/5 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Multiply equation 1 by -1:

{x+0 y+0 z = -22/5 | (equation 1)

0 x+y+0 z = -4/5 | (equation 2)

0 x+0 y+z = -3/5 | (equation 3)

Collect results:

Answer: {x = -22/5, y = -4/5, z = -3/5

Answer:

ans : it is order wise

a) 6/125 cm³

b) 8/125 cm³

c) 1/125 cm³

d) 36/125 cm³

Step-by-step explanation:

a)

for rectangular prism = length × width × height

= (1/5) × (2/5) × (3/5)

= 6/125 cm³

b)

for cube = length³

= (2/5)³

= 8/125 cm³

c)

for cube = (1/5)³

= 1/125 cm³

d)

for rectangular prism = (3/5) × (4/5) × (3/5)

= 36/125 cm³

Answer:

10x +30

Step-by-step explanation:

2(3 + 5x) + 24

Distribute

2*3 + 2*5x+24

6+10x+24

Combine like terms

10x +30

Answer:

the answer would be D i got a 100 on the quiz

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

No because the wrist circumference of 16 cm is paired with two heights.

Answer:

[tex] - \frac{9}{2} [/tex]

Step-by-step explanation:

Rate of change of y with respect to x

[tex] = \frac{60 - 96}{ - 12 - ( - 20)} \\ \\ = \frac{ - 36}{ - 12 + 20} \\ \\ = \frac{ - 36}{ 8} \\ \\ = - \frac{9}{2} [/tex]

Answer:

0

Step-by-step explanation:

when the term has a coefficient of, it does not have to be written.

x- X/1

The sum of two opposites equals o

So the solution would be o

Step-by-step explanation:

let n be the number of working hour

so total income is 24n + 6

now 1/6 of the income will be into saving

so the saving is (24n + 6) /6

The expression representing the amount that will go into his savings each week is $4h + $1.

An expression is combination of variables, numbers and operators.

Mike's weekly pay is given by:

Pay = (hourly rate) x (hours worked) + sales bonus

Pay = $24h + $6

To find one-sixth of his weekly pay, we can multiply his pay by 1/6:

Savings = (1/6) x Pay

Savings = (1/6) x ($24h + $6)

Savings = $4h + $1

Therefore, the simplified expression representing the amount that will go into his savings each week is $4h + $1.

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Answer:

Step-by-step explanation:

1)

Three-Fourth

2)

Twelve Million One Hundred Thirty One Thousand Two Hundred Sixty Seven and Twenty Five Hundredths

3)

Seventy Five Percentage

4)

One Thousand Two Hundred and Fifty Six

5)

Twelve is to Twenty Six

Rathan is correct- because every even number is a multiple of 2 and will therefore have 2 as a factor.

I hope this helps!

Answer:

Rathan is correct- because every even number is a multiple of 2 and will therefore have 2 as a factor

Step-by-step explanation:

just took this test and got 100

Answer:

An inscribed polygon might refer to any

polygon which is inscribed in a shape,

especially: A cyclic polygon, which is

inscribed in a circle

Answer:

A square

Step-by-step explanation:

Answer:

6ft

Step-by-step explanation:

javahvpaiudbajbd;kjbzcuvbjkabr;kabga

Answer:

2 2/3 ft

Step-by-step explanation:

w = A/l

plug in the values

w = 16/6

solve.

2.6... = 2 2/3

therefore the width of the rug is 2 2/3 ft

Answer:

A

Step-by-step explanation:

First you simplify both sides to get -2.4x+14.4 > 52.8

then you need to subtract the 14.4 from both sides giving -2.4x> 38.4

then divide both sides by -2.4 giving an answer of

x is less than or equal to -16 meaning you point to the left with a closed circle

Answer:

x=8

Step-by-step explanation:

the y-value in the first pair decreased by half, so the x-value must double due to inverse variation.