Let f(x) = x^2-6 and g(x) =10x . Find (g ° f)(x)

Answer:

D

Step-by-step explanation:

Given the 2 equations

2x + 3y = 11 → I(1)

y = x - 3 → (2)

Substitute y = x - 3 into (1)

2x + 3(x - 3) = 11 ← distribute parenthesis and simplify left side

2x + 3x - 9 = 11

5x - 9 = 11 ( add 9 to both sides )

5x = 20 ( divide both sides by 5 )

x = 4

Substitute x = 4 into (2) for corresponding value of y

y = 4 - 3 = 1

Solution is (4, 1 ) → D

The correct ordered pairs for the equations 2x+3y=11, y=x-3 is (4,1)

In the substitution method we have to calculate the value of one variable by  putting the value of another variable in terms of first variable.

We are having two equations

2x+3y=11.......1

y=x-3........2

Put the value of y from2 in 1

2x+3(x-3)=11

2x+3x-9=11

5x=20

x=4

put the value of x=4 in 2

y=4-3

y=1

Hence the ordered pairs becomes (4,1)

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Answer:

8.55 inches

Step-by-step explanation:

We can use the slope intercept form to write this equation

y = mx+b where m is the lope and b is the y intercept

The y intercept, b, is how tall the candle is when we start, 12 inches

The slope is the rate at which it is burning or -.75  (the negative is because it is burning or getting smaller)

y = -.75x+12

or rewriting

t = 12-.75h  where h is the hours and t is how tall

We are burning for 4.6 hours

t = 12-.75(4.6)

t = 12 -3.45

t= 8.55

Answer:

B+

Step-by-step explanation:

Grades earned in five subjects are;

A,C+,A-,B- and B+

Remaining subject is biology

Total number of subjects will be=6

3.2 gpa as a percentile =86

For her to maintain 3.2 gpa total sum of percentile in the 6 subjects should be at least

6×86=516

Emily total sum of subjects in percentile is 93+77+90+80+87=427

Find the difference , 516-427=89

89 is grade B+

Emily should earn a grade of B+ to keep her 3.2 gpa

Answer:

45ml of pure water to obtain 135ml of the desired 30% solution

Step-by-step explanation:

45% of 90 = 40.5

So, 40.5ml of alcohol in 90ml

We want 30% and therefore need a ratio of 3:7

40.5÷3=13.5

so one part of our ratio is 13.5

we then times this by 7

13.5 x 7 = 94.5

so, 94.5ml of water

to work out how much we already have, we should do 90ml- 40.5ml = 49.5ml

and then 94.5- 49.5 = 45ml

We need 45ml of water and the total mo of the desired solution will be 90+45=135ml

To dilute a 45% alcohol solution to a 30% alcohol solution by adding pure water, you will need to add 45 mL of pure water to the initial 90 mL to achieve a total volume of 135 mL with the desired 30% alcohol concentration.

To dilute a 45% alcohol solution to a 30% alcohol solution using pure water, we can use the concept of concentration dilution in chemistry. This involves calculating the amount of diluent (in this case, water) to add to an existing solution to achieve a desired concentration.

Let's denote the amount of pure water to add as x mL. The initial volume of the alcohol solution is 90 mL with a 45% concentration, meaning it contains 40.5 mL of pure alcohol. Since adding water doesn't change the amount of alcohol, the final mixture's alcohol volume remains at 40.5 mL.

To find the final volume of the solution and the amount of water needed, we use the formula for the final concentration: Final Concentration = (Volume of Solute) / (Final Volume of Solution). Substituting the given and desired values gives us 30% = 40.5 mL / (90 mL + x).

Rearranging and solving for x gives: x = (40.5 / 0.3) - 90 = 135 - 90 = 45 mL. Therefore, 45 mL of pure water must be added to the original solution to get a 30% alcohol solution.

In conclusion, adding 45 mL of pure water to the 90 mL of 45% alcohol mixture yields a total volume of 135 mL of the desired 30% solution.

Answer:

25,5 miles

Step-by-step explanation:

4.25 inch on map

4.25/0.5 = 8,5

8,5 * 3 = 25,5 miles

Final answer:

To find the actual distance between two towns on a map, set up a proportion using the given scale. By solving the proportion, you can determine the real distance between the towns.

Explanation:

To find the actual distance between the two towns, we can set up a proportion using the given scale:

if EF ≅ WV and JK is intersecting both at a right-angle, the distances OK = JP and likewise PG = GO, namely

[tex]\bf 2(4x-3)-8=4+2x\implies 8x-6-8=4+2x\implies 8x-14=4+2x \\\\\\ 6x-14=4\implies 6x=18\implies x=\cfrac{18}{6}\implies x=3[/tex]

Step-by-step explanation:

Let the number be x

ATQ,

-200+x =45

x=45+200

x=245

The other integer is equal to 245.

We know that [tex]x+y=45[/tex].  We also know that [tex]x=-200[/tex].

Substitute the value into the equation.  [tex]-200+y=45[/tex]

Add 200 to both sides of the equation.  [tex]y=45+200=245[/tex]

Now, you have the answer.  [tex]y=245[/tex]

Answer:

[tex]\sqrt[5]{13^3} = 13^{\frac{3}{5}}[/tex]

Step-by-step explanation:

Answer:

D on EDGE

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

54=2x3x3x3

12=2x2x3

common factors are 2 and 3 so 2x3=6

The formula for the volume of a pyramid, V = 1/3 BH, can be rearranged to solve for the height, 'H', by multiplying both sides of the equation by 3 and then dividing by 'B'. This gives the formula H = 3V/B.

The formula for the volume of a pyramid can be rearranged to solve for the height, 'H' as follows:

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Answer:

the answer is A

Step-by-step explanation:

always multiply by the 1.8% (or .018) and then add it to the number you multiplied the .018 to

start with the 950 * .018 = 171.00

950 + 171.00 = 1121.00

then you follow this process

1121.00 * .018 = 201.78

1121.00 + 201.78 = 1322.78

The answer is A

Always multiply by the 1.8% (or .018) and then add it to the number you multiplied the .018 to

Start with the 950 *.018 = 171.00

950 + 171.00 = 1121.00

Then you follow this process

1121.00 * .018 = 201.78

1121.00 + 201.78 = 1322.78

Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.

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Answer:

4 ropes.

Step-by-step explanation:

There are 100 cms in a meter.

So 10 meters = 10* 100

= 1000 cms.

1000 / 210 = 4  ropes with  160 cms remaining.

Answer:

John F. Kennedy

The feline expanded in weight compared with the canine's underlying weight which is steady with the data given.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Let c be the feline's unique weight. Let c* be the feline's new weight.

Let d be the canine's unique weight. The d* be the canine's new weight.

The equation is given as,

c = 1.2 c

d = .9 d

c = d

The other equation is given as,

p = (d - c)/d = 1 - c/d

We know that the given condition,

c = d = 0.9 d

Then the equation is written as,

p = 1 - 0.9d/d

p = 1 - 0.9

p = 0.1 or 10%.

Hence, toward the beginning, the rate contrast compared with the canine was,

q = (d - c)/d = 1 - 0.75 = 0.25 or 25%.

That is, the feline weighed not exactly like the canine toward the beginning. Since p < q, the feline expanded in weight compared with the canine's underlying weight — which is steady with the data given.

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Answer:

One side is 10

Step-by-step explanation:

10*10 is equal to 100

Answer:

[tex]y+1=\dfrac{1}{3}(x+2)[/tex] - point-slope form

[tex]f(x)=\dfrac{1}{3}x-\dfrac{1}{3}[/tex] - function notation

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

From the graph we have the points (-2, -1) and (1, 0).

Substitute:

[tex]m=\dfrac{0-(-1)}{1-(-2)}=\dfrac{1}{3}[/tex]

[tex]y-(-1)=\dfrac{1}{3}(x-(-2))[/tex]

[tex]y+1=\dfrac{1}{3}(x+2)[/tex] - point-slope form

[tex]y+1=\dfrac{1}{3}(x+2)[/tex]          use the distributive property

[tex]y+1=\dfrac{1}{3}x+\dfrac{2}{3}[/tex]           subtract 1 = 3/3 from both sides

[tex]y=\dfrac{1}{3}x-\dfrac{1}{3}[/tex]

Answer:

1. 3rd option

2. 2nd option

Step-by-step explanation:

Answer:

  AC = 26

Step-by-step explanation:

AD = DC . . . . . .these segments are marked congruent

8x-1 = 6x+9 . . . substitute the given expressions

2x = 10 . . . . . add 1-6x

x = 5

__

AC = 2·AB = 2(3x-2) = 2(3·5-2) . . . . substitute into expression for AB

AC = 26

Answer:

75 yd^2.

Step-by-step explanation:

If the width = x yards, the length will be 3x yards.

The perimeter = 2 * length + 2 * width

= 2* 3x + 2*x = 40

6x + 2x = 40

8x = 40

x = 5

So the width is 5 and the length is 15 yards.

The area = 5 * 15 = 75 yd^2.

Answer:

75

Step-by-step explanation:

x=breadth

3x=length

perimeter=2(x+3x)=8x

40=8x

x=5

length=15

breadth=5

area=15*5=75

Answer:

I think that the answer is A.

Answer:

No options is correct.    

Step-by-step explanation:

Given : The product of -4 and 3.

To find : Which expression could be used to determine the product ?

Solution :

The product of -4 and 3 is [tex]-4\times 3=-12[/tex]

To know which expression we solve each options and get whose result is same as ours,

A) [tex](-4)(3)\times (-4)(\frac{1}{4})[/tex]

Solve,

[tex](-4)(3)\times (-4)(\frac{1}{4})= -12\times -1=12[/tex]

B) [tex](-4)(3)+(-4)(\frac{1}{4})[/tex]

Solve,

[tex](-4)(3)+(-4)(\frac{1}{4})= -12+(-1)=-13[/tex]

C) [tex](3)(-4)\times (3)(\frac{1}{4})[/tex]

Solve,

[tex](3)(-4)\times (3)(\frac{1}{4})=-12\times\frac{3}{4}=-9[/tex]

D) [tex](3)(-4)+(3)(\frac{1}{4})[/tex]

Solve,

[tex](3)(-4)+(3)(\frac{1}{4})=-12+\frac{3}{4}=-11.25[/tex]

From the given options, No options will get the product.

Answer:

Step-by-step explanation:

distribute the first part of each term

(21/5x+12)+(-3+5/2x)

combine the xs and the numbers

9+6.7x

For this case we must simplify the following expression:

[tex]3(\frac{7}{5}x+4)-2(\frac{3}{2}-\frac{5}{4}x)=\\\frac{3*7}{5}x+ 3*4-\frac{2*3}{2} +\frac{2*5}{4}x=\\\frac{21}{5}x +12-\frac{6}{2} +\frac{10}{4}x=\\\frac{21}{5}x +12-3+ \frac{10}{4}x=[/tex]

We add similar terms:

[tex]\frac{21}{5}x+ \frac{10}{4}x+ 9=\\(\frac{21}{5} +\frac{10}{4})x +9=\\\frac{67}{10}x +9[/tex]

ANswer:

[tex]\frac{67}{10}x+9[/tex]

Answer:

(9,7)

Step-by-step explanation:

The goal is to write in standard form for a circle.

That is write in this form: [tex](x-h)^2+(y-k)^2=r^2[/tex] where [tex](h,k)[/tex] is the center and [tex]r[/tex] is the radius.

So you have

[tex]x^2+y^2-18x-14y+124=0[/tex]

Reorder so you have your x's together, your y's together, and the constant on the other side:

[tex]x^2-18x+y^2-14y=-124[/tex]

Now we are going to complete the square using

[tex]x^2+bx+(\frac{b}{2})^2=(x+\frac{b}{2})^2[/tex].

This means we are going to add something in next to the x's and something in next to y's.  Keep in mind whatever you add on one side you must add to the other.

[tex]x^2-18x+(\frac{-18}{2})^2+y^2-14y+(\frac{-14}{2})^2=-124+(\frac{-18}{2})^2+(\frac{-14}{2})^2[/tex]

The whole reason we did is so we can write x^2-18x+(-9)^2 as (x-9)^2 and y^2-14y+(-7)^2 as (y-7)^2.  We are just using this lovely thing I have I already mentioned: [tex]x^2+bx+(\frac{b}{2})^2=(x+\frac{b}{2})^2[/tex].

[tex](x-9)^2+(y-7)^2=-124+81+49[/tex]

[tex](x-9)^2+(y-7)^2=6[/tex]

Comparing this to [tex](x-h)^2+(y-k)^2=r^2[/tex] tells us

[tex]h=9,k=7,r^2=6[/tex]

So the center is (9,7) while the radius is [tex]\sqrt{6}[/tex].

Answer: (9,7)

Step-by-step explanation:

The equation of the circle in Center-radius form is:

 [tex](x - h)^2 + (y - k)^2 = r^2[/tex]

Where the center is at the point (h, k) and the radius is "r".

To rewrite the given equation in Center-radius form, we need to complete the square:

1. Move 124 to the other side of the equation:

[tex]x^2+y^2-18x-14y+124=0\\\\x^2+y^2-18x-14y=-124[/tex]

2. Group terms:

[tex](x^2-18x)+(y^2-14y)=-124[/tex]

3. Add [tex](\frac{-18}{2})^2=81[/tex] to the group of the variable "x" and to the right side of the equation.

4. Add [tex](\frac{-14}{2})^2=49[/tex] to  the group of the variable "y" and to the right side of the equation.

Then:

[tex](x^2-18x+81)+(y^2-14y+49)=-124+81+49[/tex]

5. Finally,  simplify and convert the left side to squared form:

[tex](x-9)^2+(y-7)^2=6[/tex]

You can identify that the center of the circle is at:

[tex](h,k)=(9,7)[/tex]

Answer: Choice C

x represents time and x is positive; y value is 45 times more than the x value

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

Explanation:

The inequality y > 45x is the same as y > 45*x

We have y greater than 45*x meaning that y is 45 times more than the x value.

As an example, if x = 2, then 45*x = 45*2 = 90 meaning that y must be larger than 90 if you picked x = 2. In this scenario, x = 2 means that if you traveled for 2 hours then you must have gone more than 90 miles in total distance.

Answer:

Leg side along the wall = x ft = 8 ft

The other leg side = 7+x ft = 7+8=15 ft

The Hypotenuse =9+x ft = 9+8 = 17 ft

Step-by-step explanation:

In the question, the shape of the pool is right triangle.

Let the leg side along the wall to be the x ft

Let the other leg side  to be 7+x ft

Let the longest side/hypotenuse to be x+9 ft

Apply the Pythagorean relationship where the sum of squares of the legs equals the square of the hypotenuse

This means;

[tex]x^2 +(x+7)^2=(x+9)^2\\\\[/tex]

Expand the terms in brackets

[tex]x^2+(x+7)^2=(x+9)^2\\\\\\x^2+x^2+14x+49=x^2+18x+81[/tex]

collect like terms

[tex]x^2+x^2-x^2=18x-14x+81-49\\\\\\x^2=4x+32\\\\\\x^2-4x-32=0[/tex]

solve for x in the quadratic equation by factorization

[tex]x^2-4x-32=0\\\\\\x^2-8x+4x-32=0\\\\\\x(x-8)+4(x-8)=0\\\\\\(x+4)(x-8)=0\\\\\\x+4=0,x=-4\\\\x-8=0,x=8[/tex]

Taking the positive value of x;

x=8ft

Finding the lengths

Leg side along the wall = x ft = 8 ft

The other leg side = 7+x ft = 7+8=15 ft

The Hypotenuse =9+x ft = 9+8 = 17 ft

Answer:

1) The profit of the company dropped by -15% compared to last year.

2) The temperature of Alaska was -5 degrees yesterday.

3) John had 1,000$ dollars deposited in the bank, and then made a poor investment, causing him to owe the bank 5,000$, making his account -4,000$

Step-by-step explanation:

With each scenario you have to try to find a new way to express a negative number which is primarily through loss. In which ways can you unique express loss of a value below zero in real world is the question, and you can do so with examples like money and temperature.

Answer:

the cost of rib eye steak dinner = $22.47

the cost of grilled salmon dinners= $10.57 .....

Step-by-step explanation:

Let x be the rib eye steak dinner.

Let y be the grilled salmon dinner.

According to the first given statement:

12x+27y= $554.98    (equation 1)

According to the second statement:

26x+9y=$584.36      ( equation 2)

Lets take a look at the 1st equation:

12x+27y= $554.98

12x=$554.98- 27y

x=$554.98- 27y/12

Now substitute the value of x in 2nd equation:

26x+9y=$584.36

26($554.98- 27y/12)+9y=$584.36

26(554.98- 27y)+9y=584.36*12

14429.48-702y=7012.32

-702y=7012.32-14429.48

-702y= -7417.16

y= 7417.16/702

y=$10.57

Now substitute the value of y in equation 1:

12x+27y= $554.98

12x+27(10.57)=554.98

12x+285.39 = 554.98

Move the constant to the R.H.S

12x=554.98-285.39

12x=269.59

Divide both the terms by 12

12x/12=269.59/12

x=$22.47

Thus the cost of rib eye steak dinner = $22.47

the cost of grilled salmon dinners= $10.57 .....

Answer:

see explanation

Step-by-step explanation:

Using the exact values of the trigonometric ratios

sin60° = [tex]\frac{\sqrt{3} }{2}[/tex], cos60° = [tex]\frac{1}{2}[/tex]

sin45° = cos45° = [tex]\frac{1}{\sqrt{2} }[/tex]

Using the sine ratio on the right triangle on the left

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{a}{4\sqrt{3} }[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex]

Cross- multiply

2a = 4[tex]\sqrt{3}[/tex] × [tex]\sqrt{3}[/tex] = 12 ( divide both sides by 2 )

a = 6

Using the cosine ratio on the same right triangle

cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{c}{4\sqrt{3} }[/tex] = [tex]\frac{1}{2}[/tex]

Cross- multiply

2c = 4[tex]\sqrt{3}[/tex] ( divide both sides by 2 )

c = 2[tex]\sqrt{3}[/tex]

------------------------------------------------------------------------------------------

Using the sine/cosine ratios on the right triangle on the right

sin45° = [tex]\frac{a}{b}[/tex] = [tex]\frac{6}{b}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex]

Cross- multiply

b = 6[tex]\sqrt{2}[/tex]

cos45° = [tex]\frac{d}{b}[/tex] = [tex]\frac{d}{6\sqrt{2} }[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex]

Cross- multiply

[tex]\sqrt{2}[/tex] d = 6[tex]\sqrt{2}[/tex] ( divide both sides by [tex]\sqrt{2}[/tex] )

d = 6

------------------------------------------------------------------------------------------------

a = 6, b = 6[tex]\sqrt{2}[/tex], c = 2[tex]\sqrt{3}[/tex], d = 6

Answer:

This is an obtuse, isosceles triangle.

Step-by-step explanation:

The largest angle is greater than 90 degrees (obtuse), and two sides are equal as you can tell by two equal angles (isosceles).

The given triangle can be classified as isosceles and acute triangle.

A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.

Sum of the interior angles of a triangle is 180 degrees.

Given is a triangle.

The three angles of the triangle are 41°, 41° and 98°.

That is, two angles of the triangle are equal. So the sides opposite these two angles are also equal.

So this is an isosceles triangle.

Obtuse triangle has one of the angles greater than 90°.

Acute triangle has all the angles less than 90°.

Here all the angles are less than 90°.

So it is acute.

Hence the given triangle is acute and isosceles triangle.

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Answer: 3

Step-by-step explanation: I jus got it right on a pex

Answer:

Option 1

Step-by-step explanation:

Tri means 3. An expression which has 3 terms and the terms are separated by plus or minus:

c^2+c+6

Thus option 1 is correct....

For this case we have that by definition, a trinomial is an algebraic expression formed by the sum or difference of three terms or monomials.

Example:

[tex]ax ^ 2y + cx + dy[/tex]

Thus, the correct option is option 1.

[tex]c ^ 2 + c + 6[/tex]

Three terms are observed.

Answer:

Option 1

Answer:

Step-by-step explanation:

She has 1 in 11 chances of getting the purple one

One of her choices is gone after she takes out the purple one. She has a 1 in 10 chance of taking out the gray one.

1/11 * 1/10 = 1/110

The probability that Gloria will draw the purple marker first and then the gray marker from her backpack on consecutive tries without replacement is 1/110.

The question asks to find the probability that Gloria will pull the purple marker and then the gray marker out of the backpack on consecutive tries without replacement. To calculate the combined probability of two independent events happening in succession, you multiply the probability of each event occurring separately.

On the first draw, the probability of selecting the purple marker is 1 out of 11 markers, or 1/11. After drawing the purple marker, it is not replaced, so there are now only 10 markers left, one of which is gray. The probability of drawing the gray marker on the second draw is then 1 out of the remaining 10 markers, or 1/10.

To find the overall probability of both events happening, multiply the two probabilities: (1/11) x (1/10) = 1/110.

The probability that Gloria will draw the purple marker first and then the gray marker is 1/110.