If AB is the midsegment, find the value of x. Show your work.

Isolating a variable involves changing the subject of the equation.

The result of isolating y^2 is: [tex]\mathbf{y^2 = \frac{42 - 9x^2}7}[/tex]

The equation is given as:

[tex]\mathbf{9x^2 + 7y^2 = 42}[/tex]

Subtract 9x^2 from both sides

[tex]\mathbf{7y^2 = 42 - 9x^2}[/tex]

Divide through by 7

[tex]\mathbf{y^2 = \frac{42 - 9x^2}7}[/tex]

Hence, the result of isolating y^2 is: [tex]\mathbf{y^2 = \frac{42 - 9x^2}7}[/tex]

Read more about subject of formulas at:

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6 numbers per cube

3 numbers are less than 4 ( 1, 2 & 3)

so you have a 3/6, reduce to 1/2 probability of rolling a number less than 4 on each cube

2 cubes

 so 1/2 * 1/2 = 1/4 probability

We know that when we are given a inverse function as: [tex]f^{-1}(x)[/tex]

Then we find the function by the method:

Put [tex]f^{-1}(x)=y[/tex]

Then we switch the places of x and y and solve for y.

1)

[tex]f^{-1}(x)=\dfrac{2x-3}{5}[/tex]

Hence, we find the function as follows:

[tex]\dfrac{2x-3}{5}=y[/tex]

Then we switch for x and y

[tex]\dfrac{2y-3}{5}=x\\\\\\i.e.\\\\2y-3=5x\\\\\\i.e.\\\\\\2y=5x+3\\\\\\i.e.\\\\\\y=\dfrac{5x+3}{2}[/tex]

Hence, inverse function is:

  [tex]f(x)=\dfrac{5x+3}{2}[/tex]

2)

[tex]f^{-1}(x)=\dfrac{x+8}{2}[/tex]

Hence, we find the function as follows:

[tex]\dfrac{x+8}{2}=y[/tex]

Then we switch for x and y

[tex]\dfrac{y+8}{2}=x[/tex]

[tex]y=2x-8[/tex]

Hence, inverse function is:

           [tex]f(x)=2x-8[/tex]

3)

[tex]f^{-1}(x)=\dfrac{x+2}{7}[/tex]

Hence, we find the function as follows:

[tex]\dfrac{x+2}{7}=y[/tex]

Then we switch for x and y

[tex]\dfrac{y+2}{7}=x[/tex]

[tex]y=7x-2[/tex]

Hence, inverse function is:

           [tex]f(x)=7x-2[/tex]

4)

[tex]f^{-1}(x)=\dfrac{1-2x}{x}[/tex]

Hence, we find the function as follows:

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

Then we switch for x and y

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

i.e.

[tex]1-2y=xy\\\\xy+2y=1\\\\i.e.\\\\y(x+2)=1\\\\y=\dfrac{1}{x+2}[/tex]

Hence, inverse function is:

  [tex]f(x)=\dfrac{1}{x+2}[/tex]

Answer: H(x)=4(x-9)^2-17

Step-by-step explanation:

Answer: The correct answer is C

Step-by-step explanation: APPEX learning quiz

Answer-

[tex]\boxed{\boxed{a_{12}=354294}}[/tex]

Solution-

If there are 2 terms of a Geometric Sequence [tex]a_n[/tex] and [tex]a_k[/tex] where (n > k), then

[tex]a_n=a_k\cdot r^{n-k}[/tex]

where, r = common ration of the G.P.

Here,

[tex]a_4 = 54\\\\a_7=1458[/tex]

Putting in the equation,

[tex]\Rightarrow a_7=a_4\cdot r^{7-3}[/tex]

[tex]\Rightarrow a_7=a_4\cdot r^3[/tex]

[tex]\Rightarrow 1458=54\cdot r^3[/tex]

[tex]\Rightarrow r^3=\dfrac{1458}{54}[/tex]

[tex]\Rightarrow r^3=27[/tex]

[tex]\Rightarrow r=3[/tex]

Again putting the values in the equation,

[tex]\Rightarrow a_{12}=a_7\cdot r^{12-7}[/tex]

[tex]\Rightarrow a_{12}=a_7\cdot r^5[/tex]

[tex]\Rightarrow a_{12}=1458\cdot 3^5[/tex]

[tex]\Rightarrow a_{12}=354294[/tex]

The 12th term of the geometric sequence is 354,294

The nth term of a geometric progression is given by the formula:

[tex]a_n = ar^{n-1}[/tex]

For n = 4

[tex]a_4=ar^{4-1}\\\\a_4=ar^3\\\\ar^3=54..................(1)[/tex]

For n = 7

[tex]a_7=ar^{7-1}\\\\a_7=ar^6\\\\ar^6=1458................(2)[/tex]

Divide equation (2) by equation (1)

[tex]\frac{ar^6}{ar^3} =\frac{1458}{54} \\\\r^3=27\\\\r^3=3^3\\\\r = 3[/tex]

Substitute r = 3 into equation (1)

[tex]a(3)^3=54\\\\27a=54\\\\a=\frac{54}{27}\\\\a=2[/tex]

The 12th term of the sequence is therefore calculated below

[tex]a_{12}=ar^{11}\\\\a_{12}=2(3^{11})\\\\a_{12}=354294[/tex]

The 12th term of the geometric sequence is 354,294

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Hey!

Hope this helps...

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First, you need to do 20 divided by 50 (or in your calculator 20/50)...
Second, you would do long division (or in the calculator, press 'enter')...

And boom-bada-boom, your answer is: 20 is 40% of 50

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For future reference, please try to avoid asking/posting questions that can be answered using the calculator...

Answer:

Sum of -8a³b+3a²b²-5,2+5a²b² and 3a³b+7-9a²b² is:

-5a³b-a²b²+4

Step-by-step explanation:

We have to find the sum of:

-8a³b+3a²b²-5,2+5a²b² and 3a³b+7-9a²b²

-8a³b+3a²b²-5+2+5a²b²+3a³b+7-9a²b²

= -5a³b-a²b²+4

Hence, sum of -8a³b+3a²b²-5,2+5a²b² and 3a³b+7-9a²b² is:

-5a³b-a²b²+4

Answer:

Step-by-step explanation:

_______

Good evening ,

_______________

f(1)=3 and f(3) = -1 so the average rate of change from x = 1 to x = 4 is 1.

Look at the photo below for more details,

________________________________

:)

Answer:

Replace critical words with variables, numbers, and operations. More than is addition, the product is multiplication and decreased by is subtraction. The constants are 1, 7, and 5. The expression is 1 + 7n – 5. To evaluate the expression, substitute 6 for the variable and then simplify the order of operations. The value when n = 6 is 38.Step-by-step explanation:

Answer:

8ft

Step-by-step explanation:

For this case, the first thing we must do is calculate the total profit.

We have then:

[tex] P = 850 - 500 [/tex]

[tex] P = 350 [/tex]

Then, we look for the number of coins.

For this, we need the total profit (which we already calculate) and the amount of profit per coin.

We have then:

[tex] N = \frac{350}{50} [/tex]

[tex] N = 7 [/tex]

Answer:

The amount of coins that was on the set is:

[tex] N = 7 [/tex]

Final answer:

The coin collector bought and sold a set of coins, making a total profit of $350. Dividing this profit by the $50 profit per coin reveals that there were 7 coins in the set.

Explanation:

The coin collector made a profit of $50 per coin by selling a set of coins. To find out how many coins were in the set, we need to calculate the total profit made from selling the coins and then divide that by the profit per coin.

The total profit is the selling price minus the buying price, so $850 - $500 = $350. If the collector made $50 profit per coin, then the number of coins in the set can be found by dividing the total profit by the profit per coin: $350 / $50 per coin = 7 coins.

Final answer:

The statement is true; a tangent line meets a circle at the point of tangency, which is the unique point where the tangent touches the circle without intersecting it.

Explanation:

True, the point at which a tangent line meets a circle is indeed called the point of tangency. This is a fundamental concept in geometry, where a tangent line is defined as a line that touches a curve at exactly one point, without crossing through it. This distinct point is known as the point of tangency.

For example, if we have a circle and a line that touches the circle at just one point and does not intersect it at that point, that line is a tangent to the circle, and the point of contact is the point of tangency. The tangent line is always perpendicular to the radius of the circle at the point of tangency, as can also be seen from the properties of the director circle, which is the locus of points of intersection of perpendicular tangents to the curves like ellipses and hyperbolas.

In the context of a director circle, perpendicular tangents to an ellipse would intersect on this special circle. Although for this particular question, we are focusing on the tangent line to a single circle and its point of tangency. It's interesting to note that according to the properties of circles, every point on a circle allows for exactly one tangent line. Whenever such a line is drawn, it illustrates the concept of tangency.

Well here are two equivalent different expressions of my making that you could use for this question.

f(x) = 2x - 7
g(x) = 3x - 28 / 2

When x = 7, these two different expressions will equate to the same value of 7. If you meant something else let me know, otherwise this is what you should put for your essay-question.

Answer:

  152 square feet

Step-by-step explanation:

The area of a rectangle is the product of its length and width. The total area of carpet required is the sum of the areas of the two rooms:

  carpet area = (12 ft)(6 ft) +(10 ft)(80 ft) = 72 ft^2 +80 ft^2

  carpet area = 152 ft^2

1 gallon = 128 ounces

 multiply 128 by 1.5 gallons:

1.5 x 128 = 192 ounces total

 divide total ounces by 8 to get number of glasses:

192/8 = 24

 you can pour 24 eight ounce glasses

Final answer:

Double vision can be caused by wearing glasses that are too strong, eye muscles being relaxed from fatigue, drugs, or alcohol, or by rapid eye blinking. Nearsightedness and farsightedness are common vision defects related to the eye's focusing ability but do not usually cause double vision, which can also be a result of misalignment.

Explanation:

Double vision can be the result of several factors including wearing glasses that are too strong, eye muscles relaxed from fatigue, drugs, or alcohol, or rapid eye blinking. It is not typically caused by looking directly into bright headlights or the action of passing other cars, which are more likely to cause temporary glare or flash blindness rather than persistent double vision.

Common vision defects such as nearsightedness (myopia) and farsightedness (hyperopia) are related to the focusing ability of the eyes. Myopia occurs when the eye over-converges the rays from a distant object in front of the retina, causing distant objects to appear blurry. Hyperopia, on the other hand, happens when the eye does not converge rays from a close object sufficiently, making close objects appear blurry. Misalignment can also cause double vision, and this can be due to a variety of factors including strabismus or nerve damage. Correction of vision defects often involves the use of glasses or contact lenses with the appropriate lens power or surgery for more severe cases.

Answer:

it is no solutions

Step-by-step explanation:

The car would use 20 litres to travel 250 km.

To determine the number of litres the car would use to travel 250 km, we can set up a proportion using the average fuel consumption rate of 8 litres per 100 km:

8 litres / 100 km = x litres / 250 km

To solve for x, we can cross-multiply and then divide:

x litres = (8 litres * 250 km) / 100 km

x litres = 20 litres

Therefore, the car would use 20 litres to travel 250 km.

Final answer:

The car would use 20 liters of fuel to travel 250 km.

Explanation:

To determine how many liters of fuel the car would use to travel 250 km, we can set up a proportion using the given information:

8 liters  ÷ 100 km = x liters  ÷ 250 km

Cross multiplying, we get:

x = (8 liters × 250 km) ÷ 100 km

x = 2000 liters ÷ 100 km

x = 20 liters

Therefore, the car would use 20 liters of fuel to travel 250 km.