Prove that: [tex](a+b)^{-1} . (a^{-1} + b^{-1} ) = (ab)^{-1}[/tex]

f(x) is maximum at x=3 and the maximum value of f(x) = 5.

The highest and smallest values of a function, respectively, can either be found inside a specific range or across the entire domain. They are sometimes referred to collectively as the function's extrema. The plural forms of the maximum and minimum functions are maxima and minima, respectively.

The given quadratic function is [tex]f(x) = -2 (x-3)^{2} +5[/tex]

Comparing it with [tex]f(x) = a (x-h)^{2} +k[/tex]

Here, a= -2, h =3 and k = 5.

Since a is negative, so parabola is open downward.

Therefore, the quadratic function has a maximum value.

Here, the vertex is (h,k) =(3,5)

Therefore, f(x) is maximum at x=3 and the maximum value of f(x) = 5.

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The painting is a square, which means all its sides are equal.

If x is the length of one side, then, all the remaining 3 sides also have the same length: x.

The area of a square is the square if its side, then, for a square with sides x:

We know that the area of the painting will be 400 square inches, then:

a. The equation that can be set up to find the length of a side is:

b. We can solve the equation by finding a number that multiplied by itself gives 400. For this case, we have two solutions. 20 and -20, since:

And:

-20 is also a solution because as a negative number, when multiplied by itself, gives a positive one. (A product between negative numbers gives always a positive number).

c. We have two solutions, however, only one of them makes sense: the 20. A negative length makes no sense, so we can discard the second solution (-20).

d. The length of the wood trim needed to go around the painting is then 20 inches. (we should not forget the units.)

Answer:

Step-by-step explanation:

The given inequality can be written as 2m - 5/4 ≤ -7/8.

An inequality -7/8 is at most the difference of twice a number m and 5/4 which is 2m - 5/4 ≤ -7/8.

Difference of twice a number 'm' and 5/4 is 2m - 5/4 and this is at most -7/8 means less than or equal to.

∴ The given statement can be written as 2m - 5/4 ≤ -7/8

Answer:

2m - 5/4 ≤ -7/8

Step-by-step explanation:

hope this helps

Given the word exprssion:

Seventy less than 9 times a number is 375

Where h represents the number.

We have:

Seventy less than 9 times a number: 9h - 70

Seventy less than 9 times a number is 375: 9h - 70 = 375

Therefore, the equation that is a correct translation of Seventy less than 9 times a number is 375 is: 9h - 70 = 375

ANSWER:

9h - 70 = 375

The number of quarters, Richard have is 3 out of 198 coins he have.

For the given question,

The total number of coins Richard have is 18.

The fraction of dimes is 1/3.

1/3 of 18 = (1/3)×18 = 6

The number of dimes is 6.

The fraction of nickles is 1/2.

1/2 of 18 = (1/2)×18 = 9

Let the number of quarters be 'x'.

Total coin = dimes + nickles + quarters.

18 = 6 + 9 + x

x = 18 - 15

x = 3

Thus, the number of quarters, Richard have is 3.

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The lengths of the axes in the elipse are given as follows:

The equation of an elipse of center (x*, y*) is given according to the following rule:

(x - x*)²/a² + (y - y*)²/b² = 1.

The lengths of the axes are given as follows:

In this problem, the equation of the elipse is given as follows:

(x - 3)²/212 + (y + 4)²/224 = 1.

Hence the measures of a and b are calculated as follows:

Hence the lengths of the axes have numeric values given by:

The difference in the measures is because I suppose there was a typo in the equation of the ellipse, but the procedure is as presented in this problem.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: 8i[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: 2 {x}^{2} = - 128[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: {x}^{2} = - \frac{ 128}{2} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: {x}^{2} = - 64[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: x = \sqrt{ - 64} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: x = \sqrt{( - 1) \sdot(64)} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: x = \sqrt{ 64} \sdot \sqrt{ - 1} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: x = 8 \sdot i[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: x = 8i[/tex]

[ i = iota, and i² = -1 ; (complex number) ]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

[tex]x=8i[/tex]

Step-by-step explanation:

Given equation:

[tex]2x^2=-128[/tex]

Divide both sides of the equation by 2:

[tex]\implies \dfrac{2x^2}{2}=\dfrac{-128}{2}[/tex]

[tex]\implies x^2=-64[/tex]

Square root both sides:

[tex]\implies \sqrt{x^2}=\sqrt{-64}[/tex]

[tex]\implies x^2=\sqrt{-64}[/tex]

Rewrite -64 as 8² · -1:

[tex]\implies x=\sqrt{8^2 \cdot-1}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies x=\sqrt{8^2}\sqrt{-1}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:[/tex]

[tex]\implies x=8\sqrt{-1}[/tex]

[tex]\textsf{Since $\sqrt{-1}=i$}[/tex]

[tex]\implies x=8i[/tex]

Imaginary numbers

Since there is no real number that squares to produce -1, the number [tex]\sqrt{-1}[/tex] is called an imaginary number, and is represented using the letter i.

An imaginary number is written in the form [tex]bi[/tex], where [tex]b \in \mathbb{R}[/tex].

Answer:

y<4

Steps:

18 + 6y < 42

6y < 42 - 18

y < 24/6

y < 4

Answer:

y<4

Step-by-step explanation:

18+6y<42

Subtract 18 from both sides.

6y<42−18

Subtract 18 from 42 to get 24.

6y<24

Divide both sides by 6. Since 6 is positive, the inequality direction remains the same.

[tex]y < \frac{24}{6} [/tex]

Divide 24 by 6 to get 4.

y<4

According to the given problem,

(i) It is given that,

The cost price of 1000 packets of peanuts = Rs. 50

We need to find the cost price of 1 packet of peanut = [tex]\frac{50}{1000}[/tex] = Rs. 0.05

(ii) Selling price at which Sipho continues to sell 1 packet = Rs. 1

Then Selling price of 1000 packets = 1000 x 1 = Rs. 1000

Then Profit made by sipho = Selling Price - Cost Price

= 1000 - 50

= Rs.950

Profit percentage gained by Sipho = [tex]\frac{Profit}{Cost Price}[/tex] x 1000

= [tex]\frac{950}{50}[/tex] x 1000

= 1900 %

(iii) The profit earned by sipho remains same, we nee to find the cost price at which Sipho should sell 100gm of her peanuts is Rs. 1

(iv) I would advice Sipho to sell peanuts at a selling price more than the cost price in order to gain profit

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If Amy, Ravi, and Bob have a total of $127 in their wallets. Bob has 4 times what Ravi has. Ravi has $7 less than Amy. The amount they have  have in their wallets is : Army has $22.33, Ravi $89.33, Henry $15.33.

Let Army represent x dollars

Let Ravi represent   4x

Let Bob represent  x - 7

Hence,

x + x - 7 + 4x = 127

Simplify by combining like terms

6x - 7 = 127

Add 7 to both sides of the equation leaving 6x

6x = 127+7

6x = 134

x =134/6

x = 22.33

x = Army has $22.33

Ravi

4x  where x = 22.33

4(22.33) = 89.33

Bob

x - 7 where x = 22.33

22.33 -7 = 15.33

Prove :

Ravi + Bob + Henry = 127

= 22.33 +89.33 + 15.33 = 126.99 ≅127 (Approximately)

Therefore the have $22.23, $89.33 and 15.33 respectively.

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The value of x is 4

The value of m ∠VUR = 126°

From the image shown, we have that;

Note that all the sides of a equilateral triangle are equal.

Then, we have;

Now, equate the side lengths of the inscribed triangle, we have;

3x + 8 = 6x - 4

collect like terms

3x - 6x = -4 - 8

subtract the like terms

-3x = -12

Make 'x' the subject of formula

x = -12/-3

Find the quotient

x = 4

Note that m ∠VRS and m ∠VUR are on a straight line, we have;

m ∠VRS +  m ∠VUR = 180

substitute the values

54° +  m ∠VUR = 180

m ∠VUR = 180 - 54

m ∠VUR = 126°

Hence, the values are 4 and 126°

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Step 1. The expression we have for the graph is:

To find the inequality that represents the graph, we need to solve for y first.

Step 2. Solve for y in the equation:

We can also represent this as follows:

Move 5x to the right side as a -5x:

Move the two that is multiplying on the left side, to divide on the right side:

Simplify:

This is the equation of the line.

Step 3. Find the inequality.

Since the shaded part is below the line, and it has a dotted line, the inequality that represents this is:

Which are the values below the dotted line.

Answer:

Answer:

y=-1/3x+5

Step-by-step explanation:

Use rise/run

Answer:

use a calculator or try math app

// ignore, made mistake//

Answer:

(4.7) and (5.-7)

Step-by-step explanation:

find the gradient using the formula:

y2-y1 (divide this by the bottom)

x2-x1

-7-7

5-4

=-14/1

-14 is the answer

then you will say y-y1= m(x-x1)

you can choose to sub any point

I will use (4;7)

therefore...

y-7=-14(x-4)

y= -14x+56+7

y= -14x+63

7.031 is greater than 7.03.

The given value is having a 2-digit decimal place.

The options which are provided are:

1)7.031

2)7.030

3)7.003

4)7.0

Comparing the first decimal placeholder of each option with the question, all options have the same digit which is zero.

Comparing the second decimal placeholder of each option with the question, only option 1)7.031 and option 2)7.030 is having .03 the rest of the options, option 3)7.0003 and 4)7.0 have .00 has their second digit hence both option 7.0003 and 7.0 are smaller than 7.03.

Out of the remaining options, when options 1)7.03 and 2)7.031 are compared it can be seen that 7.031 is greater because the third decimal placeholder of 7.031 is 1 and 7.03 is 0 hence 7.031 is greater than 7.03.

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Answer:

23

Step-by-step explanation:

3-(-20)

Answer:

i cant really see the words

Step-by-step explanation:

Answer:

m∠QPT = 32°

Step-by-step explanation:

∠QPT and ∠SPR are vertical angles, meaning that the measure of their angles are congruent (the same).

Vertical angles are formed when two lines intersect, creating opposite angles. Those opposites are congruent (equal).

Step 1: Set the measure of the angles to equal each other.

[tex]\implies m \angle QPT = m \angle SPR[/tex]

[tex]\implies (2x+12) = (4x - 8)[/tex]

Step 2: Subtract 4x from both sides.

[tex]\implies 2x-4x+12 = 4x - 4x - 8[/tex]

[tex]\implies -2x+12 = - 8[/tex]

Step 3: Subtract 12 from both sides.

[tex]\implies -2x+12-12 = - 8-12[/tex]

[tex]\implies -2x = -20[/tex]

Step 4: Divide both sides by -2.

[tex]\implies \dfrac{-2x}{-2} = \dfrac{-20}{-2}[/tex]

[tex]\implies x = 10[/tex]

Step 5: Find the measure of ∠QPT by substituting 10 for x.

[tex]\implies [2(10)+12]^{\circ}[/tex]

[tex]\implies 32^{\circ}[/tex]

Therefore, the measure of ∠QPT is 32°.

⇒To get the difference we subtract.

[tex]2.5-7.5=-5\\[/tex]

⇒To get the sum we add.

[tex]2.75+9.55=12.3[/tex]

Goodluck!!

Answer:

m<2=m<5=50

m<4=85

m<6=45

Step-by-step explanation:

Answer:

1:85 2:50 3:45 4:85 5:50 6:45

Step-by-step explanation:

pls give brainliest

1 should be like 4 and 3 should be like 6.

Like 6+1 is 130 so 2 is 50

The missing lengths of the sides of the congruent triangles described are:

AC = 25 units.

PQ = 3 units.

The corresponding side lengths of any two or more triangles that are congruent to each other are always equal in measure. That is, the three sides of one triangle have lengths that are equal to the corresponding three sides of the other triangle, if both triangles are congruent triangles.

We are told that triangles ABC and LMN are congruent to each other, therefore:

AB = LM = 41 units [corresponding sides]

AC = LN = 25 units [corresponding sides]

BC = MN = 38 units [corresponding sides].

Therefore, the length of AC is 25 units.

Also, it is assumed that triangles FGH and PQR are congruent triangles, therefore:

FG = PQ = 3 units [corresponding sides]

GH = QR = 4.5 units [corresponding sides]

Therefore, the length of PQ is 3 units.

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The constant of proportionality (K ) we will write

Perimeter = 3 ( side)  where K = 3

Perimeter of any polygon is defined as the sum of all sides of  polygon.

Given polygon is a triangle. A triangle is any polygon which has three sides.

And as the sides of a polygon increases the perimeter also increases.

One can say that perimeter and side of a polygon has a direct relationship.

That is when we write it mathematically we write it like:

Perimeter ( P ) ∝ Sides of polygon

However given is an equilateral triangle

this means that all sides of the triangle are equal

so let us consider the side of the triangle as "s"

Thus we get that perimeter will be 3 times s

which when mathematically written will be:

Perimeter ∝ ( side)

to remove the constant of proportionality (K ) we will write

Perimeter = 3 ( side)  where K = 3

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As shown in the reference graph attached hereby with the question statement, if the linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time "x" measured in seconds, then,

(A) During (2 ≤ x ≤ 5) seconds in the time domain, the water balloon's height remains the same.

(B) During (0 ≤ x ≤ 2) seconds, the height of the water balloon is increasing.

(C) During (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.

(D) From Part (C), it can be justified that 5 ≤ x ≤ 9.5 is the interval where the balloon's height is decreasing, and, (5 ≤ x ≤ 6) is the interval where the slope is the steepest.

As per the question statement and the reference graph attached alongside, the linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time "x" measured in seconds.

We  are required to determine the correct time domains for four different situations, by observing the plotted graph.

Part (A) is to determine the correct time domain where the water balloon's height remains the same.

From the graph, it is clear that, the height remains constant at (y = 70), parallel to the x-axis from the 2nd second to the 5th second. Hence, During (2 ≤ x ≤ 5) seconds in the time domain, the water balloon's height remains the same.

Part (B) is to determine the correct time domain where the height of the water balloon is increasing.

From the graph, it is clear that, the slope of the concerned graph rises only from [(y = 40) to (y = 70)], starring from the 0th second until the 2nd second. Hence, During (0 ≤ x ≤ 2) seconds in the time domain, , the height of the water balloon is increasing.

Part (C) is to determine the correct time domain where the height of the water balloon decreases the fastest.

From the graph, it is clear that, the graph decreases thrice, first from [(y = 70) to (y = 40)], starting at the 5th second uptil the 6th second, then from [(y = 40) to (y = 10)], starting at the 6th second uptil the 9th second and lastly, from [(y = 10) to (y = 0)], starting at the 9th second till the 9.5th second. Here, we can easily calculate that, the balloon dropped 30ft in 1 sec at the first instance, 30ft in 3 seconds at the second instance and, 10ft in 0.5 seconds.

Since, [(30/1) > (10/0.5) > (30/3)],

Or, [30 > 20 > 10],

Thus, During (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.

Part (D) is to determine the correct statement mentioned under it's options, with judgement based on Part (C).

Option (i) states that [(5 ≤ x ≤ 9.5) is the interval where the balloon's height is decreasing] which is true, as we can observe from the graph that the slope is decreasing during the time interval of 5 to 9.5th seconds, although at different rates at different intervals.

Option (ii) states that [(8 ≤ x ≤ 9.5) is the interval where the slope is the steepest] which means that, during this above said interval, the height of the balloon drops the fastest which is false, as we have already proved in part (C) that during (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.

Option (iii) states that, [(6 ≤ x ≤ 8) is the interval where the balloon's height decreases the most] which is false, as balloons height falls the farthest by 30fts in two separate intervals, between (5 ≤ x ≤ 6) seconds and (6 ≤ x ≤ 9) seconds.

Finally, Option (iv) states that [(5 ≤ x ≤ 6) is the interval where the slope is the steepest] which means that, during this above said interval, the height of the balloon drops the fastest which is true, as we have already proved in part (C) that during (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the maximum in the shortest time period.

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Answer:

The average cost for a gallon of gasoline in 2006 was $2.45. In 2007, the average cost of a gallon of gasoline was $3.29.