Which value is needed in the expression below to create a perfect square trinomial?

x2+8x+______

4
8
16
64

Answer:

Option B is correct.

Step-by-step explanation:

[tex]10^{(3/4)x}[/tex]

We need to write the above equation in square root form.

We know that 1/4 = [tex]\sqrt[4]{x}[/tex]

So, [tex]10^{(3/4)x}[/tex] can be written as:

[tex](\sqrt[4]{10})^{3x}[/tex]

Option B is correct.

For this case we have that by definition of properties of powers and roots it is fulfilled:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

Then, we have the following expression:

[tex](10) ^ {\frac{3} {4} x}[/tex]

So, in an equivalent way we have:

[tex](\sqrt [4] {10}) ^ {3x}[/tex]

Answer:

Option b

Answer:

Product B

Step-by-step explanation:

Divide the number of ounces i the bottle by the price of the bottle. Product A has a unit price of $0.17 and Product B has a unit price of $0.20. Therefore Product B has a lower unit price :))

Answer:

  22 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the necessary relationship. If the sledding slope is modeled as the hypotenuse of a right triangle with 25° as one of the acute angles, the side opposite the angle (the hill height) satisfies ...

  Sin = Opposite/Hypotenuse

  Opposite = Hypotenuse × Sin

  height = (52 ft)sin(25°) ≈ 22.0 ft

The height of the hill is about 22 feet.

The height of the hill can be calculated using the formula Height = sin (angle) x length of ride. By substituting the given values, it comes out to be approximately 22.05 ft.

In this question we are given an angle of elevation and the length of the ride. The problem is essentially about using trigonometry to estimate the height of the hill. The hill forms a right triangle, with the length of the ride as the hypotenuse and the height we want to find as the opposite side. In trigonometry, the sine of an angle is equal to the opposite side divided by the hypotenuse. So to find the height of the hill, we take the sin of the angle, multiplied by the length of the ride.

Therefore, Height = sin (angle) x Length of ride = sin (25°) x 52 ft = approximately 22.05 ft. The estimated height of the hill is around 22.05 ft.

https://brainly.com/question/31896723

#SPJ11

I will assume that you meant to type (g o f)(8).

First we find f(8).

f(8) = 8 - 1 or 7.

We now find g(f(8)), which means g(7).

g(7) = 7^3 or 343

Answer:

(g o f)(8) = 343

Answer:7^3

Step-by-step explanation:

f(8)=8-1=7

g(f(8))= 7^3

Answer:

  2/105

Step-by-step explanation:

"r" is the greatest common divisor (GCD) of the two fractions. It can be found using Euclid's algorithm in the usual way.

  (8/15) - (18/35) = 56/105 - 54/105 = 2/105 . . . . . this is (8/15) mod (18/35)

We can see that the next step, division of 54/105 by 2/105, will produce a remainder of 0, so the GCD is 2/105.

The greatest rational number r is 2/105.

_____

Check

The ratios are (8/15)/(2/105) = 28; (18/35)/(2/105) = 27. These whole numbers are relatively prime, so there is no larger r than the one we found.

Rational numbers are numbers that can be represented as a fraction of two integers. The greatest rational number (r) such that [tex]\frac 8{15} \div r : \frac {18}{35} \div r[/tex] is a whole number is [tex]\frac{2}{105}[/tex]

Let the numbers be represented as:

[tex]n_1 = \frac 8{15} \div r[/tex]

[tex]n_2 = \frac {18}{35} \div r[/tex]

To calculate the value of r such that [tex]n_1 : n_2[/tex] is a whole number, we make use of Euclid's algorithm.

Using Euclid's algorithm, the value of r is the common divisor between both fractions

[tex]r = n_1 - n_1[/tex]

[tex]r =\frac 8{15} \div r - \frac {18}{35} \div r[/tex]

Ignore the "r"

[tex]r =\frac 8{15} - \frac {18}{35}[/tex]

Take LCM

[tex]r=\frac {8 \times 7 - 18 \times 3}{105}[/tex]

[tex]r =\frac {2}{105}[/tex]

Hence, the greatest rational number is such that [tex]n_1 : n_2[/tex] is a whole number is [tex]\frac{2}{105}[/tex]

Read more about greatest rational numbers at:

https://brainly.com/question/24338971

Answer:

V = $3.50t + $90.5....

Step-by-step explanation:

V(t) is a function of t that expresses the value in year 2000+t.  

We know that the increase is $3.50 times t.

So,

V(t) = $3.50t + c  

where c is the constant.

V(15) =  $3.50 (15) + c = $143     [t=15 as mentioned in the question]

and therefore  

c = $143 - $3.50 (15)

c= $143 - $52.50

c= $90.5  

Now we got the value of c. We can write the equation as  

V = $3.50t + $90.5....

The subject of this question is linear equation. The dollar value of a product expected to change over several years can be calculated using the future value formula V = P(1 + r)^(t-15), where P is the present value, r is the rate of change per year, and t represents the year.

To develop a linear equation that represents the dollar value V of a product in a certain year t, you can use the formula for future value received years in the future: V = P(1 + r)^(t-15), where P is the present value in 2015, r is the rate of change per year, and t represents the year.

For example, if a firm's payment was $20 million in 2015 and was expected to increase by 10% per year, then the value in 2020 (t = 20) would be calculated as: V = $20 million * (1 + 0.10)^(20-15).

From this equation, you can predict the future value of the product in terms of the year and rate of inflation.

For more such questions on linear equation, click on:

https://brainly.com/question/32634451

#SPJ6

Answer:

25 years

Step-by-step explanation:

Solution:-

- Data for the average daily temperature on January 1 from 1900 to 1934 for city A.

- The distribution X has the following parameters:

                    Mean u = 24°C

                    standard deviation σ = 4°C

- We will first construct an interval about mean of 1 standard deviation as follows:

  Interval for 1 standard deviation ( σ ):                                    

                    [ u - σ , u + σ ]

                    [ 24 - 4 , 24 + 4 ]

                    [ 20 , 28 ] °C

- Now we will use the graph given to determine the number of years the temperature T lied in the above calculated range: [ 20 , 28 ].

           T1 = 20 , n1 = 2 years

           T2 = 21 , n2 = 3 years  

           T3 = 22 , n3 = 2 years

           T4 = 23 , n4 = 4 years  

           T5 = 24 , n5 = 3 years

           T6 = 25 , n6 = 3 years  

           T7 = 26 , n7 = 5 years

           T8 = 27 , n8 = 2 years

           T5 = 28 , n9 = 1 years

- The total number of years:

               ∑ni = n1 + n2 + n3 + n4 + n5 + n6 + n7 + n8 + n9

                     =  2 + 3 + 2 + 4 + 3 + 3 + 5 + 2 + 1

                     = 25 years          

Answer:

22,25,27 there are multiple questions that have the same question but different answers on Edge

Step-by-step explanation:

I hope this helped :)

Note that,

[tex]9x^2+24x+20=4\Longrightarrow9x^2+24x+16[/tex]

Which factors to,

[tex](3x+4)^2=0\Longrightarrow3x+4=0[/tex]

And simplifies to solution C,

[tex]\boxed{x=-\dfrac{4}{3}}[/tex]

Hope this helps.

Any additional questions please feel free to ask.

r3t40

Answer:

[tex]\large\boxed{C.\ x=-\dfrac{4}{3}}[/tex]

Step-by-step explanation:

[tex]9x^2+24x+20=4\qquad\text{subtract 4 from both sides}\\\\9x^2+12x+12x+16=0\\\\3x(3x+4)+4(3x+4)=0\\\\(3x+4)(3x+4)=0\\\\(3x+4)^2=0\iff3x+4=0\qquad\text{subtract 4 from both sides}\\\\3x=-4\qquad\text{divide both sides by 3}\\\\x=-\dfrac{4}{3}[/tex]

Answer:

3.13

Step-by-step explanation:

Given :

y = 2x + 4 -------- eq1

y = 2x - 3 -------- eq2

sanity check : both equations have same slope, so we can conclude that they are both parallel to one another.

Step 1: consider equation 1, pick any random x-value and find they corresponding y-value. we pick x = -2

This gives us y = 2(-2) + 4 = 0

Hence we get a point (x,y) = (-2,0)

Step 2: express equation 2 in general form (i.e Ax + By + C = 0)

y = 2x-3 -------rearrange---> 2x - y -3 = 0

Comparing with the general form, we get A = 2, B = -1, C = -3

Recall that the distance between 2 parallel lines is given by the attached formula (see attached picture).

substituting the values for A, B, C and (x, y) from the previous step:

d = | (2)(-2) + (-1)(0) + (-3) |  / √(2² + (-1)²)

d = | -4 + 0 - 3 |  / √(4 + 1)

d = | -7 |  / √5

d = 7  / √5

d = 3.13

The distance between the pair of given parallel lines is;

A: 3.13

We are given equation of the two lines as;

y = 2x + 4 - - - (eq 1)

y = 2x - 3 - - - (eq 2)

Let us put 1 for x in eq 1 to get;

y = 2(1) + 4

y = 6

Ax + By + C = 0

We have;

2x - y - 3 = 0

Thus;

A = 2

B = -1

C = -3

D = |Ax1 + By1 + c|/√(A² + B²)

Where;

x1 is the value of x imputed into the first equation

y1 is Tha value of y gotten from the input of x1

Thus;

D = |(2 × 1) + (-1 × 6) + (-3)|/(√(2² + (-1²))

D = |-7|/√5

We will take the absolute value of the numerator to get;

D = 7/√5

D = 3.13

Read more about distance between lines at;https://brainly.com/question/13344773

Using the law of sin.

Sin(angle) = Opposite leg / hypotenuse

Sin(33) = x / 23

Solve for x:

Multiply both sides by 23:

x = sin(33) * 23

x = 12.5267

Rounded to the nearest hundredth = 12.53 cm.

Check the picture below.

make sure your calculator is in Degree mode.

The sequence "emdangl" rearranges to "mangled" (an appropriately fitting word scramble solution).

There are 7 letters in the sequence "emdangl", so there are 7! = 7*6*5*4*3*2*1 = 5040 different permutations of the seven letters. The exclamation mark is shorthand to represent factorial notation. Factorials are the idea of multiplying from that integer counting down until you get to 1. The reason why this works is because we have 7 letters to pick from for the first slot, then 6 for the next, and so on until all seven slots are filled out.

Since there is one solution ("mangled") out of 5040 total permutations, this means the probability of getting the solution just by random chance/guessing is 1/5040

Use a calculator shows that 1/5040 = 0.0001984 approximately.

The word 'emdangl' can be arranged in 5040 ways. The probability of randomly selecting one arrangement is 1/5040.

The word 'emdangl' has 7 letters. To find the number of ways the letters can be arranged, we use the formula for permutations of distinct objects, which is n-factorial (n!). For this word, there are 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040 ways to arrange the letters.

Now, let's determine the probability of randomly selecting one arrangement of the given letters. Since there is only one correct unscrambling, the probability is 1 out of the total number of arrangements, which is 1/5040.

https://brainly.com/question/23283166

#SPJ2

Answer:

Step-by-step explanation:

1, 2. Central Angle, Interior Angle

See the 3rd attachment for the values. (Angles in degrees.)

The central angle is 360°/n, where n is the number of vertices. For example, the central angle in a pentagon is 360°/5 = 72°.

The interior angle is the supplement of the central angle. For a pentagon, that is 180° -72° = 108°.

These formulas were implemented in the spreadsheet shown in the third attachment.

3. Angles vs. Number of Sides

The size of the central angle is inversely proportional to the number of sides. In degrees, the constant of proportionality is 360°.

_____

Comment on the drawings

The drawings are made by a computer algebra program that is capable of computing the vertex locations around a unit circle based on the number of vertices. The only "work" required was to specify the number of vertices the polygon was to have. The rest was automatic.

The above calculations describe how the angles are computed. Converting those to Cartesian coordinates for the graphics plotter involves additional computation and trigonometry that are beyond the required scope of this answer.

These figures can be "constructed" using a compass and straightedge. No knowledge of angle measures is required for following the recipes to do that.

Answer:

The other guy is right but I wrote this

Step-by-step explanation:

Answer:

The height of the house is between 9 and 10 feet.

Step-by-step explanation:

The shaped formed with the ground, the ladder, and the house is a right triangle.

I'm going to apply Pythagorean Theorem here.

The length of the hypotenuse is given as 24 feet.

The length from the base of the ladder and the house is 22 feet.

So to find the height the ladder reaches on the house, we need to solve

[tex]a^2+22^2=24^2[/tex]

[tex]a^2+484=576[/tex]

Subtract 484 on both sides:

[tex]a^2=576-484[/tex]

Simplify:

[tex]a^2=92[/tex]

Square root both sides:

[tex]a=\sqrt{92}[/tex]

[tex]a \approx 9.59166[/tex] feet

Answer:

56 degrees

Step-by-step explanation:

So those angles are called alternate exterior angles because they happened at the difference intersections along the transversal on opposite sides of that transveral while on the outside of the lines that the transversal goes through.

If these lines that the transversal goes through are parallel then the alternating angles are congruent.

So they are because of the little >> things on those lines.

So x=56 degrees

Answer:

0.390 to the nearest thousandth or 39%.

Step-by-step explanation:

That would be 0.79^4

= 0.3895.

The probabilities are multiplied  because each selection is independent.

The probability that 4 adults randomly selected from a town with 79% health insurance coverage will all have health insurance is approximately 0.389.

The probability that 4 adults selected at random from a town where 79% of adults have health insurance, will all have health insurance. To solve this, we use the concept of independent events in probability. Since each selection is independent, and the probability that one adult has health insurance is 0.79, the probability that all four adults have health insurance is the product of their individual probabilities.

So the calculation would be:
0.79 times 0.79 times 0.79 times 0.79

This equals approximately 0.389 or rounded to the nearest thousandth, 0.389.

Answer:

The answer is  

√3/2

Step-by-step explanation:

The value of sin 30°=1/2.

The special right triangle is the triangle used to know the side ratio without using Pythagoras theorem every time.

There are some types of special right triangles present like 30-60-90 triangle, 45-45-90 triangles, and the Pythagorean triple triangles.

Here for deriving the value for sin 30°, we will use the 30-60-90 triangle.

The 30-60-90 triangle is given below.

the value sine is calculated by the ratio of the opposite side and the hypotenuse of the right-angled triangle.

In 30-60-90 triangle the side opposite to 30° angle is x and the hypotenuse is 2x then the side opposite to 60° angle is x√3.

In 30-60-90 triangle,

sin 30°=opposite side/hypotenus

= x/2x

⇒sin 30°=1/2

Therefore, the value of sin 30°=1/2.

Learn more about the special right triangle

here: https://brainly.com/question/14729820

#SPJ2

Step-by-step explanation:

10 is the value of A ......

Answer:

Value of A = 10

Step-by-step explanation:

Here Isoke is solving the quadratic equation by completing the square

        10x² + 40x – 13 = 0

         10x² + 40x – 13 + 13 = 0 + 13

         10x² + 40x + 0 = 13

         10x² + 40x = 13

          10 ( x² + 4x) = 13

   Here it is given as

           A(x² + 4x) = 13  

Comparing both

           We will get A = 10

Value of A = 10

Answer:

area of circle = 9/64 π square inches

Step-by-step explanation:

Points to remember

Area of circle = πr²

Where 'r' is the radius of circle

It is given that diameter of circle = (3/4) in

Therefore radius  r = diameter/2 = (3/4)/2 = 3/8 in

To find the area of circle

Area =  πr²

 =  π(3/8)²

 =  π * 9/64

 = 9/64 π square inches

The correct answer is 9/64 π square inches

Answer:

26/35

Step-by-step explanation:

If the events are mutually exclusive, all you have to do for P(S or T) is do P(S)+P(T).

So we are doing 1/7 + 0.6.

I prefer the answer as a fraction so I'm going to rewrite 0.6 as 6/10=3/5.

So we are going to add 1/7 and 3/5.

We need a common denominator which is 35.

Multiply first fraction by 5/5 and second fraction by 7/7.

We have 5/35+21/35.

This gives us 26/35.

Answer:

A. The CV is a relative measure of risk/return.

Step-by-step explanation:

The coefficient of variation of any investment, is used to measure and calculate the total risk of that investment with respect to its per unit expected return rate.

We can also define the coefficient of variation as a ratio of standard deviation to the expected value of an investment.

The answer is - A. The CV is a relative measure of risk/return.

The coefficient of variation (CV) is a relative measure of risk/return; thus, statement A is correct, and statement D is correct as it relates to the preferences of risk-averse investors. This measure is useful for assessing the consistency of investment returns, especially when comparing different investment options.

The coefficient of variation (CV) is a statistical measure that is used to assess the relative variability of data. It is calculated by dividing the standard deviation by the mean and multiplying by 100. This ratio provides a standardized measure of the dispersion of data points in a data set around the mean, which is particularly useful when comparing the variability between datasets with different units or scales.

Now let's examine the given statements:

A. The CV is a relative measure of risk/return.

B. The CV is an absolute measure of risk/return.

C. The higher the CV value the more acceptable the risk/return profile for a risk-averse investor.

D. The lower the CV value the more acceptable the risk/return profile for a risk-averse investor.

Statement A is correct: the CV is indeed a relative measure because it expresses the standard deviation as a percentage of the mean, making it unitless and thus comparable across different data sets and scales.

Statement D is also correct: a lower CV indicates that the returns are less volatile relative to the mean return, which is generally preferred by risk-averse investors. Risk-averse investors prefer investments with more predictable and stable returns, as such investments are associated with lower levels of relative risk.

Answer:

F and E

Step-by-step explanation:

[tex](3x+4)^2=14[/tex]

We could get rid of the square on the (3x+4) by square rooting both sides:

[tex]3x+4=\pm \sqrt{14}[/tex]

Now you are left with a linear equation to solve.

Subtract 4 on both sides:

[tex]3x=-4 \pm \sqrt{14}[/tex]

Divide both sides by 3:

[tex]x=\frac{-4 \pm \sqrt{14}}{3}[/tex]

You could rearrange the numerator using commutative property:

[tex]x=\frac{\pm \sqrt{14}-4}{3}[/tex]

If you wanted two write the two answers out, you would write:

[tex]x=\frac{\sqrt{14}-4}{3} \text{ or } \frac{-\sqrt{14}-4}{3}[/tex].

So I see this in F and E.

You could separate the fraction:

[tex]x=\frac{\sqrt{14}}{3}-\frac{4}{3} \text{ or } -\frac{\sqrt{14}}{3}-\frac{4}{3}[/tex].

The solutions to the given equation (3x + 4)^2 = 14 are x = (√14 - 4) / 3 and x = (-√14 - 4) / 3.

To find the solutions to the equation (3x + 4)2 = 14, first we need to take the square root of both sides of the equation to remove the square from (3x + 4):

√{(3x + 4)2} = √14, which simplifies to 3x + 4 =  √14 and 3x + 4 = -√14.

Then, we solve for x in each equation by subtracting 4 from both sides, which gives us 3x = √14 - 4 and 3x = -√14 - 4.

Lastly, we divide each side by 3 in both equations to isolate 'x', thus our solutions are: x = (√14 - 4) / 3 and x = (-√14 - 4) / 3.

https://brainly.com/question/29011747

#SPJ2

Check the picture below.

Answer:

2.

Step-by-step explanation:

(f o g)(x) =  2(√(x-5)) - 8

So (f o g)(30) = 2 √(30-5) - 8

= 2 * √25 - 8

=  2* 5 - 8

= 2.

To find (f ° g)(30) for the functions f(x) = 2x - 8 and g(x) = √x-5, you first calculate g(30), which is 5, and then apply f to this result to get f(5) = 2. Therefore, (f ° g)(30) equals 2.

If f(x) = 2x - 8 and g(x) = √x-5, we want to find (f ° g)(30). The notation (f ° g)(x) means we apply g(x) first and then apply f(x) to the result of g(x). Thus, we first find g(30).

Calculate g(30):
g(30) = √(30 - 5)g(30) = √25g(30) = 5

Now that we have g(30), we apply f to this value:
f(g(30)) = f(5)f(5) = 2(5) - 8f(5) = 10 - 8f(5) = 2

Therefore, (f ° g)(30) = 2.

Answer:

3192 persons! ✔️

Step-by-step explanation:

From the statement, we know that μ = 40 [minutes] and σ = 6 [minutes]

There are 3900 people. And we need to find how many of the lie within one standard deviation below the mean and two standard deviations above the mean.

We need to find the probability between: 34 minutes and 52 minutes. With the help of a calculator we get that the probability is: P(34<z<52) = 0.8186

Therefore, 0.8186×3900 = 3192 persons! ✔️

Answer:

1/2

Step-by-step explanation:

Given:

sinx=-1/2

cosy=√3/2

finding x

x=sin^-1(-1/2)

x=-π/6

x=-30°

finding y

cosy=√3/2

y=cos^-1(√3/2)

y=π/6

y=30°

Now finding cos(x-y)

cos(-π/6-π/6)

=cos(-π/3)

=1/2!

Answer:

1.5 feet

Step-by-step explanation:

Bob wants to plant a 7 foot by 10 foot garden.

Area = [tex]7\times10=70[/tex] square feet

He wants to make a uniform border of petunias around the outside and still have 28 square feet to plant tomatoes and roses in the middle.

Means we have to factor 28 in a way that the length and width is less than 10 and 7.

28 = 2 x 2 x 7

Means 4 feet can be width and 7 feet the length of the area where tomatoes need to be planted.

So, we have [tex]10-7=3[/tex] feet less than outer garden means at each side [tex]3/2=1.5[/tex] feet decreases.

Similarly, we have [tex]7-4=3[/tex] feet less width and at each side it is 1.5 feet.

Therefore, the border of petunias will be 1.5 feet wide on all sides.

Answer:

Width of the border is 1.5 feet.

Step-by-step explanation:

Let x be the width ( in feet ) of the border,

Given,

The dimension of the garden =  7 foot by 10 foot,

So, the dimension of the middle ( garden area excluded border )= (7 - 2x) foot by (10 - 2x) foot

Hence, the area of the middle = (7 - 2x)(10 - 2x)

According to the question,

[tex](7 - 2x)(10 - 2x)=28[/tex]

[tex]70 -14x-20x + 4x^2=28[/tex]  

[tex]4x^2 -34x+70-28=0[/tex]

[tex]4x^2 -34x+42=0[/tex]        ( Combine like terms )

[tex]4x^2-(28+6)x+42=0[/tex]  ( Middle term splitting )

[tex]4x^2-28x-6x+42=0[/tex]

[tex]4x(x-7)-6(x-7)=0[/tex]

[tex](4x-6)(x-7)=0[/tex]

By zero product property,

4x - 6 or x - 7 = 0

⇒ x = 1.5 or x = 7

Since, width of the border can not be equal to the dimension of the garden,

Therefore, the width would be 1.5 foot.

Answer:4

Step-by-step explanation:16/4 = 4

if 75% of equipment is iron then do the math

So it would be 4(2) + 4 = 75% of 16
So if 75% of 16 is 12 you need that extra 4 to get you to 16

The number of woods in the golf club is equal [tex]4[/tex].

" Number is defined as the count of any given quantity."

According to the question,

[tex]'x'[/tex] represents the number of irons

[tex]'y'[/tex] represents the number of woods

As per given condition we have,

[tex]x= 2y +4[/tex]                                  [tex](1)[/tex]

[tex]x = 75\%(x+ y)\\\\\implies x = \frac{75}{100}(x + y)\\ \\\implies x = \frac{3}{4} (x+y)\\\\\implies 4x= 3x + 3y\\\\\implies x = 3y \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2)[/tex]

Substitute the value of [tex](2)[/tex] in [tex](1)[/tex] to get the number of woods,

[tex]3y = 2y +4\\\\\implies y =4[/tex]

Therefore,

[tex]x= 3\times 4\\\\\implies x=12[/tex]

Hence, the  number of woods in the golf club is equal [tex]4[/tex].

Learn more about number here

brainly.com/question/3589540

#SPJ2

Answer:

73920

Step-by-step explanation:

Number of ways to choose 9 appetizers from 12: ₁₂C₉

Number of ways to choose 3 main courses from 8: ₈C₃

Number of ways to choose 2 desserts from 4: ₄C₂

The total number of ways is:

₁₂C₉ × ₈C₃ × ₄C₂

= 220 × 56 × 6

= 73920

Answer:

  30

Step-by-step explanation:

You can try the answer choices to see what works.

  15·10 ≠ 750

  25·20 ≠ 750

  30·25 = 750 . . . . the larger number is 30

  50·45 ≠ 750

Answer:

The value of the greater number is 30.

Step-by-step explanation:

We need to find the values of x that satisfy the equation :

[tex]x(x-5)=750[/tex]

Working with the equation ⇒

[tex]x(x-5)=750[/tex]

[tex]x^{2}-5x=750[/tex]

[tex]x^{2}-5x-750=0[/tex]

Given an equation with the form

[tex]ax^{2}+bx+c=0[/tex]

We can use the quadratic equation to find the values of x

[tex]x1=\frac{-b+\sqrt{b^{2}-4ac}}{2a}[/tex] and

[tex]x2=\frac{-b-\sqrt{b^{2}-4ac}}{2a}[/tex]

With [tex]a=1\\b=-5\\c=-750[/tex] we replace in the equations of x1 and x2 ⇒

[tex]x1=\frac{-(-5)+\sqrt{(-5)^{2}-4.(1).(-750)}}{2.(1)}=30[/tex]

[tex]x1=30[/tex] is a solution of the equation [tex]x^{2}-5x-750=0[/tex]

Now for x2 ⇒

[tex]x2=\frac{-(-5)-\sqrt{(-5)^{2}-4.(1).(-750)}}{2.(1)}=-25[/tex]

[tex]x2=-25[/tex] is a solution of the equation [tex]x^{2}-5x-750=0[/tex]

Given that both numbers are positive ⇒

[tex]x>0[/tex] and [tex](x-5)>0\\x>5[/tex]

Therefore, x2 is not a possible value for the greater number

The greater number is [tex]x1=30[/tex]

Answer:

  x = 5

Step-by-step explanation:

You want to find x such that ...

  x^2 +(x +1)^2 = 61

  2x^2 +2x -60 = 0 . . . . . simplify, subtract 61

  x^2 +x -30 = 0 . . . . . . . divide by 2

  (x +6)(x -5) = 0 . . . . . . . . factor; solutions will make the factors be zero.

The relevant solution is x = 5.