What is the slope of the line that passes through the points e (5,1) and f (2, -7)

Answer:

Step-by-step explanation:

4 + x = 133......to solve this, u would subtract 4 from both sides

so that would be the subtraction property of equality

Answer:

Step-by-step explanation:

4 + x = 13              subtract 4 from both sides

4 - 4 + x = 13 - 4

Answer:

Step-by-step explanation:

1)w=−4/3x+−1/3y+2/3z+26/3

2)w=−3/2x+1/2y+−1/2z+7

3)w=1/2x+y+3/2z−9

4)w=2x+2y−z−10

Hope this helps, mark me as brainlist pls

Answer:

The aircraft has a height of 1000 m at t=2 sec, and at t=8 sec

Step-by-step explanation:

Finding Exact Roots Of Polynomials

A polynomial can be expressed in the general form    

[tex]\displaystyle p(x)=a_nx^n+a_{n-1}\ x^{n-1}+...+a_1\ x+a_0}[/tex]  

The roots of the polynomial are the values of x for which    

[tex]P(x)=0[/tex]

Finding the roots is not an easy task and trying to find a general solution has been discussed for centuries. One of the best possible approaches is trying to factor the polynomial. It requires a good eye and experience, but it gives excellent results.    

The function for the trajectory of an aircraft is given by    

[tex]\displaystyle h(x)=0.5(-t^4+10t^3-216t^2+2000t-1200)[/tex]

We need to find the values of t that make H=1000, that is

[tex]\displaystyle 0.5(-t^4+10t^3-216t^2+2000t-1200)=1000[/tex]

Dividing by -0.5

[tex]\displaystyle t^4-10t^3+216t^2-2000t+1200=-2000[/tex]

Rearranging, we set up the equation to solve

[tex]\displaystyle t^4-10t^3+216t^2-2000t+3200=0[/tex]

Expanding some terms

[tex]\displaystyle t^4-8t^3-2t^3+200t^2+16t^2-1600t-400t+3200=0[/tex]

Rearranging

[tex]\displaystyle t^4-8t^3+200t^2-1600t-2t^3+16t^2-400t+3200=0[/tex]

Factoring

[tex]\displaystyle t(t^3-8t^2+200t-1600)-2(t^3-8t^2+200t-1600)=0[/tex]

[tex]\displaystyle (t-2)(t^3-8t^2+200t-1600)=0[/tex]

This produces our first root t=2. Now let's factor the remaining polynomial

[tex]\displaystyle t^2(t-8)+200(t-8)=0[/tex]

[tex]\displaystyle (t^2+200)(t-8)=0[/tex]

This gives us the second real root t=8. The other two roots are not real numbers, so we only keep two solutions

[tex]\displaystyle t=2,\ t=8[/tex]

Answer:

[tex]\frac{5}{7}-(-\frac{1}{7})=\frac{6}{7}[/tex]

Step-by-step explanation:

To evaluate :

[tex]\frac{5}{7}-(-\frac{1}{7})[/tex]

Solution:

Two negatives multiply to become a positive.

Thus, we can remove parenthesis by reversing the signs of the fraction by multiplying the negative outside.

⇒ [tex]\frac{5}{7}+\frac{1}{7}[/tex]

Since the denominators are same for both fractions, so we simply add the numerators.

⇒ [tex]\frac{5+1}{7}[/tex]

⇒ [tex]\frac{6}{7}[/tex]  (Answer)

Answer:

D. None of the above.

Step-by-step explanation:

OPTIONS A and C. The Olympic final had faster average times and more noticeable variation compared to the top 888 U.S. qualifier times.

Looking at the dot plots, we can draw the following conclusions:

A. The times in the Olympic final were faster on average than the top 888 U.S. qualifier times. - True, since the lower dot plot represents Olympic final times and the lower values (faster times) are more concentrated.

B. All of the times in the Olympic final were faster than all of the top 888 U.S. qualifier times. - False, as there are some times in the U.S. qualifier dot plot that are faster than some times in the Olympic final dot plot.

C. The Olympic final times varied noticeably more than the times of the top 888 U.S. qualifiers. - True, since the spread of dots in the lower plot seems to be wider compared to the upper plot, indicating greater variation in Olympic final times.

So, the correct choices are A and C.

Answer: the answer is correct

Step-by-step explanation: edge 2020 trust me

The half of 14 is 7 and the half of 77 is 38.5

Hope this helped! (Plz mark me brainliest)

Answer:

The weight of the larger box   = 15.75 kg.

The weight of the smaller box = 13.75 kg.

Step-by-step explanation:

We have the two equations based on the scenario.

The equations are:

[tex]$ 7x + 9y = 234 \hspace{20mm} \hdots {(1)} $[/tex]

[tex]$ 5x + 3y = 360 \hspace{20mm} \hdots {(2)} $[/tex]

'x' represents the weight of the larger box.

and 'y' the weight of the smaller box.

Multiplying Equation (2) by 3 throughout, we get:

[tex]$ 15x + 9y = 360 $[/tex]

Subtracting this and Equation (1), we get:

[tex]$ -8x = -126 $[/tex]

[tex]$ \implies x = 15.75 $[/tex] kg.

∴ The weight of the Larger box is 15.75 kg.

Substituting the value of 'x' in either of the equations will give us the value of 'y', the weight of the smaller box.

We substitute in Equation (1).

We get: 9y = 234 - 7(15.75)

⇒ 9y = 123.75

⇒ y = 13.75

∴ The weight of the smaller box is 13.75 kg.

Answer:

We typically construct graphs with the input values along the horizontal axis and the output values along the vertical axis. The most common graphs name the input value x and the output value y , and we say y is a function of x , or y=f(x) y = f ( x ) when the function is named f .

Step-by-step explanation:

Answer:

Ans => 4, 5

Step-by-step explanation:

let the integers be x and y

if they are consecutive, that means the larger integer is one greater than the smaller

=> y = x+1

2 = 3x - 2y

3x - 2(x+1) = 2

3x - 2x - 2 = 2

x = 4

y = 4+1 = 5

There is no way to determine the rate of change [slope], so it is impossible to answer this question. I apologise.

Answer:

The water she need is [tex]7\frac{7}{8} \ cups.[/tex] and strawberry syrup [tex]11\frac{13}{16}\ cups[/tex].

Step-by-step explanation:

Given:

Dina wants to make 15 3/4 cups of strawberry drink by mixing water and strawberry syrup with a ratio of 2 1/4 cup of water for every 3/4 cup of syrup.

Now, to find the quantity of water and syrup she need to use.

As given in question ratio so:

Strawberry syrup = 2 1/4 = 9/4.

Water = 3/4.

Total cups of strawberry drink = 15 3/4 = 63/4.

Let the strawberry syrup be [tex]\frac{9}{4} x[/tex].

And let the water be [tex]\frac{3}{4} x[/tex].

According to question:

[tex]\frac{9x}{4} + \frac{3x}{4}=\frac{63}{4}[/tex].

On adding the fractions:

⇒[tex]\frac{9x+3x}{4} =\frac{63}{4}[/tex]

⇒[tex]\frac{12x}{4} =\frac{63}{4}[/tex]

Multiplying both sides by 4 we get:

⇒[tex]12x=63[/tex]

Dividing both sides by 12 we get:

⇒[tex]x=\frac{63}{12}[/tex]

Dividing numerator and denominator by 3 on R.H.S we get:

⇒[tex]x=\frac{21}{4}[/tex]

Now, putting the value of [tex]x[/tex] on ratios:

Strawberry syrup =  [tex]\frac{9}{4}\times x=\frac{9}{4}\times\frac{21}{4}[/tex]

                             =  [tex]\frac{189}{16}[/tex]

                             =  [tex]11\frac{13}{16}\ cups[/tex]  

Water = [tex]\frac{3}{4}\times x =\frac{3}{4} \times\frac{21}{4}[/tex]

          = [tex]\frac{63}{8}[/tex]

          = [tex]7\frac{7}{8} \ cups.[/tex]

Therefore, the water she need is [tex]7\frac{7}{8} \ cups.[/tex] and strawberry syrup [tex]11\frac{13}{16}\ cups[/tex].

Answer:

y-4=3/4(x+8)

Step-by-step explanation:

y-y1=m(x-x1)

y-4=3/4(x-(-8))

y-4=3/4(x+8)

The factorization of [tex]\(3x^3+7x^2-18x+8\)[/tex] is [tex]\((x-1)(3x^2 + 10x - 8)\)[/tex]. So, the factors are [tex](x-1), (3x^2 + 10x - 8)[/tex], and any additional factors that [tex]\(3x^2 + 10x - 8\)[/tex] may have, which can be further factored if possible.

Given that  x-1 is a factor of the expression [tex]\( 3x^3+7x^2-18x+8 \)[/tex], we can use the long division method to find the other factors.

Set up the division as follows:

            [tex]3x^2 + 10x - 8[/tex]

       ______________________

[tex]x - 1 | 3x^3 + 7x^2 - 18x + 8 \\ - (3x^3 - 3x^2)[/tex]

        ___________________

                [tex]10x^2 - 18x + 8 \\ - (10x^2 - 10x)\\[/tex]

                 ______________

                          -8x + 8

                          - (-8x + 8)

                          __________

                                 0

The quotient is [tex]\(3x^2 + 10x - 8\)[/tex], and since there is no remainder, \(x-1\) is indeed a factor.

Therefore, The factorization of [tex]\(3x^3+7x^2-18x+8\)[/tex] is [tex]\((x-1)(3x^2 + 10x - 8)\)[/tex]

So, the factors are [tex](x-1), (3x^2 + 10x - 8)[/tex], and any additional factors that [tex]\(3x^2 + 10x - 8\)[/tex] may have, which can be further factored if possible.

The complete factorization of the original expression [tex]\(3x^3 + 7x^2 - 18x + 8\)[/tex] is:[tex]\[ (x - 1)(x + 4)(3x - 2) \][/tex]

To factorize the expression [tex]\(3x^3 + 7x^2 - 18x + 8\)[/tex] given that one of the factors is [tex]\(x - 1\)[/tex], we can use polynomial division to divide the expression by [tex]\(x - 1\)[/tex] and find the quotient. The factors of the expression will then be [tex]\(x - 1\)[/tex]  and the factors of the quotient.

The expression to be factorized is: [tex]\(3x^3 + 7x^2 - 18x + 8\).[/tex]

Let's perform the division step-by-step.

1.Divide the first term of the dividend (3x³) by the first term of the divisor (x):

  [tex]\(3x^3 ÷ x = 3x^2\)[/tex].

Write this as the first term of the quotient.

2. Multiply the divisor by this term and subtract the result from the dividend:

Multiply [tex]\(x - 1\)[/tex] by [tex]\(3x^2\)[/tex] to get [tex]\(3x^3 - 3x^2\)[/tex].

Subtract this from the original polynomial: [tex]\(3x^3 + 7x^2\)[/tex]becomes [tex]\(10x^2\)[/tex].

3.Bring down the next term of the original polynomial to form a new dividend:

The new dividend is [tex]\(10x^2 - 18x\)[/tex].

4.Repeat this process for the new dividend**:

  Divide [tex]\(10x^2\) by \(x\) to get \(10x\)[/tex].

  Multiply [tex]\(x - 1\) by \(10x\)[/tex] to get [tex]\(10x^2 - 10x\)[/tex].

  Subtract this from the new dividend:[tex]\(10x^2 - 18x\)[/tex]  becomes [tex]\(-8x\)[/tex].

5.Bring down the next term of the original polynomial to form a new dividend:

  The new dividend is [tex]\(-8x + 8\)[/tex].

6.Repeat this process for the new dividend**:

  Divide [tex]\(-8x\) by \(x\)[/tex] to get [tex]\(-8\)[/tex].

  Multiply [tex]\(x - 1\) by \(-8\)[/tex] to get [tex]\(-8x + 8\)[/tex].

  Subtract this from the new dividend: [tex]\(-8x + 8\)[/tex] becomes 0.

The quotient we obtain from this division is [tex]\(3x^2 + 10x - 8\)[/tex]. Now, we need to factorize this quadratic expression. Let's proceed with the factorization.

The roots of the quadratic expression [tex]\(3x^2 + 10x - 8\)[/tex] are [tex]\(-4\)[/tex] and[tex]\(\frac{2}{3}\)[/tex]. This means that the quadratic expression can be factored as [tex]\((x + 4)(x - \frac{2}{3})\)[/tex].

However, to express the factors in a more standard form, we'll rewrite the factor [tex]\(x - \frac{2}{3}\) as \(3x - 2\)[/tex], which is obtained by multiplying the numerator and denominator of [tex]\(\frac{2}{3}\)[/tex] by 3.

Therefore, the factorized form of [tex]\(3x^2 + 10x - 8\)[/tex] is [tex]\((x + 4)(3x - 2)\)[/tex].

Combining this with the given factor [tex]\(x - 1\)[/tex], the complete factorization of the original expression [tex]\(3x^3 + 7x^2 - 18x + 8\)[/tex] is:[tex]\[ (x - 1)(x + 4)(3x - 2) \][/tex]

From Patrick's gains, tax rates, and the inflation rate, the following are true: $346.25, $1,731.25, $145.43 and $4,702.08.

State tax on initial profit can be calculated by;

= (17,000 - 10,000 - 25 - 25 - 25) x 5%

= $346.25

The federal tax is:

= 25% x (17,000 - 10,000 - 25 - 25 - 25) x 25%

= $1,731.25

Inflation after taxes is:

= (17,000 - 7,000 - 25 - 25 - 25 - 346.25 - 1,731.25) * (1% + 1% + 1%)

= $145.43

Real value in profit is:

= 17,000 - 7,000 - 25 - 25 - 25 - 346.25 - 1,731.25 - 145.43

= $4,702.08

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Patrick's initial profit is $7,000, and after state and federal taxes, he has $4,900. When adjusted for a 1% annual inflation rate over three years, the real value of his profit is approximately $4,805.03.

Patrick's profit from selling his stock is calculated by subtracting the initial investment from the current value, $17,000 - $10,000 = $7,000. The state tax he must pay on this profit is 5% of $7,000, which equals $350. Similarly, the federal tax on the profit is 25% of $7,000, equaling $1,750. After state and federal taxes, the remaining amount is $7,000 - $350 - $1,750 = $4,900. Lastly, the inflation effect over three years at 1% per year diminishes the purchasing power of the remaining amount. The cumulative effect of inflation can be calculated by the formula P = P0 * ((1 - r)^n), where P is the future value, P0 is the present value, r is the inflation rate, and n is the number of years. Thus, Patrick's remaining profit adjusted for inflation would be $4,900 * ((1 - 0.01)^3), which gives a result of approximately $4,805.03. This is the real value of Patrick’s profit after taxes and inflation adjustments.

Answer:

[tex]x = 2\sqrt{10}[/tex]

Step-by-step explanation:

We have to solve for x from the logarithmic equation as follows:

[tex]\log x^{2} + \log 25 = 3[/tex]

⇒ [tex]\log 25x^{2}  = 3[/tex]  

{Since, using logarithmic property [tex]\log A + \log B = \log AB[/tex]}

Now, converting this logarithmic equation above into exponential equation we get,

[tex]25x^{2}  = 10^{3}[/tex]  

{Since we know that if [tex]\log_{10}a = b[/tex] then, we can write [tex]a = 10^{b}[/tex]}

⇒ [tex]25x^{2}  = 1000[/tex]

⇒ [tex]x^{2}  = 40[/tex]

⇒ [tex]x = 2\sqrt{10}[/tex] (Answer)

Answer:

the number is X=2

Step-by-step explanation:

Suppose number is X

8X-1 =X+13

8X-X= 13+1

7X=14

X=2

Answer:

8n-1= 13+n is the equation, n=2 is the answer for the variable.

Step-by-step explanation:

8n-1= 13+n

Move the variable to one side.

8n-1= 13+n

-1n         -1n

7n-1= 13

Now, add to both sides, since that is the opposite of subtracting.

7n-1= 13

   +1  +1

Then, divide to both sides by 7 to leave the variable by itself.

7n= 14

7     7

n= 2

Answer:

y = -3x + 14

Step-by-step explanation:

Answer:

[tex]\frac{n^{2} }{n+5}[/tex]

Step-by-step explanation:

We can see that for nth term of this sequence,numerator is square of the term number([tex]n^{2}[/tex]) and denominator is 5 added to the term number(n+5).

Therefore , the nth term of this sequence is

[tex]\frac{n^{2} }{n+5}[/tex]

Para levantar 500 toneladas de mineral a una altura de 90 pies en una hora, se requieren aproximadamente 90.91 caballos de fuerza (HP), calculados utilizando la fórmula de trabajo y potencia.

Para calcular la potencia requerida en caballos de fuerza (HP) para levantar 500 toneladas de mineral hasta una altura de 90 pies en una hora, necesitamos utilizar la fórmula de trabajo y la potencia. La potencia se mide en unidades de trabajo por unidad de tiempo.

Primero, convirtamos la altura a pies a la misma unidad que la tonelada, que es la tonelada-pie (ton-ft). 1 tonelada-pie es igual al trabajo necesario para levantar una tonelada a una altura de un pie.

500 toneladas * 90 ft = 45,000 ton-pie

El trabajo total necesario es de 45,000 toneladas-pie.

Dado que el trabajo se realiza en una hora (3600 segundos), podemos usar la siguiente fórmula para calcular la potencia en HP:

[tex]\[Potencia (HP) = \frac{Trabajo (ft-lbf)}{Tiempo (s)} \times \frac{1}{550}.\][/tex]

Donde 1 HP es igual a 550 ft-lbf/s.

Sustituyendo los valores conocidos:

[tex]\[Potencia (HP) = \frac{45,000 \text{ ton-pie} \times 2,000 \text{ lbf/ton} \times 1 \text{ ft}}{3600 \text{ s} \times 550 \text{ ft-lbf/s}} = \frac{180,000,000 \text{ lbf-ft}}{1,980,000 \text{ ft-lbf/s}} \approx 90.91 HP.\][/tex]

Por lo tanto, se requieren aproximadamente 90.91 caballos de fuerza (HP) para realizar este trabajo en una hora.

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Answer:

$2,444.95

Step-by-step explanation:

A = P (1 + r)^(nt)

where A is the final amount,

P is the principal,

r is the rate,

n is the compoundings per year,

and t is the number of years.

500,000 = P (1 + 0.03)^(12 × 15)

500,000 = P (1.03)^180

P = 500,00 (1.03)^-180

P ≈ 2,444.95

Final answer:

To determine the principal amount that must be invested at a rate of 3%, compounded monthly, to have $500,000 available for retirement in 15 years, the formula for compound interest can be used. The principal that must be invested is approximately $310,334.84.

Explanation:

To determine the principal amount that must be invested at a rate of 3%, compounded monthly, to have $500,000 available for retirement in 15 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the future value, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

Plugging in the given values, we have:

A = $500,000, r = 0.03 (3%), n = 12 (compounded monthly), and t = 15.

Substituting these values into the formula, we get:

$500,000 = P(1 + 0.03/12)^(12*15)

Solving for P gives:

P = $500,000 / (1 + 0.03/12)^(12*15)

Calculating this expression gives P ≈ $310,334.84. Therefore, the principal that must be invested is approximately $310,334.84.

Answer:

Step-by-step explanation:

[tex]f(x)=\dfrac{12}{4x+2}\\\\f(-1)-\text{put}\ x=-1\ \text{to}\ f(x):\\\\f(-1)=\dfrac{12}{4(-1)+2}=\dfrac{12}{-4+2}=\dfrac{12}{-2}=-6[/tex]

Answer:

f(-1) = -6

Step-by-step explanation:

substitute -1 into the equation and solve, you'll get -6

Answer:

[tex]\angle{A}=53.1^{\circ}[/tex]

[tex]\angle{A}=80.9^{\circ}[/tex]

[tex]b=12.4[/tex]

Step-by-step explanation:

Please find that attachment.

We have been given that in ΔABC, ∠C measures 46° and the values of a and c are 10 and 9, respectively.

First of all, we will find measure of angle A using Law Of Sines:

[tex]\frac{\text{sin(A)}}{a}=\frac{\text{sin(B)}}{b}=\frac{\text{sin(C)}}{c}[/tex], where, A, B and C are angles corresponding to sides a, b and c respectively.

[tex]\frac{\text{sin(A)}}{10}=\frac{\text{sin(46)}}{9}[/tex]

[tex]\frac{\text{sin(A)}}{10}=\frac{0.719339800339}{9}[/tex]

[tex]\frac{\text{sin(A)}}{10}=0.0799266444821111[/tex]

[tex]\frac{\text{sin(A)}}{10}*10=0.0799266444821111*10[/tex]

[tex]\text{sin(A)}=0.799266444821111[/tex]

Upon taking inverse sine:

[tex]A=\text{sin}^{-1}(0.799266444821111)[/tex]

[tex]A=53.060109978759^{\circ}[/tex]

[tex]A\approx 53.1^{\circ}[/tex]

Therefore, the measure of angle A is 53.1 degrees.

Now, we will use angle sum property to find measure of angle B as:

[tex]m\angle{A}+m\angle{B}+m\angle{C}=180^{\circ}[/tex]

[tex]53.1^{\circ}+m\angle{B}+46^{\circ}=180^{\circ}[/tex]

[tex]m\angle{B}+99.1^{\circ}=180^{\circ}[/tex]

[tex]m\angle{B}+99.1^{\circ}-99.1^{\circ}=180^{\circ}-99.1^{\circ}[/tex]

[tex]m\angle{B}=80.9^{\circ}[/tex]

Therefore, the measure of angle B is 80.9 degrees.

Now, we will use Law Of Cosines to find the length of side b.

[tex]b^2=a^2+c^2-2ac\cdot\text{cos}(B)[/tex]

Upon substituting our given values, we will get:

[tex]b^2=10^2+9^2-2(10)(9)\cdot\text{cos}(80.9^{\circ})[/tex]

[tex]b^2=100+81-180\cdot 0.158158067254[/tex]

[tex]b^2=181-28.46845210572[/tex]

[tex]b^2=152.53154789428[/tex]

Upon take square root of both sides, we get:

[tex]b=\sqrt{152.53154789428}[/tex]

[tex]b=12.3503663060769173[/tex]

[tex]b\approx 12.4[/tex]

Therefore, the length of side b is approximately 2.4 units.

Answer:

∠A = 53.1°, ∠B = 80.9°, b = 12.4

Step-by-step explanation:

i got it right on my test

[tex]\pi[/tex] is a Irrational Number .

[tex]\sqrt{12}[/tex] is a Irrational Number .

3.14 is a Rational Number .

[tex]4 . \overline{123}[/tex] is a Rational Number .

[tex]\sqrt{49}[/tex]  is Natural, Whole, Rational Number and Integer .

[tex]-\frac{240}{6}[/tex] is Integer and Rational number.

In order to answer this question, we need to know what are Natural Numbers, Whole Numbers, Integer, Rational and Irrational Numbers.  

We cannot represent [tex]\pi[/tex] as a fraction of two integers and hence is Irrational.

[tex]\sqrt{12}[/tex] can be simplified as [tex]\sqrt{(4 \times 3)}=2 \times \sqrt{3} \times \sqrt{3}[/tex]  again cannot represent the same as a fraction of two integers, and [tex]\sqrt{12}[/tex]  is irrational.

3.14 can be represented in terms of [tex]\frac{314}{100}=\frac{157}{50}[/tex], and hence it is a Rational Number.

[tex]4 . \overline{123}[/tex] is the case of Repeating decimals, and repeating decimals are always Rational Numbers.

[tex]\sqrt{49}[/tex] is equal to 7 and hence is Natural Number. 7 can also be included in the whole number, rational number and Integer.

[tex]-\frac{240}{6}[/tex] is equal to -40, so it is Integer and Rational Number.

Answer:

the answer is (6, 1)

Step-by-step explanation:

x² + y² - 12 x - 2 y + 12 = 0

(x²-12x) +(y² -2y) +12 = 0

(x²-2(6)(x)+6²)-6² +(y² -2y+1) -1+12 = 0

(x-6)² +(y-1)² = 5²

the center of a circle is (6, 1)

Answer:

77

Step-by-step explanation:

Simplify the following:

52 + 7×3 + 4

7×3 = 21:

52 + 21 + 4

| 5 | 2

| 2 | 1

+ | | 4

| 7 | 7:

Answer: 77

To evaluate the expression 52 + 7 ⋅ 3 + 4, follow the order of operations (PEMDAS). First, multiply 7 by 3 to get 21, then add 52 and 4 to get the final result of 77.

Evaluation of the Expression:

To evaluate the expression 52 + 7 ⋅ 3 + 4, it is important to follow the order of operations (PEMDAS/BODMAS):

Using these rules, solve the expression step-by-step:

Therefore, the correct answer is:

77

Answer:

If Discriminant,[tex]b^{2} -4ac >0[/tex]

Then it has Two Real Solutions.

Step-by-step explanation:

To Find:

If discriminant (b^2 -4ac>0) how many real solutions

Solution:

Consider a Quadratic Equation in General Form as

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

then,

[tex]b^{2} -4ac[/tex] is called as Discriminant.

So,

If Discriminant,[tex]b^{2} -4ac >0[/tex]

Then it has Two Real Solutions.

If Discriminant,[tex]b^{2} -4ac < 0[/tex]

Then it has Two Imaginary Solutions.

If Discriminant,[tex]b^{2} -4ac=0[/tex]

Then it has Two Equal and Real Solutions.