what is the hcf of 12 45 and 75​

Given:

The quadratic equation is:

[tex]-5x^2-3x-2=0[/tex]

To find:

The discriminant of the given equation and the number of real solutions.

Solution:

If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then the value of discriminant is:

[tex]D=b^2-4ac[/tex]

If D<0, then the quadratic equation has no real roots or two imaginary roots.

If D=0, then the quadratic equation has two equal real roots.

If D>0, then the quadratic equation has two distinct real roots.

We have,

[tex]-5x^2-3x-2=0[/tex]

Here, [tex]a=-5,b=-3,c=-2[/tex]. So, the discriminant of the given equation is:

[tex]D=(-3)^2-4(-5)(-2)[/tex]

[tex]D=9-40[/tex]

[tex]D=-31[/tex]

Since D<0, therefore the number of real solutions is 0.

Hence, the value of the discriminant is -31 and the number of real solutions is 0.

Answer:

939 girls

Step-by-step explanation:

Let us start by writing an equation. We can set the number of boys as x, and the number of girls as 3x since the number of girls is three times the number of boys:

Step 1, writing an equation:

[tex]1252=3x+x[/tex]

We will assume in this case, that the number of girls plus the number of boys adds up to the total number of learners at Petit High School

Step 2, solving the equation:

We can simplify the above equation and isolate the term containing x.

[tex]1252=4x\\x=313[/tex]

Step 3, determining values:

There are [tex]\fbox{939}[/tex] girls at Petit High School.

I hope this helps! Let me know if you have any questions :)

Answer:

SSS (Side side side)

Step-by-step explanation:

Answer:

[tex]{ \tt{y = y {}^{x} }} \\ y - intercept : { \tt{y = {y}^{0} }} \\y = 1[/tex]

Answer:

The answer to this situation would be that Japhet will be most likely to pick the letter “I.”

Step-by-step explanation:

First, calculate how many letters each word has:

P R O B A B I L I T Y - 11 Letters

S T A T I S T I C S - 10 Letters

Next, calculate how many “I”'s each letter has:

"Probability" has two “I”'s.

"Statistics" has two “I”'s.

Finally, divide the amount of “I”'s in the word by it's letter count:

"PROBABILITY" - 2 “I”'s / 11 Letters ≈ 18%

"STATISTICS" - 2 “I”'s / 10 Letters = 20%

So, Japhet would have the better probability to choose the letter “I.”

Hope this helps!

Answer:

y=63x+65

Step-by-step explanation:

Answer:

4,5

Step-by-step explanation:

Your welcome! :)

Good Luck!

Answer:

B is 4 and A is 5 --> 4,5

Step-by-step explanation:

Answer:

không

Step-by-step explanation:

Answer:

(a + b)(a - b) = a² - b²

Step-by-step explanation:

(a + b)(a - b) = a (a - b ) + b (a - b )

                 = a²  - ab + ba  - b²             [ ab = ba ]

                 = a² - ab + ab - b²               [ ab - ab = 0 ]

                 = a² - b²

Two consecutive odd integers with a sum of 36 are 17 and 19.

Hope it helps you I'm from ph❤️

Answer:

Two consecutive odd integers with a sum of 36 are 17 and 19.

Step-by-step explanation:

hope i helped

Answer:

Ben = $ 41

Kaden = $ 31

Step-by-step explanation:

Let initially Ben has $ p and then Kaden has $ (p  - 10).

After that

Ben has= $ (p + 4)

Kaden has = $ (p- 10 + 4) = $ ( p - 6)

According to the question,

[tex]p- 6 = \frac{7}{9}\times (p+4)\\\\9 p- 54 = 7 p + 28 \\\\2 p = 82\\\\p =41[/tex]

Initially Ben has $ 41 and Kaden has $ 31.  

Answer:

Solution: {x = 2, y = -1/3}

Step-by-step explanation:

On observation, we see that the y-terms are equal and opposite in sign, therefore to solve the system, we add the two equations.

2x-3y = 5 ..........(1)

3x+3y = 5............(2)

(1) + (2)

2x - 3y + 3x + 3y = 5+5

5x = 10

x = 2 .......(3)

Substitute (3) in (2) and solve for x

3x+3y = 5 .....(2)

3(2) + 3y = 5

3y = 5-6 = -1

y = -1/3  .......(4)

assemble (3) and (4) to give the answer

Solution: {x = 2, y = -1/3}

50 - 2x; x = 3

____________________

50 - 2(3)

= 50 - 6

= 44

Answer:

$40

Step-by-step explanation:

Fraction Navin gave his brother = 1/5

Remainder = 1 - 1/5

5/5 - 1/5 = 4/5

Fraction Navin gave his sister = 4/5 x 5/8 = 1/2

total amount Navin gave his siblings :

[tex]\frac{1}{5} + \frac{1}{2}[/tex]

[tex]\frac{2 + 5}{10}[/tex] = [tex]\frac{7}{10}[/tex]

Fraction that remains = 1 - 7/10

10/10 - 7/10 = 3/10

Let a = amount Navin has initially

3/10 x a = 12

a = (12 x 10) / 2  = $40

Answer: Thought I’d return the favor and help u with this question! But anyways, the axis of symmetry is at x = -3.

Explanatio: This can be found by looking at the basic form of vertex form:

y = (x - h)^2 + k

In this basic form the vertex is (h, k). By looking at what is plugged into the equation, it is clear that h = -3 and k = -4. This means the vertex is at (-3, -4).

It is a fact that the axis of symmetry is a vertical line of x = (vertex value of x). So we can determine that the axis of symmetry is at x = -3

i hope this helps u

Answer:

The answer is 3.

[tex]\longrightarrow{\purple{3}}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex] \frac{(6a + b)(a + b) - 7b(a + b)}{2 {a}^{2} - 2 {b}^{2} } [/tex]

[tex] \\= \frac{(a + b)(6a + b - 7b)}{2( {a}^{2} - {b}^{2}) } [/tex]

[tex] \\= \frac{(a + b)(6a + b - 7b)}{2(a + b)(a - b)} [/tex]

[tex] \\= \frac{6a - 6b}{2(a - b)} [/tex]

[tex] \\= \frac{6(a - b)}{2(a - b)} [/tex]

[tex] \\= 3[/tex]

( OR )

[tex] \frac{(6a + b)(a + b) - 7b(a + b)}{2 {a}^{2} - 2 {b}^{2} } [/tex]

[tex] \\= \frac{6 {a}^{2} + 6ab + ab + {b}^{2} - 7ab - 7 {b}^{2} }{2( {a}^{2} - {b}^{2} )} [/tex]

[tex] \\= \frac{6 {a}^{2} - 6 {b}^{2} + 7ab - 7ab }{2( {a}^{2} - {b}^{2} )} [/tex]

[tex] \\= \frac{6 {a}^{2} - 6 {b}^{2} }{2( {a}^{2} - {b}^{2} )} [/tex]

[tex] \\= \frac{6( {a}^{2} - {b}^{2} )}{2( {a}^{2} - {b}^{2} )} [/tex]

[tex] \\= \frac{6}{2} [/tex]

[tex] \\= 3[/tex]

[tex] {a}^{2} - {b}^{2} = (a + b)(a - b)[/tex]

[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♬}}}}}[/tex]

Answer:

length-14cm width-7cm

Step-by-step explanation:

To work out the sides, you can use 2l+2w=42. Since the length is twice the width, this becomes 2(2w)+2w=42.

This can be expanded to 4w+2w=42 or 6w=42.

From there, we can divide both sides by 6 to isolate w, meaning w=7.

Since the length is twice the width, it is given by l=2×7 or l=14.

**This question involves writing and solving algebraic equations from worded questions, which you may wish to revise. I'm always happy to help!

Answer:

The fourth angles is 105

Step-by-step explanation:

The sum of the angles of a quadrilateral is 360

3*85 = 225

Let the fourth angle be x

225 +x = 360

x = 360 -225

x =105

Answer:

The blue dot is at 3.

Answer:

correct 42 in bsae 10 is 60

Answer:

x = 15

Step-by-step explanation:

Given that,

The length of the base of an isosceles triangle is x.

The length of a leg is 3x-4.

Perimeter, P = 97

An isosceles triangle has one base. The perimeter of a triangle is given by :

97=x+3x-4+3x-4

97 = 7x-8

97+8=7x

105 = 7x

x = 15

So, the value of x is 15.

Answer:

6.78 m

Step-by-step explanation:

Since the set up forms a triangle with length of ropes two sides of the triangle a = 8 m and b = 7 m respectively, the distance between them which is c = 6 m forms the third side of the triangle.

To find the height of the pole, we need to find the angle between any of the ropes and the ground. So, choosing the 8 m long rope side and using the cosine rule,

b² = a² + c² - 2accosФ where Ф is the angle opposite the 7 m long side which is also the angle between the 8 m long side and the ground.

So, making, Ф subject of the formula, we have

b² - (a² + c²) = 2accosФ

cosФ = [b² - (a² + c²)]/2ac

Ф = cos⁻¹{[b² - (a² + c²)]/2ac}

substituting the values of the variables into the equation, we have

Ф = cos⁻¹{[b² - (a² + c²)]/2ac}

Ф = cos⁻¹{[7² - (8² + 6²)]/2(8)(6)}

Ф = cos⁻¹{[49 - (64 + 36)]/96}

Ф = cos⁻¹{[49 - 100]/96}

Ф = cos⁻¹{-51/96}

Ф = cos⁻¹{-0.53125}

Ф = 122.09°

Since the height of the pole, h is a perpendicular bisector to the base of the triangle, and the 8 m long side form a triangle with it and the ground and the 8 m long side being the hypotenuse side of this triangle, we have that

sinФ = h/a where a = 8 m and Ф = 122.09° = the angle between the 8 m long side and the ground.

h = asinФ

substituting the values of the variables into the equation, we have

h = asinФ

h = (8 m)sin122.09°

h = 8 m × 0.8472

h = 6.78 m

a polygon with seven sides is called a heptagon

Answer:

Hyptagon

Step-by-step explanation:

In geometry, a heptagon is a seven-sided polygon or 7-gon.

The heptagon is sometimes referred to as the septagon, using "sept-" (an elision of septua-, a Latin-derived numerical prefix, rather than hepta-, a Greek-derived numerical prefix; both are cognate) together with the Greek suffix "-agon" meaning angle.

Answer:

A) 8d^2/3c

B) 3a^2b^3

Step-by-step explanation:

Answer:

Step-by-step explanation:

In exponent division, if base are same , subtract the exponents.

[tex]\frac{a^{m}}{a^{n}}=a^{m-n} , m>n\\\\ \frac{a^{m}}{a^{n}}= \frac{1}{a^{n-m}}, m<n[/tex]

a) 8c²d⁵ ÷ 2c³d³ = [tex]\frac{8}{2}* \frac{d^{5-3}}{c^{3-2}}= 4*\frac{d^{2}}{c}= \frac{4d^{2}}{c}[/tex]

b) 9a³b⁵ ÷ 3ab² = [tex]\frac{9}{3}* a^{3-1}*b^{5-2} = 3a^{2}b^{3}[/tex]

Step-by-step explanation:

the answer is in the image above

Answer:

C. Consecutive Exterior Angles Theorem states that if the transversal passes through the two parallel lines then any two exterior angles are congruent

Answer:

B

Step-by-step explanation:

Answer:

10 1/2

Step-by-step explanation:

/ = divide

21 divided by 2 is 10 remainder 1 ~ 10 1/2 as a mixed number

21/2 as a improper fraction

THE CORRECT EQUATION IS..

(8X+3)°=(7X+12)°

[BEING VERTICALLY OPPOSITE ANGLES ARE ALWAYS EQUAL ]

HOPE THIS HELPS YOU...

Answer:

8x + 3 = 7x + 12

8x -7x= 12-3

x=9

Answer: 4

Step-by-step explanation:

The exponent in the given number [tex]4^{2}=16[/tex] is  2.

An exponent refers to the number of times a number is multiplied by itself.

For example, [tex]3^{4}[/tex] means we are multiplying 3 four times. Here the base is 3 and exponent is 4.

According to the question

We have a number

[tex]4^{2} =16[/tex]

Here, we are multiplying 4 two times. So, the base is 4 and the exponent is 2.

Hence, the exponent in the given number [tex]4^{2}=16[/tex] is  2.

Learn more about the exponent here:

https://brainly.com/question/5497425

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