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3 years ago

Find the particular equation of quadratic function containing (-2,-11) (4,13) and (6,29)

1 answer:

6 0

F(x) = a*x^2 + b*x + c; where a is not 0;
f(-2) = -11 => 4a -2b + c = -11;
f(4) = 13 => 16a +4b + c = 13;
f(6) = 29 => 36a + 6b + c = 29;
You must find a, b, c;

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Please help, I will give you brainliest!

V125BC [204]

Answer:

$12 = 12 \\ 12 - 12 = 12 - 12 \\ 0 = 0$

7 0

3 years ago

In a group of 40 people, 27 can speak English and 25 can speak Spanish. How many can speak

Svetradugi [14.3K]

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{Information \: provided \: with \: us }}}}}\: \bigstar}$

➻ In a group of 40 people, 27 can speak English and 25 can speak Spanish.

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{What \: we \: have \: to \: find ? }}}}}\: \bigstar}$

➻ The required number of people who can speak both English and Spanish .

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{Assumption}}}}}\: \bigstar}$

Consider ,

➻ A → Set of people who speak English.

➻ B → Set of people who speak Spanish

➻ A∩B → Set of people who can speak both English and Spanish

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{Given}}}}}\: \bigstar}$

➻ n (A) = 27

➻ n (B) = 25

➻ n (A∪B) = 40

➻ n(A∩B) = ?

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{Now}}}}}\: \bigstar}$

➻ n(A∪B) = n(A) + n (B) - n(A∩B)

➻ 40 = 27 + 25 - n (A∩B)

➻ 40 = 52 - n (A∩B)

➻ n (A∩B) = 52 - 40

➻ ∴ n (A∩B) = 12

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{Therefore}}}}}\: \bigstar}$

∴ Required Number of persons who can speak both English and Spanish are 12 .

━━━━━━━━━━━━━━━━━━━━━━

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{Verification}}}}}\: \bigstar}$

➻ n(A∪B) = n(A) + n (B) - n(A∩B)

➻ 40 = 27 + 25 - 12

➻ 40 = 52 - 12

➻ 40 = 40

➻ ∴ L.H.S = R.H.S

━━━━━━━━━━━━━━━━━━━━━━

6 0

2 years ago

Please help me and explain it please questions 28

klasskru [66]

Answer:

$1.35

Step-by-step explanation:

x: quarter=$0.25

y: dime=$0.10

z: nickel=$0.05

so total amount of changes

= (0.25*x)+(0.10*y)+(0.05*z)

x=3, y=5, z=2

substituting into the eqn

total = (0.25*3)+(0.10*5)+(0.05*2)

= 0.75 + 0.5 + 0.1

= $1.35

5 0

3 years ago

Read 2 more answers

Do these side lengths make a right triangle? 2.1, 7.2, 7.5

mariarad [96]

Answer:Yes

Step-by-step explanation:

6 0

3 years ago

Evaluate the integral. (Use C for the constant of integration.) cos(x) (8 + 7 sin^2(x)) dx

UNO [17]

Answer: $8 \sin x +7(\dfrac{\sin^3x}{3})+C$

Step-by-step explanation:

Consider $\int \cos(x) (8+7 \sin^2(x)) \, dx$

Substitute t= sinx

then dt = cos x dx

$\int \cos(x) (8+7 \sin^2(x)) \, dx = \int (8+7t^2)dt\\\\ =8t+7(\dfrac{t^3}{3})+C$

$[\int x^ndx=\dfrac{x^{n+1}}{n+1}+C]$

$=8 \sin x +7(\dfrac{\sin^3x}{3})+C$

Hence, $\int \cos(x) (8+7 \sin^2(x)) \, dx=8 \sin x +7(\dfrac{\sin^3x}{3})+C$

5 0

3 years ago