how can i solve this

Answer:

[tex](x−3)(x+5) .....is.. the.. factorised.. form.. of.. the.. expression[/tex]

Step-by-step explanation:

[tex]x^2 + 2x > =15 \\x^2 + 2x - 15 > = 0 \\(x + 4)(x - 2) < 0 , \\{x + 4 < 0 and .x - 2 > 0} or {x + 4 > 0 ,\\and .x - 2 < 0} , \\{x < -4 and .x > 2} or {x > -4 and. x < 2},\\ Discard .x < -4 and. x > 2 because. it. has. no. solutions,\\ leaving .just x > -4 and .x < 2 , -4 < x < 2[/tex]

Answer:

130 cm³

Step-by-step explanation:

Volume of the pyramid = 1/3 × base area × height

Calculating base area;

Area = length × width

= 8 × 7

= 56 cm²

Now, Volume = ⅓ × 56 × 7

= ⅓ × 392

= 130.6 cm³.

Answer:

exponential function, x = time in minutes, y = number of bacteria

Step-by-step explanation:

y = 20 × (2)^x

Step-by-step explanation:

Find the HCF of 9m 80cm 8m 40cm 4m 20cm

Answer:

radius = 40 / 2 = 20ft

Circle area = πr² = π × 20² = 1256.6 sq. ft

Answer:

$10,700.

Step-by-step explanation:

Answer:

First option is the correct answer

[tex] A(\triangle ABC) =572\: yd^2[/tex]

Step-by-step explanation:

Answer:

the answer is 5 and (-7,5)

Step-by-step explanation:

The radius is 5, and the points (-7, 5) and (-7, -1) both lie on the circle.

Given that:

The points at which the circle is centered are (-3,2)

Passing points = (1,5)

The radius is calculated using the distance formula:

d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2[/tex]

Substituting the coordinates, we have:

d =[tex]\sqrt{({1 - (-3))^2 + (5 - 2)^2[/tex]

 = [tex]\sqrt{(1 + 3)^2 + (5 - 2)^2[/tex]

 =[tex]\sqrt{(4^2 + 3^2)[/tex]

 = [tex]\sqrt{(16 + 9)[/tex]

  = 5

Therefore, the radius of the circle is 5 units.

The equation of a circle with center (h, k) and radius r is given by:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

Substituting the values, we have:

[tex][-7 - (-3)]^2 + (y - 2)^2 = 5^2[/tex]

[tex](-7 + 3)^2 + (y - 2)^2 = 25[/tex]

[tex](-4)^2 + (y - 2)^2 = 25[/tex]

[tex]16 + (y - 2)^2 = 25[/tex]

[tex](y - 2)^2 = 9[/tex]

Taking the square root of both sides, we have:

y - 2 = ±3

Solving for y, we have two possible values:

y - 2 = 3    

y = 5

y - 2 = -3

 y = -1

The points (-7, 5) and (-7, -1) both lie on the circle.

Thus, the radius is 5, and the points (-7, 5) and (-7, -1) both lie on the circle.

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Answer:

Algebra is simple and the answer is infinity due to there being over one million diffrent possoblitlitys, We know that because of albert ienstine so the answer has been solved.

Step-by-step explanation:

Answer:

1) 16 : 30

2) 8 : 15

3)  [tex]\displaystyle \frac{8}{15}[/tex]

Step-by-step explanation:

Boys = 14

Girls = 16

Total students:

= 14 + 16

= 30

Ratio of Girls to total number of students in class:

= 16 : 30

÷2     ÷2

= 8 : 15

= [tex]\displaystyle \frac{8}{15}[/tex]

[tex]\rule[225]{225}{2}[/tex]

We can represent this drawing as follows: 1/5÷3

Fraction is a representation of a division between two real integers. A fraction, can be named as a ratio between two natural terms, integers, rational and/or reals. They consist of a numerator and a denominator.

Looking at the image, we can see that it is divided into 5 parts. In one of these parts, there is one that is divided into three ''group''.

- We know that the numerator indicates the amount that was divided and the denominator indicates the total amount. Therefore, the answer will be:

5 parts in total.                                   =  1  ÷ 3

1 whole part - divided into three           5

So, the correct answer is 1/5 ÷ 3

Since Suzy return took 1/4 hr longer, how far Suzy travelled to her appointment is 50 mi

To answer the question, we need to know what distance travelled by Suzy is

The distance between Suzy and her appointment is d = vt where

So, d = 50t   (1)

Now, since Suzy returns home at a speed of v' = 40 mph and takes her 1/4 hr longer to return home,her return time is , t' = (t + 1/4) h

Since the distance she ruturns home is the same, we also have that

d = v't'

= 40(t + 1/4)  (2)

Equating (1) and (2), we have

50t = 40(t + 1/4)

50t = 40t + 10

50t - 40t = 10

10t = 10

t = 10/10

t = 1 hr

Substituting t = 1 into d = 50t, we have

d = 50(1)

d = 50 m

So, how far Suzy travelled to her appointment is 50 mi

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From the figure given above, angel < ABE = 40°

The angle of a straight line = 180°

That is angle <ABC = 180°

If <EBC is = 140°

Therefore, <ABE = 180 - 140

= 40°

Therefore, from the figure given above, angel < ABE = 40°

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Answer:

Yes, Sophia is correct

Step-by-step explanation:

The expression is correct and if you solve it, you get 23 which should be her uncle's age.

Answer:

y=4

Step-by-step explanation:

steps

3×9+4y=43

4y=43-27

4y=16

Divide both side by 4

4y/4=16/4

y=4

Answer:

it is b

Step-by-step explanation:

that is the most effective way to measure how well the fertilizer works with all of the plants

Answer:

3 = x

Step-by-step explanation:

Well, the two unknown sides share the same size due to the same angle, so now, using the fact we only have the info about one side, we need to do a reverse pythagorean theorem.

[tex]c^{2} = a^{2} + b^{2}[/tex]

Our a and b are the same, so I will change them to "x" and combine them.

[tex]c^{2} = 2(x)^{2}[/tex]

Now we plug in our "c" and square it ("C" in this case is: [tex]3\sqrt{2}[/tex] )

[tex]18 = 2(x)^{2}[/tex]

[tex]9 = x^{2}[/tex]

3 = x

Answer:

f(3) = 42

Step-by-step explanation:

f(x) = 3x² + 5x

Then

f(3) = 3(3)² + 5(3)

      = 3×9 + 5×3

      = 27 + 15

      = 42

Answer:

Here is the answer...hope it helps

[tex]\textbf{(i)}\\\\~~~~~~~y= e^{3x} \sin 2x\\\\\\\implies \dfrac{dy}{dx} = \dfrac{d}{dx} \left( e^{3x} \sin 2x \right)\\\\\\~~~~~~~~~~~~=e^{3x} \dfrac{d}{dx} \sin 2x + \sin 2x \dfrac{d}{dx} e^{3x}\\\\\\~~~~~~~~~~~~=2e^{3x} \cos 2x + 3e^{3x}\sin 2x \\\\\\[/tex]

[tex]\textbf{(ii)}\\\\~~~~~~~~y = \dfrac{e^{3x}}{\cos 2x}\\\\\\\implies \dfrac{dy}{dx} = \dfrac d{dx} \left(\dfrac{e^{3x}}{\cos 2x} \right)\\\\\\~~~~~~~~~~~=\dfrac{\cos 2x \dfrac{d}{dx}\left(e^{3x} \right) -e^{3x} \dfrac{d}{dx}( \cos 2x) }{\cos^2 (2x)}\\\\\\~~~~~~~~~~~=\dfrac{3e^{3x} \cos 2x+2e^{3x}\sin2x }{\cos^2(2x)}\\\\\\~~~~~~~~~~~=\dfrac{3e^{3x} \cos 2x}{ \cos^2(2x)} + \dfrac{2e^{3x} \sin 2x}{\cos^2(2x)}\\\\\\~~~~~~~~~~~=3e^{3x}\sec (2x) + 2e^{3x}\sec (2x) \tan (2x)[/tex]

[tex]\textbf{(iii)}\\\\~~~~~~~~~y=( 3x+2)^3\\\\\\\implies \dfrac{dy}{dx} = \dfrac{d}{dx}(3x+2)^3\\\\\\~~~~~~~~~~~=3(3x+2)^2 \dfrac{d}{dx} (3x+2)\\\\\\~~~~~~~~~~~=3(3x+2)^2 \cdot 3\\\\\\~~~~~~~~~~~=9(3x+2)^2[/tex]

[tex]\textbf{(iv)}\\\\~~~~~~~~~x^2 +y^2 = 5xy\\\\\\\implies \dfrac{d}{dx}(x^2 +y^2) = 5\dfrac{d}{dx} (xy)\\\\\\\implies 2x + 2y \dfrac{dy}{dx} = 5\left(x \dfrac{dy}{dx} +y\right)\\ \\\\\implies 2x +2y \dfrac{dy}{dx} = 5x \dfrac{dy}{dx} +5y\\\\\\\implies 2y \dfrac{dy}{dx} - 5x \dfrac{dy}{dx} = 5y-2x\\\\\\\implies (2y-5x) \dfrac{dy}{dx} = 5y-2x\\\\\\\implies \dfrac{dy}{dx} = \dfrac{5y-2x}{2y-5x}[/tex]

Answer:

1/20

Step-by-step explanation:

1/4 = 0.25

0.25 / 5 = 0.05

0.05 as a fraction = 5/100

simplified

5 / 5 = 1

100 / 5 = 20

1/20

Answer:

(3, 2)

(9, 10)

Step-by-step explanation:

Ordered pairs (3, 2) and (9, 10) is the solution of the equation 4x -1 = 3y + 5

Answer:

D. 5/6 and 10/12

Step-by-step explanation:

Answer:

530.93

Step-by-step explanation:

area of a circle = πr²

where r = radius

here we are given the diameter

to convert to radius , we divide by 2

so radius = 26 / 2 = 13

so we have A = πr²

==> plug in r = 13

A = π13²

==> evaluate exponent

A = 169π

==> multiply 169 and π

A = 530.93 ( approximately )

The possibility of selecting a 4 characters long password consisting of 3 letters and one number if letters cannot be repeated and the password must end with a number is 156000

An equation is an expression that shows the relationship between two or more number and variables.

The possibility of selecting the password = 26 * 25 * 24 * 10 = 156000

The possibility of selecting a 4 characters long password consisting of 3 letters and one number if letters cannot be repeated and the password must end with a number is 156000

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Answer:

//Solve equation [2] for the variable  y

  [2]    y = 4

// Plug this in for variable  y  in equation [1]

  [1]    (4) - x = -2

  [1]     - x = -6

// Plug this in for variable  y  in equation [4]

  [4]    (4) - 2x = 1

  [4]     - 2x = -3

// Solve equation [1] for the variable  x

  [1]    x = 6

// Plug this in for variable  x  in equation [3]

  [3]    (6) = 3

  [3]    0 = -3 =>  NO solution

No solution

the measure of the radius is 2.9

Answer:

28 caffinated  teas

Step-by-step explanation:

    If your options are:

A. x(12-3)

B. 8x

C. 3 (3x-x)

D. 9

      Then the following is true.

Answer: (A) x(12-3)

   First, we will simplify the given expressions;

A. x(12-3)     = 12x - 3x

B. 8x           = 8x

C. 3 (3x-x)   = 9x - 3x

D. 9             =9

   This means the answer to your question is;

          A. x(12-3)

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