what will be the index of 2 for its value equal to 1/2​

Answer: u = 3

Step-by-step explanation:

Divide each side by -7 to get u = 3.

Answer:

3

Step-by-step explanation:

-7u = -21

To solve the problem we need to isolate u. Since -7 is being multiplied by u, we could divide to get rid of it.

-7u

[tex] \frac{ - 7u}{ - 7} = - 21 \div - 7[/tex]

u= -21/-7

u = 3

Answer:

Cost of case = $5

Step-by-step explanation:

x = cost of camera and y = cost of case

x = y + 90

x + y = 100

y + 90 + y = 100

2y = 10

y = 5

x = y + 90

x = 5 + 90

x = 95

Therefore, the cost of the camera is $95 and the cost of the case is $5.

The cost of case is 5 dollars.

The equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal.

Let,

Cost of camera = a and

Cost of case = b

Given that, camera and a case cost 100 dollars

a + b = 100

Since, the camera cost 90 more dollars than the case

So, a = b + 90

Substitute the value in the equation a + b = 100

b + 90 + b = 100

2b = 10

Divided by 2 both the sides

b = 5

Substitute the value of b in equation

a = b+ 90

a = 5 + 90

a = 95

So, the cost of the camera is $95 and the cost of the case is $5.

Hence, the cost of the case is 5 dollars.

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Answer: The gradient of the line segment between the points (-5,2) and (4,3) is [tex]\dfrac{1}{9}[/tex].

Step-by-step explanation:

Formula for gradient of a line segment :

[tex]\text{Gradient}=\dfrac{\text{Difference between y-coordinates}}{\text{Difference between x-coordinates}}[/tex]

Given points of the line segment: (-5,2) and (4,3)

[tex]\text{Gradient} =\dfrac{3-2}{4-(-5)}[/tex]

[tex]\text{Gradient} =\dfrac{1}{4+5)}[/tex]

[tex]\text{Gradient} =\dfrac{1}{9}[/tex]

Therefore , the gradient of the line segment between the points (-5,2) and (4,3) is [tex]\dfrac{1}{9}[/tex].

Answer:

sinU = 0.96

Step-by-step explanation:

sinU = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{WV}{UV}[/tex] = [tex]\frac{24}{25}[/tex] = 0.96

Answer:

This system has infinite solutions and it would be much easier to solve it by elimination but substitution it is.

Step-by-step explanation:

-3x+3y=9

-x+y=3

Isolate either x or y in any of the equations. I'll go with the second.

y = 3+x

Now substitute this for y in the first equation.

-3x+3(3+x)=9

Distribute the 3

-3x+9+3x=9

Combine like terms:

9=9

0=0

It's infinite

Answer:

Maximum value.

it = -1.

Step-by-step explanation:

Maximum value as the coefficient of x^2  is negative.

To find this value we convert to vertex form:

y = -3x^2 + 6x - 4

y = -3(x^2 - 2x) - 4

y = -3[(x - 1)^2 - 1] - 4

y = -3(x - 1)^2 + 3 - 4

y = =3(x - 1)^2 - 1

Minimum value = -1.

Answer:

y=41

Step-by-step explanation:

Let us start by writing an equation. 4 plus y divided by 5 equals to 9 :

[tex]\frac{4+y}{5}=9[/tex]

Great! Now let us solve for the variable, y, by isolating the terms:

[tex]4+y=45\\y=41[/tex]

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

Answer:

first number = 7

second number = 11

Step-by-step explanation:

A first number is 4 less than a second number

f = s - 4

Four times the first number is 6 more than twice the second

4f = 2s + 6

-----------------------------

Substitute for f = s - 4

4(s - 4) = 2s + 6

distribute

4s - 16 = 2s + 6

subtract 2s from both sides

2s - 16 = 6

add 16 to both sides

2s = 22

Divide both sides by 2

s = 11

Substitute for s = 11 in

f = s - 4

f = 11 - 4

f = 7

Answer:

Step-by-step explanation:

formula of volume of cone is given so u simply substitute the values given and calculate.

Work is done for u .

Hope this helps u

Answer:

x = 11

Step-by-step explanation:

(7x + 5)° = (3x + 19)° + (2x + 8)°

7x + 5 = 5x + 27

2x = 22

x = 11

Answer:

k = -12

Step-by-step explanation:

When lines are perpendicular, their slopes are the opposite reciprocal of each other.

The opposite reciprocal of [tex]\frac{1}{4}[/tex] is -4

[tex]\frac{k}{3}=-4[/tex]

k = -12

Answer:

<2 = 75

Step-by-step explanation:

<1 and <2 form a straight line which means that they add to 180

<1+<2 =180

105+<2 =180

Subtract 105 from each side

<2 =180-105

<2 = 75

Answer:

a = 8

Step-by-step explanation:

a ÷ 2 - 8 + 8 = - 4 + 8

a ÷ 2 = 4

a ÷ 2 × 2 = 4 × 2

a = 8

Answer:

a = 8

Step-by-step explanation:

Given

[tex]\frac{a}{2}[/tex] - 8 = - 4 ( add 8 to both sides )

[tex]\frac{a}{2}[/tex] = 4 ( multiply both sides by 2 to clear the fraction )

a = 8

Answer:

Step-by-step explanation:

Answer:

190,000

190,000

190,000

Step-by-step explanation:

190,000

190,000

Answer:

ur answer is 8.06

Step-by-step explanation:

a² + b²= c²

4² + 7² = c²

16 + 49 = c²

65 sooo u do √65= 8.06

Answer:

10 pounds

Step-by-step explanation:

Let x represent the amount of raisins Meg have in her supply. She uses 1/2 of her supply of raisins  to make trail  mix and 3/10 of her supply of raisins to make  cookies which gives a total of 8 pounds of raisins being used. To find the amount of raisins she has in her supply, we use the equation:

(1/2)x + (3/10)x = 8

multiply through by 20:

(1/2)x * 20 + (3/10)x * 20 = 8 * 20

10x + 6x = 160

16x = 160

Divide both sides of the equation by 16:

16x/16 = 160/16

x = 10 pounds

Therefore she have 10 pounds of raisins in her supply

Answer:

48 ft

Step-by-step explanation:

Here, we want to find the length of the wire

from the diagram, we can identify two similar triangles

The smaller one and a bigger one

Mathematically, when two triangles are similar, the ratio of their corresponding sides are equal

We can start by getting the height of the tower

we have this as:

8/11 = 28/x

8 * x = 28 * 11

8x = 308

x = 308/8

x = 38.5 ft

So as we can see, the wire represents the hypotenuse of the larger triangle that measures 28 ft base and 38.5 ft height

So we can use the Pythagoras’ theorem to get the hypotenuse

Let us call this g

mathematically according to the theorem, the square of the hypotenuse equals the sum of the squares of the two other sides

thus, we have it that;

g^2 = 38.5^2 + 28^2

g^2 = 2,266.25

g = √2,266.25

g = 47.61 which is approximately 48 ft

Answer: 299

Step-by-step explanation:

Given

Family removes one-third of tress in June as much as they dd in July

They remove twice the number of July in august

Suppose they removed x trees in July

for June it is, [tex]\frac{x}{3}[/tex]

for August, it is [tex]2x[/tex]

If they removed less than 1000 tress in 3 months

[tex]\Rightarrow \dfrac{x}{3}+x+2x<1000\\\\\Rightarrow \dfrac{x+3x+6x}{3}<1000\\\\\Rightarrow \dfrac{10x}{3}<1000\\\\\Rightarrow \dfrac{x}{3}<100\\\\\Rightarrow x<300[/tex]

So, maximum number of tress removed in July is 299

Answer:

3(n-8)

Step-by-step explanation:

Answer:

[tex]\text{(C) }300\pi\:\mathrm{cm^3}[/tex]

Step-by-step explanation:

The volume of a cylinder with radius [tex]r[/tex] and height [tex]h[/tex] is given by [tex]V=r^2\pi \cdot h[/tex].

What we're given:

Substituting given values, we get:

[tex]V=5^2\pi \cdot 12 =\boxed{300\pi\:\mathrm{cm^3}}[/tex]

Answer:

c

Step-by-step explanation:

The formula for the volume of a cylinder is [tex]V=\pi r^2h[/tex]

We know r is 5, and h is 12.

Then we can just plug the values into the formula.

[tex]V=\pi (5)^2(12)\\ V=\pi (25)(12)\\\V=\pi (300)[/tex]

So the answer is c, 300pi

Answer:

x = 8/k

Step-by-step explanation:

kx - 3 = 5

Add 3 to each side

kx -3+3= 5+3

kx = 8

Divide by k

kx/k = 8/k

x = 8/k

Answer:

x = 8 / k

Step-by-step explanation:

Let's solve for x.

kx − 3 = 5

Step 1: Add 3 to both sides.

kx −3 +3 = 5 + 3

kx = 8

Step 2: Divide both sides by k.

kx / k = 8k

x = 8 / k