Doug split a pack of cards so that he and his friends each got 6 cards. If there were 24 cards in the pack, how many friends did Doug share his cards with ?

Answer is not 4.

Answer: The answer is x < 5/2 and x > -5.

Step-by-step explanation:

First you need to separate the inequality and keep x on one side to maintain consistency. For instance the problem-

[tex]\frac{5-2x}{3} > 0\\\frac{5-2x}{3} < 5\\[/tex]

Now solve as normal.

*Note: When dividing a side or multiplying a side by a negative number, the sign of the inequality switches (this will be shown when I do the equation if it doesn't make since how I word it).

[tex]5-2x > 0*3\\5-2x < 5*3[/tex]

[tex]-2x > 0-5\\-2x < 15-5[/tex]

[tex]x < \frac{-5}{-2} =x < \frac{5}{2} \\x > \frac{10}{-2} =x > -5[/tex]

So, x < 5/2 and x > -5.

If anything is confusing about the procedure just leave a comment, and I'll try to explain further.

The slope of the given line is -2, and since perpendicular lines have negative reciprocal slopes, the slope of the line we want to find is 1/2.

Substituting into point-slope form,

[tex]y+4=\frac{1}{2}(x-8)\\\\y+4=\frac{1}{2}x-4\\\\\boxed{y=\frac{1}{2}x-8}[/tex]

Answer:

Equation of line perpendicular to y= -2x-9 is y=x/2-8 .

Step-by-step explanation:

The slope of a line gives the measure of its steepness and direction. The slope of a curve at a point is equal to the slope of the straight line that is tangent to the curve at that point.

The general equation of a line is y = mx + c, where m is the slope of the line and c is the y-intercept. It is the most common form of the equation of a straight line that is used in geometry.

The product of slopes of two perpendicular lines gives (-1).

m1m2=(-1)

(-2)m2=(-1)

m2=1/2

y=m2x+c

Point (8,-4) satisfies the given equation :

(-4)=1/2 x 8 + c

c = (-8)

Line perpendicular to y= -2x-9 will be -

y=x/2-8

Learn more about equation of lines -https://brainly.com/question/27263630

#SPJ10

Step-by-step explanation:

please mark me as brainlest

Answer:

1780

Step-by-step explanation:

multiply the length value by 1760

and then divide the length value by 3

Answer:

K

Step-by-step explanation:

(1*500 * 5) + (10 * 3*500)

The value of x will be 3

From given diagram, triangle ABC and EDC meet at a common vertex C.

So, triangle ABC and EDC both are congruent to each other.

Applying the similarity property of congruence, ratio of the congruent triangles' corresponding sides will be equal.

Therefore,

[tex]\frac{AB}{ED} = \frac{AC}{EC} = \frac{BC}{CD}[/tex]

[tex]\frac{AC}{EC} = \frac{BC}{CD}[/tex]

Simplifying the expression,

We get

(18-x)/x = 25/5

(18-x)/x = 5

18-x = 5x

18-x-5x = 0

18 - 6x = 0

- 6x = -18

x = 3

Hence, the value of x is 3.

Learn more about congruent triangle here:

https://brainly.com/question/2938476

#SPJ10

Answer:

[tex]x=\dfrac{-3\pm3\sqrt{5}}{2}[/tex]

Step-by-step explanation:

Given equation:

[tex]x^2+3x-9=0[/tex]

Completing the square

Move the constant to the right side by adding 9 to both sides:

[tex]\implies x^2+3x=9[/tex]

Add the square of half the coefficient of x to both sides:

[tex]\implies x^2+3x+\left(\dfrac{3}{2}\right)^2=9+\left(\dfrac{3}{2}\right)^2[/tex]

[tex]\implies x^2+3x+\dfrac{9}{4}=\dfrac{45}{4}[/tex]

Factor the trinomial on the left side:

[tex]\implies \left(x+\dfrac{3}{2}\right)^2=\dfrac{45}{4}[/tex]

Square root both sides:

[tex]\implies x+\dfrac{3}{2}=\pm\sqrt{\dfrac{45}{4}}[/tex]

[tex]\implies x+\dfrac{3}{2}=\pm\dfrac{\sqrt{45}}{\sqrt{4}}}[/tex]

[tex]\implies x+\dfrac{3}{2}=\pm\dfrac{\sqrt{9 \cdot 5}}{2}[/tex]

[tex]\implies x+\dfrac{3}{2}=\pm\dfrac{\sqrt{9} \sqrt{5}}{2}[/tex]

[tex]\implies x+\dfrac{3}{2}=\pm\dfrac{3\sqrt{5}}{2}[/tex]

Subtract 3/2 from both sides:

[tex]\implies x=\pm\dfrac{3\sqrt{5}}{2}-\dfrac{3}{2}[/tex]

[tex]\implies x=\dfrac{-3\pm3\sqrt{5}}{2}[/tex]

The inequality equation will be -5x + 20 < -10.

Inequality is defined as an equation that does not contain an equal sign.

The weather report says the temperature is 20°c and will drop 5°c per hour for the next 6 hours.

Daryl plans to be gone at least 6 hours, and he has a plant outside.

If he wants the plant to remain in temperatures above -10° should Daryl move the plant to a warmer location before leaving will be

The inequality equation will be

-5x + 20 < -10

where x is the number of hours.

Then we have

-10 < -5x + 20

5x > 30

   x > 6 hours

More about the inequality link is given below.

https://brainly.com/question/19491153

#SPJ1

Answer:

A

Step-by-step explanation:

sin*sec=tan

tan^2+1=sec^2 by an identity

Answer:

a, b, d

Step-by-step explanation:

its one of those

Answer:

A, the first one

Answer:

B. x = 3

Step-by-step explanation:

Simplifying

4 + 3x = 2(3x + -7) + 9

Reorder the terms:

4 + 3x = 2(-7 + 3x) + 9

4 + 3x = (-7 * 2 + 3x * 2) + 9

4 + 3x = (-14 + 6x) + 9

Reorder the terms:

4 + 3x = -14 + 9 + 6x

Combine like terms: -14 + 9 = -5

4 + 3x = -5 + 6x

Solving

4 + 3x = -5 + 6x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-6x' to each side of the equation.

4 + 3x + -6x = -5 + 6x + -6x

Combine like terms: 3x + -6x = -3x

4 + -3x = -5 + 6x + -6x

Combine like terms: 6x + -6x = 0

4 + -3x = -5 + 0

4 + -3x = -5

Add '-4' to each side of the equation.

4 + -4 + -3x = -5 + -4

Combine like terms: 4 + -4 = 0

0 + -3x = -5 + -4

-3x = -5 + -4

Combine like terms: -5 + -4 = -9

-3x = -9

Divide each side by '-3'.

x = 3

Simplifying

x = 3

Answer:

A. 0.78

Step-by-step explanation:

A rational number is a number that you can express as [tex]\frac{x}{y}[/tex] where [tex]y\neq 0[/tex].

i beilive this is unknown

The second derivative of the first function is s"(x) = = -[8e^(x/5) - 2]e^(x/5)/25(e^(x/5) + 2)³.

The second derivative of the second function is; k''(t) = (36t² - 6)e^(-3t²)

1)  We are given the function;

s(x) = 4/(1 + 2e^(-0.2x)

First derivative is;

ds/dx = [8e^(x/5)]/5(e^(x/5) + 2)²

Second Derivative is;

d²s/dx² = -[8e^(x/5) - 2]e^(x/5)/25(e^(x/5) + 2)³

At x = 0;

d²s/dx² = -[8e^(0/5) - 2]e^(0/5)/25(e^(0/5) + 2)³

d²s/dx² = 8/675

B) We are given the function;

k(t) = e^(-3t²)

The first derivative is;

dk/dt = -6te^(-3t²)

The second derivative is;

k''(t) = (36t² - 6)e^(-3t²)

At t = 1, we have;

k''(t) = (36(1)² - 6)e^(-3(1²))

k"(t) = 1.494

Read more about Second derivatives at; https://brainly.com/question/15180056

#SPJ1

The missing values are shown in the attached picture, and 41 degrees F = 5 degrees C.

It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.

We have:

[tex]\rm F = \dfrac{9}{5}C + 32[/tex]

Make subject C and solve:

[tex]\rm \dfrac{5}{9}(F-32) = \dfrac{5}{9}\times\dfrac{9}{5}C[/tex]

[tex]\rm \dfrac{5}{9}(F-32) = C[/tex]

Plug F = 41

[tex]\rm \dfrac{5}{9}(41-32) = C[/tex]

[tex]\rm \dfrac{5}{9}(9) = C[/tex]

41 degrees F = 5 degrees C

Thus, the missing values are shown in the attached picture, and 41 degrees F = 5 degrees C.

Learn more about the unit conversion here:

brainly.com/question/14350438

#SPJ1

Answer:

i think the answer is the second one D and A

Answer:

( 2, -1)

Step-by-step explanation:

(X1 + X2)/2 , (Y1 + Y2)/2

(6-2)/2 , (3-5)/2

4/2 , -2/2

2 , -1

Answer:

(2, -1)

Step-by-step explanation:

(x1, y1)=(6, 3)

(x2, y2)=(-2, -5)

[(6+(-2))/2, (3+(-5))/2]

=(4/2, -2/2)

=(2, -1)

Answer: 31 cm.

explanation:

Given, Radius = 5 cm (near to)

this means the radius is near 5 cm. It can be 4.9, 4.99, 4.999.....or 5.01,5.001,5.001...... and so on.

So, the circumference of the circle is given by:-

Circumference = 2× [tex]\pi[/tex] × r

⇒ 2 × 22/7 × 5    (for the smallest value, we'll consider r as 5 and then round off the circumference to the smallest value)

⇒ 220/7 ≈ 31.43 cm

rounding off to the smallest integer, we have

Circumference = 31 cm.

The smallest value that the circumference could have is 10 [tex]\pi[/tex]cm

Using Formula,

Circumference = 2 [tex]\pi \\[/tex] r

Radius = 5 cm

So, C = 2 [tex]\pi[/tex] 5

C = 10 [tex]\pi[/tex]cm

Therefore circumference is 10 [tex]\pi[/tex]cm.

To learn more about the circumference of circles, refer to :

https://brainly.com/question/2407529

#SPJ2

Answer:

3/8

Step-by-step explanation:

probability = wanted outcomes / total outcomes

odds = wanted outcomes / unwanted outcomes

Odds of 3:5 losing means 3 losing outcomes and 5 winning outcomes.

The total outcomes is 8

The probability of losing which is the probability that the event will fail to occur is 3/8.

The corresponding part of PQ is WX

The congruent statement is given as:

polygon WXYZ ≅ polygon PQRS.

This means that the corresponding points are:

W and P, X and Q, Y and R, Z and S

When two points Q and P are joined together, we have:

polygon WX ≅ polygon PQ

Hence, the corresponding part of PQ is WX

Read more about congruent shapes at:

https://brainly.com/question/24430586

#SPJ1

Answer:

1) D because the answer to 8.42*10^3=8420

and 8420 lies between 8400 and 8500

2) C because when you take the absolute value of -2.3 and -3.2, they become positive numbers => 2.3 < 3.2

3)D because 6 < 6.3 < 6.6

Hope it helps!

‐10+35=25 and 25 × 20=300

1) ∠E and ∠F are supplementary and ∠F and ∠G are supplementary (given)

2) m∠E+m∠F=180 degrees, m∠F+m∠G=180 degrees (supplementary angles have measures that add to 180 degrees)

3) m∠E=m∠G (subtraction property of equality)

4) ∠E≅∠G (angles with equal measure are congruent)

By applying algebraic handling on the two equations, we find the following three solution pairs: x₁ ≈ 5.693 ,y₁ ≈ 10.693; x₂ ≈ 1.430, y₂ ≈ 6.430; x₃ ≈ - 0.737, y₃ ≈ 4.263.

In this question we have a system formed by a linear equation and a non-linear equation, both with no trascendent elements and whose solution can be found easily by algebraic handling:

x - y = 5      (1)

x² · y = 5 · x + 6       (2)

By (1):

y = x + 5

By substituting on (2):

x² · (x + 5) = 5 · x + 6

x³ + 5 · x² - 5 · x - 6 = 0

(x + 5.693) · (x - 1.430) · (x + 0.737) = 0

There are three solutions: x₁ ≈ 5.693, x₂ ≈ 1.430, x₃ ≈ - 0.737

And the y-values are found by evaluating on (1):

y = x + 5

x₁ ≈ 5.693

y₁ ≈ 10.693

x₂ ≈ 1.430

y₂ ≈ 6.430

x₃ ≈ - 0.737

y₃ ≈ 4.263

By applying algebraic handling on the two equations, we find the following three solution pairs: x₁ ≈ 5.693 ,y₁ ≈ 10.693; x₂ ≈ 1.430, y₂ ≈ 6.430; x₃ ≈ - 0.737, y₃ ≈ 4.263.

To learn more on nonlinear equations: https://brainly.com/question/20242917

#SPJ1

Answer:

k = 1

Step-by-step explanation:

Discriminant

[tex]b^2-4ac\quad\textsf{when }\:ax^2+bx+c=0[/tex]

[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}[/tex]

[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real root}[/tex]

[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real roots}[/tex]

As we need to determine the value of k that will give one solution, set the discriminant to zero.

Given equation:

[tex]y=kx^2-4x+4[/tex]

Therefore:

Substitute these values into the discriminant and solve for k:

[tex]\begin{aligned}b^2-4ac & = 0\\\implies (-4)^2-4(k)(4) & = 0\\16-16k & = 0\\16k & = 16\\\implies k & = 1\end{aligned}[/tex]

Since everything to the right of the line is shaded, the linear inequality which represents the graph is equal to: A. y ≥ 1/3x - 4.

In order to determine the linear inequality which represents the graph, we would find the slope of the given points.

Mathematically, the slope of a straight line can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Substituting the given points into the formula, we have;

[tex]Slope = \frac{-4\;-\;(-5)}{0\;-\;(-3)}\\\\Slope = \frac{1}{3}[/tex]

Slope = 1/3.

From the standard equation, we have:

y - y₁ = m(x - x₁)

y - (-5) = 1/3(x - (-3))

y + 5 = 1/3x + 1

y = 1/3x + 1 - 5

y = 1/3x - 4

y ≥ 1/3x - 4.

Read more on slope here: brainly.com/question/3493733

#SPJ1