write the equation of the direct variation that includes the given point (-6,5)

Answer:

the answer is negative infinity to infinity because it's all real numbers.

The domain of g(x) is the set of all real numbers.

A real number is a value of a continuous quantity that can represent a distance along a line.

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Answer:

49.6mL

Step-by-step explanation:

Given parameters:

Volume of solution = 386mL

Percentage composition of acid = 12.86%

Solution

The solution is made up of water and acid in their respective proportions.

We have been given the percentage composition of acid to be 12.86%, so we can easily obtain the exact volume of the acid in the compositon.

Volume of acid in solution = perenctage of acid x volume of solution

Volume of acid = [tex]\frac{12.86}{100}[/tex] x 386mL = 49.6396mL

Rounding to the nearest tenth gives: 49.6mL

Answer:

If you're trying to find x or y, you cannot find the exact value since there is one equation. If there was, for example, 2 equations, [a system of equations] you could solve that. But here we only have one equation.

So, if you're trying to solve for x;

x = 7 - 3y

And if you're trying to solve for y;

y = 7/3 - x

Answer:

5/9

Step-by-step explanation:

F(-2)for f(x)=5•3^x

Let x = -2

f(-2)=5•3^(-2)

      = 5 * 1/3^2

     = 5 * 1/9

     = 5/9

Answer:

f(-2) = 5/9

Step-by-step explanation:

* lets explain the problem

∵ f(x) = 5(3)^x

- It is an exponential function

- (3) is the base of the function

- x is the exponent

- To find f(-2) means substitute x by -2

∵ [tex]f(x)=5(3)^{x}[/tex]

∵ x = -2

∴ [tex]f(-2)=5(3)^{-2}[/tex]

- If the power of the base is negative we can change its sign to

  positive by reciprocal the base

# Ex: [tex](a)^{-n}=(\frac{1}{a})^{n}[/tex]

- Lets do that withe the base 3 and power -2

∵ [tex](3)^{-2}=(\frac{1}{3})^{2}[/tex]

∴ [tex]f(-2)=5(\frac{1}{3})^{2}=5(\frac{1}{9})=\frac{5}{9}[/tex]

* f(-2) = 5/9

Answer:

[tex]b=6.8\ units[/tex]

Step-by-step explanation:

we know that

Applying the law of sines in the triangle ABC

[tex]\frac{AB}{sin(C)}=\frac{AC}{sin(B)}[/tex]

substitute the given values

[tex]\frac{15}{sin(140\°)}=\frac{b}{sin(17\°)}[/tex]

Solve for b

[tex]b=(sin(17\°))\frac{15}{sin(140\°)}[/tex]

[tex]b=6.8\ units[/tex]

Answer:

[tex]y_Q=\dfrac{21}{5}=4.2[/tex]

Step-by-step explanation:

If the point Q that is located two over three the distance from point P to point R, then PQ:QR=2:3.

Use formula to find the coordinates of the point Q:

[tex]x_Q=\dfrac{3x_P+2x_R}{3+2}\\ \\y_Q=\dfrac{3y_P+2y_R}{3+2}[/tex]

In your case, P(-2,7) and R(1,0), then

[tex]x_Q=\dfrac{3\cdot (-2)+2\cdot 1}{3+2}=\dfrac{-4}{5}\\ \\y_Q=\dfrac{3\cdot 7+2\cdot 0}{3+2}=\dfrac{21}{5}[/tex]

Answer:

3/10

Step-by-step explanation:

Step 1 : Write the formula of calculating probability

Probability = Number of favourable outcomes/Number of total outcomes

Step 2 : Identify the favourable (requires) outcomes and the total outcomes

       12, 14, 18 = 3 cards

Step 3 : Substitute the values in the formula

Probability = Number of favourable outcomes/Number of total outcomes

Probability = 3/10

Therefore, the probability of picking a card with and even number is 3/10.

!!

Answer:

6^ (1/12)

Step-by-step explanation:

6 ^ 1/3

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

6 ^ 1/4

x^a / x^b = x^ (a-b)

6^(1/3-1/4)

Getting a common denominator)

6^(4/12-3/12)

6^1/12

Answer:

6^1/12

Step-by-step explanation:

You can rewrite the numbers as 6^1/3 and 6^1/4. Now we need common denominators on the powers. You can make the 1/3 into 4/12 and the 1/4 into 3/12. When you divide powers, you just subtract the numerators for each fraction. So you do 4-3. This leaves you with 6^1/12. Hope this helps :)

Answer:

The area of the pattern is 43.6 inches²

Step-by-step explanation:

* Lets explain how to solve the problem

- A decorative pillow can be modeled by Δ ABC

- In Δ ABC: AB = 9 inches , BC = 15 inches , AC = 10 inches

- To find the area of the triangle we can use the rule:

  A = 1/2 × (AB) × (BC) × sin∠B

- We will use the cosine rule to find the measure of angle B

∵ [tex]cos(B)=\frac{(AB)^{2}+(BC)^{2}-(AC)^{2}}{2(AB)(BC)}[/tex]

∵ AB = 9 , BC = 15 , AC = 10

∴ [tex]cos(B)=\frac{9^{2}+15^{2}-10^{2}}{2(9)(15)}=\frac{81+225-100}{270}=\frac{206}{270}=\frac{103}{135}[/tex]

∴ m∠B = [tex]cos^{-1}\frac{103}{135}=40.27[/tex]°

* Lets find the area of the triangle

∴ The area = 1/2 × (9) × (15) × sin(40.27) = 43.6 inches²

* The area of the pattern is 43.6 inches²

Answer:

A given point on a line graph represents a data point with the value of the responding variable as the height of the point at the given value of the manipulated variable on the horizontal axis.

Step-by-step explanation:

A given point in a line graph signifies a specific value of an ordered pair of variables. The x-coordinate represents one variable, and the y-coordinate another. It essentially reflects the relationship between these two variables at a particular time.

In mathematics, specifically in the field of graphs and data visualization, a given point on a line graph represents a specific value for an ordered pair of variables. The horizontal coordinate (x-value) stands for one variable, while the vertical coordinate (y-value) represents another variable.

For example, if we're graphing a student's test scores over time, the time period will be represented on the x-axis, and the test score would be represented on the y-axis. If we have a point at coordinates (3, 85), then that means the student scored 85 on their test in the third time period.

This single point, therefore, is a representation of the interaction or relation between these two variables at a particular interval.

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Answer:

It increased by 94 percent or 94%.

Answer:

162% ( to the nearest percent )

Step-by-step explanation:

The percentage change is calculated as

[tex]\frac{change}{original}[/tex] × 100%

Change = 152 - 58 = 94, so

percent change = [tex]\frac{94}{58}[/tex] × 100% = [tex]\frac{94(100)}{58}[/tex] = 162%

Answer:

[tex]\large\boxed{a(V)=\sqrt{\dfrac{3V}{8}}}[/tex]

Step-by-step explanation:

The formula of a volume of a square pyramid:

[tex]V=\dfrac{1}{3}a^2h[/tex]

a - base edge

h - height of a pyramid

We have H = 8in.

Substitute and solve for a:

[tex]\dfrac{1}{3}a^2(8)=V\\\\\dfrac{8}{3}a^2=V\qquad\text{multiply both sides by}\ \dfrac{3}{8}\\\\\dfrac{3\!\!\!\!\diagup^1}{8\!\!\!\!\diagup_1}\cdot\dfrac{8\!\!\!\!\diagup^1}{3\!\!\!\!\diagup_1}a^2=\dfrac{3}{8}V\\\\a^2=\dfrac{3V}{8}\Rightarrow a=\sqrt{\dfrac{3V}{8}}[/tex]

Answer:

Answer:

Step-by-step explanation:

The formula of a volume of a square pyramid:

a - base edge

h - height of a pyramid

We have H = 8in.

Substitute and solve for a:

diavinad8 and 53 more users found this answer helpful

Step-by-step explanation:

Answer:

The radius is 5

Step-by-step explanation:

The equation for Area of a sphere is

4pi*r^2

Since you have the area and not the radius you do the opposite of the equation so instead of multiplying you divide

100/4 = 25

Then find the square root of 25, which is 5

So your radius is 5.

Hope This Helps!!! :}

Answer: 54 bags; equation is 51=213-3x

Step-by-step explanation:

If you divid 213 by 3, you see it’s divisible and equals 71. 51 divided by 3 is 17. 71 minus 17 is 54.

Answer:

x < 54 (bags)

Step-by-step explanation:

213 - 3x < 51, or  

162 - 3x < 0, or

162 > 3x, or, finally,

162

----- > x, or x < 54 (bags)

 3

Answer:

The perimeter of the triangle is 135 cm

Step-by-step explanation:

* Lets explain how to find the perimeter of a triangle

- The perimeter of any triangle is the sum of the lengths of its three sides

- The perimeter of the scalene triangle is P = S1 + S2 + S3

- The perimeter of the isosceles triangle is P = 2S + S1

- The perimeter of the equilateral triangle is P = 3S

* Lets solve the problem

∵ The length of the 1st side is 55 cm

∴ S1 = 55 cm

∵ The length of the 2nd side is 48 cm

∴ S2 = 48 cm

∵ The length of the 3rd side is 32 cm

∴ S3 = 32 cm

∵ The triangle is scalene

∴ P = S1 + S2 + S3

∴ P = 55 + 48 + 32 = 135 cm

* The perimeter of the triangle is 135 cm

Answer:

m=22.5

Step-by-step explanation:

m is proportional to n means there is some constant k such that:

m=kn

If m=5 when n=4 then we have the following equation to solve for our constant k:

5=k(4)

5=4k

Divide both sides by 4:

5/4 =k

So k=5/4 no matter what (m,n) pair they give you where the equation is m=kn.

m=(5/4)n

What is m when n=18?

m=(5/4)(18)

m=(5/2)(9)

m=45/2

m=22.5

Final answer:

To find the value of m when n=18 for a proportional relationship where m is 5 when n is 4, calculate the constant of proportionality (k=5/4) and multiply by 18 to get m=22.5.

Explanation:

The question asks to find the value of m when n=18 given that m is proportional to n and m=5 when n=4. To solve this, we first establish the relationship between m and n using the provided values:

m = kn
(where k is the constant of proportionality)

Given that m=5 when n=4:

5 = k × 4
k = 5/4

Now we can determine the value of m when n=18 with the constant k:

m = (5/4) × 18
m = 22.5

The value of m when n is 18 is 22.5.

Answer:

[tex]7\frac{15}{16}[/tex]

Step-by-step explanation:

[tex]8-\frac{1}{16}=\frac{8}{1}-\frac{1}{16}=\frac{128}{16}-\frac{1}{16}=\frac{127}{16}=7\frac{15}{16}[/tex]

Hi there!

Simplfly 8:

[tex]8= 7 \frac{16}{16}[/tex]

Now subtract:

[tex]7-0=7[/tex]

[tex]16-1=15[/tex]

Denominator stays the same so the answer would be 7 15/16.

[tex]\bf \begin{array}{ccll} liters&gallons\\ \cline{1-2} 1&0.26\\ 5.5&x \end{array}\implies \cfrac{1}{5.5}=\cfrac{0.26}{x}\implies x=(5.5)(0.26)\implies x=1.43[/tex]

Answer:

d).2

Step-by-step explanation:

Use the following equation:

slope (m) = (y₂ - y₁)/(x₂ - x₁)

Let:

(x₁ , y₁) = (1 , -3)

(x₂ , y₂) = (2 , -1)

Plug in the corresponding numbers to the corresponding variables:

m = (-1 - (-3))/(2 - 1)

Simplify. Combine like terms. Remember to follow PEMDAS. Remember that two negatives = one positive:

m = (-1 + 3)/(2 - 1)

m = (2)/(1)

m = 2

d).2 is your slope.

~

Answer:

[tex]\displaystyle =2[/tex]

Step-by-step explanation:

The slope formula is ⇒ [tex]\displaystyle\frac{Y_2-Y_1}{X_2-X_1}[/tex]

[tex]\displaystyle Y_2=(-1)\\\displaystyle Y_1=(-3)\\\displaystyle X_2=2\\\displaystyle X_1=1\\[/tex]

[tex]\displaystyle \frac{(-1)-(-3)}{2-1}=\frac{2}{1}=2[/tex]

Therefore, the slope is 2, and the correct answer is 2.

Hope this helps!

Answer:

This is an obtuse triangle

Step-by-step explanation:

Pythagoras theorem is used to determine if a triangle is right, acute or obtuse

If the sum of squares of two shorter lengths is greater than the square of third side then the triangle is an acute triangle.

If the sum of squares of two shorter lengths is less than the square of third side then the triangle is an obtuse triangle.

If the sum of squares of two shorter lengths is equal the square of third side then the triangle is a right triangle.

so,

[tex](41)^2 = (36)^2+(9)^2\\1681 = 1296+81\\1681>1377[/tex]

As 1681>1377, the given triangle is an obtuse triangle ..

Answer:

The value of the discriminate is -27 and there are 2 complex roots

Step-by-step explanation:

* Lets explain what is discriminant

- The form of the quadratic equation is y= ax² + bx + c

- The roots of the equation is the values of x when y = 0

- There are three types of roots:

# Two different real roots

# One real root

# No real roots or two complex roots

- We can know the types of roots of the equation without solve it by

 using the discriminant which depends on the value of a , b , c

- The discriminant = b² - 4ac, where a is the coefficient of x² , b is the

  coefficient of x and c is the numerical term

# If b² - 4ac > 0, then there are two different real roots

# If b² - 4ac = 0, then there is one real root

# If b² - 4ac < 0, then there is no real root (2 complex roots)

* Lets solve the problem

∵ x² + x + 7 = 0

∴ a = 1 , b = 1 , c = 7

∵ The discriminant = b² - 4ac

∴ The discriminant = (1) - 4(1)(7) = 1 - 28 = -27

∵ -27 < 0

∴ There is no real solution there are two complex roots

* The value of the discriminate is -27 and there are 2 complex roots

Answer:

The number of roots are 2 and type of roots is complex

Step-by-step explanation:

Points to remember

Discriminant of a quadratic equation ax² + bx + c = 0

x = b² - 4ac

To find the discriminant of the given equation

Here quadratic equation be x² + x + 7 = 0

a = 1, b = 1 and c = 7

discriminant =  b² - 4ac

 =  1² - (4 * 1 * 7)

 = 1 - 28

 = -27

To find number and type of roots

Here discriminant  is negative

Therefore the number of roots are 2 and type of roots is complex

Answer:

B. See explanation

Step-by-step explanation:

Use the distance formula between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2):[/tex]

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

Find the lengths of all sides of quadrilateral DEFG:

[tex]DE=\sqrt{(-a-b-0)^2+(c-2c)^2}=\sqrt{(a+b)^2+c^2}\\ \\

EF=\sqrt{(a+-b-0)^2+(c-2c)^2}=\sqrt{(a+b)^2+c^2}\\ \\

FG=\sqrt{(a+b-0)^2+(c-0)^2}=\sqrt{(a+b)^2+c^2}\\ \\

GD=\sqrt{(-a-b-0)^2+(c-0)^2}=\sqrt{(a+b)^2+c^2}\\ \\[/tex]

All sides are of the same length. Now fond the slopes of all sides:

[tex]DE=\dfrac{2c-c}{0-(-a-b)}=\dfrac{c}{a+b}\\ \\EF=\dfrac{c-2c}{a+b-0}=-\dfrac{c}{a+b}\\ \\FG=\dfrac{c-0}{a+b-0}=\dfrac{c}{a+b}\\ \\GD=\dfrac{c-c}{-a-b-0}=-\dfrac{c}{a+b}\\ \\[/tex]

The slopes of the sides DE and FG are the same, so these sides are parallel. The slopes of the sides EF and GD are the same, so these sides are parallel.

Answer:

see below

Step-by-step explanation:

Y=x^2

x=-3            -2           -1       0       1       2        3

y=(-3)^2    (-2)^2    (-1)^2    0^2    1^2    2^2   3^2

       9           4           1         0        1         4       9

Answer:

Volume: 45000cm^3

Surface area: 6600cm^2

Step-by-step explanation:

The volume is all the side lengths multiplied, so 60*25*30 = 45,000 cm^3.

Now let's calculate the surface area.

The bottom is the width * the length, or 60*25 cm^2.

One of the sides is the length * the height, or 60*30 cm^2. This is multiplied by 2 because there are 2 of those sides.

The other pair of sides is the width * the height, or 25*30 cm^2, again multiplied by 2.

In total, the surface area is

60*25+2*60*30+2*25*30 = 6600cm^2

To fill the aquarium to the top with water, it will take 7800 cubic centimeters (cm³). To make the aquarium, it will take 7800 square centimeters (cm²) of glass.

Find the volume of the aquarium: Since there is no top to the aquarium, we will consider the volume as the combined volume of the five faces of the rectangular prism (4 faces with dimensions Length x Width and 1 face with dimensions Length x Height).

Volume = 4 * (Length * Width) + (Length * Height)

Volume = 4 * (60 cm * 25 cm) + (60 cm * 30 cm)

Volume = 4 * 1500 cm² + 1800 cm²

Volume = 6000 cm² + 1800 cm²

Volume = 7800 cm³

So, it will take 7800 cubic centimeters (cm³) of water to fill the aquarium to the top.

Find the surface area of the aquarium: To find the surface area, we will consider the area of each face and add them together.

Area of the 4 faces with dimensions Length x Width:

4 * (60 cm * 25 cm) = 4 * 1500 cm² = 6000 cm²

Area of the face with dimensions Length x Height:

(60 cm * 30 cm) = 1800 cm²

Total Surface Area = 6000 cm² + 1800 cm² = 7800 cm²

It will take 7800 square centimeters (cm²) of glass to make the aquarium.

Answer:

{x|⅘ ≠ x} → Set-Builder Notation

(-∞, ⅘) ∪ (⅘, ∞) → Interval Notation

Step-by-step explanation:

Plug the g(x) function into the f(x) function for every x you see.

Answer:

domain is the set of all real numbers except 0

Step-by-step explanation:

If f(x)=x-3/x and g(x)=5x-4

(f•g)(x) is f(x) times g(x)

multiply f(x) and g(x)

(f•g)(x) is f(x) times g(x)

Replace f(x) and g(x)

[tex]f(x) \cdot g(x)= (x-\frac{3}{x})(5x-4)[/tex]

Apply FOIL method to multiply it

multiply x inside the parenthesis

[tex]5x^2-4x[/tex]

Multiply the fraction inside the parenthesis

[tex]-5 +\frac{12}{x}[/tex]

[tex]5x^2-4x -5 +\frac{12}{x}[/tex]

We have x in the denominator . Domain is the set of x value for which the function is defined.

When denominator x is 0 then the function is undefined

So domain is the set of all real numbers except 0

Answer:

The measure of angle AXY is 55°

Step-by-step explanation:

we know that

If ray XY bisects AXB

then

∠AXY=∠YXB=∠AXB/2

therefore

∠AXY=110°/2=55°

see the attached figure to better understand the problem

Answer:

Hi there!

The answer to this question is: A

y= [x] + 5

Answer:

D

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The question has no division answer. That makes C and D incorrect.

A for some reason is backwards. It makes no sense to use that. You are left with B. The reason A or B  is correct is that the burn of calories must get larger with an increase in hours.

Using the quadratic formula x = (-b ± √(b^2 - 4ac)) / (2a) to find the solutions, which are (13 + √185) / 2 and (13 - √185) / 2.

To find the solutions of the equation x^2 = -13x - 4, we can rearrange it to the form ax^2 + bx + c = 0.

In this case, we have a = 1, b = -13, and c = -4.

We can then use the quadratic formula x = (-b ± √(b^2 - 4ac)) / (2a) to find the solutions.

Substituting the values into the formula, we get x = (-(-13) ± √((-13)^2 - 4(1)(-4))) / (2(1)). Simplifying further, we have x = (13 ± √(169 + 16)) / 2. T

herefore, the solutions of the equation are x = (13 + √185) / 2 and x = (13 - √185) / 2.

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[tex]8v-6j-10v+8j =2j-2v[/tex]