A granola bite contains 27 calories. Most of the calories come from c grams of carbohydrates. The rest come from other ingredients. One gram of carbohydrate contains 4 calories. The equation 4c + 5 = 27 represents the relationship between these quantities. Step 1: Answer the following questions: a. What could the 5 represent in this situation? b. Priya said that neither 8 nor 3 could be the solution to the equation. Explain why she is correct. c. Find the solution to the equation.

Answer:

xy = [tex]\frac{2}{5}[/tex]

Step-by-step explanation:

Given the reciprocal of x is 0.25, that is [tex]\frac{1}{4}[/tex] then

x = [tex]\frac{1}{\frac{1}{4} }[/tex] = 4

Given the reciprocal of y is 10 then

y = [tex]\frac{1}{10}[/tex]

xy = 4 × [tex]\frac{1}{10}[/tex] = [tex]\frac{4}{10}[/tex] = [tex]\frac{2}{5}[/tex]

Answer:

2/5=0.4

Step-by-step explanation:

[tex]\frac{1}{x}\\[/tex]=0.25 ==> x=4

[tex]\frac{1}{y}\\[/tex]=10    ==> y=1/10

Now multiply both x and y

xy=4(1/10)=2/5=0.4

Answer:

Since there are no common factors, the only common factor for [tex]\frac{4}{x+5}[/tex] is  1

Answer:

[tex]k=4[/tex]

Step-by-step explanation:

So we have the graphs of f(x) and g(x).

And we know that g(x) is defined as  f(kx), where k is some constant.

First, from the graph we can note two points:

For g(x), we have the point (1,10) and for f(x), we have the point  (4,10).

In other words:

[tex]g(1)=10[/tex]

And since we know the g(x) is f(kx), this means that:

[tex]g(1)=10\\g(1)=10=f(1(k))=10[/tex]

And we know the for f(x) to be 10, the initial value is 4. Therefore:

[tex]f(1(k))=10=f(4)\\1k=4\\k=4[/tex]

Therefore, the value of k is 4.

Answer:

[tex]\huge \boxed{k=4}[/tex]

Step-by-step explanation:

The graph of g(x) crosses the point (1, 10).

The graph of f(x) crosses the point (4, 10).

So, g(1) = 10. The x (input) is 1. The output is 10.

f(4) = 10. The x (input) is 4. The ouput is 10.

g(1) = f(4)

g(x) = f(k ⋅ x)

g(1) = f(k ⋅ 1)

f(k ⋅ 1) = f(4)

k ⋅ 1 = 4

k = 4

Answer:

Step-by-step explanation:

Add like terms. 3x & 7x are like terms

3x +7x - 2 = 10x - 2

Answer:

0.2

Step-by-step explanation:

3x+7x-2

3x+7x-2=0

3x+7x=2

10x=2

x=2/10

x=[tex]\frac{1}{5}[/tex]

Answer:

75.9 km/hr

Step-by-step explanation:

Distance between the highway and farmhouse is given as = 2km = a

The distance after the intersection and the highway = b

Let the distance between the farmhouse and the car = c

Using the Pythagoras Theorem rule

c² = a² + b²

c² = 2² + b²

Step 1

Since distance is involved, time is required. Hence, we differentiate the equation above in respect to time

c² = 2² + b²

dc/dt (2c) = 4 + 2b

dc/dt =[ b/(√b² + 4)] × db/dt

We are told in the question that:

the car travels past the farmhouse on on the highway at a speed of 80 km/h.

We are asked to calculate the speed at which the distance between the car and the farmhouse kept increasing when the car is 6 km past the intersection of the highway and the road.

This calculated using the obtained differentiation above:

dc/dt = [ b/(√b² + 4)] × db/dt

Where b = 6km

db/dt = 80km/hr

[6/(√6² + 4)] × 80km/hr

6/√36 + 4 × 80km/hr

6 × 80/√40

480/√40

= 75.894663844km/hr

Approximately = 75.9km/hr

In this exercise we want to calculate the speed of the vehicle to reach the farm, in this way we will find a speed of approximately:

[tex]75.9 km/hr[/tex]

To start this exercise we have to use some data informed in the text, like this:

Since distance is involved, time is required. Hence, we differentiate the equation above in respect to time

[tex]c^2 = 2^2 + b^2\\\frac{dc}{dt} (2c) = 4 + 2b\\\frac{dc}{dt} =[ b/(\sqrt{b^2} + 4)] ( \frac{db}{dt})[/tex]

Calculate the speed at which the distance between the car and the farmhouse kept increasing when the car is 6 km past the intersection of the highway and the road. This calculated using the obtained differentiation above:

[tex]\frac{dc}{dt} = [ 6/(\sqrt{6^2} + 4)] (80)\\=6/\sqrt{36} + 4 * 80\\=6 * 80/\sqrt{40} \\=480/\sqrt{40} \\= 75.9km/hr[/tex]

See more about speed at brainly.com/question/312131

Answer:

(0, -2), (1, -3), (2, -2) y (3, 7) son pares ordenados de [tex]f(x) = x^{3}-2\cdot x^{2}-2[/tex].

Step-by-step explanation:

Un par ordenado es un elemento de la forma [tex](x,f(x))[/tex], donde [tex]x[/tex] es un elemento del dominio de la función, mientras [tex]f(x)[/tex] es la imagen de la función evaluada en [tex]x[/tex]. Entonces, un par ordenado que está contenido en la citada función debe satisfacer la siguiente condición:

La imagen de la función existe para un elemento dado del dominio. Esto es:

[tex]x \rightarrow f(x)[/tex]

Dado que [tex]f(x)[/tex] es una función polinómica, existe una imagen para todo elemento [tex]x[/tex]. Ahora, se eligen elementos arbitrarios del dominio para determinar sus imágenes respectivas:

x = 0

[tex]f(0) = 0^{3}-2\cdot (0)^{2}-2[/tex]

[tex]f(0) = -2[/tex]

(0, -2) es un par ordenado de [tex]f(x) = x^{3}-2\cdot x^{2}-2[/tex].

x = 1

[tex]f(1) = 1^{3}-2\cdot (1)^{2}-2[/tex]

[tex]f(1) = -3[/tex]

(1, -3) es un par ordenado de [tex]f(x) = x^{3}-2\cdot x^{2}-2[/tex].

x = 2

[tex]f(2) = 2^{3}-2\cdot (2)^{2}-2[/tex]

[tex]f(2) = -2[/tex]

(2, -2) es un par ordenado de [tex]f(x) = x^{3}-2\cdot x^{2}-2[/tex].

x = 3

[tex]f(3) = 3^{3}-2\cdot (3)^{2}-2[/tex]

[tex]f(3) = 7[/tex]

(3, 7) es un par ordenado de [tex]f(x) = x^{3}-2\cdot x^{2}-2[/tex].

(0, -2), (1, -3), (2, -2) y (3, 7) son pares ordenados de [tex]f(x) = x^{3}-2\cdot x^{2}-2[/tex].

Answer:

10.58 feet

Step-by-step explanation:

Hello!

If you think about how it would look in life you will notice that it looks like a right triangle which means we can use the Pythagorean theorem to find the far the ladder needs to be from the house.

The Pythagorean theorem is [tex]a^{2}+ b^{2}= c^{2}[/tex]

a is a leg

b is the other leg

c is the hypotenuse

Since the ladder has to go from the ground to the window ledge it is the hypotenuse and the window ledge is a leg

Put in what we know

[tex]a^{2} +12^{2} =16^{2}[/tex]

Now we solve for a

Simplify

a^2 + 144 = 256

Subtract 144 from both sides

a^2 = 112

Take the square root of both sides

a = 10.583

The answer is 10.58 feet

Hope this helps!

Answer:

11 ft

Step-by-step explanation:

Try to imagine it or draw it out to help you. The ladder is 16 feet long and the window ledge is 12 feet high, so this is a right triangle.

The ladder is the hypotenuse, so use the given values in the pythagorean theorem.

a^2 + b^2 = c^2

12 + b^2 = 16

b = 11

12^2 + 11^2 = 16^2

1 44 + 121 = 265

√265 = 16

Answer:

B

Step-by-step explanation:

Any number, regardless of its sign, raised to an even power will always be positive. Therefore, a⁷² will be positive. We know that -3/7 is negative, and since a positive times a negative is negative, the answer will be negative.

Answer:

<o=180-132=48

so,<s=24(The angle at the circumference is half of its corresponding angle at center)

Step-by-step explanation:

hi the answer is x= 3/5

i have added 2 methods of solving it in the above picture. ask me if you have any questions

Answer:

x = 3/5

Step-by-step explanation:

This equation can be solved with algebraic techniques. We will simplify the equation by combining like terms and then use algebraic techniques in order to solve for x.

2(x - 4) + 2x = -6x - 2 Use the distributive property.

2x - 8 + 2x = -6x - 2 Combine like terms (variable terms first).

4x - 8 = -6x - 2 Add 6x to both sides of the equation.

10x - 8 = -2 Add 8 to both sides of the equation.

10x = 6 Divide by 10 on both sides of the equation.

x = 6/10 Simplify the fraction.

x = 3/5

Answer:

The average rate of change for the given function in the interval (-5, -1) is 0 (zero)

Step-by-step explanation:

The average rate of change of a function over an interval is the quotient between the difference between the function evaluated at the ends of the interval divided by the length of the interval. That is for our case:

the average rte of change of h(t) in the interval (-5, -1) is:

[tex]\frac{h(-1)-h(-5)}{-1+5}[/tex]

so we find:

[tex]h(-1)=(-1+3)^2+5=2^2+5=4+5=9\\and\\h(-5)=(-5+3)^2+5=(-2)^2+5=4+5=9[/tex]

then the average rate of change becomes:

[tex]\frac{h(-1)-h(-5)}{-1+5}=\frac{9-9}{4} =\frac{0}{4} =0[/tex]

Answer:

-9

Step-by-step explanation:

Two negatives when adding them together make a negative.

Answer:

(-5)+(-4) = -9

Step-by-step explanation:

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1

<------------

Answer:

0 < k < 2

Step-by-step explanation:

In the first quadrant both of x and y get positive values, so

And replacing x with 2k in the second equation:

Since y > 0:

Combining both k > 0 and k < 2, we get:

Answer:

  0 < k < 2

Step-by-step explanation:

The intersection will lie in the first quadrant when the solution has the characteristics: x > 0, y > 0.

For x > 0, we require ...

  x = 2k

  x > 0

  2k > 0 . . . . substitute for x

  k > 0 . . . . . divide by 2

__

For y > 0, we require ...

  y = (12 -3x)/2

  y = (12 -3(2k))/2 = 6 -3k . . . . . substituted for x and simplify

  y > 0

  6 -3k > 0 . . . . . . substitute for y

  2 -k > 0 . . . . . . . divide by 3

  k < 2 . . . . . . . . . add k

So, the values of k that result in the intersection being in the first quadrant are ...

  0 < k < 2

Answer:

Step-by-step explanation:

1). 6x + 7 - 18x + 4

  = (6x - 18x) + (7 + 4)

  = -12x + 11

2). 5x - 7x + 5x + 4 - 9

  = (5x + 5x - 7x) + (4 - 9)

  = 3x - 5

3). 3x + 8y - 5x + 3y

  = (3x - 5x) + (8y + 3y)

  = -2x + 11y

4). 17x² - 7x²- 5x + 3x + 14

  = (17x² - 7x²) + (-5x + 3x) + 14

  = 10x² - 2x + 14

5). 3xy - 9xy - 5x + 4x - 7 + 3

  = (3xy - 9xy) + (-5x + 4x) + (-7 + 3)

  = -6xy - x - 4

6). 9x + 7y - 15x + 4x - 9y

  = (9x - 15x + 4x) + (7y - 9y)

  = -2x - 2y

7). 3x + 7 - 5x - 8y + 4x - 2y + 7

  = (3x - 5x + 4x) + (-8y - 2y) + 14

  = 2x - 10y + 14

8). 3xy - xy + 15x + 4 - 11

  = (3xy - xy) + 15x + (4 - 11)

  = 2xy + 15x - 7

9). -8x + 3x + 7y - 5x + 4y - 2

  = (-8x - 5x + 3x) + (7y + 4y) - 2

  = -10x + 11y - 2

10). 3x² + 6x - 3y + 2x - 7

  = 3x² + (6x + 2x) - 3y - 7

  = 3x² + 8x - 3y - 7

Answer:

40 feet

Step-by-step explanation:

We know that the area of a rectangle is represented as [tex]lw=a[/tex], where l is the length and w is the width.

We already know the width, and we know the area, so we can plug these values into the equation.

[tex]l\cdot 6 = 240[/tex]

Our goal is to now isolate the variable l, and to do this we can divide both sides by 6.

[tex](l\cdot6) \div6 = 240\div6\\\\l = 40[/tex]

Hope this helped!

Answer:

l=a/w

Step-by-step explanation:

Length equals area divided by width.

Solution:

x+9=13

then,

13-9=4

so the value of x is 4

Answer:

Step-by-step explanation:

X +9 equals 13

X+9 =13

X=13 - 9

X= 4

[tex]hope \: this \: helps[/tex]

[tex]have \: a \: nice \: life! :) [/tex]

Answer:

4

Step-by-step explanation: midpoint means between so from 1 to b the midpoint is 4

Answer:

[tex]96ft^{3}[/tex]

Step-by-step explanation:

Step 1: Find area of base

[tex]\frac{bh}{2}=\frac{(6)(8)}{2} =\frac{48}{2}=24ft^{2}[/tex]

Step 2: Find Volume

[tex]V=\frac{1}{3} (24)12\\V=\frac{1}{3} (288)\\V=96ft^{3}[/tex]

Therefore the volume of the triangular pyramid is [tex]96ft^{3}[/tex]

The volume of the triangular pyramid will be 96 cubic feet.

Let h be the height of the pyramid, l be the slant height and A be the base area of the pyramid.

Then the volume of the pyramid will be

Volume = (1/3) × A × h

The base area of the triangular pyramid is calculated as,

A = 1/2 x 6 x 8

A = 3 x 8

A = 24 square feet

Then the volume of the triangular pyramid is calculated as,

V = 1/3 x 24 x 12

V = 8 x 12

V = 96 cubic feet

The volume of the triangular pyramid will be 96 cubic feet.

More about the volume of the pyramid link is given below.

https://brainly.com/question/17615619

#SPJ2

Answer:

Answer:

72°

Step-by-step explanation:

Start by putting the information you’re given into an equation. The angle measure is 4 times the compliment so it has the measure 4x.

Complementary angles are two angels with a sum of 90°.

So our equation will be 4x + x = 90

Add your like terms to get 5x = 90

Divide 90 by 5 to get x by itself.

X = 18

Since the angle we’re trying to find is 4 times the compliment you’re going to multiply 18 by 4 which will give you your answer of 72°

Answer:

25 miles

Step-by-step explanation:

We need to convert 30 minutes to hours

30 minutes * 1 hour/ 60 minutes = .5 hours

distance = speed x time

distance = 50 mph * .5 hours

             = 25 miles

Answer: 117?

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find g-¹( 2) we must first find g-¹(x)

To find g-¹(x) equate g(x) to y

That's

y = g(x)

We have

y = - 2x + 7

Now interchange the terms that's x becomes y and y becomes x

We have

x = - 2y + 7

Make y the subject in order to find g-¹(x)

Move 7 to the left side of the equation

- 2y = x - 7

Multiply both sides by - 1

We have

2y = 7 - x

Divide both sides by 2 to make y stand alone

That's

So we have

Now to find g-¹(- 2) substitute the value of x that's - 2 into the expression

We have

We have the final answer as

Hope this helps you

Answer:

-10

-12

Step-by-step explanation:

Step-by-step explanation:

The solution of the line x<5

Inequalities are used to represent unequal expressions

The solution to the inequality [tex]4x + 20 < 40[/tex] is [tex]x < 5[/tex]

The inequality is given as:

[tex]4x + 20 < 40[/tex]

Subtract 20 from both sides of the inequalities

[tex]4x < 20[/tex]

Divide both sides of the inequalities by 4

[tex]x < 5[/tex]

This means that the solution to the inequality [tex]4x + 20 < 40[/tex] is [tex]x < 5[/tex]

See attachment for the number line

Read more about inequalities at:

https://brainly.com/question/18881247

Answer: False!

This equation is in slope - intercept form, where y = mx + b. B is the y - intercept and m is the slope. They got the location of the y - intercept right, but they forgot to add the negative. It's actually -8.

Hope this helps!

The y-intercept is -8 as the minus always stays with the number to the right of it

Answer:

  B

Step-by-step explanation:

The square of 1 is 1, so 1 is less than the square root of 3.

The square of 2 is 4, so 2 is more than the square root of 3.

The point that lies between 1 and 2 is the best approximation of √3.

Answer:

B

Step-by-step explanation:

=========================================

Work Shown:

f(x) = x^2 - 2x

f(2) = 2^2 - 2*2 ... replace every x with 2

f(2) = 4 - 4

f(2) = 0

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

g(x) = 12-8x

g(3) = 12-8*3 ... replace every x with 3

g(3) = 12-24

g(3) = -24

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

Subtract the results of the previous two sections

f(2) - g(3) = 0 - (-24)

f(2) - g(3) = 0 + 24

f(2) - g(3) = 24