Find the slope and initial value of the graph below. Then write the equation of the line. Write the equation of the line.

The number of gallons of the 35% acid solution eli should add is; 0.125 gallons

From the given table, since Eli wants to combine 0.5 gallon of a 10% acid solution with some 35% acid solution to make a 15% acid solution, then we can say that;

(0.10)(0.5) + 0.35g = 0.15(g + 0.5)

where g is number of gallons

Now,  for us to determine how many gallons of the 35% acid solution eli should add, we will solve the word problem earlier to get;

(0.10)(0.5) + 0.35g = 0.15(g + 0.5)

⇒ 0.05 + 0.35g = 0.15g + 0.075

⇒ 0.35g - 0.15g = 0.075 - 0.005

⇒ 0.2g = 0.025

g = 0.025/0.2

g = 0.125 g

Read more about Algebra Simplification at; https://brainly.com/question/723406

#SPJ1

The coefficient of (3y² + 9)5 is 15.

A polynomial is of the form a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² + ... + aₙ₋₁x + aₙ.

Here, x is the variable, aₙ is the constant term, and a₀, a₁, a₂, ..., and aₙ₋₁, are the coefficients.

a₀ is the leading coefficient.

In the question, we are asked to identify the coefficient of (3y² + 9)5.

First, we expand the given expression:

(3y² + 9)5

= 15y² + 45.

Comparing this to the standard form of a polynomial, a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² + ... + aₙ₋₁x + aₙ, we can say that y is the variable, 15 is the coefficient, and 45 is the constant term.

Thus, the coefficient of (3y² + 9)5 is 15.

Learn more about the coefficients of a polynomial at

https://brainly.com/question/9071229

#SPJ1

[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]

Step-by-step explanation:

To find an unknown side of a right angled triangle we use a theorum called pythagorus theorum..

(Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2

(h)^2 = (p)^2 + (b)^2

(a) hypotenuse = x cm, base = √30 cm, perpendicular = √12 cm.

→ h^2 = p^2 + b^2

→ (x)^2 = (√12)^2 + (√30)^2

→ x^2 = 12 + 30

→ x^2 = 42

→ x = √42

→ x = 6.480...

→ x = 6.5 cm. (approx)

(b) hypotenuse = √300 cm, base = √200 cm,perpendicular = x cm.

→ h^2 = p^2 + b^2

→ (√300)^2 = (x)^2 + (√200)^2

→ 300 = x^2 + 200

→ x^2 = 300 – 200

→ x^2 = 100

→ x = √100

→ x= 10 cm.

(c) hypotenuse = √66 cm, base = √17 cm,perpendicular = x cm.

→ h^2 = p^2 + b^2

→ (√66)^2 = (x)^2 + (√17)^2

→ 66 = x^2 + 17

→ x^2 = 66 – 17

→ x^2 = 49

→ x = √49

→ x = 7 cm.

(d) hypotenuse = x cm, base = 5√12 cm,perpendicular = 2√3 cm.

→ h^2 = p^2 + b^2

→ (x)^2 = (2√3)^2 + (5√12)^2

→ x^2 = 12 + 50

→ x^2 = 62

→ x = √62

→ x = 7.874...

→ x = 7.9 cm. (approx)

For the expression to be equal to the original one, we have;

[(x + 1) * 5(x - 1)(x + 4)]/[(x - 1) * 7x]

We are given the algebraic expression;

(5x² + 25x + 20)/(7x)

Now, looking at the numerator, a common factor to all terms is 5. Thus, we will factorize it out to get;

5(x² + 5x + 4) = 5((x + 1)(x + 4))

Now, we see that the expression that simplifies the algebra is given as;

[(x² + 2x + 1) * ( )]/[( ) * (7x² + 7x)]

Now, the numerator and denominator can be factorized to get;

[(x + 1)(x + 1) * ( )]/[( ) * 7x(x + 1)]

Thus, x + 1 will cancel out to get;

[(x + 1) * ( )]/[( ) * 7x]

For the expression to be equal to the original one, we have;

[(x + 1) * 5(x - 1)(x + 4)]/[(x - 1) * 7x]

Read more about Algebraic Expressions at; https://brainly.com/question/723406

#SPJ1

[tex]\textbf{Heya !}[/tex]

✏[tex]\bigstar\textsf{Given:-}[/tex]✏

✏[tex]\bigstar\textsf{To\quad find:-}[/tex]✏

▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪

✏[tex]\bigstar\textsf{Solution\quad steps:-}[/tex]✏

First, subtract both sides by 7:-

[tex]\sf{-\cfrac{y}{4} > -1-7}}[/tex]

[tex]\sf{-\cfrac{y}{4} > -8}[/tex]

Now multiply both sides by 4:-

[tex]\sf{-y > -8*4}[/tex]

[tex]\sf{-y > -32}[/tex]

last step:-

[tex]\sf{y < 32}[/tex]

`hope it was helpful to u ~

[tex] \implies \: \sf{ - \dfrac{y}{4} \: + \: 7 \: > \: - 1} \\ \\ \implies \: \sf{ - \dfrac{y}{4} \: > \: - 7 \: - 1} \\ \\ \implies \: \sf{ - \dfrac{y}{4} \: > \: - 8} \\ \\ \implies \: \sf{ \cancel- \: \dfrac{y}{4} \: > \: \cancel- \: 8} \\ \\ \implies \: \sf{ \dfrac{y}{4} \: < \: 8} \\ \\

\implies \: \sf{ y \: < \: 8 \times 4} \\ \\ \implies \: \bf{ y \: < \: 32}[/tex]

The measure of side c is 9 cm. The correct option is the last option 9 cm

From the question, we are to determine the measure of side c

From the law of sines, we have that

[tex]\frac{c}{sinC} =\frac{b}{sinB}[/tex]

From the given information,

b = 11 cm

B = 80°

C = 54°

Putting the parameters into the equation, we get

[tex]\frac{c}{sin54^\circ} =\frac{11}{sin80^\circ}[/tex]

[tex]c =\frac{11\times sin54^\circ}{sin80^\circ}[/tex]

c = 9.03647

c ≈ 9 cm

Hence, the measure of side c is 9 cm. The correct option is the last option 9 cm

Learn more on Law of sines here: https://brainly.com/question/15140698

#SPJ1

Given the dimension of the length and area of the rectangle, the dimension of the breadth x is 9in.

Hence, option A is the correct answer.

This question is incomplete, the missing diagram is uploaded along this answer below.

Area of a rectangle is expressed as; A = l × b

Given that;

A = l × b

180in² = 20in × x

x = 180in² / 20in

x = 9in

Given the dimension of the length and area of the rectangle, the dimension of the breadth x is 9in.

Hence, option A is the correct answer.

Learn more about area of rectangle here: brainly.com/question/12019874

#SPJ1

The quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively as 3 /2 and 5 is 2x² - 3x + 10

A quadratic polynomial is a polynomial of the form ax² + bx + c

For any given quadratic polynomial we have

x² - (sum of zeros)x + (products of zeros) = 0

Given that the sum and product of its zeroes respectively 3/2 and 5,

We have that

Substituting the values of the variables into the equation, we have

x² - (sum of zeros)x + (products of zeros) = 0

x² - (3/2)x + (5) = 0

x² - (3/2)x + (5) = 0

Multiplying through by 2, we have

2 × x² - 2 × (3/2)x + 2 × (5) = 0 × 2

2x² - 3x + 10 = 0

So, the quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively as 3/2 and 5 is 2x² - 3x + 10

Learn more about quadratic polynomial here:

https://brainly.com/question/7784687

#SPJ1

a) The fire is out of the reach of helicopter 1.

b) Only helicopter 3 can be sent to stop the fire.

We have both the location of the fire and the initial position of the three helicopters set on a Cartesian plane. The locations are listed below:

The distance is found by the straight line distance formula, an application of Pythagorean theorem:

a) [tex]d = \sqrt{[1 - (- 3)]^{2}+[4-(-5)]^{2}}[/tex]

[tex]d = \sqrt{4^{2}+9^{2}}[/tex]

[tex]d = \sqrt{97}[/tex]

d ≈ 9.849

The fire is out of the reach of helicopter 1.

b) Helicopter 2

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

[tex]d = \sqrt{1^{2}+8^{2}}[/tex]

[tex]d = \sqrt{65}[/tex]

d ≈ 8.062

Helicopter 3

[tex]d = \sqrt{[4 - (- 3)]^{2}+ [- 2 - (-5)]^{2}}[/tex]

[tex]d = \sqrt{7^{2}+3^{2}}[/tex]

[tex]d = \sqrt{58}[/tex]

d ≈ 7.616

Only helicopter 3 can be sent to stop the fire.

To learn more on Pythagorean theorem: https://brainly.com/question/26183488

#SPJ1

Answer:

  (c)  f(x) = 3(x -3)(x -7)

Step-by-step explanation:

The correct function can be chosen by looking at the x-intercepts and the behavior around the vertex.

The graph crosses the x-axis at x=3 and x=7. Each x-intercept x=p gives rise to a factor (x -p). These two x-intercepts mean the function will have factors ...

  (x -3)(x -7) . . . . . . . . eliminates choices A and D

The vertical scale factor of the quadratic is easily found by looking at the function behavior near the vertex. Specifically, the scale factor is the change in y-value at a distance of 1 unit either side of the vertex.

Here, the y-value at the vertex (x=5) is -12. The y-value at x=4 and x=6 is -9, three units up from the value at the vertex. This means the vertical scale factor (leading coefficient) is 3. (This eliminates choice B.)

Putting these observations together, we have determined the equation of the function to be ...

  f(x) = 3(x -3)(x -7) . . . . . . matches choice C

The height of package is 34 inches.

According to the statement

we have given that the perimeter of cylinderical package is 123 inches.

and we have to find the volume of this package.

So,

According to the perimeter

2(Pi)r + h = 123

and then

h = 123 - 2(Pi)r

then the volume become

V = (Pi) r^2h

V= (Pi) r^2 * [ 123 - 2(Pi)r ] = 123 (Pi) r^2  - 2(Pi)r^3

then differentiate it

dV/dr = 246(Pi) r - 6(Pi)r^2

Now take

r(246(Pi) - 6(Pi)r) = 0

then neglect r=0 and then find another value of r.

r = 246(Pi) / 6(pi)

here r=41 then

h = 123 - 2(Pi)r

h = 123 - 2(3.14)41

h = 123 - 2(Pi)r

Then put the value of r then h = 34 inches.

So, The height of package is 34 inches.

Learn more about Volume here https://brainly.com/question/1972490

#SPJ4

An integrated transcriptomic and epigenomic analysis identifies the CD44 gene as a potential biomarker for weight loss within an energy-restricted program: TRUE

Therefore, the statement "an integrated transcriptomic and epigenomic analysis identifies the CD44 gene as a potential biomarker for weight loss within an energy-restricted program" is TRUE.

Know more about weight loss here:

https://brainly.com/question/1519447

#SPJ4

Complete question:

An integrated transcriptomic and epigenomic analysis identifies the CD44 gene as a potential biomarker for weight loss within an energy-restricted program. TRUE or FALSE

Answer:

B is the answer

Step-by-step explanation:

Answer:

probability of all the four women chosen over people needed in a committee=4 over 4 =1

[tex]\textbf{Heya !}[/tex]

basic math tips -»

"of" means multiply

[tex]\sf{\cfrac{1}{10}\cdot\cfrac{5}{1}}[/tex]

multiply the numerators and denominators times each other -»

[tex]\sf{\cfrac{5}{10}}[/tex]

reduce:-

[tex]\sf{\cfrac{1}{2}}[/tex]

`hope it was helpful to u ~

See below for the solution to each question

Yes, the graph is a function.

This is because all x values have different y values

This is the set of input values of the graph.

From the graph, we have

x = 0 to x = 17

Hence, the domain is [0, 17]

This is the set of output values of the graph.

From the graph, we have

y = 0 to y = 10

Hence, the range is [0, 10]

This is the maximum point on the graph.

From the graph, we have

Maximum = (12, 10)

This is the minimum point on the graph.

From the graph, we have

Minimum = (0, 0)

These are the intervals where the y values increase as x increase.

From the graph, we have

Increasing intervals = (0, 5) ∪ (10, 12) ∪ (14, 15)

These are the intervals where the y values decrease as x increase.

From the graph, we have

Decreasing intervals = (7, 10) ∪ (12, 14) ∪ (15, 17)

These are the intervals where the y values remain unchanged as x changes.

From the graph, we have

Constant intervals = (5, 7)

Read more about functions at

https://brainly.com/question/1600302

#SPJ1

Answer:

Answer should be 15

Step-by-step explanation:

25 divided by 15 is 1.6666666667 so if use that multiply 9 you'll get 15.

Answer:

Step-by-step explanation:

A^2 + B^2=C^2

30^2 -25^2= 16.5

answer= 16.5

Answer:

[tex]69 = 6x - 8[/tex]

Step-by-step explanation:

All 3 numbers must sum to 69, so we can draw out the second option [tex]x = 6x - 8[/tex]

Let the first number be x, adding 5x to the first x would give you 6x for the sum of the first and third numbers, therefore you can remove [tex]69 = 7x - 8[/tex] from your considerations as it includes 7x not 6x.

This leaves you with the one final answer [tex]69 = 6x - 8[/tex]

The Law of sines defines that in a triangle, (Sin A)/a = (Sin B)/b = (Sin C)/c and as per law of sines the length of BC is 24.

The given triangle is ΔABC, we split the given triangle into two right-angled triangle ΔABD and ΔBCD.

In the triangle ΔABD,

sin θ = opposite side/hypotenuse

sin A=BD/AB

BD=(sin A)/AB

And in the triangle ΔBCD,

sin θ = opposite side/hypotenuse

sin B=BD/BC

BD=(sin B)/BC

Hence, BD=(sin A)/AB=(sin B)/BC

Let say, (sin A)/a=(sin B)/b

As per law of sine, (sin A)/a=(sin B)/b

Then,

(sin 46°)/a=(sin 31°)/17

a=(17 × sin 46°)/(sin 31°)

a=23.74

a=24

Hence, the value of BC, rounded to the nearest tenth of a unit is 24.

Learn more about law of sine at

https://brainly.com/question/13983159

#SPJ1

The system of equation have an infinite solution.

6x   = -6y - 30

-3x -3y = 15

Therefore, let's rearrange the system of equations.

6x + 6y = -30

-3x - 3y = 15

multiply equation(ii) by 2

6x + 6y = -30

-6x - 6y = 30

add the equations

0 = 0

Since 0 = 0 for any value of x, the system of equations has infinite solutions.

learn more on equations here: https://brainly.com/question/14943216

#SPJ1

Answer:

(f - g)(300) = $1,300 is the profit made from 300 tablets

Step-by-step explanation:

(f - g)(300) is the profit made from 300 tablets

(f - g)(x) = (3 x + 6,000) - (20 x - 400)

- Simplify it

(f - g)(x) = 3 x + 6,000 - 20 x + 400

- Add like terms

(f - g)(x) = -17 x + 6,400

Substitute x by 300

(f - g)(300) = -17(300) + 6,400

(f - g)(300) = -5,100 + 6,400

(f - g)(300) = $1,300

The profit is $1,300

The equivalent expression is:

[tex](m^5)^{1/2} = \sqrt{m^5}[/tex]

Which is the one in option A.

Here we start with the expression:

[tex]m^{5/2}[/tex]

Now, remember that:

[tex]\sqrt{x} = x^{1/2}[/tex]

[tex](x^a)^b = x^{a*b}[/tex]

if we define a = 5 and b = 1/2, we get:

[tex]m^{5/2} = (m^5)^{1/2}[/tex]

Using the first property, we get:

[tex](m^5)^{1/2} = \sqrt{m^5}[/tex]

Then we conclude that the correct option is A.

If you want to learn more about equivalent expressions:

https://brainly.com/question/2972832

#SPJ1

The friend's probability of beating the next level on her first attempt are 22.5 percent.

Describe probability.

To forecast how likely occurrences are to occur, probability has been introduced in mathematics. This is the fundamental theory of probability, which is also applied to the probability distribution, and from which you will discover the likelihood of results for a random experiment.

This idea is used to discuss the probability or likelihood of an event happening.

The frequency of the number 8 is seven.

The frequency of the number 9 is 11.

The full list of frequencies is provided as

10 + 9 + 6+ 7 + 8 + 12 + 4 + 6 + 7 + 11 = 80

7 + 11 = 18

18/80 is the probability.

= 0.225 x 100

22.5 percent

Click here to learn more about probability:

brainly.com/question/251701

#SPJ4

Using proportions, it is found that the boat can go 6 m/s in still water.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, we have that:

He goes twice as fast down the river, hence:

v + 2 = 2(v - 2).

v + 2 = 2v - 4

2v - v = 2 + 4

v = 6.

The boat can go 6 m/s in still water.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Answer:

  (d)  f(x) = -x²

Step-by-step explanation:

For the vertex of the quadratic function to be at the origin, both the x-term and the constant must be zero. That is, the function must be of the form ...

  f(x) = a(x -h)² +k . . . . . . . . . . vertex form; vertex at (h, k)

  f(x) = a(x -0)² +0 = ax² . . . . . vertex at the origin, (h, k) = (0, 0)

Of the offered answer choices, the only one with a vertex at the origin is ...

  f(x) = -x² . . . . . a=-1

Answer:

1. a = 32, c = 24

Step-by-step explanation:

a = c+8

a-20 = 3(c-20)

(c+8)-20 = 3c-60

c = 24

a = 24+8

a = 32

2. t = 15, j = 9

t-3 = 2(j-3)

t-3 = 2j-6

t = 2j-3

t + 2 + j + 2 = 28

(2j-3)+ 2 + j + 2 = 28

3j + 1 = 28

3j = 27

j = 9

t-3 = 2(9-3)

t-3 = 2(6)

t-3=12

t = 15

3. b=36, s=31

b = s + 5

b+s = 67

(s+5)+s = 67

2s+5 = 67

2s = 62

s = 31

b = 31+5

b = 36

4. 231

h + t + u = 6

(with h=hundreds digit, t=tens digit, u=units digit)

h = 2u

t = h+u

t = (2u) + u

(2u) + (2u +u) + u = 6

6u = 6

u = 1

h = 2

t = 3

the number is 231

5. 48

u = 2t

the 2-digit number is 10t+u

2(10t+u) = 10u+t+12

2(10t + 2t) = 10(2t) + t + 12

20t + 4t = 20t + t + 12

24t = 21t + 12

3t = 12

t = 4

u = 2*4

u = 8

the number is 48

The domain of the function will therefore be 0≤x<∞

Domain of a function are the independent value for which a function exists. Given the function below;

f(x) = [tex]\sqrt[4]{x}[/tex]

Since the value in the root cannot be negative hence the domain of the function will be all positive real numbers.

The domain of the function will therefore be 0≤x<∞

Learn more on domain here: https://brainly.com/question/25959059

#SPJ1

If Angle A ≅ Angle T, then the triangles would be congruent by ASA

If Angle B ≅ Angle P, then the triangles would be congruent by AAS.

We are told that;

Sides AC and TQ are congruent.

Angles BCA and  PQT are congruent.

Thus, we can say that;

Side AC and side TQ are congruent.

Angle BCA and angle PQT are congruent too.

Since angle A and angle T are congruent, it means the congruency theorem used will be ASA(Angle - Side - Angle) Theorem.

Lastly, if angle B were to be congruent to angle P,  it means the congruency theorem used will be AAS(Angle - Angle - Side) Theorem.

The missing options are;

A) If AngleA ≅ AngleT, then the triangles would be congruent by ASA.

B) If AngleB ≅ AngleP, then the triangles would be congruent by AAS.

C) If all the angles are acute, then the triangles would be congruent.

D) If AngleC and AngleQ are right angles, then triangles would be congruent.

E) If BC ≅ PQ, then the triangles would be congruent by ASA.

Read more about congruency at; https://brainly.com/question/1675117

#SPJ1

Answer:

D. none

Step-by-step explanation:

we only know about the right angle at the bottom right.

that is not enough information.

we always need 3 pieces of confirmed information of each triangle to be able to say that the 2 triangles are indeed of the same shape and size.

like the other answer options would indicate :

SAS : side - angle - side.

2 sides and the enclosed angle. if we know they are equal, then the rest of the triangles follow automatically.

SSS : all 3 sides. with 3 defined sides there is only one possible shake and size for that triangle.

HL : Hypotenuse and a leg of a right-angled triangle (also 3 pieces of information - 2 sides and the right angle).

since we have only the right angle and nothing else, we cannot prove that the triangles are congruent.

Answer:

B. Yes, because it passes the vertical line test.

Step-by-step explanation:

Vertical line test - if a vertical line passes through more than one pone, the relation is not a function

Any vertical line will only pass through one point, so this relation is a function

The relation is a function because it passes the vertical line test