Pls, look at picture for the question.

Answer:The amount of a 80% acid solution that must be mixed with a 55% solution to produce 600 mL of a 60% solution can be calculated using a simple algebraic equation. Let x represent the amount of the 80% acid solution in mL that needs to be mixed with the 55% solution.

The equation can be set up as follows:

0.80x + 0.55(600 - x) = 0.60(600)

Step-by-step explanation: The left-hand side of the equation represents the total amount of acid in the mixture. The first term, 0.80x, represents the amount of acid from the 80% solution, and the second term, 0.55(600 - x), represents the amount of acid from the 55% solution. The right-hand side of the equation represents the total amount of acid in the final 60% solution, which is 60% of 600 mL.

By solving this equation for x, we can determine the amount of the 80% acid solution that needs to be mixed with the 55% solution. Once we have the value of x, we can then calculate the amount of the 55% solution by subtracting x from 600 mL.

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Let x=amount of 80% solution needed

Then 600-x=amount of 30% solution needed

Now we know that the pure acid in the 80% solution (0.80x) plus the amount of pure acid in the 30% solution ((0.30)(600-x)) has to equal the amount of pure acid in the final mixture(0.40*600), so our equation to solve is:

0.80x+0.30(600-x)=0.40*600 get rid of parens

0.80x+180-0.30x=240 subtract 180 from each side

0.80x+180-180-0.30x=240-180 collect like terms

0.50x=60 divide each side by 0.50

x=120 ml---------------------amount of 80% solution needed

600-x=600-120=480 ml---------------amount of 30% solution needed

CK

120*0.80+480*0.30=0.40*600

96+144=240

240=240

Answer:

D is your answer

Step-by-step explanation:

Answer:

Here the slope formula m = ( y 2 − y 1 )/( x 2 -x 1 ) = Δy/Δx

Step-by-step explanation:

The steps which you would take to determine if these figures are similar include the following:

2. Multiply the vertices of polygon ABCD by 1/2.

5. Reflect the intermediate image.

In Mathematics and Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.

Therefore, the dimension or side lengths of the dilated geometric object would be stretched or compressed (shrunk) depending on the scale factor that is applied.

By critically observing the graph representing polygon ABCD, we can logically deduce that a sequence of transformations that would polygon ABCD (pre-image) onto polygon A"B"C"D" (image) is a dilation by a scale factor of 1/2 and a reflection of intermediate image.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The time it will take the roller coaster to reach the ground is 171.65 seconds

Given the roller coaster’s height given by the following parameters

h = –0.025t² + 4t + 50

On the ground level, the height will be zero. Substitute h = 0 and determine the value of t

–0.025t² + 4t + 50 = 0

0.025t² - 4t - 50 = 0

Factorize

On factorizing the time it will take the roller coaster to reach the ground is 171.65 seconds

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The scale factor is \($\frac{3}{16}$\) or approximately 0.1875.

What is Scale Factor?

In mathematics, a scale factor is a number that scales, or multiplies, a quantity or dimension by a certain amount. It is commonly used in geometry and is a measure of how much the size of an object or figure has been changed from its original size.

To find the scale factor when 9 inches is equivalent to 4 feet, we need to compare the ratio of the two measurements. We can start by converting the measurements to the same units, such as inches:

\(4 \text{ feet} &= 4 \times 12 \text{ inches}\) \(&= 48 \text{ inches}\)

Now we can compare the ratio of the two measurements:

\($$9 \text{ inches} : 48 \text{ inches}$$\)

To simplify this ratio, we can divide both numbers by their greatest common factor, which is 3:

\($\frac{9 \text{ inches}}{3} : \frac{48 \text{ inches}}{3}$$\)

\($$3 \text{ inches} : 16 \text{ inches}$$\)

The scale factor is the ratio of the corresponding lengths in the two figures, so in this case, the scale factor is:

\($$3 \text{ inches} : 16 \text{ inches}$$\)

or, in fractional form:

\($\frac{3}{16}$$\)

Therefore, the scale factor is \($\frac{3}{16}$\) or approximately 0.1875.

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Answer:

One ounce of almonds is $0.78

One ounce of cashews is $0.63

Step-by-step explanation:

Set up a system of equations where a is the price of one ounce of almonds and c is the price of one ounce of cashews:

20a + 12c = 23.16

18a + 14c = 22.86

Solve by elimination by multiplying the top equation by 7 and the bottom equation by -6:

140a + 84c = 162.12

-108a - 84c = -137.16

Add them together and solve:

32a = 24.96

a = 0.78

Now, plug in 0.78 for a and solve for c:

20a + 12c = 23.16

20(0.78) + 12c = 23.16

15.6 + 12c = 23.16

12c = 7.56

c = 0.63

Answer:

11 ÷ 942 = 84

Answer

84

8

4

4

Answer:

Step-by-step explanation:

y

=

1

3

x

−

3

Use the slope-intercept form to find the slope and y-intercept

Slope:

1

3

y-intercept:

(

0

,

−

3

)

Any line can be graphed using two points. Select two

x

values, and plug them into the equation to find the corresponding

y

values.

x

y

0

−

3

3

−

2

Graph the line using the slope and the y-intercept, or the points.

Slope:

1

3

y-intercept:

(

0

,

−

3

)

x

y

0

−

3

3

−

2

image of graph

The value of R(A) = 4, N(AT ) = 3, R(AT ) = 4, and N (A) = 3.

Given that

Dimension of matrix  = 7×5

Rank of matrix = 4

The range space of A,

Which is a subspace of R, is known as R(A).

It is made up of all conceivable linear combinations of A's columns.

The dimension of R(A) =  rank of A,

Which is 4 in this case.

The null space of the transpose of A,

Which is also a subspace of R, is designated as N(AT).

All potential answers to the equation ATx = 0,

Where x is a R column vector, are included in it.

N(AT) has a dimension = nullity of A,

which in this case is 3 in this example.

The range space of the transposition of A, is designated as R(AT).

The rows of A are arranged in all conceivable linear configurations.

The rank of A = 4

Thus it equal to dimension of R(AT).

N(A) is the null space of A.

Axe = 0, where x is a column vector in R, are included in it.

The nullity of AT, which is three, is likewise equivalent to the dimension of N(A).

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Answer:

6

Step-by-step explanation:

|-6| = 6

|6| = 6

- -6 = +6

so, we have

6 - 6 + 6 = 6

Answer:

1)  You should add 49 to both sides to complete the square.

    \(\textsf{Solutions:}\;\;\;x=3,\;\;x=-17\)

2)  The discriminant of the equation is 261.

    There are 2 solutions.

    \(\textsf{Solutions:}\;\;\;n=\dfrac{1 +3\sqrt{29}}{10},\;\;n=\dfrac{1 -3\sqrt{29}}{10}\)

Step-by-step explanation:

Given quadratic equation:

\(x^2+14x-51=0\)

To solve the given quadratic equation by completing the square, first move the constant to the right side of the equation:

\(\implies x^2+14x=51\)

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

\(\implies x^2+14x+\left(\dfrac{14}{2}\right)^2=51+\left(\dfrac{14}{2}\right)^2\)

Simplify:

\(\implies x^2+14x+\left(7\right)^2=51+\left(7\right)^2\)

\(\implies x^2+14x+49=51+49\)

\(\implies x^2+14x+49=100\)

Therefore, we added 49 to both sides of the equation to complete the square.

To solve, factor the perfect square trinomial on the left side of the equation:

\(\implies (x+7)^2=100\)

Square root both sides:

\(\implies \sqrt{(x+7)^2}=\sqrt{100}\)

\(\implies x+7=\pm10\)

Subtract 7 from both sides of the equation:

\(\implies x=-7\pm10\)

Therefore, the solutions are:

\(x=3,\;\;x=-17\)

\(\boxed{\begin{minipage}{4 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}\)

Given quadratic equation:

\(5n^2-n=13\)

To solve using the quadratic formula, subtract 13 from both sides so that the equation is in the form ax² + bx + c = 0:

\(\implies 5n^2-n-13=0\)

Therefore:

The discriminant of the equation is b² - 4ac:

\(\begin{aligned}\implies b^2-4ac&=(-1)^2-4(5)(-13)\\&=1+260\\&=261\end{aligned}\)

Therefore, the discriminant is 261.

As the discriminant is positive, there are 2 solutions.

To find the solutions, substitute the values of a, b and c into the quadratic formula and solve for n:

\(\implies n=\dfrac{-(-1) \pm \sqrt{(-1)^2-4(5)(-13)}}{2(5)}\)

\(\implies n=\dfrac{1 \pm \sqrt{1+260}}{10}\)

\(\implies n=\dfrac{1 \pm \sqrt{261}}{10}\)

\(\implies n=\dfrac{1 \pm \sqrt{9\cdot29}}{10}\)

\(\implies n=\dfrac{1 \pm3\sqrt{29}}{10}\)

Therefore, the solutions are:

\(n=\dfrac{1 +3\sqrt{29}}{10},\;\;n=\dfrac{1 -3\sqrt{29}}{10}\)

The rate at which the depth of the liquid is increasing when it reaches one-third of the height of the bowl is (7/3)π cm³/s.

To ascertain the rate at which the liquid's depth rises, let's find the derivative of the depth function with respect to time.

Let;

The rate of change of the volume of the liquid with respect to time is constant and equal to 7π cm³/s.

To determine the height of the bowl, we can evaluate the curve y = [-4 / (8 - x)] - 1 when x = 4 and y = 7.6 and then find the absolute difference between the values.

h = |[-4 / (8 - 4)] - 1 - [-4 / (8 - 7.6)] - 1|

Let's calculate the rate at which the depth rises when it reaches one-third of the bowl's height.

D = depth of bowl

Using this relationship from the question given;

D = (1/3) * h

In order to determine the rate at which D will change with respect to time, let's differentiate both sides of the equation.

dD/dt = (1/3) * dh/dt

Since dh/dt is the rate at which the depth of the liquid is changing, which is constant and equal to 7π cm³/s, we can substitute it into the equation:

dD/dt = (1/3) * (7π)

Simplifying, we have:

dD/dt = (7/3)π cm³/s

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Answer:

3/5 is the probability of drawing a blue card

Answer:

3/5

Step-by-step explanation:

total sum of probability is 1.

for the probability of drawing a red ball to be 2/5, then probability of drawing a blue ball is

1 - 2/5

Answer: 5

Step-by-step explanation:

Because there are 35 when you add yourself so u subtract 30 to get 5

There would be 4 people left in the garden.

34 - 30 = 4.

Subtraction is a mathematical operation that involves taking away one number from another to find the difference between them. For the question, At first, there were 34 people in the garden and later 30 people were no longer alive in the garden, so the difference between 30 people and 34 people is 4.

Subtraction is the opposite of addition, and it is used to measure the distance between two values on the number line.

Subtraction is represented by minus Sign (-). For example, subtracting 5 from 10 gives you a difference of 5 (10 - 5 = 5).

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Answer:

\((m-n)^{2}-9r\)

Step-by-step explanation:

m²-2mn+n²-9r​

\((m-n)^{2}-9r\)

The formula for the centripetal force, as a function of the radius, is given as follows:

F = 896/r.

The equation that defines a direct proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality.

For an inverse proportional relationship, the equation is given as follows:

y = k/x.

The centripetal force varies inversely with the radius, hence the equation is given as follows:

F = k/r.

When F = 56, r = 16, hence the constant k is obtained as follows:

56 = k/16

k = 56 x 16

k = 896.

Hence the equation is given as follows:

F = 896/r.

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Answer:

n-27

Step-by-step explanation:

If we assume the number is n, the expression will be n-27. You could use any other variable, too. Hope it helps!

Answer:

f - 27

Step-by-step explanation:

we don't know the number that's being subtracted so it would be any integer minus 27

Answer:

The company charged $500 for its services,and Mia gives the movers a 16% tip. Now, we can add the tip amount to the cost of the service to find the total amount Mia paid: Total amount = Cost of service + Tip amount = $500 + $80 = $580

Step-by-step explanation:

Step-by-step explanation:

To determine the value of x that satisfies the expression x^2 + 3x - 5 when x = 9, we simply substitute 9 for x and evaluate the expression:

9^2 + 3(9) - 5 = 81 + 27 - 5 = 103

Therefore, when x = 9, the expression x^2 + 3x - 5 evaluates to 103.

rate my answer, please.

Answer:

10

Step-by-step explanation:

Answer:

10 apples

Step-by-step explanation:

20% of 50 = 10

10 apples

Answer:

Perimeter = 11m

Area: 7.56 m^2

Step-by-step explanation:

Perimeter: 2(2.7) + 2(2.8) = 5.4 + 5.6 = 11 m

Area: 2.7m x 2.8 m = 7.56 m^2

The sentence with proper subject-verb agreement is the student as well as the teacher want to go to the museum. In this sentence, the subject is what we call a compound subject, meaning that the verb refers and agrees with more than just one singular word.

The compound subject is "student" and "teacher" and they are connected by "as well as", which functions as a coordinating conjunction would. That's why the verb should conjugate in its plural form.

Option A is incorrect because the structure inside parentheses is not related to the verb and does not influence its conjugation. Options C and D have a verb in the singular form for a compound subject - that would demand a plural conjugation.

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Amplitude of  f(x)=5cosx

= 5

The amplitude of a periodic variable is a measure of its change in a single period. The amplitude of a non-periodic signal is its magnitude as compared with a reference value. there are numerous definitions of amplitude, which can be all functions of the magnitude of the differences between the variable's extreme values.

It refers to most displacement from the equilibrium that an object in periodic motion show. as an example, a pendulum swings through its equilibrium point (straight down), and then swings to a maximum distance away from the center.

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Therefore , the solution of the given problem of area comes out to be

r = 8.

The term "area" describes the amount of space occupied by a 2D form or surface. We use cm2 or m2 as our units for measuring area. A shape's area is determined by dividing its length by its breadth.

Here,

A 90 degree sector occupies 1/4 of a circle, which has 360 degrees. Consequently, the area of the whole circle can be written as

Sector Size/Sector Area = Circle Area/360

16 ft2/90 = n/360

(360) (16 ft2)/90 = n

(4)(16 ft2) = n

The total size of the circle is n = 64 ft2.

Since Area of a Circle equals r2,

∏r2 = 64

r2 = 64/∏

r = √(64/∏)

We multiply by / to get by rationalizing the denominator.

r = √(64∏)/√(∏2) Then using the denominator's square root, we can obtain the solution of

r = √(64∏)/∏

r = 8

Therefore , the solution of the given problem of area comes out to be

r = 8.

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Answer:

-6x + 21

Step-by-step explanation:

9 - 3(2x - 4)

9 - 6x + 12

-6x + 21