Add parentheses to make this equation true 7 + 8 - 2 x 3 = 25

Answer:

Justin has 10 nickels and 5 dimes.

Step-by-step explanation:

Given that Justin has x nickels and y dimes, and he has a minimum of 15 coins worth at most $ 1 combined, to determine one possible solution the following calculation must be performed:

Nickel = 0.05

Dime = 0.10

15 x 0.05 + 0 x 0.1 = 0.75

14 x 0.05 + 1 x 0.1 = 0.80

13 x 0.05 + 2 x 0.1 = 0.85

12 x 0.05 + 3 x 0.1 = 0.90

11 x 0.05 + 4 x 0.1 = 0.95

10 x 0.05 + 5 x 0.1 = 1

So, Justin has 10 nickels and 5 dimes.

Answer:

The work done to stretch or compress the spring is stored in the spring as elastic potential energy. The elastic potential energy of a spring is one half the product of its spring constant multiplied by the square of its deformation.

Step-by-step explanation:

0.05 Joule energy is stored in a spring with an elastic constant of 1000N/m when it is compressed 10cm.

Elastic potential energy is stored in the spring as a result of the work required to stretch or compress it. A spring's elastic potential energy is equal to one-half the sum of its spring constant times its deformation squared.

It is given that, a spring with an elastic constant of 1000N/m is compressed 10cm.​

The energy stored in the spring is,

E= 1/2Kx²

Where E is the energy stored, K is the spring constant and x is the spring compression.

Substitute the given value as

E =  1/2(1000)(0.01)²

E= 0.05 J

Thus, 0.05 Joule energy is stored in a spring with an elastic constant of 1000N/m when it is compressed 10cm.

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Answer:

x = 2 and y = 1

Step-by-step explanation:

First, solve for y by substituting the second equation as x into the first equation

-2x - 3y = -7

-2(y + 1) - 3y = -7

Simplify and solve for y

-2y - 2 - 3y = -7

-5y - 2 = -7

-5y = -5

y = 1

Solve for x by plugging in 1 into the second equation

y + 1 = x

1 + 1 = x

2 = x

So, the answer is x = 2 and y = 1

As a result, -3/10 csc⁵-3x + C is the antiderivative of 9csc-3xcot-3x⋅ csc³-3x.

In mathematics, an integral is either a number representing the region under a function's graph for a certain interval or an added to the initial, the derivative which is the previous function (indefinite integral).

9csc-3xcot-3x ⋅ csc³-3x = 9csc⁴-6x cot-3x

Then, we can use u-substitution, with u = csc-3x and du/dx = -3csc-3xcot-3x dx, as in the previous problem. We get:

∫9csc-3xcot-3x⋅ csc³-3x dx = -3/2 ∫u⁴ du

= -3/2 × u⁵ / 5 + C

= -3/10 csc⁵-3x + C

Therefore, the antiderivative of 9csc-3xcot-3x⋅ csc³-3x is -3/10 csc⁵-3x + C.

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Answer:

  (c)  The x-intercept of f⁻¹(x) is the same as the y-intercept of f(x).

Step-by-step explanation:

You want to know the relationship between the graphs of function f(x) and its inverse f⁻¹(x).

The inverse of a function maps every y-value of the original function to its corresponding x-value. That is if you have ...

  f(a) = b

then the graph of f(x) contains the ordered pair (a, b).

The inverse function will have the ordered pair (b, a). That is,

  f⁻¹(b) = a

If an ordered pair (x-intercept) of the inverse function is ...

  (P, 0)

Then there will be an ordered pair (0, P) on the graph of the original function. That point is the y-intercept, and its y-coordinate is the same as the x-coordinate of the x-intercept of the inverse function.

The x-intercept of f⁻¹(x) is the same as the y-intercept of f(x).

__

Additional comment

The graphs of the two functions are mirror images of each other across the line y=x.

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Is that all they give because if so I'd say 100 but if there is more can u add that

The solution set includes all real numbers less than -5, and all real numbers greater than 1, but does not include -5 or 1 themselves.

Option D is the correct answer.

We have,

We need to isolate the absolute value |x + 2| on one side of the inequality.

We subtract 7 from both sides.

|x + 2| > 3

Next, we can split this inequality into two separate inequalities, one for when the expression inside the absolute value is positive, and one for when it is negative:

x + 2 > 3

or

- (x + 2) > 3

Solving for x in the first inequality.

x > 1

Solving for x in the second inequality.

-x - 2 > 3

Adding 2 to both sides and multiplying by -1.

x < -5

So the solution set for the inequality |x + 2| + 7 > 10 is the set of all x-values that satisfy either x > 1 or x < -5.

Using interval notation.

(-∞, -5) U (1, ∞)

Thus,

The solution set includes all real numbers less than -5, and all real numbers greater than 1, but does not include -5 or 1 themselves.

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Answer:

A, 616 cm^2

Step-by-step explanation:

Area- πr^2

A- 3.14(14^2)

A- 3.14(196)

A- 615.44 cm^2 or ≈ 616 cm^2

Answer:

A.

Step-by-step explanation:

The time taken will be 38 years.

Given:

Principal= $1000

Rate= 0.045

Amount =5000

Number of time it is compounded = 12, time =?

Using the formula;

A= P(1+r/n)^{nt}

where A is the amount, P is the principal , n is the number of time it is compounded and t is the time taken.

Substitute the values and solve for t,

5000= 1000(1+0.045/12)^{12t}

5000=1000(1.00375)^{12t}

Divide both-side by 1000

5= (1.00375)^{12t}

Take the log of both-side

12t= ㏑5÷ 12t㏑(1.0035)

Divide both-side by In(1.0035)

12t= 460.64

Divide both-side of the equation by 12

t= 460.64÷ 12t

t = 38.38t≅ 38

Hence, the time taken will be 38 years.

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Answer50.5

ffffffffffffffff

Answer:

No

Step-by-step explanation:

I don't think it is proportional

Here it is not proportional.

What is proportional?

Proportional relationships are relationships between two variables where their ratios are equivalent.

Another way to think about them is that, in a proportional relationship, one variable is always a constant value time the other.

Here given that,

\(y=-\frac{5}{9x}\)

Here it is not proportional.

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The quotient of - 3.32 / - 2.2 is 8 ÷5.

Given fraction:

-3.32 / -2.2

First step is to re-write the given fraction which is - 3.52 / - 2.2

3.52 / 2.2

Second step is to convert the decimal to fraction

352 ÷ 100 / 22 ÷10

Third step is to reduce the fraction

reducing 352/100

=(2^5 × 11)/(2^2 × 5^2)

= [(2^5 × 11) ÷ 2^2] / [(2^2 × 5^2) ÷ 2^2]

= (2^3 × 11)/5²

= 88/25

Reducing 22/10

Divide the numerator and denominator by the greatest common divisor

= 22 ÷ 2 / 10 ÷ 2

= 11 /5

Now let determine  or find the quotient

88 ÷ 25 × 11 ÷ 5

= 8 ÷ 5

Therefore we can conclude that 8 ÷ 5 is the quotient.

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Answer:

r = 6

Step-by-step explanation:

(13+5)/(3-r)=8

18=24-r

r =6

Value is = r-89

Explanation

Point-slope form is represented as y y 1 = m (x x 1), where (x 1, y 1) is the supplied point and m is the given slope. The variables "x" and "y" remain.

m = (y2 - y1) / (x2 - x1)

Point 1:  (-5, r)

Point 2:  (3, 7)

m = 12

(7 - r) / [6 - (-2)] = 12

(7 - r) / (6 + 2) = 12

(7 - r) / 8 = 12

 7 - r = 96

   -r = 89

   r = - 89

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The tax on a property assessed at $900,000 is,

⇒ $10,800

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

In Portland, the tax on a property assessed at $400,000 is $4,800.

Now, Let value of the tax on a property assessed at $900,000 = x

Hence, By definition of proportion we get;

4800/400,000 = x/900,000

4800/4 = x/9

1200 = x/9

x = 1200 × 9

x = $10,800

Thus, The tax on a property assessed at $900,000 is,

⇒ $10,800

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Answer:

Length(L)=18kg

=18×100cm=1800

Breadth(B)=360kg

Height(H)=m3

Volume (V)=?

We know,

V=l×b×h

or, V=18×360×m3

=6480

Step-by-step explanation:

The inverse function of the function f(x) = log₂(3x + 4) − 5 is y = [2^(x + 5) - 4]/3

From the question, we have the following equation that can be used in our computation:

f(x) = log2(3x + 4) − 5.

Rewrite as

f(x) = log₂(3x + 4) − 5.

Express f(x) as y

This gives

y = log₂(3x + 4) − 5.

Swap the positions of x and y

So, we have the following representation

x = log₂(3y + 4) − 5.

Add 5 to both sides

log₂(3y + 4) = x + 5

So, we have

3y + 4 = 2^(x + 5)

Subtract 4 from both sides

3y = 2^(x + 5) - 4

Divide b y3

y = [2^(x + 5) - 4]/3

Hence, the inverse function is y = [2^(x + 5) - 4]/3

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Answer:

See below

Step-by-step explanation:

When \(-\frac{\pi}{2} < \theta < \frac{\pi}{2}\), the x-coordinate of the rotated point will be positive since they cover Quadrants I and IV, both of which have positive x-values.

When \(\frac{\pi}{2} > \theta > \frac{3\pi}{2}\), the x-coordinate of the rotated point will be negative since they cover Quadrants II and III, both of which have negative x-values.

The x-coordinate of the rotated point will be equal to cosθ since both of these values depend on the angle of θ.

cos(90°) = 0, cos(180°) = -1, and cos(270°) = 0

This is why referring to a unit circle is crucial in understanding this material.

Answer:

-2.88

Step-by-step explanation:

6.36-9.24= -2.88

Answer:

196+104

Step-by-step explanation:

I hope this helps you an dhave a good day

The rate of change of the Distance between the planes is zero. This means that the distance between the planes remains constant throughout their respective flights.

The rate of change of the distance between the planes, we need to determine how the distance between them changes over time.

the distance between the two planes is represented by the variable D, and time is represented by the variable t.

At noon, the southbound plane starts flying and continues for 4 hours until 4 pm. During this time, the plane covers a distance of 900 km/h * 4 hours = 3600 km due south.

Meanwhile, the eastbound plane is also traveling towards the airport. It starts from a distance of 2000 km away from the airport at 4 pm.

To find the distance between the planes at any given time, we can use the Pythagorean theorem, as the planes are moving at right angles to each other. The distance D between the planes can be calculated as:

D^2 = (2000 km)^2 + (3600 km)^2

Simplifying the equation:

D^2 = 4000000 km^2 + 12960000 km^2

D^2 = 16960000 km^2

Taking the square root of both sides:

D = sqrt(16960000) km

D = 4120 km

Now, we can find the rate of change of the distance between the planes by calculating the derivative of the distance equation with respect to time

dD/dt = 0

Since the distance between the planes is constant, the rate of change is zero.

Therefore, the rate of change of the distance between the planes is zero. This means that the distance between the planes remains constant throughout their respective flights.

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Assuming that f(x)=x, we need to shift f(x) to the left by 5 and up by 2 in order to get g. (x). The equation g(x) may be written in mathematical terms as

G(x)=(x+5)+2

This is further explained below.

Generally, In the field of mathematics, an assignment of one element from set Y to each and every element in set X is the definition of a function. This particular set, X, is referred to as the function's domain, and this particular set, Y, is referred to as the function's codomain.

In conclusion, Assuming f(x)=x, f (x) is shifted left 5 and shifted up 2 to create g(x).  the equation g(x) is mathematically given as

G(x)=(x+5)+2

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Answer:

25 degreea bestie hope thiis helped

Answer:

\(\sqrt{\frac{2*2*2*2*3}{5*5*7}}\)

Step-by-step explanation:

Through prime factorization,

\(\sqrt{\frac{48}{175}}=\\\\\sqrt{\frac{2*2*2*2*3}{5*5*7}}\)

Answer:

b

Step-by-step explanation:

The distance of the run Will be 16miles and the Distance of the bicycle race will be 81 miles.

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.

Distance = average velocity × time

Let the time and distance of the run, respectively, be t₁ and.d₁

Let those of the bicycle race be t₂ and d₂

From the question,

t₁ + t₂ = 5

d₁ = 8t₁

d₂ = 27t₂

Total distance = 97

8t₁ + 27t₂ = 97

8 ( 5 - t₂ ) + 27t₂ = 97

40 - 8t₂ + 27t₂ = 97

40 + 19 t₂ = 97

19t₂ = 57

t₂ = 3 hours

t₁ + t ₂ = 5

t₁ = 5 - t₂

t₁ = 5 - 3 = 2 hours

Now the distances are calculated as:-

d₁ = 8t₁ = 8 x 2 = 16 miles

d₂ = 27t₂ = 27 x 3 = 81 miles

Therefore the distance of the run Will be 16miles and the Distance of the bicycle race will be 81 miles.

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QUESTION 1

the solution is (-1,-5)

To verify the solution algebraically, we need to multiply the first equation with -1 and then sum them up

-y=5

y=3x-2

0=3x+3

3x=-3

x=-3/3

x=-1

Then, we use this value to find the other one

y=3x-2

y=3(-1)-2

y=-3-2

y=-5

Therefore, the solution is (-1,-5), which is the same showed graphically.

QUESTION 2.

Using the same process as we did in the QUESTION 1. The image attached shows both lines and the interception point which is the solution. So, the solution is (6,0).

To verify the solution algebraically, we must multiply the second equation by -6

x+6y=6

-6y=-2x+12

x=-2x+18

x+2x=18

x=18/3

x=6

Then, we use this value to find the other one

x+6y=6

6+6y=6

6y=6-6

y=0/6

y=6

Therefore, the solution is (6,0),

The  volume of rectangular prism is 90 unit³.

We can consider the 1 block = 1 unit.

Length of prism = 5 unit

width of prism = 6 unit

Height of prism = 3 unit

So, Volume of rectangular prism

= l w h

= 5 x 6 x 3

= 90 unit³

Thus, the volume of rectangular prism is 90 unit³.

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