please someone help me how do I do workout this and explainn please

The value of p from the given equation is 4.5.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign \(=\\\).

The given equation is \(0.5p-3.45=-1.2\)

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

The equation can be solved as follows

\(0.5p-3.45=-1.2\)

\(0.5p= -1.2+3.45\)

\(0.5p= 2.25\)

\(p= 2.25\div0.5\)

\(p= 4.5\)

Therefore, the value of p is 4.5.

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Yes , there can be a Right triangle with two side lengths as simple fraction and other side length as an integer .

In the question ,

we have to find , whether a Right Triangle can be made by two fractions and an integer length .

yes, we can make a Right Triangle with two lengths as fractions and other length as integer .

let us prove it with the help of an example .

Consider the triplet 7 , 24 , 25 .

let the two fractions side be 7/25 and 24/25 , and the hypotnuse of the right triangle be  1 .

We know that for the Right Triangle

(side1)² + (side2)² = hypotnuse²

(7/25)² + (24/25)² = 1²

49/625 + 576/625 = 1

(49+576) / 625 =1

625/625 = 1

1 = 1

hence ,it is a Right Triangle .

Therefore , Yes , there can be a Right triangle with two side lengths as simple fraction s and other side length as an integer .

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C. exponential decay

With a credit card balance of $17,426, a minimum monthly payment of $461, and an interest rate of 15.5%, we need to calculate the number of years it will take to pay off the card without adding any additional debt.

To determine the time required to pay off the credit card, we consider the monthly payment and the interest rate. Each month, a portion of the payment goes towards reducing the balance, while the remaining balance accrues interest.

To calculate the time needed for repayment, we track the decreasing balance each month. First, we determine the interest accrued on the remaining balance by multiplying it by the monthly interest rate (15.5% divided by 12).

We continue making monthly payments until the remaining balance reaches zero. By dividing the initial balance by the monthly payment minus the portion allocated to interest, we obtain the number of months needed for repayment. Finally, we divide the result by 12 to convert it into years.

In this scenario, it will take approximately 3.81 years to pay off the credit card (17,426 / (461 - (17,426 * (15.5% / 12))) / 12).

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The difficulty of range as a measure of variability that is overcome by interquartile range is option b that is The range is influenced too much by extreme values.

The variance is the mean squared difference between each data point and the mean-centered distribution. A statistical assessment of the dispersion of values in a data collection is referred to as variance. Variance explicitly assesses how distant each number in the set is from the mean (average), and consequently from every other number in the set. Variance is a measure of how data points differ from the mean, whereas standard deviation is a measure of statistical data distribution. The primary distinction between the two is that standard deviation is expressed in the same units as the mean of the data, whereas variance is expressed in squared units.

Here,

The interquartile range overcomes the problem of range as a measure of variability. Extreme values have an undue impact on the range.

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Mine is not heating up I don't know about others

Answer:

U = x + 3 and V = 7

Step-by-step explanation:

Let U = x + 3 and V = 7, then:

=> (x + 3)^2 + 14(x + 3) + 49

= (x + 3)^2 + 2*7*(x + 3) + 7^2

= U^2 + 2UV + V^2

= (U + V)^2

(correct)

Given:

The graph of a quadratic function opens downward and has its vertex at (0, 1).

To find:

The quadratic function.

Solution:

The vertex form of a quadratic function is:

\(y=a(x-h)^2+k\)          ...(i)

Where, a is a constant and (h,k) is the vertex.

If a<0, then graph opens downward and if a>0, then graph opens upward.

It is given that the quadratic function opens downward and has its vertex at (0, 1). It means a must be negative.

Putting h=0 and k=1 in (i), we get

\(y=a(x-0)^2+1\)

\(y=ax^2+1\)

For \(a=-1\),

\(y=(-1)x^2+1\)

\(y=x^2+1\)

So, option A is correct.

In other options the leading coefficient is positive it means their graphs open upward. So, options B, C and D are incorrect.

Therefore, the correct option is A.

Answer: (-5)+(-5)=-10

Step-by-step explanation:

have a great day

Two sides of an isosceles triangle are 20 and 30. Then the difference of the largest and the smallest possible perimeters is 10.

These are the specified parameters:

Two sides of an isosceles triangle are 20 and 30.

The perimeter of the largest isosceles triangle

With a side measurement of 30 feet and a base of 20.

Roving = 30 + 30 + 20

            = 80

The perimeter of the smallest isosceles triangle

With a side measurement of 20 feet and a base of 30.

Roving = 20 + 20 + 30

            = 70

The difference of the largest and the smallest perimeters

= 80 - 70

= 10

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Answer:

Step-by-step explanation:

c is correct.  To verify this, look at the point (4, 4) on the black graph.  For the same x value (4), we have on the red graph the point (4, 2).  If we now look at this point (4, 2) on the red graph we see that the y-value (2) is half that of the point (4, -4) on the black graph:  f(x) = (1/2)y

Putting it all together, the final result is:

\($ \rm \[ \int \frac{{x^2 - x - 2}}{{2x^3 - 2x^2 - 7x + 3}} \, dx = \frac{1}{3}\ln|x - 1| + \frac{1}{12}\ln|2x^2 + x - 3| + C,\]\)

where (C) is the constant of integration.

To evaluate the integral \($ \(\int \frac{{x^2 - x - 2}}{{2x^3 - 2x^2 - 7x + 3}} \, dx\)\),

we can use partial fraction decomposition.

First, let's factor the denominator:

\(\(2x^3 - 2x^2 - 7x + 3 = (x - 1)(2x^2 + x - 3)\)\)

Now, let's decompose the rational function into partial fractions:

\($ \rm \(\frac{{x^2 - x - 2}}{{2x^3 - 2x^2 - 7x + 3}} = \frac{{A}}{{x - 1}} + \frac{{Bx + C}}{{2x^2 + x - 3}}\)\)

To find the values of \(A\), \(B\), and \(C\), we need to equate the numerators:

\($ \rm \(x^2 - x - 2 = A(2x^2 + x - 3) + (Bx + C)(x - 1)\)\)

Expanding and comparing coefficients:

\(\rm \(x^2 - x - 2 = 2Ax^2 + Ax - 3A + Bx^2 + (B - A)x + (C - B)\)\)

Comparing the coefficients of like powers of \(x\), we get the following equations:

\(\(2A + B = 1\) (coefficient of \(x^2\))\\\(A - A + B - C = -1\) (coefficient of \(x\))\\\(-3A + C - 2 = -2\) (constant term)\)

Simplifying the equations, we have:

(2A + B = 1)

(B - C = -1)

(-3A + C = 0)

Solving these equations, we find \(\(A = \frac{1}{3}\), \(B = \frac{1}{3}\), and \(C = \frac{1}{3}\)\).

Now we can rewrite the integral as:

\($ \rm \(\int \frac{{x^2 - x - 2}}{{2x^3 - 2x^2 - 7x + 3}} \, dx = \int \frac{{\frac{1}{3}}}{{x - 1}} \, dx + \int \frac{{\frac{1}{3}(x + 1)}}{{2x^2 + x - 3}} \, dx\)\)

Integrating the first term:

\($ \rm \(\int \frac{{\frac{1}{3}}}{{x - 1}} \, dx = \frac{1}{3}\ln|x - 1|\)\)

For the second term, we can use a substitution:

Let \(\(u = 2x^2 + x - 3\)\), then \(\(du = (4x + 1) \, dx\)\)

Substituting and simplifying:

\($ \rm \(\int \frac{{\frac{1}{3}(x + 1)}}{{2x^2 + x - 3}} \, dx = \frac{1}{12}\int \frac{1}{u} \, du = \frac{1}{12}\ln|u| + C\)$ \rm \(= \frac{1}{12}\ln|2x^2 + x - 3| + C\)$\)

When all of this is added up, the final result is: \($ \rm \(\int \frac{{x^2 - x - 2}}{{2x^3 - 2x^2 - 7x + 3}} \, \\\\$dx = $ \frac{1}{3}\ln|x - 1| + \frac{1}{12}\ln|2x^2 + x - 3| + C\)$\) where \(C\) is the constant of integration.

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The laser dot on the wall at point a moves at a pace of 6 times the circle's diameter, while the laser dot at point (ii) moves at 6π radians per minute.

i. The equation for linear speed, can be used to calculate the speed of the laser dot on the wall at point a. The distance in this instance is equal to the diameter of the circle created by the rotation of the laser, and the amount of time required to transit it is equal to one revolution, or 1/6 of a minute. The diameter of the circle is divided by 1/6 of a minute or six times the circumference of the circle.

ii. The equation for angular speed is used to calculate the speed of the laser dot on the wall at position b. In this instance, the angle is 2 radians, and it takes 1/6 of a minute to cross that angle. Therefore, 2 radians divided by 1/6 of a minute, or 6π radians per minute, is the speed of the laser dot on the wall at point b.

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Answer:

- 3, - 2, - 1 and 6

Step-by-step explanation:

To find the first 3 terms, substitute n = 1, 2, 3 into the nth term rule

a₁ = 1 - 4 = - 3

a₂ = 2 - 4 = - 2

a₃ = 3 - 4 = - 1

The first 3 terms are - 3, - 2, - 1

similarly substitute n = 10 into the rule for 10th term

a₁₀ = 10 - 4 = 6

∇f|(0, 0, 4π) = (-8)i + (π/2 + 1)j + 0k, where i, j, and k are the standard unit vectors in the x, y, and z directions, respectively.

To find ∇f at the given point (0, 0, 4π) for the function f(x, y, z) = ex + ysinz + (y + 9)cos⁻¹x, we need to compute the partial derivatives of f with respect to x, y, and z and evaluate them at the given point.

Partial derivative with respect to x (fₓ):

fₓ = ∂f/∂x = eˣ + (y + 9)(-sin⁻¹x)'

The derivative of (-sin⁻¹x) is (-1 / √(1 - x²)), so:

fₓ = eˣ- (y + 9)(1 / √(1 - x²))

Partial derivative with respect to y (fᵧ):

fᵧ = ∂f/∂y = sinz + cos⁻¹x + 1

Partial derivative with respect to z (f_z):

f_z = ∂f/∂z = ycosz

Now, let's evaluate these partial derivatives at the point (0, 0, 4π):

fₓ(0, 0, 4π) = e⁰ - (0 + 9)(1 / √(1 - 0²)) = 1 - (9 / 1) = -8

fᵧ(0, 0, 4π) = sin(4π) + cos⁻¹(0) + 1 = 0 + π/2 + 1 = π/2 + 1

f_z(0, 0, 4π) = 0

Therefore, ∇f|(0, 0, 4π) = (-8)i + (π/2 + 1)j + 0k, where i, j, and k are the standard unit vectors in the x, y, and z directions, respectively.

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An equation is formed of two equal expressions. The correct option is x+y=557 and Three-fifths(x)+five-sixths(y)=407.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the total number of pages in the shorter book be represented by x, and the total number of pages in the longer book be represented by y.

Given the total number of pages of the shorter book and the longer book is  557. Therefore, the equation can be written as,

x+y =557

Also, Scott reads Three-fifths of the shorter book and StartFraction 5 Over 6 EndFraction of the longer book, which is equal to 407 pages. Therefore,

(3/5)x + (5/6)y = 407

Hence, the correct option is x+y=557 and Three-fifths(x)+five-sixths(y)=407.

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Answer:100,000,000

Step-by-step explanation:

1,000,000 x 100 = 100,000,000

Answer:

100+80+9+0.2+0.07+0.001

If Sparky weights (lets call it K) 7 units and it is 7 times the Solo's weigth (lets call it S), then we can write:

Then, the weight of Solo is 1 unit.

Answer:

It’s A.

Step-by-step explanation:

Took the test and got it right

Approximately 97 cans must be sampled to achieve a margin of error of 0.01 ounce.

To estimate the number of cans that must be sampled for the margin of error to be equal to 0.01 ounce, we'll use the formula for the sample size in a confidence interval:

\(n = \left(\frac{Z \cdot \sigma}{E}\right)^2\)

where n is the sample size, Z is the Z-score for the desired confidence level (95% in this case), σ is the standard deviation (0.05 ounce), and E is the margin of error (0.01 ounce).

For a 95% confidence interval, the Z-score is approximately 1.96. Plugging the values into the formula, we get:

n = \(\(\left(\frac{{1.96 \cdot 0.05}}{{0.01}}\right)^2\)\)
n ≈ (9.8)²
n ≈ 96.04

Since we can't have a fraction of a can, we'll round up to the nearest whole number. Therefore, a sample size of approximately 97 cans is needed for the margin of error to be equal to 0.01 ounce with a 95% confidence interval.

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Answer:  9/10

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

Explanation:

Imagine a pizza split into 5 equal slices. Then imagine that you split each slice in half. This means we now have 5*2 = 10 slices.

Eating 3 out of the original 5 is equivalent to eating 6 smaller slices out of the now 10 total.

In other words:  The fraction 3/5 is the same as 6/10

Put another way: Multiply top and bottom of 3/5 by 2 to get 6/10.

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

Gary painted 3/10 of the fence in the morning, and then 3/5 of it in the afternoon. We can replace the "3/5" with "6/10".

3/10 + 6/10 = (3+6)/10 = 9/10 total

Going back to the pizza scenario, we can imagine 3/10 as eating 3 slices out of 10 total. Then 6/10 adds 6 more slices to get 3+6 = 9 slices total. That's how we end up with 9/10 as the answer.

Answer: 80%

Step-by-step explanation: In the store every 4 out of 5 costumers purchase an product.

If you multiply numbers by 20, you get the demoninator to be 100, which then you can get the percentage by finding 4x20=80.

Therefore, converted, 4/5=80%.

Answer: x = 5

Step-by-step explanation:

Hey there! If you have any questions, feel free to let me know in the comments.

Step 1: Simplify  20 - 4x - 15 - 4x  to  5 - 8x.

5 - 8x = -6x - 45 + 8x

Step 2: Simplify -6x - 45 + 8x to 2x - 45.

5 - 8x = 2x-44

Step 3: Add 8x to both sides.

5 = 2x - 45 + 8x

Step 4: Simplify 2x - 45 + 8x to 10x - 45.

5 = 10x - 45

Step 5: Add 45 to both sides.

5 + 45 = 10x

Step 6: Simplify 5 + 45 to 50.

50 = 10x

Step 7: Divide both sides by 10.

50/10 = 10x/10

Step 8: Simplify 50/10 to 5.

x = 5

Answer:

Step-by-step explanation:

Here you go mate

step 1

20-4x-15-4x=-6x-45+8x  equation

step 2

20-4x-15-4x=-6x-45+8x  simplify for x

20+(-4x)+(-15)+(-4x)=(-6x)+(-45)+8x

step 3

(-4x+-4x)+(20+(-15)=(-6x+8x)+(-45)  add brackets to seperate the equations

step 4

-8x+5=2x+-45  combine the terms that are alike

step 5

-8x+5(-2x)=2x-45(-2x)  subtract -2x(the ones in the brackets)

-10x+5=-45

step 6

−10x+5(-5)=−45(-5)  subtract -5

-10x=-50

step 7

-10x/-10=-50/-10  divide by -10

step 8

50/10  Divide

Answer

x=5

Answer:

5 feet

Step-by-step explanation:

The two angles are vertical angles, which mean they are the same.

6s-2 = 94

Add 2 to both sides:

6s = 96

Divide both sides by 6:

S = 96/6

S = 16

Answer:

y = - 3x + 15