How to solve 4x+25+10

Answer:

I think it's 27

because length is 3 times its width

Answer:

7 x 8 = 56

-3 x -5 or -5 + -5 + -5 = -15

Step-by-step explanation:

The numbers that result in the top and bottom numbers are: -7 and -8

System of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.

You should convert the given text into linear equations.

x*y=56 (1)

x+y=-15 (2)

For equation 2, you have x=-15-y. Thus, you can replace this variable into equation 1.

(-15-y)*y=56

-15y-y²=56

-y²-15y-56=0

You find a quadratic equation. Solving this equation:

\(y_{1,\:2}=\frac{-\left(-15\right)\pm \sqrt{\left(-15\right)^2-4\left(-1\right)\left(-56\right)}}{2\left(-1\right)}\\ \\ y_{1,\:2}=\frac{-\left(-15\right)\pm \:1}{2\left(-1\right)}\\\)

\(y_1=\frac{-\left(-15\right)+1}{2\left(-1\right)}=-8\\ \\ y_2=\frac{-\left(-15\right)-1}{2\left(-1\right)}=-7\)

For equation 2,

       x+y=-15

       x+(-8)=-15

       x=-15+8=-7

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The length of the arc defined by the central angle of 312 degrees is 26π cm.

The formula for the arc length of a circle is given by:

L = (θ/360) × 2πr

where L is the length of the arc, θ is the central angle in degrees, and r is the radius of the circle.

Substituting the given values, we get:

L = (312/360) × 2π(30)

L = (26/30) × π × 30

L = 26π cm

Therefore, the length of the arc defined by the central angle of 312 degrees is 26π cm.

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Answer:

B 18.38

Step-by-step explanation:

log4x = 2.1

logx/log4 = 2.1

logx = log(4) x 2.1

logx = 1.2643

x = antilog(1.2643)

x = 18.38 (to 2 d.p)

Answer:

X=18.38

Step-by-step explanation:

Answer:

6 + (d * 2)

Step-by-step explanation:

You are adding 6 to the equation after the amount d times 2. In that case, a parentheses is required to round up d * 2.

The person is approximately 8.43 miles from home, and they need to walk in the direction of approximately 26.6 degrees east of north to head directly home.

To determine the distance from home, we can use the concept of vector addition. The person walks 4 miles west, which can be represented as a vector (-4, 0) in a coordinate plane. Then, they walk 5 miles southwest, which can be represented as a vector (-3.54, -3.54) since southwest is a combination of west and south. Adding these two vectors together gives us (-7.54, -3.54).

To find the magnitude or distance from home, we use the Pythagorean theorem. The distance is given by sqrt((-7.54)^2 + (-3.54)^2) = 8.43 miles (approximately).

To determine the direction to head directly home, we need to find the angle between the vector (-7.54, -3.54) and the positive x-axis. We can use trigonometry to find this angle. The tangent of the angle is given by the ratio of the y-coordinate to the x-coordinate, which is -3.54 / -7.54. Taking the inverse tangent of this value gives us approximately 26.6 degrees.

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Using only the trig ratios of 45 and 60 degrees, we use angle-sum to compute \(\tan 105^\circ=\tan(60^\circ+45^\circ)=\frac{\tan 60^\circ+\tan 45^\circ}{1-\tan 60^\circ\tan 45^\circ}=\frac{\sqrt{3}+1}{1-\sqrt{3}}=-2-\sqrt{3},\) so \(\cot 105^\circ=\frac{1}{\tan 105^\circ}=-2+\sqrt{3}\) and \(\tan 105^\circ-\cot105^\circ=\boxed{-2\sqrt{3}}.\)

The weight of the beaker, including the weight of the water, is approximately 173.1 ounces when rounded to the nearest tenth. To find the weight of the beaker when filled with water, including the weight of the cylindrical beaker itself, we need to calculate the weight of the water and add it to the weight of the empty beaker.

First, let's find the volume of the water in the beaker. The beaker is filled to one inch from the top, which means the height of the water is 11 - 1 = 10 inches.

The volume of the water can be calculated using the formula for the volume of a cylinder: \(V = \pi r^2h\), where r is the radius and h is the height.

\(V = \pi (3^2)(10) = 90\pi\) cubic inches

Next, we need to find the weight of the water. Given that one cubic inch of water weighs 0.6 ounces, we can multiply the volume of the water by 0.6 to get the weight of the water.

Weight of water = 90π x 0.6 = 54π ounces

Finally, we need to add the weight of the empty beaker, which is 3.5 ounces, to the weight of the water.

Weight of beaker with water = 54π + 3.5 ounces

To find the approximate value, we can use the value of π as 3.14.

Weight of beaker with water ≈ 54 x 3.14 + 3.5 ≈ 169.56 + 3.5 ≈ 173.06 ounces

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Answer:

9 x 4 1/4 x 8 1/2 = 325 1/8 cubic feet.

4 1/4 x 2 = 8 1/2

Answer:

\(\text{27}\)

Step-by-step explanation:

Given that :

\(\text{Dimension of poster board} = 1 \ \text{yd} \ \text{by} \ 1 \ \text{yd}\)

\(\text{Dimension of each poster board} = \dfrac{1}{3} \ \text{yd} \ \text{by} \ \dfrac{1}{9} \ \text{yd}\)

Number of poster signs that can be cut :

\(\text{Area of poster sign} = \dfrac{1}{3} \times \dfrac{1}{9} = \dfrac{1}{27} \ \text{yard}^2\)

\(\text{Area of poster board} = 1 \ \text{yard}^2\)

Number of poster signs that can be cut :

\(\dfrac{\text{Area of poster board}}{\text{Area of poster sign}}\)

\(1 \ \text{yard}^2\div (\dfrac{1}{27} ) \ \text{yard}^2\)

\(1 \div \dfrac{1}{27}\)

\(1 \times \dfrac{27}{1}\)

\(\bold{= 27 \ poster \ signs}\)

Answer:

The maximum probability for each of the components in a system to fail, for you to still achieve your objective, is 0.008992

Step-by-step explanation:

- There are 1,000 different components in each system.

- The Objective:

Each system should have a 0.999 probability of functioning properly. In other words, your department (or you) expects that each system will have a high probability of functioning properly, hence the closeness of 0.999 to 1.

- Each system is such that at most 8 components out of 1,000 can be bad, for it to still function.

- Question:

What must be the maximum probability for each component in a system to fail, for the system to still have a 0.999 probability of functioning properly?

ANSWER:

When the question says maximum, you need to assume that for each system, 8 components are actually bad!

1000 - 8 = 992

So with 992 components (at least or minimum) functioning, a system will still function.

Next Step:

Since the objective (the expected probability) for a system to function is 0.999, the probability of each of the minimum 992 components to function (which is same as the maximum probability for each of the 1,000 components to function) is

992/1000 × 0.999    

=0.992 × 0.999

=0.991008

Now, remember that the question says fail, not succeed. So, if the figure above is the maximum success rate for each of the 1,000 component parts (same as the success rate for each of the minimum of 992 component parts), then the failure rate or probability is (1 - 0.991008 = 0.008992).

FINAL ANSWER:

The maximum probability for each of the components in a system to fail, for you to still achieve your objective, is 0.008992

The missing 3 steps for the given equivalent equation are as follows:

1st step: 2x - 6 = 4x

2nd step: -6 = 2x

3rd step: -3 = x

Algebraic equations with equivalent solutions or roots are called equivalent equations.

An analogous equation is one that is created by adding or removing the identical quantity or expression from both sides of a given equation.

An equation is equivalent if both sides are multiplied or divided by the same non-zero value.

So, we have the equation:

2(x-3) = 4x

Now, solve further as follows:

2(x-3) = 4x

1st step: 2x - 6 = 4x

2nd step: -6 = 2x

3rd step: -3 = x

Therefore, the missing 3 steps for the given equivalent equation are as follows:

1st step: 2x - 6 = 4x

2nd step: -6 = 2x

3rd step: -3 = x

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Answer:

\(log_35=x\)

Step-by-step explanation:

I am going to assume you meant \(5=3^x\)

When converting exponential equations into logarithmic form, remember this: \(y = log_bx\) is equivalent to \(x = b^y\)

Answer:

D. -3 + 2i and E. 3+2i are the zeroes for the equation.

Step-by-step explanation:

Step-by-step explanation:

Do not know sorry

........ M

The probability that a randomly selected point within the circle would fall in the red- shaded area is 45. 833 %

The arc that is covered by the red - shaded area in the circle has a degree measure of 165 degrees. This is out of the total circle angle measure of 360 degrees.

This therefore means that the probability that a randomly selected point within the circle would fall in the red- shaded area can be found to be :

= Angle measure of red - shaped area / Total area x  100 %

= 165 / 360 x 100 %

=0. 45833 x 100 %

= 45. 833 %

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Answer:

d,e

Step-by-step explanation:

rational numbers are positive and negative whole numbers.

Answer:

d,e

Step-by-step explanation:

The number nearest to hundredth among the given options is 0.96

To change a number into an approximation having fewer significant digits.

Given are the numbers 0.89, 0.90, 0.92 and 0.96

We need to find which one of these is the nearest hundredth

Among all the options, only 0.96 is the number which is nearest to 100.

Hence, The number nearest to hundredth among the given options is 0.96

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Answer:

Every investment carries some degree of risk, All investments carry some degree of risk. Stocks, bonds, mutual funds, and exchange-traded funds can lose value, even all their value, if market conditions sour. Even conservative, insured investments, such as certificates of deposit (CDs) issued by a bank or credit union, come with inflation risk. They may not earn enough over time to keep pace with the increasing cost of living.

Step-by-step explanation:

First Bus = x

Second Bus = x-15

They are going in opposite directions, so, we have to add the speeds:

x+x-15 = 2x-15

Time = 7 hours

Distance = speed * time

1393 = (2x-15)7

1393 = 2x(7)-15(7)

1393 = 14x-105

1393+105 = 14x

1498 =14x

1498/14 = x

107 =x

First bus: 107 km/h

Second bus = x-15 = 107-15 = 92 km/h

Answer:

8/12=0.667

5/8=0.625

6/10=0.6

2/3=0.667

Step-by-step explanation:

6/10 would be your answer being that it is the smallest of them all

The top five percent of the distribution's lowest weight as calculated from the given data  for a bag is 246.

Average population = 240

Standard deviation for the population; 3

Z-score can be calculated as ,

z = (x' - μ)/σ

Now, in order to determine which of the top 5 values in the distribution has the least weight, we will use the significance threshold of 1 - 0.05/2 = 0.025.

Z-score is 1.96 at significance level 0.025.

Thus;

1.96 = (x' - 240)/3

3 × 1.96 = x' - 240

x' = 240 + 5.88

x' = 245.88

Getting close to a whole number results ,

x' = 246

The two z-score tables are as follows:

Positive Z Score Table: The observed value is greater than the average of all values.

An observed value that is below the mean of all values is shown by a negative Z score table.

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The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities.

If Mofor only has time to do two homework assignments out of the five subjects, he will need to choose which subjects to prioritize. The specific subjects he chooses to work on will depend on various factors such as his strengths, weaknesses, upcoming deadlines, and personal preferences. Here are a few strategies he could consider:

1. Prioritize based on importance: Mofor can prioritize the homework assignments that carry more weight in terms of grades or have upcoming deadlines. This way, he ensures that he completes the assignments that have a higher impact on his overall academic performance.

2. Focus on challenging subjects: If Mofor finds certain subjects more difficult or time-consuming, he can prioritize those assignments to allocate more time and effort to them. This approach allows him to concentrate on improving his understanding and performance in subjects that require extra attention.

3. Balance workload: Mofor can choose to distribute his efforts evenly across subjects, selecting two assignments from different subjects. This strategy ensures that he maintains a balanced workload and avoids neglecting any particular subject.

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities. It is essential for him to consider his academic goals, time constraints, and personal strengths to make an informed decision.

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Answer:

B a vertical translation 50units right

The probability that a comfortable chair in the store is blue is 4%

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

Proportion of blue chairs = 20%

Proportion of orange chairs = 50%

Proportion of black chairs = 30%

Comfortable Blue chairs = 20%

Comfortable non-blue chairs = 5%

The required probability is then calculated as

Probability = Proportion of blue chairs x Comfortable Blue chairs

Substitute the known values in the above equation, so, we have the following representation

Probability = 20% * 20%

Evaluate

Probability = 4%

Hence, the probability is 4%

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Let's see the sketch:

The function is differentiable at x = 0 as you can see from the graph. It doesn't have any cusp or discontinuity.

Now, to find the derivate, we use the bottom function (as x = 0 falls in this).

So,

The derivative is -1

Given z = 3 + i, right away we can find

(a) square

z ² = (3 + i )² = 3² + 6i + i ² = 9 + 6i - 1 = 8 + 6i

(b) modulus

|z| = √(3² + 1²) = √(9 + 1) = √10

(d) polar form

First find the argument:

arg(z) = arctan(1/3)

Then

z = |z| exp(i arg(z))

z = √10 exp(i arctan(1/3))

or

z = √10 (cos(arctan(1/3)) + i sin(arctan(1/3))

(c) square root

Any complex number has 2 square roots. Using the polar form from part (d), we have

√z = √(√10) exp(i arctan(1/3) / 2)

and

√z = √(√10) exp(i (arctan(1/3) + 2π) / 2)

Then in standard rectangular form, we have

\(\sqrt z = \sqrt[4]{10} \left(\cos\left(\dfrac12 \arctan\left(\dfrac13\right)\right) + i \sin\left(\dfrac12 \arctan\left(\dfrac13\right)\right)\right)\)

and

\(\sqrt z = \sqrt[4]{10} \left(\cos\left(\dfrac12 \arctan\left(\dfrac13\right) + \pi\right) + i \sin\left(\dfrac12 \arctan\left(\dfrac13\right) + \pi\right)\right)\)

We can simplify this further. We know that z lies in the first quadrant, so

0 < arg(z) = arctan(1/3) < π/2

which means

0 < 1/2 arctan(1/3) < π/4

Then both cos(1/2 arctan(1/3)) and sin(1/2 arctan(1/3)) are positive. Using the half-angle identity, we then have

\(\cos\left(\dfrac12 \arctan\left(\dfrac13\right)\right) = \sqrt{\dfrac{1+\cos\left(\arctan\left(\dfrac13\right)\right)}2}\)

\(\sin\left(\dfrac12 \arctan\left(\dfrac13\right)\right) = \sqrt{\dfrac{1-\cos\left(\arctan\left(\dfrac13\right)\right)}2}\)

and since cos(x + π) = -cos(x) and sin(x + π) = -sin(x),

\(\cos\left(\dfrac12 \arctan\left(\dfrac13\right)+\pi\right) = -\sqrt{\dfrac{1+\cos\left(\arctan\left(\dfrac13\right)\right)}2}\)

\(\sin\left(\dfrac12 \arctan\left(\dfrac13\right)+\pi\right) = -\sqrt{\dfrac{1-\cos\left(\arctan\left(\dfrac13\right)\right)}2}\)

Now, arctan(1/3) is an angle y such that tan(y) = 1/3. In a right triangle satisfying this relation, we would see that cos(y) = 3/√10 and sin(y) = 1/√10. Then

\(\cos\left(\dfrac12 \arctan\left(\dfrac13\right)\right) = \sqrt{\dfrac{1+\dfrac3{\sqrt{10}}}2} = \sqrt{\dfrac{10+3\sqrt{10}}{20}}\)

\(\sin\left(\dfrac12 \arctan\left(\dfrac13\right)\right) = \sqrt{\dfrac{1-\dfrac3{\sqrt{10}}}2} = \sqrt{\dfrac{10-3\sqrt{10}}{20}}\)

\(\cos\left(\dfrac12 \arctan\left(\dfrac13\right)+\pi\right) = -\sqrt{\dfrac{10-3\sqrt{10}}{20}}\)

\(\sin\left(\dfrac12 \arctan\left(\dfrac13\right)+\pi\right) = -\sqrt{\dfrac{10-3\sqrt{10}}{20}}\)

So the two square roots of z are

\(\boxed{\sqrt z = \sqrt[4]{10} \left(\sqrt{\dfrac{10+3\sqrt{10}}{20}} + i \sqrt{\dfrac{10-3\sqrt{10}}{20}}\right)}\)

and

\(\boxed{\sqrt z = -\sqrt[4]{10} \left(\sqrt{\dfrac{10+3\sqrt{10}}{20}} + i \sqrt{\dfrac{10-3\sqrt{10}}{20}}\right)}\)

Answer:

\(\displaystyle \text{a. }8+6i\\\\\text{b. }\sqrt{10}\\\\\text{c. }\\\sqrt{\sqrt{\frac{5}{2}}+\frac{3}{2}}+i\sqrt{\frac{\sqrt{10}-3}{2}},\\-\sqrt{\sqrt{\frac{5}{2}}+\frac{3}{2}}-i\sqrt{\frac{\sqrt{10}-3}{2}}\\\\\\\text{d. }\\\text{Exact: }z=\sqrt{10}\left(\cos\left(\arctan\left(\frac{1}{3}\right)\right), i\sin\left(\arctan\left(\frac{1}{3}\right)\right)\right),\\\text{Approximated: }z=3.16(\cos(18.4^{\circ}),i\sin(18.4^{\circ}))\)

Step-by-step explanation:

Recall that \(i=\sqrt{-1}\)

Part A:

We are just squaring a binomial, so the FOIL method works great. Also, recall that \((a+b)^2=a^2+2ab+b^2\).

\(z^2=(3+i)^2,\\z^2=3^2+2(3i)+i^2,\\z^2=9+6i-1,\\z^2=\boxed{8+6i}\)

Part B:

The magnitude, or modulus, of some complex number \(a+bi\) is given by \(\sqrt{a^2+b^2}\).

In \(3+i\), assign values:

\(|z|=\sqrt{3^2+1^2},\\|z|=\sqrt{9+1},\\|z|=\sqrt{10}\)

Part C:

In Part A, notice that when we square a complex number in the form \(a+bi\), our answer is still a complex number in the form

We have:

\((c+di)^2=a+bi\)

Expanding, we get:

\(c^2+2cdi+(di)^2=a+bi,\\c^2+2cdi+d^2(-1)=a+bi,\\c^2-d^2+2cdi=a+bi\)

This is still in the exact same form as \(a+bi\) where:

Thus, we have the following system of equations:

\(\begin{cases}c^2-d^2=3,\\2cd=1\end{cases}\)

Divide the second equation by \(2d\) to isolate \(c\):

\(2cd=1,\\\frac{2cd}{2d}=\frac{1}{2d},\\c=\frac{1}{2d}\)

Substitute this into the first equation:

\(\left(\frac{1}{2d}\right)^2-d^2=3,\\\frac{1}{4d^2}-d^2=3,\\1-4d^4=12d^2,\\-4d^4-12d^2+1=0\)

This is a quadratic disguise, let \(u=d^2\) and solve like a normal quadratic.

Solving yields:

\(d=\pm i \sqrt{\frac{3+\sqrt{10}}{2}},\\d=\pm \sqrt{\frac{{\sqrt{10}-3}}{2}}\)

We stipulate \(d\in \mathbb{R}\) and therefore \(d=\pm i \sqrt{\frac{3+\sqrt{10}}{2}}\) is extraneous.

Thus, we have the following cases:

\(\begin{cases}c^2-\left(\sqrt{\frac{\sqrt{10}-3}{2}}\right)^2=3\\c^2-\left(-\sqrt{\frac{\sqrt{10}-3}{2}}\right)^2=3\end{cases}\\\)

Notice that \(\left(\sqrt{\frac{\sqrt{10}-3}{2}}\right)^2=\left(-\sqrt{\frac{\sqrt{10}-3}{2}}\right)^2\). However, since \(2cd=1\), two solutions will be extraneous and we will have only two roots.

Solving, we have:

\(\begin{cases}c^2-\left(\sqrt{\frac{\sqrt{10}-3}{2}}\right)^2=3 \\c^2-\left(-\sqrt{\frac{\sqrt{10}-3}{2}}\right)^2=3\end{cases}\\\\c^2-\sqrt{\frac{5}{2}}+\frac{3}{2}=3,\\c=\pm \sqrt{\sqrt{\frac{5}{2}}+\frac{3}{2}\)

Given the conditions \(c\in \mathbb{R}, d\in \mathbb{R}, 2cd=1\), the solutions to this system of equations are:

\(\left(\sqrt{\sqrt{\frac{5}{2}}+\frac{3}{2}}, \sqrt{\frac{\sqrt{10}-3}{2}}\right),\\\left(-\sqrt{\sqrt{\frac{5}{2}}+\frac{3}{2}},- \frac{\sqrt{10}-3}{2}}\right)\)

Therefore, the square roots of \(z=3+i\) are:

\(\sqrt{z}=\boxed{\sqrt{\sqrt{\frac{5}{2}}+\frac{3}{2}}+i\sqrt{\frac{\sqrt{10}-3}{2}} },\\\sqrt{z}=\boxed{-\sqrt{\sqrt{\frac{5}{2}}+\frac{3}{2}}-i\sqrt{\frac{\sqrt{10}-3}{2}}}\)

Part D:

The polar form of some complex number \(a+bi\) is given by \(z=r(\cos \theta+\sin \theta)i\), where \(r\) is the modulus of the complex number (as we found in Part B), and \(\theta=\arctan(\frac{b}{a})\) (derive from right triangle in a complex plane).

We already found the value of the modulus/magnitude in Part B to be \(r=\sqrt{10}\).

The angular polar coordinate \(\theta\) is given by \(\theta=\arctan(\frac{b}{a})\) and thus is:

\(\theta=\arctan(\frac{1}{3}),\\\theta=18.43494882\approx 18.4^{\circ}\)

Therefore, the polar form of \(z\) is:

\(\displaystyle \text{Exact: }z=\sqrt{10}\left(\cos\left(\arctan\left(\frac{1}{3}\right)\right), i\sin\left(\arctan\left(\frac{1}{3}\right)\right)\right),\\\text{Approximated: }z=3.16(\cos(18.4^{\circ}),i\sin(18.4^{\circ}))\)

Answer:

8

Step-by-step explanation:

45 points for a free movie - 25 points = 20 remaining points needed

20 / 2.5 = 8

She would need 8 visits to earn a free movie ticket.

Answer:

8

Step-by-step explanation:

25+2.5x=45

subtract 25 from each side

2.5x=20

divide both sides by 2.5

x=8