what is the absolute value of the complex number -4 - square root of -2i

Answer:

c

Step-by-step explanation:

Final answer:

To find the quadratic equation with roots 5 and -2, we can use the quadratic formula. Substituting the values of the roots into the formula, we get the equation (x - 5)(x + 2) = 0.

Explanation:

A quadratic equation in standard form is written as ax² + bx + c = 0, where a, b, and c are constants. To find the equation with roots 5 and -2, we can use the fact that the solutions of a quadratic equation are given by the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Substituting the values of the roots into the quadratic formula, we have:

x = (-b ± √(b² - 4ac)) / (2a)

For the first root, x = 5:

5 = (-b ± √(b² - 4ac)) / (2a)

Substituting a = 1, b = -7, and c = 10, we get:

5 = (-(-7) ± √((-7)² - 4(1)(10))) / (2(1))

Simplifying further:

5 = (7 ± √(49 - 40)) / 2

5 = (7 ± √9) / 2

5 = (7 ± 3) / 2

So, the first root gives us the equation:

x = 5, which translates to x - 5 = 0.

For the second root, x = -2:

-2 = (-b ± √(b² - 4ac)) / (2a)

Substituting a = 1, b = -7, and c = 10, we get:

-2 = (-(-7) ± √((-7)² - 4(1)(10))) / (2(1))

Simplifying further:

-2 = (7 ± √(49 - 40)) / 2

-2 = (7 ± √9) / 2

-2 = (7 ± 3) / 2

So, the second root gives us the equation:

x = -2, which translates to x + 2 = 0.

Therefore, the quadratic equation in standard form with roots 5 and -2 is:

(x - 5)(x + 2) = 0

Answer:

y = (x + 1)^2

Step-by-step explanation:

I used desmos and put each answer choice into the graphing calculator and answer choice D was the only one that matched with the image in the question.

The equation in standard form passing through (-4, 2) with a slope of 9/2 is 9x - 2y = -10.

Since the equation is in standard form, rearrange it to slope-intercept form y = mx + b.

Given slope m = 9/2 and point (-4, 2), substitute these values to find the correct equation.

After substitution, the equation is 9x - 2y = -10.

To make 'h' the subject of the formula, multiply both sides by 10 to get the equation 10t = gh. Then divide both sides by 'g' to get h = 10t/g.

The formula given in the question is t = gh/10. To make h the subject of the formula, we'll need to isolate it. To do this, you should start off by multiplying both sides of the equation by 10, thus removing the divide by 10 part. This will give you 10t = gh. Finally, divide both sides of the equation by g. So, your revised formula would be h = 10t/g. This formula now clearly places h as the subject.

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To solve the logarithmic equation 3 log5 x - log5 4 = log5 16, we use logarithmic properties to combine terms and then solve for x, finding that x = 4.

To solve the logarithmic equation 3 log5 x - log5 4 = log5 16, we can use the properties of logarithms.

First, we rewrite the equation using the property that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number. This gives us:

log5 x^3 - log5 4 = log5 16.

Next, we utilize the property that the logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers. So we can combine the left side of the equation into a single logarithm:

log5 (x^3 / 4) = log5 16.

Now, since the bases of the logarithms are the same, we can equate the arguments of the logarithms:

x^3 / 4 = 16

Solving for x, we multiply both sides by 4 and then take the cube root:

x^3 = 64

Therefore, x = 4, since 4 cubed equals 64.

The complete question is: Solve logarithm Equation: 3 log5 x-log5 4= log5 16 is:

To solve the logarithmic equation, apply the properties of logarithms to simplify and solve for x.

To solve the logarithmic equation, we can use the properties of logarithms. First, let's apply the property that states the logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers. This gives us: 3 log5 x - log5 4 = log5 16. Next, we can apply the property that states the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number. This gives us: log5 x3 - log5 4 = log5 16. We can simplify the equation by combining the logarithms and solving for x.

x3 / 4 = 16

x3 = 64

x = 4

the correct simplification of (7x^3 − 8x − 5) + (3x^3 + 7x + 1),

Is 10x^3 − x − 4

Answer:

The correct option is 1.

Step-by-step explanation:

It is given that in ΔRST , segment SU is an altitude. It means the angle SUR and angle SUT are right angles.

It triangle RST and SUT,

[tex]\angle RST=\angle SUT=90^{\circ}[/tex]         (Definition of altitude)

[tex]\angle STR=\angle UTS[/tex]         (Common angle)

Two corresponding angles are equal. So by AA property of similarity,

[tex]\triangle RST\sim \triangle SUT[/tex]              .... (1)

It triangle RST and RUS,

[tex]\angle RST=\angle SUR=90^{\circ}[/tex]         (Definition of altitude)

[tex]\angle SRT=\angle URS[/tex]         (Common angle)

Two corresponding angles are equal. So by AA property of similarity,

[tex]\triangle RST\sim \triangle RUS[/tex]              .... (2)

According to transitive property of equality,

if a=b and b=c, then a=c.

From (1) and (2), we get

[tex]\triangle RUS\sim \triangle SUT[/tex]             ( Transitive property of equality)

Therefore the correct option is 1.

Final answer:

To determine the number of radios with both digital tuners and CD players, we use the principle of inclusion-exclusion. With 70 radios featuring digital tuners and 90 featuring CD players out of 100, the calculation reveals that 60 radios had both features.

Explanation:

The question asks how many radios sold recently in a department store had both digital tuners and CD players, given that 70 had digital tuners and 90 had CD players out of a total of 100 clock radios. To find the number of radios that had both features, we can use the principle of inclusion-exclusion. The formula for this principle is: Total = A + B - (A and B), where A and B are the two groups, and (A and B) is the intersection of the two groups. In this case, A is the number of radios with digital tuners, and B is the number of radios with CD players.

Substituting the given values: 100 = 70 + 90 - (A and B). Solving for (A and B), which represents the radios with both features, we get: (A and B) = 70 + 90 - 100 = 160 - 100 = 60.

Therefore, 60 radios had both digital tuners and CD players.

we have

[tex](3x^{2} -2y^{2}+5x)+(4 x^{2}+12y^{2}-7x)[/tex]

Combine like terms

[tex](3x^{2} -2y^{2}+5x)+(4 x^{2}+12y^{2}-7x)\\=(3x^{2}+4x^{2})+(-2y^{2}+12y^{2})+(5x-7x)\\=7x^{2} +10y^{2}-2x[/tex]

therefore

the answer is the option C

He combined the terms [tex]-2y^{2}[/tex] and [tex]12y^{2}[/tex] incorrectly

Answer:

16 years

Step-by-step explanation:

Given,

Number of students in group A = X,

Sum of their ages = 221,

So, the average age of students in group A = [tex]\frac{\text{Sum of ages}}{\text{Total students}}[/tex]

[tex]=\frac{221}{X}[/tex]

According to the question,

[tex]\frac{221}{X}=\text{Integer}[/tex]

∴ X must be a factor of 221,

∵ 221 = 13 × 17,

Now, If X = 13,

Then the number of students in group B = 26 ( NOT POSSIBLE )

If X = 17,

Then the number of students in group B = 34

Which is between 30 and 40,

Now, Let S be the sum of ages of students in group B,

So, the average age in group B = [tex]\frac{S}{34}[/tex]

Again according to the question,

[tex]\frac{S+221}{17+34}=\frac{S}{34}-1[/tex]

[tex]\frac{S+221}{51}=\frac{S-34}{34}[/tex]

[tex]34S+7514 = 51S - 1734[/tex]

[tex]34S - 51S = -1734 - 7514[/tex]

[tex]17S = 9248[/tex]

[tex]\implies S = 544[/tex]

Therefore, the average age of B = [tex]\frac{544}{34}[/tex] = 16 years.

To find the actual length of the object, multiply the length on the blueprint by the scale factor of 5 feet/inch. The length of the object in actual size is 42 feet 6 inches.

To find the actual length of the object represented on the blueprint, we can use the scale factor provided. The scale on the blueprint is 1 inch = 5 feet. So, if the object is 8 1/2 inches long on the blueprint, we can multiply it by the scale factor to find the actual length.

Step 1:

Convert 8 1/2 inches into a mixed number fraction by adding 1 to the whole number.
8 1/2 inches = 8 + 1/2 = 17/2 inches

Step 2:

Multiply the length on the blueprint by the scale factor:
17/2 inches * 5 feet/inch = 85/2 feet

Step 3:

Simplify the fraction if possible:
85/2 feet = 42 feet 6 inches

Therefore, the length of the object in actual size is 42 feet 6 inches.

To find the actual length of an object that is 8 1/2 inches long on a blueprint with a scale of 1 inch = 5 feet, you multiply 8.5 by 5, resulting in an actual length of 42.5 feet.

If the scale on a blueprint is 1 inch = 5 feet, then to determine the actual length of an object that is 8 1/2 inches long on the blueprint, we simply multiply the length on the blueprint by the scale factor.

So, for every inch on the blueprint, there are 5 feet in reality. Therefore, we calculate the actual length as follows:

Thus, the actual length of the object is 42.5 feet.

Answer:

A. The class and exam medians are almost the same.