BRAINLIEST if correct, 5th grade geometry

The equation of the plane containing the line x = 2 + t, y = 4 − t, z = 3 − 3t and is parallel to the plane 5x + 2y + z = 3 is 5x + 2y + z = 21

What is a plane?

Any flat, three-dimensional, infinitely long surface is considered to be a plane. It can alternatively be thought of as the two-dimensional equivalent of a point with zero dimensions, a line with one dimension, and a space with three dimensions.

Given that, a plane is containing the line x = 2 + t, y = 4 − t, z = 3 − 3t and is parallel to the plane 5x + 2y + z = 3

Any  plan e parallel to the plane 5x + 2y + z = 3 , should be in the form of 5x + 2y + z = k

Now, this plane should contain the line mentioned above

On substituting the terms,

5(2 + t) + 2(4 - t) + (3 - 3t) = k

10 + 5t + 8 - 2t + 3 -3t = k

21 = k

Therefore, The equation of the required plane is 5x + 2y + z = 21

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Answer:

140

Step-by-step explanation:

(5*7*8)/2= 280/2 =140

Using the distributive property of matrix multiplication A(cu) = 0, which implies that cu also satisfies the equation Ax = 0 for any scalar c.

We have given that Ax = 0, where A is an m × n matrix and x is an n-dimensional vector in Rn.

To show that A(cu) = 0 for any scalar c, we can use the distributive property of matrix multiplication, which states that A(B + C) = AB + AC for any matrices A, B, and C of appropriate dimensions.

Let us substitute cu for x in the equation Ax = 0, then we get:

A(cu) = A(c × u)

Using the distributive property, we can write:

A(c × u) = c × A(u)

Since u satisfies the equation Ax = 0, we have:

A(u) = 0

Substituting this into the above equation, we get:

c × A(u) = c × 0 = 0

Therefore, we have shown that A(cu) = 0, which implies that cu also satisfies the equation Ax = 0 for any scalar c.

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Answer:

3

Step-by-step explanation:

Parenthesis

Exponent

Division

Multiplication

Addition

Subtraction

(1.3+0.2) ÷ 5+2.7

paranthesis first

1.5 ÷ 5 + 2.7

Division next

0.3 +2.7= 3

Answer:

Set up the equation ... 60 + 40X = total charges... where X is the number of hours (6.5)

60 + 40(6.5) = ?

60 + 260 = ?

320 = total charges

Answer:

Step-by-step explanation:

Here's a step-by-step explanation of the reflections:

Point R is located at (1, 1) on the coordinate plane.

Reflection over the y-axis: This reflection changes the sign of the x-coordinate. In other words, if the point (x, y) is reflected over the y-axis, the reflected point will be ( -x, y). So, for point R at (1, 1), the reflection over the y-axis creates R' at (-1, 1).

Reflection over the x-axis: This reflection changes the sign of the y-coordinate. In other words, if the point (x, y) is reflected over the x-axis, the reflected point will be (x, -y). So, for point R' at (-1, 1), the reflection over the x-axis creates R'' at (-1, -1).

So the final location of R'' is at the ordered pair (-1, -1).

Step-by-step explanation:

(a) To convert feet to fathoms, we can use the conversion factor 1 fathom = 6 feet. Hence, we can divide the depth in feet by 6 to find the depth in fathoms:

36,078 feet / 6 feet/fathom = 6,013 fathoms

So the depth of the seabed is 6,013 fathoms.

(b) To convert feet to leagues (marine), we can use the conversion factor 1 league (marine) = 5,556 feet. Hence, we can divide the depth in feet by 5,556 to find the depth in leagues (marine):

36,078 feet / 5,556 feet/league (marine) = 6.52 leagues (marine)

So the depth of the seabed is approximately 6.52 leagues (marine).

Answer:

letter R rounded off to the nearest tenth is 40

15 is the answer because this is the nearest

Answer:B

Step-by-step explanation:

The number of years, t , after which the value of the company's new equipment will be less than 7500 is 2.64 years

To solve this problem, we can use the formula for exponential growth:

V(t) = V₀ * (1 + r)^t

Given that the parameters are;

To determine time t when the value of the equipment will be less than $7500.

Let's set up an inequality;

V(t) < 7500

Substituting the formula for V(t), we get:

V₀ * (1 + r)^t < 7500

Substitute the values

(1 + 0.159)^t < 0.5

t * log(1 + 0.159) < log(0.5)

t > log(0.5) / log(1 + 0.159)

Using a calculator, we get:

t > 2.64

Hence, the value is 2.64 years.

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The final price of Thomas Peters' new SUV  is $30,309 , can be calculated by subtracting the rebates from the initial cost.

The initial cost of the SUV was $32,984, and he received a $2,175 rebate from the car dealer and a $500 rebate from the manufacturer. So, the final price would be calculated as follows:

Final Price = $32,984 - $2,175 - $500

Final Price = $30,309

Therefore, the final price of Thomas Peters' new SUV is $30,309.

It is important to note that rebates can play a significant role in reducing the cost of a car purchase. In this case, Thomas Peters was able to receive a total of $2,675 in rebates, which reduced the cost of his new SUV by over 8%. This shows that it is often worth the time and effort to research available rebates and incentives when making a car purchase. Additionally, it is also a good idea to negotiate the price with the car dealer, as there may be room for further discounts.

By taking these steps, you may be able to save a significant amount of money on your car purchase and get a better value for your money. Ultimately, it is important to weigh the cost and benefits of each car option to determine the best choice for your needs and budget.

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Answer:

[tex]a \sqrt[5]{b} [/tex]

Step-by-step explanation:

solution Given:

[tex] \sqrt[5]{ {a}^{3} {b}^{2} } \times \sqrt[5]{ {a}^{2}{b }^{ - 1} } [/tex]

since i indices rule if the power is same it can be multiplied or divided.

[tex] \sqrt[5]{ {a}^{3} {b}^{2} \times {a}^{2} {b}^{ - 1} } [/tex]

since power is added of like terms in multiplication

[tex] \sqrt[5]{ {a}^{3 + 2} {b}^{2 - 1} } [/tex]

again simplifying

[tex] \sqrt[5]{ {a}^{5} b} [/tex]

by using indices formula

[tex] \sqrt[x]{ {a}^{y} } = {a}^{ \frac{y}{x} } [/tex]

we get

[tex]a \sqrt[5]{b} [/tex]

Answer:

[tex]a \sqrt[5]{b}[/tex]

Step-by-step explanation:

Given expression:

[tex]\sqrt[5]{a^3b^2} \times \sqrt[5]{a^2b^{-1}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]

[tex](a^3b^2)^{\frac{1}{5}} \times (a^2b^{-1})^{\frac{1}{5}}[/tex]

As the exponents are the same,

[tex]\textsf{apply exponent rule} \quad a^n \cdot c^n=(a \cdot c)^n:[/tex]

[tex](a^3b^2a^2b^{-1})^{\frac{1}{5}}[/tex]

Collect like terms:

[tex](a^3a^2b^2b^{-1})^{\frac{1}{5}}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex](a^{(3+2)}b^{(2-1)})^{\frac{1}{5}}[/tex]

Simplify the exponents:

[tex](a^5b^1)^{\frac{1}{5}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^bc^d)^n=(a^b)^n \cdot (c^d)^n:[/tex]

[tex](a^5)^{\frac{1}{5}} \cdot (b^1)^{\frac{1}{5}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]a^{\frac{5}{5}} \cdot b^{\frac{1}{5}}[/tex]

Simplify:

[tex]a^1 \cdot b^{\frac{1}{5}}[/tex]

[tex]a \cdot b^{\frac{1}{5}}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{\frac{1}{n}}=\sqrt[n]{a}:[/tex]

[tex]a \sqrt[5]{b}[/tex]

The input is 8, the output of the function f(x) would be -5.

What is the function?

Function is a relationship or expression involving one or more variables.  It has a set of input and outputs.

Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences. The modern definition of function was first given in 1837 by the German mathematician Peter Dirichlet

To find the output of the function f(x) when x is 8, we substitute x = 8 into the function and simplify:

f(x) = 8/x - 6

f(8) = 8/8 - 6

f(8) = 1 - 6

f(8) = -5

Hence, if the input is 8, the output of the function f(x) would be -5.

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The probability that the hacker guesses the password on his first try is, 0.001600.

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

The probability of a hacker guessing the correct password on their first try would be 1 in 10,000, since there are a total of 5⁴ possible combinations of 4 digits, each between 0 and 4, inclusive.

The probability can be calculated as:

= 1 / 5⁴

= 1 / 625

= 0.0016

Rounded to six decimal places, the probability is: 0.0016 = 0.001600.

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The volume of the Cone A will be 4m³.

What is a cone?

A cone is a shape constructed by connecting a common point, known as the apex or vertex, to all the points of a circular base using a collection of line segments (which does not contain the apex). The height of the cone is the distance from the vertex to the base. The radius of the circular base has been measured. The slant height is the length of the cone from the apex to any point on the perimeter of the base. Based on these values, formulae for the cone's surface area and volume have been developed. The cone in the illustration is characterised by its height, radius of base, and slant height.

Volume of cone=πr²h where r=radius of base and h=height of cone

Curved surface area=πrL , where L=slant height

Now,

As given Cone B is the image of cone A after dilation by a scale factor of 1/4. If the volume of cone B is 1 m³

After dilation volume also decreases/increases with respect to scale factor of dilation. Here scale factor is 1/4

and Then volume of A=1*4

=4 m³

hence,

          The volume of the Cone A will be 4m³.

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Answer: it is actually 64m^3

Step-by-step explanation:

i did it and this was the right answer

(1) The cost of the phone call was less than $4.16

(2) The cost of the phone call was greater than $3.35

While this is a seemingly simple min/max problem, I was wondering if there is a faster way to deal with decimals—as it took me ~4mins to arrive at the solution.

The cost of a certain phone call was $0.75 for the first 3 minutes and $0.20 for each additional minute after the first 3 minutes. Did the phone call last longer than 15 minutes

According to the above the cost for n minutes, where n>3, is 75 + (n−3)∗20=20n+15

cents. W need to find whether n>15. The cost for 15 minutes is 20n+15=20∗15+15=315

, so we need to find whether the cost is greater than 315 cents.

(1) The cost of the phone call was less than $4.16. Not sufficient.

(2) The cost of the phone call was greater than $3.35. Sufficient.

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Answer:

132ft

Step-by-step explanation:

The height of the Great Sphinx can be found by using the relationship between the height of an object, the length of its shadow, and the angle of elevation of the sun.

Let h1 be the height of the Great Sphinx and h2 be the height of the person. We know that the length of their shadows are 220 ft and 20 ft, respectively.

Since the sun is at the same elevation for both objects, we can set up the following proportion:

h1/220 = h2/20

Cross multiplying, we get:

h1 = (h2 * 220) / 20

Plugging in h2 = 6 ft, we get:

h1 = (6 * 220) / 20 = 132 ft

So, the height of the Great Sphinx is approximately 132 ft.

Thus, the correct answer is 132 ft, which is not in the options provided, but it is a reasonable estimate of the height of the Great Sphinx.

The balance in the account after 1 year due to continuous compounding is approximately $1030.45 and AYP is 3.04%.

What is meant by continuous compounding?

If compound interest is calculated and reinvested into the balance of an account across an essentially unlimited number of periods, continuous compounding is the mathematical limit that compound interest can reach. Continuous compounding determines interest by assuming constant compounding across an infinite number of periods, as opposed to computing interest on a finite number of periods, such as annually or monthly.

Given,

rate per period  = 3%

Principal amount = $1000

Compounding is done after 1,5 and 20 years.

But we are asked to find the amount after continuous compounding after 1 year.

The formula of the amount after continuous compounding is:

[tex]A = Pe^{rt}[/tex]

where A = amount after continuous compounding

        r = rate of period

     t = time period

    P  = principal amount

[tex]A = Pe^{rt} = 1000e^{0.03*1}[/tex] = $1030.45

Annual yield formula (AYP) = [tex](1+\frac{r}{n} )^n-1[/tex]

n = times it compounds per year = 365

r = 0.03

AYP = [tex](1+\frac{0.03}{365} )^{365}-1 = 0.0304[/tex]

                                  = 3.04%

Therefore The balance in the account after 1 year due to continuous compounding is approximately $1030.45 and AYP is 3.04%.

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The factors of given polynomial are (x+3), (x-3), (x+2) and (x-2).

The factors are the polynomials which are multiplied to produce the original polynomial.

The given polynomial is x⁴-13x²+36

Here, x⁴-13x²+36 can be written as x⁴-9x²-4x²+36

= x²(x²-9)-4(x²-9)

= (x²-9)(x²-4)

= (x²-3²)(x²-2²)

By using the identity a²-b²=(a+b)(a-b)

So, (x+3)(x-3)(x+2)(x-2)

Therefore, the factors are (x+3), (x-3), (x+2) and (x-2).

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The distance from the origin to point A graphed on the complex plane below is √13, Option C is the correct answer.

The complex plane in mathematics is the plane made up of complex numbers, with real and imaginary numbers making up the x-axis (also known as the real axis) and the y-axis (also known as the imaginary axis) of the Cartesian coordinate system.

Complex numbers can be geometrically interpreted using the complex plane. They add like vectors when addition is applied. Polar coordinates make it simpler to represent the product of two complex numbers, whose magnitude or modulus is the sum of their absolute values.

The coordinates of the point A are (-3, -2).

If we extend the line from the origin to the point A it forms a right angled triangle with base = 3 and height = 2.

Using the Pythagoras theorem:

c² = a² + b²

Substituting the values:

c² = (2)² + (3)²

c = √13

Hence, the distance from the origin to point A graphed on the complex plane below is √13, Option C is the correct answer.

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The length of the dotted line would be 7.922 ft.

What is the diameter of the circle?

The diameter of a circle is the distance across the circle through its center. It is equal to twice the length of the radius, which is the distance from the center of the circle to any point on the circle.

In mathematical terms, if d represents the diameter of a circle, and r represents its radius, we have the formula:

d = 2r

In the given circle, for finding the inner diameter we have to remove the thickness of the circle from outer diameter, we get

q = 17.708 - 4.893 - 4.893

By solving this, we get

q = 7.922

Hence, the length of the dotted line would be 7.922 ft.

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Answer:

see image

Step-by-step explanation:

First of all, the problem might be that we need to set this up differently than how it is written.

"Subtract THIS from THAT" means that you have to put the second thing first and minus the first thing:

THAT - THIS



Next, the minus in the middle has to go to all three of the terms in the second part. This is going to change the sign of all three parts. See image.

Last, hopefully fraction addition with positive and negative signs isn't too terribly confusing.

1/5 - 2/5 is -1/5.

And -1/4 - 1/4 is -2/4, which is -1/2.

see image.

Make sure the y^2 and the y look like they are next to the whole fraction and are not on the bottom of the fraction.

Answer:

[tex] \frac {3}{8} + \frac{2}{8} = \frac{5}{8} = 1 \frac{3}{8} [/tex]

[tex] = \frac{5}{ \\ 8} = 1 \frac{3}{8} [/tex]

Answer:

I know that answer

Step-by-step explanation:

answer is -23

In right triangle ACB with CD bisects angle ACB and intersects at midpoint of AB at point D the value of x is equal to 5.625.

In right triangle ABC,

BC is the base.

Midpoint of AB is D.

CD bisects ACB.

Measure of ∠ACD = Measure of ∠BCD

AC = 4

BC = 7.5

AD = 3

BD = x

CD bisects angle ACB and intersect at midpoint of AB at point D.

This implies

BD / AD = BC / AC

⇒x / 3 = 7.5 / 4

⇒ x = ( 7.5 × 3 ) / 4

⇒ x = 22.5 / 4

⇒ x = 5.625

Therefore, the value of x in the right triangle ACB with given dimensions is equal to 5.625.

The above question is incomplete , the complete question is :

What is the value of x? Enter your answer, as a decimal, in the box. x= A right triangle with vertices labeled as A, B, and C. Side C B is the base and the top vertex is A. Side A B contains a midpoint D. A line segment drawn from C to D bisects angle A C B into two parts labeled as A C D and B C D. Angles A C D and B C D are marked with single arc. Side A C is labeled as 4. Base C B is labeled as 7.5. Segment A D is labeled as 3. Segment B D is labeled as x.

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Answer:

Below

Step-by-step explanation:

See image

L side goes from    3 units   to   6 units    so scale factor is 2

Answer:a

Step-by-step explanation:

Answer:

Step-by-step explanation:

m∠2 = 90° - 56° = 34°. So, m∠1 = m∠2 = 34°

here the answers

The correct options are sample more families, sample families having children who are not in seventh grade.

Sample families that do not have children. Sample families living in every third house in neighborhood.

To increase the validity of the results of Kai's survey, he could make the following improvements to his sample:

Sample more families: Increasing the sample size would make the results more representative of the neighborhood as a whole, reducing the impact of random variation and making the estimates more precise.

Sample families that have children who are not in seventh grade: This would make the sample more diverse and representative of families with children of different ages.

Sample families that do not have children: Including families without children would make the sample more diverse and representative of the entire neighborhood.

Sample families living in every third house in the neighborhood: This would help to ensure that the sample is geographically representative of the neighborhood, reducing the chance of

sampling bias.

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The perimeter of the figure after a dilation with a scale factor of 4 is

Suppose the initial measurement of a figure was x units.

And let the figure is scaled and new measurement is of y units.

Since the scaling is done by multiplication of some constant, that constant is called scale factor. Let that constant be 's'.

Then we have:

[tex]s \times x = y\\s = \dfrac{y}{x}\\[/tex]

Thus, scale factor is the ratio of the new measurement to the old measurement.

Given;

The perimeter= 12units

Scale factor=4

Now,

Dilation with the given scale factor;

= 12*1/4

=12/4

=3

Therefore, dilation by the given scale factor will be 3.

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