Write each expression in radical form
[tex]\sqrt[4]{6^5}[/tex]

Let's say you are paddling at 5mph and the current is 3 mph. Going upstream, you are going 2 mph and downstream, 8 mph.

8(b - c) = 464

7(b + c) = 644

b - c = 58

b + c = 92

Adding the two together

2b = 150

b = 75

75 - c = 58

c = 17

The boat's speed is 75 mph and the current's speed is 17 mph.

Answer:

(x - 3) is a factor of P(x)

Step-by-step explanation:

if (x - 3) is a factor of P(x) then P(3) = 0

P(3) = 2(3)³ + 5(3)² - 28(3) - 15

      = 2(27) + 5(9) - 84 - 15

      = 54 + 45 - 99

      = 99 - 99

      = 0

since P(3) = 0 then (x - 3) is a factor of P(x)

Answer:

(-21, 54.5)

Step-by-step explanation:

Hello there!

We have two methods to solve this problem.

We will limit ourself to Substitution method.

3x – 2y = -4.................... 1.

4x + 2y = 25................... 2.

First lets manipulate eq.2 in terms of y.

4x + 2y = 25

2y = 25 - 4x

y = 25/2 - 2x .............. eq.3

Substitute eq.3 into eq.1

3x – 2(25/2 -2x) = -4

Solve for x.

Opening the brackets

3x - 25 - 4x = -4

-x = 21

x = -21

Substitute x into equation 3

y = 25/2 - 2x

=> y = 25/2 - 2(-21)

= 54.5

In terms of x and y; (x,y)

= (-21, 54.5)

I hope this helps.

Have a nice studies.

[tex]~~~~~~~4x^2-12x+9=0\\\\\implies (2x)^2-2 \cdot 2x \cdot 3+3^2 = 0\\\\\implies (2x-3)^2 = 0\\\\\implies 2x -3 = 0\\\\\implies x =\dfrac 32[/tex]

Answer:

Step-by-step explanation:

Let the number of people were surveyed is x.

We have 60% of x is 48 people.

Set this as equation and solve:

Correct choice is C.

Answer:

C.  80

Step-by-step explanation:

Given:

Let x be the total number of people surveyed.

Set up a ratio of people to percentage and solve for x:

[tex]\implies \sf 48 : 60 = x : 100[/tex]

[tex]\implies \sf \dfrac{48}{60}=\dfrac{x}{100}[/tex]

[tex]\implies \sf x=100 \cdot \dfrac{48}{60}[/tex]

[tex]\implies \sf x=\dfrac{4800}{60}[/tex]

[tex]\implies \sf x=\dfrac{480}{6}[/tex]

[tex]\implies \sf x=80[/tex]

Therefore, the total number of people who were surveyed was 80.

The formula for calculating the volume of a cube is expressed as V = L³. The volume of the cube is 1/27 cubic meters

The formula for calculating the volume of a cube is expressed as:

V = L³

where:

L = 1/3cm

Substitute

V = (1/3)³
V = 1/3³

V = 1/27 cubic meters

Hence the volume of the cube is 1/27 cubic meters

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By subtracting the given addend to the sum, we see that the other addend is:

[tex]6d^5 - 2c^3d^2 + 5c^2d^3 - 12cd^4 - 8[/tex]

We know that the sum of two polynomials is:

[tex]8d^5 - 3c^3d^2 + 5c^2d^3 - 4cd^4 + 9[/tex]

One of the addends is:

[tex]2d^5 - c^3d^2 + 8cd^4 + 1[/tex]

To get the other addend, we can subtract the given addend to the sum:

[tex]8d^5 - 3c^3d^2 + 5c^2d^3 - 4cd^4 + 9 - (2d^5 - c^3d^2 + 8cd^4 + 1)\\\\6d^5 - 2c^3d^2 + 5c^2d^3 - 12cd^4 - 8[/tex]

Then we can conclude that the other addend is:

[tex]6d^5 - 2c^3d^2 + 5c^2d^3 - 12cd^4 - 8[/tex]

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Answer:

(4, -6)

Step-by-step explanation:

(x1+x2)/2 + (y1+y2)/2 = midpoint

(11+-3)/2 = 8/2 = 4.     x = 4

(-5 + -7)/2 = -12/2.      y = -6

4, -6 is the midpoint

give brainliest please! hope this helps :)

An x-intercept of the continuous function in the table is (-1, 0)

The x-intercept of a line is the point where the line crossed the x-axis or the  point where the value of y is zero.

From the table, the x-intercept are all the point where the value of f(x) is zero. Hence the Which is an x-intercept of the continuous function in the table is (-1, 0)

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Step-by-step explanation:

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Step-by-step explanation:

a = hours at job A

b = hours at job B

a + b = 24

a = 24 - b

5.8a + 7.4b = 158.4

note we can use the a = 24 - b identity in the second equation :

5.8×(24 - b) + 7.4b = 158.4

139.2 - 5.8b + 7.4b = 158.4

1.6b = 19.2

b = 12 hours

a = 24 - b = 24 - 12 = 12 hours

she worked 12 hours on job A and 12 hours on job B.

Interpretation 1:

[tex]5x = 15 \\ [/tex]

Divide both sides by 5:

[tex]\implies \boxed{x = 3}[/tex]

(Which is the final answer.)

[tex]\huge\mathfrak\colorbox{white}{}[/tex]

Interpretation 2:

[tex] 5^{x}=15[/tex]

Take logarithm to the base 5 on both sides:

[tex]\implies log_5(5^{x})=log_5(15)\\\implies x=log_5 (15) \\\implies x= \frac{ln(15)}{ln(5)} \\\implies \boxed{x≈1.683} [/tex]

(Which is a thing too!)

[tex]\huge\mathfrak\colorbox{white}{}[/tex]

P. S.: Now please don't tell me that this is a PhD level question and this is referring to the Knuth's Up-Arrow Notation. Which translates the question into something like: [tex]^{5}x=15[/tex]

Answer:

Step-by-step explanation:

what would be the answer to this ?

Solve.

5x=15

x = 15 : 5

x = 3

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

check

5 * 3 = 15

the answer is good

Step-by-step explanation:

please mark me as brainlest

Step-by-step explanation:

Use the product rule for finding the derivative of a product of functions. Use the quotient rule for finding the derivative of a quotient of functions.

The attached number line represents points of the lowest recorded temperatures

The table is given as:

City                 Lowest Recorded Temperature

Morgantown       7°F below 0

Charlotte            6°F above 0

Huntsville           4°F above 0

Bluefield            8°F below 0

To rewrite the table, we use the following representations:

So, we have:

City                 Lowest Recorded Temperature

Morgantown       -7

Charlotte            6

Huntsville           4

Bluefield            -8

See attachment for the number line that represents the above points

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The figure is the combination of the rectangle and square. Then the area of the figure will be 13 square units.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

Then the area of the geometry will be

The figure is the combination of the rectangle and square.

Then we have

Area = 3 x 3 + 4 x 1

Area = 9 + 4

Area = 13 square units

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Step-by-step explanation:

this is very easy u can do urself

2x - 3y = 7 can be rewritten as y = 2/3x - 7/3, therefore, the equation that is a linear equation is: C. 2x - 3y = 7.

A linear equation is expressed in the slope-intercept form as y = mx + b.

2x - 3y = 7, rewritten in slope-intercept form would be:

-3y = -2x + 7

y = -2x/-3 + 7/-3

y = 2/3x - 7/3

m = 2/3 and b = -7/3

Therefore, the equation that is a linear equation is: C. 2x - 3y = 7.

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Answer:

2x+15 =6x-45 [Alternate Angles]

or, 15+45 =6x-2x

or, 60 =4x

or 60/4 =x

or 15 = x

# x=15

Answer:

[tex]P(36 < X < 43)\approx83.5\%[/tex]

Step-by-step explanation:

Use a TI-84 to calculate the probability

[tex]P(\text{Lower} < X < \text{Upper})=\text{normalcdf}(\text{Lower},\text{Upper},\mu,\sigma)\\\\P(36 < X < 43)=\text{normalcdf}(36,43,38,2)\approx0.8351\approx83.5\%[/tex]

Answer:

Step-by-step explanation:

[tex]\text {modulus of z } = =\sqrt{\left( -3\right)^{2} +\left( 1\right)^{2} } =\sqrt{9+1} =\sqrt{10}[/tex]

Answer:

square root of 10

Step-by-step explanation:

The What is the population of interest are:

The data collection method according to the group below

The best data collection method for the first one oatmeal  and GMC students is survey because the population is large and opinions may differ.

The best data collection method for the cars  is Experiment as one needs to study the cars that pass the red lights

For one of the three studies, a census is possible in the first one because the study population is the Georgia which is very large.

For the two studies the one that a census is not needed is GMC students and cars at red light because the population is not too big.

Based on the study I will use 500 people, 200 students, or 300 cars and the  sampling technique would be Systematic sampling, Simple random sampling and Judgmental/purposive sampling.

A  Simple random sampling is known to be the easiest method of selecting a sample as every member is known to have an equal chance of being selected in the sample.

See the other part of the question below

Write a reply

Consider the following statistical studies:

1. A study (in Georgia) of the effect of eating oatmeal on lowering cholesterol.

2. A study of current GMC students next career move after graduating or transferring from GMC.

3. A study of how many cars run the red light at a certain intersection in Macon, GA.

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We conclude that the sum of the first 8 terms of the arithmetic sequence is 17/5.

In an arithmetic sequence, the difference between any two consecutive terms is a constant.

Here we know that:

[tex]a_1 = 3/5\\a_8 = 1/4[/tex]

There are 7 times the common difference between these two values, so if d is the common difference:

[tex]a_1 + 7*d = a_8\\\\3/5 + 7*d = 1/4\\\\7*d = 1/4 - 3/5 = (5 - 12)/20 = -7/20\\\\d = -1/20[/tex]

Then the sum of the first 8 terms is given by:

[tex]3/5 + (3/5 - 1/20) + (3/5 - 2/20) + ... + (3/5 - 7/20)\\\\8*(3/5) - (1/20)*(1 + 2 + 3+ 4 + 5 + 6 + 7) = 3.4 = 34/10 = 17/5[/tex]

So we conclude that the sum of the first 8 terms of the arithmetic sequence is 17/5.

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Answer:

z = 86 °

and, x = 2

Step-by-step explanation:

We know that a straight line is a 180 degree-angle. So, we know that

94 + z must equal 180, because they are the only two angles that make up the straight line.

from this information, (that 94 + z = 180) we can easily find z.

(this is typically an intuitive method of subtracting 94 from 180)

94   +   z   =   180

-94                  -94

z = 86 °

-- we know that the relation between z and (10x + 74) must also be equal to 180, as they make up a straight line

if z = 86, then we can know that (10x + 74) must be equal to

(10x + 74) + 86 =    180

                - 86        -86

(10x + 74) = 94

10x + 74 = 94

      - 74   - 74

  10 x     =    20

÷ 10            ÷ 10

     x    =   2

so, z = 86 °

and, x = 2

(I am assuming that this "unprotected placement assessment" has already taken place, and you would like to understand a question. Or, this is a practice assessment. Because there is no point to cheating on a placement assessment--you will just skip over material you don't know. And, it wouldn't align with Brainly's honor policy. Hope you learn from this!!)

Answer:  [tex]y^9[/tex]

This is the same as saying y^9

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

Explanation:

When we apply the square root to the expression [tex]a^{2b}[/tex], we end up with [tex]a^b[/tex]

[tex]\sqrt{a^{2b}} = a^b[/tex]

The exponent 2b divides in half to get b

Based on that rule, we can then say:

[tex]\sqrt{y^{18}} = y^{18/2} = y^9[/tex]

The question is incomplete because it was not properly and correctly arranged

Complete Question:

A rectangular prism has a length of 7 m, a height of 5 m, and a volume of 140 m³. What is the width? A prism has a length of 7 meters, width of w, and height of 5 meters.

Which steps are correct? Check all that apply.

a) Substitute the known values into the formula: 140 = 7(w)(5).

b) Substitute the known values into the formula: 7 = 140(w)(5).

c) Substitute the known values into the formula: 5 = 7(w)(140).

d) Solve for the unknown: w = 4 m.

e) Solve for the unknown: w = 7 m.

f) Solve for the unknown: w = 2 m.

Answer:

a) Substitute the known values into the formula: 140 = 7(w)(5).

d) Solve for the unknown: w = 4 m.

Step-by-step explanation:

The steps that are correct are Options a) and d). This is because:

Step 1

The volume of a rectangular prism is calculated as:

Volume of a rectangular prism = Length (l) × Width(w) × Height(h)

The unit of the volume or a rectangular prism is in cubic metres (m³)

In the question, we are asked to find the unknown value which is the width and we were given the following known values:

Length = 7 m,

Height = 5 m

Volume = 140 m³

Step 2

Solve for the unknown value( Width)

Volume of a rectangular prism = Length (L) × Width(W) × Height(H)

140m³ = 7m × Width(m) × 5m

140m³ = 35m² × Width(m)

Width(w) = 140m³ ÷ 35m²

Width(w) = 4m

Hence, the unknown Width(w) = 4m

From the above explanation we can see that the correct steps is Option a) and Option d)

Answer:

Step-by-step explanation:

Volume of rectangular prism= Length x width x height

V=L x W x H

140=7 x W x 5

140= 35 x w

W= 140/35

W= 4

Answer:

  (b)  -7.275i -4.244j

Step-by-step explanation:

The projection of vector u onto vector v is the product of the unit vector v, the magnitude of vector u, and the cosine of the angle between them.

__

The dot product gives the product of the magnitudes of the two vectors and the cosine of the angle between them. To find the projection, we must divide the dot product by the magnitude of v and multiply by the unit vector in the direction of v.

  [tex]proj(u,v)=(\vec{u}\cdot\vec{v})\cdot\dfrac{\vec{v}}{|\vec{v}|^2}=\dfrac{((-8)(-12)+(-3)(-7))(-12\vec{i}-7\vec{j})}{(-12)^2+(-7)^2}\\\\=\dfrac{-(96+21)(12\vec{i}+7\vec{j})}{144+49}=-\dfrac{117}{193}(12\vec{i}+7\vec{j})\approx\boxed{-7.275\vec{i}-4.244\vec{j}}[/tex]

Answer:

D, x = 9

Step-by-step explanation:

[tex]x\left(2+5\right)=63[/tex]

=> divide both side by 7

[tex]\frac{x\left(2+5\right)}{7}=\frac{63}{7}[/tex]

x=9

Answer:

D) 9

Step-by-step explanation:

Given :

⇒ 18 + 45 = x (2 + 5)

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

Simplify both sides :

⇒ 18 + 45 = x (2 + 5)

⇒ 63 = 7x

⇒ 7x = 63

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

Divide both sides by 7 :

⇒ 7x/7 = 63/7

⇒ x = 9

Answer:

18

Step-by-step explanation:

my answer is correct,try to read the question,

if the length of larger triangle is 6 times so it means 6 ×5= 30 and you will times 3 to 6=18

so that's why it has lenght of 30

because the. larger triangle is 6 times bigger than smaller rectangle

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The equation for the sinusoidal function described is given as follows:

[tex]y = 4\cos{\left(\frac{1}{2}x\right)} + 2[/tex]

We want a function with a y-intercept at it's maximum value, hence we use the cosine equation, given by:

[tex]y = A\cos{\left(\frac{2\pi}{B}x\right)} + C[/tex]

In which:

The amplitude is of 8, hence 2A = 8 -> A = 4. This would represent a function between -4 and 4, but we want between -2 and 6, hence the vertical shift is of C = 2.

As for the period, we have that:

[tex]B = 4\pi[/tex]

Then, the equation is given by:

[tex]y = 4\cos{\left(\frac{1}{2}x\right)} + 2[/tex]

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