a woman at a point a on the shore of a circular lake with radius 1.2 mi wants to arrive at the point B diametrically opposite A on the other side of the lake in the shortest possible time (see the figure). she can walk at the rate of 5 mi/h from C to B and row a boat at 3.5 mi/h from A to C . setting T (x) function to the time by interlaced AC, x is interlacted AC. how to move for shortest.

Answer:

x + 3y = 30

Step-by-step explanation:

We are given that a line contains the points (12,6) and (-3,11)​.

We want to write the equation of this line in standard form.

Standard form is written as ax+by=c, where a, b, and c are free integer coefficients, however a and b cannot be 0, and a cannot be negative.

Regardless, before we write an equation in slope-intercept form, we must first write the equation in a different form, such as slope-intercept form.

Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y-intercept.

So first, let's find the slope of the line.
The slope (m) can be found using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points.

Even though we already have 2 points, let's label their values to avoid any confusion and mistakes when calculating.

[tex]x_1=12\\y_1=6\\x_2=-3\\y_2=11[/tex]

Now substitute these values into the formula.

m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m=[tex]\frac{11-6}{-3-12}[/tex]

Subtract

m=[tex]\frac{5}{-15}[/tex]

Simplify

m=[tex]-\frac{1}{3}[/tex]

The slope is -1/3

Here is the equation of the line so far in slope-intercept form:

[tex]y=-\frac{1}{3} x + b[/tex]

We need to solve for b.

As the equation passes through (12,6) and (-3,11)​, we can use either one to help solve for b.

Taking (12, 6) for example:

[tex]6=-\frac{1}{3}(12) + b[/tex]

Multiply

[tex]6=-\frac{12}{3} + b[/tex]

Divide

6 = -4 + b

Add 4 to both sides.

10 = b

Substitute 10 as b in the equation.

[tex]y = -\frac{1}{3} x + 10[/tex]

Here is the equation in slope-intercept form, but remember, we want it in standard form.

In standard form, the values of both x and y are on the same side, so let's add -1/3x to both sides.

[tex]\frac{1}{3} x + y = 10[/tex]

Remember that a (the coefficient in front of x) has to be an integer, 1/3 is not an integer.

So, let's multiply both sides by 3 to clear the fraction.

[tex]3(\frac{1}{3} x + y) = 3(10)[/tex]
Multiply.

x + 3y = 30

Topic: finding the equation of the line (standard form)

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Answer:

(-5, -7) and the x-axis

Step-by-step explanation:

when looking for a point that is 7 points away, we are looking for a difference of 7 in either the x-value or the y-value.

[remember: a point is written as (x, y) ]

We know that the x-value is -7, meaning that it is 7 units under the x-axis (meaning that it is 7 units away)

We know that our point, (2 , -7) has the same y-value as (-5, -7), so we are looking for a change in x. The difference (which is the change) between:

-5 and 2 is 7

(2 - (-5) = 2 + 5 = 7)

so, both the x-axis and the point (-5, -7) are 7 units away from (2, -7)

(the other point (-7, 7) is not near (2 , -7) at all--they have a larger difference on both the y-values, the x-values, and the length of if you made a diagonal line)

(I've attached an image to help you visualize what we're doing)

hope this helps!!

Answer:

Angle 1: 55 degrees
Angle 2: 55 degrees
Angle 3: 70 degrees

Step-by-step explanation:

Finding angle 1: We know that in a triangle, all three angles must add up to 180 degrees. In the triangle on the left, 2 of the angle measures are already given to us. Therefore, we can simply do 180 - 40 - 85, thus the measure of angle 1 is 55 degrees.
Finding angle 2: We know that opposite angles are congruent. Therefore, angle 2 and angle 1 have the same measure.
Finding angle 3: Using the same thought process as we used when finding the measure of angle 1, we can subtract the other 2 angles. 180 - 55 - 55 is equal to 70.

Answer:

first, we take the first triangle( the right one), since a triangle is equal to 180 we add 85 and 40 which gives us 125, we then subtract 125 with 180 getting 55 so (1) =55

to find (2) we put 55 the same number as no. (1) because of the property VERTICALLY OPPOSITE ANGLES.

then to find (3) we do the same steps as (1), we add 55 and 55 and subtract by 180. 55+55=110

             =110 - 180

             =70

There u go, please mark me as brainless

Using the z-distribution, the minimum sample size required by this student is of 385.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

We want a margin of error of M = 0.05, with no prior estimate, hence [tex]\pi = 0.5[/tex], then we have to solve for n to find the minimum sample size.

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.05 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.05\sqrt{n} = 1.96(0.5)[/tex]

[tex]\sqrt{n} = 1.96 \times 10[/tex]

[tex](\sqrt{n})^2 = (1.96 \times 10)^2[/tex]

n = 384.16

Rounding up, the minimum sample size is of 385.

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Answer:

93 boxes

Step-by-step explanation:

sixth row has 23 boxes

fifth row has 20 boxes

fourth row has 17 boxes

third row has 14 boxes

second row has 11 boxes

first row has 8 boxes

the total is thus 23+20+17+14+11+8=93

Answer: -1

Step-by-step explanation:

[tex]f(-1)=(-1)^2 - (-1)-1=1\\\\f(1)=1^{2}-1-1=-1\\\\\therefore \frac{f(-1)-f(1)}{-1-1}=\frac{1-(-1)}{-1-1}=\frac{2}{-2}=\boxed{-1}[/tex]

Answer:

See below

Step-by-step explanation:

Area of a circle = pi * r^2

  for this circle  :    Area = 3.142 * 10 * 10 =  314.2 cm^2

The formula for area of a circle is [tex]\pi r^{2}[/tex]

So using pi as 3.142, we can do 3.142 • 100 which is 314.2 when moving place values.

Even though you did not ask, the circumference formula is 2[tex]\pi[/tex]r.

If we were given the same information, where the radius is 10, and we were solving circumference, then we would do 3.14 • 20 = 62.8.

Brainliest if helpful.

Answer:

[tex]3^2=x+5[/tex]

Step-by-step explanation:

Given equation:

[tex]\log_3(x+5)=2[/tex]

Method 1

[tex]\textsf{Using the Log law:} \quad \log_ab=c \:\: \Longleftrightarrow \:\: a^c=b[/tex]

[tex]\implies \log_3(x+5)=2[/tex]

[tex]\implies 3^2=x+5[/tex]

Method 2

Make both sides of the equation the index to base 3:

[tex]\implies \log_3(x+5)=2[/tex]

[tex]\implies 3^{\log_3(x+5)}=3^2[/tex]

Apply the log law [tex]a^{\log_ax}=x[/tex] :

[tex]\implies x+5=3^2[/tex]

Swap sides:

[tex]\implies 3^2=x+5[/tex]

Solve for x

Although the question hasn't asked to solve for x, here is the solution:

[tex]\implies 3^2=x+5[/tex]

[tex]\implies 9=x+5[/tex]

[tex]\implies x=9-5[/tex]

[tex]\implies x=4[/tex]

Check

Substitute the found value of x into the original equation:

[tex]x=4 \implies \log_3(4+5)=\log_39=2 \quad \leftarrow\textsf{correct}[/tex]

[tex]\\ \rm\Rrightarrow log_3(x+5)=2[/tex]

[tex]\\ \rm\Rrightarrow x+5=3^2[/tex]

[tex]\\ \rm\Rrightarrow x+5=9[/tex]

[tex]\\ \rm\Rrightarrow x=9-5[/tex]

[tex]\\ \rm\Rrightarrow x=4[/tex]

Answer:

B, 54

Step-by-step explanation:

Step-by-step explanation:

please mark me as brainlest

The equation of the line with points (2,10) and (0,0) is: y = 5x.

The line given has two points which are stated as:

(2,10) and (0,0).

Find the slope(m):

Slope (m) = change in y / change in x = (10 - 0)/(2 - 0)

Slope (m) = 10/2

Slope (m) = 5

The y-intercept (b) = 0

Substitute m = 5 and b = 0 into y = mx + b

y = 5x + 0

y = 5x

The equation of the line is: y = 5x.

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[tex]{\huge \underline{{ \fbox \color{red}{A}}{\fbox \color{green}{n}}{\fbox \color{purple}{s}}{\fbox \color{brown}{w}}{\fbox \color{yellow}{e}}{\fbox \color{gray}{r } }}}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf \red{ \dfrac{1}{2} + \dfrac{1}{4} = \dfrac{3}{4} }[/tex]

Step by step explanation :-

The only thing you have to do is add the numerator to the denominator, in this case you have to add the first ones from the front, which can be these 2+1/4, which would result in 3/4, and this is called the Commutative Property.

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \bf \gray{ \dfrac{1}{2} + \dfrac{1}{4} = \dfrac{1}{4} + \dfrac{1}{2} }}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \bf \green{\dfrac{2 + 1}{4} = \dfrac{1 + 2}{4} }}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed {\bf \blue{\dfrac{3}{4} = \dfrac{3}{4}} }[/tex]

Answer :- The answer is 3/4

¿What is commutative property?

It is to change different ways in order of the addends the result would be the same.

Example :-

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed {\bf \blue{\dfrac{a}{b} + \dfrac{c}{d}} = {\dfrac{c}{d} + \dfrac{a}{b}} }[/tex]

I hope I've helped : )

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: Final \:\: value = \cfrac{3}{4}[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{1}{2} + \cfrac{1}{4} [/tex]

[ take LCM ]

[tex]\qquad \tt \rightarrow \: \cfrac{2}{4} + \cfrac{1}{4} [/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{2 + 1}{4} [/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{3}{4} [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The proportion can be used to find the distance on the map (x) that represents 50 miles will be x/50 = 5 / 200. Then the correct option is A.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

The scale on a map shows that 200 miles is represented by 5 inches on a map.

Then the proportion can be used to find the distance on the map (x) that represents 50 miles will be

x/50 = 5 / 200

Then  the correct option is A.

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basically you treat y like a number and not a variable

Answer:

a is 4

b is 2y

c is -10y²+9

discriminant is 4(41y²-36)

Step-by-step explanation:

4x²+2xy-10y²+9=0

rewrite in standard form of a quadratic equation like ax² + bx + c = 0

4x²+2yx-10y²+9=0

basically you treat y like a number and not a variable

a is the number with the x²

right away we know a is 4 because of 4x²

b is the one with x so in this formula b is 2y

c is the number without the x which in this case is -10y²+9

discriminant is

b² - 4ac

(2y)²- (4)(4)(-10y²+9)

4y²-(16)(-10y²+9)

4y²-(16)(-10y²+9)

4y²+160y²-144

164y²-144 =

4(41y²-36)

The absolute value function that will be wider than the graph of the parent function, f(x) = |x| is (d) f(x) = 9|x|

The parent function is given as:

f(x) =|x|

A wider function would have the following equation

f(x) = k|x|

Where:

k > 0

From the list of options, we have:

f(x) = 9|x|

Hence, the absolute value function that will be wider than the graph of the parent function, f(x) = |x| is (d) f(x) = 9|x|

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Answer:

getting to the point , D.

Step-by-step explanation:

trust

Answer:

50.24 mm^2

Step-by-step explanation:

The area of a circle is given by

A = pi r^2  where r is the radius

A = 3.14 ( 4)^2

   = 50.24 mm^2

Answer:

c. 50.24 square millimeters

Step-by-step explanation:

Radius of circle = 4 milimeters.

Area of a circle = πr²

Area = 3.14 × 4² (π = 3.14)

= 50.24 square millimeters

For the function F(x)=[tex]a(x+k)^{1/n}+C[/tex] the value of a is less than zero and the correct option is option d.

Given the value of function  F(x)=[tex]a(x+k)^{1/n}+C[/tex].

We have to put the function equal to 0 for finding the nature of a and C is a fixed number in the function :

a[tex](x+k)^{1/n}[/tex]+C=0

a[tex](x+k)^{1/n}[/tex]=-C

a=-C/[tex](x+k)^{1/n}[/tex]

Since negative sign is coming before a and the value of rest of the expression cannot be negative so the value of a should b negative which means less than 0. The rest of the expression cannot be negative because it has a power of 1/n which only gives positive values like modulas.

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The sum of the geometric series will be 1/4. And the sum of the series will be the negative 0.13.

The complete question is attached below.

Let a be the first term and r be the common ratio. Then the sum of the geometric series will be

S = a / (1 – r)     if r < 1

S = a / (r – 1)     if r > 1

The series is given below.

1/16 + 3/64 + 9/256 + 27/1024 ....

Then we have

a = 1/16

r = (3/64) / (1/16) = 3/4

Then the sum of the series will be

S = (1/16) / [1 – (3/4)]

S = (1/16) / (1/4)

S = 1/4

Let [tex]\rm S = (-0.13)^m[/tex], where m = 1

Then the value of S will be

S = (-0.13)¹

S = -0.13

Hence, the sum of the series will be the negative 0.13.

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The value of angle ∠DEC  = 60 degree.

The complete question is

In the given the figure above, m∠BAC = 64° and m∠CBA = 56°.

Part I: Find the m∠DEC.

Part II: Explain the steps you took to arrive at your answer. Make sure to justify your answer by identifying any theorems, postulates, or definitions used.

A triangle is a polygon with three sides and three vertices and three angles.

As it is given that

AB || CD

Let BC be the transversal , then

∠CBA = ∠DCB (alternate opposite angles)

∠DCB = 56 degree

As the sum of opposite interior angle sis equal to exterior angle therefore ∠ ECB = 120 degree

∠DCE = 120-56 = 64 degree

BC || DE

∠EDC = ∠DCB = 56 degree (alternate opposite angles)

Sum of all the interior angles of a triangle is equal to 180 degree

56 +64+∠DEC = 180

∠DEC  = 60 degree.

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The simplified expression of [tex]\frac{x^3 + (-y)^3}{(x - y}[/tex] is [tex]x^2+xy+y^2[/tex]

Simplify the expression: (x³ + (-y)³) / (x - y)

Do not include parentheses in your answer.

The expression is given as:

[tex]\frac{x^3 + (-y)^3}{(x - y}[/tex]

Open the inner bracket

[tex]\frac{x^3 -y^3}{(x - y}[/tex]

Apply the difference of two cubes to the numerator

[tex]\frac{(x-y)(x^2+xy+y^2)}{(x - y}[/tex]

Cancel out the common factors

[tex]x^2+xy+y^2[/tex]

Hence, the simplified expression of [tex]\frac{x^3 + (-y)^3}{(x - y}[/tex] is [tex]x^2+xy+y^2[/tex]

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Answer:

A.

Step-by-step explanation:

let me know if you want an explanation :))

Answer:

A

Step-by-step explanation:

The fraction of the journey Sapna traveled by car and train is 3/8 and 5/8 respectively.

We know that fraction is an expression in mathematics used to denote the division of two whole numbers.

Given that the total distance = 48 km.

The distance Sapna traveled by car = 18 km.

So, the fraction is = distance traveled by car/total distance = 18/48 = 3/8

The distance Sapna traveled by train = 48 - 18 km = 30 km.

So, the fraction is = distance traveled by train/total distance = 30/48 = 5/8

Therefore the fraction of the journey Sapna traveled by car and train is 3/8 and 5/8 respectively.

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The graph of the linear inequality 2x – 3y < 12 is given below. Then the correct option is A.

The missing options are given below.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality is given below.

2x – 3y < 12

Then the correct graph will be given below.

Then the correct option is A.

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N = 0

2(0)² + 4(0) = 0

0 + 0 = 0

When faced with an unknown variable in a maths problem, it is advised to find the subject formula and then use it to solve the equation to find the answer.

This refers to the type of variable in a given equation that has to be solved for because its properties or value is not known.

Hence, we can see that when faced with an unknown variable in a given math problem, it is better to find the subject formula, then input the value of this into an equation, to find the value of the variable.

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Answer:

The cost of 1 taco = $4

The cost of 1 quesadilla = $7.50

Step-by-step explanation:

Let the cost of tacos be x and the cost of quesadillas be y.

x + 3y = 26.50 ------------------(1)

3x + y = 19.50 -------------------(2)

Multiply Eq. (2) by 3

3(3x + y) = 19.50 * 3

9x + 3y = 58.5 -----------------(3)

Subtract Eq. (3) from (1)

x + 3y - 9x - 3y = 26.50 - 58.50

x - 9x = -32

-8x = -32

8x = 32

Divide 8 to both sides

x = $4

Put x = 4 in (1)

4 + 3y = 26.50

Subtract 4 to both sides

3y = 26.50 - 4

3y = 22.50

Divide 3 to both sides

y = $7.50

So,

The cost of 1 taco = $4

The cost of 1 quesadilla = $7.50

[tex]\rule[225]{225}{2}[/tex]

[tex]\triangleright[/tex]Hii! [tex]\triangleleft[/tex]

     _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Answer}}}\circ\leftharpoonup[/tex] Equation: [tex]\bullet[/tex] y=43x-3 ✅

[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation}}}\circ\leftharpoonup[/tex]

Do you need to know the equation of the line with a slope of -43 and a y-intercept of (0,-3)? No problem! Luckily, there's a formula to find it! (:

The slope intercept formula, [tex]\boldsymbol{y=mx+c}[/tex], comes in handy when we need to find the equation of a line!

In this formula,

--                                         ↩

This particular question provides us both "m" and "c."

Stickin the values

[tex]\boldsymbol{y=43x+(-3)}[/tex]

Simplify!

[tex]\boldsymbol{y=43x-3}[/tex]

--

Hope that this helped! Best wishes.

[tex]\textsl{Reach far. Aim high. \: Dream big. }[/tex]

--

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--

Answer: 4.5

Step-by-step explanation:

[tex]\frac{6+3}{2}=\boxed{4.5}[/tex]

We want to find the median for the given density curve.

The value of the median is 4.5. ({3+6)/2}

Let's see how to solve this.

First, for a regular set {x₁, ..., xₙ} we define the median as the middle value.

The difference between a set and a density curve is that the density curve is continuous, so getting the exact middle value can be harder.

Here, we have a constant density curve that goes from 3 to 6.

Because it is constant, the median will just be equal to the mean, thus the median is the average between the two extreme values.

Remember that the average between two numbers a and b is given by:(a + b)/2

So we get: m = (6 + 3)/2 = 4.5

So we can conclude that the value of the median is 4.5, so the correct option is the second one, counting from the top.

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Answer:

180

Step-by-step explanation:

Find the LCM of 12, 18, and 20

[tex]12 = 2 \times 2 \times 3[/tex]

[tex]18 = 2 \times 3 \times 3[/tex]

[tex]20 = 2 \times 2 \times 5[/tex]

LCM = 2 × 2 × 3 × 3 × 5 = 180