A motorboat, that has speed of 10 km/hour in still water, left a pier traveling against the current of the river. Forty-five minutes after the boat left the pier, the motor of the boat broke, and the boat began drifting with the current. After three hours of drifting with the current, the boat was back at the pier where it had started. What is the speed of the current of the river?

C. 4(x-3)-x

All of the given expressions are equivalent to 3x+12 except selection C. Using that in your equation makes it be ...

... 3(x +1) +9 = 4(x -3) -x

... 3x +12 = 3x -12

... 12 = -12 . . . . . false

There is no value of x that will make this true, hence NO SOLUTION.

_____

Comment on the other choices

3x+12 = 3x+12 has an infinite number of solutions, as any value of x will make this true.

c

BECAUSE I SAID SO HUH YOU GOTTA PROBLEMO??

5/2

The ratio of perimeters is the same as the ratio of corresponding sides:

... (140 cm)/(56 cm) = 5/2

Answer:

5:2

Step-by-step explanation:

We have been given that triangles △ABC and △DFG are similar. The lengths of the two corresponding sides are 1.4 m and 56 cm.

Since both triangles are similar, therefore all corresponding sides will have same proportion.

Let us find proportion of corresponding sides of both triangles.

1 meter = 100 centimeter

1.4 meter = 1.4* 100 centimeters = 140 centimeters.

[tex]\frac{\text{Side of triangle ABC}}{\text{Side of triangle DFG}}=\frac{140}{56}[/tex]

[tex]\frac{\text{Side of triangle ABC}}{\text{Side of triangle DFG}}=\frac{5}{2}[/tex]

The ratio of sides of △ABC to sides of△DFG is 5:2.

Since perimeter of a triangle is sum of lengths of three sides of the triangle and all sides of both triangle have the ratio 5:2, therefore, their perimeters will be in same ratio, that is 5:2.

∠K = ∠N = 60°

∠L = ∠M = 120°

In the attached, we have renamed F to G so Brainly will let us talk about it more easily. We have also added altitude MX.

AG is also a midsegment of ΔKLM, so LM = 2×AG = 4. Then ...

... NX = AB - LM = 7 -4 = 3

and we have right ΔMXN with hypotenuse 6 and leg 3. This is recognizable as a 30°-60°-90° triangle, with the 60° angle at N.

The angle at M is supplementary to that at N (because LM ║ KN), so measures 120°

The trapezoid is isosceles, so angles K and L have the same measures as angles N and M.

Answer:

0.009

Step-by-step explanation:

So 9/1000 can be written as 0.009

Answer:

The answer is 0.009.

Step-by-step explanation:

The total number of people from which only 9 earned a perfect score = 1,000.

The number of people who earned a perfect score = 9

The decimal that represents the number of people who earned a perfect score = The number of people who earned a perfect score ÷ The total number of people concerned = 9 ÷ 1,000 = 0.009.

For each birdhouse built, the total cost increases by $3.50.

The number 3.5 multiplies b, so when b increases by 1, f(b) increases by 3.5. Making 1 more birdhouse increases the total cost by $3.50.

Answer: For each birdhouse built, the total cost increases by $3.50.

Step-by-step explanation:

Given: The total cost for Sophia to build b birdhouses is represented by the function [tex]f(b)=3.5b+24[/tex]

We can see in the function 3.5 is multiplied to b, so when b increases , f(b) increases by 3.5.

[tex]f(1)=3.5(1)+24=3.5+24=27.5[/tex]

[tex]f(2)=3.5(2)+24=7+24=31[/tex]

[tex]f(3)=3.5(3)+24=10.5+24=34.5[/tex]

and [tex]f(2)-f(1)=f(3)-f(2)=3.5[/tex]

Therefore, the value of 3.5 represents that for each birdhouse built, the total cost increases by $3.50.

Answer:

The Answer is 48 miles.

Step-by-step explanation:

Linda has driven 36 miles home and that is 3/4 of the way home.  If you divide 36 by 3 equals 12 miles per 1/4 drive.  Multiply 12x4 and the answer is 48.

Hope that helps!

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

If a polynomial function P(x) with rational coefficients has a root z. the so is the complex conjugate of z is a root. (In order to see that, take the complex conjugates of the equation P(x)=0, and note that complex conjugates of rational numbers equal to itself.)

Therefore the complex conjugates of the given roots i and 7+8i , are -i and 7-8i is the required answer.

Answer:

The answer is 96 when X= 8

Step-by-step explanation:

We have given that :

AE= [tex]x^2-16[/tex]  and CE=[tex]6x[/tex]

where AE and CE are the diagonals of the paralleogram

The diagonals of parallelogram bisect each other therefore,

 [tex]x^2-16 = 6x[/tex]

⇒ [tex]x^2-6x-16=0[/tex]

factors are (x+2)(x-8)=0

setting to each factor 0 the value of x= -2 or x= 8

therefore, two values of AC is

X= -2  ,AC= 2([tex]x^2-16[/tex])=2(-12)=-24

X= 8 ,AC= 2([tex]x^2-16[/tex])=2(48)=96

The answer is 96 when X= 8

Answer:

 b.) and Kyle traveled 185 miles

Step-by-step explanation:

x+240=425

 -240  -240

x=185

The question is about simple subtraction in mathematics. Given that Kyle and Tyler together traveled 425 miles and Kyle traveled 240 miles, we use subtraction to find out that Tyler traveled 185 miles.

This is a classic problem of simple subtraction in mathematics. Given, Kyle and Tyler together traveled 425 miles. Now, if Kyle traveled 240 miles, Tyler must have covered the remaining distance. So, to find out how far Tyler traveled, subtract the distance that Kyle traveled from the total distance. This is represented by the equation (option B) x + 240 = 425, where x represents the distance that Tyler traveled. Solving this equation for x will give you the answer.

Setup the equation: x + 240 = 425

Subtract 240 from both sides: x = 425 - 240

This results in x = 185, meaning Tyler traveled 185 miles.

3 11/15 cm

AE is the angle bisector of ∠A, so divides the sides of the triangle into a proportion:

... BE:CE = BA:CA = 7:8

Then ...

... BE:BC = 7 : (7+8) = 7:15

ΔDBE ~ ΔABC, so DE = 7/15 × AC

... DE = 7/15 × 8 cm = (56/15) cm

... DE = 3 11/15 cm

To find the side of the inscribed rhombus, we can use the Pythagorean theorem and the properties of inscribed rhombuses.

To find the side of the rhombus, we need to understand the properties of inscribed rhombuses. In an inscribed rhombus, the diagonals are perpendicular bisectors of each other.

Let's label the side of the rhombus as 's'.

Using the given information, we can see that AB and AC are the diagonals of the rhombus.

Since AB = 7 cm and AC = 8 cm, we know that the diagonals bisect each other and form right angles.

Therefore, we can use the Pythagorean theorem to find the side of the rhombus:
s^2 = (AB/2)^2 + (AC/2)^2
s^2 = (7/2)^2 + (8/2)^2
s^2 = (49/4) + (64/4)
s^2 = (113/4)
s = sqrt(113/4)

Answer:

1. x =8

2.  x=9

Step-by-step explanation:

Since these figures are parallelograms, the opposite sides are equal.

1.     6 = 2x-10

Add 10 to each side

   6+10 = 2x-10+10

   16 = 2x

Divide  each side by 2

16/2 = 2x/2

 8 =x

2.  x+14 =23

    Subtract 14 from each side

x+14-14 = 23-14

x = 9

Answer:

25

Step-by-step explanation:

You must divide 75/3. This is because for every 3 hours, there is a distace of 75 miles. You have to find out his average speed by finding his distance each hour. 75/3 is 25.

Answer:  The average speed of Rohit is 25 miles per hour.

Step-by-step explanation:  Given that Rohit drove around the city for 3 hours and he traveled a total distance of 75 miles.

We are to find Rohit's average speed.

We know that

[tex]speed =\dfrac{distance}{time}.[/tex]

For the given situation, we have

distance, d = 75 miles  and  time, t = 3 hours.

So, the average speed of Rohit is given by

[tex]S=\dfrac{d}{t}=\dfrac{75}{3}=25.[/tex]

Thus, the average speed of Rohit is 25 miles per hour.

Answer:

∠MSR is right angle

Step-by-step explanation:

It is given that RHOM is a Rhombus

Also ΔHOM, ΔMHR, ΔRHO and ΔOMR are isosceles triangles

Let us take ΔMSR and ΔRSH

∠MRS =∠HRS            ( since it is given that the diagonal RO bisects ∠R)

∠RMS =∠RHS     ( since Δ MRH is isosceles triangle )

RS = RS        ( common side )

By AAS congruency rule ΔMSR ≅ ΔHSR

so we have

∠MSR=∠RSH  ( corresponding parts of congruent triangles are congruent)

also we have

∠MSR +∠RSH =180°   ( supplementary angles)

∠MSR +∠MSR=180°          ( since ∠MSR=∠RSH)

2∠MSR= 180°

∠MSR =90°

Hence ∠MSR is right angle

Answer:

It must be a right angle.

Step-by-step explanation:

The figure attached shows the rhombus RHOM with RO and HM as diagonals and are the angle bisectors of the vertex angles.

Let S be the point where the diagonals RO and HM intersects each other.

ΔHOM, ΔMHR, ΔRHO, ΔOMR are four isosceles triangles in the given rhombus.

Since, Diagonals of a rhombus bisect each other at right angle.

Therefore, we have ∠MSR= 90°

That is, ∠MSR is a right angle.

To determine the number of ways to choose two students to go first and second in a group of 17 students, we use permutations, resulting in a total of 17 * 16 = 272 ways.

The question inquires about the number of ways two students can be chosen from a group of 17 to go first and second in a spelling bee, which can be solved using combinatorics.

To choose the first student, we have 17 options. After choosing the first student, we have 16 remaining students to choose from for the second student. Therefore, the total number of ways to choose students for these two positions is the product of these two numbers. This scenario calls for a permutation calculation since the order in which we select the students matters.

The formula is n!/(n-r)!, where n is the total number of items to pick from, and r is the number we are picking. For our case, n = 17 and r = 2.

Total number of ways (permutations) = 17 * 16 = 272 ways.

6 cm, 8 cm, 12 cm

The perimeter of the reference triangle is  ...

... (15 +20 +30) cm = 65 cm

Then the similar triangle has a scale factor of ...

... (26 cm)/(65 cm) = 2/5

Multiplying the side lengths of the reference triangle by 2/5, we get ...

... {15 cm, 20 cm, 30 cm) × 2/5 = {6 cm, 8 cm, 12 cm}

These are the side lengths of the smaller similar triangle. (Check: their sum is 26 cm.)

Find the x and y for each dot:

5,35

10,70

15,105

etc.

Divide the Y by the X:

35 / 5 = 7

70 / 10 = 7

etc.

The answer would be C) y = 7x

Answer:

Option C is correct

[tex]y = 7x[/tex]

Step-by-step explanation:

Direct variation states that:

[tex]y \propto x[/tex]          ......[1]

then, the equation is in the form of:

[tex]y=kx[/tex], where k is the constant of variation

From the given graph we have points in the form of (x, y) i.e,

(0, 0), (5, 35), (10, 70), (15, 105), (20, 140), (25, 175) and (30, 210)

Substitute any points i.e (5, 35) in [1] we have;

[tex]35 = 5k[/tex]

Divide both sides by 5 we have;

7 = k

or

k = 7

then;

[tex]y = 7x[/tex]

Therefore, the constant of  proportionality for the graph is, 7 and its form is, [tex]y = 7x[/tex]

Answer: The correct answer would be D: Model J

Step-by-step explanation:

For there are 3 segments in each box and 3 boxes are shaded leaving only 2 unshaded :)

Answer:

D. Model J

Step-by-step explanation:

c. Both A and B

A function is a mapping that maps each element of its domain (student's name) to exactly one element of its co-domain (favorite ...). Assuming student names are unique and the notion of "favorite" is exclusive (can't have two or more "favorites" of the same type), then both A and B describe mappings that are functions.

Answer:

c. Both A and B

Step-by-step explanation:

A function means each input  goes to only one output.  As long as each student is only entered once,  and they only have one favorite color and one favorite math teacher, then A and B are functions.

Answer:

1/92

Step-by-step explanation:

There are C(3, 2) = 3 ways to select 2 jelly-filled donuts from the 3 in the box. There are C(24, 2) = 276 ways to select 2 donuts from the box.

The probability that you will select 2 jelly-filled donuts is ...

... 3/276 = 1/92

_____

C(n, k) = n!/(k!(n-k)!)

C(3, 2) = (3·2)/2 = 3

C(24, 2) = (24·23)/2 = 276

Answer: 45

Step-by-step explanation:

Divide 90 by 2 and you will the the answer of 45.

Answer:

g + h =  -4

g - h =  -10

h -g = 10

gh =  -21

g+ h^2 =  2

g^2 -h =  46

Step-by-step explanation:

We know g = -7 and h = 3

g + h = -7 +3 = -4

g - h = -7 - 3 = -10

h -g = 3 --7 = 3+7 = 10

gh = (-7) * 3 = -21

g+ h^2 = -7 + (3)^2 = -7+9 = 2

g^2 -h = (-7)^2 -3 = 49 -3 = 46

The range is [minimum y-value, maximum y-value), so the range expression tells you directly what those values are.

For the function described, with range [1, ∞), ...

... minimum y-value = 1

... maximum y-value = infinity

y = 21·0.7^x

The pair (0, 21) tells you the multiplier is 21. (The exponential factor is 1 for x=0.)

Any adjacent pair of y-values can tell you the common ratio, hence the base of the exponential term. For example, using the y-values associated with x=0 and x=1, we find the base to be ...

... 14.7/21 = 0.7

Then the equation is ...

... y = multiplier · base^x

... y = 21·0.7^x

Answer: They are fed 4/9 of what the polar bears are fed.

Step-by-step explanation:

7/9*4/7=

1/9*4/1=4/9

The 7's get cancelled out.

The penguins at the zoo are fed 4/9 bucket of fish a day. This fraction has been calculated by multiplying the amount of food the polar bears get (7/9 bucket) by 4/7 as specified in the problem.

To find out how much the penguins are fed, we first understand the given units involving the polar bears and penguins. The polar bears are fed 7/9 bucket of fish a day, and the penguins are fed 4/7 that amount. Therefore, to calculate the amount the penguins are fed, we multiply the amount the polar bears are fed by 4/7.

We get this by performing the calculation (7/9) * (4/7). The sevens cancel out, leaving us 4/9, which is the fraction of the bucket of fish that the penguins are fed each day.

https://brainly.com/question/29633725

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tan(Q) = RS/RQ

The mnemonic SOH CAH TOA reminds you that ...

... Tan = Opposite/Adjacent

The side opposite angle Q is RS. The side adjacent is RQ. (QS is the hypotenuse, which does not come into play in the tangent function.)

Then ...

... tan(Q) = Opposite/Adjacent = RS/RQ

In right triangle QRS, with angle R being 90 degrees, tan Q is represented by the length of the side opposite to angle Q divided by the length of the side adjacent to Q which tan Q = SR/ QR.

In right triangle QRS, with angle R being 90 degrees, the ratio that represents tan Q is the length of the opposite side to angle Q divided by the length of the adjacent side.

In trigonometry, the tangent (tan) of an angle in a right triangle is a ratio of the length of the side opposite to the angle to the length of the side adjacent to the angle.

Therefore, if we label the sides opposite and adjacent to angle Q as opposite and adjacent respectively, the formula for tan Q would be:

tan Q = opposite/adjacent

         = SR/QR

For example, if a right triangle has sides of lengths 3, 4, and 5, with the side lengths of 3 and 4 being adjacent to and opposite angle Q respectively, the tan Q would be calculated as 4/3.

Answer:

Republican residents of County 1:  

10.1 %  

Democratic residents of County 1:  

16.5 %

Total Republican residents:  

58.9 %

Total Democratic residents:  

41.1 %

Step-by-step explanation:

Answer:

Question 1)

Republican residents of County 1: (10.1)

Question 2)

Democratic residents of County 1: (16.5)

Question 3)

Total Republican residents: (58.9)

Question 4)

Total Democratic residents: (41.1)

Answer:

D U E = { 6,8,9,10,11}

Step-by-step explanation:

U stands for union, which is join the sets together

D U E = { 6,8,9,10,11}

Answer:

No it is not.

Step-by-step explanation:

Answer:

Null Hypothesis : The true mean height of children is more than 60 inches.

Step-by-step explanation: Null Hypothesis is defined as a hypothesis that there is no significant difference between the observed and sampled mean.

So, if alternative hypothesis is " the true mean height of children is less than 60 inches" which denotes there is significant difference between sampled and observed mean heights so null hypothesis is taken as " true mean height of children is more than 60 inches"

[tex]9.36\cdot10^4=9.36\cdot10,000=93,600[/tex]