Shawn hike 12 miles and 4 hours at the same rate what is the total number of miles he could hike in 9 hours

Final answer:

The value of 17 tens can be written in standard form as 170, in expanded form as (1 × 10²) + (7 × 10¹), and in unit form as '1 hundred 7 tens 0 ones'.

Explanation:

When asked to write the value of 17 tens three different ways, we first recognize that '17 tens' is essentially the number 170, since 17 tens are 17 multiplied by 10.

Standard Form

The standard form is simply writing the number as it is, so in this case, it would be 170.

Expanded Form

The expanded form breaks down the number into its place value components. Since 170 comprises 1 hundred, 7 tens, and 0 ones, it can be written as:
(1 × 10²) + (7 × 10¹) + (0 × 10°)

Unit Form

Last, the unit form expresses each digit's value according to its place value, which for 170 is '1 hundred 7 tens 0 ones'.

In order to find \( f(x+h) \) given the function \( f(x) = \fraction{x²}{x+3} \), we need to replace every instance of \( x \) in the function with \( x+h \). Here are the steps to do so:

1. Write down the original function:
  \( f(x) = \fraction{x²}{x+3} \)

2. Substitute \( x+h \) for \( x \) in the function to get \( f(x+h) \):
  \( f(x+h) = \fraction{(x+h)²}{(x+h)+3} \)

3. Now expand the numerator and simplify the expression:
  \( (x+h)² = x² + 2xh + h² \)
  Therefore, \( f(x+h) = \fraction{x² + 2xh + h²}{x+h+3} \)

That is the expression for \( f(x+h) \) given the function \( f(x) = \fraction{x²}{x+3} \). Note that you could further simplify the expression depending on the context or the specific question asked, but as it stands, this is the correct substitution and form of \( f(x+h) \).

Answer:

Option 4. x = 0

Step-by-step explanation:

we know that

The rule of the reflection of a point across the y-axis is equal to

(x,y) -----> (-x,y)

The rule for reflecting over the Y axis is to negate the value of the x-coordinate of each point, but leave the y-value the same

The coordinates of triangle PQR are

P(1, 4), Q(3, 6), and R(5, 2)

Applying the rule of the reflection across the y-axis we have

P(1, 4) -----> P'(-1, 4)

Q(3, 6) ----> Q'(-3, 6)

R(5, 2)----> R'(-5, 2)

The reflection line is the y-axis

Remember that the equation of the y-axis is x=0

therefore

The equation of the reflection line is x=0

Answer: The correct answer is (x = 0)

Step-by-step explanation: Took the assignment.

The total number of questions on the practice test is at least 66.

Since the number of geography questions is 65, and geography was one of the topics on the practice test, the total number of questions on the practice test must be greater than 65.

One option is that there were 66 questions on the practice test, with the remaining question being on a different topic.

Another option is that there were more than 66 questions on the practice test, with geography being one of multiple topics.

Therefore, the total number of questions on the practice test is at least 66.

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x+y≤525 and 9x+5y≤1200 represents the scenario.

Step-by-step explanation:

Given,

Room for people at summer camp = 525 people

Maximum budget = $1200

Cost per adult = $9

Cost per camper = $5

It means that there cannot be spent more than $1200.

x represents the number of adults.

y represents the number of campers.

x+y≤525      

9x+5y≤1200

x+y≤525 and 9x+5y≤1200 represents the scenario.

Keywords: inequality, budget

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Answer:  

x+y≤525      

9x+5y≤1200

Step-by-step explanation:

Answer:

Step-by-step explanation:

sales - expenses = profit

lets x represent number of shirts sold

12x - (3x + 150) > = 300

12x - 3x - 150 > = 300

9x - 150 > = 300

9x > = 300 + 150

9x > = 450

x > = 450/9

x > = 50 <== they would need to sell at least 50 shirts

Answer:

The correct option is (a).

Step-by-step explanation:

See the diagram attached.

Whatever be the translation done on a figure the dimensions of the figure will remain unchanged and only the coordinates of the vertices will change according to the rule of translation.

Therefore, if a rectangle FGHJ is translated by 6 units right and one unit up to produce a rectangle F'G'H'J', then the length F'G' = FG = 3 units and G'H' = GH = 5 units.  

So, the correct option is (a). (Answer)

Rectangle F'G'H'J' will have sides, F'G' = J'H' = 3 units, and, F'J'=G'H'=6 units.

Given to us,

Rectangle FGHJ, with sides, FG = JH = 3 units, and, FJ=GH=6 units.

Now, as given to us, Rectangle FGHJ has translated 6 units up to produce rectangle F’G’H’J', but even if the rectangle is translated it will still be a rectangle making no changes in its sides.

Therefore, Rectangle F'G'H'J' will have sides, F'G' = J'H' = 3 units, and, F'J'=G'H'=6 units.

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Answer:

Step-by-step explanation:

(b - 4)(3b - 1) is the factored form of some second degree polynomial.  Once you factor to this point, you can solve for the values of b using the Zero Product Property, which says that one of the those factors has to equal 0 for the product to equal 0 (cuz any number times 0 is equal to 0).  The first expression is b - 4.  If we set b - 4 equal to 0, we can solve for b:

b - 4 = 0 so

b = 4

Likewise with the second factor, 3b - 1.  Set it equal to 0 and solve for b:

3b - 1 = 0 and

3b = 1 so

b = 1/3

To solve the equation (B-4)(3b-1)=0 using the zero product property, set each factor equal to zero and solve for the variable. The solutions are B = 4 and b = 1/3.

To solve the equation (B-4)(3b-1)=0 using the zero product property, we set each factor equal to zero and solve for the variable:

First factor: B-4 = 0

Second factor: 3b-1 = 0

Solving each equation separately:

So the solutions to the equation (B-4)(3b-1)=0 are B = 4 and b = 1/3.

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Answer:

90+x=30-3[x]

Step-by-step explanation:

collect like terms

x+3x=30-90

4x=-260

divide both sides by 4

x=-60/4

x=-4*3*5/4

x=-[3*5/1]

x=-[3*5]

x=-15

Answer:

The number is 60.

Step-by-step explanation:

Let x = unknown number.

Now we translate the sentence into an equation, one piece at a time.

When 90 is added to a number it equals 30 less than 3 times the number.

x + 90

When 90 is added to a number it equals 30 less than 3 times the number.

x + 90 = 3x - 30

We now solve the equation for x.

Subtract 3x from both sides.

-2x + 90 = -30

Subtract 90 from both sides.

-2x = -120

Divide both sides by -2.

x = 60

The number is 60.

Check:

When 90 is added to a number it equals 30 less than 3 times the number.

Add 90 to 60:

90 + 60 = 150

We get 150.

When 90 is added to a number it equals 30 less than 3 times the number.

Now multiply 60 by 3 and subtract 30.

3(60) - 30 = 180 - 30 = 150

We also get 150.

That means our answer of 60 is correct.

Answer: 60

Answer:

The value of x is 3 ,

The measure of each side is 55 units .

Step-by-step explanation:

Given as :

The sides of the equilateral Triangle are pq , qr , pr

The measure of side pq = 18 x + 1

The measure of side qr = 24 x - 17

The measure of side pr = 15 x + 10

∵ The triangle is equilateral then all sides are equal

i.e pq = qr = pr

So, 18 x + 1 = 24 x - 17

Or, 24 x - 18 x = 17 + 1

Or, 6 x = 18

∴  x = [tex]\dfrac{18}{6}[/tex]

i.e x = 3

So, Putting the value of x

The measure of side pq = 18 × 3 + 1 = 55 unit

The measure of side qr = 24 × 3 - 17 = 55 unit

The measure of side pr = 15 × 3 + 10 = 55 unit

Hence The value of x is 3 ,

And The measure of each side is 55 units . Answer

Answer:

x = 3.

Measure of each side is 55 units.

Step-by-step explanation:

In an equilateral triangle, the length of all the three sides are equal.

Therefore, Side PQ = QR = PR.

⇒ 18X + 1 = 24X - 17

⇒ 24X - 18X = 18

⇒ 6X = 18

⇒ X = 3

Substituting the value of X, we get:

PQ = 18(3) + 1 = 55 Units.

QR = 24(3) - 17 = 55 units.

PR = 15(3) + 10 = 55 units.

We see the length of all the sides are equal.

Answer:

y=-2x+6

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-8-0)/(7-3)

m=-8/4

m=-2

y-0=-2(x-3)

y=-2(x-3)+0

y=-2(x-3)

y=-2x+6

Explanation:

All proportional relationships have a common ratio. In a set of data, if the ratio between terms are not the same, the relationship is non-proportional. The common ratio is found by dividing a term value by the previous term value. On a graph, proportional relationships form a straight line and non-proportional relationships do not.

Answer:

The sum of - 2 and - 5 is - 7.

[tex]1\frac{2}{3} + 3\frac{1}{2} = 5\frac{1}{6}[/tex]

Step-by-step explanation:

The sum of - 2 and - 5 is [- 2 + (- 5)] = - 2 - 5 = - 7. (Answer)

Let two mixed fractions are [tex]1\frac{2}{3}[/tex] and [tex]3\frac{1}{2}[/tex] that we have to add with steps.

Now, we have to sum the mixed numbers after converting then into improper fractions.

So,  [tex]1\frac{2}{3} = \frac{5}{3}[/tex] and  

[tex]3\frac{1}{2} = \frac{7}{2}[/tex]

Hence, [tex]1\frac{2}{3} + 3\frac{1}{2}[/tex]

= [tex]\frac{5}{3} + \frac{7}{2}[/tex]

= [tex]\frac{5\times 2 + 7 \times 3}{6}[/tex] {Because the  L.C.M. of 2 and 3 is 6}

= [tex]\frac{ 10 + 21}{6}[/tex]

= [tex]\frac{31}{6}[/tex]

= [tex]5\frac{1}{6}[/tex] (Answer)

Answer:

Hi im on odyssey ware and i had this question too, Just remember that the fractions are pictures, so they wont go on the question. Another way to write fractions is like this 4/8 so the actual question is, find the sum of -2 9/10 and -5 4/15. Then, in two or more complete sentences, explain the steps you used to add the mixed numbers.

Step-by-step explanation:

Answer:

n=0.64

Step-by-step explanation:

-5/8n=-0.4

n=-0.4/(-5/8)

n=-0.4(-8/5)

n=3.2/5

n=0.64

Answer:

D. [tex]\frac{-9}{2} \leqx <\frac{27}{2}[/tex]

Explanation:

Before proceeding, please remember the following:

1. When you do a certain operation on one side of the inequality, you have to do the same operation on ALL other sides to keep the original value of the inequality unchanged

2. To solve an inequality means that we want to isolate the variable.

Now, for the given inequality, we have:

[tex]-3 \leq\frac{2x-3}{4} <6[/tex]

Based on the above, for the middle part of the inequality, we want to have the x variable standing alone.

This can be done as follows:

1. Multiply all sides by 4

This would give us: [tex]-12 \leq 2x-3 < 24[/tex]

2- Add 3 to all sides

This would give us: [tex]-9 \leq2x < 27[/tex]

3- Finally, divide all sides by 2 to have the x on its own

This would give us: [tex]\frac{-9}{2} \leq x < \frac{27}{2}[/tex]

Hope this helps :)

Answer:

1 and 12

Step-by-step explanation:

each # is mult by 2

The expression for distance AB is :389 tan 88.60°. The angle D is 88.35°.The value of angle CAD in radians is 0.0532 rad.

Step-by-step explanation:

Given the information, you can sketch triangle ACB with ∠C=88.60° and a perpendicular bisector of segment CD as AB that forms 90° at B where the diatnace from C to B given as 389 ft you can find the length of the perpendicular bisector AB which is the distance between tower A and B.

Apply the tangent of an angle rule, where tangent of angle = opposite side length/adjacent side length

tan 88.60°=O/A

tan 88.60°=AB/389

AB=389 tan 88.60° = 15916.87 ⇒ 15917 (nearest foot)

B.

Given distance BD as 459 ft and the distance between tower A and B as 15917 ft you can calculate the value of angle ∠D by applying the tangent of an angle formula.

tan Ф=O/A where Ф=∠D

tan ∠D =15917/459

tan ∠D =34.6772834701

tan⁻(34.6772834701) =88.35°

C.

Finding angle ∠A in radians will be;

Applying the sum of angles in a triangle theorem

∠A=180°-(88.60°+88.35°) = 180°-176.95°=3.05°

Changing degrees to radians, multiply value of degrees by π/180°

3.05×π/180 =0.05323254 ⇒ 0.0532 rad

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Keywords : horizontal distance,towers, elevation, perpendicular line, distance, equation, expression,hundredth

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-Answer: -3

Step-by-step explanation:

Answer:

a=-75

Step-by-step explanation:

-15=a/5

a=5*-15

a=-75

Question:

The park district is paying to enlarge the area of a square-shaped dock at a local lake. The area of the dock will increase by 16 square feet. Complete the equation below that can be used to find the area, x, of the original dock if the side length of the new dock is 20 feet.

So, the square root of what (?) equals(=) 20

Answer:

The complete equation is square root of(x + 16) = 20

Solution:

Given that Dock has a shape of square

[tex]\text{ area of square }= (side)^2[/tex]

From question, it is given that side length of new dock is 20 feet

Therefore, area of new dock is given as:

[tex]\text{ area of new dock}= (20)^2[/tex]

Taking square root on both sides,

square root of (new area ) = 20  --- eqn 1

Let "x" be the area of original dock

The area of the dock will increase by 16 square feet

New area = original area + 16

New area = x + 16 ---- eqn 2

From eqn 1,

square root of (new area ) = 20

From eqn 2

square root of(x + 16) = 20

Thus the complete equation is: square root of(x + 16) = 20

Final answer:

To find the area of the original dock, the equation x + 16 = 20^2 can be used, where x is the original area. By solving the equation, we find that x equals 384 square feet.

Explanation:

The area of the original square-shaped dock can be found using the equation for the area of a square, with the area being equal to the side length squared. Given that the new square dock has a side length of 20 feet, and the area is increased by 16 square feet, we can set up an equation to find the original area, x.

The equation is x + 16 = 20^2, where 20^2 is the area of the new, larger dock, and x is the original area of the dock before the enlargement. Therefore, the side length of the original dock is the square root of x. To find x, we can solve the equation:

x + 16 = 400
x = 400 - 16
x = 384

So the area of the original dock is 384 square feet.

Answer:

1) A. Not a direct variation 2) D. Direct Variation, constant of variation is -2 C) B. Direct Variation, constant of variation is ½

Step-by-step explanation:

Direct Variation requires that [tex]y=kx[/tex] with k≠0. K its constant of variation and its slope. It is a linear function with b =0

1) Examining 2y =5x + 1. Rewriting it as standard form:

[tex]2y =5x + 1\\\\y=\frac{5}{2}x+\frac{1}{2} \\\\[/tex]

Since this function cannot be written as y=kx as b ≠ 0 (b=1) then we can say that this is not a direct variation.

A. Not a direct variation

2) [tex]2). -12x=6y \Rightarrow y=-2x[/tex]

This linear function has no linear parameter. And its line goes through the origin varying directly. The constant k is equal to -2. So,

D. Direct Variation, constant of variation is -2

3) [tex]0.7x-1.4y=0\\\\-1.4y=-0.7x* (-1)\\y=0.5 \:or\,y=\frac{1}{2}[/tex]

The Constant of Variation is 1/2 and K>0. There is a direct variation between x and y of 1/2. So it's B.

B. Direct Variation, constant of variation is ½

The equation 2y = 5x + 1 represents a direct variation with a constant of variation of 5/2. The equation -12x = 6y represents a direct variation with a constant of variation of -2. The equation 0.7x - 1.4y = 0 represents a direct variation with a constant of variation of 0.5.

For the equation 2y = 5x + 1, we need to determine if it represents a direct variation. In a direct variation, y is directly proportional to x, meaning that when x increases, y also increases or when x decreases, y also decreases. To check if it's a direct variation, we can rearrange the equation to y = mx + b form, where m is the constant of variation. In this case, rearranging the equation gives us y = (5/2)x + 1/2, so the constant of variation is 5/2. Therefore, the equation represents a direct variation and the constant of variation is 5/2.

For the equation -12x = 6y, we can rearrange it to y = (-12/6)x = -2x. Since the constant of variation is -2, the equation represents a direct variation.

For the equation 0.7x - 1.4y = 0, we can rearrange it to y = (0.7/1.4)x = 0.5x. Since the constant of variation is 0.5, the equation represents a direct variation.

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Answer:

Step-by-step explanation:

To find out the area just compare the amount of green space and yellow space then calculate the numbers.

Answer:

The answer is D

Step-by-step explanation:

[tex]sector = \frac{θ}{360} \times π {r}^{2} [/tex]

Given that θ = 75° and r = 3in, so use the formula to find the shaded region :

A = (75/360)×π×3²

= (15/8)π

Answer:

FALSE

Step-by-step explanation:

78 thousands = 78 x 1000 = 78,000

Answer:false

Step-by-step explanation:

78,000 is 78 thousands

7,800 is only 7 thousand and 8 hundred

Answer:

1. 24          2. 21:15          3. 36:21

Step-by-step explanation:

18:27 is 2:3 and 24 is 16/2*3

7:5 is also 21:15

36:21 fully simplified is 12:7 not 9:7

Answer:

1:24 2: 21:15 3: 36:21

Step-by-step explanation:

Hope this helps!!!

Answer:

Step-by-step explanation:

a + b = 140.......a = 140 - b

5.75a + 4.10b = 677.95

sub in 140 - b in for a in the other equation....and solve for b, the number of lbs of type B coffee

5.75(140 - b) + 4.10b = 677.95

805 - 5.75b + 4.10b = 677.95

-5.75b + 4.10b = 677.95 - 805

- 1.65b = - 127.05

b = -127.05 / -1.65

b = 77 <======= lbs of type B coffee used

a + b = 140

a + 77 = 140

a = 140 - 77

a = 63.........lbs of type A coffee used

check..

5.75a + 4.10b = 677.95

5.75(63) + 4.10(77) = 677.95

362.25 + 315.70 = 677.95

677.95 = 677.95 (correct)

I found both just so I could check my answer....and it checked out....

The number of pounds of coffee Type A and Type B will be 63 and 77, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Martina's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Martina $5.75 per pound, and type B coffee costs $4.10 per pound. This month, Martina made 140 pounds of the blend, for a total cost of $677.95.

Let 'x' and 'y' be the number of pounds of coffee Type A and Type B. Then the equations are given as,

x + y = 140                               ....1

5.75x + 4.10y = 677.95          ....2

From equations 1 and 2, then we have

5.75x + 4.10(140 - x) = 677.95

5.75x + 574 - 4.10x = 677.95

1.65x = 103.95

x = 63

Then the value of 'y' is given as,

63 + y = 140

y = 77

The number of pounds of coffee Type A and Type B will be 63 and 77, respectively.

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Answer: [tex]\frac{25}{6} a^{9} b^{10}[/tex]

Step-by-step explanation:

Assuming the described expression is:

[tex]\frac{(5ab)^{3}}{30 a^{-6} b^{-7}}[/tex]

And knowing the condition [tex]a \neq 0[/tex] and [tex]b \neq 0[/tex]

We cansimplify it following the rules related to the exponents with the same base:

[tex]\frac{25}{6} a^{3} b^{3} a^{6} b^{7}[/tex]

Finally:

[tex]\frac{25}{6} a^{9} b^{10}[/tex]

Answer:

Answer: \frac{25}{6} a^{9} b^{10}

Step-by-step explanation:

100% on ed

Final answer:

The photo takes up 3/16 of the magazine page.

Explanation:

To find out how much of the page is taken up by the photo, we need to calculate the proportion of the page that the photo occupies. Given that the article fills 1/2 of the page and the photo takes up 3/8 of the article, we can find the fraction of the page the photo takes by multiplying these two fractions together:

Proportion of page taken by photo = (1/2) × (3/8) = 3/16

So, the photo takes up 3/16 of the magazine page.

Answer:

2a+7

Step-by-step explanation:

Answer:

Area of trapezium = 4.4132 R²

Step-by-step explanation:

Given, MNPK is a trapezoid

MN = PK and ∠NMK = 65°

OT = R.

⇒ ∠PKM = 65° and also ∠MNP = ∠KPN = x (say).

Now, sum of interior angles in a quadrilateral of 4 sides = 360°.

⇒ x + x + 65° + 65° = 360°

⇒ x = 115°.

Here, NS is a tangent to the circle and ∠NSO = 90°

consider triangle NOS;

line joining O and N bisects the angle ∠MNP

⇒ ∠ONS = [tex]\frac{115}{2}[/tex] = 57.5°

Now, tan(57.5°) = [tex]\frac{OS}{SN}[/tex]

⇒ 1.5697 = [tex]\frac{R}{SN}[/tex]

⇒ SN = 0.637 R

⇒ NP = 2×SN = 2× 0.637 R = 1.274 R

Now, draw a line parallel to ST from N to line MK

let the intersection point be Q.

⇒ NQ = 2R

Consider triangle NQM,

tan(∠NMQ) = [tex]\frac{NQ}{QM}[/tex]

⇒ tan65° = [tex]\frac{NQ}{QM}[/tex]

⇒ QM = [tex]\frac{2R}{2.1445}[/tex]

QM = 0.9326 R .

⇒ MT = MQ + QT

          = 0.9326 R + 0.637 R  (as QT = SN)

⇒ MT = 1.5696 R

⇒ MK = 2×MT = 2×1.5696 R = 3.1392 R

Now, area of trapezium is (sum of parallel sides/ 2)×(distance between them).

⇒ A = ([tex]\frac{NP + MK}{2}[/tex]) × (ST)

       = ([tex]\frac{1.274 R + 3.1392 R}{2}[/tex]) × 2 R

       = 4.4132 R²

⇒ Area of trapezium = 4.4132 R²