Alfonso runs 10 km at an average speed of x km/h.
The next day he runs 12 km at an average speed of (x - 1) km/h.
The time taken for the 10km run is 30 minutes less than the time taken for the 12 km run.
(a) (i)
Write down an equation in x and show that it simplifies to x? – 5x – 20 = 0.​

Answers

Answer 1

Step-by-step explanation:

Note that t = d/r where t is time, d is distance, and r is rate/speed.

We can come up with two equations with the information given and the equation:

t_1 hr = (10 km)/(x km/hr)

t_2 hr = (12 km)/(x - 1 km/hr)

where t_1 is the time taken to run the 10km the first day and t_2 is the time taken to run the 12km the second day.

We know that 30 minutes is 1/2 of an hour and that t_1 is 30 minutes less than t_2 (as stated in the question). Therefore, we can write:

t_1 = t_2 - 1/2

Substituting the values we derived:

(10 km)/(x km/hr) = (12 km)/(x - 1 km/hr) -1/2

Then we can evaluate by multiplying by 2x(x-1) on both sides:

20(x-1) = 24x - (x)(x-1)

20x - 20 = 24x - x^2 + x

x^2 -5x -20 = 0

And we are done.

I hope this helps! :)

Answer 2

An equation is formed when two equal expressions. The equation for the time can be written as (12/x-1)-(10/x)=0.5. The value of x is 7.623.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

A.) Given Alfonso runs 10 km at an average speed of x km/h. Therefore, the time taken by Alfonso to rum 10km is 10/x hour.

Also, The next day he runs 12 km at an average speed of (x - 1) km/h. Therefore, the time taken by Alsonso to run 12km is 12/(x-1) hour.

Now, the time taken for the 10km run in 30minutes(0.5 hours) is less than the time taken for the 12 km run. Therefore, we can write,

[tex]\dfrac{12}{(x-1)}-\dfrac{10}{x} =0.5[/tex]

The equation for the time can be written as (12/x-1)-(10/x)=0.5.

B.) The value of x can be written as,

[tex]\dfrac{12}{(x-1)}-\dfrac{10}{x} =0.5\\\\12x-10(x-1)=0.5 \times x \times (x-1)\\\\12x - 10x +10 = 0.5x^2-0.5x\\\\2x+10 = 0.5x^2-0.5x\\\\0=0.5x^2 - 2.5x -10\\\\x = -2.623, 7.623[/tex]

Since the time can not be negative. Hence, the value of x is 7.623.

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Related Questions

Which of the following equations are written in standard form?

А. 3x + 5y = -7

B. 2y + x = 12

C. 5x+10y = -21

D. 1.2x + 5y = 23.7
PLEASE HELP ME ASAP

Answers

Answers A, C, and D are written in standard form.

Answer B is NOT written correctly in standard form.

A paraboloid container is being filled with fluid at the rate of 4.5 cubic feet per minute. At what rate is the level of fluid changing when the depth
is 2.5 feet? The ratio of the radius to the height of the container is 3:7.
"V = 1/2 pir^2h

Answers

Answer:

2.62 ft./min

Step-by-step explanation:

Just took the test.

Assuming each area code is just as likely as any other, what's the probability that the area code of two back to back spam calls are 804

Answers

Complete Question:

Yanay gets a lot of spam calls. An area code is defined to be a three digit number from 200-999 inclusive. In reality, many of these area codes are not in use, but for this question we'll simplify things and assume they all are.

Assuming each area code is just as likely as any other, what's the probability that the area code of two back to back spam calls are 804?

Answer:

1/6400 or 0.0000015625

Step-by-step explanation:

Given

Area Codes = 200 to 999 (inclusive)

Required

Determine the probability that back to back calls have area code 804

[First, we need to calculate the totality of area codes]

Total Area Codes = 999 - 200 + 1

Total Area Codes = 800

The probability of each code is 1/800

So, the probability of having back to back code of 804 is:

Probability = 1/800 * 1/800

Probability = (1/800)²

Probability = 1/640000

Hence, the required probability is 1/640000 or 0.0000015625

COLOR THEME
O Q ZOOM
5. Mrs. All collected notebook paper from her students at the beginning of the
school year. The model is shaded to show the fraction of notebook paper
that Mrs. Ali used in each of the following three months.
First month
Second month
Third month
What fraction of the notebook paper Mrs. All collected was used during
these three months?

Answers

Answer:

6

Step-by-step explanation:

3(x – 2) – (1 – x) > 2x – 7

Answers

The answer is x > 0

Factor completely
w^2 + 12w -f^2+ 36

Answers

Factored:
(w+6-f)x (w+6+f)

Assume you have a balance of $1,900 on a credit card.
If the credit card has an annual interest rate of 13.6% and only the minimum monthly
payment of $35 is made, how many months will it take to pay off the credit card?

Answers

principal=$1900

rate =13.6 %

simple interest= $35

Time=?

SIMPLE INTEREST ={PRINCIPAL×RATE×TIME}/{100}

$35= [tex]{$1900 ×13.6× TIME}{100} /[/tex]

$35×100=25840× TIME

TIME=[tex]\bold\frac{ 3500}{25840}[/tex]

TIME=[tex] 700/5168 [/tex]

TIME=[tex]{\tt{\green{\underline{\underline{\huge{0.1354489164}}}}}}[/tex] years

sorry I can't solve wrong answer

68=u-11
i need help lol pls

Answers

Answer:

u=79

Step-by-step explanation:

68=u-11

add 11 to 68

u=79

i think the answer might be 79

expression with parentheses..example and non-example​

Answers

Answer:

With parentheses:

(3 - 4)(4 + 5)/3

Without parentheses:

7 + 6 - 11 × 2

Hope this helps! :)

Find the area, in square units, of ABC plotted below.

Answers

Answer:

43.55

Step-by-step explanation:

1. Use the distance formula on both points AC and AB.

Distance formula is this:

[tex]d=\sqrt{(x2-x1)^2+(y2-y1)^2} \\\\d=\sqrt{(1--5)^2+(8--7)^2} \\\\d=\sqrt{(6)^2+(15)^2} \\\\d=\sqrt{36+225} \\\\d=\sqrt{261} \\\\[/tex]

Distance for AC  is  16.16

Now do the same with the numbers for AB and get the distance of 5.39

2. To get the area, use the formula 1/2 x base x height

AB is the base and AC is the height.

1/2 x 16.16 x 5.39 = 43.55

The area of triangle ABC is 43.5 square units.

What is a triangle?

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

The shape ABC is a triangle.

Where,

AB = Base

AC = Height

A = (1, 8)

B = (6, 6)

C = (-5, -7)

First, let's find the length of AB using the distance formula:

AB = √((6-1)² + (6-8)²)

= √(25 + 4)

= √(29)

Next, let's find the length of AC using the distance formula:

AC = √((1-(-5))² + (8-(-7))²)

= √(36 + 225)

= √(261)

The area of the triangle ABC can be found using the formula:

Area = (1/2) x base x height

We know that AB is the base and AC is the height,

Area = (1/2) x AB x AC

Area = (1/2) x √(29) x √(261)

Area = (1/2) x √(7569)

Area = (1/2) x 87

Area = 43.5

Therefore,

The area of triangle ABC is 43.5 square units.

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Rewrite the following to show the distributive property
4x(5+3)

Answers

Step-by-step explanation:

4x+8

basically u solve the number that is in parentheses then you are left with the number with a variable so u can't solve so that's ur equation

Answer:

32x

Step-by-step explanation:

1. rewrite

4x(5)+4x(3)

4(3) means 4*3

2. multiply

4x(5)= 20x

4x(3)= 12x

20x+12x

3. combine like terms

20x+12x= 32x

32x

If this is right can you make me brainliest

Please help me out.
Can the lengths 40, 60, and 80 form a supplementary triangle?

Answers

Answer: Yes

Step-by-step explanation:

A supplementary triangle has sides adding up to 180°.

We have the side lengths 40, 60, and 80.

To find out if it is a supplementary triangle, we will add all the sides.

40 + 60 + 80 = 180

We get 180° as our answer when we add.

We got 180°, so the answer is yes, it can.

Best of Luck!

Answer:

yes.

Step-by-step explanation:

Any angle that adds up to 180 is a supplementary angles.

based on your examples 40, 60, 80, if you sum it up...

it equates to 180. so the answer is yes.

How far from the base of the house do you need to place a 13-foot ladder so that it exactly reaches the top of a 10- foot tall wall

Answers

Answer:
3 feet from the house
Step-by-step explanation:
well since 3 extra feet is one the ladder than the wall 3feet should do it

Which graph shows the points (−11
2
, 1
2
) and (1.5, −0.5) plotted correctly?

On a coordinate plane, a point is 0.5 units to the right and 1.5 units up. Another point is 0.5 units to the left and 1.5 units down.
On a coordinate plane, a point is 1.5 units to the left and 0.5 units up. Another point is 1.5 units to the right and 0.5 units down.
On a coordinate plane, a point is 0.5 units to the left and 1.5 units up. Another point is 0.5 units to the right and 1.5 units down.
On a coordinate plane, a point is 1.5 units to the left and 0.5 units down. Another point is 1.5 units to the right and 0.5 units up.

Answers

Answer:

b

Step-by-step explanation: got it right on edge

Answer:

B

Step-by-step explanation:

got it right on edge

Through (2,-5); perpendicular to 3y=x-6

Answers

Answer:

y=-3x+1

Step-by-step explanation:

Have a good one.

The $99.99 digital camera Mia purchased was on sale for 15% off. What amount did Mia get off the price? please leave an explanation

Answers

Answer: Sale Price = $84.99 (answer). This means the cost of the item to you is $84.99. You will pay $84.99 for a item with original price of $99.99 when discounted 15%. In this example, if you buy an item at $99.99 with 15% discount, you will pay 99.99 - 14.9985 = 84.99 dollars.

Step-by-step explanation:

Solve the quadratic equation using any appropriate method.
- 2x2 + 7x - 7 = 0

Answers

X=11/7 i think that would be the answer

What is the quotient of 8/9 ÷ 16/9

Answers

Answer:

1/2 or 0.5

Step-by-step explanation:

which table of values matches the equation y=2x-3

Answers

Answer:

What are the possible answer??/

Step-by-step explanation:

The set of points satisfying the equation y = 2x - 3 is a. {(0, -3), (1, -1), (1.5, 0), (2,1)}.

An equation is the combination of 2 or more expressions separated by the equality sign(=), signifying the equality of expressions.

To obtain the set of points satisfying the equation y = 2x - 3.

The given equation is y = 2x - 3.

Let's take x = 0,

y = 2 × 0 - 3 = -3,

the point is (0, -3).

Let's take y = 0,

0 = 2x - 3

2x = 3

x = [tex]\frac{3}{2}[/tex]

x = 1.5,

the point is (1.5, 0).

Let's take x = 1,

y = 2 × 1 - 3 = -1,

the point is (1, -1).

Let's take y = 1,

1 = 2x - 3

2x = 1 + 3

2x = 4

x = [tex]\frac{4}{2}[/tex]

x = 2,

the point is (2,1).

Hence, the set of points satisfying the equation is {(0, -3), (1, -1), (1.5, 0), (2,1)}.

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The complete question is as follows:

Which table of values matches the equation y = 2x - 3,

a. {(0, -3), (1.5, 0), (1, -1), (2,1)}.

b. {(0, -2), (1.5, 0), (1, -1), (2,1)}.

c. {(0, -3), (1.5, 0), (1, -4), (2,1)}.

d. {(-1,1), (0, -3), (1.5, 0), (1, -1)}.

Does anyone know the answers to this?

Answers

Answer:

i think the correct answer of these qusion is `B´

Answer:it’s 5

Step-by-step explanation:

Annie spent $143.89 at Kohls and there is a 6.25% sales tax. What will she pay in sales tax and
what is the total purchase price?

Answers

Answer:

net amount 143 89 tax 6.25 % which is $8.99 gross amount is $152.88

The IQ scores of the middle 50% of a population can be written as

I

100

15

where x is a person's IQ. Solve the inequality to find the IQ scores for the middle 50% of the population.

x 270 and x s 130

Ox570 and x 2 130

Oxs 90 and x 2 110

x 290 and x s 110

Answers

Complete question :

The IQ scores of the middle 50% of a population can be written as (x - 100) / 15 ≤ 2/3

Answer: 90 ≤ x ≤ 110

Oxs 90 and x 2 110

Step-by-step explanation:

Given the inequality:

The middle 50% of the population :

(x - 100) / 15 ≤ 2/3

The upper bound :

(x - 100) / 15 ≤ 2/3

multiply both sides by 15

(x - 100) / 15 * 15 ≤ 2/3 * 15

(x - 100) ≤ 2/3 * 15

x - 100 ≤ 10

x ≤ 10 + 100

x ≤ 110

The lower bound :

- (x - 100) / 15 ≤ 2/3

(-x + 100) / 15 ≤ 2/3

multiply both sides by 15

(-x + 100) / 15 * 15 ≤ 2/3 * 15

(-x + 100) ≤ 2/3 * 15

-x + 100 ≤ 10

-x ≤ 10 - 100

-x ≤ - 90

x ≤ 90

90 ≤ x ≤ 110

The equation x^2/24^2 - y^2/b^2 = 1 represents a hyperbola centered at the origin with a directrix of x = 576/26.

What is the value of b?
A. 10
B. 16
C. 20
D. 26​

Answers

Answer:

a

Step-by-step explanation:

edge

The value of B is 16.

The correct option is B

What is a quadratic equation?

A basic quadratic equation, or a second-order polynomial equation with a single variable, is represented by the equation x : ax² + bx + c = 0, where a≠0 for the variable x. As it is a second-order polynomial equation, which is ensured by the algebraic fundamental theorem, it must have at least one solution.

The standard equation for a hyperbola centered at the origin is:

(x²)/(a²) - (y²)/(b²) = 1

where "a" and "b" are the lengths of the transverse and conjugate axes, respectively. To find the value of "b" for the given hyperbola equation, we need to first rewrite it in the standard form.

(x²)/(24²) - (y²)/(b²) = 1

Multiplying both sides by (24²)(b²), we get:

b²(x²) - (24²)(y²) = (24²)(b²)

Dividing both sides by (24²), we get:

b²(x²)/(24²) - y² = b²

Comparing this with the standard equation, we can see that a = 24 and b is the square root of the constant term, which is b² = 576. Therefore, b = 24.

However, the given directrix of x = 576/26 is not consistent with the equation of the hyperbola. The directrix for a hyperbola with center at the origin and transverse axis along the x-axis is given by x = a²/b. Using the value of a = 24, we can find the directrix as:

x = (24²)/b

Setting this equal to 576/26, we get:

(24²)/b = 576/26

Solving for b, we get:

b = 16

Therefore, the correct answer is (B) 16.

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does anyone understand this

Answers

For this problem, 0.25 in = 50 m. So

11 in = (11 in) • (50/0.25 m/in) = 2200 m

Alternatively, if 0.25 in = 50 m, that means 1 in = 200 m. So 11 in = 11 (200 m) = 2200 m.

Harold brought 5 apples for $3.90.What is the unit price?

Answers

Answer:

.78

Step-by-step explanation:

3.90/5 = .78

Help pls :))))))))))))))

Answers

Answer:left is 7 right is 6

Step-by-step explanation:

left is 7 right is 6

Answer:

the right side is 6 and the left side is 7

Step-by-step explanation:

These triangles are similar. Since the bottom side goes from 15 to 5, that means you divide the other 2 sides by 3 also.

solve for x and y!! will give brainliest !

Answers

Answer:

x = 60 and y=25

Step-by-step explanation:

it is equilateral triangle and  an equilateral triangle is a triangle in which all three sides have the same length. In the familiar  geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°.

Write the equation of the line parallel to the line y= 5x + 3 that passes through the point (3,3)

Answers

Answer:

y=5x-12

Step-by-step explanation:

y=5x+3, and just replace the x and y to get the b. The slope is the same.

1) 3=5(3)+b

2)3=15+b

3)-12=b

4) y=5x-12

Randy Houck deposited his paycheck for $385.15, a refund check from a mail

order purchase for $125.95, and $37.20 in cash.

Answers

Answer:

The correct option is c. $548.30.

Step-by-step explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question. Please, see the attached pdf file for the complete question.

Also Note: This template does not allow the explanation to be added and saved here as it keeps on indicating that it contains some swearwords. The explanation is now given in the attached pdf file. Please, see the attached pdf file for the answer and explanation.

What is the perimeter of this figure?
6x+6
6x+10
4x+6
4x+8

Answers

Answer: 4x+8

Step-by-step explanation:

Okay since the area for the block is X, two numbers multiplied together is X.

Since the big block has an area of X^2, then this shows the sides to be X.

This gives the sides of the block with area X to be 1 and X.

Now just add up every side like this : 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + x + x + x + x to get 4x+8

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