Alex biked a 48-mile trail in 4 hours. For the first half of the time, he biked twice as fast as he did the second half of the time. What speed did Alex bike the first half?

Answer:

\(\frac{30meters}{second}\)

600meters

Step-by-step explanation:

Use conversion factors that represent 1.  You can cross cancel wods just like numbers.

\(\frac{108km}{1hour}\) · \(\frac{1hour}{60 minutes}\) · \(\frac{1minute}{60seconds}\) ·\(\frac{1000meters}{1 km}\)

\(\frac{108000meters}{3600seconds}\)

\(\frac{30meters}{second}\)

\(\frac{30meters}{second}\) ·\(\frac{20seconds}{1}\)

600 meters

Helping in the name of Jesus.

The value of every variable in the parallelogram is: a = 9 HK = 27.0 GK = 46 G = 63.5°

A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.These shapes include squares, rectangles, rhombuses, and rhomboids. All of these shapes have four sides, four corners, and four angles

We know that sides of a parallelogram are parallel and congruent, as opposite angle

According to question  that GA equals HK, as:

46 is equal to 3a plus 19 When we subtract 19 from both sides, we get:

27 x 3a is the result of dividing both sides by 3:

we know that opposite angles in a parallelogram are congruent, we can use a = 9. Since angle H is 56 degrees, angle K must also be 56 degrees. The length of side HK can be determined using the Law of Cosines:

HK2 = GA2 + GK2 - 2(GA)(GK)cos(H) When we substitute the values we are familiar with, we obtain:

After solving the equation we obtain: HK2 = 462 + (3a + 19)2 - 2(46)(3a + 19)cos(56°).

HK2 = 2112 + 9a2 + 342a - 2764cos(56°) HK2 = 2112 + 9(9)2 + 342(9) - 2764cos(56°) HK2  732.4 By taking the square root of both sides, we obtain the following results:

∵ GA = 46, we can use the parallelogram's opposite sides being congruent to determine the length of side GK: HK  27.0

Then, we can use the Law of Cosines to determine the angle G's measurement:

cos(G) = (HK2 + GA2 - GK2) / (2(HK)(GA)) Using the values we are familiar with, we get,

cos(G) = (27.02 + 462 - 462) / (2(27.0)(46)) cos(G)  0.465 Using the inverse cosine, we get the following:

G ≈ 63.5°

Hence, the worth of every variable in the parallelogram is:

a = 9 HK = 27.0 GK = 46 G = 63.5°

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Answer:

5 ≤ L ≤ 35

Step-by-step explanation:

Let w represent the width of the rectangle.

The perimeter (P) of the rectangle is given by:

P = 2w + 2L

Where L is the length of the rectangle.

We know that w = 30 cm and that the perimeter is between 100 and 160 cm. We can now set up our compound inequality:

100 ≤ 2(30) + 2L ≤ 160

100 ≤ 90 + 2L ≤ 160

10 ≤ 2L ≤ 70

We can now divide both sides by 2 to solve for L:

5 ≤ L ≤ 35

Therefore, the compound inequality that represents the graph of a rectangle with a width of 30 centimeters and a perimeter of 100 centimeters to 160 centimeters is:  5 ≤ L ≤ 35

Answer:

f(x) = x³ + 19x² + x + 19

Step-by-step explanation:

Zeros: -19 , -i, complex conjugate root: +i

Function: (x+19)(x+i)(x-i) = 0

(x + 19) (x² - i²) = (x + 19) ( x² + 1) = x³ + 19x² + x + 19

check: when x = 1

f(1) = 1 + 19 + 1 +19 = 40

Answer:

547 500

Step-by-step explanation:

Interest for 1 year:

0.01%×365=3.65 a year

3.65×10=36.5% for 10 years

36.5×1,500,000÷100=547 500

The interest paid after 10 years is 547 ,500 Baht.

Interest is the amount paid or earned when a loan is taken or an investment is done respectively.

It is given that

Principal = 1,500,000 Baht

Rate = 0.01 % per day

Time period = 10 years

Interest = ?

Interest = P *R *T/100

Interest = 1500000 * 0.01 *365* 10 / 100

Interest = 547,500 Baht

Therefore the interest paid after 10 years is 547 ,500 Baht.

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Answer:

Step-by-step explanation:

4-10(9m-7)

4-90m+70

74-90m

56x+24/8

8(7x + 3)/8

7x + 3

24r + 16

8(3r + 2)

is 2m-3 same as 4(1/2m-3)

2m-3 = 2m-12

: no

-2(10-15x) same as 14x-20+16x

-20+30x = -20+30x

: yes

The measure of m∠A in the triangle is:

m∠A = 38.44°

The cosine rule is used for solving triangles which are not right-angled in which two sides and the included angle are given. The following are cosine rule formula for angles:

cos(A) = (b² + c² − a²)/2bc

cos(B) = (c² + a² − b²)/ 2ac

cos(C) = (a² + b² − c²)/2ab

Where a, b and c are the length of the sides, and A, B, and C are the measures of the angles

We have:

a = BC = 20

b = AC = 23

c = AB = 32

Substituting into:

cos(A) = (b² + c² − a²)/2bc

cos(A) = (23² + 32² − 20²)/(2*23*32)

cos(A) = 0.7833

A = cos⁻¹(0.7833)

A = 38.44°

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The relationship between two variables are proportional if their ratios are equivalent (taken from Khan Academy).

To determine whether or not a relationship is proportional, we can see if two given ratios are the same.

We're given:

These pieces of information are ratios. We can write them in the following format:

\(\dfrac{400\hspace{4}meters}{1.5\hspace{4}minutes}\) and \(\dfrac{800\hspace{4}meters}{3\hspace{4}minutes}\)

We can see if they're equivalent by finding a common denominator.

Multiply the first ratio by \(\dfrac{2}2\):

\(\dfrac{400\hspace{4}meters}{1.5\hspace{4}minutes}*\dfrac{2}{2}\\\\= \dfrac{800\hspace{4}meters}{3\hspace{4}minutes}\)

The ratios are equivalent. Therefore, the relationship between the number of meters Joe ran and the number of minutes he ran is proportional.

Yes, there is a proportional relationship.

Answer:

I think the answer are C, B, C, and A.

Answer:

Fred is 28 yrs old. Nathalie is 12yrs old

Step-by-step explanation:

Let Nathalie's age be x

Let Fred's age be a

x+a=40 yrs•••••1

4x+a=76yrs•••••2

a=40-x

Substitute a for 40-x in equation (2)

4x+40-x=76

3x=76-40

3x=36

x=12

a=40-12

a=28

Hello

To solve this question, we were given a particular function and asked to evalute when the function is defined with a particular variable

For f(-6)

For g(-9)

For f(-9) + g(-9)

for g(-6) - f(-9)

For f(-9).g(-7)

For f(-6) / g(-7)

From the calculations above, i believe you must've seen your mistaken and taken the necessary correction.

Therefore the answers are

1 = 27

2 = 297

3 = 336

4 = 87

5 = 6825

6 = 27/175

As it lies in 3rd quadrant and tan is positive

Answer:

1) 9

2) 27

3) Read explanation below!

Step-by-step explanation:

1) Use the Pythagorean theorem to find AD. Show your working

To find '?' we first have to expand the indices...

Now work out '?'

2) Find AC. Show your working

We have found out that AD is 9 and to find AC we have to add 18!

3) Is ΔABC a right triangle? Explain

We can that ΔABC is not a right angle as none of the angles in the triangle are 90°!  If it was a right angled triangle we would see the ∟sign on one of the angles. Even though there are two of those in the middle it does not count as the question is asking about ΔABC!!

Have a lovely day :)

Answer:

(C) 12

Step-by-step explanation:

To solve this problem, we can use the following steps:

Find half of 80: 80/2 = 40

Add 20 to half of 80: 40 + 20 = 60

Find one fifth of the result: 60/5 = 12

Therefore, one fifth of twenty more than half of 80 is equal to 12. The correct answer is (C) 12.

Answer:

(C) 12

Step-by-step explanation:

What is one fifth of twenty more than half of 80

0.5 × 80 = 40

What is one fifth of twenty more than half of 80

40 + 20 = 60

What is one fifth of twenty more than half of 80

1/5 × 60 = 60/5 = 12

The right response is c. To find the test statistic, we utilize the formula for a one-sample t-test: t =  (x - μ)/(s/√n)

where x is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Connecting the given qualities, we get:

t = (101 - 100)/(5/√400)

t = 1/0.25

t = 4

This is a positive worth, so we reject the invalid speculation and presume that there is adequate proof to guarantee that the mean endurance time is more noteworthy than 100 days.

For this situation, an increment of 1 day in the mean endurance time may not be significant for malignant growth patients, particularly taking into account the conceivable secondary effects or expenses of the new medication. In this manner, the albeit test is statistically huge, the increment of 1 day isn't essential.

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Answer:

21 y power 5

Step-by-step explanation:

The confidence interval for the slope of the regression line relating performance score is 0.71
                   
sample size (n) = 20

slope (b1) = 3.92 and SE of slope = 0.71

Degrees of freedom = 20 - 2 = 18          

Using t-table we get, t-critical value at significance level of 0.10 with 18 degrees of freedom is,

tα/2=1.734

The 90% confidence interval for the slope of the regression line relating performance score and time to fatigue is,

B1±Tα/2*SE

3.92±1.734(0.71) (c)

Regression analysis is a statistical measure that is used in many different fields, including investing, finance, sales, marketing, science, mathematics, and others. It tries to figure out how closely one dependent variable is related to a set of other changing variables. They are commonly referred to as independent variables.

For example, how commodity prices relate to the shares of companies that trade in those commodities.


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Answer:  the number that can be placed in the box to make the statement true is 3.

Step-by-step explanation:

To make the statement true, we need to find a number that, when added to 7, equals 10. From the given options, the number that satisfies this condition is 3.

If we substitute 3 for the box in the statement, it becomes:

If +7=10, then 10-7=3.

Turn me into a superhero

The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.

To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.

The slope of a line can be found using the formula:

slope = (change in y) / (change in x)

For the line containing (1,2) and (5,3), the slope is:

slope1 = (3 - 2) / (5 - 1) = 1 / 4

To find the slope of the line containing (x,4) and (3,0), we use the same formula:

slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.

So, we can set up the equation:

-1 / (1/4) = -4 / (3 - x)

Simplifying this equation:

-4 = -4 / (3 - x)

To remove the fraction, we can multiply both sides by (3 - x):

-4(3 - x) = -4

Expanding and simplifying:

-12 + 4x = -4

Adding 12 to both sides:

4x = 8

Dividing both sides by 4:

x = 2

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The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

The complete question is attached in the diagram.

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The solution of the linear equation  is determined as x = -4.

The solution of the linear equation is calculated by applying the following method as follows;

The given linear equation;

2/x+3 - 1/x = -4/x² +3x

We can start by simplifying the equation and getting rid of the fractions.

Multiplying every term by x will help us achieve that:

2 + 3x - 1 = -4/x + 3x²

Simplifying further:

2 + 3x - 1 = (-4 + 3x²) / x

Combining like terms:

3x + 1 = (-4 + 3x²) / x

(x)(3x + 1) = -4 + 3x²

3x² + x = -4 + 3x²

We can subtract 3x² from both sides:

x = -4

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The radius of the semicircle protractor is approximately 4.693 cm.

Given,Perimeter of a semicircle protractor = 14.8 cm.

To find:The radius of a semicircle protractor.Solution:We know that the perimeter of a semicircle protractor is the sum of the straight edge of a protractor and half of the circumference of the circle whose radius is the radius of the protractor.

Circumference of a circle = 2πrWhere, r is the radius of the circle.If the radius of the semicircle protractor is r, then Perimeter of a semicircle protractor = r + πr [∵ half of the circumference of a circle =\((1/2) × 2πr = πr]14.8 = r + πr14.8 = r(1 + π) r = 14.8 / (1 + π)r ≈ 4.693\) cm.

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Answer:

positive and odd

Step-by-step explanation:

If a is a negative odd number, then a² can't be negative, because a number squared is always positive.

I'll illustrate this with an example.

Let's choose -7 as an example. Instead of a.

-7² = 49

So we see that the result is positive & odd.

So the words that describe a^2 are positive and odd.