Clock a runs 1 minute fast per hour. Clock b runs 7 minutes slow per day. If the clocks show the same time at noon, how many minutes ahead of clock b will clock a be 48 hours later?.

The  angle measures are as shown below:

∠1 is 90°

∠2 = 60°

∠3 = 30°

∠4 = 20°

∠5 = 90°

What are transversal lines ?

In geometry, a transversal is any line that intersects two straight lines at distinct points

∠1 is 90° because it is a right angle

To find angle 2, we must add the given angles and x then make the equation equal to 180°, which we next solve for x;

x + 90 + 30 = 180

x + 120 = 180

-120        -120

x = 60, ∠2 = 60°

Angle 5 is vertical to angle 1 which equals 90 degrees, and vertical angles are congruent meaning that they measure the same degrees so therefore ∠5 = 90°

Angles 4 and 40° are vertical to angle 2 which measures 60 degrees;

40 + x(where x equals angle 4) = 60

-40       -40

x = 20, ∠4 = 20°

Specified earlier, angles 40° and 4 are equal to 60°, this means that angle three added to angles 40° and 4 will be equal to 90 degrees since angle 1 is 90 degrees and the other three angles will have to equal 90 degrees because they are supplementary.

So we set up the equation;

40 + 20(angle four) + x = 90

60 + x = 90

-60       -60

x = 30, ∠3 = 30°

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The graph of an inequality x miles < 8.5 minutes to depict the situation in the question is as attached.

We are told that Jack can run a mile in less than 8¹/₂ minutes. Now, this can also be written as 8.5 miles.

Now, let the number of miles ran be x miles and it means we can write the inequality of the situation as;

x miles < 8.5 minutes

Now, for the number line graph to depict this situation, it means that the arrow will point to the left and the circle at 8.5 will be unshaded.

Thus, the inequality line graph would be drawn as shown in the image attached to depict the situation that x miles < 8.5 minutes

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The required value of x for the given equation of line is 3.

The equation of straight line is defined as the y = mx +c or ax + by = c, where y is point on y-axis and x is the point n x-axis, m is slope of the line.

According to given data in the question:

we have,

8x-3y=21-----(1)

And 3x+y=10

multiply 3 both sides

9x+3y=30------(2)

To find the value of x,

Add equation 1 and 2, we get

x = 3

Thus required value of x is 3.

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When he is halfway to the first base, the distance between the second base and the distance is decreasing at the rate of about 10.73 ft/s.

The length of the side of the base is 90 ft. Its speed is 24 ft/s.

Let x = distance he has run at time t and

D = distance from second base at time t, then speed dx/dt = 24 and we calculate dD/dt where x = 45.

From Pythagorean Theorem,

[tex]D^{2} =(90-x)^{2} +90^{2}[/tex] ,

differentiating with respect to t

2D*dD/dt = 2 (90 − x) (−1) dx/dt + 0

D*dD/dt = − (90 − x)dx/dt

Now, when x = 45,

D =[tex]\sqrt{(90-45)^{2}+90^{2} }[/tex]

[tex]=\sqrt{45^{2}+90^{2} }[/tex]

by substituting D we get,

[tex]\sqrt{45^{2}+90^{2} }[/tex]dD/dt = − (90 − 45) · 24

dD/dt = −45 · 24/[tex]\sqrt{45^{2}+90^{2} }[/tex]

= −10.73 ft/s

Hence, when he is halfway to the first base, the distance between the second base and the distance is decreasing at the rate of about 10.73 ft/s.

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The missing side we get for the triangle DOG s 56 and the triangle CAT is 90 when the triangle are congruent.

Given that,

In the picture we have 2 triangles,

We have to find the missing sides of the 2 triangles.

We have triangle DOG is congruent to triangle CAT.

Then we can say as,

Take the missing sides as a and b.

CT/ GD= CA/ OD= AT/ GO

126/b= 54/24= a/40

126/b = 9/4 =a/40

Take,

126/b = 9/4

126×4=9×b

504= 9b

b=504/9

b= 56

Now, take

9/4 =a/40

9×40= a×4

360=4a

a=360/4

a=90

Therefore, The missing side we get for the triangle DOG s 56 and the triangle CAT is 90 when the triangle are congruent.

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The least square regression line implies a mathematical equation that models the relationship between the dependent and independent variables. Hence, it may be used to predict a value of y if the corresponding x value is given. The least square regression line also called the best fit line, gives a mathematical relationship between variables in slope-intercept form.The predicted value of y or x if the corresponding value of either variable is given.

what is regression?

A statistical method called regression links a dependent variable to one or more independent (explanatory) variables. A regression model can demonstrate whether changes in one or more of the explanatory variables are related to changes in the dependent variable.

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Answer:

15 miles per hour

Step-by-step explanation:

unit rate is when you how much it is for 1 like 3 dollars for 1 pound or 15 miles per hour

Hopes this helps please mark brainliest

Answer:

15 miles per hour

Step-by-step explanation:

Let's remember what exactly unit rate is:

Unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate. Or, it takes one second to run the 7 yards.

For this question, I first notice that we have 2 answers that pertain to the same thing:

15 miles per hour and 30 miles in two hours

We have 1 cake / 3 hours, but the 1 is not in the denominator so it is not a unit rate.

And we have $5.50 per 1.5 pounds. Again, the one is not in the denominator so it is not a unit rate.

Going back to the other two (15 miles per hour and 30 miles in two hours)

We can write these in fraction form

[tex]\frac{15 miles}{1hour}[/tex] and [tex]\frac{30miles}{2hours}[/tex]

The 15 miles per hour has the one in it's denominator, so it is the unit rate.

Check the picture below.

well, the red one is one, now the green one is another and yet if we tiptoe over the circle made by KL we'll always get a right-triangle as you see in the dashed lines, how many? well infinite many.

A viable method of numeration that contained zero and allowed for the solution of equations was developed by Muslim academics, who also used logic to establish mathematical ideas and relationships.

The current arithmetic decimal system and the basic operations associated with it—addition, subtraction, multiplication, division, raising to a power, and extracting the square root and cubic root—were created by Muslim mathematicians.

The Indian numeral system, which is now known as Arabic numerals, was swiftly adopted by Islamic mathematicians. The development of algebra, the use of decimals, mathematical induction, and trigonometry were among the further contributions.

The Arabic translation of mathematical, medicinal, and astronomical writings from their original languages is one of the Islamic world's greatest contributions to contemporary science.

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Total Number of ways of selecting 7 characters accoring to tthe given condition will be 786240000

What is Permutation?

The term permutation refers to a mathematical computation of the number of possible arrangements of a given collection. Simply said, a permutation is a term that defines the amount of different ways something may be organised or arranged. The order of the arrangement is important in permutations.

Solution:

Assuming Repetation is not allowed

There are 26 letter in alphabet

So, number of ways of selectting three characters will be

26P3 = 26!/ 23!

26P3 = 15600

There are 10 basic digits in the number system

So, number of ways of selecting four characters will be

10P4 = 10!/6!

10P4 = 5040

Total Number of ways will be 15600 * 5040 = 78624000

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Answer:

negative

Step-by-step explanation:

Answer:

The graph/slope is negative. The slope intercept form is : y=-2x+5

Step-by-step explanation:

Table is

x   y

0  5

2  3

4  1

mui

Step-by-step explanation:

Answer:

60%

Step-by-step explanation:

3 divided by 5 is 0.6

Multiply this by 100 to get the percent and you will end ups with 60%

Hopes this helps please mark brainliest

The following equations represents all the solutions (x, y) to the system of the equation is y=x²−x−5

The definition of an equation in algebra is a mathematical statement that proves that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.

An equation is a mathematical statement that states that two amounts or values are equal, for as 6 x 4=12x2. An equation is a scenario in which two or more pieces must be considered together in order to understand or describe the total situation.

The given equations are:

y=x−2

y=x²−x−5

Let us take the second equation.

y=x²−x−5

x-2=x²−x−5

x²−2x-3=0

x²-3x+x-3=0

x(x-3)+1(x-3)=0

x-3=0, x+1=0

x=3, x=-1

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The solutions to the inequalities are given as follows:

6. x < 4.

7. x ≤ 1.8.

8. x ≥ -7.

An inequality is solved similarly to an equality, isolating the variable and then finding a range of values.

For item 6, the inequality is:

x < 0.25(3x + 4)

x < 0.75x + 1

x - 0.75x < 1

0.25x < 1

x < 1/0.25

x < 4.

For item 7, the inequality is:

1.5 + 0.25(x/0.2) ≤ 3.75.

The composition is explained as follows:

Hence the solution is obtained as follows:

1.5 + 0.25(x/0.2) ≤ 3.75.

1.25x ≤ 2.25

x ≤ 2.25/1.25

x ≤ 1.8.

For item 8, the inequality is:

2(x + 4) ≤ 3(x + 7) - 4

No more = less or equal than

Hence
2x + 8 ≤ 3x + 21 - 4

2x + 8 ≤ 3x + 15

x ≥ 8 - 15

x ≥ -7.

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Slope of the line in simplest form is -1/2.

From the graph:

Take any two points that the line is passing.

(-6, 0) and (2, -4)

slope = rise/run

rise = y2 - y1

run = x2 - x1

slope m = -4 - 0 / 2 - (-6)

= -4/2+6

= -4/8

= -1/2.

Therefore slope of the line in simplest form is -1/2.

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41,01,06,666.6666667 are possible combinations of a that license plate

Permutations and combinations are  ways of representing groups of objects by selecting them  and subsetting them into sets. It defines different ways of arranging a particular data group. When we choose data or objects from a particular group, it is called a permutation and the order in which they are presented is called a combination. Both concepts are very important in mathematics.

Let's assume the license plate has the 3 letters on the left hand side in a row, and the four letters on the right hand side in a row, like this:

AAA1234

We have have 26 possible letters to choose from, and we make this choice three times. So this gives us 26^3 possible letter combinations. Next, we have 10 single-digit numbers to choose from, and we make this choice 4 times. This gives us 10^4 possible number combinations. Multiplying these gives us 26^3×10^4 possible plates.

On the other hand, if there is no restriction on the placement of letters and numbers, we could have something like this:

A1A2A34B

But we can still only have 3 letters and 4 numbers.

So, to start out let's decide where to put our three letters. We need to pick 3 places out of 7, so thats (7/3) possibilities. Now that we have decided where to put our three letters, the other four spots must be numbers. At this point we have returned to our original problem where we know the positions of the letters and numbers. So the final answer should be

(7/3)×26^3×10^4 = 41,01,06,666.6666667 are possible combinations of a that license plate.

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Answer:

x is -3

Once the expression has equal bases, it is a bit easier

By using the concept of exponent, the result is-

The correct option is the third option

6 over 7 times 6 over 7 equals 36 over 49

What are exponent?

Exponent tells us how many times a number is multiplied by itself.

For example : In [tex]2^4 = 2 \times 2 \times 2 \times 2[/tex]

Here, 2 is multiplied by itself 4 times.

If [tex]a^m = a \times a \times a \times.... \times a[/tex] (m times), a is the base and m is the index.

The laws of index are

[tex]a^m \times a^n = a^{m + n}[/tex]

[tex]a^m \div a^n = a^{m - n}[/tex]

[tex]a^0 = 1[/tex]

[tex](a^m)^n = a^{mn}[/tex]

[tex](\frac{a}{b})^m = \frac{a^m}{b^m}[/tex]

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

Here, the given exponent is [tex](\frac{6}{7})^2[/tex]

[tex](\frac{6}{7})^2 \\\\= \frac{6}{7}\times \frac{6}{7}\\\= \frac{36}{49}[/tex]

[tex]= \frac{36}{49}[/tex]

So the correct option is the third option

6 over 7 times 6 over 7 equals 36 over 49

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Complete Question

Which of the following shows the correct evaluation for the exponential expression 6 over 7 to the power of 2?

6 over 7 plus 2 equals 2 and 6 over 7

6 over 7 times 2 equals 12 over 7 which equals 1 and 5 over 7

6 over 7 times 6 over 7 equals 36 over 49

6 over 7 divided by 2 equals 6 over 14

Properties we are going to use :
1. (a^m)^n = a^mn
2. a^m : a^n = a^(m-n)

((a^-2)^-1)^-1 = (a^(-2 x -1))^-1 = (a^2)^-1 = a^-2

(a : a^-1)^2 = (a^1 - (-1))^2 = (a^2)^2 = a^4

Therefore, the expression is simplified down to a^-2 : a^4

a^-2 : a^4 = a^(-2 - 4) = a^-6.

The compound interest at the end of 14 years compounded annually at a rate of 5% is $98,996.58

Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period. In Mathematics, compound interest is usually denoted by C.I.

The formula is given as

C.I = P(1 + r/n)^nt

Substituting the values into the formula

A = 50000(1 + 0.05/1)^1 * 14

A = 98,996.58

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Answer: neither

Step-by-step explanation:

For a graph to be parallel, it must have the same slope.

e.g., y = 2x    and    y = 2x + 1      are parallel because they both have the slope "2"

For a graph to be perpendicular, its slopes must be the reciprocal of each other, and the sign (positive/negative) is flipped

e.g., y = 2x    and    y = -1/2x + 1    are parallel because their slopes are reciprocals to each other, and the sign is flipped.

To know whether   y = 4x + 3    and    4x + y = 3 are parallel, perpendicular, or neither, we have to identify the slopes and use what was mentioned previously:

Identifying the slope:

y = 4x + 3        slope = 4

4x + y = 3   -->   y = -4x + 3           slope = -4

The slopes are different, so they are not parallel

As the slopes are not reciprocals, they are not perpendicular.

The graphs are neither parallel nor perpendicular.

Answer:

106 ft^2

Step-by-step explanation:

we can make this a full rectangle and find the area of that

10 by 16 is the dimensions of the new rectangle so we multiply

16x10

160

And then we subtract by what we added by finding the are of the tiny rectangle with the dimensions of 6 and 9

6x9

54

Now we subtract 54 from 160

160-54

106

Hopes this helps please mark brainliest

Answer:

-11

Step-by-step explanation:

-36/9 + (-7)

= -4 + (-7)

= -11

Answer:

well lets see here

30.5/2

which if they divide it equally, it is 15.25

I hope this helps!

Answer:

Yes

Step-by-step explanation: Because ever eight years the money in the account doubles, and 48/6=8 so your money would double 6 times, just like it does in the expression.

The value of 36.8/2.3 is 16

How do you divide expressions?

Multiply the first fraction by the reciprocal of the second to divide rational expressions. We factor everything and search for common factors after rewriting the division as the multiplication of the first statement by the reciprocal of the second.

What are equivalent expressions?

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

Here,

we have to simplify the given division expression

So we start by solving the expression. i.e. divide 36.8 by 2.3

This means that when 36.8 divided by 2.3 is 16

Hence, the value of 36.8/2.3 is 16.

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The scale which Mr. Seals used to create the scale of the drawing as required is; Choice A; 1 inch represents 4 feet.

It follows from the task content that the scale used by Mr. Seals is to be determined.

According to the task content; the width of the classroom is 5 inches and the width of the actual classroom is 20 feet.

On this note, it follows by proportion that we have;

5 inches / 20 feet.

= 1 inch / 4 feet.

Consequently, it can be inferred that the required scale is; 1 inch represents 4 feet.

Hence, Choice A is correct.

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Answer:

Step-by-step explanation:

So the first thing that you'll have to recognize is that  the interior angles of a triangle add to 180°

Next, note that the angle that is given as 5y -23 is also the same angle as the inside of the triangle,  as well as the angle it's written on.

recognizing both of these let's  you write this.

180 = 2x+13 + 47 + 5y - 23

this doesn't help us too much because there are two unknowns and only one equation.  we would need two equations to solve this :(  

but.....

now note, that the angle  3x  and  5y - 23 are also equal.  Assuming that the lines are parallel that look parallel. I think for this problem we can assume that they are.

now revise the problem

180 = 2x+13 +47 +3x

now  use your algebra skillz

180 = 5x 60

180-60 = 5x

120 = 5x

120/5 = 5x/5

24 = x

now plug x into the earlier equation

180 = 2x+13 + 47 + 5y - 23

180 = 2(24) + 13 + 47 +5y - 23

180 = 48 + 13 + 47 +5y -23

180 = 109 - 23 + 5y

180 = 85 + 5y

180 - 85 = 5y

95 = 5y

19 = y

The value of a for which the equation has an infinite number of solutions is 5.

The solution to the equation: The result is a distribution of weights to the variables involved, establishing a balance in the calculation.

The equation given is written below:

Both sides of the equation must have the same value for an infinite number of solutions.

12x + 30 = 6(2x + a)

Simplifying the equation:

12x + 30 = 12x + 6a

Canceling 12x both sides. We get,

the value of a = 5

The value of a for which the equation has an infinite number of solutions is 5.

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