8. If mZABC is one degree less than three times mZABD and m2DBC = 47°, find each measure.

The quotient of 30 × 10⁻²⁴/5 × 10⁻²⁴ in scientific notation is equal to: C. 6 x 10^0.

Quotient can be defined as a mathematical expression that is simply used to represent the division of a number by another number.

In Mathematics, laws of indices can be defined as the standard principles and rules that are used for simplifying a mathematical equation or expression that involves powers of the same base.

By applying the laws of indices, the quotient is given by:

Quotient = 30 × 10⁻²⁴/5 × 10⁻²⁴

Quotient = 30/5 × 10⁽⁻²⁴ ⁺ ²⁴)

Quotient = 6 × 10⁰

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a)The acceleration, in km/h², in the first 15 mins = 200  km/h².

b) The distance between the two cities = 125 km.

c) The average speed during 20 the journey =  62.5  km/hr.

For the given question;

Every horizontal block is 1/8 hour = 7.5 minutes long.

Each vertical block has a speed of 10 km/hr:

The table drawn as per the data given in the table:

Time                    Velocity  km/hr

0 Min  ( 0 hr)   --->         0

15 Min (1/4 hr)   -->       50

45 Min (3/4 hr)  -->      50

60 MIn  ( 1 hr)      -->    100

90 Min  ( 3/2 hr)   --->  100

120 Min ( 2hr)     --->    0

The formula for acceleration:

Part a: Acceleration = final velocity - initial velocity / final time - initial time

Acceleration in the first 15 minutes:  (1/4 hr)  =  (50 - 0)/(1/4 - 0)  

= 50/(1/4)

=200

Thus, acceleration in the first 15 minutes is 200 kmph.

Part b: Distance among two cities:

= (1/2)(0 + 50)(1/4 - 0)  + 50 * (3/4 - 1/4)  + (1/2)(50 + 100)(1 - 3/4)  + 100 * (3/2 - 1) + (1/2)(100 + 0)(2 - 3/2)

=  25/4  + 25 + 75/4   + 50 + 25

= 125

The difference distance for two cities is 125 kilometers.

Part c: Average speed = distance/2

Average Travel Speed = 125/2 = 62.5 km/hr

Therefore,

a: Acceleration in the first 15 minutes = 200  km/h²

b: The distance between two cities is 125 kilometers.

c: The average speed of the journey is 62 miles per hour.

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Answer:[tex]\sqrt 7,2.8,\pi ,\sqrt{17, 4.6[/tex]

Step-by-step explanation:

The solution for the expression ( -8x³) ⁻ ⁴/₃ = 1 / 16x⁴

Given expression is ( -8x³) ⁻ ⁴/₃

= ( -8x³) ⁻ ⁴/₃

It can be written as

We know that 8 = 2³ then

= ((-2x)³) ⁻ ⁴/₃

= ((-2x)³* ⁻ ⁴/₃

On the exponents '3' will be canceled then we get

= (-2x) ⁻ ⁴

We know that x ⁻ ¹ can be written as 1/x, then

= 1/(-2x)⁴

= 1 / 16x⁴

∴  ( -8x³) ⁻ ⁴/₃ = 1 / 16x⁴

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Step-by-step explanation:

first : the sum of all angles in a triangle is always 180°.

second : the law of sine

a/sin(A) = b/sin(B) = c/sin(C)

a, b, c are the sides, A, B, C are the the corresponding opposite angles.

therefore,

angle J = 180 - 71 - 46 = 63°

j/sin(J) = k/sin(K)

11/sin(63) = k/sin(46)

k = 11×sin(46)/sin(63) = 8.880673249... m

[Mathematical Problem]

[tex](2x)^2y; x=4,y=8[/tex]

Solution:

Substitute the value of the variable into the expression, then simplify.

[tex](2(4))^2[/tex] × [tex]8[/tex]

↓

[tex](8)^2[/tex]

↓

[tex](8)^2[/tex] × [tex]8[/tex]

↓

[tex]64[/tex]

↓

[tex]64[/tex] × [tex]8[/tex] = 512

Hence, our solution is 512.

Hope this helps! It's been a while since I've done this, but this should be correct. Lmk if it helps! Thanks and good luck!

The characteristics of the parallelogram and star gives;

Parallelogram;

Rotational symmetry: Yes

Point symmetry: Yes

Star:

Rotational symmetry: Yes

Point symmetry: Yes

Rotational symmetry is one in which a shape assumes its original appearance after a rotation.

Point symmetry are the property of two points that are equidistant from and on opposite sides of the coordinate axis

The parallelogram has rotational symmetry of 180°

The parallelogram has point symmetry

Therefore;

Parallelogram:

Rotational symmetry; Yes

Point symmetry; Yes

The star has rotational symmetry of 360°/5 = 60°

Given that points on the star when rotated about its center can be made to match up with opposite side, it is said to have point symmetry.

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The negative exponent of 1/16 is   2⁻^{4}.

A statement is considered to be an expression if it has a minimum of two numbers or variables as well as at least one mathematical action.

The multiplicative inverse of the base raised to the power opposite to the provided power is the definition of a negative exponent. In plain English, we write the number's reciprocal and solve it just like positive exponents. For instance, (2/3)-2 may be represented as (3/2)2.

1/16 = 16⁻¹  

1/16 = 16⁻¹  = 4⁻²

1/16 = 16⁻¹  = 4⁻² =  (2^2)⁻²  =  2⁻^{4} .

1/16 =   2⁻^{4} .

Hence, the negative exponent of 1/16 is   2⁻^{4}.

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Answer: Shade 10 of the pieces.

Step-by-step explanation: To figure this out, divide 15 by 3(5) and then multiple 5 by two and you will get 10!

Answer: You need to shade 10 of the pieces.

Take 15/3 and get 5

Then take 5 * 2 and get 10

Step-by-step explanation:

The correct option is (A) The y-coordinate is -5. If point D(-1, 5) is reflected across the x-axis then the coordinates of D’ are (-1, -5).

Geometry. The x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the x-axis as (x, -y).

Determine the location of the mirror line before reflecting an object on a coordinate plane. Simply multiply the coordinate of the point by -1 to reflect over the axis. Use the symbols. Simply multiply the coordinate of the point by -1 to reflect over the axis.

Given coordinates of D= (-1, 5)

While reflecting any points across the x-axis with coordinates as (x, y) becomes, (x, -y). i.e sign of y-coordinate changes.

The rule is: (x, y) arrow (x, -y)

Applying so, after reflecting point D, its reflection D' will have coordinates as (-1, -5)

Therefore, the y-coordinate is -5.

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The match is

A number system is defined as a system of writing to express numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner.

Given:

10 + 14

=2(5 +7)

25 + 10

=5(5 +2)

32 + 12

=4(8 + 3)

6+9

=3(2 +3)

So, the matching is

10 + 14 -------> 2(5 +7)

25 + 10 --------> 5(5 +2)

32 + 12 --------->4(8 + 3)

6 + 9-----------> 3(2 +3)

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The answer to the question is 9±√21/2

By using the quadratic formula x=-b±√b²-4ac/2a

By comparing  x²-9 x+15=0  with ax²+bx+c

we get a=1 b=-9 c=15

x=-(-9)±√(-9)²-4×1×15/2×1

x=9±√81-60/2

x=9±√21/2

So the answer to the question is x=9+√21/2

and x=9-√21/2

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Answer:

3

Step-by-step explanation:

3

Answer:

4

Step-by-step explanation:

7.185629 x 102985 =   740,012.002565 which has 4 zeros

The logarithm expression can written as log₆ 24 - log₆ 4 = 1

There are 7 properties of logarithms: Product Rule, Quotient Rule, Power Rule, Zero Rule, Identity Rule, Inverse Property of Logarithm, Inverse Property of Exponent, Change of base formula.

In this question, we use the Quotient Rule of logarithms.

Quotient rule of logarithms states that the logarithm of a quotient is equal to a difference of logarithms.

Example: logₐ (x/y) = logₐ x - logₐ y

So, we get that:

log₆ 24 - log₆ 4

= log₆ (24 / 4)

= log₆ 6

which will also be equal to

= 1

Therefore, in the equation log₆ 24 - log₆ 4 = 1 and the property of the quotient rule of logarithms is used.

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Function composition exists a mathematical procedure where two functions, f and g, are taken and a function, h = g ⁰ f, exists produced such that h(x) = g(f(x)).

If the function be f(x) = 10x - 10 then the value of (f ⁰ f⁻¹)(d) is 99.

Function composition exists a mathematical procedure where two functions, f and g, exists taken and a function, h = g ⁰ f, exists produced such that h(x) = g(f(x)). The function g is used in this operation on the outcome of applying the function f to x.

Let the function be f(x) = 10x -10

We want to find (f ⁰ f⁻¹)(d)

To differentiate with respect to X, then we get

[tex]F^{-1}[/tex](x) = 10

To find the value of (f ⁰ f⁻¹)(d)

F([tex]f^{-1}[/tex](x)) = F(10)

F([tex]f^{-1}[/tex](x)) = 10x - 10

substituting the values in the above equation, then

F([tex]f^{-1}[/tex](x)) = 10(10) - 10

simplifying the above equation, we get

F([tex]f^{-1}[/tex](x)) = 100 -10

F([tex]f^{-1}[/tex](x)) = 99

Therefore, the value of (f ⁰ f⁻¹)(d) = 99

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Using linear functions, it is found that:

a) The cheaper costs are given as follows:

b) Due to the same cost per game and higher cost for the pair of shoes, bowling alley A will never be cheaper than bowling alley B.

A linear function is modeled by:

y = mx + b

In which:

For this problem, we have that:

Hence the cost functions are given as follows:

The costs are equal when:

A(x) = B(x)

3.75 + 4x = 2.5 + 4.5x

0.5x = 1.25

x = 1.25/0.5

x = 2.5.

Hence the cheaper costs are given as follows:

Alley B has the lower initial cost due to the lower cost for the pair of shoes.

For item b, if we increase the cost per game by $0.50 for alley A, we have that:

A(x) = 4.5x + 3.75.

Hence:

Due to the same cost per game and higher cost for the pair of shoes, bowling alley A will never be cheaper than bowling alley B.

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Answer:

k=4

Step-by-step explanation:

−4k+6−2k=−3(4k−10)

−4k+6−2k=−3(4k−10)

−4k+6+−2k=(−3)(4k)+(−3)(−10)

−4k+6+−2k=−12k+30

(−4k+−2k)+(6)=−12k+30

−6k+6=−12k+30

−6k+6=−12k+30

−6k+6+12k=−12k+30+12k

6k+6=30

6k+6−6=30−6

6k=24

6k/6=24/6

k=4

(sorry if this was confusing)

Answer:

-3.5

Step-by-step explanation:

-4k+ 6 - 2k= -3(-6k)

-4k+ 4k= 18k

-4k = 18k-4k

-4k = 14

-4k/-4 = 14/-4

K= -3.5

If Jodi wants to visit her extended family in Barbados next summer, and the flight costs $450, then she needs to save 50$ each month if she wants to buy the flight in exactly 9 months.

If the flight costs $450, then the amount of money Jodi needs to save each month can be determined by using division.

Division is one of the four basic operations of arithmetic and involves the separation into equal parts.

By dividing the cost of the flight by the number of months, the money Jodi needs to save each month can be calculated.

Considering x to be money Jodi needs to save each month,

x = flight cost / number of months

x = 450 / 9

x = 50

Hence, the money Jodi needs to save each month if she wants to buy the flight in 9 months is calculated to 50$.

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total utensils = 3915

it is given that Mrs. Meester is purchasing supplies for her art class.

The arts are a very wide range of human practices of creative expression, storytelling and cultural participation. They encompass multiple diverse and plural modes of thinking, doing and being, in an extremely broad range of media. Both highly dynamic and a characteristically constant feature of human life, they have developed into innovative, stylized and sometimes intricate forms. This is often achieved through sustained and deliberate study, training and/or theorizing within a particular tradition, across generations and even between civilizations. The arts are a vehicle through which human beings cultivate distinct social, cultural and individual identities, while transmitting values, impressions, judgments, ideas, visions, spiritual meanings, patterns of life and experiences across time and space.

Mrs. Meester purchase some utensils for their scholars.

number of different types of utensils for each scholar are:-

total number of utensils for 1 scholar= 64+25+36+10

                                                            = 135

   64

   25

   36

+   10

   135

total number of utensils for 29 scholars=135*29

                                                                  =3915

hence, number of utensils Mrs. Meester buy= 3915

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The required solution of each person's contributions showing all steps in long division is 3687/100, 2937/100, 2627/100 and 3527/100.

An expression is a set of terms combined using the operations +, – , x or ÷. An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An expression is in simplest form when no terms can be combined.

Given:

The given expression  is

#1 $36.87

#2 $29.37

#3 $26.27

#4 $35.27

According to given question we have

By the long division method we get

1.  $36.87 =36+0.87

  $36.87 = 36+87/100

GCD( 87,100)=1

$36.87 = 36+87/100=36+1

$36.87 = 36+87/100

$36.87=3687/100

2. $29.37 =29+0.37=29+37/100

GCD( 37,100)=1

$29.37 =29+37/100

$29.37 =2937/100

3. $26.27  =26+0.27 =26+27/100

GCD( 27,100)=1

    $26.27  =26+27/100

$26.27  =2627/100

4. $35.27 =35+0.27=35+27/100

GCD( 27,100)=1

$35.27 =35+27/100

$35.27 =3527/100

Therefore, the required solution of each person's contributions showing all steps in long division is 3687/100, 2937/100, 2627/100 and 3527/100.

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Tristian and Barry both are correct as 9,32 is a rational and terminating decimal.

A rational number is one that can be written as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively.

A terminating decimal is a decimal number with a finite number of digits after the decimal point. The repeating decimal 5.6500000000... can be used to represent a terminating decimal like 5.65, however, when it is zero, the value is typically referred to as terminating.

A decimal number having a limited number of digits following the decimal point is referred to as a terminating decimal. Therefore, all decimal numbers that terminate are rational numbers.

Hence both are correct.

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Converting the radicals into exponent numbers, √3 (⁴√3) = ⁴√27

To work with radical numbers or roots, it is easier to express them in exponent:

[tex]\sqrt[n]{a^{b}}=a^{\frac{b}{n}[/tex]

Recall the rules of exponent operations:

Note that the first 3 rules use the same base. If there are more than 1 base number, then group the exponent that have the same base first.

Example:

[tex](2^{3}.3^{-2}) : (2^{-3}.3^{2})=( 2^{3}:2^{-3}).(3^{-2}:.3^{2})[/tex]

Tips: To simplify exponent numbers, sometimes it is useful to modify the base whenever possible.

Example:

8².2⁻⁵ = (2³)². 2⁻⁵ = 2⁶. 2⁻⁵ = 2⁶⁻⁵ = 2¹ = 2

The given problem:

Simplify  √3 (⁴√3)

[tex]\sqrt{3}=3^{1/2}[/tex]

[tex]\sqrt[4]{3} =3^{1/4}[/tex]

Hence,

[tex]\sqrt{3}.\sqrt[4]{3} =3^{1/2}.3^{1/4}\\ =3^{1/2+1/4}=3^{3/4}\\ =\sqrt[4]{3^{3}}= \sqrt[4]{27}[/tex]

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Answer: where's the question?

Step-by-step explanation:

Answer:

your question please

Step-by-step explanation:

If Zen design a character for a video game he just three sizes of the character on grid paper then uses the expression 6+ X to the power of two.  the number of grid squares in a character of size 7 is 55.

Given:

Expression=6+x²

Now using the expression to determine the number of grid square in a character of size 7.

Expression=6+x²

Where:

x=7

Hence,

6+7²

=6+49

x=55

Therefore If Zen design a character for a video game he just three sizes of the character on grid paper then uses the expression 6+ X to the power of two.  the number of grid squares in a character of size 7 is 55.

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The solutions of the equation [tex]4(3x-3)^{\frac{2}{3} } = 36[/tex] are x = 10 and x = - 8.

An extraneous solution is one that results from the process of addressing the problem but is not a legitimate solution to the problem, such as the answer to an equation.

A formula known as an equation uses the equals sign (=) to express how two expressions are equal.

Consider the equation,

[tex]4(3x-3)^{\frac{2}{3} } = 36[/tex]

Now, divide each side of the equation by 4.

[tex]\frac{4(3x-3)^{\frac{2}{3} }}{4}=\frac{36}{4}[/tex]

[tex](3x-3)^{\frac{2}{3} } = 9[/tex]

Cubing the above equation.

[tex]((3x-3)^{\frac{2}{3} })^{3}=(9)^{3}[/tex]

( 3x - 3 )² = 729

3x - 3 = ( √729 )

3x - 3 = ± 27

Now,

3x - 3 = 27

3x = 30

x = 10

and;

3x - 3 = - 27

3x = - 24

x = - 8

Checking for extraneous solutions,

x = 10

[tex]4(3x-3)^{\frac{2}{3} }=36\\4(3(10)-3)^{\frac{2}{3} }=36\\4(27)^{\frac{2}{3} }=36\\27^{\frac{2}{3} }=9\\(3^{3})^{\frac{2}{3} } = 9\\3^{2}=9\\9=9[/tex]

When x = - 8,

[tex]4(3x-3)^{\frac{2}{3} }=36\\4(3(-8)-3)^{\frac{2}{3}}=36\\(-27)^{\frac{2}{3}}=9\\(-27)^{2}=(9)^{3}\\729=729[/tex]

The solutions for the equation are x = 10 and x = - 8.

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if you make 2 1/5 a improper fraction it would be 6/5

6/5÷3/5 is easy because 6÷3=2

the answer is 2.

Answer:

3 2/3

Step-by-step explanation:

2 1/5 ÷ 3/5

Convert 2 1/5 to an improper fraction

2 1/5 -- > 5 × 2 + 1 = 11/5

= 11/5 ÷ 3/5

Change the operator to multiplication

= 11/5 × 5/3

Cross multiply

= 11/3

Convert improper fraction to a mixed number

= 3 2/3