(9.42x10^4)(6.45x10^2)
Simplify using a scientific calculator.
Write each answer in scientific notation.
Sone help me understand how to do this

By ASA (Angle side angle) theorem, triangle △ABD≅ triangle △CBD.

What is a triangle?

In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.

Based on the sides of a triangle, a triangle is classified into 3 types, namely:

Scalene Triangle – All the sides are of different measures.

Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.

Equilateral Triangle – All the 3 sides of a triangle are of the same measure.

Based on the angles of a triangle, a triangle is classified into 3 types, namely:

Acute Angle Triangle – All the angles of a triangle is less than 90°.

Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.

Right Angle Triangle – One of the angles of a triangle is equal to 90°.

Now

As BD is common for both triangles ABD and CBD.

and

∠ADB=∠CDB=90°

also as DB bisects ∠ABC

∠ABD=∠CBD

Hence,

By Angle Side Angle theorem, triangle △ABD≅ triangle △CBD

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The maximum weight of objects which the container can hold as required is; 1.12 pounds.

As evident in the task content;

The maximum which the container can is able to hold is; 17.75 pounds.

However, there are two objects in the can in which case one weighs 6.53 pounds and the other weighs 10.1 pounds.

On this note, the total weight which the can can hold more is given as;

= 17.75 - 6.53 - 10.1

= 1.12 pounds.

Ultimately, the maximum weight which the container can hold more is; 1.12 pound.

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The expression denominator is 1.

What is denominator?

In mathematics, a denominator is the lowest number in a fraction that indicates how many equal parts are divided into a whole. It is a fraction's divisor. In this case, the denominator is 4, thus there are four components overall.

Here the given is x-3+5

Now simplifying them

=> x-3+5 = x+2.

We know that the whole number or Integer always has 1 as Denominator. Then,

=> [tex]\frac{x-2}{1}[/tex]

Hence the denominator of the given is 1.

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Let's review the information given to us to answer the question correctly this way:

     Juniors  Seniors   Totals

Yes       28         97          125

No       56         19           75

Totals   84        116          200

2. Find the probability of each of the events.

Let's recall that the formula of probability is:

P = Number of favorable outcomes/Total number of possible outcomes

A. P (a junior who did not attend prom)

P = Juniors who did not attend prom/Total number of students surveyed

P = 56/200

P = 7/25 (Diving by 8 numerator and denominator)

B. P (did not attend prom | senior)

P = Seniors who did not attend prom/Total number of seniors surveyed

P = 19/116

C. P (junior | attended prom)

P = Juniors who attend prom/Total number of students attended prom

P = 28/125

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Answer:

300 degrees.

Step-by-step explanation:

a = 180 degrees

c = 180 - 60 = 120 degrees

Answer:

1. 26

2. x = 1.5

Step-by-step explanation:

1. C(0.7) means to plug in 0.7 into the equation

here, C(x) = 30x + 5. replace x with 0.7 to get

C(0.7) = 30*0.7 + 5= 26

2. C(x) = 30x + 5 = 50

30x+5 = 50

subtract 5 from both sides to isolate x and its coefficient

30x = 45

divide both sides by 30 to find x

x = 1.5

The result of the addition of the polynomials is -15x^3 + 4x - 11.

We have to note that the polynomials have to do with those kind of functions in which the power of x in the equation may range form 1 to infinity. We have in the question that the expression can be written as;

(−6x^3 + 3 −4x) − (14 − 8x + 9x^3)

Then we have;

−6x^3 + 3 −4x - 14 + 8x - 9x^3

We can now collect the like terms as follows;

−6x^3 - 9x^3 −4x  + 8x + 3 - 14

-15x^3 + 4x - 11

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The standard form of the equation for the line which is as described is; x - 4y = 8.

It follows from the task content that the equation of the line in discuss in point-slope form as given in the question is;

( y - 1 ) = 1/4 ( x - 12 )

Therefore, the equation above can be written so that we have that;

4 ( y - 1 ) = ( x - 12 )

4y - 4 = x - 12

4y - x = -12 + 4

x - 4y = 12 - 4

x - 4y = 8

Therefore, the standard form equation of the line as required is; x - 4y = 8.

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Answer: 20%

Step-by-step explanation:

Im SOO sorry if i got it wrong but you make a porportion, it would look like this. 8.24/41.76 = x/100, were assuming x is the percent, we then do cross multiplication which would then look like. 41.76x=824. After this we want to seperate the variable so divide 41.76 on both sides.

We were informed that an is a matrix with numerous elements in this query. A is an order matrix, and we also have  an order matrix.

3 by 3, resulting in a determinant of b that is -5. We were successful in locating a matrix c that is equal to minus three times of a b cube times a.

We must determine the determinant because an is equivalent to a transport and an is equal to an identity matrix. If I take into account the period of a transposition, what is the determinant of a so-called determinant of this identity, which is equal to 1 accurate and we are aware of this characteristic.

This will be the result of those who are in a situation where a transposition is crucial. This is the first result is that the cube's time has the same determinant as a matrix's time.

Because a 3 by 3 matrix and lambda are real numbers, we can leverage this property. Using this property, it will be -3 q in this case. Once more, I'll be able to obtain a transposition b times c times a determinant. Splitting it is a possibility. The times of the b cube determinant are determined by minus 3 c. We know that the determinants of a transpose and the determinant of a that is 1 are, so what we are obtaining is just minus 27.

We shall obtain the b cube's determinant from this location. This is only multiplied by 1 minus 27. There won't be an entire cube. The determinant of c is equal to 3125, which is the product of -27 and -125.

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Answer:

Robert will spend $27 on shirts for the team.

Step-by-step explanation:

Therefore, Robert will spend $27 on shirts for the team.

Please let me know if this helped!!!

The equation that shows Group A's distance from the start, given their speed and the number of hours is C. y = 3 x.

When trying to find the distance that a person or object has travelled in a given time, the general formula is;

= Speed x Time

The speed is given as 3 miles per hour for Group A.

The time is given as x for either group

This means that the distance that Group A has gone since the hike up the glacier started is :

Distance from the start = Speed x Time

y = 3 miles per hour × x

y = 3x

In conclusion, given the speed that Group A is using, this means that their distance from the start can be modelled by the equation, y = 3 x.

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Answer:

Step-by-step explanation:

Answer:

To graph this linear relationship, we can plot two points on a coordinate plane: (3,12) and (5,20). These points represent the number of hours Jen babysits (x-coordinate) and the amount of money she earns (y-coordinate).

We can connect these two points with a line to form a linear equation that represents the relationship between the number of hours babysat and the money earned.

The slope of this line can be found using the formula: (change in y) / (change in x) = (20-12) / (5-3) = 8/2 = 4

Therefore, Jen earns $4 per hour by babysitting.

It is important to note that this is a linear relationship, and the earnings are proportional to the number of hours babysat. This means that for any number of hours babysat, the earnings can be found by multiplying that number by $4.

Step-by-step explanation:

Answer: For every hour she babysits, she earns $4. ✅

Step-by-step explanation:

To graph the linear relationship, we can start by plotting two points: (3,12) and (5,20).

This represents that for 3 hours of babysitting, Jen earns $12, and for 5 hours of babysitting, she earns $20.

We can then use these points to find the slope of the line, which is the rate at which her earnings change as the number of hours increases.

The slope can be found by using the formula: (change in y) / (change in x) = (20 - 12) / (5 - 3) = 8/2 = 4

This means that for every hour she babysits, she earns $4.

So, the equation of the line is : y = 4x + b

Where b is the y-intercept, which can be found by substituting one of the points into the equation.

For example, by substituting (3,12) in the equation:

12 = 4(3) + b

b = 0

So, she earns per hour $4. ✅

The ratio of these two figures would be for every 1cm in image A, in image B there are 2cm. So the ratio would be 1:2

The ratio is a mathematical term that refers to the quantified relationship between two magnitudes that reflects a proportion, that is, the ratio is the way of representing the proportion between two magnitudes. In this case, the ratio refers to the length of each side of these triangles and their relationship to each other.

According to the above, the ratio could be 1:2 because the larger triangle has lengths that are twice the lengths of the sides of the smaller triangle. For example, the left side of the small triangle is 6 cm, while the left side of the large triangle is 12 cm.

It's a proportionality relationship twice as big. Therefore, the ratio would be 1:2.

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If 3/4 cup of chai tea latte concentrate is 60 calories, we can use proportion to find out how many calories 1/2 cup of chai tea latte concentrate is.

What does a math ratio mean?

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could athe ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.

We know that:

(3/4 cup) = 60 calories

To find out the number of calories in 1/2 cup, we can set up a proportion using the information we have:

(1/2 cup) / x = (3/4 cup) / 60

we can cross-multiply to get:

x = (1/2 cup) * (60 / (3/4 cup))

then we can simplify

x= (1/2)*(4/3)*60

x= 80/3

Therefore, 1/2 cup of chai tea latte concentrate is 80/3 calories.

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Answer:

The Answer is (D)

Step-by-step explanation:

When determining when a taxpayer wants to file as head, then the answer will become clearer when checking for their position on the house

The shape of the parallelogram with vertices P(−4,0), Q(0,4), R(4,0), and S(0,−4) is a square

In order to get the shape using the vertices that we have, we would have to find the length of the diagonals

We have P(−4,0), Q(0,4), R(4,0), and S(0,−4)

The length of the diagonal PQ is given as:

PQ = [tex]\sqrt{(0-4)^2+(4-0)^2}[/tex]

= [tex]\sqrt{32}[/tex]

Next we have to solve for the length of the diagonal RS

RS = [tex]\sqrt{(4-(-4))^2+(0-(-4))^2[/tex]

RS = [tex]\sqrt{32}[/tex]

Since PQ = RS we would have to conclude that the shape is a square.

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Answer:

x = 4

Step-by-step explanation:

The sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle.

We can write the following equation to find the value of x based on this information:

6x + 6 + 17x + 2 = 100

23x + 8 = 100

23x = 92

x = 4

This statement is false. Two subspaces of R^n can have the same dimension but still be different.

Here are a few bullet points that elaborate on this:

Therefore, the statement "If s1 and s2 are subspaces of R^n of the same dimension, then s1 = s2" is not true in general.

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Therefore , the solution of the given problem of slope comes out to be the y-intercept value is 5.

A line's slope determines how steep it is. A gradient-based equation is referred to as having a gradient overflow. By dividing average horizontal difference (run) between 2 places by both the vertically change (rise) between those same two points, the slope is determined. The equation of a horizontal path is expressed as y = mx + b and is known as the hill form of an equation. The y-intercept of the line is located where the grade is m, b = b, and (0, b). In the case of the equations y = 3x - 7, the slope y y-intercept are (0, 7). The y-intercept is situated where the slope of the line is m and b is

Here,

Given :

that m=2, the point (x1,y1)=(— 3, —1)

Equation for the necessary straight line:

=>(y — y1)=m(x — x1)

=>y+1=2(x+3)

X=0 on the y-axis indicates that nothing is being measured.

=>y=2+3

The y-intercept value is 5.

Therefore , the solution of the given problem of slope comes out to be the y-intercept value is 5.

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The solution of the compound inequality is -2 ≤ x ≤ 1 and -4 ≥ x ≥ -7.

An inequality that combines two other inequalities by using either "and" or "or" is referred to as a compound inequality. In certain cases, "and" won't be stated explicitly, but it is still understood. For instance, 1 x 3 simply means "x > 1 and x 3". However, a compound inequality using "or" is always explained in detail using "or." Compound inequalities may be divided into two categories: conjunction and disjunction.

The given compound inequality is:

1 ≤ | x + 3 | ≤ 4

As the equation contains a mod sign, we can write the inequality as follows:

1 ≤ x + 3 ≤ 4, and

1 ≤ - x - 3 ≤ 4

Simplify the first equation:

1 ≤ x + 3 ≤ 4

Subtract 3 from both the sides of the equation:

1 - 3 ≤ x + 3 - 3 ≤ 4 -3

-2 ≤ x ≤ 1

Simplify the second equation:

1 ≤ - x - 3 ≤ 4

Add 3 on both sides of the equation:

1 + 3 ≤ - x - 3 + 3≤ 4 + 3

4 ≤ -x ≤ 7

Convert the negative term to positive:

-4 ≥ x ≥ -7

Hence, the solution of the compound inequality is -2 ≤ x ≤ 1 and -4 ≥ x ≥ -7.

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Answer:

---------------------------

Given is the parallelogram.

Area of a parallelogram:

Substitute the values and find the area:

The average rate of change of the equation is 7

The average rate of change of an equation can be determine by using the formula below:

average rate of change = (f(x₂)- f(x₁)) / [x₂- x₁]

From the given information, f(x) = 2x²-5x-2 and x₁ = 2, x₂ = 4

average rate of change =  ([2(4)²-5(4)-2] - ([2(2)²-5(2)-2]) / (4- 2)

average rate of change = (10-(-4)) / 2

average rate of change = 14/2

average rate of change = 7

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Answer:

0 on the left side

Step-by-step explanation:

Since in the diagram, transversal t cuts parallel lines a and b, an equation which is necessarily true include the following: B. m∠3 = m∠6.

In Mathematics, the Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent.

Based on the diagram representing (showing) the two parallel horizontal lines a and b, we can reasonably infer and logically conclude that angle 3 (m∠3) and angle 6 (m∠6) forms a pair of alternate interior angles because line a is parallel to line b and transversal (t) cuts parallel lines a and b.

Similarly, angle 4 (m∠4) and angle 7 (m∠4) forms a pair of alternate interior angles because line a is parallel to line b.

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Answer: C

Step-by-step explanation:

4x - 12y = -10

-3x + 10y = 10

In order to solve this using substitution method, you will have to

divide one equation by the coefficient of x or y

e.g. divide 4x-12y = -10 by 4 to get x-3y = -5/2

x = 3y-5/2

and substitute x for 3y-5/2 which is pretty complicated.

Not sure what you mean by "readily solved", though.

Answer:

1,200 40×30=. h. h= hours

Answer:

answer is 341

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