Question 6 of 10
Using the graphing function on your calculator, find the solution to the system
of equations shown below.
A. More than 1 solution
B. x = 4, y = 3
C. No solution
D. x = 3, y = 4
y-2x = -2
y-x = 1

The zeros of a function are the values of x that, when evaluated in the function, make the output of the function to be zero.

A function is written in general form as y = f(x)

That notation says that, when we use the input "x" in a given function, that function "transforms" that input x into an output "y"

So y = f(x) is the value that the function takes for the input x.

A zero is an input of the function such that:

0 = f(x)

So the zeros are the inputs that have an output of zero, in this case you know that the function has a zero at 3, and as you can see, when x = 3, the function intercepts the x-axis, which is the axis defined by y = 0.

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The Largest Angle has a measure of 100 degrees and measure of other two angles is 40 degrees each.

What is angle sum property of a triangle?

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

According to the given question:

In triangle ABC, angle ABC equals to angle ACB and BAC is the largest angle.

Let angle measure of ABC and ACB angles be x degree then, measure of third angle BAC will be x + 60 degrees.

Since sum of all angles of any triangle is 180 degree.

      x  + x + (x + 3) = 180

       3x  = 180 - 60

        3x = 120

         x = 40 degrees

So, First angle = 40 degree

Second angle = 40 degree

Third Angle = 100 degree.

The Largest Angle angle has a measure of 100 degrees.

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With the help of similar triangles the height of Flagpole is 15.13 feet

what is similar triangle?

Triangles that are similar in shape but differ in size are known as similar triangles. Examples of related objects are all equilateral triangles and squares with any side length. To put it another way, if two triangles are comparable, then their corresponding angles and sides are congruent and equal in size.

solution:

let C is the point of reflection in triangle ABC and EDC

∠ ABC = ∠ EDC ( 90 Degree)

∠ ACD = ∠ ECD ( Reflective angle )

By symmetry,

AB/ED = BC/CD

5.6/ x  = 7.4 / 20

       x  =  15.13 feet

Hence the height of flagpole is 15.13 feet

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Answer:

HL

Step-by-step explanation:

the two triangles are right and have the same hypotenuse (the diagonal side) and one congruent leg (the horizontal side)

The percentage increase in the number of cars from hour 2 to hour 3 is 16.7%

In this question, we have the given figures that can be used in our computation:

Hour 1 = 22 cars

Hour 2 = 30 cars

Hour 2 = 35 cars

We want to calculate the percentage increase in the number of cars

So, we make use of only the following parameters

Hour 2 = 30 cars

Hour 2 = 35 cars

These figures can be represented as

Initial amount = 30

Final amount = 35

The percentage of the increase of the cars is then calculated using the following percentage equation

Increase percentage = (Final amount - Initial amount)/Initial amount * 100%

Substitute the known values in the above equation, so, we have the following representation

Increase percentage = (35 - 30)/30* 100%

Evaluate

Increase percentage = 16.7%

Hence, the increase percentage is 16.7%

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Answer:

[tex]\textsf{a)} \quad y=1.8(3.2)^x[/tex]

[tex]\textsf{b)} \quad y=5(7)^x[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

Given ordered pairs:

The y-intercept is the y-value when x = 0.

Therefore, as the y-intercept is 1.8, a = 1.8.

[tex]\implies y=1.8b^x[/tex]

Substitute point (1, 5.76) into the equation and solve for b:

[tex]\begin{aligned} y&=1.8b^x\\\implies 5.76&=1.8 \cdot b^1\\5.76&=1.8b\\b&=\dfrac{5.76}{1.8}\\b&=3.2\end{aligned}[/tex]

Therefore, the exponential equation is:

[tex]\boxed{y=1.8(3.2)^x}[/tex]

To complete the given table, simply substitute the values of x into the found equation:

[tex]\begin{array}{c|l}x&\phantom{189}y\\\cline{1-2} \vphantom{\dfrac12}}0&\phantom{18}1.8\\\vphantom{\dfrac12}}1&\phantom{18}5.76\\\vphantom{\dfrac12}}2&\phantom{1}18.432\\\vphantom{\dfrac12}}3&\phantom{1}58.9824\\\vphantom{\dfrac12}}4&188.74368\end{array}[/tex]

Given ordered pairs:

The y-intercept is the y-value when x = 0.

Therefore, as the y-intercept is 5, a = 5.

[tex]\implies y=5b^x[/tex]

Substitute point (2, 245) into the equation and solve for b:

[tex]\begin{aligned} y&=5b^x\\\implies 245&=5 \cdot b^2\\49&=b^2\\b&=\sqrt{49}\\b&=7\end{aligned}[/tex]

Therefore, the exponential equation is:

[tex]\boxed{y=5(7)^x}[/tex]

To complete the given table, simply substitute the values of x into the found equation:

[tex]\begin{array}{c|l}x&\phantom{11}y\\\cline{1-2} \vphantom{\dfrac12}}0&\phantom{1111}5\\\vphantom{\dfrac12}}1&\phantom{111}35\\\vphantom{\dfrac12}}2&\phantom{11}245\\\vphantom{\dfrac12}}3&\phantom{1}1715\\\vphantom{\dfrac12}}4&12005\end{array}[/tex]

Answer: 7

Step-by-step explanation:

3 x 3 = 9 - 2(3)+4

9-6+4

=7

When the figure passed through the transformations the image formed is similar to the image at B as attached

The figure is in the second quadrant

clockwise rotation 90degrees about the origin will being the figure to the first quadrant

Translation 9 units down will bring an image to the -6 of the y direction in the fourth quadrant

reflection over the y axis will create a mirror image of the figure and make the image at the third quadrant

The option B correctly shows the final image

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The triangle ΔBAE is congruent to the triangle ΔCDE by ASA postulate.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

If two lines intersects, then the opposite angle of the line will be congruent to each other.

In ΔBAE and ΔCDE,

AB = DC, (Given)

∠BAE = ∠CDE, (Right angle)

∠BEA = ∠DEC, (Opposite angle)

The triangle ΔBAE is congruent to the triangle ΔCDE by ASA postulate.

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Answer:

-8/3

Step-by-step explanation:

Answer: x = 1/0 in exact form. x = 0.1 in decimal form.

First step, distribute:

[tex]-6x-3 = 4x-4[/tex]    

Next, isolate x to one side :

[tex]-6x - 4x=-4+3[/tex]

[tex]-10x=-1[/tex]

Last step, divide both sides by -10:

[tex]x=\frac{1}{10}[/tex]

Thus, the answer is [tex]\frac{1}{10}[/tex]

Hope this helped :)

Answer:500 I hope this helpful

Step-by-step explanation:

3000 divided by 48 times 8

To make the calculation easier, first multiply the numbers that result in multiples of 10

24000 divided by 48

Divide the numbers
=500

Answer:

250

Step-by-step explanation:

If we follow the rules of PEMDAS, we go from left to right. Therefore, first, do 3,000 divided by 48.

3,000/48=62.5

Now, multiply 62.5 by 4.

62.5x4= 250

250 is your answer :D

Hope this helps and have a wonderful day!

Answer:7

Step-by-step explanation:

13000 divided by 3000 = 4.33 repeating meaning the 33 keps going like 4.33333333333333333333333333333333333333333333333333

The value of numerical expression 4(16)³ / 10³ will be 16.384.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The expression is given below.

⇒ 4(16)³ / 10³

Simplify the expression, then we have

⇒ 4(16)³ / 10³

⇒ 4 x 4096 / 1000

⇒ 16384 / 1000

⇒ 16.384

The value of numerical expression 4(16)³ / 10³ will be 16.384.

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The answer is x = -70.

To solve for x, bring the variable to one side, and bring all the remaining values to the other side by applying arithmetic operations on both sides of the equation. Simplify the values to find the result.

Multiply all terms by the same value to eliminate fraction denominators

/7 = −10

7⋅/7 = 7(−10)

Cancel multiplied terms that are in the denominator

7⋅/7 = 7 (−10)

x =7(-10)

Multiply the numbers

=7(−10)

=−70.

Hence The answer is x = -70.

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Answer:

  (c)

Step-by-step explanation:

You want the graph that has a domain of x ≥ 5.

The domain of a function is the set of x-values for which the function is defined. A domain of x ≥ 5 means the function is defined for x-values at least 5. The graph of the function will extend from x=5 indefinitely to the right.

Graph C is like that.

Answer: D

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

830 to 1130   is 3 hours

Hours per gallon =    3hrs / 2100 gal

3 hr / 2100 gal    * 3500 gal =   5hrs to fill from 830 = 13:30   ( 1:30 PM)

The probabilities that they are all different, All fruit drops, All the same, All not fruit drops are 2.22%, 7.03%, 11.2%, and 18.96%, respectively.

Probability helps us to know the chances of an event occurring. The sum of all the probabilities of an event is always equal to 1. The formula for probability is given as,

Probability= Desired Outcomes / Total Number of outcomes possible

Given that the bag of mixed sweets contains 20 fruit drops, 15 chewing gum and 12 toffees. Therefore, the probabilities can be written as,

Probability of getting a fruit drop = 20/47

Probability of not getting a fruit drop = 1 - (20/47) = 0.574468

Probability of getting a chewing gum = 15/47

Probability of getting a toffee = 12/47

Now, we can write the following probabilities as,

a.) Probability of getting All different

        = (20/47) × (15/46) × (12/45)

= 0.2553 × 0.326 × 0.2667

= 0.02219

= 2.22%

b.) Probability of getting all fruit drops,

        = (20/47) × (19/46) × (18/45)

= 6840 / 97290

= 0.0703

= 7.03%

c.) Probability of getting all the same

= Probability of getting all fruit drops + Probability of getting all chewing gum + Probability of getting all toffee

= [(20/47) × (19/46) × (18/45)] + [(15/47) × (14/46) × (13/45)] + [(12/47) × (11/46) × (10/45)]

= (6840/97290) + (2730/97290) + (1320/97290)

= 0.112

= 11.2%

d.) Probability of getting all not fruit drops

= (Probability of not getting a fruit drop)³

= 0.574468³

= 0.189582

= 18.96%

Hence, the probabilities are calculated for different cases as shown above.

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Answer: C

Step-by-step explanation:

38520 *.12 = $4,622.40

Answer:

Part A: The bill is $27.32

Part B: The percentage is 19%

My work:

Part A

   ?                   8

---------     =    ---------

25.30             100

equals 2.02400

then round to get the tax amount which is $2.02

to find the bill cost we need to add the tax and the cost of the meal:

2.02 + 25.30 = 27.32

Part B

to find the tip we need to subtract the bill from the total lunch cost:

27.32 + t = 4.92                              (t = tip)

32.24 - 27.32 = 4.92

So now that we know the tip we can figure out how much percentage that is of the cost of the meal:

4.92              ?

--------    =   --------

25.30         100

which equals 19.4466403/100

the percentage is 19%

Answer:

21.64 % probability of rain at a random year

Step-by-step explanation:

79/365 * 100

21.64 %

Answer:

Step-by-step explanation:

option 2 since it equals 14/4

Answer:x=-9

Step-by-step explanation:-12/4=-3 then do 3*-3=-9

Answer:

C

Step-by-step explanation:

(√2) can be interpreted as 2^(1/2) and the second term can be interpreted as 2^(1/3). The law of exponents tells us that we must add the exponents when multiplying two numbers with the same base. 1/2 + 1/3 is 3/6+2/6 = 5/6 so the final answer would be 2^(5/6)

Yes, human can distinguish pixels on a same-sized HDTV with 2 times 10 to the 6th power pixels.

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.

In the scientific form, we write a number in the form of base×10ⁿ.

Where 0 ≤ base < 10 and n can be any rational number.

Given,

Humans can distinguish up to 18,400,000 individual dots called pixels on a typical computer display

We need to check whether human distinguish pixels on a same sized HDTV with 2 x 10 to the 6th power pixels

2×10⁶ pixels.

= 2000000 pixels.

As  2000000 < 18400000

Hence, human can distinguish pixels on a same-sized HDTV with 2 times 10 to the 6th power pixels.

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78.9 kg.

To convert 78,900 grams to kilograms, we can divide the number of grams by 1,000. Since 1 kilogram is equal to 1,000 grams, dividing the number of grams by 1,000 will give us the equivalent number of kilograms.

Therefore, 78,900 grams is equivalent to 78,900 / 1,000 = 78.9 kilograms.