A shop has a sale that offers 20% off all prices. On the final day they reduce all the sale prices by 25%. Linz buys a radio on the final day
Work out the overall percentage reduction on the price of the radio.

The solution for this function will be x = -1 and x = 3

Quadratic polynomials are those with at least one variable and a variable with a maximum exponent of two. Since the second-degree term is the highest degree term in a quadratic function, it is sometimes referred to as the polynomial of degree 2. In a quadratic function, at least one term must be of the second degree. It has qualities in algebra.

The given function is -2x² + 4x + 6

So, we'll employ the middle term splitting strategy.

-2x² + 4x + 6 = 0

- 2x² + 6x - 2x + 6 = 0

-2x ( x-3) -2 (x-3) = 0

(-2x-2) (x-3) = 0

So, the solution will be

-2x - 2 = 0

-2x = 2

x = 2/-2

x = -1

And, x-3 =0

x = 3

So, the solution of the quadratic function will be

x =-1 and x = 3

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from the options;

The correct is B

because 2860 is greater than 2806

Other options are false

X has a value of 11

What is an angle?

The vertex of an angle is the common point of contact where two straight lines or rays come together to produce an angle.

As far as we are aware, this question is answered utilizing a quadrilateral's unique property that the sum of its adjacent angles is 180 degrees.

By quadrilateral, what do you mean?

A closed polygon with four sides, four vertices, and four angles is known as a quadrilateral.

thus, A.T.Q:-

We possess 5x+9x+26=180

14x +26=180

14x=154

x = 11 degrees

Consequently, x = 11 degrees.

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A line is said to bisect an angle if it divides it in two equal parts.

Since the segment OB bisects the angle AOC, then the angles AOB and BOC have the same measure.

Therefore, the complete statement is:

To the nearest tenth, the distance across the lake is DE = 207.68 m.

The corresponding side lengths of two triangles that are similar are always proportional to each other.

ΔCDE  and ΔCFG are similar to each other

FG = 142.1 m

FC = 130 m

DF = 60 m

DC = 130 + 60 = 190 m

Therefore,

DE/FG = DC/FC

Substitute

DE/142.1 = 190/130

Cross multiply nearest hundredth

Therefore, applying the similarity theorem, the distance across the lake to the nearest hundredth is DE = 207.68 m

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hello

to solve this question, we have to use trigonometric ratios and in this case, it was specified to use tangent

from the image above, we can see that we have the value of angle and opposite and we need to look for adjacent

trigonometric ratio is given as SOH CAH TOA

now, let's use the formula of tangent to solve this problem

from the calculations above, the value of x is equal to 20.48

Answer:

  12.  68%

  13.  50%

  14.  0.15%

  15.  8 students

Step-by-step explanation:

Given a normal distribution with mean 20 and standard deviation 5, you want several probabilities based on the empirical rule.

The empirical rule tells you the percentages of a normal distribution that are within 1, 2, or 3 standard deviations of the mean. They are ...

Wait times between 15 and 25 are within 20±5, so within 1 standard deviation of the mean. The percentage of students waiting 15–25 minutes is 68%.

The mean of the distribution is 20, which is its line of symmetry.

50% of students will wait less than 20 minutes.

35 is 3 standard deviations above the mean, so the fraction in this group is half of the difference between 1 and 99.7%.

0.15% of students will wait more than 35 minutes.

Of 5300, the number waiting more than 35 minutes is ...

  0.15% × 5300 = 7.95 ≈ 8

About 8 students will wait more than 35 minutes.

__

Additional comment

These values are based on the empirical rule, as required by the problem statement. The actual number for P(Z>3) is about 0.0013499 (0.13%), and the number of students is about 7.15 ≈ 7. That is, the result using the empirical rule is slightly different than what you get using a calculator, spreadsheet, or table.

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The closest distance or the number of miles Teri ran is equal to 5 miles.

What is the unitary method ?

The unitary method is a method in which you find the value of one unit and then the value of required no. of units.

It is given that Teri ran 8 kilometers.

It is also given that , 1 mile is approximately equal to 1.6 kilometers.

This is a question of unitary method. We know that value of one unit is given as 1 mile is equal to 1.6 kilometers approximately. We know have to calculate the no. of miles Teri ran , by converting 8 kilometers to miles.

So ,

1 miles = 1.6 kilometers

This implies :

8 kilometers = 8 / 1.6 miles

or

8 kilometers = 5 miles

or

8 kilometers is approximately equal to 5 miles.

Therefore , the closest distance or the number of miles Teri ran is equal to 5 miles.

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Answer:

  (c)  8, 12, 16

Step-by-step explanation:

You want to identify the side lengths that are proportional to lengths 4, 6, and 8.

Reducing the ratios to lowest terms, we can compare them:

Side lengths 8, 12, 16 will form a triangle similar to ∆DEF.

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ANSWER

x = 21.6

EXPLANATION

We have that:

c = 23.2

To be able to solve this, we must first find angle

The sum of angles in a triangle is 180 degrees.

This means that:

=> 52 + 70 + 122+ =>

Sine Law says that the ratio of angle and side opposite the angle for any triangle equal.

This means that:

So, we can say that:

That is the value of x.

Answer:

x ≥ 2

Step-by-step explanation:

Given inequality:

[tex]-\dfrac{4(x+3)}{5} \leq 4x-12[/tex]

Values of x less than 2

Substitute two values where x < 2 into the inequality:

[tex]\begin{aligned}x=1 \implies -\dfrac{4(1+3)}{5} & \leq 4(1)-12\\\\ -\dfrac{4(4)}{5} & \leq 4-12\\\\ -\dfrac{16}{5} & \leq -8 \quad \Rightarrow \textsf{Not a solution}\end{aligned}[/tex]

[tex]\begin{aligned}x=0 \implies -\dfrac{4(0+3)}{5} & \leq 4(0)-12\\\\ -\dfrac{4(3)}{5} & \leq 0-12\\\\ -\dfrac{12}{5} & \leq -12 \quad \Rightarrow \textsf{Not a solution}\end{aligned}[/tex]

The values of x < 2 are not solutions to the inequality.

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

Substitute the value of x = 2 into the inequality:

[tex]\begin{aligned}x=0 \implies -\dfrac{4(2+3)}{5} & \leq 4(2)-12\\\\ -\dfrac{4(5)}{5} & \leq 8-12\\\\ -\dfrac{20}{5} & \leq -4\\\\ -4 & \leq -4 \quad \Rightarrow \textsf{Yes, a solution}\end{aligned}[/tex]

The value of x = 2 is a solution to the inequality.

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

Values of x more than 2

Substitute two values where x > 2 into the inequality:

[tex]\begin{aligned}x=3 \implies -\dfrac{4(3+3)}{5} & \leq 4(3)-12\\\\ -\dfrac{4(6)}{5} & \leq 12-12\\\\ -\dfrac{24}{5} & \leq 0 \quad \Rightarrow \textsf{Yes, a solution}\end{aligned}[/tex]

[tex]\begin{aligned}x=4 \implies -\dfrac{4(4+3)}{5} & \leq 4(4)-12\\\\ -\dfrac{4(7)}{5} & \leq 16-12\\\\ -\dfrac{28}{5} & \leq 4 \quad \Rightarrow \textsf{Yes, a solution}\end{aligned}[/tex]

The values of x > 2 are solutions to the inequality.

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

Therefore, the solution to the inequality appears to be x ≥ 2.  

To check, solve the inequality:

[tex]\begin{aligned} \implies -\dfrac{4(x+3)}{5} &\leq 4x-12\\-4(x+3) &\leq 5(4x-12)\\-4x-12 &\leq 20x-60\\ -24x & \leq-48\\x & \geq 2\end{aligned}[/tex]

When graphing inequalities on a number line:

To graph the solution to the inequality on number line, place a closed circle at x = 2 and shade to the right.  (See attachment).

the given equation is

x - 4y = -16

put x = 0

0 - 4y = -16

y = 4

so at x = 0 ,, y is 4

put x = 4

4 - 4y = -16

-4y = -16- 4

y = 20/4

y = 5

so, at x = 4 the value of y is 5

thus, the correct graph is option B

The term that should go in the space to complete the statement is 5.

The complete statement is 5c + 15 = 5(c + 3).

The given statement is 5c + 15 = __(c + 3).

Now, we will combine the like term from the left side of the expression which is 5, and place it on the right side space to make the expression equivalent.

Hence, the complete statement is 5c + 15 = 5(c + 3).

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The order of the values using the basic unit of meters from smallest to largest. is: 109000 mm < 2.6 km < 41.7 hm

What are the units of measurement of distance or length?

Distance is the gap between any two points under consideration.

The basic unit for measuring distance is the meter.

There are larger as well as smaller units for measuring length or distance which are based on the unit of meter.

The units are as follows:

millimeter, mm = 0.001 m

centimeter, cm = 0.01 m

decimeters, dm = 0.1 m

meter, m = 1 m

kilometer, km = 1000 m

hectometer, hm = 100 m

Now to compare the given quantities making the units same as two quantities can only be compared only when there units are same :

Considering the given values;

2.6 km = 2600 m

109,000 mm = 109 m

41.7 hm = 4170 m

Therefore, after comparison arranging the quantities in order from smallest to largest is 109000 mm < 2.6 km < 41.7 hm

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We have to calculate the mean absolute deviation (MAD) for these temperatures.

We can express the MAD as:

So first we have to calculate the mean of the sample. We can do this as:

Now we can calculate the MAD as:

Answer: The MAD is approximately 3.3.

Given:

Few data is given

Required:

To calculate which option is correct

Explanation:

157+ ml = 6 means a rest area built along the highway exactly 6 miles away from milepost 57.Therefore this is the correct answer

Required answer:

Option D

a) The types of angles present are:

- 1 right angle

- 1 angles of 50 degrees and 1 angle of 4x degrees

b) their relationship is add up to 90°

c) 50° + 4*x° = 90°

4*x° = 90 - 450

x° = 40/4 = 10

x = 10°

The coordinate of the point C on the line segment is (9, -4)

On the segment, we have the following endpoints

A = (-3, 4)

B = (-9, 8)

The ratio of point A on the line is given as

Ratio, B : C = 1 : 2

Rewrite as

m : n = 1 : 2

The coordinate of point A is calculated using

A = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)

Where x and y are the coordinates defined above

So, we have

(-3, 4) = 1/(1+2) * (1 * x + 2 * -9, 1 * y + 2 * 8)

Evaluate

(-3, 4) = 1/3 * (x - 18, y + 16)

So, we have

(x - 18, y + 16) = (-9, 12)

This means that

x - 18 = -9

y + 16 = 12

Solve

x = 9

y = -4

Hence, the location of the point C is (9, -4)

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Given the rational function;

To determine the constraint for this function, we shall set the denominator equal to zero;

This means the equation does not exist when x = 0, and when x = 2.

ANSWER:

The correct answer is option C.

Part A)

Recall that:

1) The function represented by the graph of the function f(x) translated vertically n units up and horizontally m units left is:

2) The function represented by the graph of the function f(x) reflected over the x-axis is:

Now, notice that g(x) is the function f(x) reflected over the x-axis and then translated vertically 6 units up and horizontally 4 units left.

Answer Part A:

Options B, C, and D.

Part B) To graph g(x) we will reflect the graph of f(x) over the x-axis and then we will translate it vertically 6 units up and horizontally 4 units left.

We know that the graph of f(x)=|x| is:

The above graph reflected over the x-axis is:

Finally, the above graph translated vertically 6 units up and horizontally 4 units left is:

Answer part B:

so the answer is pi/2, 3pi/2, and pi/3

Two possible diagrams of the triangle are shown below

To find angle B in each triangle, we would apply the law of sines which is expressed as

a/SinA = b/SinB = c/SinC

For either of the triangles, by applying the sine law, we have

33/Sin B = 32/Sin 64

By crossmultiplying, we have

32 SinB = 33 Sin 64

Sin B = (33 Sin 64)/32 = 0.9269

We would find angle B by finding the inverse of sine 0.9269

Thus,

B = Sin^-1(0.9269) = 68

This is an acute angle. B can also be an obtuse angle. Greater than 90 but less than 180 degrees). Thus, another value for B is

ANSWER

The circumference doubles

EXPLANATION

Let the radius of the circle be r and the circumference be C.

The circumference of a circle is given as:

If the radius is doubled, the radius becomes:

The circumference now becomes:

Therefore, the circumference doubles when the radius is doubled.

The company should must sell 923 radios to break even.

Fixed cost refer to those costs which do not vary directly with the level of output. For example salary given to staff.

Variable cost that cost which vary directly with the level of output..

The selling price of radio is $59.

Total radios sell are of value $41500. This is the fixed cost.

Let us say that they sell x number of radios,

As we know,

For break even point,

Total revenue = Total cost

Cost of one radio x number of radio = fixed cost plus variable cost of all radios

54x = 41500 + 14x

40x = 41500

x = 922.22~923

So, they should sell 923 radio to break even.

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Answer

The 1.45 dollar chocolates will weigh (20 - x) pounds.

Explanation

We are told that the mixture weighed 20 pounds and one of the chocolates in the mixture weighed x pounds.

We are then to cslculate the weight of the other type of chocolate in the mixture.

Total mixture = 20 pounds

0.90 dollar chocolate weighed x pounds

The 1.45 dollar chocolates will weigh (20 - x) pounds.

Hope this Helps!!!

SOLUTION

From the question, town B is 3.5cm from town A and town C is 2cm from town B. Therefore C is 5.5 cm from town A.

The scale is 2cm for every 100miles. This means 1cm for every 50 miles.

You get this by dividing 100 by 2.

Now 5.5 cm becomes 5.5 x 50 miles = 275miles.

So town A and town C are 275 miles apart

Explanation

In the question,

The number of tomatoes is described as x

The number of lettuce is described as y

As per the question, the number of vegetables Aneil can plant in the garden is modelled by:

The graph of the above model can be seen above.

From the graph, we have the y-intercept to be 20 and the x-intercept to be 30.

Answer:

Y-intercept = 20 ---- This is the number of lettuce plants Aneil can plant if he plants zero tomatoes

X- intercept =30 ---- This is the number of tomatoes plants Aneil can plant if he plants zero lettuce

Answer:

hola comasa due when 123 dfosb971 24

ANSWER

EXPLANATION

h. We want to find the volume of the rectangular prism given.

The volume of a rectangular prism is given as:

where L = length

w = width

h = height

Therefore, we have that the volume of the prism is:

Answer:

The answer is: r is equal to -22.