Ward is planning to install a new counter top in kitchen, as shown in the figure. Determine the area of the countertop.

The form of quadratic is:

Since (0,6) is given, we know c = 6, thus we have:

Point 2 is (2,8), replace x and y and find equation:

Putting point 2 (3,0), we have:

Solving the 2 simulatenous equations for a and b, we get:

a = -3

b = 7

Now u have all the values, a, b, and c.

Just put it in the general form of parabola :

y = -3x^2 + 7x + 6

Let the total number of offices in the building be x.

We can represent the information provided in the question mathematically as:

Solving for x:

Cross-Multiply:

Hence, there are 140 offices in the building.

Answer: 140 offices

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{3}x^2\stackrel{\stackrel{b}{\downarrow }}{+6}x\stackrel{\stackrel{c}{\downarrow }}{+1} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 6}{2(3)}~~~~ ,~~~~ 1-\cfrac{ (6)^2}{4(3)}\right) \implies \left( - \cfrac{ 6 }{ 6 }~~,~~1 - \cfrac{ 36 }{ 12 } \right) \\\\\\ (-1~~,~~1-3)\implies {\Large \begin{array}{llll} (-1~~,~~-2) \end{array}}[/tex]

f(x) = (x + 1)^3

g(x) = cubic root x + 1

f(g)(x) =

result

f(g(-64)) = -8

The total number of ways she can hang the painting is 720 after applying the concept of permutation and combination.

The variety of possible arrangements of a set is its permutation however order is important in permutations but not in combinations.

It is given that:

Alicia wants to place her ten paintings side by side on the wall.

We can get the factorial of 6 and use that knowledge to calculate how many ways there are to multiply 6 by multiplying it by all positive integers that are more than or equal to that number, in this case, 6.

Alicia can arrange her six paintings:

6! = 6x5x4x3x2x1

6! = 720

Thus, the total number of ways she can hang the painting is 720 after applying the concept of permutation and combination.

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Based on the graph of the function shown, we can logically deduce the following:

The vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

Similarly, the horizontal extent of a graph represents all domain values and they are also read and written from smaller to larger numerical values, and from the left of the graph to the right.

By critically observing the graph of the given function shown above, we can reasonably and logically deduce the following:

In conclusion, the function which this graph represent is a continuous function because both the domain and range is defined for all set of values in the interval above.

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Answer:

False

Step-by-step explanation:

Domain is the x-axis, range is the y-axis. In an ordered pair, the x-values go first, not second.

The equation of a line in point-slope form is given by

Where

Thus, if we substitute the above values into the equation:

The product of 21 and the difference between one whole number 1/2 and -1/2​ is; 42

We want to find the product of 21 and the difference between one whole number 1/2 and -1/2​. This can be expressed as;

21 * (1¹/₂ - (-¹/₂))

Let us first solve the bracket out using the order of operations rule named PEMDAS which stands for  P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction to get;

1¹/₂ - (-¹/₂)

= 1¹/₂ + ¹/₂

= 2

Thus;

21 * (1¹/₂ - (-¹/₂)) = 21 * 2

= 42

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Answer:

7

Step-by-step explanation:

14/2=7

Answer:

a) DE = 15 cm

b) AB = 6 cm

Step-by-step explanation:

Explanation #a)

- Relating the triangle ABC with triangle DCE, a scale factor fomula is used;

[tex]{ \rm{ \frac{ \bar{DE}}{ \bar{BC} }} = \frac{ \bar{CE}}{ \bar{AC} } } \\ \\ { \rm{ \frac{\bar{DE}}{5} = \frac{24}{8} }} \\ \\ { \rm{\bar{DE}} = \frac{24 \times 5}{8} } \\ \\ { \rm{\bar{DE}} = 15 \: cm}[/tex]

Explanation #b)

[tex]{ \rm{ \frac{ \bar{CE}}{ \bar{AC}} } = \frac{ \bar{CD}}{ \bar{AB} }} \\ \\ { \rm{ \frac{24}{8} = \frac{18}{\bar{AB}} }} \\ \\ { \rm{\bar{AB} = \frac{18 \times 8}{24} }} \\ \\ { \rm{\bar{AB} = 6 \: cm}}[/tex]

- Therefore, the scale factor is 2, triangle CDE = 2ABC

[tex]{ \boxed{ \red{ \delta}}}{ \underline{ \red{ \mathfrak{ \: \: creed}}}}[/tex]

In the small triangle

There are a right angle and an acute angle of measure 53 degrees

Since the sum of the angles of a triangle is 180 degrees

Then 90 + 53 + < 1 = 180 degrees

Then 143 + < 1 = 180

Subtract 143 from both sides

Then < 1 = 37 degrees

Since <2 is an exterior angle of the small triangle

Then its measure = the sum of <1 and 90 degrees

Then < 2 = 37 + 90 = 127 degrees

In the triangle of angles 2, n3 and 30

< 2 + < 3 + 30 = 180

127 + < 3 + 30 = 180

Add 127 and 30

157 + <3 = 180

<3 = 23

The answer is < 2 = 127 degrees and < 3 = 23 degrees

Tristan should make 8 pieces of length 0.125 yards each to make a steps to the deck 1 yards above.

Division is breaking a number up into an equal number of parts. Mathematically, we can write "[a] divided by [b]" as a ÷ b. The division algorithm is given by -

D = dq + r

[D] - Dividend

[d] - Divisor

[q] - Quotient

[r] - remainder

Given is Tristan who is building steps up to a deck that is 1 yards above the ground. The steps must all be the same height an he wants to make 8 steps.

Total number of steps to be made = [n] = 8

Height of deck = [h] = 1 yard.

Now, we have to divide 1 yard into 8 equal parts. Therefore, assume

that -

A = 1 ÷ 8

A = 1/8

0.125

We get the length of each step to be 0.125 yards.

Therefore, Tristan should make 8 pieces of length 0.125 yards each to make steps to the deck 1 yards above.

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This can be solved using ratio and proportions.

What is ratio?

A ratio in mathematics illustrates how many times one number contains another. For example, if a dish of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the proportion of lemons to oranges is 6:8 (or 3:4), while the proportion of oranges to overall fruit is 8:14. (or 4:7). A ratio's numbers can be any quantity, such as a count of persons or things, or measures of lengths, weights, time, and so forth. In most situations, both numbers must be positive. A ratio in mathematics illustrates how many times one number contains another.

First, we find the ratio of trees planted to trees cut

= 48/8 = 6

So, no. of trees to be planted when 5 trees are cut = 5x6 = 30

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Answer:

Step-by-step explanation:

f(x)=|5x|    

f(2)= |5(2)|      Substitute 2 for x

f(2)= 10   Answer

Answer:

f(2) = | 5 • 2 | = | 10 | = 10

Step-by-step explanation:

Replace x with 2 then solve with the absolute value

Division stops after a certain number of steps as the remainder becomes zero and When division continues as there is a remainder after every step.

a division is a process of splitting a specific amount into equal parts.

We can stop the long division process when converting a fraction to a decimal number.

There can be two situations in converting fractions to decimals:

When division stops after a certain number of steps as the remainder becomes zero.

When division continues as there is a remainder after every step.

Hence When division stops after a certain number of steps as the remainder becomes zero and When division continues as there is a remainder after every step.

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Hello there. To solve this question, we'll need to remember how to find the variance and standard deviation of a data set.

First, given a data set with values:

The variance can be calculated by the formula:

In this case, μ is the arithmetic mean of the data set and x_i is the i-th element of the data set.

The data set given is:

{4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 9}

To calculate the mean, we add every term and divide by the number of terms:

Now, we calculate the square of the difference between every term and mean.

Notice we have some repeated terms, we rewrite the sum like this:

Adding the terms and calculating the squares, we have:

This is the variance of the values of this data set. We can round it up to the nearest tenth as 1.6

The standard deviation is the square root of the variance.

Then, we calculate:

Again, rounding it to the nearest tenth, we have 1.3;

The final answer is: The variance of this data set is 1.6 and its standard deviation is 1.3.

Solving the second question:

We apply the same formula. First, find the mean of the values:

Now, as every term is different from each other, we apply the formula and get the following:

Calculating the difference, squaring it, adding the values and dividing by 9, we get:

Variance is approximately equal to 4.84

The Standard deviation is the square root of the variance, namely 2.2

Answer:1,086

Step-by-step explanation: Initial Deposit

$400

Contributions

$0

Investment Time Span

20

Estimated Rate of Return

5.00%

Hello!

What is an x-intercept:

 ⇒ value of x when the value of y equals '0'

       [tex]8x + 5y=25\\8x+5(0)=25\\8x=25\\\\x=\dfrac{25}{8}[/tex]

  x-intercept is 25/8

What is a y-intercept:

 ⇒ value of y when the value of x equals '0'

       [tex]8x+5y=25\\8(0)+5y=25\\5y=25\\y=5[/tex]

   y-intercept is 5

Hope that helps!

Part A.

From the given table, we can see that the variable occupation is a Categorical variable becasue the occupation can divide a set of people into groups. Then, the level of measurement is Nominal because the occupation describes the objects by labels, with no quantitative value.

Part B.

Temperature is a Quantitave variable because we can measure the temperature of an object. Regarding the level of measurement, the temperature is an Interval variable because zero temperature is not the lowest possible temperature.

Part C.

The price is a Quantitative variable because the price is a numerical value with a meaningful order. Regarding the level of measurement, the price is a Ratio variable because it has a true zero, meaning that we can take ratios of values.

The given figure can be divided into a rectangle and a triangle

The rectangle has the dimensions 10 m by 12 m

so, the area of the rectangle = 10 x 12 = 120 square meters

Now, we will find the area of the triangle:

Base = 12 - 10 1/4 = 1 3/4 m

Height = 15 - 10 = 5 m

Area = 1/2 x base x height =

So, the total area =

Solution

For this case we have the following:

g = 12 and h=19

And we want to find 3h(h-g)

If we replace we got:

3*19 (19-12) =57*7=399

Then the answer would be:

D. 399​

From the given table, it is found that:

a. The average population decline was of 2,250 deer a year.

b. The population would have reached 225 thousand deer during the years of 2017 and 2018.

The average rate of change of a function is given by the change in the output divided by the change in the input of the function. Hence, over an interval [a,b], the average rate of change is given as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

In 1984 and 2018, the populations are given as follows:

Hence the rate of change is given as follows:

r = (173.5 - 250)/34 = -2.25.

(2.25 thousand = 2,250).

For item b, the following linear function is built:

y = 230.5 - 1.45x.

The amount would be of 225 when:

230.5 - 1.45x = 225

1.45x = 5.5.

x = 5.5/1.45

x = 3.79.

Hence between the years of 2017 and 2018.

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From the information given,

MAD for the heights of some sixth graders = 1.2

MAD for the heights of some seventh graders = 1

Number of times = MAD of data1/MAD of data 2 = 1.2/1

The answer is 1.2

The measure of "a" in the above-given right-angled triangle is 32°

Note that a triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same.

Key properties of a right-angled triangle to note are:

To solve for "a" recall the following. It is given that:

AB = BC

∠BEC=90°

∠DCE=42°

Because CD bisects ∠ACB, Hence,

∠ACD = ∠DCB = x.............................1

∠DCE= ∠BCE + ∠DCB .....................2

= ∠BCE + x = 42° ................................3

To find  ∠A, we use deductive reasoning to state:

∠A +∠E +∠ACD + ∠DCB + ∠BCE = 180° (Sum of Interior Angles)

Recall equation 1 hence, replacing ∠ACD with ∠DCB we have:

∠A +∠E +∠DCB + ∠DCB + ∠BCE = 180°

Recall equation 2, where ∠DCB = x, hence

∠A +∠E +x + x + ∠BCE = 180°

Recall equation three where 3 where  ∠BCE + x = 42°, hence

∠A +∠E +x + (x + ∠BCE) = 180°

⇒ ∠A +∠E + x + 42° = 180°

Recall that ∠E = 90° so

⇒ ∠A +90° + x + 42° = 180° (Collect like terms)

⇒ ∠A + x = 180° - 90° - 42° = 48°; Hence

∠A + x = 48°...........................4

Recall that in Δ ABC

AB =  BC (given)  

Hence, ABC is an Isosceles triangle. Since this is true, then

⇒ ∠A = ∠ACB = 2x ...........................5 (Two angles opposite the equal sides are equal)

Substituting 2x in equation 5 into equation 4, we have
2x + x = 48°

3x = 48

x = 48/3

x = 16°

Recall that

∠A = 2x...........equation 5, hence,

∠A = 2 * 16

∠A = 32°

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The probability is 0.9999

Given that the mean is 17.6 inches

standard deviation is 3.3/37 = 0.089

We have:

z(18.9)

Now, we have

P(x > 18.9) = P(z > 14.6067)

= 0.9999

z(0.394) = 0.6532

The pre-image ABC in order to become the reflection at A'B'C' is reflected across the x-axis.

The pre-image ABC in order to become A"B"C" both are CONGRUENT, because the image and pre-image are BOTH RIGID.

**Please note that the rules for the transformation from ABC to A"B"C" were not provided**

The population after 5 years is approximately 337,465 people

The population of the city is 250,000

Annual growth rate is 6%

The population after t years is:

After 5 years, t = 5 and the population becomes:

The population after 5 years is approximately 337,465 people

Answer:

Step-by-step explanation:

x/7=12