Find the value of a.

Notice that the empty circle means that the point circled doesn't belong to the range of the function. Otherwise, the fulfilled circle means the point belongs to that range.

The first horizontal line represents the values of the function for x in the interval 0 < x ≤ 15 (notice the empty circle in point (0, 35) ).

Since this line is horizontal, it means that the function has the same value for all those x's:

f(x) = 35, for 0 < x ≤ 15

Now, let's look at the other horizontal line. It represents the values of the function for all x's in the interval 15 < x ≤ 40 (again, notice the empty circle in point (15, 40) ).

Again, since it's a horizontal line, the function has the same value for all those x's:

f(x) = 40, for 15 < x ≤ 40

Finally, the third line has a slope that we have to consider in order to find the form of the function for the last values of x.

We can find the slope in the following way:

1. first, we choose two points in this line whose coordinates are easy for us to identify. Let's take the points (40, 40) and (45, 50).

2. then, we calculate the difference between the y values of these two points:

y2 - y1 = 50 - 40 = 10

3. then, we calculate the difference between the x values of these two points (remember to take the second one minus the first one):

x2 - x1 = 45 - 40 = 5

4. now, we divide the y's differences by the x's differences (this will be the slope m):

m = (y2 - y1)/(x2 - x1) = 10/5 = 2

Now we know the slope m, we write the function of this line in the form:

f(x) - f(x0) = m * (x - x0)

f(x) - f(x0) = 2 * (x - x0)

Finally, to find the final form of this function, we choose any point in the line and use its x value replacing x0, and its y value replacing f(x0). Let's use the point (40, 40):

f(x) - f(x0) = 2 * (x - x0)

f(x) - 40 = 2 * (x - 40)

f(x) - 40 = 2x - 80

f(x) = 2x - 80 + 40

f(x) = 2x -40

Notice that this function for x = 40 has to assume the same value as the one we find for x = 40 using the function for the second horizontal line (f(x) = 40 ), because they both are defined for the same point:

f(x) = 2x -40

f(40) = 2*40 - 40 = 80 - 40 = 40

For this reason, as the second line already defines the function for x = 40, we can write the third part of the function only for values above x > 40.

Therefore, the function that represents the whole graph is:

f(x) = 35, for 0 < x ≤ 15

f(x) = 40, for 15 < x ≤ 40

f(x) = 2x -40, for x > 40

Answer:

Step-by-step explanation:

Convert every ratio into percentage and then find the missing value

Peanuts

Chocolate chips

Chec mix

Option A

$90 + $4 each time

Option B

$13 each time

Procedure

Equations

The cost would be

The answer would be $130

Elevator will take 0.82 minute for travel from the ground floor to the roof. (Option B is correct).

rate by an elevator ascends = 29.6 feet per second

height of the  building = 1,450 feet

Time to travel from the ground floor to the roof is calculated as :

we use rate formula.

i.e

rate = distance/ time

time = distance/rate

time = 1450/ (29.6 feet/sec )

time = 1450/29.6

       = 48.98sec

as we know

60 second = 1mint

1 second = 1/60 minutes

therefore,

 time = (48.98 / 60) minutes

time = 0.8163

time = 0.812 minutes

Elevator will take 0.82 minute for travel from the ground floor to the roof. (Option B is correct).

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Given data:

The given graph.

The domain is the value of x, for the given function domain is,

Thus, the domain is

Answer:

D. (3, 7)

Explanation:

First, we need to draw the triangle to identify the hypotenuse, so using the points P(-2, 5), Q(5, 2), and R(8, 9), we get:

Therefore, the hypotenuse is side PR.

Then, the midpoint of a segment that goes from (x1, y1) to (x2, y2) is

So, replacing (x1, y1) = P(-2, 5) and (x2, y2) = R(8, 9), we get that the midpoint of the hypotenuse is

Therefore, the answer is D. (3, 7)

The the height of the bottom of the hold after second day is 1517.45 feet.

What is height?

Height is a way to measure someone or something from base to top or head to toe

Day 1 height = -[tex]32^{2}/12[/tex] feet

Day 2 height = [tex]192^{2} /23[/tex] more than first day

=36864/23+(-1024/12)

=1602.78-85.33

=1517.45 feet

Therefore, the height of the bottom of the hole after the second day is 1517.45 feet.

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Answer:

37.5, 75 and 67.5 degrees

Explanation:

The sum of angle in the given triangle is 180 degrees

Hence;

x + x + 30 + 2x = 180

4x + 30 = 180

4x = 180 - 30

4x = 150

x = 150/4

x = 37.5 degrees

Get angle 2x

2x = 2(37.5)

2x = 75 degrees

Get angle x + 30

x + 30 = 37.5 + 30

x = 30 = 67.5 degrees

Hence the angles of the triangle are 37.5, 75 and 67.5 degrees

The equation for Tisha and her team is a equals T plus b plus c plus d all over 4 or , a = (T-b-c-d)/4

An equation is created by joining two expressions with the equals sign ("=").

The points that are earned from the three local matches are b , c, and d.

points earned from the district game = 4a

The total points earned is T

Therefore forming the equation:

T = (4a + b + c + d )

Now we make a the subject of formula:

or , a = ( T - b - c - d) / 4

Therefore the required equation is a equals T plus b plus c plus d all over 4 .

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Answer:

a = (T-b-c-d)/4

Step-by-step explanation:

took test

Write the mixed number -5 4/9 as a decimal

we have the number

5 4/9

step 1

convert to an improper fraction

5 4/9=5+4/9=49/9

and

49/9=5.444444...

Part 2

we have the number

7/-35-------> is the same that -7/35

simplify

Divide by 7 the numerator and denominator

-1/5

Find out an equivalent fraction

Multiply by (3/3)

-3/15

therefore

we have

7/-35

-7/35

-1/5

-3/15

decimal number

-1/5=-0.20

The inverse of the given equation is given by f⁻¹(x) = (x+8)²/49 - 8

What is an equation?

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. Equations are used to describe geometric shapes in Cartesian geometry. Since the investigated equations, such as implicit equations or parametric equations, have an unlimited number of solutions, the goal has changed. Now, one utilizes equations to analyze the attributes of figures rather than explicitly providing the solutions or counting them, which is impossible. The fundamental concept of algebraic geometry, a significant branch of mathematics, is presented here. Equations involving one or more functions and their derivatives are known as differential equations. By identifying a derivative-free formulation for the function, they may be resolved. Processes involving rates are modeled using differential equations.

given equation,

f(x) = 7√(x+8) - 8

y = 7√(x+8) - 8 (replace f(x) with y)

x = 7√(y+8) - 8 (interchange x and y)

y = (x+8)²/49 - 8 (solve for y)

f⁻¹(x) = (x+8)²/49 - 8 (replace y with f(x))

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The value of Brand A is $75 billion and Brand B is $32 billion.

An expression is used to illustrate the relationship between the variables.

Let brand B value = x

Brand A has a recognition value worth 43$ billion more than brand B. This will be x + 45

The total value of these two brands is 107$ billion.

The expression to find the value is for each brand will be:

x + x + 43 = 107

2x + 43 = 107

Collect like terms

2x = 107 - 43

2x = 64

Divide

x = 64/2

x = 32

Brand B is $32 billion

Brand A = x + 43 = 32 + 43 = $75 billion.

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Option (D) "Few trees, mostly grass, rich soil, cold winters, the average rainfall and good for agriculture" perfectly describes the climate and vegetation of Savana.

Therefore, option (D) "Few trees, mostly grass, rich soil, cold winters, the average rainfall and good for agriculture" perfectly describes the climate and vegetation of Savana.

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Answer:

C

Step-by-step explanation:

Its the Little Rain

Adding 1 to both sides gives

and then multiplying both sides by 3 gives

At this point, this absolute value inequality can be decomposed into two separate inequalities

We first solve the first inequality.

Multiplying both sides by -1 reverses the sign of the inequality and gives

subtracting -3 from both sides we get

and finally dividing both sides by 2 gives

That is the first solution, the second solution is given by the second inequality 2x+ 3 <27.

Subtracting 3 from both sides and then dividing the equation by 2 gives

Hence, the solution to our inequality is

For a discontinuous function ,maximun value is found by replacing every region for the values x ,y

So then for x≤2. and y≤1 and f(x,y) = x +y

theres a maximum value but no minimum ( because is minus infinite). The maximum value for this area is

x+y = 2+1= 3

Now for area y ≥-2x -3

rearrange the equation as y+2x ≥ -3

is the equation of a plane , the plane or area that goes over the straight line y= -2x-3.

So now replace y = -2x-3 in the function f(x,y) = x+y

then f(x,y)= x -2x-3 = -x-3

Now the third region is y≥ 2x -3

this is the area over a line with slope positive equal to 2

now replacing again for this area we find

f(x,y) = x+y = 2x-3 +x = 3x -3

because x≤2. So then replace x by 2 in f(x,y) to find the maximum value

f(x,y) in 2nd region is f(x,y) = -x-3= -2-3= -5

f(x,y) in 3rd region is f(x,y) = 3x -3= 3•2 -3= 3

Finally in conclusion, the máximum value is 3 , the minimum value is -5

Answer:

x = 8.9

Explanation:

The sine ratio for 43 degrees gives

Now, the side opposite to the 43 degree angle is x

The solution of a system of two linear equations interprets the point of intersection of the two lines geometrically

When the two lines intersect each other at a point, then the system of two linear equations has a unique solution.

If two linear equations in the given system represent two lines parallel to each other, then the system becomes inconsistent and in that case, it has no solution.

If the system is dependent i.e. there is only one linear equation in two variables, then every point on the line is the solution of the equation.

So, in that case, it has infinitely many solutions.

Answer:

20

Step-by-step explanation:

70% of x = 14
0.7x = 14
x = 14/0.7
x = 20

The weight that Taylor's dad lifted higher will be 30g.

It should be noted that weight simply means the mass that a body contains.

From the information, Taylor's dad lifted 80g of weight and Davin's dad lifted 50g of weight.

The weight that Taylor's dad lifted more than Davin's dad will be:

= Weight of Taylor's dad - Weight of Davin's dad

= 80 - 50

= 30g

The difference is 30g.

The complete question is written below.

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Taylor's dad lifted 80g of weight and Davin's dad lifted 50g of weight. How much more did Taylor's dad lift than Davin?

Answer:

Year     Jessica         Tom          Who earns more?
1              $400            $400        They earn the same amount

2             $408            $400         Jessica earns more

3             $416             $400         Jessica earns more

Step-by-step explanation:

At simple interest, the amount of interest is the same each year

First year: Since compounding takes place only at the end of the year, both of them earn the same amount of interest

Interest earned = 20,000 x 0.02 = $400

Same for both boxes for first year

Both of their deposits will increase by $400 to $20,400

For second year
Jessica's interest is calculated on 20,400 = 20,400 x 0.02 = $408
Her deposit value at the end of year 2 = 20, 400 + 408 = $20,808

Tom's interest is calculated on the original deposit since it is simple interest. So in year 2, Tom still makes $400.

In year 2 Jessica earns more interest than Tom
Jessica: $408
Tom : $400

For third year, Jessica's interest is calculated on her deposit value of 20,800 = 20,800 x 0.02 = $416

Tom's interest for 3rd year is the same as for the previous years = $400

So in third year, Jessica earns more

26.14 ft²

1) Considering that triangular herb:

2) Let's calculate the area of that triangle using the Heron formula so that we can not need to find the height:

2.1) Calculate the Perimeter:

2P = 2+3+4

2P = 9 yd

2 yards = 6 ft

3 yd = 9ft

4 yd = 12 ft

Converting into feet

9 yards = 27 feet

And the Semi perimeter (half the perimeter):

P = 9/2

27/2

Now we can plug that into Heron's Formula:

3)

So the area of that triangular garden is approximately 26.14 ft²

The vertex form of a quadratic equation is expressed as

y = a(x - h)^2 + k

where

h and k are the x and y x and y coordinates of the vertex of the parabola.

a is the leading coefficent

From the information on the graph,

h = 13

k = 13

By substituting these values into the formula,

y = a(x - 13)^2 + 13

On the graph, when x = 26, y = 0

Substituting these values into the equation, we have

0 = a(26 - 13)^2 + 13

0 = a * 13^2 + 13

0 = 169a + 13

169a = - 13

a = - 13/169

a = - 1/13

By substituting a = - 1/13, h = 13 and k = 13 into the verte form equation, the quadratic equation written in vertex form is

y = - 1/13(x - 13)^2 + 13

C) 52 feet

Explanation:

Since the deck will be 14 feet by 12 feet and it has four sides, we can deduce that it's a rectangle.

Therefore all you need to do is sum up all the sides together

14 + 14 + 12 + 12 => 14 * 2 + 12 * 2 = 52 feet

You have the following inequality:

2(5t - 25) + 5t < -80

In order to solve the previous inequality, proceed as follow:

Expand the factor left side and simplify like term:

2(5t) - 2(25) + 5t < -80

10t - 50 + 5t < -80

15t < -80 + 50

15t < -30

Divide by 15 both sides and simplify:

t<-30/15

t<-2

Hence, the solution to the given inequality is t<-2

Cos 12° expressed as an integer or as a decimal

Hence the value of cos 12° as a decimal to the nearest hundredth = 0.99

The answer is follows,

[tex]-3^5[/tex]       = -243

[tex](-3)^5[/tex]    = -243

[tex]\left(-3^5\right)[/tex]     = -243

[tex]-\left(-3\right)^5[/tex]  = 243

An exponent is a number or letter written above and to the right of the base of a mathematical expression.

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The phrase y varies directly as x can be understood that y gets bigger when x gets bigger as well, this can be written as,

then, using the point (6,48) find the value when x is 2,

clear for y2,

Answer:

The equation that has same solution as that of equation 2x - 5 = 15 is 2x = 10.

An equation in mathematics is used to equate two expressions using a equals sign. For example -

x = 4y

3x = 7y

Given is the following equation -

2x - 5 = 15

The solution of the equation will be the value of [x] for which the LHS equals to RHS. On solving -

2x - 5 = 15

2x = 10

x = 5

Only equation [A] has the same solution as that of equation -

2x - 5 = 15

Equation [A] is -

2x = 10

x = 5

Therefore, the equation that has same solution as that of equation 2x - 5 = 15 is 2x = 10.

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The correct option regarding the skewness of the given distribution is:

The data is clumped to the right.

To find the skewness of the distribution, we need to look at the mean and the median of the distribution.

The mean is the sum of all the observations in the distribution divided by the number of observations. The graph shows the number of times that each observation appears, hence the mean is found as follows:

Mean = (1 x 2 + 2 x 5 + 3 x 8 + 4 x 2 + 5 x 12 + 6 x 7 + 7 x 13 + 8 x 3 + 9 x 5 + 10 x 11)/(2 + 5 + 8 + 2 + 12 + 7 + 13 + 3 + 5 + 11) = 6.12.

The median is the middle term of the distribution. There are 68 terms in the distribution, hence the median is the observation in which the count reaches 34. Then:

Hence the median is of 6, which is less than the mean. Since the median is less than the mean, the data is right skewed, that is, clumped to the right.

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