4+a≥18 What is the value of a?

k0ka [10]

The shaded region is a triangle. Triangle area can be determined with formula
a = 1/2 × b × h

From the question, we know that the triangle consists of
base = 10 - 6 = 4 m
and the height is the dimension which is perpendicular to the base,
height = 6 m

Find the triangle area
a = 1/2 × b × h
a = 1/2 × 4 × 6
a = 1/2 × 24
a = 12

The area of the shaded region is 12 m²

5 0

3 years ago

Identify a transformation of the function f(x) = x by observing the equation of the function g(x) = x − 90.

ycow [4]

The transformation of a function may involve any change. The transformation of the function is Right shift by 90 units.

<h3>How does the transformation of a function happen?</h3>

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units:

y=f(x+c) (same output, but c units earlier)

Right shift by c units:

y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: $y = k \times f(x)$

Horizontal stretch by a factor k: $y = f\left(\dfrac{x}{k}\right)$

Since the function is transformed from f(x)=x to g(x)=x-90, therefore, the transformation of the function is Right shift by 90 units.

Learn more about Transforming functions:

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5 0

2 years ago

The admission fee at an amusement park is 20$ for children and 35$ adults. On a certain, day 264 people entered the park, and th

shtirl [24]

Answer:

100 Adults and 164 Children

Step-by-step explanation:

To solve this we will need to write two equations to solve for the two unknowns. Firstly, we know that tickets are 20 for children and 35 for adults, and that the total price was 6780. We can write an expression to represent this. 6780 is the total price, this also means it is the price of all the adults + the price of all the children. The total price of the adults tickets is the price of each ticket multiplied by the number of adults, so the total price of adult tickets can be represented by: 35A, 35 being the ticket price per adult, and A being the number of adults. Similarly the total children's price can be expressed as such: 20C, 20 being the price per child, and C being the number of children. Since we know that these two values total to 6780, we can now form an equation:

35A (total adult price) + 20C (total children price) = 6780

35A+20C=6780

Now we need another expression so we can substitute for one of the values. The other piece of information we are given, is that a total of 264 people entered the park. This means that the total number of adults + the total number of children = 264. Since we already have variables for the numbers of adults and children we now have our second equation:

A (number of adults) + C (number of children) = 264

A+C=264

Now we can use this second equation to substitute for one of the values in the first equation. Let's substitute for children:

If we rearrange the second expression we will get:

A+C-A=264-A

C=264-A

So now we substitute this expression into our first formula:

35A+20C=6780

C=264-A

35A+20(264-A)=6780

Now since we only have one unknown, we can simplify, expand and solve!

35A+20*264-20*A=6780

35A+5280-20A=6780

35A-20A+5280-5280=6780-5280

15A=1500

15A/15=1500/15

A= 100

A total of 100 adults were admitted.

Now we can use the number of adults to find the number of children using our second formula:

C=264-A

C=264-100

C=164

And there we are! A total of 100 adults and 164 children were admitted.

Hope this helped!

4 0

4 years ago

Suppose that 30% of all houses need a paint job. Also, 15% of all houses need both a paint job and a new roof. Further, 7% of al

ivann1987 [24]

Answer:

0.0105

Step-by-step explanation:

given that 30% of all houses need a paint job. Also, 15% of all houses need both a paint job and a new roof. Further, 7% of all houses that need a new roof also need new windows.

If total houses are 100, then 30 require a paint along. 15 require both paint and new roof.

Out of 15 houses which require new roof 7% need new windows

i.e. no of houses which need new windows = $15*7%\\=1.05$

If there are total 100 houses, 1.05 houses require a new window

So probability that a randomly selectede house needs a new window

= 0.0105

8 0

3 years ago

A store is having a sale on jelly beans and trail mix. For 3 pounds of jelly beans and 5 pounds of trail mix, the total cost is

Maurinko [17]

Set up your two equations:
9x+7y=53 
3x+5y=25 
X=cost per pound of jelly bean 
Y=cost per pound of trail mix 
Multiply the second equation by (-3): 
-9x-15y=-75 
+ 9x+7y=53 <---- copy first equation and add them 
—————— 
0x-8y=-22 
Then solve for y: 
Y=2.76 this is your cost per pound of trail mix. 
Then plug y back in to one of the original equations and solve for x: 
3x+7(2.75)=25 
X=3.75 this is you cost per pound of jelly beans

6 0

3 years ago