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melomori [17]
3 years ago
14

A jar contains $14.25 in quarters and dimes. There are 75 coins in the jar. Find the number of quarters in the jar.

Mathematics
1 answer:
Marianna [84]3 years ago
8 0
Set up a system of equations.
d + q = 75
.1d + .25q = 14.25

Multiply the first equation by -.1 so that the "d's" will cancel.
-.1d -.1q = -7.5
.1d +.25q = 14.25
Now add the two equations together
      .15q = 6.75
divide both sides by .15
        q = 45
There are 45 quarters in the jar
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Can someone help me to find length CD
uysha [10]

Answer:

CD = 3.602019190339

Step-by-step explanation:

CD = DA - CA

DA = DB×Cos(29) = 18.7×cos(29) = 16.355388523507

BA = BA×cos(43) = 18.7×cos(43) = 13.676314220278

CA = BA÷tan(47) = 13.676314220278÷tan(47) = 12.753369333168

Then

CD = 16.355388523507 - 12.753369333168 = 3.602019190339

7 0
3 years ago
Verify the trigonometric identity. convert the left side of the relationship to look like the right side.
Tomtit [17]

Answer:

Verified

Step-by-step explanation:

Use \tan{x}=\frac{\sin{x}}{\cos{x}}  , \sin^2{x}+\cos^2{x}=1 and \sec{x}=\frac{1}{\cos{x}}

LHS=\tan^2{x}+1=\frac{\sin^2{x}}{\cos^2{x}} + 1=\frac{\sin^2{x}+\cos^2{x}}{\cos^2{x}}=\frac{1}{\cos^2{x}}=\sec^2{x}=RHS

5 0
2 years ago
The exponential function f(x) = 2^x undergoes two transformations to
Eddi Din [679]

Option A: It is vertically stretched

Option B: it is shifted down

Solution:

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<u>To determine how the graph changes:</u>

Consider the given exponential function f(x)=2^{x}.

Let y = f(x)

Vertically compressed or stretched:

A vertically compression (stretched) of a graph is compressing the graph toward x-axis.

• if k > 1 , then the graph y = k• f(x) , the graph will be vertically stretched by multiplying each y coordinate by k.

• if 0 < k < 1 if 0 < k < 1 , the graph is f(x) vertically shrunk (or compressed) by multiplying each of its y-coordinates by k.  

• if k should be negative, the vertical stretch or shrink is followed by a reflection across the x-axis.  

Here, k = 5  

So the graph will be vertically stretched.

Also, Adding 3 to the graph will move the graph 3 units down so, the graph is shifted down.

So, The graph is shifted down.  

Hence option A and option B is the correct answer.

5 0
3 years ago
What are the correct options
kondor19780726 [428]
The third one because each banner costs $16 and x is the number of banners, $32 is just a one time fee so there is no x.
5 0
3 years ago
I have a box that is 5 inches wide 2 inches deep and 4 inches tall I want to fill with sand. how much sand can I fit inside the
myrzilka [38]

Answer:

40

Step-by-step explanation:

5x2 is 10 and 10x4=40

8 0
2 years ago
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