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atroni [7]
3 years ago
12

Jess takes a board that is 50 inches long and cuts it into two pieces, one of which is 16 inches longer than the other. How long

is each piece?
Mathematics
2 answers:
sergejj [24]3 years ago
4 0

Answer:

The lengths are 17 in and 33 in.

Step-by-step explanation:

Let x = the length of the shorter piece

x +x +16=50

2x = 50-16

2x= 34

x= 17

and

x + 16 = 17+ 16

x + 16 = 33

The lengths are 17 in and 33 in.

Check your answer:

17+33=50

sergey [27]3 years ago
3 0
Let x = the length of the shorter piece
x+x+16=50in
2x=50-16
2x=34
x=17

Then

x+16=17+16
x+16=33
Subtract 16 from both sides

The lengths are 17in and 33in
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The longer leg of a right triangle is 7 ft longer than the shorter leg. The hypotenuse is 9ft longer than the shorter leg. Find
julia-pushkina [17]

Answer:

8, 15 and 17 feet respectively

Step-by-step explanation:

Let the shorter leg=l feet

The longer leg of a right triangle is 7 ft longer than the shorter leg, therefore Length of the longer leg=(l+7) feet

The hypotenuse is 9ft longer than the shorter leg. Therefore Length of the hypotenuse=(l+9) feet

Using Pythagoras Theorem

Hyp^2=Opp^2+Adj^2\\(l+9)^2=l^2+(l+7)^2\\(l+9)(l+9)=l^2+(l+7)(l+7)\\l^2+9l+9l+81=l^2+l^2+7l+7l+49\\l^2+18l+81=2l^2+14l+49

This results into:

2l^2-l^2+14l-18l-81+49=0

l^2-4l-32=0\\l^2-8l+4l-32=0\\l(l-8)+4(l-8)=0\\(l-8)(l+4)=0

l-8=0 or l+4=0

l=8 or -4

Since length cannot be negative, The length l=8 feet

The sides of the rectangle are therefore: 8, 15 and 17 feet respectively

5 0
3 years ago
Choose which function is represented by the graph
Viefleur [7K]

Given:

The graph of a function.

To find:

The function.

Solution:

From the given graph, it is clear that the graph intersect the x-axis at x=-4, -2, 1. It means -4, -2 and 1 are zeros of the given function graph.

If c is a zero of a function f(x), then (x-c) is a factor of f(x).

Using the above definition, we conclude that (x+4), (x+2) and (x-1) are the factors of given function. So,

f(x)=(x+4)(x+2)(x-1)

f(x)=(x-1)(x+2)(x+4)

Therefore, the correct option is A.

4 0
3 years ago
An education firm measures the high school dropout rate as the percentage of 16 to 24 year olds who are not enrolled in school a
posledela

Answer:

The value of the test statistic z = -0.6606

Step-by-step explanation:

From the question we are told that

      The high dropout rate is \mu  = 6.1%  = 0.061

      The  sample size is  n = 1000

       The  number of dropouts x = 56

       The probability of having a dropout in 1000 people  \= x  = \frac{56}{1000}  =  0.056

Now setting up Test Hypothesis

 Null  H_o :  p = 0.061

 Alternative  H_a : p < 0.061        

The Test statistics is mathematically represented as

                 z = \frac{\= x - p}{\sqrt{\frac{p(1 -p)}{n} } }

substituting values

               z = \frac{0.056 - 0.061}{\sqrt{\frac{0.061(1 -0.061)}{1000} } }

               z = -0.6606

6 0
3 years ago
Another teacher decides to average the height of all 15-year-old male students in his classes throughout the day. By the end of
Tanya [424]

Answer: 0.47

Step-by-step explanation:

0.47% = 0.0047 in decimal form. Percent means 'per 57'. So, 67Inches means 0.47 per 100 or simply 0.47/100. If you divide 0.47 by 100, you'll get 0.0047 (a decimal number).

4 0
3 years ago
Do natural numbers have multiplicative inverse
hodyreva [135]
No,because a multiplcative inverse is when your changing a division or multiplcation sign!
6 0
3 years ago
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