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inessss [21]
3 years ago
15

angle 1 and angle 2 are complementary angles. given the following information, find measures of both angles

Mathematics
1 answer:
kifflom [539]3 years ago
7 0
∠1 and ∠2 are complementary.
∠1 + ∠2 = 90°

Question a:

∠1 = 23°
∠2 = 90 - 23 = 67°

Ans:  67°

Question b:
∠1 = x
∠2 = 2x + 3
x + 2x + 3 = 90
3x + 3 = 90
3x = 90 - 3
3x = 87
x = 29

∠1 = 29°
∠2 = 2(29) + 3 = 61°

Ans: ∠1 = 29°, ∠2 = 61°


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Which graph shows a linear function? ​
Stolb23 [73]

Answer:

Step-by-step explanation:

You have shared only one graph, that of a quadratic function with vertex at (0, 0) and an equation based upon y = ax^2, where a is a constant coefficient.

Please go back to the source of  your question and describe the other graphs that were given to you.

The graph that shows a straight line is the linear function.

4 0
3 years ago
F(x)=x^4-5x^2-6x-10 is divided by x-3
LiRa [457]

Answer:

Step-by-step explanation:

STEP

1

:

           10

Simplify   ——

           x

Equation at the end of step

1

:

                       10

 ((((x4)-(5•(x2)))-6x)-——)-3

                       x

STEP

2

:

Equation at the end of step

2

:

                           10    

 ((((x4) -  5x2) -  6x) -  ——) -  3

                           x      

STEP

3

:

Rewriting the whole as an Equivalent Fraction

3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  x  as the denominator :

                     x4 - 5x2 - 6x     (x4 - 5x2 - 6x) • x

    x4 - 5x2 - 6x =  —————————————  =  ———————————————————

                           1                    x        

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

STEP

4

:

Pulling out like terms

4.1     Pull out like factors :

  x4 - 5x2 - 6x  =   x • (x3 - 5x - 6)

Polynomial Roots Calculator :

4.2    Find roots (zeroes) of :       F(x) = x3 - 5x - 6

Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  1  and the Trailing Constant is  -6.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,2 ,3 ,6

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        -2.00    

     -2       1        -2.00        -4.00    

     -3       1        -3.00        -18.00    

     -6       1        -6.00        -192.00    

     1       1        1.00        -10.00    

     2       1        2.00        -8.00    

     3       1        3.00        6.00    

     6       1        6.00        180.00    

Polynomial Roots Calculator found no rational roots

Adding fractions that have a common denominator :

4.3       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x • (x3-5x-6) • x - (10)     x5 - 5x3 - 6x2 - 10

————————————————————————  =  ———————————————————

           x                          x        

Equation at the end of step

4

:

 (x5 - 5x3 - 6x2 - 10)    

 ————————————————————— -  3

           x              

STEP

5

:

Rewriting the whole as an Equivalent Fraction

5.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  x  as the denominator :

        3     3 • x

   3 =  —  =  —————

        1       x  

Checking for a perfect cube :

5.2    x5 - 5x3 - 6x2 - 10  is not a perfect cube

Trying to factor by pulling out :

5.3      Factoring:  x5 - 5x3 - 6x2 - 10

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  -6x2 - 10

Group 2:  x5 - 5x3

Pull out from each group separately :

Group 1:   (3x2 + 5) • (-2)

Group 2:   (x2 - 5) • (x3)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Polynomial Roots Calculator :

5.4    Find roots (zeroes) of :       F(x) = x5 - 5x3 - 6x2 - 10

    See theory in step 4.2

In this case, the Leading Coefficient is  1  and the Trailing Constant is  -10.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,2 ,5 ,10

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        -12.00    

     -2       1        -2.00        -26.00    

     -5       1        -5.00       -2660.00    

     -10       1       -10.00       -95610.00    

     1       1        1.00        -20.00    

     2       1        2.00        -42.00    

     5       1        5.00        2340.00    

     10       1        10.00       94390.00    

Polynomial Roots Calculator found no rational roots

Adding fractions that have a common denominator :

5.5       Adding up the two equivalent fractions

(x5-5x3-6x2-10) - (3 • x)      x5 - 5x3 - 6x2 - 3x - 10

—————————————————————————  =  ————————————————————————

            x                            x            

Polynomial Roots Calculator :

5.6    Find roots (zeroes) of :       F(x) = x5 - 5x3 - 6x2 - 3x - 10

    See theory in step 4.2

In this case, the Leading Coefficient is  1  and the Trailing Constant is  -10.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,2 ,5 ,10

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        -9.00    

     -2       1        -2.00        -20.00    

     -5       1        -5.00       -2645.00    

     -10       1       -10.00       -95580.00    

     1       1        1.00        -23.00    

     2       1        2.00        -48.00    

     5       1        5.00        2325.00    

     10       1        10.00       94360.00    

Polynomial Roots Calculator found no rational roots

Final result :

 x5 - 5x3 - 6x2 - 3x - 10

 ————————————————————————

            x            

3 0
3 years ago
The sum of 3 consecutive integers is 72 find the integers
Elis [28]
-----------------------------------------
Define x :
-----------------------------------------
Let the smallest number be x.
The other two numbers will be x + 1 and x + 2.

-----------------------------------------
Construct Equation :
-----------------------------------------
Sum of these numbers is 72
⇒ x + x + 1 + x + 2 = 72

-----------------------------------------
Solve for x :
-----------------------------------------
x + x + 1 + x + 2 = 72
3x + 3 = 72
3x = 69
x = 23

-----------------------------------------
Find the numbers :
-----------------------------------------
1st number = x = 23
2nd number = x + 1 = 23 + 1 = 24
3rd number = x + 2 = 23 + 2 = 25

----------------------------------------------------------------------------------
Answer : The numbers are 23, 24 and 25.
----------------------------------------------------------------------------------
5 0
3 years ago
Read 2 more answers
Jay estimates that a basketball weights about .5 pounds. Shawna estimates that a basketball weights about.05. Whose estimate is
Natasha_Volkova [10]

Answer:

Jay's estimate is closer to the actual weight of the basketball

Step-by-step explanation:

The standard weight of an NBA basketball is 1.4 pounds.

Judging the accuracy of Jay's and Shawna's answer based on their percentage error when compared with the standard, we have that Jay's answer has a lower error as shown below

Error  = (Standard value - Estimated value)/ Standard Value ×100

Error in Jays answer = \frac{1.4 - 0.5}{1.4} × 100 = 64.28 %

Error in Shawna's answer = \frac{1.4 - 0.05}{1.4} × 100 = 96.42%

From this, It is obvious that Jay's answer has a lower percentage error when compared to the actual value.

8 0
3 years ago
Does the line y = 3x + 1 pass through the point (4,15)
Firdavs [7]
No. when the line reaches 4 on the x axis it is at 13 on the y axis.
3 0
2 years ago
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