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2 years ago

Katie wants to create a rectangular frame for a picture. She has 60 inches of material. If she wants the length to be

Mathematics

1 answer:

LenKa [72]2 years ago

7 0

Step-by-step explanation: 2*(l+b)=60, 2*(2*b+b);60

2*(2b+b)=60, 4b+2b=60, 6b=60

b=60/6=10, width is 10inch and length is 2*10=20 inches

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Diego’s history teacher writes a test for the class with 26 questions. The test is worth 123 points and has two types of questio

maria [59]

Answer:

Number of essay questions are 9.

Step-by-step explanation:

Let the number of multiple choice questions = x and the number of essay questions = y.

As, the total number of question are 26. We get, $x+y=26$

Also, the multiple choice and the essay questions worth 3 and 8 points each.

Since, the total number of points of the test are 123.

So, we have, $3x+8y=123$

So, the system of equations is,

x+y=26 ...........................(1)

3x+8y=123 ............................(2)

Multiply (1) by 3 and subtracting by (2), we get,

5y = 45 i.e. y = 9

So, x+y=26 implies x = 26 - y i.e. x = 26 - 9 i.e x = 17

Thus, the number of multiple choice questions and essay questions are 17 and 9 respectively.

5 0

2 years ago

Three years ago, Sherman was twice as old as Clive. If Clive’s present age is c, which expression represents Sherman’s present a

OLEGan [10]

First establish variables for current age.

Clive's current age = c
Sherman's current age = s

"Three years ago,"
Clive was: (c - 3)
Sherman was: (s - 3)

"Sherman was twice as old as Clive."
(s - 3) = 2(c - 3)

Then in terms of Sherman's present age, distribute 2, combine like terms
s - 3 = 2c - 6
s = 2c - 6 + 3
s = 2c - 3

7 0

2 years ago

What is the completely factored form of f(x)=x3+5x2+4x−6?

Gre4nikov [31]

$f(x)=x^3+5x^2+4x-6$
$f(-3)=(-3)^3+5(-3)^2+4(-3)-6=0\implies x+3\text{ is a factor of }f(x)$

Synthetic division yields

-3 | 1   5   4   -6
.    |      -3 -6    6
- - - - - - - - - - - - -
.    | 1   2 -2    0

which translates to

$\dfrac{x^3+5x^2+4x-6}{x+3}=x^2+2x-2$

with remainder 0. Now by the quadratic formula,

$x^2+2x-2=0\implies x=\dfrac{-2\pm\sqrt{2^2-4(1)(-2)}}2=-1\pm\sqrt3$

and so

$f(x)=x^3+5x^2+4x-6=(x+3)(x-(-1+\sqrt3))(x-(-1-\sqrt3))$

3 0

2 years ago

Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat's weight is

Liula [17]

Answer:

The variance in weight is statistically the same among Javier's and Linda's rats

The null hypothesis will be accepted because the P-value (0.53 ) > ∝ ( level of significance )

Step-by-step explanation:

considering the null hypothesis that there is no difference between the weights of the rats, we will test the weight gain of the rats at 10% significance level with the use of Ti-83 calculator

The results from the One- way ANOVA ( Numerator )

with the use of Ti-83 calculator

F = .66853

p = .53054

Factor

df = 2 ( degree of freedom )

SS = 23.212

MS = 11.606

Results from One-way Anova ( denominator )

Ms = 11.606

Error

df = 12 ( degree of freedom )

SS = 208.324

MS = 17.3603

Sxp = 4.16657

where : test statistic = 0.6685

p-value = 0.53

level of significance ( ∝ ) = 0.10

The null hypothesis will be accepted because the P-value (0.53 ) > ∝

where Null hypothesis H0 = ∪1 = ∪2 = ∪3

hence The variance in weight is statistically the same among Javier's and Linda's rats

7 0

1 year ago

Students were asked to write 6x^5 + 8x-3x^3+7x^7 in standard form

WINSTONCH [101]

Answer:

The standard form is $7x^7 +6x^5-3x^3 + 8x$

Step-by-step explanation:

Given:

$6x^5 + 8x-3x^3+7x^7$

To Find :

standard form of $6x^5 + 8x-3x^3+7x^7$

Solution:

A polynomial is in standard form when its term of highest degree is first, its term of 2nd highest is 2nd etc.

In order to write any polynomial in standard form, you look at the degree of each term. You then write each term in order of degree, from highest to lowest, left to write.

Now lets check the degree of each term in the polynomial

The degree of 6x is 5

The degree of 8x is 1

The degree of 3x is 3

The degree of 7x is 7

Now rewrite the polynomial in the order of the degree, from highest to lowest

$7x^7 +6x^5-3x^3 + 8x$

4 0

2 years ago