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2 years ago

Use properties to find the sum or product 5x23x2

1 answer:

3 0

The properties of multiplication and addition to find the product and sum of these numbers 5 , 23 and 2.
1. Commutative property of multiplication
a. 5 x 23 x 2 = 230 = 23 x 5 x 2

2. Associative property of multiplication 
a. 5 x (23 x 2) = 230 = (23 x 5) x 2

3. Commutative property of addition 
a. 5 + 23 + 2 = 30 = 23 + 5 + 2 

4. Associative property of multiplication 
a. 5 + (23 + 2) = 30 = (23 + 5) + 2

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Find the cube root of 27d3 + 54a2b + 36ab2 + 8b3

enot [183]

Answer:

(3a + 2b)3

Step-by-step explanation:

STEP 1 :

Equation at the end of step 1

(((27•(a3))+((54•(a2))•b))+(36a•(b2)))+23b3

Step 2:

(((27•(a3))+((54•(a2))•b))+(22•32ab2))+23b3

Step 3:

(((27•(a3))+((2•33a2)•b))+(22•32ab2))+23b3

Step 4:

((33a3 + (2•33a2b)) + (22•32ab2)) + 23b3

Step 5:

Factoring: 27a3+54a2b+36ab2+8b3

8 0

2 years ago

In equilateral ∆ABC with side a, the perpendicular to side AB at point B intersects extension of median AM in point P. What is t

Sergeeva-Olga [200]

Answer:

Perimeter = (2 + √3)·a

Step-by-step explanation:

Given: ΔABC is equilateral and AB = a

The diagram is given below :

AM is a median , PB ⊥ AB , PM = b

Now, by using properties of equilateral triangle, median is perpendicular bisector and each angle is of 60°.

We get, ∠AMB = 90°. So, by linear pair ∠AMB + ∠PMB = 180° ⇒ ∠PMB = 90°. Also, ∠ABC = 60° and ∠ABP = 90° (given) So, ∠PBM = 30°

Since, AM is perpendicular bisector of BC. So,

$MB = \frac{a}{2}$

Now in ΔAMB , By using Pythagoras theorem

$AB^{2}=AM^{2}+MB^{2}\\AM^{2}=AB^{2}-MB^{2}\\AM^{2}=a^{2}-(\frac{a}{2})^{2}\\AM=\frac{\sqrt{3}\cdot a}{2}$

Now, in ΔBMP :

$sin\thinspace 30^{o}=\frac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\sin\thinspace 30^{o}=\frac{\text{MB}}{\text{PB}}\\\\PB=\frac{\text{MB}}{\text{sin 30}}\\\\PB=\frac{\frac{a}{2}}{\frac{1}{2}}\implies PB = a\\\\tan\thinspace 30^{o}=\frac{\text{Perpendicular}}{\text{Base}}\\\\tan\thinspace 30^{o}=\frac{\text{MB}}{\text{PM}}\\\\PM=\frac{\text{MB}}{\text{tan 30}}\\\\PM=\frac{\frac{a}{2}}{\frac{1}{\sqrt3}}\implies PM=b= \frac{\sqrt{3}\cdot a}{2}$

Perimeter of ABM = AB + PB + PM + AM

$\text{Perimeter = }a+a+b+ \frac{\sqrt{3}\cdot a}{2}\\\\=2\cdot a + \frac{\sqrt{3}\cdot a}{2} +\frac{\sqrt{3}\cdot a}{2}\\\\=2\cdot a +\sqrt{3}\cdot a\\\\=(2+\sqrt3})\cdot a$

Hence, Perimeter of ΔABP = (2 + √3)·a units

3 0

2 years ago

Kim only has $24 to buy pens and notebooks. Each pen costs $2. Each

aksik [14]

Answer:

There are probably more than this but here

$12 for pens would give you 6

$12 for notepads would give you 4

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$18 for notepads would give you 6

$6 for pens would give you 3

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$21 for for notepads would give you 7

$2 or pens would give you 1

and $1 left

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$6 for notepads would give you 2

$18 for pens would give you 9

7 0

2 years ago

Read 2 more answers

An insurance company reported that, on average, claims for a certain medical procedure are $942. An independent organization con

kirza4 [7]

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is:

An insurance company reported that, on average claims for a certain medical procedure are $942. an independent organization constructed a 95% confidence interval of ($930, $950) for the average amount claimed for the particular medical procedure. what conclusion best evaluates the truthfulness of the number reported by the insurance company?

a) with 95% certainty, the average claim for this medical procedure is $942.

b) with 95% certainty, the average claim for this medical procedure is not $942.

c) the confidence interval is consistent with an average claim of $942 for this medical procedure

Solution:

Confidence interval is used to express how confident we are that the population parameter that we are looking for is contained in a range of given values. Looking at the given confident interval, the lower limit is $930 and the upper limit is $950. We can see that the population mean, $942 lies within these values. The correct option would be

c) the confidence interval is consistent with an average claim of $942 for this medical procedure

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2 years ago

A local Latin restaurant specializes in Peruvian, Cuban, and Tex-Mex cuisines in their recipes. Lomo Saltado, “Beef Stir-fry,” i

Vikentia [17]

Answer:

The cost per meal not including the $5

Step-by-step explanation:

or whatever is says something like that

3 0

2 years ago

Read 2 more answers