Read the following statement: All prime numbers are odd. Which of the following choices is a counterexample to the statement?
1
17
2
7

Answers

Answer 1
All prime numbers are odd.
A counter-example is one that will prove this statement to be false.

ur answer is : 2....it is 2 because 2 is a prime number and it is even...in fact, it is the only even number that is a prime number.


Answer 2

The choice which is a counterexample to the statement is 2.

What are prime numbers?

"It is a number that is divisible only by itself and 1 "

For given question,

We have been given a statement 'All prime numbers are odd. '

We need to select a counterexample to given statement.

Consider a number 2.

2 is divisible only by itself and 1

This means, 2 is a prime number.

We know that 2 is an even number.

Therefore, the choice which is a counterexample to the statement is 2.

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Related Questions

A rectangle has a base of 3 inches and a height of 9 inches. If the dimensions are doubled, what will happen to the area of the rectangle?

Answers

check the picture below

how many times is 27 into 108?

Answer:

Area will increase by 4 times

Step-by-step explanation:

Given: A rectangle has a base of 3 inches and a height of 9 inches.  

To find: If the dimensions are doubled, what will happen to the area of the rectangle?

Solution:

It is given that a rectangle has a base of 3 inches and a height of 9 inches.

Now, to find if the dimensions are doubled what will happen to the area, first we need to find the original area.

Original area of rectangle, when base is 3 inches and height 9 inches is

[tex]9\times3=27[/tex] square inches

Now, when dimensions are doubled , the base becomes 6 inches and height becomes 18 inches

So, new area becomes [tex]6\times18=108[/tex] square inches.

Now,

[tex]\frac{\text{new area}}{\text{original area} }=\frac{108}{27}[/tex]

[tex]\implies\frac{\text{new area}}{\text{original area} }=\frac{4}{1}[/tex]

Hence, the area will increase by 4 times.

A sample of 4 different calculators is randomly selected from a group containing 18 that are defective and 35 that have no defects. what is the probability that at least one of the calculators is defective?

Answers

1.

P(at least one of the calculators is defective)= 

1- P(none of the selected calculators is defective).

2.

P(none of the selected calculators is defective)

           =n(ways of selecting 4 non-defective calculators)/n(total selections of 4)

3.

selecting 4 non-defective calculators can be done in C(35, 4) many ways, 

where  [tex]C(35, 4)= \frac{35!}{4!31!}= \frac{35*34*33*32*31!}{4!*31!}= \frac{35*34*33*32}{4!}= \frac{35*34*33*32}{4*3*2*1}= 52,360[/tex]

while, the total number selections of 4 out of 18+35=53 calculators can be done in C(53, 4) many ways,

[tex]C(53, 4)= \frac{53!}{4!*49!}= \frac{53*52*51*50}{4*3*2*1}= 292,825[/tex]

4. so, P(none of the selected calculators is defective)=[tex] \frac{52,360}{292,825} =0.18[/tex]


5. P(at least one of the calculators is defective)= 

1- P(none of the selected calculators is defective)=1-0.18=0.82



Answer:0.82

Find the value of 'y' in the equation 3/y-3 =8

A.) y= -2 3/8

B.) y= -1 5/8

C.) y= 1 5/8

D.) y= 2 3/8

Answers

3 / (y - 2) = 8....multiply both sides by (y - 2), eliminating it on the left side

3 = 8(y - 2)
3 = 8y - 16
3 + 16 = 8y
19 = 8y
19/8 = y
2 3/8 = y <==
answer : D , y= 2 3/8

The following is a geometric sequence 5,3,1,-1

Answers

No it is not.  All geometric sequences have a common ratio that is a constant found when you divide any term by the previous one.

3/5 !=1/3

So it is not a geometric sequence.

It IS an arithmetic sequence though, as all arithmetic sequences have a common difference that is a constant found when you find the difference between any term and the term preceding it.

3-5=1-3=-1-1=d=2

So there is a  common difference of 2 so this is an arithmetic sequence.  And all arithmetic sequences can be expressed as:

a(n)=a+d(n-1), a(n)=nth term, a=initial term, d=common difference, n=term number, in this case a=5 and d=-2 so

a(n)=5-2(n-1)  which of course can be simplified...

a(n)=5-2n+2

a(n)=7-2n

Determine how many, what type, and find the roots for f(x) = x^3 - 5x^2 – 25x + 125

Answers

x^3-5x^2-25x+125

(x^3+125)-5x^2-25x

(x+5)(x^2-5x^2+25)-5x^2-25x

(x+5)(x^2-5x^2+25)-5x(x+5)

(x+5)(x^2-5x+25-5x)

(x+5)(x^2-10x+25)

(x+5)(x-5)(x-5)

x= -5 and 5

So there are two roots when x= ±5

df/dx=3x^2-10x-25

d2f/dx2=6x-10

So when x=-5, acceleration is negative and this is a local maximum for f(x) and when x=+5, acceleration is positive and this is a local minimum for f(x).

If x is inversely proportional to y, and x = 60 when y = 0.5, find x when y = 12. A. 0.4 B. 25 C. 360 D. 2.5

Answers

"x is inversely proportional to y" means x = k/y

Plug in x = 60 and y = 0.5 then solve for k
x = k/y
60 = k/0.5
60*0.5 = k
k = 30

Now plug in y = 12 to find x
x = k/y
x = 30/y
x = 30/12
x = 2.5
Answer is choice D


Solve for the unknown side.

last option is none of these

Answers

36+16 = 52
unknown side = square root 52 = 2 square root 13

answer
2 square root 13 (second choice)

The side of the triangle which is the hypotenuse side is [tex]2\sqrt{13}[/tex]

What is the hypotenuse side?

Using trigonometry, Trigonometry is the area of mathematics that deals with particular angle functions and how to use them in computations. In trigonometry, an angle can have six common functions. The terms sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc) are their names and abbreviations.

[tex]c^{2} =4^{2} +6^{2} \\\\c^{2}=16+36\\\\c^{2}=52\\\\c=\sqrt{52} \\\\c= 2\sqrt{13}[/tex]

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16x^2=100
How many solutions will there be to the following equation?

Answers

16x^2 = 100
x^2 = 100/16
x^2 = 6.25
x = (+-) sqrt 6.25
x = (+-) 2.5

x = 2.5 and x = - 2.5........2 solutions

Answer:

There are two solutions [tex]x=\frac{5}{2},-\frac{5}{2}[/tex]

Step-by-step explanation:

Given : Equation [tex]16x^2=100[/tex]

To find : How many solutions will there be to the following equation?      

Solution :

Equation [tex]16x^2=100[/tex]

Solve the equation,

Divide by 16 both side,

[tex]\frac{16x^2}{16}=\frac{100}{16}[/tex]

[tex]x^2=\frac{100}{16}[/tex]

Taking root both side,

[tex]x=\sqrt{\frac{100}{16}}[/tex]

[tex]x=\sqrt{\frac{10^2}{4^2}}[/tex]

[tex]x=\pm\frac{10}{4}}[/tex]

[tex]x=\pm\frac{5}{2}}[/tex]

Therefore, There are two solutions [tex]x=\frac{5}{2},-\frac{5}{2}[/tex]

Can someone help me with this math question?

Answers

it would be 19

42-23=19
42-23=19

Let me know if you need any further help.

Provide the reasons for the proof:
Given: Trapezoid RIAG with RI = RG = GA
m angle I = m angle NAG
Prove: angle T ≈ angle N

Answers

Line RG || Line IA = Parallel property of a trapezoid

We know that shape RIAN is a parallelogram with RN || IA and RI || NA
RG is a part of the line RN, so RG is also parallel to IA

-----------------------------------------------------------------------------------------------------------------

m∠TRG = m∠I : Corresponding angle on a transversal

Line TI is a transversal to the parallel lines RN and IA.
m∠TRG and m∠I are corresponding to each other

----------------------------------------------------------------------------------------------------------------

m∠TGR = m∠NGA: Opposite angles on a transversal

Line TA is a transversal on line RN and IA

----------------------------------------------------------------------------------------------------------------

ΔTGR = ΔNGA: Opposite angles property in a parallelogram

Opposite angles on a parallelogram are equal

---------------------------------------------------------------------------------------------------------------

∠T = ∠N: Angle sum of triangle 

∠T = 180° - (∠R + ∠G)
∠N = 180° - (∠G + ∠N)

Find the missing values for the exponential function represented by the table below.

xy
-2 4
-1 6
0 9
1
2

a.
-13.5
-20.25

c.
6
4

b.
-13.5
20.25

d.
13.5
20.25

Answers

d if I'm not mistaking

Answer: c.  

6  

4

Step-by-step explanation:

The exponential function is given by :-

[tex]y=Ab^x[/tex], where A is the initial amount , b is common ratio and x is time period.

We know that in exponential functions, the ratio of the consecutive value of y is same.

From the table ,  [tex]b=\dfrac{6}{4}=\dfrac{3}{2}[/tex]

At x = 0

[tex]9=A(\dfrac{2}{3})^0\\\\\Rightarrow\ A=9[/tex]

At x=1

[tex]y=9(\dfrac{2}{3})^1=6[/tex]

At x=2

[tex]y=9(\dfrac{2}{3})^2=4[/tex]

Hence, the missing values for the exponential function : c.  6  4.

PLEASE HELP IMAGE ATTACHED! These triangles are similar. Find the area of the smaller triangle to the nearest whole number.

Answers

Area of a triangle = (1/2)base × height. you have the area and the base so substitute. 105=(1/2)16h... 105/8=13.125 so the height of the first triangle is 13.125.... now set up a proportion using the heights and bases of the similar triangles: 13.125/16=x/12... so x, the height of the second triangle is about 9.84.... now use the original formula to calculate the area of the second triangle... 9.84×12×.5= approx 59 sq ft

The area of smaller triangle is 59 square feet

What are the similar triangles?

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

What is the formula for the area of triangle?

The formula for the area of triangle is

[tex]Area = \frac{1}{2} \times base \times \ height[/tex]

According to the given question.

The area of the larger triangle is 105 square feet.

And the one side of the larger triangle and the smaller traingle is 16 and 12 feet respectively.

Suppose the height of thesmaller triangle be x feet and the height of the larger triangle be y feet.

Since, the corresponding edges of similar triangles are proportional.

Therefore,

[tex]\frac{y}{x} = \frac{16}{12}[/tex]

[tex]\implies y = \frac{4}{3} x[/tex]

Also, the area of larger triangle is 105 square feet.

[tex]\implies \frac{1}{2} \times \frac{4}{3} x \times 16 = 105[/tex]

The above euqtaion can be written as

[tex]\implies \frac{1}{2}\times \frac{4}{3} x \times \frac{4}{3} \times 12 = 105[/tex]

[tex]\implies \frac{1}{2} \times (\frac{4}{3} )^{2} \times x \times 12 = 105[/tex]

[tex]\implies \frac{1}{2} \times x \times 12 = 105 \times \frac{9}{16}[/tex]

[tex]\implies \frac{1}{2} \times x \times 12 = 59[/tex]

Area of smaller triangle  = 59 square feet

Hence, the area of smaller triangle is 59 square feet.

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Suppose that ​$88 comma 00088,000 is invested at 3 and one half3 1 2​% ​interest, compounded quarterly. ​a) find the function for the amount to which the investment grows after t years

Answers

I don't know what you mean by comma 00088,000
But
Amount = 88(1+.035/4)^(.04)(t) is the formula

Which equation is equivalent to 4s=t+2
a. s=t-2
b. s=4/t+2
c. s=t+2/4
d. s=t+6

Answers

4s=t+2  all of the solutions are in terms of s so divide both sides by 4

s=(t+2)/4

the equivalent equation of the equation 4s=t+2 is s = [tex]\frac{t+2}{4}[/tex] .

What is Equivalent equations?

Equivalent equations are algebraic equations that have identical solutions or roots. Adding or subtracting the same number or expression to both sides of an equation produces an equivalent equation. Multiplying or dividing both sides of an equation by the same non-zero number produces an equivalent equation.

According to the question

The equation  

4s=t+2

Now,

its Equivalent equations  is  :

Dividing equation by 4 both side  

i.e

s = [tex]\frac{t+2}{4}[/tex]

Hence , the equivalent equation of the equation is s = [tex]\frac{t+2}{4}[/tex] .

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A local university accepted 2300 students out of 4500 applicants for admission. What was the acceptance rate expressed as a percent

Answers

(2300 / 4500) * 100 = 51.1%

Hope this helps! :)

Given a polynomial f(x), if (x + 7) is a factor, what else must be true? Help plzzz im running out of time
f(0) = 7
f(0) = −7
f(−7) = 0
f(7) = 0

Answers

Answer: f(-7) = 0
For the factored form of f(x), if x = -7, then one of the factors will be equal to 0, since (-7 + 7) = 0. This will cause the entire y-value to be 0, because anything multiplied by 0 = 0.

For what values of x does f(x) = x^2 +5x +6 reach its minimum value?

Answers

That factors to:
(x+2) * (x+3)
Therefore, x = -2 and x = -3

The minimum value of the function occurs at [tex]\( x = -\frac{5}{2}[/tex], and the function reaches its minimum value of [tex]\( -\frac{1}{4} \)[/tex] at this point.

To find the minimum value of the quadratic function [tex]\( f(x) = x^2 + 5x + 6[/tex], we can use the vertex formula. The vertex of a quadratic function [tex]\( ax^2 + bx + c \) is given by the point \( \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right) \).[/tex]

[tex]For \( f(x) = x^2 + 5x + 6 \), \( a = 1 \), \( b = 5 \), and \( c = 6 \).[/tex]

The x-coordinate of the vertex is [tex]\( -\frac{b}{2a} = -\frac{5}{2(1)} = -\frac{5}{2} \).[/tex]

To find the minimum value, we substitute [tex]\( x = -\frac{5}{2} \)[/tex] into the function:

[tex]\[ f\left(-\frac{5}{2}\right) = \left(-\frac{5}{2}\right)^2 + 5\left(-\frac{5}{2}\right) + 6 \]\[ = \frac{25}{4} - \frac{25}{2} + 6 \]\[ = \frac{25}{4} - \frac{50}{4} + \frac{24}{4} \]\[ = \frac{-1}{4} \][/tex]

So, the minimum value of the function occurs at [tex]\( x = -\frac{5}{2}[/tex], and the function reaches its minimum value of [tex]\( -\frac{1}{4} \)[/tex] at this point.

If y varies inversely as the square of x and y=4 when x=5, find y when x is 2

Answers

need to kind K

Y=k x 1/x^2 = k/x^2

Find K when y=4 & x=5

Y=k/x^2 =

4=k/5^2=

4=k/25

K=4*25 =100

When x = 2

Y=100/2^2

Y=100/4

Y=25


A mouse spots an owl flying 10.1 feet over a nearby bush. The mouse is 30 feet away from the bush, and it sees the owl at a certain angle of elevation.

Which trigonometric equation can be used to solve for x, the angle of elevation from the mouse to the owl?

Answers

It's the first one ([tex]10.1 = 30 tan x[/tex]). 10.1m makes the opposite side and 30m makes the adjacent side of the right angle triangle. [tex]tanx = 10.1/30[/tex], so 30 tan x[/tex]= [tex]10.1.


For a hypothesis test of H0:p1 − p2 = 0 against the alternative Ha:p1 − p2 ≠ 0, the test statistic is found to be 2.2. Which of the following statements can you make about this finding?

The result is significant at both α = 0.05 and α = 0.01.
The result is significant at α = 0.05 but not at α = 0.01.
The result is significant at α = 0.01 but not at α = 0.05.
The result is not significant at either α = 0.05 or α = 0.01.
The result is inconclusive because we don't know the value of p.

Answers

The test result is not significant at α = 0.05 or α = 0.01.

For a hypothesis test of H0:p1 − p2 = 0 against the alternative Ha:p1 − p2 ≠ 0, the test statistic is found to be 2.2. Given the information provided, the result is not significant at either α = 0.05 or α = 0.01. This conclusion is drawn based on the p-value and the 95% confidence interval.

On compared the test statistic to critical values for α = 0.05 and α = 0.01. Since the test statistic falls within the critical region for α = 0.05 but not for α = 0.01, we concluded that the result is significant at α = 0.05 but not at α = 0.01. The correct options B.

To determine the significance of the test statistic at different levels of significance, we need to compare it to critical values associated with the chosen alpha levels.

Given that the test statistic is 2.2, we need to refer to the critical values of the test statistic for a two-tailed test at α = 0.05 and α = 0.01. These critical values are typically obtained from statistical tables or software.

Let's assume the critical value at α = 0.05 is [tex]\( z_{\alpha/2} = \pm 1.96 \)[/tex]and the critical value at α = 0.01 is [tex]\( z_{\alpha/2} = \pm 2.58 \)[/tex](for a standard normal distribution).

If the test statistic falls within the range defined by these critical values, we can conclude that the result is significant at the corresponding alpha level. Otherwise, the result is not significant.

Since the test statistic of 2.2 falls between the critical values of [tex]\( \pm 1.96 \)[/tex] for α = 0.05 but outside the critical values of [tex]\( \pm 2.58 \)[/tex] for α = 0.01, we can conclude that:

The result is significant at α = 0.05 but not at α = 0.01.

Final answer: The result is significant at α = 0.05 but not at α = 0.01.

We compared the test statistic to critical values for α = 0.05 and α = 0.01. Since the test statistic falls within the critical region for α = 0.05 but not for α = 0.01, we concluded that the result is significant at α = 0.05 but not at α = 0.01. This interpretation aligns with standard hypothesis testing procedures.

Complete question

For a hypothesis test of H0:p1 − p2 = 0 against the alternative Ha:p1 − p2 ≠ 0, the test statistic is found to be 2.2. Which of the following statements can you make about this finding?

A)The result is significant at both α = 0.05 and α = 0.01.

B)The result is significant at α = 0.05 but not at α = 0.01.

C)The result is significant at α = 0.01 but not at α = 0.05.

D)The result is not significant at either α = 0.05 or α = 0.01.

E)The result is inconclusive because we don't know the value of p.

The scale of a map is 0.5 inch : 20 miles. on the map, the distance between two cities is 1.5 inches. what is that actual distance between the two cities?

Answers

0.5 inch : 20 miles
1.5 inch-?
1.5*20/0.5=60 (miles)
answer:60 miles

Answer:

60 miles.

Step-by-step explanation:

We have been given that the scale map is 0.5 inch : 20 miles. On the map, the distance between two cities is 1.5 inches. We are asked to find the actual distance between the two cities.

We will use proportions to solve for the actual distance between both cities as:

[tex]\frac{\text{Actual distance}}{\text{Map distance}}=\frac{20\text{ miles}}{\text{0.5 inch}}[/tex]

[tex]\frac{\text{Actual distance}}{\text{1.5 inches}}=\frac{20\text{ miles}}{\text{0.5 inch}}[/tex]

[tex]\frac{\text{Actual distance}}{\text{1.5 inches}}*\text{1.5 inches}=\frac{20\text{ miles}}{\text{0.5 inch}}*\text{1.5 inches}[/tex]

[tex]\text{Actual distance}=20\text{ miles}*3[/tex]

[tex]\text{Actual distance}=60\text{ miles}[/tex]

Therefore, the actual distance between both cities is 60 miles.

An 800 gallon swimming pool is being drained. After five hours, 500 gallons have been drained. If the rate of drainage continues, how long will it take to drain the pool?

A) 0.125 hours

B) 5 hours

C) 8 hours

D) 9 hours

Answers

I think it's 8 hours. If it takes 5 hours to drain 500 gallons, then the rate is 100 gallons drained per hour. So if it continues at this rate, the remaining 300 gallons would be drained in three hours, plus the five spent on the other 500 gallons, so it would be 8 hours for all 80p gallons to empty the swimming pool .

Find an equation in standard form for the ellipse with the vertical major axis of length 18 and minor axis of length 10.

Answers

[tex]\bf \textit{ellipse, vertical major axis}\\\\ \cfrac{(x-{{ h}})^2}{{{ b}}^2}+\cfrac{(y-{{ k}})^2}{{{ a}}^2}=1 \qquad \begin{cases} center\ ({{ h}},{{ k}})\\ vertices\ ({{ h}}, {{ k}}\pm a)\\ \textit{major axis}\ a+a=18\\ \qquad 2a=18\implies \boxed{a=9}\\ \textit{minor axis}\ b+b=10\\ \qquad 2b=10\implies \boxed{b=5} \end{cases} \\\\\\ \begin{cases} h=0\\ k=0\\ a=9\\ b=5 \end{cases}\implies \cfrac{x^2}{5^2}+\cfrac{y^2}{9^2}=1[/tex]

check the picture below.

Answer:

x^2/25 + y^2/81 =1

Step-by-step explanation:

solved it

I need some assistance in figuring this out

Answers

Test if each is a function by the vertical line test. Do this by drawing vertical lines down on each grid unit. If there is more than one point on the line, it isn't a function. So, by using this information, the answer is C.


Ryan flew from Wiley Post to Ponca City and back. Ryan maintained an average rate of 450 mph going to Ponca City and an average rate of 400 mph returning to Wiley Post. If the actual flying time for the round trip was one hour, about how far is it from Wiley Post to Ponca City? Round to nearest mile.

A.
0.47 miles

B.
212 miles

C.
239 miles

D.
3,600 miles

Answers

The answer is B, and here's why.  Set up a table for "there" and "back" and use the distance = rate * time formula, like this:
               d             r            t
there       d           450         t
back        d           400        1-t

Let me explain this table to you.  The distance is d, we don't know what it is, that's what we are actually looking for.  We only know that if we go somewhere from point A to point B, then back again to point A, the distance there is the same as the distance back.  Hence, the d in both spaces.  There he flew 450 mph, back he flew 400 mph.  If the total distance was 1 hour, he flew an unknown time there and one hour minus that unknown time back.  For example, if he flew for 20 minutes there, one hour minus 20 minutes means that he flew 60 minutes - 20 minutes = 40 minutes back.  See? Now, because the distance there = the distance back, we can set the rt in both equal to each other.  If d = rt there and d = rt back and the d's are the same, then we can set the rt's equal to each other.  450t = 400(1-t) and
450t = 400 - 400t and 850t = 400.  Solve for t to get t = .47058.  Now, t is time, not the distance and we are looking for distance. So multiply that t value by the rate (cuz d = r*t) to get that the distance one way is
d = 450(.470580 and d = 211. 76 or, rounded like you need, 212.

Circle A is inscribed in a quadrilateral. What is the perimeter of the quadrilateral?

Answers

AB + CD = BC + DA 
Where A, B, C, and D are points on the quad, and AB is the length of the line A to B, etc. 

Since you know three sides, you can easily solve for the fourth. 

Kara has 90 lollipops, 36 chocolate bars, and 72 gumballs to put in goody bags for her party. What is the largest number of goody bags that Kara can make so that each goody bag has the same number of lollipops, the same number of chocolate bars, and the same number of gumballs?

Answers

the greatest common factor of 90, 36, and 72 = 18

90/18 = 5 lollipops
36/18 = 2 chocolate bars
72/18 = 4 gumballs

answer : Kara can make 18 goody bags, each containing 5 lollipops, 2 chocolate bars, and 4 gumballs

The largest number of goody bags that Kara can make are [tex]18[/tex] .

What is Highest Common Factor ?

Highest or greatest Common Factor is the largest common factor that all the numbers have in common.

We have,

Number of Lollipops [tex]=90[/tex]

Number of chocolate bars [tex]=36[/tex]

Number of gumballs [tex]=72[/tex]

So,

To find the number of bags;

First find out the Highest Common Factor of [tex]90,36,72[/tex];

[tex]90=2*3*3*5[/tex]

[tex]36=2*2*3*3[/tex]

[tex]72=2*2*2*3*3[/tex]

So, from the factors of all numbers we have,

Highest Common Factor [tex]=18[/tex]

Now,

Lollipops [tex]=\frac{90}{18} =5[/tex]

Chocolate bars [tex]=\frac{36}{18} =2[/tex]

Gumballs [tex]=\frac{72}{18} =4[/tex]

So, the largest number of goody bags that Kara can make are [tex]18[/tex] so that each goody bag has [tex]5[/tex] number of lollipops, [tex]2[/tex] number of chocolate bars, and [tex]4[/tex] number of gumballs.

Hence, we can say that the largest number of goody bags that Kara can make are [tex]18[/tex] .

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A turtle is 20 5/6 inches below the surface of a pond. It dives to a depth of 32 1/4 inches. What was the change in the turtles position? Write your answer as a mixed number and show your work.

Answers

alrite, so their change is just their difference, namely 32 1/4 - 20 5/6.

let's change those to "improper" fractions first.

[tex]\bf 20\frac{5}{6}\implies \cfrac{20\cdot 6+5}{6}\implies \cfrac{125}{6} \\\\\\ 32\frac{1}{4}\implies \cfrac{32\cdot 4+1}{4}\implies \cfrac{129}{4}\impliedby \textit{let's use an LCD of \underline{12}}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \cfrac{129}{4}-\cfrac{125}{6}\implies \cfrac{(3\cdot 129)+(2\cdot 125)}{12}\implies \cfrac{387-250}{12}\implies \cfrac{137}{12} \\\\\\ \textit{hmmm 12 goes into 137, 11 times, thus}\quad \boxed{11\frac{5}{12}} \\\\\\ \textit{because}\qquad \cfrac{11\cdot 12+5}{12}\implies \cfrac{132+5}{12}\implies \cfrac{137}{12}[/tex]

Which of the following equations have graphs that are parallel to the graph of the equation y=-3/2x+8?

I. 3x + 2y = 10
II. 2x − 3y = 9
III. 6x + 4y = 28
IV. 3x − 2y = 8

 I and III only
 II and III only
 IV only
 III only

Answers

parallel lines will have the same slope, but different y int
y = -3/2x + 8....slope = -3/2....y int = 8

(I) 3x + 2y = 10
    2y = -3x + 10
    y = -3/2x + 5....slope = -3/2, y int = 5....this IS parallel

(II) 2x - 3y = 9
     -3y = -2x + 9
     y = 2/3x - 3...slope = 2/3, y int = -3....is not parallel

(III) 6x + 4y = 28
       4y = -6x + 28
       y = -3/2x + 7...slope = -3/2, y int = 7....this IS parallel

(IV) 3x - 2y = 8
      -2y = -3x + 8
      y = 3/2x - 4...slope = 3/2...y int = -4...this is not parallel

solution is : I and III

Hey rectangular pan has a link that is for third the with the total area of the pan is 432 in.² what is the width of the cake pan

Answers

check the picture below
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