Out of 150 coins, 90 are quarters. Of the remaining coins, 40% are
nickels and the rest are dimes and pennies. There are 5 dimes for
every penny. How many pennies are there?
A) 3
B) 4
C)6
D) 12

The matrix AB = [tex]\left[\begin{array}{ccc}-2&16&11\\7&46&-3\\11&26&-9\end{array}\right][/tex]

Given,

In the question:

The matrix is given as:

A = [tex]\left[\begin{array}{ccc}-4&-3&5\\-5&-4&-2\\-1&-2&-4\end{array}\right][/tex]   & B = [tex]\left[\begin{array}{ccc}3&-4&-1\\-5&-5&1\\-1&-3&2\end{array}\right][/tex]

To find the AB :

Now, According to the question:

AB =  [tex]\left[\begin{array}{ccc}-4&-3&5\\-5&-4&-2\\-1&-2&-4\end{array}\right][/tex]  [tex]\left[\begin{array}{ccc}3&-4&-1\\-5&-5&1\\-1&-3&2\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-2&16&11\\7&46&-3\\11&26&-9\end{array}\right][/tex]

The basic Addition and Multiplication:

= -4 x 3 + (-3)x (-5) + 5 x (-1) = -12 +15 -5 = -2

= (-4) x (-4) + (-3)x (-5) + 5x (-3) = 16 + 15 -15 = 16

=(-4)x (-1) + (-3) x 1 + 5x 2 = 4 - 3 +10 = 11

= (-5) x 3 +(-4) x(-5) + (-2) x (-1) = -15 + 20 +2 = 7

= (-5) x(-4) + (-4)x (-5) + (-2) x (-3) = 20 + 20 + 6 = 46

= (-5) x (-1) + (-4) x 1 + (-2) x 2 = 5 - 4 - 4 = -3

= (-1) x 3 + (-2) x (-5) + (-4) x(-1) = -3 + 10 +4 =  11

=(-1) x(-4)+ (-2)x (-5) + (-4) x (-3) = 4 + 10 + 12 = 26

= (-1) x(-1) + (-2) x 1 + (-4) x 2 = 1 - 2 +(-8) = -9

Hence, The matrix AB = [tex]\left[\begin{array}{ccc}-2&16&11\\7&46&-3\\11&26&-9\end{array}\right][/tex]

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A real world situation that could be modeled by the expression, 300+7x is that Bob bought goods for $300 and then bought 6 pens that cost x dollar each.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both

In this case, Bob bought goods for $300 and then bought 6 pens that cost x dollar each. The total cost will be:

= 300 + (7 × x)

= 300 + 7x

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Answer:

Tan a =1

Step-by-step explanation:

TRIG identity:

Tan ( a+b) =  (tan a + tan b )/ (1 - tan a  tan b)     Sub in the given values

      -2       = ( tan a + 3) / ( 1 - 3 tan a)

-2 + 6 tan a = tan a + 3

5 tan a = 5

  tan a = 1

Answer:

-x^5+2x³-x²-1x-1

Step-by-step explanation:

First order the terms based on highest degree or exponent.

-x^5+2x³-x²-3x¹+2x-1

Next combine like terms.

-3x¹ is simply -3x so -3x+2x = -1x

-x^5+2x³-x²-1x-1

The statement that are correct from the graph is:

Some input values are negative.

some output values are negative.

Some input values are integers.

Some output values are integers.

From the graph:

The x value is -2,-4 that is negative.

so the some inputs are negative.

Y has values -2 ,-4 which are negative.

So the some outputs are negative.

The point values from the graph is -4,-2,0,2,4 which belong to integers.

So some input values and output values are integers.

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Answer:

Step-by-step explanation:

they are expecting you to know a few things.

first,  that ∠x   is asking for the interior angle of the labeled angle, here they call it  1 , so find that angle and look at the inside of the triangle,  it's also referred to as the minor angle.

second, they are expecting you to know how many degrees it is around the interior or a triangle... do you know?

then , just take that number and subtract the two given numbers to find the final number ,  or the  ∠1

got it?

Answer:

[tex]250\pi[/tex] cm³

Step-by-step explanation:

If the radius is 20 cm, the diameter is 10 cm.

Thus, the volume is [tex]\pi(10^2)(25)=250\pi[/tex] cm³.

Answer:

The answer to the question is B or 8

Step-by-step explanation:

this is because ther is 3x meaning three time what ever the answer is and because 8x3=24 it is equal to 24 so 24 is less than or equal to 24 hence the corr6 answer is 8.

Answer:

the answer is 8

Answer:

40/9

Step-by-step explanation:

Answer: there are 4 ways the committee can be formed

Step-by-step explanation:

Answer:(-7, infinite down)

Step-by-step explanation: -7,-8,-9...

Answer:

if what I think you want is the number of bachelor degrees from from 1970 to 2014 for both men and women is then:

men: 617.6

women: 940.8

Step-by-step explanation:

from 1970 to 2014 it is 44 years so we plug 44 into x for both equations

Men:

y = 3.9(44) + 446

y = 171.6 + 446

y = 617.6

Women:

y = 14.2(44) + 316

y = 624.8 + 316

y = 940.8

Answer:

[tex]10\sqrt{6}[/tex] feet by [tex]\frac{20}{3}\sqrt{6}[/tex] ft

Step-by-step explanation:

If the length is [tex]l[/tex], then the width is [tex]\frac{2}{3}l[/tex].

Using the formula for the area of a rectangle,

[tex]l \cdot \frac{2}{3}l=400 \\ \\ \frac{2}{3}l^2=400 \\ \\ l^2=600 \\ \\ l=10\sqrt{6}[ \\ \\ \implies w=\frac{20}{3}\sqrt{6}[/tex]

Answer:

-30

Step-by-step explanation:

the order of multiplication doesn't matter

a*b*c = 5*-2*3 = -30

Answer:

Slope = -3/4, y-intercept = -4

Step-by-step explanation:

[tex]6x+8y=-32 \\ \\ 3x+4y=-16 \\ \\ 4y=-3x-16 \\ \\ y=-\frac{3}{4}x-4[/tex]

So, the slope is -3/4 and the y-intercept is -4.

The chicken breast being brought at store B is more expensive than store A as it costs $5.01 more per pound.

Given,

Violet was comparing the price of chicken breast at two stores.

The equation which represents the total cost, in dollars and cents, y, that it costs for x pounds of the chicken breast at Super grocery B is:

y = 11.38x

whereas at store A the chicken breast of 3 pounds costs $19.11.

we are asked to determine how expensive is it per pound to buy chicken breast at store B than store A.

⇒ at store B the total cost is:

y = 11.38x

check the total cost of 3 pounds of chicken breast at store B:

⇒ y = 11.38(3)

since x represents the number of pounds.

⇒ y = $34.14

at store the chicken breast of 3 pounds costs $19.11

⇒ cost difference at both stores for simillar quantity:

⇒ 34.14 - 19.11

= 15.03

The cost of chicken per pound = 15.03/3

= $5.01

Hence the chicken breast at store B is $5.01 more expensive per pound than the chicken breast at store A.

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Answer: 35

Step-by-step explanation:

[tex]f(4)=7(4+2)-7\\\\f(4)=7(6)-7\\\\f(4)=7(5)\\\\f(4)=35[/tex]

Answer:

28

Step-by-step explanation:

Translate words into math -- "warmer" means +, "is" means =

So  D + 50 = 78
D = 78 - 50

D = 28

The equation that models the height of the plant H in terms of number of days is H = 1.875+0.125d and the height of the plant after 15 days is 3.75 inches.

According to the question,

We have the following information:

Initially the plant was 2 inches tall and it grew at an average rate of change of 0.125 inches per day.

2, 2.125, ...

Now, this series will become an arithmetic progression.

Formula to find the nth term:

an = a+(n-1)d

H = 2+(d-1)0.125

H = 1.875+0.125d

Now, the height after 15 days will be:

H = 1.875+0.125*15

H = 1.875+1.875

H = 3.75 inches

Hence, the equation that models the height of the plant H in terms of number of days is H = 1.875+0.125d and the height of the plant after 15 days is 3.75 inches.

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A 270° counterclockwise rotation about the origin is the different one

Rotation simply means turning

In order to answer this question, you need to know some rules about rotation. They are as follows:

1. If a point P, whose position vector is (x,y), is rotated 90° counterclockwise rotation about the origin, the position of the image P' is (-y, x)

2. If a point P, whose position vector is (x,y), is rotated  270° clockwise rotation about the origin, the position of the image P' is (-y, x). This is the same number 1

3. A 90° leftward rotation about the origin is the same as a 90° counterclockwise rotation about the origin. This is the same with number 1

4.  If a point P, whose position vector is (x,y), is rotated  270° counterclockwise rotation about the origin, the position of the image P' is (y, -x). This is different from the other three.

From the graph: A(1, 2), B(2, 4), C(4, 2)

Answer for the different question: A'(2, -1), B'(4, -2), C'(2, -4)

Answer for the same three question: A'(-2, 1), B'(-4, 2), C'(-2, 4)

Therefore, a 270° counterclockwise rotation about the origin is the different one. The 4th option is the answer

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Let the present age of student be x

Present of teacher will be 4x

After 20 years,

Age of student = x + 20

Age of teacher = 4x + 20

According to the given condition after 20 years,

x + 20 = (4x + 20)/2

x + 20 = 2x + 10

2x - x = 20 - 10

x = 10

So student's present age is 10 years while teacher's is 4 x 10 i.e 40 years.

Hope This Helps You!

The ratio of cranberry juice to apple juice to orange juice in the fruit punch is  = 1 : 2 : 3

Let the total quantity of juice is 60 ml .

Now the apple juice is 1/3 of 60 = 20 ml

The orange juice is 1/2 of 60 = 30 ml

Therefore cranberry juice = 60 -(20+30) ml = 10 ml

Now the ratio of cranberry juice to apple juice to orange juice

= 10 : 20 : 30

= 1 : 2 : 3

We can exactly find out how much of one simple quantity is included in the other by simply comparing two amounts of the same units. Ratios can be divided into two smaller groups.

One is the part to the whole ratio; the other is the part to the part ratio. The exact relationship that is between the two distinct entities or groupings is only exactly depicted by the part-to-part ratio.

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The value of g, for a  30-sided regular polygon has an angle measure represented as 6g° is calculated to be 28

The problem is solved using the formula for number of angles for n sided polygon

The formula is (n - 2)180

where n = number of sides

for 30-sided polygon the angles is solved as below

= (n - 2)180

= ( 30 - 2 ) * 180

= 28 * 180

= 5040

this is represented as 6g

each angle is measured 5040 / 30 = 168

6g = 168

g = 28

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Answer: 28

Step-by-step explanation: 168 is the whole polygon, so 6 times 28 is 168 therefore its correct, btw i also did the test

Answer: 1 3\5

explanation :  since the denominator of both fractions are same we can go ahead and the numerators which will make the fraction 16\10 or 8/5 (simplified) and  to make this a mixed numeral 5 fits into 8 once with 3 leftover thus making 1 3/5.

hope this helps .

8 pants wil cost 192 u.m.

10 pants ----> 240u.m

8 pants  ----> x

In a rule of 3, whenever the x is located at the bottom right corner, you always have to multiply upwards and to the right, and then divide the resulting number by the number on the top left. This is the operation you need to make:

x= (8 x 240) / 10

x= 192

Check the attached image to get a better understanding of this process.

8 pants wil cost 192 u.m.

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Proportional quantities are divided into directly and inversely proportional.

Two magnitudes are said to be directly proportional

when we multiply one of them by a number, the other is multiplied by the same number, and when we divide one of them by a number, the other is divided by the same number.

Problem :

If 10 pants cost 240u.m, how much will 8 pants cost?

We have:

[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: + \\ \bold{ Assumption \: { \rightarrow} 10 \: pants \: \rightarrow 240 \: u.m\\\sf \: \: \: \: \: \: \: \: \: Question \rightarrow8 \: pants \rightarrow \: x \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]

As can be seen, the number of pants and the cost are magnitudes directly proportional, and therefore, we put the + sign below the pants and the - sign above.

Therefore we will have:

[tex]\boxed{ \bold{ \: x = \dfrac{240 * 8}{10} = 192 \: u.m} }[/tex]

So the 8 pants cost 192.

Step-by-step explanation:

a polynomial of degree n (that means the highest exponent of x is n) must have n zeroes.

in our case that means 3 zeroes.

the best way to find them is to have the factorial form of the polynomial : to see how several terms are multiplied to give us the polynomial.

the first f(x) gives us exactly that (the second f(x) is just the form with all the multiplications done) :

f(x) = x(x + 6)(x - 2)

when is the product of factors 0 ?

only when at least one factor is 0.

so, let's see,

when is x 0 ? well, x = 0.

when is (x + 6) = 0 ? x = -6.

when is (x - 2) = 0 ? x = 2.

so, the 3 zeroes are

x = -6

x = 0

x = 2

The solution of the trigonometry function is  2√3/3.

What is the trigonometric function?

Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

Given trigonometric function is

sec^(-1) x = csc^(-1) 2

Assume that,

csc^(-1) 2 = z

→ 2 = csc z

→ 1/2 =1/ (csc z)

→ 1/2 =sin z

The trigonometry identity is [tex]\cos x =\sqrt{1-\sin^2x}[/tex].

[tex]\sqrt{1-(\frac{1}{2})^2 } =\cos z[/tex]

→ cos z = √3/2

→ sec z = 2/√3

→ sec z = 2√3/(√3×√3)

→ sec z = 2√3/3

→  z =sec^(-1) ( 2√3/3) = csc^(-1) 2

Putting csc^(-1) 2 = sec^(-1) ( 2√3/3):

sec^(-1) x = sec^(-1) ( 2√3/3)

→ x = 2√3/3

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The average rate of change of the function f(x) on the interval −9≤x≤1 is of:

r = -0.2.

The average rate of change of a function is obtained by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given by the equation presented as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

Over the interval −9≤x≤1, the bounds of the interval are given as follows:

a = -9, b = 1.

From the graph shown by the image presented at the end of the answer, the numeric value of the function at each of these bounds is given as follows:

Hence the average rate of change of the function on the interval is calculated as follows:

r = (1 - 3)/(1 - (-9)) = -2/10 = -0.2.

The graph is shown by the image at the end of the answer.

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