A pharmacist found at the end of the day she had 5/4 as many prescriptions for antibiotics then tranquilizers. She had 18 prescriptions all together. How many did she have for tranquilizers?

AnswerB. because x is in denominator

Step-by-step explanation:

Answer:

x = -3 or x = 2

Step-by-step explanation:

It is given a quadratic equation,

(x + 3)(x - 2) = 0

To find the solution of given equation

Let  (x + 3)(x - 2) 0

⇒ either (x + 3) = 0 or (x - 2) = 0

If (x + 3) = 0 then  x = -3

If (x - 2) = 0 then x = 2

Therefore the solution of given equation are

x = -3 or x = 2

Answer:

This is an obtuse, isosceles triangle.

Step-by-step explanation:

The largest angle is greater than 90 degrees (obtuse), and two sides are equal as you can tell by two equal angles (isosceles).

The given triangle can be classified as isosceles and acute triangle.

A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.

Sum of the interior angles of a triangle is 180 degrees.

Given is a triangle.

The three angles of the triangle are 41°, 41° and 98°.

That is, two angles of the triangle are equal. So the sides opposite these two angles are also equal.

So this is an isosceles triangle.

Obtuse triangle has one of the angles greater than 90°.

Acute triangle has all the angles less than 90°.

Here all the angles are less than 90°.

So it is acute.

Hence the given triangle is acute and isosceles triangle.

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Answer:

[tex]\boxed{\text{1. y + 5 = -4(x - 3); \qquad 2. y - 8 = x + 1}}[/tex]

Step-by-step explanation:

Question 1

The point-slope formula for a straight line is

y – y₁ = m(x – x₁)

x₁ = 3; y₁ = -5; m = -4  

Substitute the values

[tex]\boxed{\textbf{y + 5 = -4(x - 3)}}[/tex]

The diagram shows the graph of equation 1 (red) with slope -4 passing through (3,-5).

Question 2

x₁ = -1; y₁ = 8; m = 1  

Substitute the values

[tex]\boxed{\textbf{y - 8 = x + 1}}[/tex]

The diagram shows the graph of equation 2 (green) with slope 1 passing through (-1,8).

Step-by-step explanation:

The sum of the product of a and b and the number c:i

[tex]a\cdot b+c=ab+c[/tex]

The sum of the product of a and b and the number c, written as a mathematical expression, is ab + c.

The question is asking for the sum of the product of a and b and the number c. In mathematical terms, this can be written as an expression: ab + c. This expression first calculates the product of a and b (represented by 'ab') then adds the number c to this product.

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if EF ≅ WV and JK is intersecting both at a right-angle, the distances OK = JP and likewise PG = GO, namely

[tex]\bf 2(4x-3)-8=4+2x\implies 8x-6-8=4+2x\implies 8x-14=4+2x \\\\\\ 6x-14=4\implies 6x=18\implies x=\cfrac{18}{6}\implies x=3[/tex]

Your answer is the third option, x = -2 and x=6

We can see this because the solutions of x^2/2 - 8 = 2x - 2 are going to be where the lines y = x^2/2 - 8 and y = 2x - 2, because this is where the two equations are equal to each other.

Therefore, we can just look on the graph at where the two lines intersect, and see that it happens when x = -2 and x = 6.

I hope this helps!

Answer:

x=-2 and x=6

Step-by-step explanation:

The solution to a graph would be where the two lines intersect. When you look at the graph you plot where they connect

(-2, -6), (6, 10)

The x value is the very first variable in an ordered pair. Therefore, the solution to this graph would be x=-2 and x=6.

5)

[tex]\bf \begin{array}{|cc|cccc|ll} \cline{1-6} sodas&x&\underline{24}&28&\underline{32}&36\\ \cline{1-6} cost&y&\underline{18}&21&\underline{24}&27\\ \cline{1-6} \end{array}~\hspace{9em} (\stackrel{x_1}{24}~,~\stackrel{y_1}{18})\qquad (\stackrel{x_2}{32}~,~\stackrel{y_2}{24}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{24-18}{32-24}\implies \cfrac{6}{8}\implies \cfrac{3}{4}[/tex]

6)

[tex]\bf \begin{array}{|cc|cc|ll} \cline{1-4} year&x&0&12\\ \cline{1-4} \$&y&720&1080\\ \cline{1-4} \end{array}~\hspace{10em} (\stackrel{x_1}{0}~,~\stackrel{y_1}{720})\qquad (\stackrel{x_2}{12}~,~\stackrel{y_2}{1080}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1080-720}{12-0}\implies \cfrac{360}{12}\implies \cfrac{30}{1}\implies 30[/tex]

7)

slope as you should already know is rise/run, or how much something moves in relation something else, namely how much the y-axis go up as the x-axis moves sideways, one moves, the other follows, but the increments will be different, sometimes the same, but usually different.

the y-intercept means, when the graph of the equation touches or intercepts the y-axis, and when that happens x = 0, or the horizontal distance is at bay.

for the slope on  6), 30 or 30/1 means, for every 1 year(x) passed, the worth(y) increased by 30, or jumped by 30 units, so as the x-axis moved 1, the y-axis moved 30.  After 12 years 30 * 12 = 360, and we add the initial 720 and we end up with 1080.

the y-intercept, well, as aforementioned is when x = 0, is year 0.

Answer:

Top:

The rate change is 4.

Bottom:

The rate change is 3.

Step-by-step explanation:

24+4= 28     28+4=32  (and)  32+4=36

18+3=21  21+3=24    (and)  24+3=27

I will get back to you on the rest>

Hope this helped tho! :3

Answer:

  AC = 26

Step-by-step explanation:

AD = DC . . . . . .these segments are marked congruent

8x-1 = 6x+9 . . . substitute the given expressions

2x = 10 . . . . . add 1-6x

x = 5

__

AC = 2·AB = 2(3x-2) = 2(3·5-2) . . . . substitute into expression for AB

AC = 26

Answer:

B+

Step-by-step explanation:

Grades earned in five subjects are;

A,C+,A-,B- and B+

Remaining subject is biology

Total number of subjects will be=6

3.2 gpa as a percentile =86

For her to maintain 3.2 gpa total sum of percentile in the 6 subjects should be at least

6×86=516

Emily total sum of subjects in percentile is 93+77+90+80+87=427

Find the difference , 516-427=89

89 is grade B+

Emily should earn a grade of B+ to keep her 3.2 gpa

Answer:

D

Step-by-step explanation:

Formula

Volume = pi*r^2*h

Givens

r = x

h = 3x

Volume= 242

Solution

242 = pi * x^2 * 3x

242 = 3.14 * 3x^3                    Divide by pi

242/3.14 = 3.14 * 3x^3 / 3.14   Do the division

77 = 3x^3                                 Divide by 3

77/3 = 3x^3 /3

25.69 = x^3                              Take the cube root of both sides.

2.95  = x

The height of the cylinder is 3 times that of the radius of the circle (x)

The answer is 8.85. I suppose the closest answer is 8.

Answer:

75 yd^2.

Step-by-step explanation:

If the width = x yards, the length will be 3x yards.

The perimeter = 2 * length + 2 * width

= 2* 3x + 2*x = 40

6x + 2x = 40

8x = 40

x = 5

So the width is 5 and the length is 15 yards.

The area = 5 * 15 = 75 yd^2.

Answer:

75

Step-by-step explanation:

x=breadth

3x=length

perimeter=2(x+3x)=8x

40=8x

x=5

length=15

breadth=5

area=15*5=75

Answer: 28 km

Step-by-step explanation: For the first 25 minutes, he drove 60 km/h. Since there is 60 minutes in an hour, we know that he drove 25 km. The rest of the journey is 15 minutes. 15 minutes is 1/4 of an hour, so get 1/4 of 12 km/h. This would be 3 km. Add 25 km and 3 km. The distance between the 2 malls is 28 km.

Answer:  The required co-ordinates of the point are (9, 0).

Step-by-step explanation:  We are given to find the co-ordinates of the point that is [tex]\dfrac{3}{5}[/tex] of the way from A(-9,3) to B(21, -2).

Let K be the required point. Then, we mus have

[tex]AK:AB=3:5\\\\\Rightarrow \dfrac{AK}{AK+BK}=\dfrac{3}{5}\\\\\\\Rightarrow 5AK=3AK+3BK\\\\\Rightarrow 2AK=3BK\\\\\Rightarrow AK:BK=3:2.[/tex]

We know that

the co-ordinates of a point that divides the line joining the points (a, b) and (c, d) in the ratio m : n are given by

[tex]\left(\dfrac{mc+na}{m+n},\dfrac{md+nb}{2}\right).[/tex]

For the given division, m : n = 3 : 2.

Therefore, the co-ordinates of the point K are

[tex]\left(\dfrac{3\times21+2\times(-9)}{3+2},\dfrac{3\times(-2)+2\times3}{3+2}\right)\\\\\\=\left(\dfrac{63-18}{5},\dfrac{-6+6}{5}\right)\\\\=\left(\dfrac{45}{5},\dfrac{0}{5}\right)\\\\=(9,0).[/tex]

Thus, the required co-ordinates of the point are (9, 0).

Building and solving an equation, it is found that the coordinates are: (9,0).

C is 3/5 of the way from A to B, thus:

[tex]C - A = \frac{3}{5}(B - A)[/tex]

This is used to find both the x-coordinate and the y-coordinate of C.

First, the x-coordinate, considering [tex]C = x, A = -9, B = 21[/tex].

[tex]C - A = \frac{3}{5}(B - A)[/tex]

[tex]x + 9 = \frac{3}{5}(21 + 9)[/tex]

[tex]x = 18 - 9[/tex]

[tex]x = 9[/tex]

Then, the y-coordinate, considering [tex]C = y, A = 3, B = -2[/tex].

[tex]C - A = \frac{3}{5}(B - A)[/tex]

[tex]y - 3 = \frac{3}{5}(-2 - 3)[/tex]

[tex]y = -3 + 3[/tex]

[tex]y = 0[/tex]

Thus, the coordinates are (9,0).

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Answer:

[tex]f(x)=2(x-2)^{3}(x+2)^{2}[/tex]

Step-by-step explanation:

we know that

2 is a zero of multiplicity 3 of the polynomial

so

we have that

x=2  is a solution of the polynomial

A factor of the polynomial is

[tex](x-2)^{3}[/tex] ----> is elevated to the cube because is a multiplicity 3

and the other solution is x=-2

since the polynomial  is fifth degree, x=-2 must have a multiplicity 2

so

the other factor of the polynomial is  

[tex](x+2)^{2}[/tex] ----> is squared because is a multiplicity 2

therefore

The polynomial is equal to multiply the factors by the leading coefficient

so

[tex]f(x)=2(x-2)^{3}(x+2)^{2}[/tex]

The polynomial function based on the given properties: zeros at 2 (with multiplicity 3) and -2 (with multiplicity 1), leading coefficient of 2, is f(x) = 2(x - 2)³(x + 2).

To construct a polynomial with given zeros and multiplicities, we need to set up a product of binomial factors based on the zeros, with each binomial factor raised to the power of its respective multiplicity. The resulting polynomial is the given function f(x).

For the given properties, the roots are 2 and -2. The root 2 has multiplicity 3 and the root -2 has multiplicity 1. Also, the leading coefficient is 2. So, we can set up the polynomial function as follows:

f(x) = 2(x - 2)3(x + 2)

This represents a fifth degree polynomial function that has the zeros and multiplicities listed, with the leading coefficient of 2.

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Answer:

6

Step-by-step explanation:

You can see how f(x) is now f(8), this implies you have to replace any x's you see with an 8.

So f(8) = 2(8-5) = 2(3) = 6

Answer:

I think that the answer is A.

Answer:

No options is correct.    

Step-by-step explanation:

Given : The product of -4 and 3.

To find : Which expression could be used to determine the product ?

Solution :

The product of -4 and 3 is [tex]-4\times 3=-12[/tex]

To know which expression we solve each options and get whose result is same as ours,

A) [tex](-4)(3)\times (-4)(\frac{1}{4})[/tex]

Solve,

[tex](-4)(3)\times (-4)(\frac{1}{4})= -12\times -1=12[/tex]

B) [tex](-4)(3)+(-4)(\frac{1}{4})[/tex]

Solve,

[tex](-4)(3)+(-4)(\frac{1}{4})= -12+(-1)=-13[/tex]

C) [tex](3)(-4)\times (3)(\frac{1}{4})[/tex]

Solve,

[tex](3)(-4)\times (3)(\frac{1}{4})=-12\times\frac{3}{4}=-9[/tex]

D) [tex](3)(-4)+(3)(\frac{1}{4})[/tex]

Solve,

[tex](3)(-4)+(3)(\frac{1}{4})=-12+\frac{3}{4}=-11.25[/tex]

From the given options, No options will get the product.

Answer:

(2,0) was already given so (-1,0) is the other one.

Step-by-step explanation:

So we are asked to use the quadratic formula.

To find the x-intercepts (if they exist) is use:

[tex]\text{ If } y=ax^2+bx+c \text{ then the } x-\text{intercepts are } (\frac{-b \pm \sqrt{b^2-4ac}}{2a},0)[/tex].

Let's start:

Compare the following equations to determine the values for [tex]a,b, \text{ and }c [/tex]:

[tex]y=ax^2+bx+c[/tex]

[tex]y=4x^2-4x-8[/tex]

So

[tex]a=4[/tex]

[tex]b=-4[/tex]

[tex]c=-8[/tex]

We are now ready to enter into our formula:

[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\frac{4 \pm \sqrt{(-4)^2-4(4)(-8)}}{2(4)}[/tex]

[tex]x=\frac{4 \pm \sqrt{16+16(8)}}{8}[/tex]

[tex]x=\frac{4 \pm \sqrt{16(1+8)}}{8}[/tex]

[tex]x=\frac{4 \pm \sqrt{16}\sqrt{1+8}}{8}[/tex]

[tex]x=\frac{4 \pm 4\sqrt{9}}{8}[/tex]

[tex]x=\frac{ 4 \pm 4(3)}{8}[/tex]

[tex]x=\frac{4 \pm 12}{8}[/tex]

[tex]x=\frac{4(1\pm 3)}{8}[/tex]

[tex]x=\frac{1(1\pm 3)}{2}[/tex]

[tex]x=\frac{1 \pm 3}{2}[/tex]

[tex]x=\frac{1+3}{2} \text{ or } \frac{1-3}{2}[/tex]

[tex]x=\frac{4}{2} \text{ or } \frac{-2}{2}[/tex]

[tex]x=2 \text{ or } -1[/tex]

So the x-intercepts are (2,0) and (-1,0).

(2,0) was already given so (-1,0) is the other one.

Answer:3 hours

Step-by-step explanation:

i did it one edg

The feline expanded in weight compared with the canine's underlying weight which is steady with the data given.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Let c be the feline's unique weight. Let c* be the feline's new weight.

Let d be the canine's unique weight. The d* be the canine's new weight.

The equation is given as,

c = 1.2 c

d = .9 d

c = d

The other equation is given as,

p = (d - c)/d = 1 - c/d

We know that the given condition,

c = d = 0.9 d

Then the equation is written as,

p = 1 - 0.9d/d

p = 1 - 0.9

p = 0.1 or 10%.

Hence, toward the beginning, the rate contrast compared with the canine was,

q = (d - c)/d = 1 - 0.75 = 0.25 or 25%.

That is, the feline weighed not exactly like the canine toward the beginning. Since p < q, the feline expanded in weight compared with the canine's underlying weight — which is steady with the data given.

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Answer:

Option 1

Step-by-step explanation:

Tri means 3. An expression which has 3 terms and the terms are separated by plus or minus:

c^2+c+6

Thus option 1 is correct....

For this case we have that by definition, a trinomial is an algebraic expression formed by the sum or difference of three terms or monomials.

Example:

[tex]ax ^ 2y + cx + dy[/tex]

Thus, the correct option is option 1.

[tex]c ^ 2 + c + 6[/tex]

Three terms are observed.

Answer:

Option 1

Answer:

[tex]\large\boxed{3^\frac{2}{3}}[/tex]

Step-by-step explanation:

[tex]Use\\\\\sqrt[n]{a^m}=a^\frac{m}{n}\\\\(a^n)^m=a^{nm}\\\\a^n\cdot a^m=a^{n+m}\\\\\bigg(\sqrt[4]{9^{15}}\cdot\sqrt{3^3}\bigg)^\frac{2}{27}=\bigg(\sqrt[4]{(3^2)^{15}}\cdot3^\frac{3}{2}\bigg)^\frac{2}{27}=\bigg(\sqrt[4]{3^{2\cdot15}}\cdot3^{\frac{3}{2}}\bigg)^\frac{2}{27}\\\\=\bigg(3^{\frac{30}{4}}\cdot3^\frac{3}{2}\bigg)^\frac{2}{27}=\bigg(3^{\frac{15}{2}}\cdot3^\frac{3}{2}\bigg)^\frac{2}{27}=\bigg(3^{\frac{15}{2}+\frac{3}{2}}\bigg)^\frac{2}{27}[/tex]

[tex]=\bigg(3^{\frac{18}{2}}\bigg)^\frac{2}{27}=\bigg(3^9\bigg)^\frac{2}{27}=3^{9\cdot\frac{2}{27}}=3^\frac{2}{3}[/tex]

Answer:

[tex]\large\boxed{4x^4\sqrt[3]{2x^2}}[/tex]

Step-by-step explanation:

[tex]\sqrt[3]{2x^5}\cdot\sqrt[3]{64x^9}\qquad\text{use}\ \sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}\\\\=\sqrt[3]{2}\cdot\sqrt[3]{64}\cdot\sqrt[3]{x^5x^9}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=\sqrt[3]2\cdot4\cdot\sqrt[3]{x^2x^3x^9}\\\\=4\sqrt[3]2\cdot\sqrt[3]{x^2x^{12}}\\\\=4\sqrt[3]2\cdot\sqrt[3]{x^2x^{4\cdot3}}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=4\sqrt[3]2\cdot\sqrt{x^2(x^4)^3}\\\\=4\sqrt[3]2\cdot\sqrt[3]{x^2}\cdot\sqrt[3]{(x^4)^3}\qquad\text{use}\ \sqrt[n]{a^n}=a\\\\=4\sqrt[3]{2x^2}\cdot x^4\\\\=4x^4\sqrt[3]{2x^2}[/tex]

Answer: it's c to put it simply

Step-by-step explanation:

Every check has an extraordinary password and changes often- You’ll probably have to finish a DBA or brief cellphone call along with your instructor to advantage get entry.

The comfortable password generator gives more protection towards unauthorized accounts getting right of entry by way of making it simpler for users to create robust passwords. LastPass gives a password generator this is easily handy on their internet site and mechanically shape-fills and syncs throughout more than one gadget to assist users to save time.

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Answer: Choice C

x represents time and x is positive; y value is 45 times more than the x value

==================================

Explanation:

The inequality y > 45x is the same as y > 45*x

We have y greater than 45*x meaning that y is 45 times more than the x value.

As an example, if x = 2, then 45*x = 45*2 = 90 meaning that y must be larger than 90 if you picked x = 2. In this scenario, x = 2 means that if you traveled for 2 hours then you must have gone more than 90 miles in total distance.

Answer:

I think the answer is d

Step-by-step explanation:

since the graph is a lot bigger than the females, but the box thing is in about the same spot as the females ( you know what i mean), but i'm not 100% sure, but i think its the safest answer

Answer:

the cost of rib eye steak dinner = $22.47

the cost of grilled salmon dinners= $10.57 .....

Step-by-step explanation:

Let x be the rib eye steak dinner.

Let y be the grilled salmon dinner.

According to the first given statement:

12x+27y= $554.98    (equation 1)

According to the second statement:

26x+9y=$584.36      ( equation 2)

Lets take a look at the 1st equation:

12x+27y= $554.98

12x=$554.98- 27y

x=$554.98- 27y/12

Now substitute the value of x in 2nd equation:

26x+9y=$584.36

26($554.98- 27y/12)+9y=$584.36

26(554.98- 27y)+9y=584.36*12

14429.48-702y=7012.32

-702y=7012.32-14429.48

-702y= -7417.16

y= 7417.16/702

y=$10.57

Now substitute the value of y in equation 1:

12x+27y= $554.98

12x+27(10.57)=554.98

12x+285.39 = 554.98

Move the constant to the R.H.S

12x=554.98-285.39

12x=269.59

Divide both the terms by 12

12x/12=269.59/12

x=$22.47

Thus the cost of rib eye steak dinner = $22.47

the cost of grilled salmon dinners= $10.57 .....

D) two parabolas one facing down with a vertex at 0, 3 and one facing up with a vertex at 0, negative 3

First of all, let's rewrite the equations in a mathematical language:

[tex]y=\frac{3}{4}x^2-3[/tex]

Since the leading coefficient, the number that accompanies [tex]x^2[/tex] is positive, that is, its value is 3/4, then the parabola opens upward. On the other hand, the vertex can be found as:

[tex](h,k)=\left(-\frac{b}{2a},f\left(-\frac{b}{2a}\right)\right) \\ \\ a=3/4 \\ b=0 \\ c=-3 \\ \\ h=-\frac{0}{2(3/4)}=0 \\ \\ k=f(0)=\frac{3}{4}(0)^2-3=-3 \\ \\ \\ \boxed{Vertex \rightarrow (h,k)=0,-3}[/tex]

[tex]y=-\frac{3}{4}x^2+3[/tex]

Since the leading coefficient is negative, that is, its value is -3/4, then the parabola opens downward. Similarly the vertex can be found as:

[tex](h,k)=\left(-\frac{b}{2a},f\left(-\frac{b}{2a}\right)\right) \\ \\ a=-3/4 \\ b=0 \\ c=3 \\ \\ h=-\frac{0}{2(-3/4)}=0 \\ \\ k=f(0)=-\frac{3}{4}(0)^2+3=3 \\ \\ \\ \boxed{Vertex \rightarrow (h,k)=0,3}[/tex]

Both graph are shown below and you can see that the conclusion of our problem is correct.

if the circle has a diameter of 25.2, its radius is half that or 12.6.

[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\pi \theta r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ \cline{1-1} r=12.6\\ \theta =168 \end{cases}\implies s=\cfrac{\pi (168)(12.6)}{180} \\\\\\ s=11.76\pi \implies \implies \stackrel{\pi =3.14~\hfill }{s=36.9264}\implies \stackrel{\textit{rounded up}}{s=36.93}[/tex]

Answer:

4 ropes.

Step-by-step explanation:

There are 100 cms in a meter.

So 10 meters = 10* 100

= 1000 cms.

1000 / 210 = 4  ropes with  160 cms remaining.