f(x) = 4x^4 – 2x^3 – 3x^2 + 6x - 9 Find the Zeros Using Descartes' Rule of Signs

Answer:

If I'm correct she bought 5 pounds of coffee.

Step-by-step explanation:

$70 (gift card)

-$26.80 (remainder on g.c.)

= $43.20 ($ spent on money)

$43.20/ $8.64 = 5

(remainder)/ cost per lb. = lbs of coffee bought

Answer: She bought 5 pounds of coffee

Step-by-step explanation:

This situation can be represent by the equation

70 - 8.64 x = 26.80  where x is the number of coffee she bought.   solve for x

-70                   -70

-8.64x = -43.20

x = 5

Answer:

x=3

Step-by-step explanation:

-2x-3=-9

Add 3 to each side

-2x-3+3=-9+3

-2x = -6

Divide by -2

-2x/-2 = -6/-2

x = 3

Answer:

x =3

Step-by-step explanation:

[tex]-2x-3=-9. \\ - 2x = - 9 + 3 \\ - 2x - 6 \\ \frac{ - 2x}{ - 2} = \frac{ - 6}{ - 2} [/tex]

[tex]x = 3[/tex]

Answer:

14.

Step-by-step explanation:

From the question given, we obtained the following information:

When angle θ = 60°

Adjacent = 7

Hypothenus = s

When angle θ = 30°

Opposite = 7

Hypothenus = s

We can use any of the above to determine the value of 's'.

Here, we shall consider when angle θ is 60°.

Cos θ = Adjacent /Hypothenus

Angle θ = 60°

Adjacent = 7

Hypothenus = s

Cos θ = Adjacent /Hypothenus

Cos 60° = 7/s

But Cos 60° = 1/2

1/2 = 7/s

Cross multiply

s = 2 x 7

s = 14

Therefore, the value of 's' is 14

Answer:

1. a. b = - 8

b. x = 8

c. x = 11

d. x = 5

2. 12 soccer balls and 8 basketballs can be purchased.

Step by step explanation

a. [tex] - 14 + 6b + 7 - 2b = 1 + 5b[/tex]

Calculate the sum

[tex] - 7 + 6b - 2b = 1 + 5b[/tex]

Collect like terms

[tex] 7 + 4b = 1 + 5b[/tex]

Move variable to L.H.S and change it's sign

Similarly, Move constant to R.H.S and change its sign

[tex]4b - 5b = 1 + 7[/tex]

Collect like terms

[tex] - b = 8[/tex]

Change the signs on both sides of the equation

[tex]b = - 8[/tex]

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

b. [tex] \frac{5x + 10}{ - 6} = - 5[/tex]

Apply cross product property

[tex]5x + 10 = - 5 \times ( - 6)[/tex]

Multiply the numbers

[tex]5x + 10 = 30[/tex]

Move constant to R.H.S and change its sign

[tex]5x = 30 - 10[/tex]

Calculate the difference

[tex]5x = 20[/tex]

Divide both sides of the equation by 5

[tex] \frac{5x}{5} = \frac{20}{5} [/tex]

Calculate

[tex]x = 4[/tex]

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

c. [tex] - 15 = \frac{ - 8x - 17}{7} [/tex]

Apply cross product property

[tex] - 15 \times 7 = - 8x - 17[/tex]

Multiply the numbers

[tex] - 105 = - 8x - 17[/tex]

Swap the sides of the equation

[tex] - 8x - 17 = - 105[/tex]

Move constant to R.H.S and change its sign

[tex] - 8x = - 105 + 17[/tex]

Calculate

[tex] - 8x = - 88[/tex]

Change the signs on both sides of the equation

[tex]8x = 88[/tex]

Divide both sides of the equation by 8

[tex] \frac{8x}{8} = \frac{88}{8} [/tex]

Calculate

[tex]x = 11[/tex]

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

D. [tex]5 = 6x + 5(x - 10)[/tex]

Distribute 5 through the parentheses

[tex]5 = 6x + 5x - 50[/tex]

Collect like terms

[tex]5 = 11x - 50[/tex]

Swap both sides of the equation

[tex]11x - 50 = 5[/tex]

Move constant to R.H.S and change its sign

[tex]11x = 5 + 50[/tex]

Calculate the sum

[tex]11x = 55[/tex]

Divide both sides of the equation by 11

[tex] \frac{11x}{11} = \frac{55}{11} [/tex]

Calculate

[tex]x = 5[/tex]

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

2.

Solution,

No.of students in soccer = x

No.of students in basketball = y

Total no.of students = 20

i.e x + y = 20 → equation ( i )

Cost of soccer ball = $ 7

Cost of basketball = $ 10

Total budget = $ 164

i.e 7x + 10 y = 165 → equation ( ii )

In equation ( i ),

x + y = 20

Move 'y' to R.H.S and change its sign

x = 20 - y

Put the value of x in equation ( i )

[tex]7(20 - y) + 10y = 164[/tex]

[tex]140 - 7y + 10y = 164[/tex]

[tex]3y = 164 - 140[/tex]

[tex]3y = 24[/tex]

[tex]y = \frac{24}{3} [/tex]

[tex]y = 8[/tex]

Now, put the value of y in equation ( i ) ,

x + y = 20

[tex]x + 8 = 20[/tex]

[tex]x = 20 - 8[/tex]

[tex]x = 12[/tex]

Hence, 12 soccer balls and 8 basketballs can be purchased.

Hope this helps...

Best regards!!

Answer:

1. b = -8

2. x = 8

3. x = 11

4. x = 5

hope that helpwd

Answer:

Step-by-step explanation:

y = -|x| + 1

Start with the absolute value function: y = |x|. Reflect it over the x-axis by making it y = -|x|. Finally, shift up 1 unit by adding one, getting a final answer of y = -|x| + 1.

Answer:

Probability of the teacher or other staff is 0.7143

Step-by-step explanation:

pr(teacher or other staff) = pr(teacher) + pr(other staff) - pr(teacher and other staff)

Total number of tickets = 1050

Number of tickets sold to teachers = 515

Number of tickets sold to other staff = 235

pr(teacher) = [tex]\frac{515}{1050}[/tex]

                 = 103 [tex]\frac{2}{10}[/tex]

                 = 0.4905

pr(other staff) = [tex]\frac{235}{1050}[/tex]

                    = 47 [tex]\frac{2}{10}[/tex]

                  = 0.2238

Since the picking of the wining ticket is mutually exclusive, then;

pr(teacher and other staff) = 0

Thus,

pr(teacher or other staff) = 0.4905 + 0.2238 - 0

                                         = 0.7143

Answer:

a proper fraction

Answer:

B

Step-by-step explanation:

Answer:

104

Step-by-step explanation:

:D

Answer:

y=-5x+16

Explanation:

We already know the slope, and in y=mx+b, m is the slope. So now we have y=-5x+b.

Next, since we do not know the y-intercept, we can substitute the y and x values we are given in the current equation we have, y=-5+b. Now we have 6=-5(2)+b.

Now we can solve for b.

6=-10+b

16=b. We know that b=16.

Therefore, the equation is y=-5x+16

Answer:

0.7

Step-by-step explanation:

multiply 2.5 by 2 first

5-4.3=0.7

Answer:

1) A. 5 + 2.75 * S ≤ 21

2) 5

Step-by-step explanation:

Well there is an initial price of $5 and $2.75 per stop, and she can only spend less than or equal to $21 we can make the following inequality,

5 + 2.75 * S ≤ 21,

Meaning, Q.1 is A

Now #2 is 5 stops because if we plug in 5 for s we get 18.75.

Thus, the most amount of stops she can afford is 5.

Hope this helps :)

Answer:

see explanation

Step-by-step explanation:

2πr (230/360) = 2(3.142)(40) = 160.59 cm = circumference

160.59 = 2πr

base radius = 25.56 cm

Use pythagorean formula for semi-vertical height

40² = h² + 25.56²

h = 30.77 cm

volume = 1/3πr²h

V = 1/3(3.142)(25.56)²(30.77) = 21,053.98 cm³

Answer:

5x² and 7x² are like terms because they contain x².

3x and 8x are like terms because they contain x.

10 and 11 are like terms because they are constants.

Step-by-step explanation:

Let's recall that the definition of like terms is that they are terms that contain the same variables raised to the same power and only like terms can be combined.

Upon saying that, we have:

5x² and 7x² are like terms because they contain x²

3x and 8x are like terms because they contain x

10 and 11 are like terms because they are constants.

Answer:

3²

Step-by-step explanation:

We have to use BPEMDAS Order of Operations:

B - Brackets

P - Parenthesis

E - Exponents

M - Multiply

D - Divide

A - Addition

S - Subtraction

We use this order left to right. Since we have parenthesis, we look at that first. Inside, we have division and exponents. Since exponents come first, we have to evaluate 3² first.

Answer:

square the 3

Step-by-step explanation:

In the order of operations, you must do the exponent inside the parentheses first, so the first step is:

4(27 ÷ 3²) =

= 4(27 ÷ 9)

Answer: square the 3

Answer:

[tex]\large \boxed{\sf \ \ y=(x-4)^2-1 \ \ }[/tex]

Step-by-step explanation:

Hello,

[tex]y = x^2-8x+15\\ \\\text{*** we need to complete the square ***} \\ \\y=(x-4)^2-4^2+15=(x-4)^2-16+15=(x-4)^2-1[/tex]

And then the vertex is (4, -1) and as a > 0 the vertex is a minimum.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer: I hope it helps :)

Step-by-step explanation:

1.

[tex]Hypotenuse =x\\Opposite =y \\Adjacent =6\\\alpha = 6\\Let's\: find\: the \:hypotenuse\: first\\Using SOHCAHTOA\\Cos \alpha = \frac{adj}{hyp} \\Cos 60 = \frac{6}{x} \\\frac{1}{2} =\frac{6}{x} \\Cross\:Multiply\\x = 12\\Let's\: find\: y\\Hyp^2=opp^2+adj^2\\12^2=y^2+6^2\\144=y^2+36\\144-36=y^2\\108=y^2\\\sqrt{108} =\sqrt{y^2} \\y=6\sqrt{3}[/tex]

2.

[tex]Opposite =x\\Hypotenuse = 46\\Adjacent =y \\\alpha =60\\Using \: SOHCAHTOA\\Sin \alpha =\frac{opp}{adj} \\Sin 60=\frac{x}{46}\\\\\frac{\sqrt{3} }{2} =\frac{x}{46} \\2x=46\sqrt{3} \\x = \frac{46\sqrt{3} }{2} \\x =23\sqrt{3} \\\\Hyp^2=opp^2+adj^2\\46^2=(23\sqrt{3} )^2+y^2\\2116=1587+y^2\\2116-1587=y^2\\529=y^2\\\sqrt{529} =\sqrt{y^2} \\y = 23[/tex]

3.

[tex]Hypotenuse = u\\Opposite =6\sqrt{3} \\Adjacent = v\\\alpha =60\\Sin\: 60 = \frac{6\sqrt{3} }{u} \\\frac{\sqrt{3} }{2} =\frac{6\sqrt{3} }{u} \\12\sqrt{3} =u\sqrt{3} \\\\\frac{12\sqrt{3} }{\sqrt{3} } =\frac{u\sqrt{3} }{\sqrt{3} } \\u = 12\\Hyp^2=opp^2+adj^2\\12^2= (6\sqrt{3} )^2+v^2\\144=108+v^2\\144-108=v^2\\36 = v^2\\\sqrt{36} =\sqrt{v^2} \\\\v =6[/tex]

4.

[tex]Hypotenuse = a\\Opposite =18 \\Adjacent = b\\\alpha =45\\Tan \alpha = opp/adj\\Tan \:45 =18/b\\1=\frac{18}{b}\\ b = 18\\\\Hyp^2=Opp^2+Adj^2\\a^2 = 18^2+18^2\\a^2=324+324\\a^2=648\\\sqrt{hyp^2} =\sqrt{648}\\ \\a =18\sqrt{2}[/tex]

5.

[tex]Hypotenuse = 13\sqrt{2}\\ Opposite =x\\Adjacent = y\\\alpha =45\\Sin\:\alpha = opp/hyp\\Sin 45=x/13\sqrt{2}\\ \\\frac{\sqrt{2} }{2} =\frac{x}{13\sqrt{2} } \\2x=26\\2x/2=26/2\\\\x = 13\\\\Hyp^2=opp^2+adj^2\\(13\sqrt{2})^2=13^2+y^2\\ 338=169+y^2\\338-169=y^2\\169=y^2\\\sqrt{169} =\sqrt{y^2} \\13 = y[/tex]

it is isosceles triangle as you see

so that 62 = other unknown angle

as it is a triangle interior angles sum = 180

124 + x = 180

x = 180 - 124

x = 56

Answer:

D

Step-by-step explanation:

the domain of 3^x  is (-∞,∞) and the range is (0,∞)

the domain of 3^x-5 is (-∞,∞) and the range is (-5,∞)

the domain doesn't change, the range (-5,∞)

Answer: C) P(y) = 150(y – 15) – 125y

Step-by-step explanation:

Hi, to answer this question we have to write an equation:

Profit = revenue - cost

Cost: a watch store paid $125 per watch for a shipment of watches

Cost = 125 y

Where y is the number of watches in the shipment

Revenue: sold all but 15 watches from the shipment for $150 per watch

Revenue = 150(y-15)

Profit(y) = 150(y – 15) – 125y

So, the correct option is:

C) P(y) = 150(y – 15) – 125y

Feel free to ask for more if needed or if you did not understand something.

Answer:

Step-by-step explanation:

[tex]In -an-obtuse -triangle;R^2>P^2+Q^2\\\\Largest-side = R\\\\.2nd -largest side =Q\\\\3rd -largest = P\\\\R^2>P^2+Q^2\\15^2 >6^2+8^2\\225>36+64\\225>100[/tex]

I hope it helps :)

Answer:

6x²-x-15

degree: second

leading coefficient : 6 , -1

constant : -15

Step-by-step explanation:

(2x + 3) (3x – 5)=

6x²+9x-10x-15=

6x²-x-15

degree: second

leading coefficient : 6 , -1

constant : -15

Answer:

20 miles

Step-by-step explanation:

I'm not sure if that is exactly how you solve it but

If its

8x+4 as the equation and x is the number of hours run

the total number of miles run should be 20 miles

8(2)+4=20

Answer:

20 miles

Step-by-step explanation:

miles already covered = 4

rate of speed = 8miles / hour

miles to be covered = 8 miles/hr× 2 hr= 16 miles ( because distance is velocity × time)

total miles covered = 16 + 4 = 20 miles.

Answer:

1.148 repetent

Step-by-step explanation:

hope this helps

Answer:

false!

Step-by-step explanation:

i just answered true and it was false. so false is correct!

The statement that the horizontal cross-sectional shapes of the given prism are all congruent is false.

Prisms are three-dimensional shapes that have its two ends to be parallel and congruent

The given prism is a trapezoidal prism.

For the horizontal sectional shapes given prism to be congruent, the prism must be cut through the middle

Since the prism can be divided at any point, then the given statement is false

Read more about prisms at:

https://brainly.com/question/1972490

#SPJ2

Answer:

The diagonal of kite intersect at the point p is C. 68°

Answer/Step-by-step explanation:

Surface area of cylinder = 2πrh + 2πr²

Surface area of the cylinder with,

height (h) = 4 ft

radius (r) = 5 ft

Surface area = 2*3.14*5*4 + 2*3.14*5²

= 125.6 + 157

= 282.6 ft²

Surface area of the cylinder with,

height (h) = 12 yd

radius (r) = 3 yd

Surface area = 2*3.14*3*12 + 2*3.14*3²

= 282.74 yd²

Answer:

Step-by-step explanation:

Given figure : Trapezoid

Base sides,

a = 2.5

b = 7.5

Height ( h ) = 2.5

Now, finding the area:

[tex] \frac{1}{2} (a + b) \times h[/tex]

Plug the values

[tex] = \frac{1}{2 } \times (2.5 + 7.5) \times 2.5[/tex]

Calculate the sum

[tex] = \frac{1}{2} \times 10 \times 2.5[/tex]

Reduce the numbers with G.C.F 2

[tex] = 5 \times 2.5[/tex]

Calculate the product

[tex]12.5 \: \: {units}^{2} [/tex]

Hope this helps...

Best regards!

Answer:

A

Step-by-step explanation:

I'm certain the answer is this, and I understand that you are in a hurry. I can update it anytime you'd like to see the explanation

Answer:

8.3 %

Step-by-step explanation:

Mayelle earns $18000 per year. Mayelle earning is increased by $19500, to calculate the percentage increase in earnings, we divide the difference between earnings after increase and earnings before increase by the earnings before increase and then multiply the result by 100. The percentage increase is given by:

Increase in pay = (Earnings before increase - earnings after increase) / Earnings before increase × 100%

Increase in pay = ($19500 - $18000)/ $18000 × 100% = 8.3 %