Use the quadratic formula to determine the exact solutions to the equation.

2x2−5x+1=0



Enter your answers in the boxes.

x =
or x =

Answer:

[tex\large\boxed{\log2-\log4=\log\frac{1}{2}}[/tex]

Step-by-step explanation:

[tex]\text{Use}\ \log_ab-\log_ac=\log_a\dfrac{b}{c}\\\\==========================\\\\\log2-\log4=\log\dfrac{2}{4}=\log\dfrac{1}{2}[/tex]

According to google your answer is c

Answer:

Parallelogram

Step-by-step explanation:

graphing them makes two sets of parallel lines

Answer:

% decrease in the cost= 6114/23782⋅100=25.71%

Step-by-step explanation:

The decrease in the cost =$23782−$17668=$6114

Hence, % decrease in the cost=6114/23782⋅100=25.71%

the decrease is 23782 - 17668 = 6114.

if we take 23782 to be the 100%, what is 6114 off of it in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 23782&100\\ 6114&x \end{array}\implies \cfrac{23782}{6114}=\cfrac{100}{x}\implies 23782x=611400 \\\\\\ x=\cfrac{611400}{23782}\implies x\approx 25.71[/tex]

Hi, hope this helps you. Have a good day. :)

Answer:

A = $5,417.42 (balance of the account)

I = $2,617.42

Answer:

The balance in the account after 12 years is $5417.42

Step-by-step explanation:

* Lets talk about the compound continuous interest

- Compound continuous interest can be calculated using the formula:

 A = P e^rt

• A = the future value of the investment, including interest

• P = the principal investment amount (the initial amount)

• r = the interest rate

• t = the time the money is invested for

- The formula gives you the future value of an investment,

  which is compound continuous interest plus the

  principal.

- If you want to calculate the compound interest only, you need

 to deduct the principal from the result.

- So, your formula is:

 Compounded interest only = Pe^(rt)  - P

* Now lets solve the problem

∵ P = $ 2800

∵ r = 5.5/100 = 0.055

∵ t = 12

∴ A = 2800 e^(0.055 × 12) = $5417.42

* The balance in the account after 12 years is $5417.42

20%

My equation:

15*100=1500

1500/75=20

The answer would be 20% off hope this helped!

ANSWER

The height is 30 feet

EXPLANATION

The volume of a cylinder is calculated using the formula;

[tex]V = \pi {r}^{2} h[/tex]

The diameter is 24 ft. This implies that the radius of the cylinder is 12ft.

We substitute known values to get:

[tex]4320\pi= \pi{(12)}^{2} h[/tex]

[tex]4320\pi=144 \pi h[/tex]

Divide both sides by 144π

[tex]h = 30ft[/tex]

Answer:

3

Step-by-step explanation:

Wire is 4 1/2 feet, or 4.5 feet.

Each smaller wire needs to be 1 1/4 feet, or 1.25 feet.

How many whole 1.25 feet wire can we have from total of 4.5 feet wire?

Let's divide:

\[tex]\frac{4.5}{1.25}=3.6[/tex]

thus we can have 3 whole "1.25 feet long" wire and fractional amount.

Hence, maximum number of smaller pieces is 3

Answer:

The equation is        y = - 1/2 x+7

Step-by-step explanation:

2 x  + 4y = 6  

4y = -2 x +6  

Divide both sides  by 4  

y = - 1/2 x + 3/2  

y=mx+b  

slope m = - 1/2  

The slope of a line parallel to another  line will be the same  

The slope of the required line will be - 1/2  

m= - 1/2 ,point ( 6 , 4 )

Plugging the values of m  and  the point in  

y=mx+b  

4 = -3 + b  

b= 7  

m= - 1/2  

Plug values   y = mx +b  

y = - 1/2 x+7

Answer:

since it double the value multiply by 2

Step-by-step explanation:

Answer:

14 inches

Step-by-step explanation:

i got it right

____________________________________________________

Answer:

The center would be (-8,12).

____________________________________________________

Step-by-step explanation:

First,we're going to have to simplify the equation. Here is the work below:

[tex]x^2+y^2+16x-24y+159=0\\\\(x+8)^2-64+y^2-24y+159=0\\\\(x+8)^2+y^2-24y=-159+64\\\\(x+8)^2+(y-12)^2-144=-159+64\\\\(x+8)^2+(y-12)^2=144-159+64\\\\(x+8)^2+(y-12)^2=49\\\\[/tex]

Now, you must use the "form of a circle" equation in order to find out the center and radius of a circle.

The equation is:

[tex](x-h)^2+(y-k)^2=r^2\\\\r=7\\h=-8\\k=12[/tex]

Since we got the answer of:

[tex](x+8)^2+(y-12)^2=49[/tex]

It matches with our equation of [tex](x-h)^2+(y-k)^2=r^2[/tex]

Our "h" represents the x axis on the graph, our "k" represents our y axis on a graph.

Therefore our x value would be -8 and our y value would be 12.

Your FINAL answer should be (-8,12)

____________________________________________________

[tex] {x}^{2} + {y}^{2} + 16x - 24y + 159 = 0 \\ \\ 1. \: x = \frac{ - 16 + 2i \sqrt{(y - 19)(y - 5)} }{2} \: \frac{ - 16 - 2i \sqrt{(y - 19)(y - 5)} }{2} \\ \\ 2. \: x = - 8 + i \sqrt{(y - 19)(y - 5)} \: \: - 8 - i \sqrt{(y - 19)(y - 5)} [/tex]

Make sure you put a comma between them

Answer:

There are 18 dimes and 12 quarters

Step-by-step explanation:

Remember that

1 Dime =$0.10

1  Quarter=$0.25

Let

x-----> the number of dimes

y-----> the number of quarters

we know that

x+y=30

x=30-y ------> equation A

0.10x+0.25y=4.80

Multiply by 100 both sides

10x+25y=480 ------> equation B

Substitute equation A in equation B and solve for y

10(30-y)+25y=480

300-10y+25y=480

15y=180

y=12 quarters

Find the value of x

x=30-y=30-12=18 dimes

therefore

There are 18 dimes and 12 quarters

Final answer:

To solve this problem, set up a system of equations and solve them simultaneously.

Explanation:

Let's solve this problem using a system of equations.

Let's assume that the number of quarters is 'x' and the number of dimes is 'y'.

We can set up two equations based on the given information:

Solving these equations simultaneously, we can find the values of 'x' and 'y', which represent the number of quarters and dimes respectively.

By substituting the value of x from Equation 1 into Equation 2, we get:

0.25(30 - y) + 0.10y = 4.80

7.50 - 0.25y + 0.10y = 4.80

-0.15y = -2.70

y = 18

Substituting the value of y into Equation 1, we get:

x + 18 = 30

x = 12

Therefore, there are 12 quarters and 18 dimes.

Answer:

it is the 2nd graph

Step-by-step explanation:

The graph of the linear equation is a right-angle triangle whose height is 2000 units and base is 200 units.

It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.

A farmer can spend no more than $4,000 on fertilizer and seeds. The fertilizer costs $2 per pound and seeds cost $20 per pound.

To summarize the situation, the farmer writes the inequality

[tex]\rm 2 y + 20 x \leq 4,000\\\\y \leq 2000 - 10x[/tex]

where y be the number of pounds of fertilizer and x be the number of pounds of seeds.

Then the graph is shown below.

More about the linear system link is given below.

https://brainly.com/question/20379472

Answer:

The total volume of juice in a six-pack is [tex]254.3\ in^{2}[/tex]

Step-by-step explanation:

step 1

Find the volume of one can

The volume of the cylinder (can of juice) is

[tex]V=\pi r^{2} h[/tex]

we have

[tex]r=3/2=1.5\ in[/tex] ----> the radius is half the diameter

[tex]h=6\ in[/tex]

assume

[tex]\pi =3.14[/tex]

substitute

[tex]V=(3.14)(1.5)^{2} (6)[/tex]

[tex]V=42.39\ in^{2}[/tex]

step 2

Find the total volume of juice in a six-pack

Multiply the volume of one can by 6

[tex]42.39*(6)=254.3\ in^{2}[/tex]

The total volume of juice in a six-pack where each can is 6 inches tall and has a diameter of 3 inches is calculated using the volume of a cylinder formula. The total volume is 254.34 in³. This is achieved by calculating the volume of one can and multiplying by six.

To calculate the total volume of juice in a six-pack where each can is 6 inches tall and has a diameter of 3 inches, we first need to find the volume of one can using the formula for the volume of a cylinder, which is V = πr²h. Since the diameter is 3 inches, the radius (r) is half of that, which is 1.5 inches. Plugging the values into the formula, we get:

Therefore, the correct answer is 254.34 in³, which represents the total volume for a six-pack of juice cans.

Answer:

A

Step-by-step explanation:

The arc length is calculated as

arc = circumference × fraction of circle

     = 2π × 6 × [tex]\frac{135}{360}[/tex]

     = 12π × [tex]\frac{3}{8}[/tex]

     = [tex]\frac{36\pi }{8}[/tex] ≈ 14.1 in

Answer

14.1 in

Step-by-step explanation:

Length of the arc formula = circumference of the circle * central angle / 360

circumference of the circle formula = [tex]2\pi r[/tex]

where r is the radius of the circle

Radius = 6 in

central angle = 135 degrees

Length of the arc = [tex]2 \pi * radius* \frac{angle}{360}[/tex]

=[tex]2\pi*6* \frac{135}{360}[/tex]

= 14.137= 14.1 in

Answer:

V = 256 mm3

Hope this helps you out!

Answer:

D,256

Step-by-step explanation:

Use multiplication to do 8*10*3.2 you get 256

Answer:

45 cubic inches

I hope this helped you : )

Step-by-step explanation:

To find the volume you must use the formula ( Volume = Length x Width x Height)

So, ( 5 x 3 x 3 = 45)

45 cubic inches, it’s just l*w*h

Answer:

0.125 m

Step-by-step explanation:

Answer:

0.125 meters

Step-by-step explanation:

There are 100 cm in a meter. 12.5/100= 0.125

im not sure of this but I think u have to subtract 37 from 12 and that is 25

I don't know e thats any helpful

Answer:

median:36.5

mean:37

Step-by-step explanation:

to find medain put all of the numbers in order. then find the center number

for the mean add all of the numbers together ad divide it by the amount of data points there are

Answer:

median:                                  36.5

mean:                                       37

Step-by-step explanation:

Answer:

The medicine treats swelling

Step-by-step explanation:

"The control group does not receive any medication; the treatment group receives the medication. The patients in the treatment group show reduced signs of swelling. What can Andria conclude from this experiment?"

If she does not give placebo, which she should, then we can only conclude that the medication might be effective. Might, because the thought of the medicine fixing swelling might actually be what helps them.

This takes us to the next topic- placebo experiments.

Most good experiments, to elaborate, are "double blind," one group receives a placebo, and another the medication, and neither know which.

In this case, assuming that the placebo was ineffective, we can conclude that the medicine is effective in treating swelling.

Answer:

1/6

Step-by-step explanation:

Candy = 5/6

5 people = 5/6

1 person

= 5/6 ÷ 5

= 5/6 x 1/5

= 1/6

Answer:

1/6

Step-by-step explanation:

Answer:

1. LA = 92 sq. m.,  SA = 132 sq. m.

2. LA = 460 sq. in.,  SA = 700 sq. in.

3. LA = 118 sq. in.,  SA = 168 in. sq.

4. LA = 468 sq. cm.,  SA = 828 sq. cm.

Step-by-step explanation:

The lateral area is the area of the non-base faces. The surface area is the area of all the faces (so lateral area + area of base).

1.

Lateral area:

There are 2 same triangles each with height and base of 3 and 4, respectively. So

Area of triangle = 1/2 * base * height = 1/2 * 4 * 3 = 6

Since there are 2, so 6 * 2 = 12

Now, the slant height is gotten by using pythagorean theorem on the triangular face.

[tex]4^2+3^2=SlantHeight^2\\16+9=SlantHeight^2\\25=SlantHeight^2\\SlantHeight=5[/tex]

If you look at the side facing away, it is a rectangle with length 10 and width 5, so area of rectangle is length * width = 10 * 5  = 50

The side facing towards us is also a rectangle with dimensions 3 and 10. So area is 3 * 10 = 30

The lateral area is 30 + 12 + 50 = 92

Surface Area:

This is the lateral area we got before (92) + the area of the base.

The base is a rectangle with dimensions 4 and 10. So area = 4 * 10 = 40

The surface area is 92 + 40 = 132

2.

Lateral area:

all the faces are rectangles.

The dimensions of two side faces are 10 and 8. So area would be 2 * (10 * 8) = 2 * 80 = 160

The dimensions of back side and front side is 15 and 10. So area would be 2 * (15 * 10) = 2 * 150 = 300

The lateral area would be 160 + 300 = 460

Surface area:

the surface area is the lateral area (580) + the area of the bases (which is also a rectangle). The dimensions of the bottom and top are  15 and 8. So area of bottom and top  is  2(15 * 8) = 240

Thus, surface area = 460 + 240 = 700

3.

Lateral Area:

There are two rectangles (left and right) with dimensions 8 x 5 and 6 x 5. So area would be 8 * 5 = 40 and 6 * 5 = 30. Area = 40 + 30 = 70

There are two triangles (back and front) with base of 6 and height of 8. The area of both are:

(1/2 * 6 * 8 ) * 2 = 48

Lateral area is 70 + 48 = 118

Surface area:

The surface are would be lateral area (118) PLUS the base, which is a rectangle with dimensions 5 and 10. So area = 5 * 10 = 50.

Total surface area = 118 + 50 = 168

4.

lateral area:

there are 2 rectangles (left and right) with dimensions 10 x 12, and 9 x 12. So the total area would be:

(10*12) + (9*12) = 228

The front and back are trapezoids. The area of trapezoid is 1/2 (base1 + base2) * height.

The height is 8 and both the bases are 10 and 20. Plugging it into the formula, we get are of 2 of the trapezoids to be:

2 * (1/2(base1+base2)*height)

2 * (1/2(10+20)*8)

= 240

The lateral area = 228 + 240 = 468

surface area:

it will be 468 (lateral area) PLUS the area of the bases. The bottom base is a rectangle with dimensions 20 and 12. So the area of the base is 20 * 12 = 240

The top is a rectangle with dimensions 12 and 10. So area = 12 * 10 = 120

Surface area = 468 + 240 + 120  = 828

Answer:

1. B

2. B

Step-by-step explanation:

** Attached picture of the situation

The bird caught the fish at point A, flew until B (which is 100 yds away, dropped the fish at C (which is horizontally 50 yards from A).

1.

We want the angle that the bird creates with the water (horizontal). It is angle BAC. With respect to the right triangle, we can say that we know "hypotenuse" and "adjacent" side to angle BAC. cosine relates hypotenuse and adjacent, thus we can write:

[tex]Cos(BAC)=\frac{50}{100}\\Cos(BAC)=\frac{1}{2}\\BAC=Cos^{-1}(\frac{1}{2})\\BAC=60[/tex]

correct answer is B

2.

Here, we want to find the distance (length) of segment BC. With respect to the angle BAC (we found to be 60), we can say BC is "opposite". We know hypotenuse to be 100. So let's use sine, since sine is ratio of opposite to hypotenuse. Thus, we can write:

[tex]Sin(BAC)=\frac{BC}{100}\\Sin(60)=\frac{BC}{100}\\BC=Sin(60)*100\\BC=86.6[/tex]

correct answer is B

The answers should be B)60 and B) 86.6

For this case we have a function of the form[tex]y = f (x)[/tex]

Where:

[tex]f (x) = - 4x + 3[/tex]

We must find the value of the function when the variable x is -5.

Then, substituting, [tex]x = -5[/tex]

[tex]f (-5) = - 4 (-5) +3[/tex]

We have that by sign law[tex]- * - = +[/tex]

[tex]f (-5) = 20 + 3\\f (-5) = 23[/tex]

Answer:

[tex]f (-5) = 23[/tex]

ANSWER

[tex]f( - 5)=23[/tex]

EXPLANATION

The given function is

[tex]f(x)=-4x+3[/tex]

To find f(-5), we substitute x=-5 to obtain;

[tex]f( - 5)=-4( - 5)+3[/tex]

We multiply out to obtain:

[tex]f( - 5)=20+3[/tex]

We simplify to get,

[tex]f( - 5)=23[/tex]

Answer:

From the measure the picture provides us, we can conclude that the prism is a cube, which also tells us that all 6 sides of this prism have equal surface area, so we only need to calculate one of them and multiply the result by 6:

The surface area of one side of the cube should be: 2/3 . 2/3 = 4/9 (ft²)

The surface area of the prism should be: 4/9 . 6 = 24/9 = 8/3 (ft²)

A prism is a polyhedron composed of an n-sided polygon basis. The surface area of the prism is 8/3 ft².

A prism is a polyhedron composed of an n-sided polygon basis, a second base that is a translated duplicate of the first, and n additional faces, all of which must be parallelograms, connecting the two bases. All parallel cross-sections to the bases are translations of the bases.

Given the length of the side is 2/3 ft. Therefore, the surface area of the given prism can be written as,

The surface area of the prism = 6s² = 6(2/3)² ft² = 8/3 ft²

Hence, the surface area of the prism is 8/3 ft².

Learn more about Prism:

https://brainly.com/question/12649592

#SPJ2

Answer:

2/9

Step-by-step explanation:

If you meant you want to find U,

1) Divide both side by 2. -> U = 4/9 divided by 2

2) You get U = 4/18, which you can further simplify by dividing 2 on top and bottom to get 2/9

Answer:

125 in³

Step-by-step explanation:

The net will form a cube.

Length of the cube = 5 in.

We will apply the formula for volume, volume = length³,  to find the volume of the cube.

Volume = 5 x 5 x 5 = 125 in³

Answer:

3.2 is the corrext amswr

Step-by-step explanation:

The answer is 3.2 because you only round up if it’s .5 or higher and round down if it’s .4 or lower

Answer:

Step-by-step explanation:

The formula of an area of a circle:

[tex]A=\pi r^2[/tex]

r - radius

The formula of a circumference of a circle:

[tex]C=2\pi r[/tex]

We have:

[tex]C=3\pi[/tex]

Substitute:

[tex]2\pi r=3\pi[/tex]            divide both sides by 2π

[tex]r=1.5[/tex]

Substitute:

[tex]A=\pi(1.5)^2=2.25\pi[/tex]

This answer is correct, I double checked it and got it right on the assignment in OW. :)