1/5√75 -10√1/2+√125-2√1/2

The quadratic equation that could be solved using the given application of the quadratic formula is x² + 2x - 1 = 3, which in standard form is x² + 2x - 4 = 0. Hence, option C is the right choice.

A standard quadratic equation of the form ax² + bx + c = 0, can be solved using the quadratic formula, which is given as:

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

In the question, we are asked for the quadratic equation, which could be solved using this application of the quadratic formula:

[tex]x = \frac{-2\pm\sqrt{2^2-4(1)(-4)} }{2(1)}[/tex]

To find the quadratic equation for which we use the quadratic formula

[tex]x = \frac{-2\pm\sqrt{2^2-4(1)(-4)} }{2(1)}[/tex]

we compare this equation with the standard quadratic formula,

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

to get a = 1, b = 2, and c = -4, to get the standard quadratic equation, ax² + bx + c = 0, as (1)x² + (2)x + (-4) = 0, or x² + 2x - 4 = 0.

Now, we convert the given options in the standard form to check for the correct choice:

Thus, the quadratic equation that could be solved using the given application of the quadratic formula is x² + 2x - 1 = 3, which in standard form is x² + 2x - 4 = 0. Hence, option C is the right choice.

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Answer:

D

Step-by-step explanation:

[tex]\\ \sf\longmapsto \dfrac{2}{3}+f=\dfrac{1}{5}[/tex]

[tex]\\ \sf\longmapsto f=\dfrac{1}{5}-\dfrac{2}{3}[/tex]

[tex]\\ \sf\longmapsto f=\dfrac{3-10}{15}[/tex]

[tex]\\ \sf\longmapsto f=\dfrac{-7}{15}[/tex]

Answer:

D. -7/15

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

f+ 2/3-2/3= 1/5-2/3

Step 2: Subtract 2/3 from both sides.

f= -7/15

Answer:

[tex](832.156, \ 847.844)[/tex]

Step-by-step explanation:

Given data :

Sample standard deviation, s = 15

Sample mean, [tex]\overline x = 840[/tex]

n = 23

a). 98% confidence interval

[tex]$\overline x \pm t_{(n-1, \alpha /2)}. \frac{s}{\sqrt{n}}$[/tex]

[tex]$E= t_{( n-1, \alpha/2 )} \frac{s}{\sqrt n}}[/tex]

[tex]$t_{(n-1 , \alpha/2)} \frac{s}{\sqrt n}$[/tex]

[tex]$t_{(n-1, a\pha/2)}=t_{(22,0.01)} = 2.508$[/tex]

∴ [tex]$E = 2.508 \times \frac{15}{\sqrt{23}}$[/tex]

  [tex]$E = 7.844$[/tex]

So, 98% CI is

[tex]$(\overline x - E, \overline x + E)$[/tex]

[tex](840-7.844 , \ 840+7.844)[/tex]

[tex](832.156, \ 847.844)[/tex]

Answer:

Sum:

[tex]{ \bf{S _{n} = \frac{n}{2} (2a + (n - 1)d) }} \\ \\ { \sf{2n(n + 3) = \frac{n}{2}(2a + (n - 1)d) }} \\ \\ { \sf{4 {n} + 12=2a + (n - 1)d }} \\ { \sf{2a = 4n - nd + d + 12}} \\ { \sf{2a = n(4 - d) + 12 + d}} \\ { \sf{a = \frac{1}{2}(n(4 - d) + 12 + d) }}[/tex]

Step-by-step explanation:

0 10

0-6

this is the answer. I am sure

The value of numbers are 6 and 10 which are a distance of 2 units from 8 on a number line.

Number line is a horizontal line where numbers are marked at equal intervals one after another form smaller to greater.

We have to given that;

Number line is shown in figure.

And, We have to find the value of numbers which are a distance of 2 units from 8 on a number line.

Now,

We can find the value of numbers as;

⇒ | 8 - 2 | = 6

⇒ | 8 + 2 | = 10

Therefore, The value of numbers are 6 and 10 which are a distance of 2 units from 8 on a number line.

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Answer:

Option B, 187.5 cm³

Step-by-step explanation:

Volume of the triangular prism,

base area × height

= (10×7.5/2)×5

= 187.5 cm³

Answer:

C. x=18

Step-by-step explanation:

note that PQ is the diameter of circle O. this means that angle QRP is a 90 degree angle. now we have 5x=90 so x=18

Answer:

[tex]8\frac{1}{2} x - 6\frac{1}{2}[/tex]

Step-by-step explanation:

[tex]Simplification (show.all.of.the.following)\\(3x-4\frac{1}{2})-(-5\frac{1}{2}x-2)\\3x-4\frac{1}{2}+5\frac{1}{2}x-2\\(3x+5\frac{1}{2}x)-(4\frac{1}{2}+2)\\(8\frac{1}{2})-(6\frac{1}{2})[/tex]

The width in feet of the given solid is 1.136

Density is defined as the ratio of the mass per unit volume

Density = Mass/Volume

Given

Weight = 360 pounds

Density = 3 pounds per cubic foot

Get the mass;

Since W = mg

m = W/g

m = 360/2.2

m =163.64  lbm/kg

Get the volume

From the formula;

Volume = Mass/Density

Volume = 163.64 /3

Volume = 54.55 ft³

Next is to get the width

Volume of the triangular prism = Base Area * Width

Base Area = 48ft²

54.55 = 48w

w = 54.55/48

w = 1.136

Hence the width of the solid in feet is 1.136ft

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Answer:

29/24 or 1 5/24

Step-by-step explanation:

5/8 + 7/12

~Have common denominators

15/24 + 14/24

~Add

29/24

Best of Luck~

Answer:

it's (2a)^6

Step-by-step explanation:

so first you need to write 64a^6 in exponential form simplifying it to 2^6a^6

then multiply the bases which gives you (2a)^6

sorry if I didn't explain it very well but I hope I helped!

Answer:

[tex]\sqrt{64a^{6} } = 8a^{3}[/tex]

8*8 = 64

a^3*a63 = a^6

Step-by-step explanation:

Answer:

{4 |8}. 96. 24

sin4B{3. |9}= ___. = ___ = cos2A

{10|10} 100. 25

{9 |9}

Answer:

True

Step-by-step explanation:

Assuming this is a true or false question, the given formula is used to convert temperatures that are in degrees Celsius to degrees Fahrenheit.

[tex]F(C)=\frac{9}{5} C+32[/tex]

Answer:

= profit in the year 1995 are $880,000

[tex]\\ \sf\longmapsto 256x^2y^2-x^2y^2+49y^2x^2[/tex]

[tex]\\ \sf\longmapsto 256x^2y^2-x^2y^2+49x^2y^2[/tex]

[tex]\\ \sf\longmapsto (256-1+49)x^2y^2[/tex]

[tex]\\ \sf\longmapsto 304x^2y^2[/tex]

Answer:

[tex] \frac{3x {y}^{2} (2xy - {y}^{2} )}{3x {y}^{2} } \\ 2xy - {y}^{2} [/tex]

Answer:

[tex]\boxed{=y(2x-y)}[/tex]

Step-by-step explanation:

[tex]\dfrac{6x^2y^3-3xy^4}{3xy^2} \\\\=\dfrac{3xy^3(2x-y)}{3xy^2} \\\\=y(2x-y)\\\\=2xy-y^2[/tex]

Answer:

Step-by-step explanation:

If a function passes the horizontal line test, then we may conclude that the inverse of the function exists and can be found.

Answer:

Each wire is 0.251 m

Step-by-step explanation:

[tex] = \frac{12.55}{50} \\ \\ = 0.251[/tex]

Answer:

length of wire= 12.55m= 1255cm

Number of pieces= 50

length of each piece=?

length of each piece = 1255/ 50

length of each piece= 25.1cm= 0.251m

mean marks of 100 students was 40.. It was discovered that 53 was misread as 83. Find the actual mean.

Total mean score = 40

[tex]mean \: = \frac{sum \: of \: observation}{number \: of \: observations} [/tex]

sum of observations

= mean × no of observations

= 40×100

= 4000

After the replacement, sum of new observation will be

=4000-83+53

= 3970

mean of new the observation will be

[tex] = \frac{3970}{100} [/tex]

[tex] = 39.7[/tex]

[Hence, the actual mean is 39.7]

Answer:

11. angles on a straight line add up to 180

so 180 -133 equal to b.b=47

12.Vertical opposite angles are equal.

therefore b=50

4x + 2y = -18

2x + y = -9

y = -2x - 9

Answer:

Step-by-step explanation:

a) Input = -9   ⇒ x = -9

y = x² + 3

Plugin x = (-9),

y = (-9)² + 3  

  =  81 +  3                {(-9)² = -9 * (-9) = 81}

y = 84    ---> Output

y = √x - 2

  = √-9 - 2          { i² = -1}

  [tex]= \sqrt{3*3 * i^{2}}-2\\\\=3i -2[/tex]    

y = 3i - 2  ------> Output

b) Output = 0

y  = x² + 3

x² + 3 = 0

x² = -3

[tex]x = \sqrt{-3}=\sqrt{3i^{2}}\\\\x = i \sqrt{3}[/tex]

y = √x -2

0 = √x - 2

√x = 2

Take square,

[tex](\sqrt{x})^{2}=2^{2}\\\x = 4[/tex]

Answer:

6,25

Step-by-step explanation:

Answer:

sin -115° = -0.91

Step-by-step explanation:

Point A is (cos 115°, sin 115°). Since cos 115° = -0.42 and sin 115° ≈ 0.91, it means that the coordinates at point A is (-0.42, 0.91).

As for point B which was revolved around -115°,

the coordinates will be similar to point A but you just have to change the negative.

B(cos -115°, sin -115°) = B(0.42, -0.91)

Answer:

PLATO ANSWER

-0.91; -0.42

Step-by-step explanation:

The sine function is an odd function, meaning that sin -x = -sin x. Because sin 115° ≈ 0.91, sin  -115° ≈ -0.91.

The cosine function is an even function, meaning that cos -x = cos x. Because cos 115° = -0.42, cos -115° = -0.42.

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

Explanation:

The result of [tex]g^{-1}(-8)[/tex] is the same as trying to find x in [tex]g(x) = -8[/tex]

Draw a horizontal line through -8 on the y axis. This horizontal line intersects the curve at point P. From point P, move upward until you reach the x axis. You should get to 7 on the x axis. Therefore, the solution to [tex]g(x) = -8[/tex] is [tex]x = 7[/tex]. In other words, [tex]g(7) = -8[/tex]. This ultimately means [tex]g^{-1}(-8) = 7[/tex]

Refer to the diagram below.

Answer:

36: G-30

37: Please add the rest of the questions, so I can answer 37.

Step-by-step explanation: