Which of the following numbers can be expressed as decimals that terminate? 5 over 2, 4 over 5, 2 over 7, 4 over 3

Answer:

Step-by-step explanation:

x² + 2x + 1 = 0

Using the quadratic formula

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

a = 1 , b = 2 , c = 1

We have

[tex]x = \frac{ - 2± \sqrt{ {2}^{2} - 4(1)(1)} }{2(1)} \\ \\ x = \frac{ - 2 ± \sqrt{4 - 4} }{2} \\ \\ x = \frac{ - 2 ± \sqrt{0} }{2} \\ \\ x = - \frac{2}{2} \\ \\ x = - 1[/tex]

Hope this helps you

Answer:

Step-by-step explanation:

To find x we use cosine

cos ∅ = adjacent / hypotenuse

From the question

The hypotenuse is x

The adjacent is 18

So we have

cos 69 = 18/x

x cos 69 = 18

Divide both sides by cos 69

x = 18/cos 69

x = 50.2

x = 50° to the nearest tenth

Hope this helps you

Answer:  3.2 yd

Step-by-step explanation:

Notice that TWV is a right triangle.  

Segment TU is not needed to answer this question.

∠V = 32°, opposite side (TW) is unknown, hypotenuse (TV) = 6

[tex]\sin \theta=\dfrac{opposite}{hypotenuse}\\\\\\\sin 32=\dfrac{\overline{TW}}{6}\\\\\\6\sin 32=\overline{TW}\\\\\\\large\boxed{3.2=\overline{TW}}[/tex]

Answer:

1

Step-by-step explanation:

Both equations are linear, and they do not have an equivalent slope, therefore they MUST intercept each other once and only once.

Answer:

How many students are in P.E? 90

How many are ONLY in P.E? 62

Step-by-step explanation:

How many students are in P.E?

200 students in 8th grade.

35=drama

75=cooking

200-110=90=PE.

How many are ONLY in P.E?

Within 90 students, 15 is also in drama, with 5 is also in cooking, and 8 is in all of 3. =28.

90-28=62

Hope this helps!

By the factor theorem,

[tex]3x^2+5x+7=3(x-u)(x-v)\implies\begin{cases}uv=\frac73\\u+v=-\frac53\end{cases}[/tex]

Now,

[tex](u+v)^2=u^2+2uv+v^2=\left(-\dfrac53\right)^2=\dfrac{25}9[/tex]

[tex]\implies u^2+v^2=\dfrac{25}9-\dfrac{14}3=-\dfrac{17}9[/tex]

So we have

[tex]\dfrac uv+\dfrac vu=\dfrac{u^2+v^2}{uv}=\dfrac{-\frac{17}9}{\frac73}=\boxed{-\dfrac{17}{21}}[/tex]

The value of [tex]\frac{u}{v} +\frac{v}{u}[/tex] is [tex]\frac{-17}{21}[/tex].

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is[tex]ax^{2} +bx+c=0[/tex], where a and b are the coefficients, x is the variable, and c is the constant term.

If [tex]ax^{2} +bx+c = 0[/tex] be the quadratic equation then

Sum of the roots = [tex]\frac{-b}{a}[/tex]

And,

Product of the roots = [tex]\frac{c}{a}[/tex]

According to the given question.

We have a quadratic equation [tex]3x^{2} +5x+7=0..(i)[/tex]

On comparing the above quadratic equation with standard equation or general equation [tex]ax^{2} +bx+c = 0[/tex].

We get

[tex]a = 3\\b = 5\\and\\c = 7[/tex]

Also, u and v are the solutions of the quadratic equation.

⇒ u and v are the roots of the given quadratic equation.

Since, we know that the sum of the roots of the quadratic equation is [tex]-\frac{b}{a}[/tex].

And product of the roots of the quadratic equation is [tex]\frac{c}{a}[/tex].

Therefore,

[tex]u +v = \frac{-5}{3}[/tex] ...(ii) (sum of the roots)

[tex]uv=\frac{7}{3}[/tex]   ....(iii)       (product of the roots)

Now,

[tex]\frac{u}{v} +\frac{v}{u} = \frac{u^{2} +v^{2} }{uv} = \frac{(u+v)^{2}-2uv }{uv}[/tex]                    ([tex](a+b)^{2} =a^{2} +b^{2} +2ab[/tex])

Therefore,

[tex]\frac{u}{v} +\frac{v}{u} =\frac{(\frac{-5}{3} )^{2}-2(\frac{7}{3} ) }{\frac{7}{3} }[/tex]         (from (i) and (ii))

⇒ [tex]\frac{u}{v} +\frac{v}{u} =\frac{\frac{25}{9}-\frac{14}{3} }{\frac{7}{3} }[/tex]

⇒ [tex]\frac{u}{v} +\frac{v}{u} = \frac{\frac{25-42}{9} }{\frac{7}{3} }[/tex]

⇒ [tex]\frac{u}{v} +\frac{v}{u} = \frac{\frac{-17}{9} }{\frac{7}{3} }[/tex]

⇒ [tex]\frac{u}{v} +\frac{v}{u} =\frac{-17}{21}[/tex]

Therefore, the value of [tex]\frac{u}{v} +\frac{v}{u}[/tex] is [tex]\frac{-17}{21}[/tex].

Find out more information about sum and product of the roots of the quadratic equation here:

https://brainly.com/question/14266582

#SPJ3

Answer:

[tex]2\sqrt{2} +2\sqrt{5}[/tex]

Step-by-step explanation:

i just got this one right

the kite has two pairs of congruent sides. using the distance formula, the two shorter sides=[tex]\sqrt{2}[/tex] (since there are two of those length sides, you multiply it by two). Again with the distance formula, the two longer sides=[tex]\sqrt{5}[/tex] (also multiply this by two).this gives the answer c or [tex]2\sqrt{2}+2\sqrt{5}[/tex]

Answer:

The answer is c [tex]\sqrt[2]{2}[/tex] + [tex]\sqrt[2]{5}[/tex] units. just took the test

Step-by-step explanation:

Answer:

Ram therefore has more amount in his account at the end of the month, and the balances in their bank accounts at the end of the month are arranged in ascending order, i.e. from the smallest to the largest, as follows:

Rahul – Debits AED 200; Rohit – Credits AED 200; and Ram – Credits AED 500.

Step-by-step explanation:

In banking and finance, a credit transaction on a bank account indicates that an additional amount of money has been added to the bank account and the balance has increased. This gives a positive balance in the account

On the other hand, a debit transaction on a bank account indicates that an amount of money has been deducted or withdrawn from the bank account and the balance has therefore reduced. This gives a negative balance in the account.

Based on the above, we have:

a. Ram – Credits AED 500 on 12th May 2020

Since there is no any other credit or debit transaction during the month, this implies that Ram still has Credits AED 500 in his account at the end of the month.

The Credits AED 500 indicates that Ram has a positive balance of AED 500 in his account at the end of the month.

b. Rahul – Debits AED 700 on 12th May 2020 and Credits AED 500 on 15th May 2020.

The balance in the account of Rahul gives Debits of AED 200 as follows:

Debits AED 700 - Credits AED 500 = Debits AED 200

The Debits AED 200 indicates that Rahul has a negative balance of AED 200 in his account at the end of the month.

c. Rohit – Credits AED 700 on 12th May 2002 and Debits AED 500 on 15th May 2020.

The balance in the account of Rohit gives Credits of AED 200 as follows:

Credits AED 700 - Dedits AED 500 = Credits AED 200

The Credits AED 200 indicates that Rohit has a positive balance of AED 200 in his account at the end of the month.

Conclusion

Arrangement of numbers or amounts of money in ascending order implies that they are arranged from the smallest to the largest number or amount.

Since Credits implies positive amount and Debits implies negative amount, Ram therefore has more amount in his account at the end of the month, and the balances in their bank accounts at the end of the month are arranged in ascending order, i.e. from the smallest to the largest, as follows:

Rahul – Debits AED 200; Rohit – Credits AED 200; and Ram – Credits AED 500.

Answer:

10a²b²6ab²

Step-by-step explanation:

Distribute the 2ab the other values

Answer:

first option

Step-by-step explanation:

Given

[tex]\frac{15}{x}[/tex] + 6 = [tex]\frac{9}{x^2}[/tex]

Multiply through by x² to clear the fractions

15x + 6x² = 9 ( subtract 9 from both sides )

6x² + 15x - 9 = 0 ( divide through by 3 )

2x² + 5x - 3 = 0 ← in standard form

Consider the factors of the product of the coefficient of x² and the constant term which sum to give the coefficient of the x- term.

product = 2 × - 3 = - 6 and sum = + 5

The factors are + 6 and - 1

Use these factors to slit the x- term

2x² + 6x - x - 3 = 0 ( factor the first/second and third/fourth terms )

2x(x + 3) - 1(x + 3) = 0 ← factor out (x + 3) from each term

(x + 3)(2x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = 0.5

Solution set is { - 3, 0.5 }

Answer:

(C)[tex]x^2+4x-2-(-x^2+2x-4)=2x^2+2x+2[/tex]

Step-by-step explanation:

The expression represented by the upper tiles is: [tex]x^2+4x-2[/tex]

The expression represented by the lower tiles is: [tex]x^2-2x+4[/tex]

Adding the two

[tex]x^2+4x-2+(x^2-2x+4)=2x^2+2x+2[/tex]

Writing it as a difference, we have:

[tex]x^2+4x-2-(-x^2+2x-4)=2x^2+2x+2[/tex]

The correct option is C.

Answer:

yeah, what newton said :]

Answer:

Series A has an r value of 2/5 and series A has an r value of 3. The sum of the series A is 50/3

Step-by-step explanation:

A geometric sequence is in the form a, ar, ar², ar³, .  .   .

Where a is the first term and r is the common ratio = [tex]\frac{a_{n+1}}{a_n}[/tex]

For series A:  10+4+8/5+16/25+32/125+⋯   The common ratio r is given as:

[tex]r=\frac{a_{n+1}}{a_n}=\frac{4}{10} =\frac{2}{5}[/tex]

For series B: 1/5+3/5+9/5+27/5+81/5+⋯   The common ratio r is given as:

[tex]r=\frac{a_{n+1}}{a_n}=\frac{3/5}{1/5} =3[/tex]

For series A a = 10, r = 2/5, which mean 0 < r < 1, the sum of the series is given as:

[tex]S_{\infty}=\frac{a}{1-r}=\frac{10}{1-\frac{2}{5} } =\frac{50}{3}[/tex]

Answer:

The mode of the above is 6.

Step-by-step explanation:

Mode-the number that occurs most frequently in a set of numbers.

The six appeared three times being the most.

I really hope this helps.

Answer:

Average consumption ( mean )  =  9

MOE = 4

Step-by-step explanation:

We know that

CI   ( 5  ;  13 )

and   CI [ μ - MOE  ;  μ + MOE ]

From the above relations we get

μ - MOE = 5

μ + MOE = 13

Adding member to member these two equations we get

2*μ  =  18

μ = 9    and MOE = 13 - 9

MOE = 4

Answer:

f(x) = 4x² + 48x + 149

Step-by-step explanation:

Given

f(x) = 4(x + 6)² + 5 ← expand (x + 6)² using FOIL

     = 4(x² + 12x + 36) + 5 ← distribute parenthesis by 4

     = 4x² + 48x + 144 + 5 ← collect like terms

     = 4x² + 48x + 149 ← in standard form

Answer:

[tex]f(x)=4x^{2} +149[/tex]

Step-by-step explanation:

Start off by writing the equation out as it is given:

[tex]f(x)=4(x+6)^{2} +5[/tex]

Then, get handle to exponent and distribution of the 4 outside the parenthesis:

[tex]f(x)=4(x^{2} +36)+5\\f(x)=4x^{2} +144+5[/tex]

Finally, combine any like terms:

[tex]f(x)=4x^{2} +149[/tex]

Answer:

83

Step-by-step explanation:

You're given two vertical angles, and vertical angles are congruent. This means that (6x - 7) = (4x + 23); x = 15. Plug it into ABC (which is (6x - 7)) to get 6(15) - 7 = 90 - 7 = 83

Answer:

[tex]\displaystyle \sin \theta = \frac{4}{5}[/tex] if [tex]\displaystyle \cos\theta = -\frac{3}{5}[/tex] and [tex]\theta[/tex] is in the second quadrant.

Step-by-step explanation:

By the Pythagorean Trigonometric Identity:

[tex]\left(\sin \theta\right)^2 + \left(\cos\theta)^2 = 1[/tex] for all real [tex]\theta[/tex] values.

In this question:

[tex]\displaystyle \left(\cos\theta\right)^2 = \left(-\frac{3}{5}\right)^2 = \frac{9}{25}[/tex].

Therefore:

[tex]\begin{aligned} \left(\sin\theta\right)^2 &= 1 -\left(\cos\theta\right)^2 \\ &= 1 - \left(\frac{3}{5}\right)^2 = \frac{16}{25}\end{aligned}[/tex].

Note, that depending on [tex]\theta[/tex], the sign [tex]\sin \theta[/tex] can either be positive or negative. The sine of any angles above the [tex]x[/tex] axis should be positive. That region includes the first quadrant, the positive [tex]y[/tex]-axis, and the second quadrant.

According to this question, the [tex]\theta[/tex] here is in the second quadrant of the cartesian plane, which is indeed above the [tex]x[/tex]-axis. As a result, the sine of this

It was already found (using the Pythagorean Trigonometric Identity) that:

[tex]\displaystyle \left(\sin\theta\right)^2 = \frac{16}{25}[/tex].

Take the positive square root of both sides to find the value of [tex]\sin \theta[/tex]:

[tex]\displaystyle \sin\theta =\sqrt{\frac{16}{25}} = \frac{4}{5}[/tex].

Answer: x=35

Step-by-step explanation:

There are 720 degrees total in a hexagon. So, all of the angles should add up to that. Write out the equation

720= (4x-5)+(117)+(3x-3)+(3x+6)+(118)+(4x-3)

720=14x+230

490=14x

x=35

hope this helped you:)

Answer:

64 : 216

Step-by-step explanation:

Given the ratio of the heights = a : b, then

ratio of volumes = a³ : b³

Here the ratio of heights = 4 : 6 = 2 : 3 ← in simplest form, thus

ratio of volumes = 4³ : 6³ = 64 : 216 = 8 : 27 ← in simplest form

Answer:

answer pic below :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

In this problem we are going find the natural logarithmic of the numbers involved and solve for x

[tex]ln65-Ln x= 39\\[/tex]

from tables

[tex]4.17-ln x= 39\4.17-39= lnx\\-34.83=lnx\\[/tex]

taking the exponents of both sides we have

[tex]e^-^3^4^.^8^3= x\\x= 7.47[/tex]

Answer:

At 2 drinks, the prices are equal. For 1 drink, Western Sizzlin is better since the buffet price is lower. From 3 drinks and up, Golden Corral is better.

Step-by-step explanation:

"Golden Corral charges $11 for a buffet plus $1 for each drink."

d + 11

"Western Sizzlin charges $9 for a buffet plus $2 for each drink."

2d + 9

Set the 2 cost functions equal:

2d + 9 = d + 11

d = 2

At 2 drinks, the prices are equal. For 1 drink, Western Sizzlin is better since the buffet price is lower. From 3 drinks and up, Golden Corral is better.

Answer:

[tex]y\ =\ \left|\frac{1}{2}x-2.5\right|+3[/tex]

Step-by-step explanation:

Look at the image below ↓

Answer:

Check below the graph.

Step-by-step explanation:

Hi, for this function, check the graph below:

1) Note that in this function the value outside the brackets points how high the graph will be traced.

2) The value within the brackets, points since it's a negative expression how far to the right the graph will be traced.

Answer: The lines are parallel.

The slopes are equal.

The y-intercepts are different.

The system has no solution.

Step-by-step explanation:

For  a pair of equations: [tex]a_1x+b_1y=c_1\\\\a_2x+b_2y=c_2[/tex]

They coincide if [tex]\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}[/tex]

They are parallel if [tex]\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}[/tex]

They intersect if [tex]\dfrac{a_1}{a_2}\neq\dfrac{b_1}{b_2}[/tex]

Given equations: [tex]8 x + 10 y = 30\\ 12 x + 15 y = 60[/tex]

Here,

[tex]\dfrac{a_1}{a_2}=\dfrac{8}{12}=\dfrac{2}{3}\\\\ \dfrac{b_1}{b_2}=\dfrac{10}{15}=\dfrac{2}{3}\\\\ \dfrac{c_1}{c_2}=\dfrac{30}{60}=\dfrac{1}{2}[/tex]

⇒[tex]\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}[/tex]  

Hence, The lines are parallel.

It has no solution. [parallel lines have no solution]

Write 8 x + 10 y = 30 in the form of y= mx+c, where m is slope and c is the y-intercept.

[tex]y=-\dfrac{8}{10}x+\dfrac{30}{10}\Rightarrow\ y=-0.8x+3[/tex]

i.e. slope of 8 x + 10 y = 30 is -0.8 and y-intercept =3

Write  12 x + 15 y = 60 in the form of y= mx+c, where m is slope

[tex]y=-\dfrac{12}{15}x+\dfrac{60}{15}\Rightarrow\ y=-0.8x+4[/tex]

i.e. slope of  12 x + 15 y = 60 is -0.8 and y-intercept =4

i.e. The slopes are equal but y-intercepts are different.

Answer: The lines are parallel.

The slopes are equal.

The y-intercepts are different.

The system has no solution.

Step-by-step explanation:

For  a pair of equations:  

They coincide if  

They are parallel if  

They intersect if  

Given equations:  

Here,

⇒  

Hence, The lines are parallel.

It has no solution. [parallel lines have no solution]

Write 8 x + 10 y = 30 in the form of y= mx+c, where m is slope and c is the y-intercept.

i.e. slope of 8 x + 10 y = 30 is -0.8 and y-intercept =3

Write  12 x + 15 y = 60 in the form of y= mx+c, where m is slope

i.e. slope of  12 x + 15 y = 60 is -0.8 and y-intercept =4

i.e. The slopes are equal but y-intercepts are different.

Answer:

12 gallons per hour

Step-by-step explanation:

Given the following :

Start time of flight = 9:30 a.m

Arrival time of flight = 1:45p.m

Gallons of gas used during duration of flight = 51 gallons

Number of hours spent during flight:

Arrival time - start time

1:45 pm - 9:30 am = 4hours and 15minutes

4hours 15minutes = 4.25hours

If 4.25hours requires 51 gallons of gas;

Then 1 hour will require ( 51 / 4.25)gallons

= 51 / 4.25

= 12 gallons

Answer:

A 95​% confidence interval for the proportion of students who eat cauliflower on​ Jane's campus is [0.012, 0.270].

Step-by-step explanation:

We are given that Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 24 ​students, she finds 2 who eat cauliflower.

Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;

                              P.Q.  =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of students who eat cauliflower

           n = sample of students

           p = population proportion of students who eat cauliflower

Here for constructing a 95% confidence interval we have used a One-sample z-test for proportions.

So, 95% confidence interval for the population proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

                                                   of significance are -1.96 & 1.96}  

P(-1.96 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 1.96) = 0.95

P( [tex]-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95

P( [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95

Now, in Agresti and​ Coull's method; the sample size and the sample proportion is calculated as;

[tex]n = n + Z^{2}__(\frac{_\alpha}{2})[/tex]

n = [tex]24 + 1.96^{2}[/tex] = 27.842

[tex]\hat p = \frac{x+\frac{Z^{2}__(\frac{\alpha}{2}_) }{2} }{n}[/tex] = [tex]\hat p = \frac{2+\frac{1.96^{2} }{2} }{27.842}[/tex] = 0.141

95% confidence interval for p = [ [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ]

 = [ [tex]0.141 -1.96 \times {\sqrt{\frac{0.141(1-0.141)}{27.842} } }[/tex] , [tex]0.141 +1.96 \times {\sqrt{\frac{0.141(1-0.141)}{27.842} } }[/tex] ]

 = [0.012, 0.270]

Therefore, a 95​% confidence interval for the proportion of students who eat cauliflower on​ Jane's campus [0.012, 0.270].

The interpretation of the above confidence interval is that we are 95​% confident that the proportion of students who eat cauliflower on​ Jane's campus is between 0.012 and 0.270.

Answer:

74°.

Step-by-step explanation:

From the question given above,

Cos A = 0.2785

To get the value of angle A, we simply find the inverse of Cos as shown below:

Cos A = 0.2785

Take the inverse of Cos.

A = Cos¯¹ 0.2785

A = 73.8° ≈ 74°

Therefore, the value of angle A is approximately 74°

Answer:

  C. (2, 6] hour jobs cost $100

Step-by-step explanation:

Let's consider each of these statements in view of the graph:

Answer:

(0,8) first option     and  50,100 or 200 in the second option

Step-by-step explanation:

Answer:

70° and 110°

Step-by-step explanation:

If two angles forms a linear pair, this means that the sum of the angles is 180°. If the measure of one angle is x and the measure of the other angle is 1.4 times x plus 12∘

Let A be the first angle = x°

Let B be the second angle = (1.4x+12)°

Since they form a linear pair, then

A+B = 180°

x + 1.4x+12 = 180°

2.4x = 180-12

2.4x = 168

x = 168/2.4

x = 70°

The measure of angle A = 70°

The measure if angle B = 1.4x+12

B = 1.4(70)+12

B = 98+12

B = 110°

The measure of both angles are 70° and 110°