Solve the equations below. Give exact solutions only. Show your work.

a) 5x^2 - 7 = 72
b) x(x + 2) = 5
c) 3x^2 + 2x - 4 = 0

Answer:

Cost of a play station game = $11.3

Cost of each water ride = $22.6

Step-by-step explanation:

Entrance tickets = $89.97

Royal meal = $10.85

Cost of a play station game = x

Cost of each water ride = 2x

Find the cost of a water ride

Entrance tickets = Royal meal + 1 play station game + 3 water rides

89.97 = 10.85 + 1(x) + 3(2x)

89.97 = 10.85 + x + 6x

89.97 = 10.85 + 7x

89.97 - 10.85 = 7x

79.12 = 7x

x = 79.12/7

x = 11.302857142857

Approximately to the nearest tenth

x = $11.3

Cost of a play station game = x = $11.3

Cost of each water ride = 2x

= 2(11.3)

= $22.6

Answer:

-44, -42, -40, -38, -36

Step-by-step explanation:

"preceding" requires an indication of the direction.

but I assume the usual left to right direction. in that sense the provided 5 even numbers are directly preceding -35

Answer: No solution

Step-by-step explanation:

-6(x - 2) + 3x = -3(x + 3) + 21

-6x + 12 + 3x = -3x - 9 + 21

Collect like terms

-6x + 3x + 3x = -9 + 21 - 12

-6x + 6x = - 9 + 9

0 = 0

In this scenario, it can be deduced that there is no solution to Kenya's equation.

Answer:

infinitely many solutions

Step-by-step explanation:

i got it right

9514 1404 393

Answer:

  after 89 years

Step-by-step explanation:

For principal p, interest rate r, and number of years t, the two account balances are ...

  a = p·e^(rt) . . . . continuous compounding

  a = p(1+r)^t . . . . annual compounding

Using the given values, we have

  3000·e^(0.07t) . . . . . compounded continuously

  20000·1.05^t . . . . . . compounded annually

We want to find t so these are equal.

  3000·e^(0.07t) = 20000·1.05^t

  0.15e^(0.07t) = 1.05^t . . . . divide by 20,000

  ln(0.15) +0.07t = t·ln(1.05) . . . . take natural logarithms

  ln(0.15) = t·(ln(1.05) -0.07) . . . . subtract 0.07t

  t = ln(0.15)/(ln(1.05) -0.07) ≈ -1.8971/-0.02121 . . . . . divide by the coefficient of t

  t ≈ 89.4 ≈ 89

The two accounts will have the same balance after 89 years.

Answer:

1:15 minuites

Step-by-step explanation:

30 minuites

Answer:

8:30 A.M.

Step-by-step explanation:

Start by adding up the total time spent traveling.

3h 30min + 1h 30min + 1h 15 min = 5h 15 min

If she arrived in Orlando at 1:45 P.M., count back 5 h 15 min.

1:45 - 15 min = 1:30 - 5h = 8:30 A.M.

Answer:

x = 5

<AED = <AEC = 37

Step-by-step explanation:

<AEF = <AEC (Vertical angles)

6x+7=8x-3

or, 8x-6x=7+3

or, 2x=10

or, x=5

6x+7 = 37

Answered by GAUTHMATH

Answer:

x=5

AED =37

Step-by-step explanation:

The angles are vertical angles and vertical angles are equal

6x+7 = 8x-3

Subtract 6x from each side

6x+7-6x = 8x-6x-3

7 = 2x-3

Add 3 to each side

7+3 = 2x-3+3

10 =2x

Divide by 2

10/2 =2x/2

5 =x

We want the AED = 6x+7 = 6*5+7 = 30+7 = 37

Answer:

I think it's the zero property

Step-by-step explanation:

Answer:

a. linear pair 5 & 6

b. pair of vertical angles 5 & 2

c. pair of angles that are congruent 3 & 8

Step-by-step explanation:

A linear pair of angles is formed when two lines intersect.

Vertical angles are a pair of non-adjacent angles formed by the intersection of two straight lines. In simple words, vertical angles are located across from one another in the corners of the "X" formed by two straight lines.

If two angles are complements of the same angle (or congruent angles), then the two angles are congruent. All right angles are congruent.

Answer:

32is the answer to yours questions

Answer:

opposite side of an angle

hypotenuse

Answer:

six x squared y over 3 x y

Answer: 4x/y

Step-by-step explanation:

6x^2y. (2/3xy^2)= (6x^2y.2)/(3xy^2)= (12x^2y)/(3xy^2)= 4x/y

Answer:

The solution to above problem is 1- $45n 2- $(250+28n) 3- $(500+20n)

Step-by-step explanation:

Answer:

[tex]15x^2 + 8x -12[/tex]

Step-by-step explanation:

(5x+6)(3x-2)

"foil" it out

F: 5x * 3x  = 15x^2

O: 5x * -2  = -10x

I: 6*3x = 18x

L: 6 * -2 = -12

Answer:

15x² + 8x - 12

Step-by-step explanation:

(5x + 6)(3x - 2)

Each term in the second factor is multiplied by each term in the first factor, that is

5x(3x - 2) + 6(3x - 2) ← distribute both parenthesis

= 15x² - 10x + 18x - 12 ← collect like terms

= 15x² + 8x - 12

[tex] \frac{9}{41} [/tex]

Step-by-step explanation:

The ratio cosine tell us that

In other words,

[tex] \cos(x) = \frac{adj}{hyp} [/tex]

The side adjacent to angle a is 9. The hypotenuse is 41.

So

[tex] \cos(a) = \frac{9}{41} [/tex]

Answer:

[tex] 3x + y = 2 [/tex]

Step-by-step explanation:

[tex] y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1) [/tex]

[tex] y - 5 = \dfrac{-7 - 5}{3 - (-1)}(x - (-1)) [/tex]

[tex] y - 5 = \dfrac{-12}{4}(x + 1) [/tex]

[tex] y - 5 = -3(x + 1) [/tex]

[tex] y - 5 = -3x - 3 [/tex]

[tex] 3x + y = 2 [/tex]

Step-by-step explanation:

The Rational Roots Test states that for a polynomial with integer coefficients, the factors of the constant / the factors of the leading coefficient are the possible rational roots.

Here, the constant (the value without an x attached to it) is -12 and the leading coefficient (the value that the x to the highest degree is multiplied by) is 1 as x⁴ is multiplied by 1. The factors of -12 are

±(1, 2, 3, 4, 6, 12), so the possible rational roots are ±(1, 2, 3, 4, 6, 12)/1 (as 1 is the only factor of 1).

Trying out a few roots until we get one that works using synthetic division, we can try

x+1 (the root is x=-1)

-1  |     1       1        -6         -14         -12

    |            -1          0          6           8

    __________________________

          1     0        -6            -8         -4

the remainder is -4, so this does not work

x+2 (the root is x=-2)

-2 |     1       1        -6         -14         -12

    |            -2          2          8          12

    __________________________

          1      -1       -4           -6         0

Therefore, x=-2 is a root and x+2 is a factor of the polynomial. The quotient of the polynomial and x+2 is

-6 + (-4)x + (-1)* x² + 1 * x³ = x³-x²-4x-6

Using the rational roots theorem, the possible roots of x³-x²-4x-6 are

±(1,2,3,6)

Starting with

x-1 (root is x=1), we have

1 |     1       -1        -4         -6      

    |            1          0         -4        

    _____________________

          1      0       -4           -10

there is a remainder, so this is not a root

next, x-2 (root is x=2)

2 |     1       -1        -4         -6      

    |            2         2         -4        

    _____________________

          1      1       -2           -10      

there is a remainder, so this is not a root

next, x-3 (root is x=3)

3|     1       -1        -4         -6      

    |            3         6         6        

    _____________________

          1      2      2          0

x-3 is a factor and 3 is a root. the quotient of (x³-x²-4x-6)/(x-3) is x²+2x+2

Answer:

[×1] +16=10

×=10-16

×=-6

Answer:

x=5 and x=-5

Step-by-step explanation:

First subtract 16 from both sides.

Then solve for x+1=6 and x+1=-6

you answer should be x=5 and x=-5

Answer:

The answer would be -a

Step-by-step explanation:

In the examples,

5 + (-5) = 0

-1.33 + 1.33 = 0

THat means there will be a negative then a positive, or a positive then a negative.

INVERSE is the key word in this problem.

3(y+11) y=12

3(12+11)=?

12+11=23

3x23=69

Answer = 69

I hope this helps :)

Step-by-step explanation:

her it go u can see it.. have a nice Day

Answer:

y = mx + b

m = slope = -2

To find the y-intercept(b), substitute the points into the function:

-3 = -2(-5)  + b

-3 = 10 + b

b = -3 - 10 = -13

Therefore, y = -2x - 13

Answer:

Step-by-step explanation:

Answer:

20 days

Step-by-step explanation:

10kg= 10,000g

10,000g/500g= 20 days

Answer:

20 days

Step-by-step explanation:

1 kg=1000 grams

10 kg=10000 grams

10000÷500

=20 days

Answer:

B

Step-by-step explanation:

when logarithms of the same base (the base in this case is 'b') are being subtracted, divide the arguments ( 'a' and 'd')

Answer:

this is the same quiestion i was doing if u get answer plz send me

Answer:

x=15.73292

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj/ hyp

cos 70 = x / 46

46 cos 70 =x

x=15.73292

Answer:

15.73

Step-by-step explanation:

cos(x) = adjacent leg / hypotenuse

cos(70) = x / 46

0.342 = x / 46

0.342 x 46 = x

x = 15.73

Answer:

45°

Step-by-step explanation:

Segments GJ and HK intersect at F.

That makes angles JFK and GFH vertical angles and congruent.

An arc has the same measure as its central angle.

m<GFH = 45°

m<JFK = m<GFH

m<JFK = 45°

Answer:

multiplying by 100 "shifts" decimal point to the right by 2

90  

1379  

2989.4

Step-by-step explanation:

Answer:

0.9 x 100=90

13.79 x 100=1379

29.894 x 100=2989.4

​

Step-by-step explanation:

Answer:

75 - 35y / 3 + 2y = -4

( 75 - 35y + 6y ) / 3 = -4 [ Taking LCM ]

( 75 - 29y ) / 3 = -4

75 - 29y = -12

29y = 75+12

29y = 87

y = 3

hope that helps ✌

It looks like you have to find the value of the sum,

[tex]C = \displaystyle \frac1{21\times22\times23} + \frac1{22\times23\times24} + \cdots + \frac1{200\times201\times202}[/tex]

so that the n-th term in the sum is

[tex]\dfrac1{(21+(n-1))\times(21+n)\times(21+(n+1))} = \dfrac1{(n+20)(n+21)(n+22)}[/tex]

for 1 ≤ n ≤ 180.

We can then write the sum as

[tex]\displaystyle C = \sum_{n=1}^{180} \frac1{(n+20)(n+21)(n+22)}[/tex]

Break up the summand into partial fractions:

[tex]\dfrac1{(n+20)(n+21)(n+22)} = \dfrac a{n+20} + \dfrac b{n+21} + \dfrac c{n+22}[/tex]

Combine the fractions into one with a common denominator and set the numerators equal to one another:

[tex]1 = a(n+21)(n+22) + b(n+20)(n+22) + c(n+20)(n+21)[/tex]

Expand the right side and collect terms with the same power of n :

[tex]1 = a(n^2+43n+462)+b(n^2+42n+440) + c(n^2+41n + 420) \\\\ 1 = (a+b+c)n^2 + (43a+42b+41c)n + 462a+440b+420c[/tex]

Then

a + b + c = 0

43a + 42b + 41c = 0

462a + 440b + 420c = 1

==>   a = 1/2, b = -1, c = 1/2

Now our sum is

[tex]\displaystyle C = \sum_{n=1}^{180} \left(\frac1{2(n+20)}-\frac1{n+21}+\frac1{2(n+22)}\right)[/tex]

which is a telescoping sum. If we write out the first and last few terms, we have

C = 1/(2×21) - 1/22 + 1/(2×23)

… … + 1/(2×22) - 1/23 + 1/(2×24)

… … + 1/(2×23) - 1/24 + 1/(2×25)

… … + 1/(2×24) - 1/25 + 1/(2×26)

… … + … - … + …

… … + 1/(2×198) - 1/199 + 1/(2×200)

… … + 1/(2×199) - 1/200 + 1/(2×201)

… … + 1/(2×200) - 1/201 + 1/(2×202)

Notice the diagonal pattern of underlined and bolded terms that add up to zero (e.g. 1/(2×23) - 1/23 + 1/(2×23) = 1/23 - 1/23 = 0). So, like a telescope, the sum collapses down to a simple sum of just six terms,

C = 1/(2×21) - 1/22 + 1/(2×22) + 1/(2×201) - 1/201 + 1/(2×202)

which we simplify further to

C = 1/42 - 1/44 - 1/402 + 1/404

C = 1,115/1,042,118 ≈ 0.00106994