What values of c and d make the equation true? assume x greater-than 0 and y greater-than-or-equal-to 0 startroot startfraction x superscript 6 baseline y cubed over 9 x superscript 8 baseline endfraction endroot = startfraction 5 y superscript c baseline startroot 2 y endroot over d x endfraction c = 1, d = 3 c = 1, d = 9 c = 2, d = 8 c = 2, d = 9

Check the picture below.

[tex]\bold{\huge{\underline{ Solution }}}[/tex]

Here ,we have

Let the three consecutive number be

(4x - 2) , 4x , ( 4x + 2)

According to the question,

[tex]\sf{ (4x - 2) + 4x + ( 4x + 2) = 144}[/tex]

[tex]\sf{ 4x - 2 + 4x + 4x + 2 = 144}[/tex]

[tex]\sf{ 8x - 2 + 4x + 2 = 144}[/tex]

[tex]\sf{ 12x = 144}[/tex]

[tex]\sf{ x = }{\sf{\dfrac{ 144}{12}}}[/tex]

[tex]\sf{ x = }{\sf{\cancel{\dfrac{ 144}{12}}}}[/tex]

[tex]\sf{ x = 12 }[/tex]

Thus, The value of x is 12

Therefore,

The three consecutive even numbers are

Hence, The highest consecutive even number is 50 .

The reasonable estimate of the current customer price index is 195. The option B is the correct option.

Customer price index is the price index which measures the weight average of price of basket of customers goods or services.

It can be given as,

[tex]\rm CPI_t=\dfrac{C_t}{C_0}\times 100[/tex]

Here [tex]\rm C_t[/tex] is the cost of market basket in current period and [tex]\rm C_0[/tex] is the cost of market basket in the base period.

Cost of market basket in current period is

[tex]\rm C_t=15.66+119.75+23.99+37.50\\\\C_t=196.9[/tex]

Cost of market basket in 1983 is,

[tex]\rm C_0=8.85+71.25+13.95+22.7\\\\C_0=116.8[/tex]

Substitute all the values in the formula

[tex]\rm CPI_t=\dfrac{C_t}{C_0}\times 100\\\\\rm CPI_t=\dfrac{196.9}{116.8}\times 100\\\\\rm CPI_t=1.685\times 100 \\\\ CPI_t=168.5\\\\\rm CPI_t= 170 \ \rm approx[/tex]

Thus the value of current CPI is 168.5 which is near about the 170.

Hence, the reasonable estimate of the current customer price index is 195. The option B is the correct option.

Learn more about the customer price index here;

https://brainly.com/question/25495502

Answer:

x = 52.2

Step-by-step explanation:

we have adjacent (56) and opposite (x) so we use tan (Toa = opposite/adjacent).

Set up like so:

tan 43 = x/56

x = 52.2208

x = 52.2

Answers:

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

Explanation:

Answer:

110

Step-by-step explanation:

101-86=15

95+15=110

110-15=95

Answer:

110

Step-by-step explanation:

In this problem, you are adding 15 to each Input to get the Output. That is why I added 15 to 95 in order to get 110.

Answer: B

Step-by-step explanation:

Answer:

x < 3

Step-by-step explanation:

Step 1: Add 20 to both sides.

Step 2: Divide both sides by 2.

Answer:

i. 7:6

ii. 7:13

iii. 6:13

Step-by-step explanation:

boys to girls = 140:120 so we can simplify by 20 to get 7:6

boys to total = 140:(120+140) = 140:260 we can simplify again to get 7:13.

girls to total = 120:(120+140) = 120:260 we can also simplify to get 6:13

Answer:

x = 2, -2

explanation:

[tex]\sf y=x^4+3x^3+x^2-12x-20[/tex]

Find a factor for this equation:

-5 < x < 5

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

f(-3) = 25

f(-2) = 0

f(-1) = -9

f(0) = -20

f(1) = -27

f(2) = 0

f(3) = 115

Hence found that ( x -2) and ( x + 2) are the factor of the following equation.

Divide both by the following equation:

[tex]\sf \rightarrow \dfrac{x^4+3x^3+x^2-12x-20}{\left(x-2\right)\left(x+2\right)}[/tex]

[tex]\sf \rightarrow \dfrac{\left(x-2\right)\left(x+2\right)\left(x^2+3x+5\right)}{\left(x-2\right)\left(x+2\right)}[/tex]

[tex]\sf \rightarrow x^2+3x+5[/tex]

Using quadratic formula: [tex]\sf x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ \ when \ \ ax^2 + bx + c = 0[/tex]

[tex]\sf \hookrightarrow x_{1,\:2}=\dfrac{-3\pm \sqrt{3^2-4\cdot \:1\cdot \:5}}{2\cdot \:1}[/tex]

[tex]\hookrightarrow x=-\dfrac{3}{2}+i\dfrac{\sqrt{11}}{2},\:x=-\dfrac{3}{2}-i\dfrac{\sqrt{11}}{2}[/tex]

Thus the zero's of the function are:

x = 2, -2

Answer:

[tex]x=2, x=-2[/tex]; [tex]\frac{-3\pm i\sqrt{11}}{2} \in \mathbb{C}[/tex]

Step-by-step explanation:

Zeroes are found by setting the RHS = 0.

Since the quantity [tex]x^4+3x^3+x^2-12x-20[/tex] is a 4th degree polynomial there isn't a formula that gives us the solution, so we're stuck having to divide: to do so we make THE LIST: you list the divisors of the constant term without its sign (20: 1,2,4,5,10,20), the divisor of the lead coefficient (1), and you divide the first by the second in any possible way, adding a plus or minus:

[tex]\pm1, \pm2, \pm4, \pm5,\pm10,\pm20[/tex]. At this point you just have to check, replacing each one in the equation until you find two values that work (why two? You need to lower the degree of the polynomial by two, if you found only one you'd be stuck with a third degree equation which doesn't have an "easy" solving formula).

After some adding and multiplying you find that both 2 and -2 make the expression to zero. At this point you have two options

First is to divide the given expression by[tex](x-2)(x-2)=(x^2-4)[/tex] or, as I did in the image, notice that you will end up with a 2nd degree polynomial, whose coefficient you find by multiplying and confronting with the original equation.

Either way, you will end up with

[tex](x+2)(x-2)(x^2+3x+5)=0[/tex]

First two factors will give [tex]x=-2; x=2[/tex] respectively, while the third term has no real solutions (it still offers a pair of solutions in [tex]\mathbb{C}[/tex] which I'll add for the sake of completeness, but you're most likely required to look for real solutions only).

man i  don't   know

Step-by-step explanation:

 i  hope  it's   like 20 ? i guess  it's  20

Answer:

4(p+1)

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

hope this helped have a nice day

Step-by-step explanation:

What is the molar mass of an element?

the total number of particles in one gram of the element

the mass of 6.02 x 1023 representative particles of the element

the number of amus (atomic mass units) in 6.02 x 1023 moles of the element

1.0 gram divided by the atomic weight of the element

Answer:

5/16 of a pound

Step-by-step explanation:

2½ x ¼ = 5/4 × 1/4 = 5/16

Answer:

B

Step-by-step explanation:

formula= principal (1+(rate÷100))^number of years

5500(1+(1.6÷100))^4

5500 (1+0.016)^4

5500(1.016)^4

5500 (1.06555245)

5,860.53

$5,860.53

Answer:

Step-by-step explanation:

15(5+2) is the Answer

The greatest common factor to rewrite 75+30 as 15(5+2)

Greatest common divisor (GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.

An expression is a combination of numbers, variables and operators.

The given expression is 75+30.

By using distributive law we can find this.

Let us find factors of 75 and 30.

The factors of 75 are 1, 3, 5, 15, 25, 75

The factors of 30 are 1, 3, 5, 9, 15, 45

Their GCF is 15.

To get 75, we will multiply 15 by 5.

To get 30, we will multiply 15 by 2.

By using distributive property

75+30 can be splitted to factors as

15(5+2)

Hence  the greatest common factor to rewrite 75+30 as 15(5+2)

To learn more on GCD click:

https://brainly.com/question/27227228

#SPJ5

The person that would have more money at the end of the year is Sara.

The formula that would be used to determine the future value of an amount is:

FV = P (1 + r/m)^nm

Jon = $7050 x (1 + 0.05/4)^4 = $7409.16

Sara = $4867 x (1 + 0.1 / 365)^365 = $5378.79

To learn more about future value, please check: https://brainly.com/question/18760477

Answer:

57.72 in^2

Step-by-step explanation:

Question 1. Shapes are triangle, semi-circle, and rectangle.

Question 2.Find area of rectangle first. Then area of triangle and circle. Subtract area of triangle and circle. Then add the difference with the rectangles area.

Question 3.

Rectangle's area:48 in^2

Triangles area:8*4/2=  16 in^2

Circle Area: pi*r^2/2(since its a semi-circle)

3.14*2^2=3.14*4=12.56/2=6.28 in^2

Question 4.

16-6.28=9.72

9.72+48=57.72 in^2

Answer:

The fourth table

Step-by-step explanation:

3(0)-1=-1

3(1)-1=2

3(2)-1=5

Hope this helps :)

Answer:

x=36°

Step-by-step explanation:

Find the answer with the theorems related to isosceles triangle and the exterior angle theorem

Answer:

5. 8

6. 5

7. 7

8. 6

9. 3

10. 4

Step-by-step explanation:

The unknown number is the the larger number divided by 10.

Like in #5 : 80 ÷ 10 = 8

Answer:

y = 24

angle V = 67

as a 4 sided shape, the angles all have to add up to 360 degrees.

we already have the answers for R, 120, and B, 53. We have 187 degrees left to work with.

Based of the information the tics on the sides of the figure gives us, we know that angle P and R are the same! First (just for fun, this isn't needed) we'll find X.

(x+95) = 120

   -95     -95

       x = 25

We know 3/4 angles now, so by subtracting their sum from 360, we'll find angle V!

360 - 53 -120 - 120 = 67

Angle V is 67

Now to find y!

(2y+19)=67

     -19  -19

     2y = 48

     /2     /2

       y = 24

Answer:  

< means y is smaller than 3, it's not equal, so it's open dots.

(number line see the attach image.)

Answer:

(A) 9

Step-by-step explanation:

Substitute 2 for X

[tex]7-(-2)=9[/tex]

Answer:

25.20

Step-by-step explanation:

Answer:

The answer is 0.7344

I'm not sure tho

Answer:

The answer is C

Step-by-step explanation:

Since the line above the letters is an arrow that means the two points have to create a line like that. Therefore, the answer is DB.

Answer:

DB

Step-by-step explanation:

Why others rejected?

E C

E B is rejected as points are not on one line

Answer:

84

Step-by-step explanation:

(92 + 96 + 88 + x) ÷ 4 = 90

92 + 96 + 88 + x/4 = 90

276 + x/4 = 90

(276 + x) × 4/4 = 90 × 4

276 + x = 360

x = 360 - 276

x = 84

PLEASE MARK ME AS BRAINLIEST AND HAVE A NICE DAY