Evaluate the following expression using the values given.

Find 2x2 − 2z4 + y2 − x2 + z4 if x = −4, y = 3, and z = 2.

Explain how you got your answer.

Answer: [tex]a_1=50,d=25[/tex] and $475 deposited into the account on her birthdays by her 18th birthday.

Step-by-step explanation:

It is given that, on Gabriela’s first birthday, her parents gave her a $50 savings account.

Initial term : [tex]a_1=50[/tex]

On every birthday after that her parents added to the account, increasing the amount they deposited by $25 each year.

Common difference : [tex]d=25[/tex]

It forms an AP: 50,75,100,...

nth term of an AP is

[tex]a_n=a_1+(n-1)d[/tex]

Substitute [tex]a_1=50[/tex] and [tex]d=25[/tex] in the above formula.

[tex]a_n=50+(n-1)25[/tex]

It represents the amount deposited into the account after n birthdays.

We need to find the amount by her 18th birthday.

Put n=18 in the above equation.

[tex]a_{18}=50+(18-1)25[/tex]

[tex]a_{18}=50+(17)25[/tex]

[tex]a_{18}=50+425[/tex]

[tex]a_{18}=475[/tex]

Therefore, $475 deposited into the account on her birthdays by her 18th birthday.

We are to calculate total amount given to Gabriela on her 18th birthday

Total amount Gabriela’s parents will have deposited into the account on her birthdays by her 18th birthday is $475

Amount given to her on her first birthday = $50

Additional amount given to her each year = $25

number of years, n = 18

a1 = $50

d = $25

n = 18

Sum = a1 + (n - 1)d

= 50 + (18 - 1)25

= 50 + (17)25

= 50 + 425

= 475

sum = $475

Read more:

https://brainly.com/question/24321873

Answer: The sunflower be  50 inches tall after 6 weeks.

Total height of sunflower in w weeks = 20+1.5 w,

Step-by-step explanation:

Given:  In the beginning, the sunflower was 20 inches tall.

The sunflower then began to grow at a rate of 1.5 inches per week.

Then, total height of sunflower in 6 weeks = 20+1.5 ×20, where 1.5 ×20= growth in 6 weeks

= 20+30

= 50 inches

So, the sunflower be  50 inches tall after 6 weeks.

Let w = number of weeks, then

Total height of sunflower in w weeks = 20+1.5 w, where 1.5 w= growth in w weeks.

Answer:         29

                   1.5w+20

Step-by-step explanation:

Answer:

96 square meters

Answer: 3/8

Step-by-step explanation:

24 min to 64 min as a fraction is [tex]\frac{24}{64}[/tex]    

Now write the fraction is simplest form  by dividing it by their greatest factor.

The GCF of 24 and 64 is 8  

24/8 = 3

64 /8 = 8    

So the ratio will be 3/8

Answer:

Assuming the repetitive part is 152, i.e. the original repeating decimal is

A=3.152152152....

then  

1000A=3152.152152152152....

subtract A

1000A-A=3152.152152....-3.152152152....

999A=3149

A=3149/999=3+152/999=3 152/999

Therefore

3.152152152.... = 3149/999 or 3 152/999

Answer:

still need help?

Step-by-step explanation:

Answer: thomas

Step-by-step explanation:

because patrick’s is 75% sugar and thomas’s is more

Answer:

Step-by-step explanation:

3:4= patrick 6:7= Thomas

=3/4 =6/7

=0.75 =about 0.86

= 75% = 86%

Thomas’ is more sugary.

Answer:

This is hard to read, but i guess that the equation is:

[tex]7*5*2/7*3^2*5^0/2^{-3}*2^{-9}[/tex]

So we have some things to solve:

First, for any number:

x^0 = 1

then 5^0 = 1.

And for negative powers,

x^-n = (1/x)^n.

And we

Then we can rewrite our equation as:

[tex]\frac{7*5*2*3^2*1*2^3}{7*2^9}[/tex]

now we can cancel the seven in the numerator and the denominator

[tex]\frac{5*2*3*2^3}{2^9}[/tex]

now, remember the relation:

a^x*a^y = a^(x+y)

then:

2*2^3 = 2^4

and 2^4/2^9 = 2^-5 = (1^2)^5

Then our equation is:

[tex]\frac{5*3}{2^5}[/tex]

15/2^5 = 0.46875

Answer:

17-4=13

13+3=16

16+6=22

Step-by-step explanation:

so it in the 22nd floor

Answer:

It is on 22nd floor.

Answer:

true

Step-by-step explanation:

because no one can eat that many big macs

Answer:

? = -611.3

I used a calculator.

hope this helps

Answer:

the answer is 4/6 or 66.7% is the probability

Answer:

[tex]x^3+x^2-2x\leq140[/tex]

Step-by-step explanation:

This is an algebra problem, and we are expected to inequality for the volume of the aquarium.

Given that the

length= 2x

width=(x – 1)

heigth=  (x + 2)

and the volume= 280 ft^3

the inequality expression for the volume is

[tex]2x*(x -1) * (x + 2) \leq 280\\\\[/tex]

open the brackets

[tex]2x*(x -1) * (x + 2) \leq 280\\\\(2x^2-2x)*(x+2)\leq 280\\\\\2x^3+4x^2-2x^2-4x\leq 280\\\\\2x^3+2x^2-4x\leq280[/tex]

divide through by 2 we have

[tex]x^3+x^2-2x\leq140[/tex]

Answer:

(1, 5]

Step-by-step explanation:

2*3n  would be the equation.

Answer:

11:3

Step-by-step explanation:

For every 11 y there is 3x

Hope it helped

Answer:

Your answer would equal the same on the other side.

-26-4m=-4m-26

if you minus 26 from both sides youll have -4m on both sides also. So it would equal. So you have an Equaled equation if that makes sense.

Answer:

48 metres.

Step-by-step explanation:

How far does the cyclist travel in 3 seconds:

First, find how far the cyclist goes in 1 second:

320 metres = 20 seconds

? = 1 second

320 ÷ 20 = 16 metres

The cyclist travels 16 metres in 1 second.

How far does the cyclist travel in 3 seconds:

1 second = 16 metres

3 seconds = ?

16 × 3 = 48 metres.

The cyclist travels 48 metres in 3 seconds.

Step-by-step explanation:

Hey there!

The equation of a st.line passing through point is;

(y + 6) = m1(x+3).........(i). [ Use one point formula]

y = -4x + 1............(ii)

Comparing 2nd equation with y = mx+c, we get;

Slope (m2) = -4.

For parallel lines;

[tex]m1 = m2[/tex]

(i.e m1=m2 = -4)

Putting value of slope in 1st equation,

[tex](y + 6) = - 4(x + 3)[/tex]

Smplify them to get equation.

[tex](y + 6) = - 4x - 12[/tex]

[tex]y = - 4x - 12 - 6[/tex]

[tex]y = - 4x - 18[/tex]

Therefore the required equation is y = -4x-18.

Hope it helps..

Answer: = x+5

Step-by-step explanation:

Jimmy is 5 years older than sally and sally is know as x

= x+5

If Sally is 10

Jimmy will be 10+5= 15 years old

~~~inuola1234

Answer:

  [tex]-\dfrac{5\sqrt{11}}{11}[/tex]

Step-by-step explanation:

Use the relationship between the various trig functions.

  [tex]\tan{\theta}=\dfrac{\sin{\theta}}{\cos{\theta}}=\dfrac{\left(-\dfrac{5}{6}\right)}{\left(\dfrac{\sqrt{11}}{6}\right)}=-\dfrac{5}{\sqrt{11}}\\\\=-\dfrac{5}{\sqrt{11}}\cdot\dfrac{\sqrt{11}}{\sqrt{11}}=\boxed{-\dfrac{5\sqrt{11}}{11}}[/tex]

Answer:

x = 12

Step-by-step explanation:

Move numbers and variables on opposite sides and flip the signs

9x - 4x = 20 + 40

Add and subtract

5x = 60

Divide and multiply

x = 60/5

x = 12

Answer:

[tex](x-h)^{2} + (y-k)^{2} = r^{2}[/tex]

Step-by-step explanation:

Answer:

y=5x−z

Step-by-step explanation:

Step 1: Multiply both sides by y.

xy−5=yz

Step 2: Add -yz to both sides.

xy−5+−yz=yz+−yz

xy−yz−5=0

Step 3: Add 5 to both sides.

xy−yz−5+5=0+5

xy−yz=5

Step 4: Factor out variable y.

y(x−z)=5

Step 5: Divide both sides by x-z.

y(x−z)x−z=5x−z

y=5x−z

Answer:

its really simple

Step-by-step explanation:  

since you dont know z you would just multiply them so you would get 48z

but since you dont know what z is i believe its 48z^2 or just 48z

Answer:

i wanna say its C,D,E,F but i get rational and irrational mixed u0