1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
a_sh-v [17]
3 years ago
8

Jaime knows that 30² is 900. He wonders if knowing that 30² can help him finds 29x31. Raquel knows what 25² equals. How can she

use the knowledge to find 24x26?
Mathematics
1 answer:
iragen [17]3 years ago
3 0

9514 1404 393

Answer:

  Jaime: yes: 29·31 = 900 -1 = 899

  Raquel: 24·26 = 25^2 -1 = 624

Step-by-step explanation:

The difference of squares factors as the product of the sum and difference of the roots:

  a^2 -b^2 = (a -b)(a +b)

<u>Jaime</u>

  29·31 = (30 -1)(30 +1) = 30^2 -1^2 = 900 -1 = 899

  Jaime can subtract 1 from 30^2 to find 29·31

__

<u>Raquel</u>

  24·26 = (25 -1)(25 +1) = 25^2 -1^2 = 625 -1 = 624

  Raquel can subtract 1^2 from 25^2 to find 24·26.

You might be interested in
Ella purchased a game that was on sale for 12% off. The sales tax in her county is 6%. Let y represent the original price of the
klio [65]

Answer:

The expression that can be used to determine the final cost of the game is

1.06(0.88 y) ⇒ (C)

Step-by-step explanation:

  • If the price of an item is discounted, that mean its new price will be less its initial price
  • The taxes on item, makes its new price greater than the initial price because tax is add

Let us solve the problem

∵ Ella purchased a game that was on sale for 12% off

→ That means the new price will (100% - 12%) of the initial price

∵ y represented the initial price of the game

→ Multiply y by (100% - 12%) to get the new price

∴ The new price = y (100% - 12%)

∴ The new price = y (88%)

→ Change 88% to normal number by divide it by 100

∴ The new price = y (\frac{88}{100})

∴ The new price = 0.88 y

∵ The sales tax in her county is 6%

→ That means the final cost will be (100% + 6%) of 0.88 y

∴ The final cost = (100% + 6%) × (0.88 y)

∴ The final cost = 106% × (0.88 y)

→ Change 106% to normal number by divide it by 100

∴ The final cost = \frac{106}{100} × (0.88 y)

∴ The final cost = 1.06(0.88 y)

The expression that can be used to determine the final cost of the game is 1.06(0.88 y)

4 0
3 years ago
Identify the statement that represents the given algebraic expression.
ollegr [7]

Answer:

n is -32

Step-by-step explanation:

- 17 \times 2 \: equals \:  - 32 \\  - 32 \div 2 \: equals \:  - 17

8 0
3 years ago
Graph the linear inequality. <br><br> x + 2y = 5
choli [55]
So you always want y in front of the equation no matter what so you have x +2y=5 so you take the x and you subtract it to both side making it 2y= 5-x so then you just have to take the 2 to both side so you have to divide it and you will get y= 5/2-x/2 so then to graph it you start with the b which is -x/2 so you go down -1 and over 2 and place your dot adn then go up 5 over 2 and then place you dot and connect them together

5 0
3 years ago
Read 2 more answers
A​ hot-air balloon is 140 ft140 ft above the ground when a motorcycle​ (traveling in a straight line on a horizontal​ road) pass
luda_lava [24]

Answer:

Step-by-step explanation:

Given

Balloon velocity is 14 ft/s upwards  

Distance between balloon and cyclist is 140 ft

Velocity of motor cycle is 88 ft/s

After 10 sec  

motorcyclist traveled a distance of d_c=88\times 10=880 ft

Distance traveled by balloon in 10 s

d_b=14\times 10=140 ft

net height of balloon from ground =140+140=280 ft[/tex]

at t=10 s

distance between cyclist and balloon is z=\sqrt{280^2+880^2}

z=923.47 ft

now suppose at any time t motorcyclist cover a distance of x m and balloon is at a height of h m

thus z^2=(88t)^2+(14t+140)^2

differentiating w.r.t time

\Rightarrow z\frac{\mathrm{d} z}{\mathrm{d} t}=14\cdot \left ( 14t+140\right )+88\cdot \left ( 88t\right )

\Rightarrow at\ t=10 s

\Rightarrow \frac{\mathrm{d} z}{\mathrm{d} t}=\frac{14\cdot \left ( 14t+140\right )+88\cdot \left ( 88t\right )}{z}

\Rightarrow \frac{\mathrm{d} z}{\mathrm{d} t}=\frac{14\times 280+88^2\times 10}{923.471}

\Rightarrow \frac{\mathrm{d} z}{\mathrm{d} t}=\frac{81,360}{923.471}=88.102\ ft/s

3 0
3 years ago
The sum of 6 consecutive even numbers is 126.<br> What is the fourth number in this sequence?
Verizon [17]

9514 1404 393

Answer:

  22

Step-by-step explanation:

The average of the 6 even integers is the odd integer halfway between the first three and the last three. That average value is 126/6 = 21, so the 4th integer is 21+1 = 22.

_____

All 6 are {16, 18, 20, 22, 24, 26}.

3 0
3 years ago
Other questions:
  • Circle the division problem that does not belong with the other three. Explain 621/6 384/3 719/7 514/5
    15·1 answer
  • What is the volume of the figure? Enter the answer in the box.
    10·2 answers
  • If m∠D = 18°, and m∠C = 45°, what is ?
    10·2 answers
  • Kevin is 3 years older than Daniel. Two years ago, Kevin was 4 times as old as Daniel. How old is Daniel now?
    15·2 answers
  • What function do you know from calculus is such that its first derivative is a constant multiple k of itself
    8·1 answer
  • Find area AND perimeter of the shape
    8·2 answers
  • Help me now i taking a quiz
    12·2 answers
  • A bottle-filling process has a low specification limit of 1.8 liter and upper specification limit of 2.2 liter. The standard dev
    10·1 answer
  • Ruby frosted 8 cookies in 20 minutes. At this rate how<br> many cookies could she frost in 2 hours?
    6·1 answer
  • The perimeter of a quarter circle is 10. 71 yards. What is the quarter circle's radius?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!