Mathematics
20. A teacher drew an area model to find the value of 6,986 +8.
Teacher's Model for 6,986 +8
R
Р
N
800
Q
8
560
M
UNIZ
not to scale
• Determine the number that each letter in the model represents and explain
each of your answers.
• Write the quotient and remainder for 6,986 + 8.
Explain how to use multiplication to check that the quotient is correct. You
may show your work in your explanation.
Enter your answers and your explanations in the space provided.
.

Step-by-step explanation:

Angles in a quadrilateral add to 360 degrees. So, x = 360-88-142-106=24 degrees

Answer:

x = 30

Step-by-step explanation:

[tex]\frac{x}{21} =\frac{20}{14}[/tex]

[tex]x=\frac{(21)(20)}{14}=\frac{420}{14} =30[/tex]

Hope this helps

Answer:

Step-by-step explanation:

Find the width as below

Substitute the values and solve for w

Now find the volume

Answer:

width = 3ft

volume = 144 ft³

Step-by-step explanation:

Pythagoras Theorem

[tex]\sf a^2+b^2=c^2[/tex]

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

The diagonal of the base of the aquarium, its height, and the length from the top corner to the opposite bottom corner forms a right triangle.  As we know two of the lengths, we can use Pythagoras Theorem to calculate the unknown length (diagonal of base).

Given:

[tex]\implies \sf 12^2+b^2=13^2[/tex]

[tex]\implies \sf b=\sqrt{13^2-12^2}[/tex]

[tex]\implies \sf b=5[/tex]

Now we know the length of the diagonal of the base, we can again use Pythagoras Theorem to find the width of the aquarium.

Given:

[tex]\sf \implies 4^2+b^2=5^2[/tex]

[tex]\sf \implies b=\sqrt{5^2-4^2}[/tex]

[tex]\sf \implies b=3[/tex]

Therefore, the width of the aquarium is 3 ft.

As the aquarium is modeled as a rectangular prism:

[tex]\begin{aligned}\textsf{Volume of a rectangular prism} & = \sf width \times length \times height\\ \implies \textsf{Volume of aquarium} & = \sf 3\:ft \times 4\:ft \times 12\:ft\\& = \sf 144 \:\:ft^3\end{aligned}[/tex]

X = 5 boxes

figure out the X for each person

Lizzy sold: 5 * 5 = 25 boxes

Suzy sold: 5 * 1 = 5 boxes

John sold: 5 * 3 = 15 boxes

Mark sold: 5 * 8 = 40 boxes

Lamar sold: 5 * 4 = 20 boxes

→ How many boxes did Lamar sell?

Answer: 20 boxes

→ How many more boxes did John sell than Suzy?

Answer: 10 boxes

workout: 15 boxes - 5 boxes = 10 boxes more

→  How many more boxes would Lizzy have to sell to equal how many Mark sold?

Answer: 15 boxes

workout: 40 boxes - 25 boxes = 15 boxes more

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Here we go ~

Each Cross (X) represents 5 boxes

Now, let's move on to questions :

-) 4 Cross = 4 × 5 = 20 boxes

-) (4× Cross) - (1 × cross)

-) (3 × 5) - (5)

-) 25 - 5 = 10more boxes than Suzy

-) (8 × Cross) - (5 × Cross)

-) (8 × 5) - (5 × 5)

-) 40 - 25

-) 15 more boxes to be sold to get equal to the number of boxes mark sold.

Answer:

5/4 pounds

Step-by-step explanation:

Using unitary method:

4 days-------5 pounds

1 day---------5/4 pounds

Answer:

$ 1875

Step-by-step explanation:

Richard invests some amount P. He want the money he invested to gain an interest of $300.

A = P(1 + n×i)

A = P + 300

i = 0.08

n = 2

P + 300 = P(1 + 2×0.08)

P + 300 = P(1.16)

300 = 1.16P - P

300 = 0.16P

300/0.16 = 0.16P/0.16

P =300/0.16

P = $1875

Richard should invest $1875 if he wants an interest of $300 in 2 years.

Answer:

Area of polygon = 42.63 mm²

Step-by-step explanation:

Given:

To find the area of the polygon (rectangle), multiply the length with the width.

⇒ Area of polygon = LW

Substitute the values into the area:

⇒ Area of polygon = (8.7)(4.9)                                [L = 8.7 mm; W = 4.9 mm]

⇒ Area of polygon = 42.63 mm²

As it's a rectangle

Area:-

Answer:

OPTION B

Step-by-step explanation:

1 cm=0.75 m

I hope it helped you

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &\$0.55\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &20\\ \end{cases} \\\\\\ A=0.55(1 + 0.05)^{20}\implies A=0.55(1.05)^{20}\implies A\approx 1.46[/tex]

Answer:

1st option

Step-by-step explanation:

A verical line parallel to the y- axis has equation

x = c ( c is the value of the x- coordinates the line passes through )

thus the x- coordinates are the same

Answer:

The 7th term is 896

Step-by-step explanation:

= ar^n-1

a = 14

r = 28/14

= 2

n = 7

= 14 X 2 ^ 7-1

= 14 X 2 ^ 6

= 14 X 64

= 896

Answer:

g + a = 24. 2 g + a = 42.

Step-by-step explanation:

Each goal gets 2 points and each assist gets 1 point

If # of goals = g , and you get 2 points for each goal, then points acquired by goals can be represented by 2g

If # of assists = a, and you get 1 point for each assist, then points acquired by assists can be represented by a

The total # of points the player had was 42. This means that 2g + a = 42 (this is the first equation)

We are also told the player scored a total of 24 goals and assists. If g = # of goals and a = of assists, then g + a = 24 (this is the second equations)

So the two equations are g + a = 24. 2 g + a = 42.

Answer:

g + a = 24. 2 g + a = 42.

Step-by-step explanation

trust

Answer:

SA = 527.52 cm²

Step-by-step explanation:

Cone SA = πr(r + √(h² + r²))

Find h

Step 1. Create a right triangle with the radius (attached image)

Step 2. Pythagorean Theorem

a² + b² = c²

7² + b² = 17²

b² = 289 - 49

b = √240

b or h = 4√15

Solve for SA

SA = πr(r + √(h² + r²))

SA = 3.14 · 7 · (7 + √(4√15² + 7²))

SA = 21.98(7 + √(240 + 49))

SA = 21.98 (7 + 17)

SA = 527.52 cm²

Hope this helps!

Answer:

(0,0)

(1,3)

(2,6)

(3,9)

(-1,-3)

(-2,-6)

(-3,-9)

Step-by-step explanation:

The equation of the graph is y=3x

Answer:

Kiko was right.

Step-by-step explanation:

When a positive integer is multiplied by another positive integer, the product is positive. When a negative integer is multiplied by a positive integer, then the product is negative. The power should also be considered as well, since it can affect whether the integer is positive or negative depending on if it's even or odd.

Step-by-step explanation:

a microscopic membrane of lipids and proteins which forms the external boundary of the cytoplasm of a cell or encloses a vacuole, and regulates the passage of molecules in and out of the cytoplasm

thx for ur poi.nts buddy

kese h.o aap

Answer:

b

Step-by-step explanation:

The mean and standard deviation of the random variable X if 60 percent of city residents support the proposal is 1200 and 21.9 respectively.

From the information given, the mean of the binomial variable x will be:

= 2000 × 60%

= 2000 × 0.6

= 1200

The standard deviation will be:

= ✓n × ✓p(1 - p)

= ✓1200 × ✓0.4

= ✓480

= 21.9

Also, the mean and standard deviation to determine the values of k1 and k2 will be -3 and 3.

Lastly, the test statistic will be:

= (0.65 - 0.60)/(✓0.60 × (0.40) /2000

= 0.05/✓0.24/2000

= 0.05/0.011

= 4.55

The z value at 5% significance level is 1.64. This supports the funding of the proposal.

Learn more about mean on:

https://brainly.com/question/1136789

Answer:

minor arc DE: (23/9)π

Major arc DGE:(49/9)π

Step-by-step explanation:

This is a simple problem.

First solve the circumference of the circle: 2π (4).

then use the length formula

L=(x*c)/360

and then plug in, so first we use 115 as x(which is degrees) to find de

so

L = (115* 2π (4))/360

and you will get (23/9)π

To get the major arc you have to get the outside angle, so 360-115, and you do the same thing but with 245 as x.

Hope this helps and im correct!

Answer:

x | -7      -5     -3  

y | -21    -15    -9

Step-by-step explanation:

y = 3x

If x = -7  then y = 3 × (-7) = -21

  x = -5  then y = 3 × (-5) = -15

  x = -3  then y = 3 × (-3) = -9

Answer:

James will need to buy 3 boxes of crackers for the party.

Step-by-step explanation:

remember: 16oz=1 pound

If James needs 3 pounds of crackers, and each box is 20oz, that means each box is a little over 1 pound. (1.25 pounds to be exact). So, we know that he needs to buy 3 boxes of crackers. This is because 20×3=60 ounces which is 3.75 pounds. Meaning, 3 boxes is the correct answer since we can't cut a box in half.

hmmm taking a peek at the triangles inside the park, hmmm let's notice both triangles have all interior angles of 60°, meaning the triangles are equilateral both, so all sides are equal, since we know one side is 50 yards, well, all sides are 50 yards, so the top and bottom straight-lines are both 50 each.

looking at the left and right sides, hmmm those are just sectors of a circle, both have a radius of 50 yards and a central angle of 120°.

[tex]\textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=50\\ \theta =120 \end{cases}\qquad \implies s=\cfrac{(120)\pi (50)}{180}\implies s=\cfrac{100\pi }{3} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{straight~lines}{2(50)}~~ + ~~\stackrel{circular~lines}{2\left( \cfrac{100\pi }{3} \right)}\implies 100+2\left( \cfrac{100(3.14) }{3} \right)~~\approx~~309~yards[/tex]

Answer:

327675

Step-by-step explanation:

the formula of the series is:

16

∑5*2^(n-1)

n=1

the formula for the sum of a geometric series is:

Sn=a(1-r^n)/(1-r)

plug in the values from above

n=16 a=5 and r=2 (values from the geometric function) so

Sn=5(1-2^16)/(1-2)

Sn=327675

Answer:

48.5 ft

Step-by-step explanation:

square is the correct answer

Answer:

There are 14 dimes and 17 nickels.

Step-by-step explanation:

Let x be number of nickels and let y be number of dimes.

Given that the total is $2.25 and there are 31 coins, we know that:

[tex]0.05x +0.10y = 2.25[/tex]

[tex]x+y = 31[/tex]

Solving for x yields:

[tex]x=31-y[/tex]

We then proceed by plugging that back into the previous equation:

[tex]0.05(31-y)+0.10y=2.25[/tex]

[tex]1.55 - 0.05y +0.10y = 2.25\\[/tex] --> Distribute

[tex]1.55 +0.05y=2.25[/tex] --> add y's together

[tex]0.05y=0.7[/tex] --> subtract 1.55

[tex]y=14[/tex] --> divide by 0.05

Therefore, x must equal 17, which means you have 14 dimes and 17 nickels.

Answer:

No.

Step-by-step explanation:

No, because the 9th decitile is equal to the 90th decitile, and so that means that you're tall.