Assessment

Read, analyze, then solve each problem. Answer each question.
A. A bowl of mango jelly was poured into a 14 cm x 8 cm x 3
cm rectangular container. If the mango jelly completely filled
the container, how much mango jelly was there?
1. What is asked in the problem? __________________________
2. Show your solutions. _________________________________
3. State the final answer. ________________________________
B. Ana is cleaning a box which is 6 dm long, 4 dm wide and 15
dm tall. What is the volume of the box?
4. What is asked in the problem? __________________________
5. What are given? _____________________________________
6. State the final answer. ________________________________
C. Wenalyn baked a cassava cake which measures 18 cm x 10
cm x 4 cm. She wants to share the cake with her two
classmates so she cuts it into three parts all of the same
sizes. How much cassava cake will each of her classmates
receive?
7. Show your solutions or illustration.

8. What is the final answer? _____________________________
D. A ream of bond paper is 28 cm long, 22 cm wide and 4 cm
thick. It contains 500 sheets. If 250 sheets were removed
from the ream of bond paper, what is the volume of the
remaining sheets?
9. Write the equation. __________________________________
10.What is the final answer? ___________________________

Answer:

Hi,

Step-by-step explanation:

[tex]\left\{\begin {array} {ccc}x&=&2*cos(t)-1\\y&=&3*sin(t)+4\\\end{array}\right.\\\\\\\left\{\begin {array} {ccc}\dfrac{x+1}{2}&=&cos(t\\\dfrac{y-4}{3}&=&sin(t)\\\end{array}\right.\\\\Squaring\\\\\boxed{(\dfrac{x+1}{2})^2+(\dfrac{y-4}{3})^2&=1}\\[/tex]

The curve is an ellipse having (-1,4) as center and half-axis (2 and 6)

Answer: Hope this explains everything for you!

y= -2x+3

Step-by-step explanation:

y= 2x-1 is wrong

First, we will start by identifying the y-int, the y-int is when x is zero. The y-int is 3 since when x is 0, y is 3, (0,3).

y= 2x+3 (So that means -1 is actually 3)

Plus even if your slope is 2, since from the 2 points you go up 2 and run by 1, if you're not going to calculate it with 2 points, you need to see if its uphill, downhill, etc. (More info in the image below) The slope is actually negative meaning it is -2.

So the equation of the line is actually y= -2x+3

Answer:

x = 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]26=-1+\left( 27x\right)^{\frac{3}{4} }[/tex]

[tex]\Longleftrightarrow 27=\left( 27x\right)^{\frac{3}{4} }[/tex]

[tex]\Longleftrightarrow \left( 27\right)^{\frac{4}{3} } =\left[ \left( 27x\right)^{\frac{3}{4} } \right]^{\frac{4}{3} }[/tex]

[tex]\Longleftrightarrow \left( 27\right)^{\frac{4}{3} } =\left( 27x\right)^{\frac{3}{4} \times \frac{4}{3} }[/tex]

[tex]\Longleftrightarrow \left( 27\right)^{\frac{4}{3} } =27x[/tex]

[tex]\Longleftrightarrow x=\frac{27^{\frac{4}{3} } }{27}[/tex]

[tex]\Longleftrightarrow x=27^{\frac{4}{3} -1}[/tex]

[tex]\Longleftrightarrow x=27^{\frac{1}{3} }[/tex]

[tex]\Longleftrightarrow x=\sqrt[3]{27}[/tex]

[tex]\Longleftrightarrow x=3[/tex]

The correct value of this equation is m = 24

This equation contains a fractional term. We note that the denominator of this equation is the term 4. Therefore, we will multiply the sides by 4:

13 = m/4 + 7

13 . 4 = 4(m/4) + 7 . 4

52 = m + 28

Now, let's isolate the variable "as negative" and after the equality - we'll be subtracting the terms:

52 = m + 28

-m = 28 - 58

-m = -24

m = 24

Therefore, the correct value of this equation will be m = 24

Answer:

[tex] \large {\boxed{ \sf{y = 2x + 5}}}[/tex]

Step-by-step explanation:

Suppose the slope of the line is k.

So,

[tex] \large {\bold {k = \frac{7 - ( - 1)}{1 - (3)} = \frac{7 + 1}{1 + 3} = \frac{8}{4} = 2 }}\\ [/tex]

So the line:

[tex] \large \bold{ \frac{y - 7}{x - 1} = k = 2 } \\ [/tex]

[tex] \: [/tex]

So,

[tex] \large \bold{y - 7 = 2(x - 1)}[/tex]

[tex]\large \bold{y - 7 = 2x - 2}[/tex]

[tex]\large \bold{y = 2x - 2 + 7}[/tex]

[tex]\large \bold{y = 2x + 5}[/tex]

[tex]{\rule{200pt}{4pt}}[/tex]

[tex] \large \bold{-N} \frak{unx-}[/tex]

Answer: x = 20

Step-by-step explanation:

   If line m is parallel to line n, the two angles given will be congruent because they will be alternate exterior angles (which are congruent).

  This means we will set them equal to each other and solve for x.

Given:

(4x - 23) = (2x + 17)

Add 23 to both sides of the equation:

4x = 2x + 40

Subtract 2x from both sides of the equation:

2x = 40

Divide both sides of the equation by 2:

x = 20

Answer:

x=7 ................................

Answer:

B.) 4,096 feet

Step-by-step explanation:

You were given a time, and time in the equation is represented by "t". To find the height, represented by "h", you just need to plug the given value in for "t" and simplify to find "h".

t = (1/4)√x                                         <--- Original equation

16 = (1/4)√x                                      <--- Plug 16 in "t"

64 = √x                                            <--- Divide both sides by (1/4)

4,096 ft = x                                    <--- Square both sides

The object reach the ground in 16 seconds, you should drop it from a height of 4096 feet.

The equation is t=1/4 √x , where t is time in seconds and x is height in feet. To determine the height  x at which an object should be dropped to reach the ground in 16 seconds, you can plug in the value of t=16 into the equation:

16 = 1/4 √x

Simplify the equation by multiplying both sides by 4:

4⋅16= √x

64= √x

Now, square both sides to isolate x:

64²=x

4096 = x

Therefore, to have the object reach the ground in 16 seconds, you should drop it from a height of 4096 feet.

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Answer:

C

Step-by-step explanation:

M is less than n because it comes before it in the number line

Answer:

the value is 14

Step-by-step explanation:

because im just trying to get points

if we take 30 to be the 100%, what is 27 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 30 & 100\\ 27& x \end{array} \implies \cfrac{30}{27}=\cfrac{100}{x} \\\\\\ \cfrac{10}{9}=\cfrac{100}{x}\implies 10x=900\implies x=\cfrac{900}{10}\implies x=90[/tex]

The measures of center and variability for the

temperatures that were lower this week than last week include mean, range, mean absolute deviation.

It should be noted that a mean simply means the average set if numbers given.

Also, the range is the difference between the highest number and the lowest number in the data.

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Answer:

mean,range,mean absolute deviation

Step-by-step explanation:

just took it on edge

Answer: Heyaa! ^^

When you simplify (17^14)^20 Your Answer is

Step-by-step explanation:

Hopefully this helps you!

Answer:

25

Step-by-step explanation:

c^2=a^2+b^2

where c = hypotenuse

so, x^2 = 24^2+7^2

x^2 = 576 + 49

x^2 = 625

x = square root of 625

x = 25

Answer:

2, 10, 50, 250

Step-by-step explanation:

For geometric sequences, multiply the previous term by the common ratio.

Using the formula for geometric sequences [tex]a_{n} =ar^{n-1}[/tex] , with [tex]a_{n}[/tex] being the nth term (so n=4 for the fourth term), a being the first term, and r being the common ratio.

Our starting term is 2. So that is automatically the first term of the four.

Second term:

[tex]a_{2} =2*5^{2-1}=2*5^1=2*5=10[/tex]

Third term:

[tex]a_{3} =2*5^{3-1}=2*5^2=2*25=50[/tex]

Fourth term:

[tex]a_{4} =2*5^{4-1}=2*5^3=2*5*5*5=10*25=250[/tex]

Two six-sided fair dice are rolled simultaneously.... 6 and the sum of the two numbers is an odd number is mathematically given as

x=7/10

Generally, the equation for Number is mathematically given as

[tex]x=P\frac{E > 3}{Enot > 5}\\\\Therefore\\\\x=P\frac{E > 3}{E\leq5}\\\\x=P\frac{4\leq E \leq5}{E\leq5}\\\\x=P\frac{7/36}{10/36}[/tex]

x=7/10

In conclusion,  the sum of the two numbers

x=7/10

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Answer:

135°

Step-by-step explanation:

That triangle in the corner is an right angle isosceles triangle as that line the midpoint of both sides :

the base angle of this triangle (x) will be :

180 = 90 + 2x

90 = 2x

x= 45

Angles on a straight line add up to 180. So to work out a :

180 = 45 + a

135 = a

Hope this helped and brainliest please

Answer:

w = 10

Step-by-step explanation:

First we take the two values for the breadth of the rectangle

So:

5x - 9 = 3x + 7

now we solve this equation as follows:

5x - 3x = 9 + 7

2x = 16

x = 8

now that we have found the value for x, we can substitute it in the equation, 5x - 9,or in the equation, 3x + 7.

when we substitute x in any of these equations, we get

5(8) - 9 = 31

3(8) + 7 = 31

now that we have the value for the breadth we can form the following equation:

31 × w = 310

31w = 310

w = 310/31 = 10

Answer:

10

Step-by-step explanation:

Firstly, we find the value of X

since 5X-9 and 3X+7 are lenghts

5X-9= 3X+7

5X-3X= 7+9

2X = 16

dividing bothsides by 2

2X/2= 16/2

X = 8

Hence,

5X-9= 5(8)-9= 40-9 = 31

3X+7=3(8)+7= 24+7= 31

To find the width

Area= lenght×width

310= 31×w

31w= 310

w= 310/31

W= 10

Answer:

60 ft

Step-by-step explanation:

a = 90

b = 108ft

the base angle can be found by using sin(x) = 120/108x2

=> x = 33.7 degrees

To find height, use tan(33.7) = Opp/ Adjacent = x / 90

=> x = 60.02 or 60 ft

Reason:

The largest sin(x) can get is 1, and the same goes for sin(3x).

Consequently, the largest 2sin(3x) can get is 2.

You can visually verify these claims by graphing each function with a tool like Desmos. Take note of the y coordinate of the highest points. See below.

Therefore, the largest f(x) = 2sin(3x)+C can get is 2+C or C+2

Answer:

X= 82⁰

z= 82⁰

Step-by-step explanation:

for X:

we can use co-interior angles sum up to make 180 so,

x+ 98= 180

x= 180-90= 82⁰

for z, we can use either angles on a straight line or corresponding angles

98 + z= 180

z= 180-98= 82⁰

corresponding angles are always equal and can be found in the F shape diagram when lines are parallel

therefore X and z are corresponding angles and since we found x= 82⁰ then z= 82⁰

Answer:

Angle AED: 40
Angle BEC: 105

Explanation:
1) To find Angle AED, you have to do arc BC minus arc AD then divide by 2.
120 - 40 = 80.
80 / 2 = 40

2) To find Angle BEC, you have to do arc BA + CD then divide by 2. But that's only angle CED. You'll have to double the number because BEA is vertical; then minus 360.

62 + 88 = 150
150 / 2 = 75
75 times 2 = 150
360 - 150 = 210
210 / 2 = 105
- You'll divide 210 by 2 because of the vertical angles of AED and BEC.

Answer:

30

Step-by-step explanation:

[tex]\frac{5\cdot\frac{6}{6} }{2\cdot\frac{6}{6} } = \frac{25}{30}, \frac{12}{30}[/tex]

Using it's concept, it is found that the probability of tossing heads and rolling a number less than 3 is given by:

C. 1/6

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there were 12 trials. Of those, 2 are H1 and H2, which are heads and a number less than 3, hence the probability is given by:

p = 2/12 = 1/6.

Which means that option C is correct.

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Answer:

M =290

Step-by-step explanation:

Subtraction of numbers

Answer:

375 plates were sold

Step-by-step explanation:

$2400 (profit) - $150 (advertising) = $6 (profit per plate $8 cost - $2 expense) times x

2400 - 150 = 6x

Simplify the left side: 2400 - 150 = 2250

2250 = 6x

Divide both sides by 6

2250/6 = 375

Answer:

25 degrees

Step-by-step explanation:

arc divided by 2 = angle

50/2=25

The amount of milk needed for a 17-pound goat and a 55-pound goat are 55 and 87.5 cubic units, respectively

The equation is given as:

y =1.5x + 5

For a 17-pound goat, we have:

x = 17

This gives

y =1.5 * 17 + 5

y = 30.5

For a 55-pound goat, we have:

x = 55

This gives

y = 1.5 * 55 + 5

y = 87.5

Hence, the amount of milk needed for a 17-pound goat and a 55-pound goat are 55 and 87.5 cubic units, respectively

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Answer:2

Step-by-step explanation:(720-240)/(240)