1 Activity
Read and study the problem.
Marcel buys 5-star apples for PhP5.00 each and 3 guyabanos for PhP32.50 each.
She gives the cashier a PhP200.00 bill. Write an expression for the total cost of the fruits
she buys and an equation for the amount of change the cashier should give her.
Il Questions to Ponder
1. How to use variables to represent the price of each fruit?
2. How to write an expression for the total cost of the fruits she bought and an
equation for the amount of change the cashier should give her?

Answer:

3x² –12x + 32, R –93

Step-by-step explanation:

(3x³ – 3x² – 4x + 3) ÷ (x + 3)

We can obtain the answer to the question given above using long division method as follow:

Please see attached photo for explanation.

(3x³ – 3x² – 4x + 3) ÷ (x + 3) =

3x² –12x + 32, Remainder –93

Answer:

30000

Step-by-step explanation:

discount (d)= 5%of M.p

=5/100 * 600000

=30000

Answer:

r = 8.28

Step-by-step explanation:

Circumference of a circle:

C = 2πr

52 = 2(3.14)r

52 = 6.28r

r = 52/6.28

r = 8.28

Answer:

44.1m

Step-by-step explanation:

we are given a quadratic function which represents the height and time of a baseball

[tex] \displaystyle h = 29.4t - 4.9 {t}^{2} [/tex]

we want to figure out maximum height of

the baseball

since the given function is a quadratic function so we have a parabola

which means figuring out the maximum height is the same thing as figuring out the maximum y coordinate (vertex)

to do so we can use some special formulas

recall that,

[tex] \displaystyle \rm t= \frac{ - b}{ 2a} [/tex]

[tex]\displaystyle H_{\text{max}}=f(t)[/tex]

notice that, our given function is not in standard form i.e

[tex] \displaystyle f(x) = a {x}^{2} + bx + c[/tex]

let's make it so

[tex] \displaystyle h = - 4.9 {t}^{2} + 29.4t[/tex]

therefore we got

our a is -4.9 and b is 29.4

so substitute:

[tex] \displaystyle\rm t= \frac{ -( 29.4)}{ 2 \cdot - 4.9} [/tex]

remove parentheses and change its sign:

[tex] \displaystyle\rm t= \frac{ -29.4}{ 2 \cdot - 4.9} [/tex]

simplify multiplication:

[tex] \displaystyle\rm t= \frac{ -29.4}{ - 9.8} [/tex]

simplify division:

[tex] \displaystyle \: t = 3[/tex]

so we have figured out the time when the baseball will reach the maximum height

now we have to figure out the height

to do so

substitute the got value of time to our given function

[tex]\displaystyle H_{\text{max}}=29.4\cdot 3-4.9\cdot {3}^2[/tex]

simplify square:

[tex]\displaystyle H_{\text{max}}=29.4\cdot 3-4.9\cdot 9[/tex]

simplify mutilation:

[tex]\displaystyle H_{\text{max}}=88.2-44.1[/tex]

simplify substraction:

[tex]\displaystyle H_{\text{max}}=44.1[/tex]

hence,

the maximum height of the baseball is 44.1 metres

Answer:

Solution given:

height

h=29.4t – 4.9t²

differentiating each term with respect to time (t)

[tex] \frac{d'(h)}{d(t)} [/tex]=[tex] \frac{d(29.4t – 4.9t²)}{d(t)} [/tex]

[tex] \frac{d'(h)}{d'(t)} [/tex]=29.4-9.8t

again second derivative

[tex] \frac{d''(h)}{d"(t)} [/tex]=-9.8

for maximum, minimum

first derivative =0

29.4-9.8t=0

t=[tex] \frac{29.4}{9.8} [/tex]=3

So it attains maximum height at t=3

so

maximum height=29.4×3-4.9×3² =44.1meters

So.

maximum height of the basketball is 44.1meters

Answer:

Step-by-step explanation:

The slope is given to you by the line y = 1/4 x

The slope is just read as the number in front of x providing that the coefficient of y is 1. If that is not so, then you must divide by the coefficient in front of y. So far what you have is y = 1/4 x + b.

The second part of the question is to use the given point to find b.

x = 4

y = -1

b = ?                       substitute x and y to find b

y = 1/4 * 4 + b

- 1 = 1/4 * 4 + b

-1 = 1 + b

-2 = b

The equation of the line is y = 1/4 x - 2 Just to confirm this, I'm going to include the graph with the point 4,-1 on it.

Answer:

$4.80

Step-by-step explanation:

Answer:

$4.80

Step-by-step explanation:

To get the price of one can, we divide 3 by 5

After doing this, we find one can costs $0.60

0.6 · 8 = $4.80

Answer:

B. 28

Step-by-step explanation:  

Answer:

B. 28

Step-by-step explanation:

for every 4 boys there is 3 girls

so,

from 4 to 16 you multiply by 4,

4 x 4 = 16 (what you do to one you do to the other:

4 x 3 = 12

It's asking for the total amount

if there is 16 boys there is 12 girls with the ration of 16:12

add them up,

16 + 12 = 28 (That's your answer).

Answer:

$11343.13

Step-by-step explanation:

From the given information:

Principal = 3000

rate = 7% = 0.07

time = 19 years.

The amount of investment after 19 years for a continuous compounded interest can be estimated by using the formula:

[tex]A = Pe^{rt} \\ \\ A = 3000 \times e^{0.07 \times 19} \\ \\ \mathbf{A = \$11343.13}[/tex]

Answer:

6 x 4 = 24 divided by 2 = 12

6 + 3 = 9 x 4 = 36 divided by 2 = 18

so 12 + 18 = 30m2

Formula of a triangle:

BH x 1/2 (basically dividing by 2)

Area of a Trapezoid:

B1 (Base 1) + B2 (Base 2) x Height (H) x 1/2 (basically dividing by 2)

Answer:

[tex]x^{2} + y^{2} -10x -16y + 39[/tex]

Step-by-step explanation:-

The equation used to find the equation of circle is :-

[tex](x-a)^{2} + (y-b)^{2} = radius^{2}[/tex]

'a' means the x coordinate of the circle, 'b' means y coordinate of the circle.

In the question, it's given that the coordinates of the circle are (5, -8) and radius is 8cm.

So, 'a' will be 5 and 'b' will be -8

So,

[tex](x-5)^{2} + (y--8)^{2} = 8^{2}[/tex]

[tex](x-5)^{2} + (y+8)^{2} = 64[/tex]

[tex]x^{2} - 10x + 25 + y^{2} - 16y + 64[/tex]

[tex]x^{2} + y^{2} -10x -16y + 64 - 25[/tex]

= [tex]x^{2} + y^{2} -10x -16y + 39[/tex]

Answer:

12

Step-by-step explanation:

Answer:

11 songs

Step-by-step explanation:

11 songs would leave him with $10.30 left

Answer:

SAS, SSS

Step-by-step explanation:

You're A>A>S

Answer:

y < x

Step-by-step explanation:

equation of line can be derived by finding slope and y-intercept

in this case the slope is 1 and the y-intercept is 0

equation is y = x

however, this is an inequality so answer is one of the following:

y > x  or  y < x

pick a point in the shaded region (these are the 'solutions'), let's pick (1, -1)

x = 1 and y = -1

which one is true?  -1 > 1  or  -1 < 1

-1 < 1 is the true one so inequality is y < x

Answer and Step-by-step explanation:

The negatives cancel out, so the negative 5 becomes a positive (adding) 5.

[tex]-2\frac{1}{3} = -\frac{7}{3}[/tex]

[tex]-\frac{7}{3} + 5 = \frac{8}{3} = 2\frac{2}{3}[/tex]

The answer choice that is correct is the last one.

#teamtrees #PAW (Plant And Water)

Answer:

hi!!! the answer is x = weight in pounds of bananas in the basket!

hope that helped

Step-by-step explanation:

so we have the total of the apple in the basket so we already know the apple but we need to know the bananas weight in the basket!

Answer:

...

Step-by-step explanation:

Answer:

C im pretty sure

Step-by-step explanation:

24 divided by 3 = 8 in 1 minute he will make 8 shots

2 = 16

5 x 8 = 40 shots in 5 minutes (correct) so its C

Answer:

C

Step-by-step explanation:

24 in 3 minutes = 8 baskets in 1 minute.

Table:

minutes = baskets

1 = 8

2 = 16

3 = 24

4 = 32

5 = 40

The answer is C, it shows 1,2,5 minutes with the correct rate of change.

Answer:

1,485

Step-by-step explanation:

The formula for area is A=bH (base x height) so you multiply 45 x 33

Answer:

D, I think

Step-by-step explanation:

Answer:

The answer is 26

Step-by-step explanation:

[tex] \purple{ \tt{ \huge{ \: ✨Answer ✨ \: }}}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \orange{ \boxed{ \boxed{ \huge{ \tt{{ \: 26 \: }}}}}}[/tex]

Step-by-step explanation:

x - 3y = 2

x=2+3y.....(1)

2x - 6y = 6

2(2+3y)-6y=6

it is not measurable.

Answer:

2.57

The mean variation in the number of pieces of fruits eaten by the classmates is 2.57

Step-by-step explanation:

Given the data:

X = 9, 4, 6, 2, 11, 10,7

The mean absolute deviation = Σ|x - xbar| / n

Xbar = mean value = Σx / n

n = sample size

The mean, xbar = (2 + 4 + 6 + 7 + 9 + 10 + 11) / 7

Xbar = 49 / 7 = 7

Take the sum of the absolute value of the difference between the mean and x ;

Σ|x - xbar| / n =

= (5 + 3 + 1 + 0 + 2 + 3 + 4) / 7

= 2.57

9514 1404 393

Answer:

  (b)  82

Step-by-step explanation:

The Pythagorean theorem tells you the length of MP is ...

  MP = √(CM² -CP²)

  MP = √(67² -53²) = √1680 ≈ 40.988

The length of MN is twice this, so is ...

  MN = 2×MP = 2×40.988 = 81.976

Rounded to the nearest tenth, ...

  MN ≈ 82.0

Answer:

Step-by-step explanation:

Answer:

z = 68, x = 9

Step-by-step explanation:

z must equal 68 since they're vertical angles.

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

180 - 68 = 112

12x + 4 = 112

---> x = 9

Answer:

z = 68 degrees

x = 9

Step-by-step explanation:

z = 68 degrees because of the vertex angle theorem

x is a little more complicated

First you set 68 + (12x + 4) equal to 180 becuase a straight line is 180 degrees.

68 + (12x + 4) = 180

-68 -68

12x + 4 = 112

-4 -4

12x = 108

/12 /12

x = 9

Answer:

I think D cause it has an exponent

Answer:

your answer is d because it is havinf power 2

Answer:

8x-34=74

Explanation-