Gaya spends $48 to buy books that cost Sx each.
(a) Write down an expression, in terms of x, for the number of books Gaya buys.
(b) Myra spends S60 to buy books that cost S(x+2) each.
Gaya buys 4 more books than Myra.
Show that x^2+5x-24 = 0.
The relationships between the amount spent on books and the cost of
each book is a proportional relationship.
The correct responses are;
[tex](a) \ \displaystyle \mathrm{The \ number \ of \ books \ Gaya \ buys \ is } \ \underline{\frac{48}{x} \ books}[/tex][tex]\mathrm{(b) \displaystyle \underline{ \left(\frac{48}{x} -4 \right) \cdot \left(x + 2 \right) - 60 = x^2 - 5 \cdot x - 24 = 0}}[/tex]Reasons:
The amount Gaya spends on books = $48
The cost of each book = $ x
(a) The expression in terms of x for the number of books Gaya buys is therefore;
Number of books Gaya buys × $ x = $48
Therefore;
[tex]\displaystyle Number \ of \ books \ Gaya \ buys = \frac{\$48}{\$ x}[/tex](b) The amount Myra spends to buy books = $60
The cost of each book = $·(x + 2)
The number of books Myra buys = The number of books Gaya buys - 4
We have;
[tex]\displaystyle Number \ of \ books \ Myra \ buys = \frac{48}{x} - 4[/tex]
Which gives;
[tex]\displaystyle \mathbf{\left(\frac{48}{x} - 4 \right) \cdot \left(x + 2 \right)} = 60[/tex]
Using a graphing calculator, we get;
[tex]\displaystyle \frac{4 \cdot x^2 - 20 \cdot x - 96}{x} = 60[/tex]
4·x² - 20·x - 96 = 60·x
Which gives;
4·x² + 40·x - 60·x - 96 = 0
4·x² - 20·x - 96 = 0
x² - 5·x - 24 = 0
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.
1/2 of David's money is
2/3 of Henry's money.
(a) Express David's money as a fraction of Henry's money
Answer:
80
Step-by-step explanation:
math
solve pls brainliest
Answer:
a) -5 meters
b)160°C
Step-by-step explanation:
. Find the range of the function y
1/4x +1 if the domain is {-8, -4, 0}.
The range of a function is the possible output values the function can have.
The range of the function is all real values except 0
The function is given as:
[tex]\mathbf{y = \frac{1}{4x + 1}}[/tex]
When the denominator of the function is 0, the function would not have a real value.
This means that:
[tex]\mathbf{y \ne 0}[/tex]
i.e. the value of y cannot be 0.
Hence, the range of the function is all real values except 0
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60
Compare
a 15% of 17 and 17% of 15
b
1.2% of 48 and 12% of 480
с
147% of 621 and 125% of 549
80% of a and 40% of 2a
f
36% of 2.5b and 1.5% of 80b
Answer:
a=2.55
b=0.576
c=912.87
f=2.295
Step-by-step explanation:
=15/100*17
=2.55
=17/100*15
=2.55
=1.2/100*48
=0.576
=12/100*480
=57.6
=147/100*621
=912.87
=125/100*549
=686.25
=80/100*2.55
=2.04
=40/100*2a
=40/100*(2*2.55)
=0.4*(5.1)
=2.04
=36/100*2.5(2.55)
=0.36*6.375
=2.295
=1.5/100*80(2.55)
=0.015*(204)
=3.06
A bag of grass seed weighs 5.8 pounds. How many pounds would 2.5 bags weigh
Answer:
Answer: 14.5 pounds
Step-by-step explanation:
Step-by-step explanation: Do 5.8 times 2.5
Answer:
14.5 lb
Step-by-step explanation:
1 bag weighs 5.8 lb.
2.5 bags weight 2.5 × 5.8 lb
2.5 × 5.8 lb = 14.5 lb
Suitcases originally priced at $50 are now on sale for $41. What percentage is the discount?
The students in Tisha's grade voted to select a guest speaker. 75% of the students voted for a famous athlete. If there are 52 students in Tisha's grade, how many students voted for the athlete?
Answer:
39
Step-by-step explanation:
75% of 52 is 39
Hope this helps!
Properties of Exponents-
Simplify (4a⁵b⁶)⁴
~exponent
===========================
(4a⁵b⁶)⁴
= 4⁴ × (a⁵)⁴ × (b⁶)⁴
= 256 × (a⁵)⁴ × (b⁶)⁴
= 256a²⁰ × (b⁶)⁴
= 256a²⁰b²⁴ ✔️
~ nice to help you ^^
(4a⁵b⁶)⁴ = ?
= 4⁴ (a⁵)⁴ (b⁶)⁴
= 256a²⁰b²⁴
0 0
2 6
4 12
6 18
What is the slope?
what is the y-intercept?
Proportional or not proportional?
Answer:
a) slope / m = 3
b) y-intercept / b = 0
c) Proportional
Step-by-step explanation:
a)
( y1 - y2 ) / ( x1 - x2 )
( 6 - 12 ) / ( 2 - 4 )
( -6 ) / ( -2 )
6 / 2
3
b)
y = mx + b
6 = 3(2) + b
6 = 6 + b
0 = b
c)
Proportional is when it crosses origin ( 0, 0 ).
Not proportional is when it does not cross origin.
Hopefully this helps!
Brainliest please?
-5x+3-2x-4+4x-5= −
x+8m2x+8m2 =
(x+6)(x+6)(x+6)(x+6)
Answer:
is this even a real question?
Step-by-step explanation:
what is 492 divided bye 2 someone help me
Answer:
246
Step-by-step explanation:
Given that,
→ what is 492 divided by 2 ?
In mathematical form,
→ 492 ÷ 2
→ 246 {final answer}
Hence, the answer is 246.
This shake is made from five congruent triangles. Find the total area of the shape
Area of one triangle = [tex]A = \frac{a·b}{2} = \frac{6 \times 3}{2} = \frac{18}{2} = 9 {cm}^{2} \\ [/tex]
For 5 triangles = [tex]9 \times 5 = 45 {cm}^{2} [/tex]
- BRAINLIEST answerer
Have i done this right, why did i not get the third mark
Answer:
because you are good with math
Step-by-step explanation:
Tim's phone service charges $24.25 plus an additional $0.18 for each text message sent per month. If Tim's phone bill was $28.75, which equation could be used to find how many text messages, x, Tim sent last month?
What is the slope of the equation
Answer:
Undefined
Step-by-step explanation:
x=-4 is a vertical line (On a graph) so it would be undefined
x + y = 8
Now let x = 7. What is y?
Answer:
1 cuz 7+1=8
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
x=7
y=1
7+1=8
A population has a mean of 80 and a standard deviation of 6. A sample of 49 observations will be taken. What is the probability that the sample mean will be larger than 82
A population has a mean of 80 and a standard deviation of 6. A sample of 49 observations will be taken. What is the probability that the sample mean will be larger than 82
if u help me your dreams will come true ya know
Answer:
Area of larger circle = [tex]\pi *r^2=3.14(11^2)=379.94[/tex]
Area of smaller circle = [tex]\pi *r^2=3.14(3^2)=28.26[/tex]
Probability that it lands in the shaded area (smaller circle):
28.26 ÷ 379.94 = 0.07438... = 0.07 (nearest hundredth)
Please help me please 38
Answer:
8 inches
Step-by-step explanation:
Area of a triangle:
[tex]a=bh/2[/tex]
We're given 2 variables already, area and base, so we just need to plug those in and solve for the 3rd variable.
[tex]40=10h/2\\40=5h\\8 = h\\h = 8[/tex]
Answer:
8
Step-by-step explanation:
a right triangle is half of a square, so (10*8)/2=10*4=40.
solve pls brainliest
Answer:
$8
Step-by-step explanation:
20% of $40
= [tex]\frac{20}{100}[/tex] × $40
= 0.2 × $40
= $8
$8 is discounted from the regular price
Answer:
$8 off
Step-by-step explanation:
Convert from a percentage to a multiplier by dividing by 100:
[tex]\frac{20}{100}=0.2[/tex]
Then multiply that by the price:
[tex]40*0.2=8[/tex]
meaning the item is $8 off.
You can confirm that like so:
[tex]\frac{8}{40} =0.2\\[/tex]
or 20%
If you need to cut 5 pieces of fabric a 14 feet length, how long should each piece be?
Answer:
I think by mental math it would be 2.8 feet.
Step-by-step explanation:
A committee consisting of three people is to be selected from ten members. How many ways are there to select the committee of three people
Answer:
120
Step-by-step explanation:
10 choose 3
theres really no simple way to do that with work unless you have a fancy calculator.
akiko sells 5 small paintings and 5 large paintings .Each large painting cost $20 more than a small painting .she earns $300. what is the price of a small painting
Answer:
$20
Step-by-step explanation:
small painting: x
large painting: x + 20
5(x + x + 20) = 300
5(2x + 20) = 300
10x + 100 = 300
10x = 200
x = 20
Answer: $20
The morning temperature in Finland was −18.3∘ F. The temperature rose 23.7°F during the day before reaching its high temperature for the day.
What was the high temperature for the day?
Enter your answer in the box.
°F
Answer:
The high temperature for the day was 5.4°F
Step-by-step explanation:
-18.3 + 23.7= 5.4
The high temperature for the day is 5.4° F.
What is temperature?Temperature is a degree of hotness or coldness the can be measured using a thermometer. It's also a measure of how fast the atoms and molecules of a substance are moving. Temperature is measured in degrees on the Fahrenheit, Celsius, and Kelvin scales.
Given that, The morning temperature in Finland was -18.3° F.
The temperature rose 23.7° F during the day before reaching its high temperature for the day.
Now, -18.3°+23.7°
= 5.4° F
Therefore, the high temperature for the day is 5.4° F.
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Can anyone help me please anyone please
Answer:
121
Step-by-step explanation:
Since the two lines are parallel, they will have the same angles, so all we need to do is find the angle that is next to 59°. Let's label this y °.
In other words, y °, the angle next to 59°, is equal to x°.
Since we are dealing with angles of a straight line, we know that the two angles of either line will add up to be 180°.
So, 59° + y ° = 180°
Isolate y by subtracting 59 from 180.
180 - 59 = 121
y ° = 121
So, x° = 121°
please help me asap
Given that 6x – 7y=4
Find x when y = 2
Answer:
x = 3
Step-by-step explanation:
6x - 7y = 4
We are given that y = 2
6x - 7(2) = 4
6x - 14 = 4
Add 14 on both sides to leave the 6x alone
6x = 18
Divide by 6 to isolate x and find the value of x
x = 3
We can further prove this by putting in the value of x
6(3) - 7(2) = 4
18 - 14 = 4
Which is correct
Answer:
3
Step-by-step explanation:
The height of an experimental plant after x days can berepresented by the formula 3(4x+2). The height of a second plant can be represented by the formula 6(2x+2). Is it possible that the two plants will ever be the same height? Explain.
Answer: No
Step-by-step explanation:
The question is whether 3(4x+2) could ever equal 6(2x+2). So let's set them equal to each other and find if there is a value of x, the days, where they are equal.
3(4x+2) = 6(2x+2)
12x + 6 = 12x+2
6 = 12?? No
They will bnever be at the same height. They are growing at the same rate (12x) but starting at different heights (6 and 12)
4 divided by 2.48
Use long division
Answer:
Step-by-step explanation:
The quotient is 0.62 and the remainder is 0.
What is the division?The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.
Given that, 2.48 divided by 4.
Long Division is a method for dividing large numbers, which breaks the division problem into multiple steps following a sequence.
Here,
4|2.48|0.62
24
24
_____
08
08
_____
0
So, quotient is 0.62 and remainder is 0.
Therefore, the quotient is 0.62 and the remainder is 0.
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