Three children each contributed toward a birthday present for their mother. The oldest contributed three times as much as the youngest, while the second oldest contributed 50 cents more than the youngest. If the present costs $10.50, how much did each contribute?
Answer:
Youngest child: $2
oldest child: $6
Second oldest: $2.50
Step-by-step explanation:
Youngest child= x
oldest child= 3x
Second oldest: .50+x
x+3x+.50+x=10.5
5x+.50=10.5
- .50= - .50
5x=10
divided both numbers by 5 and x is equal to 2. So, the youngest child is $2 and you add .50, which is $2.50, and thats for the second child. Last, you do 2 times 3 equals $6 which is the oldest child.
The youngest contributed $1.90, the oldest contributed $5.27, and the second oldest contributed $2.85.
Three children each contributing to their mother's birthday present. The eldest gave three times more than the youngest, while the second oldest contributed 50 cents more. If the gift costs $10.50 which is given in the question.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
Let the youngest sibling contribute the amount of x dollars
As per the given information,
3x + 0.50 x + x + x = 10.50
Apply the addition operation,
4.50x = 10.50
x = 10.50 / 6.50
Apply the division operation to get
x = 1.90
So the youngest sibling contributed = $1.90
The oldest contributed 1.90 × 3 = $5.27
And the second oldest contributed (1.50)1.90= $2.85
Therefore, the youngest contributed $1.90, the oldest contributed $5.27, and the second oldest contributed $2.85.
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I forgot how to do this lol
What is the value of k?
Answer:
k = 10
Step-by-step explanation:
the sum of any two interior angles is equal to the exterior angle of the unknown interior angle
4k+5 + 6k+10 = 115
10k + 15 = 115
10k = 100
k = 10
what is the factor of this 3x - 12
Answer:
3 (x - 4)
Step-by-step explanation:
I need help correct answers plzz
Step-by-step explanation:
Pythagoras, Pythagoras, Pythagoras.
c² = a² + b²
for c being the Hypotenuse (the side opposite of the 90 degree angle).
that is something you should really burn into your brain for life. you will need that many times.
1.
89² = 80² + side²
side² = 89² - 80² = 1521
side = sqrt(1521) = 39 ft
2.
D
because here the x value of 2 has to different assigned result (y) values. but for a function it had to be exactly 1 value.
3.
the longer of the 2 given sides must be the Hypotenuse, because otherwise we would get a negative length.
97² - 72² = side² = 4225
sqrt(4225) = side = 65 cm
4.
the distance between 2 point is the Hypotenuse of a right-angled triangle, with its legs being the differences in x and y coordinates.
F = (-1, 6)
G = (3, 4)
FG² = (-1 - 3)² + (6 - 4)² = 16 + 4 = 20
FG = sqrt(20) = 4.472135955... ≈ 4.5
so, A is the right answer.
5.
that creates a right-angled triangle, with the flag pole and the distance on the floor to the flag pole as the legs, and the rope as Hypotenuse.
rope² = 53² + 28² = 3593
rope = sqrt(3593) ≈ 60 ft
6.
A
85² = 36² + 77²
7225 = 1296 + 5929 = 7225
correct. this is a right-angled triangle.
B
101² = 99² + 20²
10201 = 9801 + 400 = 10201
correct. this is a right-angled triangle.
C
123² = 120² + 27²
15129 = 14400 + 729 = 15129
correct. this is a right-angled triangle.
D
42² = 33² + 24²
1764 = 1089 + 576 = 1665
incorrect.
1764 - 567 = 1089 ?
1197 = 1089
also incorrect.
as is 1764 - 1089 = 567 and 1089 - 567 = 1764
so, this is not a right-angled triangle.
7.
the sum of all angles in a triangle (also in general triangles) is always 180 degrees.
since the right angle is already 90 degrees, it leave only 90 degrees for the other 2 angles.
A is the only correct option. 25 + 65 = 90.
8.
BC = 13
AC = 3
AB² = AC² + BC² = 3² + 13² = 9 + 169 = 178
AB = sqrt(178) = 13.34166406... meter
the tree was then originally
3 + 13.34166406... = 16.34166406... meter high
12.1.1
35² = 21² + side²
side² = 35² - 21² = 1225 - 441 = 784
side = sqrt(784) = 28 m
12.1.2
side² = 16² + 30² = 256 + 900 = 1156
side = sqrt(1156) = 34 ft
12.2.3
61² = 60² + 11²
3721 = 3600 + 121 = 3721
correct. this is a right-angled triangle.
12.2.4
40² = 37² + 9²
1600 = 1369 + 81 = 1450
incorrect. this is not a right-angled triangle.
neither is 1600 - 1369 = 81 nor 1600 - 81 = 1369 nor 1368 - 89 = 1600
12.2.5
38² = 35² + 15²
1444 = 1225 + 225 = 1450
incorrect. this is not a right-angled triangle.
neither is 1444-1225=225 nor 1444-225=1225 nor 1225-225 = 1444
12.2.6
53² = 45² + 28²
2809 = 2025 + 784 = 2809
correct. this is a right-angled triangle.
12.3.8
the x and y coordinate differences between A and B are 6 and 3.
AB² = 6² + 3² = 36 + 9 = 45
AB = sqrt(45) = 6.7
12.3.9
the x and y coordinate differences between B and C are 1 and 7.
BC² = 1² + 7² = 1 + 49 = 50
BC = sqrt(50) = 7.1
12.3.10
the x and y coordinate differences between A and C are 5 and 4.
AC² = 5² + 4² = 25 + 16 = 41
AC = sqrt(41) = 6.4
final question : you need that in many distance calculations, side lengths, diagonals, heights,... for rooms, yards, acres, buildings, mountains, ...
Order these numbers from least to greatest
Answer:
5.125, 5.14, ¹⁰³/₂₀, 5²/₉
Step-by-step explanation:
When you convert 103/20 to decimal you get 5.15 which is greater than 5.125 and 5.14.
When you convert 5²/₉ to fraction you get ⁴⁷/₉ which when converted to decimal is 5.222 which is greater than 5.125, 5.14 and 5.15.
if a is more than b, what is the equation for an ellipse with a centre at the origin and a horizontal major axis?
Answer:
[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1[/tex]
which expression is equal to 4 to the power of 5 times 4 to the power of -7 divided by 4 to the power of -2
Step-by-step explanation:
4⁵ × 4^-7 / 4^-2
it is important to understand that a negative exponent means 1/...
a^-n = 1/(a^n)
in that sense we have therefore
4⁵ × 1/4⁷ × 4² (as (1/ 1/a^n) = a^n)
4⁵ × 4² × 1/4⁷ = 4⁷ × 1/4⁷ = 1
so, "1" is the fully simplified expression equal to the original expression.
Select all values equal to the fraction below:
Can someone help me with this please?!
Answer:
x < 6
Step-by-step explanation:
1) -5x > -30
2) divide both sides by -5
3) flip the sign as we divided inequality by a negative
4) x < 6
solve for x: 2-3(2x-2)=17
Answer:
x = - 1.5
Step-by-step explanation:
2 - 3(2x - 2) = 17 ← distribute parenthesis
2 - 6x + 6 = 17 , simplify
8 - 6x = 17 ( subtract 8 from both sides )
- 6x = 9 ( divide both sides by - 6 )
x = [tex]\frac{9}{-6}[/tex] = - [tex]\frac{3}{2}[/tex] = - 1.5
Which number is closest to 1/2
Answer:
0.56
it's basically the number closest to 50. Don't get tricked by the 0.05 because that's only 5% not 50%
help with these pleaseee
Percent Change = (new quantity - old quantity) / old quantity
#2:
(64 - 52) / 52
12 / 52
0.2308
23%
#4:
(12 - 18) / 18
-6 / 18
-0.33
33% decrease
#5:
(10 - 16) / 16
-6 / 16
-0.375
38% decrease
Hope this helps! :)
An account earns 8.4% interest compounded monthly. If 12,000 is invested in the account initially, how much
interest is earned in this account over a 25 year period?
Answer:
$30,2400
Step-by-step explanation:
First, we need to find how much interest he earns in a month
8.4% of $12,000 = $1,008
Next, we multiply the amount of interest per month by the number of months in 25 years
25 years = 300 months
Now we can multiply the two values to get our final answer
1,008 x 300 = $30,2400
Triangle ABC is translated 2 units right and 5 units down to form triangle A’B’C’. This triangle is then translated 5 units right and 4 units up to form triangle A”B”C”. If the vertex A is at (-4, 2), what are the coordinates of vertex A”?
Answer:
(3,1)
Step-by-step explanation:
(x,y) (-4,2)
so -4 +2 = - 2 ; -2 +5 = 3
and for y: 2 - 5 = - 3 ; - 3 + 4 = 1
(3,1)
Use the information in the diagram to determine the height of the tree. The diagram is not to scale.
Step-by-step explanation:
the scenario creates 2 similar triangles :
one main triangle with the house height the double floor distance and the double line of sight from the left point on the floor to the top of the house.
and the other triangle is the height of the tree, the single floor (from the left point to the tree) distance, and the single line of sight from the left point on the floor to the top of the tree.
similar triangles means : all angles are the same. and the side lengths of one triangle correlate to the corresponding side lengths in the other triangle by the same multiplication factor.
and that means that the floor distances of small and large triangle have the same ratio, as the view of line distance AND the height sizes.
we see : large triangle side / small triangle side = 2/1 = 2
and therefore, the same factor (2) applies to the heights.
so,
height of house / height of tree = 2
therefore,
height of tree = height of house / 2 = 150/2 = 75 ft
Select perpendicular lines from the given pairs of lines :
Select one:
a.
y = 2x + 3, y = 2x + 7
b.
y = x / 2 + 3, y = − x / 2 + 7
c.
y = 2x + 3, y = − x / 2 + 7
d.
y = 2x + 3, y = x / 2 + 7
What is the equation of the line that passes through the point (5, 6) and has a slope
of 2
Answer:
y = 2x - 4
Step-by-step explanation:
Given:
x1 = 5
y1 = 6
slope (m) = 2
Solution:
y - y1 = m ( x - x1 )
y - 6 = 2 ( x - 5 )
y - 6 = 2x - 10
y = 2x - 10 + 6
y = 2x - 4
Simplify.
(2⁴)³
its telling me to write at least 20 characters so uhm-- ignore the rest of this weeeeeeeeeeeeeeeeee
Answer:
4096
Step-by-step explanation:
Explanation:
The rule we use is (a^b)^c = a^(b*c). It says to multiply the exponents when we raise one exponential expression to another exponent. The base stays the same.
So, (2^4)^3 = 2^(4*3) = 2^12
You could take the slightly longer path to say the following
(2^4)^3 = (2^4)*(2^4)*(2^4) = 2^(4+4+4) = 2^12
what are some expressions that are equivalent to
–
2(5n).
[tex]\huge\textbf{Hey there!}[/tex]
[tex]\large\text{Gu\textbf{id}\textsf{e}}\bf\downarrow[/tex]
[tex]\large\textbf{2 negatives = positive}\\\large\textbf{2 positives = positive}\\\large\textbf{1 negative \& 1 positive = negative}\\\large\textbf{1 positive \& 1 negative = negative}\\\\\large\text{Negatives are BELOW 0}\\\large\text{Positives are ABOVE 0}\\\\\large\textsf{Negatives are on the LEFT side of zero.}\\\large\textsf{Positives are on the RIGHT side of zero.}[/tex]
[tex]\huge\textsf{-2(5n) \boxed{\rightarrow} \bf -10n}\\\\\\\\\huge\boxed{\rightarrow\text{-2n + (-2n) + (-2n) + (-2n) + (-2n)}}\\\huge\boxed{\rightarrow \text{\bf -2n - 2n - 2n - 2n - 2n}}\\\huge\boxed{\rightarrow{\text{-4n - 2n - 2n - 2n}}}\\\huge\boxed{\rightarrow \text{-6n - 2n - 2n}}\\\huge\boxed{\rightarrow \text{\bf -8n - 2n}}\\\huge\boxed{\rightarrow \boxed{\text{ -10n}}}[/tex]
[tex]\huge\text{\bf -5(2n)}\\\huge\boxed{\rightarrow \text{-10n}}[/tex]
[tex]\huge\boxed{\text{\bf Therefore, your answers \underline{\underline{could}} be: }}\\\huge\boxed{\bullet \textsf{ -2n - 2n - 2n - 2n -2n}}\huge\checkmark\\\huge\boxed{\bullet \textsf{ -8n - 2n}}\huge\checkmark\\\huge\boxed{\bullet \textsf{ -5(2n)}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A standard die is rolled find the probability that the number rolled is greater than 4 Express your answer as a fraction in lowest terms or a decimal number rounded to three decimal places if necessary
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
A standard die has 6 numbers, so the probability it will be greater than 4 is 6-4, or 2. Therefore the answer is [tex]\frac{2}{6}[/tex], but this can be simplified to [tex]\frac{1}{3}[/tex].
Can you please help me?
Step-by-step explanation:
60 cookies with 4 cups
that means 60 per 4 = 60/4 = 15
and that means that he can make 15 cookies with 1 cup.
that is clear : from 60/4 we immediately know 15/1.
and now, as we know how many cookies can be made with 1 cup, it is easy to say how many cookies can be made with 3 cups. right, 3 times a much.
so, yes, we multiply 15 by 3 and get 45 cookies as answer.
Which is greater?
48 fl oz
10 3/4 c
1. How many small squares are in Step 10?
Image below
A. 10
B. 11
C. 90
D. 110
Answer:
110 squares
Step-by-step explanation:
= 10 x 11
= 110 small squares.
From the question,
Step one : • • = 1(2) small squares
Step two : • • • = 3 squares in two layers = 2(3) = 6 small squares
• • •
Step three : • • • • = 4 squares in 3 layers = 3(4) = 12 small squares
• • • •
• • • •
Can someone please help me with 54? It’s the last one and it’s due in 1 hour Tysm if you do!!
Answer:
4
Step-by-step explanation:
Well 3 x 4 equals 12, 12 x 4 equals 48, and so on.
hope this helps!
The perimeter of the figure below is 41.6 in.
Find the length of the missing side.
Answer:
the answer is 5.9 since both sides are the same and on the other side its 5.9
Hope This Helps!!!
Please helpppppppppp
Answer:add 126 and 21 and 1.19
Step-by-step explanation:
126+21+1.19=
hope this helped
Answer:
7.14
Step-by-step explanation:
126 miles divided by 21 miles is 6 miles
So 6 gallons for 126 miles
1.19 times 6 is 7.14
8 less than the sum of 6 and a number
Answer:
(6 + n) - 8
Hope this helps.
Pls mark brainliest. :D
Answer:x < 2
Step-by-step explanation: 6+x < 8
x < (8-6)
x < 2
Please help!
A rock is dropped down from the top of a 500-foot cliff. After 1 second, the rock is traveling 32 feet per second. After 4 seconds, the rock is traveling 128 feet per second.
a. Assume that the relationship between time, t, and speed, s, is linear and write an equation describing this relationship. Use ordered pairs of the form (time, speed).
b. Use this equation to determine the speed of the rock 7 seconds after it is dropped.
Answer:
Part A:
The equation describing the relationship between speed and time is:
s = 32t
Ordered pairs of the form (speed, time) are:
(32, 1)
(64, 2)
(96, 3)
(128, 4)
Part B:
s = 32t
s = 32 * 5 = 160 feet per second
Step-by-step explanation:
1. Let's review the information provided to us to answer the question correctly:
Height of the cliff = 500 feet
Speed after one second = 32 feet per second
Speed after four seconds = 128 feet per second
2. Assume the relationship between time, t, and speed, s, is linear and write an equation describing the relationship. Use ordered pairs of the form (speed, time)
The equation describing the relationship between speed and time is:
s = 32t
Ordered pairs of the form (speed, time) are:
(32, 1)
(64, 2)
(96, 3)
(128, 4)
3. Use the equation to determine the speed of the rock 5 seconds after is dropped.
s = 32t
s = 32 * 5 = 160 feet per second
The first step for deriving the quadratic formula from the quadratic equation, 0 = ax^2 + bx + c, is shown.
Step 1: –c = ax^2 + bx
Which best explains or justifies Step 1?
subtraction property of equality
completing the square
factoring out the constant
zero property of multiplication
Answer:
Subtraction property of equality
Step-by-step explanation:
You subtracted c from both sides of the equation to preserve equality
The step 1 is explained by subtraction property of equality.
The correct option is A.
The standard form of Quadratic Equation is
ax² + bx + c = 0
Also, we must remove c from the right side and move it to the left side in order to derive the quadratic formula from the quadratic equation.
And to do that, we must subtract c from both sides, which is
-c = ax² + bx
Then, we have used subtraction property here.
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