Step-by-step explanation:
[tex] \frac{1}{3} (z + 4) - 6 = \frac{2}{3} (5 - z) \\ \\ \therefore \: \frac{ (z + 4) - 6 \times 3}{3} = \frac{2(5 - z) }{3} \\ \\ \therefore \: \frac{ z + 4 -18}{3} = \frac{10 - 2z }{3} \\ \\ \therefore \: \frac{ z - 14}{3} = \frac{10 - 2z}{3} \\ \\ \therefore \: z - 14 = 10 - 2z \\ \\ \therefore \: z + 2z = 10 + 14\\ \\ \therefore \: 3z =24 \\ \\ \therefore \: z = \frac{24}{3} \\ \\ \: \: \: \: \: \: \: \: \huge \orange{ \boxed{ \therefore \: z = 8}}[/tex]
sum of money is placed at simple interest for 3 years at 10% per annum and then the amount is invested for 2 years at the same rate at compound interest . If the total amount of 5 years became Rs. 471900, what was the sum?
Answer:
sum was 300000
Step-by-step explanation:
let sum of money is placed is x rs
Term T = 3 years, rate R = 10%
Then simple interest for for 3 years is
[tex]SI= \frac{PTR}{100}\\ SI=\frac{x\times 3\times 10}{100} \\SI = 0.3x[/tex]
Sum of x will become x+0.3x = 1.3x after 3 years. now this 1.3x is kept for compound interest for two years. ie
[tex]A =P[1+R]^t\\471900=1.3x[1+\frac{10}{100} ]^2\\x=\frac{471900}{1.573} \\x=300000[/tex]
Sum was 300000
At the simple interest rate, the rate is applied only to the initial sum, while
at the compound interest, the rate is applied to the amount in the account.
The sum of money is approximately Rs 355,847.466Reasons:
Let P represent the sum of money invested, we have;
[tex](P + P \cdot r \cdot t_1) \times (1 + r)^{t_2} = \mathbf{ 471900}[/tex]Where;
P = The initial sum invested
r = The simple and compound interest rate applied = 10% = 0.1
t₁ = The number of years the money is placed at simple interest = 3 years
t₂ = The number of years the money is placed at compound interest = 2 years
Therefore;
[tex]\mathbf{(P + P \times 0.1 \times 3) \times (1 + 0.01)^{2}} = 471900[/tex]
Which gives;
[tex]P \cdot (1 + 0.3 ) \times (1 .01)^{2} = 471900[/tex]
[tex]\displaystyle P =\mathbf{\frac{471900}{(1 + 0.3 ) \times (1 .01)^{2} }} \approx 355,847.466[/tex]
The sum of money invested, P ≈ Rs 355,847.466
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Which symbol makes the following number sentence correct?
4.567 4.576
Answer:
←
Step-by-step explanation:
less than as 4.567 is less than 4.576
The correct symbol to use between 4.567 and 4.576 is '<', since 4.567 is less than 4.576.
Explanation:The question is asking to choose the correct mathematical symbol that makes the given number sentence true. The two numbers are 4.567 and 4.576. In this case, since 4.576 is greater than 4.567, the correct symbol would be less than ('<'). Thus, the correct number sentence is 4.567 < 4.576.
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Each class at Greenville school has 22 children enrolled.the school has 24 classes how many children are enrolled at Greenville school?
Answer:
528
Step-by-step explanation:
because each class has 22 students and there are 24 classes you multiply them
Answer: 528 children
Step-by-step explanation: 22 children in each class. 24 total classes.
22•24=528
Together, teammates Pedro and Ricky got 2687 base hits last season. Pedro had 283 more hits than Ricky. How many hits did each player have?
Answer:
Ricky hits 1202 base
Pedro hits = 1485 base
Step-by-step explanation:
Pedro + Ricky = 2687 hits
Let Ricky hits = x
So the Pedro hits will be = x + 283
( x + 283 ) + x = 2687
2 x + 283 = 2687
2 x = 2687 - 283
2 x = 2404
x = 1202
So the Ricky hits 1202 base
Pedro hits (1202 + 283) = 1485 base
Final answer:
To determine the number of hits Ricky and Pedro had, a system of equations was set up and solved. Ricky had 1202 hits, while Pedro had 1485 hits last season.
Explanation:
To solve the problem involving teammates Pedro and Ricky's base hits, we need to set up a system of equations based on the information given:
Pedro and Ricky's hits together total 2687.
Pedro had 283 more hits than Ricky.
Let's denote Ricky's hits as R and Pedro's hits as P. The two equations representing the situation are:
R + P = 2687
P = R + 283
To find the number of hits Ricky had, we can substitute the second equation into the first:
R + (R + 283) = 2687
2R + 283 = 2687
2R = 2687 - 283
2R = 2404
R = 2404 / 2
R = 1202
Now that we have Ricky's hits, we can find Pedro's hits by adding 283 to Ricky's total:
P = R + 283
P = 1202 + 283
P = 1485
Therefore, Ricky had 1202 hits, and Pedro had 1485 hits last season.
Which ordered pair (x,y) makes this relation a function?
{(2,3), (–2,5), (4,4), (-4,5), (x,y)}
A. (-4, -1)
B. (-1,-1)
C. (-2,-1)
D. (2, -1)
Answer:
Step-by-step explanation:
A i think sorry if it is wrong
The only ordered pair that can be added to make the relation a function, without repeating an x-value, is option B. (-1,-1).
The question is asking which ordered pair (x,y) makes the given set of ordered pairs a function. A function is defined as a relation where every x-value (input) is associated with exactly one y-value (output). We already have the points (2,3), (–2,5), (4,4), and (-4,5) in our set. To maintain the definition of a function, the x-value of the ordered pair we are going to add cannot be the same as any x-value already present in the set. Looking at our options:
A. (-4, -1) - This would not work because the x-value -4 is already paired with the y-value 5 in our set.B. (-1,-1) - This is a possibility as the x-value -1 is not in the set.C. (-2,-1) - This would not work because the x-value -2 is already paired with the y-value 5 in our set.D. (2, -1) - This would not work because the x-value 2 is already paired with the y-value 3 in our set.Therefore, the only ordered pair that makes the relation a function is option B. (-1,-1).
Roy is hiking down a mountain at an average rate of 3 miles per hour. He wants to know how far he can hike in a given number of hours. Which is the dependent variable in this problem situation?
Answer:
can you be more clear
Step-by-step explanation:
Answer:
distance is the dependent variable because it depends on the time hiked.
Step-by-step explanation:
if f(x)=3x-2 and g(x)=2x+1 find (f-g) (x)
Answer:x-1
Step-by-step explanation:
Simplify 7x+4-2x+6 pls help
Answer:
5x+10
Step-by-step explanation:
you will add 7x_2x=5x
then 4+6=10
A ladder leaning against a wall forms a triangle and exterior angles with the wall and the ground. What is the measure of exterior angle formed on the ground?
5 degrees
90 degrees
125 degrees
180 degrees
Yo sup??
we know that the sum of all the angles of a triangle is 180
therefore
11x+7x+90=180
18x=90
x=5
exterior angle formed on the ground=180-11x
=180-55
=125
Hope this helps
Prove that the value of the expression: (5^18–25^8)(16^4–2^13–4^5) is divisible by 30 and 44.
Final answer:
The expression given is factored to identify common factors of 30 and 44. By identifying factors like 3, 5 (for 30) and 2, 11 (for 44), it's shown that the expression is indeed divisible by both 30 and 44.
Explanation:
The student asked to prove that the value of the expression: (518−258)(164−213−45) is divisible by 30 and 44. To approach this proof, we will simplify and factor the expression where possible to find common factors of 30 (2*3*5) and 44 (4 × 11).
First, let's factor each part of the expression:
518 = (52)9 = 259
258 = (52)8 = 516
164 = (24)4 = 216
213 remains the same
45 = (22)5 = 210
Now, we rewrite the original expression with these factors:
(259 − 516)(216 − 213 − 210)
Looking at the first parenthesis, we see that 259 and 516 have a common factor of 516, so we can factor it out:
516(25−1)(216−213−210)
Recognizing that 25−1 = 24, and that 24 is divisible by both 3 and 8 (and thus 4), we have a clear division by 30.
For the second parenthesis, we can see that 210 is a common factor:
210(26−23−1)
Again, noticing that 26−23−1 leaves us with numbers of the form 2n − 2n-k − 1, we can confirm divisibility by 2 and potentially by 4 depending on the value of n. Checking the values, 26 − 23 − 1 equals 57, which is also divisible by 3.
So the original expression has factors that include 2, 3, 5, and 11, thereby confirming that the expression is divisible by both 30 and 44.
the length of a rectangle is 8 feet more its width.the area of the rectangle is 84 square feet find its length and width
Answer:
length=8+w........1
area=84square feet........2
area of rectangle =length x width
area=(8+w)x W
area=8w+w^2
84=8w+w^2
w^2+8w+(4^2)=84+(4^2)
(w+4)^2=84+16
(w+4)^2=100
√(w+4)^2=√100
w+4=±100
w+4=100 or w+4=-100
w=96 or w=-104
the answer is 96
Solve these word problems by graphing, substitution or elimination.
(1) The numbers are 8 and 16.
(2) John have 12 nickels and 6 dimes.
Solution:
(1) Let x and y be the two numbers.
Sum of two numbers = 24
⇒ x + y = 24 – – – – (1)
One number = Other number – 8
⇒ x = y – 8 – – – – (2)
Substitute equation (2) in equation (1), we get
⇒ y – 8 + y = 24
⇒ 2y – 8 = 24
Add 8 on both side of the equation, we get
⇒ 2y = 32
Divide by 2 on both sides.
⇒ y = 16
Substitute y = 16 in equation (2)
⇒ x = 16 – 8
⇒ x = 8
Hence the numbers are 8 and 16.
(2) Let n and d be the nickels and dimes respectively.
Nickels + Dimes = 18
⇒ n + d = 18 – – – – (1)
Nickles = Dimes + 6
⇒ n = d + 6 – – – – (2)
Substitute equation (2) in equation (1), we get
⇒ d + 6 + d = 18
⇒ 2d + 6 = 18
Subtract 6 from both side of the equation.
⇒ 2d = 12
Divide by 2 on both side of the equation, we get
⇒ d = 6
Substitute d = 6 in equation (1), we get
⇒ n = 6 + 6
⇒ n = 12
Hence John have 12 nickels and 6 dimes.
Compare and contrast the methods used by African and Asian nations to achieve independence.
Answer: Decolonization as a result of World War II.
Step-by-step explanation:
With the end of World War II, the process of decolonization of the African and Asian continents began. It is the result of the destruction brought with it by World War II, but also by the liberalization that took place in Europe after World War II. In this context, it isn't effortless to point out the particular methods used by nations on these two continents. Decolonization is, however, an independent will and intervention of European countries.Yet the colonization of nations was not entirely passive in terms of resistance to the European invaders. There were several uprisings against the colonists. However, what characterizes both fights for independence is the emergence of nationalism. This is the pattern that African and Asian countries have taken over from Europeans. The form of resistance also consisted in the fact that there was a specific political will on the part of certain domestic elites, as in the case of the West African National Congress or the South African National Congress.A particular form of struggle for independence existed in India. This Asian country led its effort by methods of civil disobedience, non-payment of taxes, and refusal to work. The creator of this form of struggle was the leader of the Indian independence movement Mahatma Gandhi. An example of diminishing "third country" influence was an international intervention. Such an example is evident in Korea, where the United States and the Soviet Union eliminated Japanese colonial pretensions by their impact.What are carbonhydrates
Answer:
According to the dictionary, it is any of a large group of organic compounds occurring in foods and living tissues and including sugars, starch, and cellulose.
48) Amily wrote the riddle below.
I am a quadrilateral.
All my sides are parallel.
I have 4 angles, but they are not all equal.
What shape could I be?
What shape does Amily's riddle best describe?
A) Pentagon B) Rectangle C) Rhombus D) Trapezoid
Answer:
C)Rhomus
Step-by-step explanation:
a rhombus is parallel
The correct answer is option C. The shape Amily's riddle best describes is Rhombus.
Let's analyze the riddle step by step to determine which shape Amily is describing.
1. Quadrilateral: The shape has four sides.
2. All sides are parallel: This indicates that opposite sides are parallel to each other, which means the shape is a type of parallelogram.
3. 4 angles, but they are not all equal: This means that although the shape has four angles, they are not all the same measure.
Given these clues, let's evaluate each option:
A) Pentagon: This is a five-sided shape, not a quadrilateral. So, this option is incorrect.
B) Rectangle: A rectangle has four sides and opposite sides are parallel. However, all the angles in a rectangle are equal (each angle is 90 degrees). So, this option is also incorrect.
C) Rhombus: A rhombus has four sides and opposite sides are parallel. Additionally, all sides are of equal length. However, a rhombus can have angles that are not all equal (typically, it has two pairs of equal angles). Given the description, this could be a potential answer, but let’s also consider the last option.
D) Trapezoid: A trapezoid has one pair of parallel sides. However, the riddle specifies that all sides are parallel, which does not match the definition of a trapezoid.
Given that the shape described has all sides parallel and the angles are not all equal, the best match is C) Rhombus.
1. I think of a positive number, multiply it by 4, add six, and then divide the answer by
2, and square the result. Then I subtract 9, and divide the result by the number I first
thought of. My answer is 20. What number did I think of?
Answer: 2
Step-by-step explanation:
2 times 4 = 8
8 plus 6 = 14
14 divided by 2 = 7
7 squared = 49
49 minus 9 = 40
40 divided by 2 = 20
In this problem we convert the operations into an equation and solve it step by step until we get two possible answers. We pick the one that fits the conditions of the problem, which gives us 9 as the positive number the student had originally thought of.
Explanation:Let's denote the number you are thinking of as x. Following your sequence of operations we can translate this into an equation:
(((4x + 6) / 2)² - 9) / x = 20
Solving this equation can be done step by step:
Multiply through by 2x to remove the denominator: ((4x + 6)² - 9x) = 40x.Expand the square on the left side: 16x² + 24x + 36 - 9x = 40x.Simplify by combining like terms: 16x² + 15x + 36 = 40x.Subtract 40x from both sides to form a quadratic equation: 16x² -25x + 36 = 0.This quadratic equation can be factored as (4x -1)(4x -36) = 0.Setting each set of parentheses equal to zero gives us two solutions for x: x = 0.25 or x = 9.Since you mentioned that the number you thought of was positive, we disregard 0.25 (since the squared result after the first operations would be too small to subtract 9 and still divide by the original number to get 20). Therefore, the number you thought of was 9.
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PLEASE HELP!!!!The point (−2,−3) is rotated 90 degrees counterclockwise using center (0,0) . What are the coordinates of the image?
a (3,−2)
b (−3,2)
c (−3,−2)
(d 3,2)
Answer: a 3,-2
Step-by-step explanation:
When a point is rotated, it must be rotated around a center.
The coordinate of the image of (-2,-3) is (3,-2)
The point is given as:
[tex](x,y) = (-2,-3)[/tex]
The rule of 90 degrees counterclockwise rotation is:
[tex](x,y) \to (-y,x)[/tex]
So, we have:
[tex](-2,-3) \to (3,-2)[/tex]
Hence, the coordinate of the image of (-2,-3) is (a) (3,-2)
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find the length of the orther leg when one leg is 20 and hypotenous is 25
Answer:
15
Step-by-step explanation:
Do 25 ^ 2 = 625
Do 20 ^ 2 = 400
Because you're finding something that's nor the hypotenuse you subtract
So you do 625 - 400 = 225
Then you do the square root of 225 to get the answer
Which is 15
Answer:
15
Step-by-step explanation:
Let 'l' be the length of the other leg
Using pythagoras theorem,
25² = 20² + l²
625 = 400 + l²
225 = l²
l = 15
Write an equation of the line in slope-intercept form that is perpendicular to this line and has a y-intercept of 9.
y=2x
Answer:
(0,9) for y-intercept
perp.: (-1/2)= m
y - 9 = (-1/2)x - 0
y = (-1/2)x + 9
Step-by-step explanation:
Please need answer quick
Answer:
900
Step-by-step explanation:
You first split it up with 12x10x25 for the smaller one and you do 20x12x25 for the other
I hope this helps if you need the work i can give it to you
A rectangle has an area of 100 square centimeters. The base of the rectangle is 25 centimeters.
What is the height of the rectangle?
O
4 cm
10 cm
76 cm
2400 cm
Next →
Answer:
The height of the rectangle is 4 cm.
Step-by-step explanation:
You find area by multiplying base and height.
The formula is A=bh
so 100=25h
25 times 4 is 100
100=25*4
4cm is your answer
please tell explain what the right answer is
Angle 3 and angle 4 are supplementary angles and when added together need to equal 180 degrees.
To find angle 4 subtract angle 3 from 180.
Angle 4 = 180 - 101 = 79 degrees.
Answer:
your answer is correct
Step-by-step explanation: because each angle equals the same thing
A ball set that is sold for $79 is discounted %15 what is the sale price
Answer:
$67.15
Step-by-step explanation:
79*(1-.15)
= $67.15
Let the population of a city be 1,006,150 people. What is the least number of people that share a birthday?
Answer:
The least number of people that share a birthday is 1, no matter what the size of the population is.
Step-by-step explanation:
Tricky Question
Suppose there is one person that has their birthday on Feb 02. It's perfectly possible that no one else in the city has their birthday on the same day, i.e. their birthdays are any time except Feb 02. So that person will be the only one who has that as a birthday. It's even possible that no one has a birthday on Feb 02, so the answer will be zero, but it's not possible to talk about sharing if no one is doing it, so the answer is
The least number of people that share a birthday is 1, no matter what the size of the population is.
Note: If this question is talking about probability calculations, then the matter is totally different.
Can someone please help me with this 7th grade math homework
Answer:
2.19
Step-by-step equation:
Simply 5(x-2)-3x+7. Please
5(x-2)-3x+7
5x-10-3x+7
2x-10+7
2x-3
Hope this step by step process helped
Plz help!!! Will give Brainliest Given a right triangle with legs a, b and hypotenuse c, solve for c if a = 11 and b = 60
Answer:
Right angle triangle hypotenuse formula
c = √a²+b²
a=11
b=60
c = √11² + 60²
c = 3611
Step-by-step explanation:
I hope this helps!
solve 2√5 as the square root of a single number
Answer: [tex]\sqrt{20}[/tex]
Work Shown:
[tex]2\sqrt{5} = \sqrt{4}*\sqrt{5}\\\\2\sqrt{5} =\sqrt{4*5} \text{ use the rule } \sqrt{x}*\sqrt{y} = \sqrt{x*y}\\\\2\sqrt{5} = \sqrt{20}[/tex]
PLEASE HELP ME :(
The base of a square pyramid has side lengths that are 14 inches. The distance from the top of the pyramid to the middle of the side of the base is 15 inches. What is the height of the pyramid? Round to the nearest tenth, if necessary.
Answer:
The height of the pyramid is 13.3 inches
Step-by-step explanation:
Let
h ----> the height of the pyramid
b ---> the base of the square pyramid
we know that
Applying the Pythagorean Theorem
[tex]15^2=h^2+(\frac{b}{2})^2[/tex]
see the attached figure to better understand the problem
we have
[tex]b=14\ in[/tex]
substitute
[tex]15^2=h^2+(\frac{14}{2})^2[/tex]
Solve for h
[tex]225=h^2+49\\h^2=225-49\\h^2=176\\h=\sqrt{176}\ in\\h=13.3\ in[/tex]
Justify each step in the solution of the equation 5(x+2)=24-2x
Final answer:
To solve the equation 5(x+2)=24-2x, distribute, combine like terms, solve for x, and check the solution. The solution x = 2 satisfies the equation, so it is valid.
Explanation:
To solve the equation 5(x+2)=24-2x, we can justify each step as follows:
Distribute the 5 to the terms inside the parentheses: 5x + 10 = 24 - 2x
Combine like terms on both sides of the equation: 5x + 2x = 24 - 10
Combine the x terms: 7x = 14
Divide both sides of the equation by 7 to solve for x: x = 2
Check the solution by substituting it back into the original equation: 5(2+2) = 24 - 2(2)
Simplify the left side: 5(4) = 24 - 4
Multiply: 20 = 20
The solution x = 2 satisfies the equation, so it is valid.