Hugo needs 15 weeks to pay back his brother completely if he pays $2 a week.
What is an equation?
An equation is written in the form of variables and constants separated by the operation of multiplication and division.
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
According to the given question:
Hugo decided to pay $2 a week to his brother to buy a bicycle.
The equation y - 10 = - 2(x – 10) models the amount of money he owes for the bike, where x is the number of weeks and y is the amount of money he still needs to pay.
To pay back to the brother he must owe no money which is y = 0.
∴ The weeks needed is,
0 - 10 = -2(x - 10).
- 10 = -2x + 20.
2x = 30.
x = 15.
He needs 15 weeks to pay back completely.
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A cylindrical can with height 12 cm has capacity 600 mL. What is its radius, to the nearest millimetre? [Remember that 1 mL = 1 cm³.]
The required radius of the cylindrical can is 4 millimeters.
What is cylinder?A cylinder is a three-dimensional solid in mathematics that maintains, at a given distance, two parallel bases connected by a curving surface. These bases often have a circular form (like a circle), and a line segment known as the axis connects the centers of the two bases.
Given that,
The height of the cylinder h = 12 cm.
And volume of the cylinder v = 600 mL
Since, 1 mL = cm³
The volume v = 600 cm³.
Let radius of cylinder is r,
To find the radius, use formula,
Volume of cylinder V = π x r² x h
22/7 x r² x 12 = 600
22/7 x r² = 50
r² = 350 / 22
r² = 15.909
r = 3.98
or r = 4 millimeters.
The radius of the cylinder is 4 millimeters.
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There are a certain number of hens and rabbits in a room. The number of feet of the hens exceeds the number of feet of the rabbits by 12, while the number of heads of the hens exceeds the number of the heads of the rabbits by 28. Then the number of hens and rabbits, respectively, in the room are:
Answer:
22 rabbits and 50 hens
Step-by-step explanation:
Let H and R stand for the numbers of Hens and Rabbits. Each hen has two feet and each rabbit has four feet. Each only has 1 head.
We can set the quantities of feet and heads:
Hens: 2H feet and 1H heads
Rabbits: 4R feet and 1R heads
We are told that:
1.) "The number of feet of the hens exceeds the number of feet of the rabbits by 12" Rewrite this as an expression:
2H - 4R = 12 [feet]
2) "while the number of heads of the hens exceeds the number of the heads of the rabbits by 28" This is written as:
1H = 1R + 28 [heads]
Since each critter only has one head, this last expression will tell us, quickly, how many more Hens there are, which is 28. But by substituting the first expression (the feet) into the second, we can detrermine the exact number of each animal.
Rearrange 2H - 4R = 12 to isolate one of the variables. I'll choose H:
2H - 4R = 12
2H = 12 + 4R
H = (12 + 4R)/2
H = 6+2R
Now use this definition of H in the second equation:
1H = 1R + 28
1(6+2R) = 1R + 28
6 + 2R = 1R + 28
R = 22 There are 22 rabbits
Use this in the second equation to find the number of hens:
1H = 1R + 28
1H = 22 + 28
H = 50 There are 50 hens.
=================
Check:
1.) "The number of feet of the hens exceeds the number of feet of the rabbits by 12."
Hens have 100 feet total. Rabbits have 88 feet. The hens have 12 more total feet: This checks
2.) "while the number of heads of the hens exceeds the number of the heads of the rabbits by 28"
There are 50 heans and 22 rabbits. The number of hen heads exceed the number of rabbit heads by 28. This also checks.
Seven line segments are shown on the coordinate plane. Which of these segments could be the image of segment AB after a sequence of reflections, rotations, and/or translations?
Select each correct answer.
A. Line segment GH
B. Line segment EF
C. Line segment LM
D. Line segment NP
E. Line segment JK
F. Line segment CD
Please hurry
The segments that could be the image of segment AB after a sequence of reflections, rotations, and/or translations include:
A. Line segment GH
D. Line segment NP
F. Line segment CD
What are the segment?From the information, the coordinates of the point A is (1, 2), the coordinates of the point B is (5, 2)
Therefore, the length of the line AB = 5 - 1 = 4 units
In this case, the transformations are, reflections, rotations, and/or translations which are rigid transformations, such that the length of the image of AB will be the same as the length of AB
Therefore, the possible images of AB are;
PN with coordinates P(5, -2) and N(9, -2) and length 9 - 5 = 4 units
HG with coordinates H(-4, -4) and G(-4, -8) and length -4 - (-8) = -4 + 8 = 4 units
CD with coordinates C(-4, 6) and D(-4, 2) and length 6 - 2 = 4 units
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Is Side-Side-Side a postulate or a theorem? Explain
Answer: Postulate
Step-by-step explanation:
Side-Side-Side (SSS) Postulate
If three sides of one triangle are congruent to three sides of another triangle, then the two are congruent.
Dee chose A as the correct answer. What was her error? Answer in a complete sentence.
Number of square feet of wall painted in 1 hour is 243 square feet. Therefore, option C is the correct answer.
Given that, it takes Zach 10 minutes to paint [tex]40\frac{1}{2}[/tex] square feet of his bedroom wall.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Here, [tex]40\frac{1}{2}[/tex] square feet = 40.5 square feet
Rate at which he paints the wall =40.5/10
= 4.05 square feet per minute
As we know 1 hour =60 minutes
Now, number of square feet
= 4.05×60
= 243 square feet
Number of square feet of wall painted in 1 hour is 243 square feet. Therefore, option C is the correct answer.
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What is the image point of (2,-7)(2,−7) after a translation right 4 units and up 3 units?
Answer: (6, -4)
Step-by-step explanation:
Because it translate right 4 units, so the x increase by 4, so x=6
It up 3, so y increase by 3, so y= -4
Selected values of the continuous function f are shown in the table below. Determine the validity of the following statement:
f(x)=0 has at least two solutionsin the interval {2,9}
True
False
could be true or false
Function may return true or false.
What does "continuous function" mean?A continuous function is one in which a continuous variation of the input (i.e., a change without a jump) results in a continuous modification of the function's value. This indicates that there aren't any discontinuities, or sudden changes in value.
Here, the function f(x) is continuous.
It follows that if x = 2 then f(x) = 3,
if x = 5 then f(x) = -9,
if x = 7 then f(x) = -15,
if x = 9 then f(x) = -13.
There are at least two solutions in the interval {2,9} for the graph of the function cross x axis f(x) = 0, hence it is not provided.
Therefore, it may be true or false.
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An ice cream shop sells a small bowl of ice cream for $2.25 and a large bowl for $3. One day, the shop sold 63 bowls of ice cream and made $159. How many of each size bowl did the shop sell?
The number of small size and large size bowls of ice cream sold in the shop is 40 and 22 respectively.
How to determine the number of each bowl size sold?let
Number of small bowl = x
Number of large bowl = y
x + y = 63
2.25x + 3y = 159
From (1)
x = 63 - y
Substitute into (2)
2.25x + 3y = 159
2.25(63 - y) + 3y = 159
141.75 - 2.25y + 3y = 159
- 2.25y + 3y = 159 - 141.75
0.75y = 17.25
divide both sides by 0.75
y = 17.25 / 0.75
y = 23
Substitute y = 23 into (1)
x + y = 63
x + 23 = 63
subtract 23 from both sides
x = 63 - 23
x = 40
In conclusion, The ice cream shop sold 40 small size bowls and 23 large size bowls
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The least common multiple of two whole numbers is 40. The ratio of the greater number to the lesser number is 5 : 4. What are the 2 numbers?
Answer:
10 and 8
Step-by-step explanation:
must be in the ratio 5:4, 5 x 4 =20, so if you multiply by 2 the ratio is 10:8 (same thing). The least common multiple of 10 and 8 is 40 because you can do 10 x 4 = 40 and 8 x 5 = 40.
Each of the 6 people in Mandy' family order 2 taco. Each taco cot $3. What
i the total cot of the taco?
Answer:
Step-by-step explanation:
12 x 3 = 36
answer is 36
Answer:
12 x 3 = 36
Step-by-step explanation:
Morgan ha 98 baeball card in hi collection, which i twelve le than the product of 5 and the number of card Tyler ha
Answer:
98-5 = 93
Step-by-step explanation:
Solve the ytem of equation by the addition method.
−4x = −4y − 12
−16x 6y = 12
For the above system of equations, 4x-4y=12 and 16x-6y=-12, the values of x and y are 4.5 and -10 respectively.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here,
4x-4y=12
16x-6y=-12
multiply equation 1 by 4,
16x-16y=48
-16x+6y=12
-10y=60
y=-10
-16x-60=12
-16x=72
x=72/16
x=4.5
The value of x is 4.5 and y is -10 for the given system of equation as 4x-4y=12 and 16x-6y=-12.
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what is the digital index of 23475
answer:the answer for digital index of 23475 is 3
answer: 3
explanation: the digital index is 3 because 23475 is divisible by 3
the ratio of the four sides of a trapezoid is 2:1:1:1 the area of the trapezoid is 27sqrt(3) find the length of the median of the trapezoid
Answer:
9
Step-by-step explanation:
;)
When do I divide in right trigonometry
The answer to this question which is based on Trignometry is that we divide when we want to calculate Trignometric Ratios
How many Trignometric ratios are available?
There are six basic trigonometric ratios: sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). These ratios are used to calculate angles and sides of a right triangle.
Whenever we need to calculate Trignometric ratios we have to divide the length of 2 sides of a triangle and one more the Trignometric ratios can be only found in Right Angled triangle
Hence we can just find the Trignometric ratios for any Triangle we can only do it for right Triangles
The values of Trignometric ratios can be negative also and it depends on the angle for which we want to find the Trignometric ratios.
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Pat and Sandy took a break for lunch.
They spent of an hour resting and
of an hour eating. What fraction
of an hour was their break?
Answer:
50%
Step-by-step explanation:
I’m so smart fr
The mean mass of 5 boys is 62kg.When the mass of a boy is excluded,the mean mass of the remaining 4 boys becomes 64kg.Find the mass of the boy that has been excluded
The mass of the boy removed is 54.
What is the linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are present. The variables in the above equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
let's take the weight of five boys is x
so,
x/5 = 62
x = 310
and let's take the weight of four boys is y.
so,
y/4 = 64
y = 256
let's take the weight of a boy which is removed from them is z
so,
x - z = y
x - y = z
310 - 256 = z
z = 54
Hence, the mass of the boy removed is 54.
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Which sentence contains an allusion?
A. The cat went as still as a statue as the bird drew dangerously close.
B.The shower spit in anger whenever someone tried to run hot water
C. She had a thousand questions to ask the senator, but time was up.
D. Let me see if I can Thomas Edison my way out of this situation.
HELP please last question for sparx due at midnight :)) i’ll give brainiest
Check the picture below.
so let's check the middle of the picture, inscribed angle "b" is intercepting the purple arc, wait a second!!! angle 22° is intercepting the same arc! ahaaa!.
now let's check the right of the picture, inscribed angle "a" is intercepting that brown arc, wait a second!!! angle 45° is intercepting the same arc!! ahaa!!.
well, you can see what's "c" and "d".
I REALLY NEED HELP WITH THIS
What is the simplified form of the expression the quantity x squared plus 10x plus 21 end quantity divided by 4 times the quantity x plus 3 end quantity?
the quantity x minus 7 end quantity divided by 4 the quantity x plus 7 end quantity divided by 4 the quantity x plus 7 end quantity divided by quantity x plus 3 end quantity the quantity x minus 7 end quantity divided by quantity x plus 3 end quantity
Answer:
[tex]\frac{x+7}{4}[/tex]
(B) is your answer :)
Step-by-step explanation:
do you need me to work it out?
Answer:
b
Step-by-step explanation: took the test
20. A gym membership
is offered in January
for $29.00 per month. If you pay upfront for
the year, you are given a 20% discount on the
monthly cost. How much money do you save
after a year by paying upfront rather than
monthly?
(4x² - 6x + 1) (5x² + 8x+6)
Step-by-step explanation:
here is your answer to your question
Answer: 20x^4 + 2x³ - 19x² - 28x + 6
Step-by-step explanation:
Marissa's mom purchased coffee from the local coffee shop. The first cup of coffee was $3.75. Each refill is $1.50. She also decided to get a bagel for $3.15. If Marissa's mom had 2 refills and a $0.50 discount as part of the rewards program, how much did she spend at the coffee shop?
$11.40
$10.65
$9.90
$9.40
Answer: ($9.40) or (d)
Step-by-step explanation:
Which equation represents the transformation formed by vertically stretching the graph of f(x)=√ by a factor of 6 and then
vertically shifting the graph 7 units up?
O g(x) = √6x + 7
O g(x)=6√x+7
○ g(x)=√x+7
O g(x)=√√√x+7
Answer:
(b) g(x) = 6√x +7
Step-by-step explanation:
You want the equation of the square root function after it has been vertically stretched by a factor of 6 and translated up 7 units.
StretchA vertical stretch is accomplished by multiplying the function value by 'a', where 'a' is the vertical stretch factor. That means the stretched square root function will be ...
f(x) = √x . . . . original square root function
h(x) = 6·f(x) = 6√x . . . . . vertically stretched by a factor of 6
TranslationA translation upward is accomplished by adding the translation amount to the function value. The translated function will be ...
h(x) . . . . . original function
g(x) = h(x) +7 . . . . . translation upward by 7 units
Our stretched and translated function is ...
g(x) = 6√x +7
express x² - 8x + 5 in the form {x-a]²-b where a and b are the integers
x² - 8x + 5 can be expressed as (x - 4)² - 11 in the form (x - a)² - b, where a = 4 and b = 11.
Let y = x² - 8x + 5 ..................( 1 )
Expanding (x - a)² - b we get,
x² - 2ax + a² - b ......................( 2 )
Equating ( 1 ) and (2), we get
x² - 8x + 5 = x² - 2ax + a² - b
Comparing the coefficient of x,
- 8 = - 2a
a = 4
Comparing constants,
a² - b = 5
since we know a = 4
4² - b = 5
16 - b = 5
b = 11
Hence x² - 8x + 5 = (x - 4)² - 11
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2. Given f(x) = |x|-4, determine the range of f.
(yl y> 0) or (0, 0)
b. {yl y < 0) or (-∞, 0)
c. (yl y2-4] or [-4, ∞)
d. (yl y s-4) or (-∞. -4]
Your answer will be letter C [-4, ∞)
PLEASEEEEHELP OMG
I NEED THE ANSWER ASAPAPPAPP
Answer:
A- negative
B-positive
C- zero
Step-by-step explanation:
Going up= positive
Going down= negative
Horizontal line= zero
vertical line= undefined
what is the probability that a randomly selected person will have a birthday in august? assume that this person was not born in a leap year. express your answer as a simplified fraction or a decimal rounded to four decimal places.
the probability of a randomly selected person having a birthday in August is 1/12 or 0.0833 rounded to four decimal places.
The probability of a randomly selected person having a birthday in August is 1/12. There are 12 months in a year and August is one of them. Therefore, The probability of a randomly selected person having a birthday in August is 1/12 because there are 12 months in a year and August is one of them. Each month has an equal chance of being chosen since they all have the same number of days. This probability remains the same regardless of whether or not it is a leap year. Therefore, the probability of a randomly selected person having a birthday in August is 1/12 or 0.0833 rounded to four decimal places.The probability of a randomly selected person having a birthday in August is calculated by dividing the number of days in August (31) by the total number of days in a year (365). This works out to be 1/12 or 0.0833 rounded to four decimal places.
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How do you solve the following:
−3+ |n-2 | >5
Please help!!!!
Step-by-step explanation: To solve this inequality, we can first isolate the absolute value term on one side of the inequality by subtracting |n-2| from both sides of the inequality. This gives us the inequality -3 + |n-2| > 2. Then, we need to consider two cases: when |n-2| is positive and when |n-2| is negative.
If |n-2| is positive, then we can drop the absolute value bars and rewrite the inequality as -3 + (n-2) > 2. Solving this inequality, we find that n > 7.
If |n-2| is negative, then we must reverse the direction of the inequality because subtracting a negative number is the same as adding a positive number. This gives us the inequality -3 - (n-2) > 2. Solving this inequality, we find that n < -1.
Therefore, the solution to the inequality is the set of all numbers that are greater than 7 or less than -1, which is the interval (-1, 7).