The solution to the equation -1/5 = -2y + 8/5 is y = 9/10
What is the solution to the given equation?Given the equation in the question;
-1/5 = -2y + 8/5
First, rewrite the equation as;
-2y + 8/5 = -1/5
Move all terms not containing y to the right side of the equation
-2y + 8/5 - 8/5 = -1/5 - 8/5
-2y = -1/5 - 8/5
Add -1/5 and -8/5
-2y = ( -1 - 8) / 5
-2y = -9 / 5
Divide both sides by -2
-2y / -2 = -9/5 ÷ -2
y = -9/5 × -1/2
y = 9/10
Therefore, the value of y is 9/10.
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Which of the following numbers is probably an irrational number? 0 1.6490221... 3/4 -5
The number that probably is an irrational number is 1.6490221...
How to determine the irrational numberAn irrational number is a number that cannot be expressed as a finite decimal or a fraction.
The number 0 is not irrational.
The number 1.6490221... is an example of a decimal that goes on forever, which is the characteristic of an irrational number.
The number 3/4 can be expressed as a fraction and is therefore not irrational.
The number -5 is not irrational.
Therefore, the answer is 1.6490221..., which is probably an irrational number.
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A mallard duck has 13 ducklings. Five of the ducklings are male. What
is the ratio of male to female ducklings?
Answer: 13 ducklings 5 male 7 female so the answer is 5:7
Step-by-step explanation:
The graph of a parent function is shown. Which function belongs to the same function family as the graphed function?
Answer:
I doubt I'm wrong but it's D
hello teacher can u help me with this
Please help! The question is in the image.
Answer:
Step-by-step explanation:
Look at the figure. Find the value of CG.
VIEW THE IMAGE ATTACHED BELOW.
Answer:
CG = 8
Step-by-step explanation:
Given CG = 4x-16 is congruent to AG = 2x -4, you want the value of CG.
SetupThe congruent segments are equal length:
CG = AG
4x -16 = 2x -4
Solution2x = 12 . . . . . . . . . . add 16 -2x
Substitute into the expression for AG:
2x -4 = 12 -4 = 8
AG is congruent to CG, so ...
CG = 8
__
Additional comment
You know triangles GBC and GBA are congruent by the HA theorem, since GB bisects angle ABG. Corresponding parts of congruent triangles are congruent, so CG ≅ AG.
A teacher is placing a border around the classroom bulletin board which measures 28 7/8 inches long by 22 one fourths inches wide what is the length of the border
On solving the provided question we cans ay that area of bulletin board would be 22*10 = 220 cm sq.
What is area?The size of an area on a surface can be expressed as an area. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a planar region or planar region refers to the area of a form or planar layer. The total amount of space filled by a planar (2-D) surface or shape of an object is known as its area. Draw a square on a piece of paper using a pencil. a character with two dimensions. The area of a shape on paper is the space it takes up. Imagine that the square is composed of more compact unit squares.
This question depends on how thick you would want the border to be.
One simple way to find this is finding the perimeter of the bulletin board. You can do this by using the formula: 2(L) + 2(W)
(L) Represents Length
(W) Represents Width
In this situation, it would be 2(4) + 2(6)
that would turn into 8 + 12
which turns into 20 feet.
area of bulletin board would be 22*10 = 220 cm sq.
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Which of the following shows independent events?
Select the correct answer below:
drawing a jack and then drawing a 7 without replacement from a standard deck of cards
drawing a 10 and then drawing a 9 without replacement from a standard deck of cards
rolling two 4's from two rolls of a standard die
rolling a sum less than 3 from two rolls of a standard die and rolling a 1 for the second throw
Answer:
Step-by-step explanation:
I'll give you brainliest and extra points if it's right! :)
Answer:
see explanation
Step-by-step explanation:
given the ratio of 2 similar figures is [tex]\frac{a}{b}[/tex]
then the ratio of perimeters is also [tex]\frac{a}{b}[/tex]
and the ratio of areas is ( [tex]\frac{a}{b}[/tex] )² = [tex]\frac{a^2}{b^2}[/tex]
the ratio of side lengths, yellow to green is
[tex]\frac{36}{60}[/tex] = [tex]\frac{3}{5}[/tex] ( cancelling 36 and 60 by 12 )
the ratio of perimeters is equal to ratio of sides, that is [tex]\frac{3}{5}[/tex]
the ratio of areas = [tex]\frac{3^2}{5^2}[/tex] = [tex]\frac{9}{25}[/tex]
let x be the area of the green figure, then by proportion
[tex]\frac{45}{x}[/tex] = [tex]\frac{9}{25}[/tex] ( cross- multiply )
9x = 1125 ( divide both sides by 9 )
x = 125
that is the area of the green figure is 125 units²
Write 23.224 as a rational number
Answer:
Step-by-step explanation:
0.10267857142000002
A savings account with simple annual interest rate of 3.92% and an initial deposit of $5,460.75 yields a final account balance of $6,370.51 after 51 months. - Part A: Using the rate and term as the simple interest account, calculate the final account balance if the initial deposit is invested for the same number of months, with interest compounded semiannually. Show all work.- Part B: Compare that simple interest final account balance with the compound interest final account balance.
The final account balance with compound interest is $6,440.30.
The final account balance when compounded semiannually is higher.
How to calculate the final account balance?
The formula for compound interest is:
A = P (1 + r/n)^(nt)
where:
A = the future value of the investment, including interest
P = the principal investment amount
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested/borrowed for
Part A:
r = 3.92% = 0.0392, P = $5,460.75, n = 2 (semiannually means twice a year), t = 51 months = 4.25 years
A = P (1 + r/n)^(nt)
A = 5,460.75 (1 + 0.0392/2)^(2*4.25)
A = 5,460.75 (1 .0196)^(8.5)
A = $6,440.30
Thus, the final account balance is $6,440.30
Part B:
difference = 6,440.30 - $5,460.75 = $975.55
When the initial deposit is invested with interest compounded semiannually, the final account balance is higher.
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Question in image, PLEASE HELP
The value of ST = 10 for the given rectangle.
What is a rectangle?A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.
Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.
In the given triangle PQRS, the diagonals bisect each other, that is they divide each other in equal halves.
Thus. PT = TR
Since, PT = 10 we have TR = 10,
The diagonals of the rectangle are equal, hence we also have:
TR = ST
Since, the value of TR = 10, then the value of ST = 10.
Hence, the value of ST = 10 for the given rectangle.
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The area of the circular base of a cone is 25π cm², and the slant height of the cone is four times the radius of the cone.
What is the approximate lateral area of the cone?
Use π≈3.14.
Enter your answer rounded to the nearest whole number in the box.
The approximate lateral area of the cone is equal to 314 cm².
How to calculate the lateral area of the cone?Mathematically, the lateral area of a cone can be calculated by using this mathematical expression:
Lateral surface area of a cone, LSA = πrl or πr√(r^2 + h^2)
Where
l represents the slant height of the cone.r represents the radius of the cone.h represents the height of the cone.How to calculate the area of a circle?Mathematically, the area of a circle can be calculated by using this formula:
Area of a circular base = πr²
25π = πr²
Radius, r = √25
Radius, r = 5 cm.
Substituting the given parameters into the lateral area of a cone formula, we have the following;
Lateral surface area of a cone, LSA = πrl = πr4(r)
Lateral surface area of a cone, LSA = 3.14 × 5 × 20
Lateral surface area of a cone, LSA = 314 cm².
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Please helppp I've been stuck on this for sooo long
The relation between a and c can be written as:
a = c + 24
Which is the relationship between a and c?First we know two equations:
a = b + 12
b = c + 12
So we have relations between a and b, and between b and c, and we want a relation between a and c.
If we replace the b of the first equation with the second equation, then we will get:
a = (c + 12) + 12
a = c + 24
That is the relation between a and c.
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over the course of an 18 year research project, the height of an oceanside cliff actually dropped due to soil erosion. At the end of this period, its height was measured as -3 inches compared to what it had been at the beginning of the research project. What was the average amount that the cliff's height changed each year?
The average amount of cliff's height that decreased each year is 1/6 inches.
What is unit rate?The rate at which one value changes with respect to per unit change in the other value is called the unit rate. Mathematically -
{ r } = y/x .... Eq { 1 }
Given is that over the course of an 18 year research project, the height of an oceanside cliff actually dropped due to soil erosion. At the end of this period, its height was measured as -3 inches compared to what it had been at the beginning of the research project.
We can write the the average amount of cliff's height that changed each year as -
{r} = |h|/|t|
{r} = 3/18
{r} = 1/6
Therefore, the average amount of cliff's height that decreased each year is 1/6 inches.
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PLEASE HELP ASAP DONT IGNORE:(((
Answer:
Step-by-step explanation:
Notebooks Total Cost
0 0.00
1 3.00
2 6.00
3 9.00
The scale on a 1:50 000 ordnance survey map indicates that 2cm on the map = 1km on the ground. How many centimetres would 1km be represented by on a 1:25 000 scale map
1km would be represented by 4cm on a 1 : 25000 scale map.
What is a scale factor?The scale factor defines a variable in a ratio of two different measurements.
Sometimes drawings of large models are represented in a scale factor of a smaller unit.
Given, The scale on a 1 : 50000 ordnance survey map indicates that 2cm on the map = 1km on the ground.
We know 1 km = 1×100000 = 100000 cm.
So, If 2 cm represents 100000 cm it has a scale factor of 100000/2 = 50000.
Now, Again 1 km = 100000 cm,
So, 1km will be represented by 100000/25000 = 4 cm.
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Samantha mixes some amount of 25% sugar syrup with x grams of 10% sugar syrup. The result is 120 grams of 15% sugar syrup. How many grams of 25% sugar syrup did Samantha use?
Answer:
40 grams
Step-by-step explanation:
Answer: 120-x
Step-by-step explanation:
The area of the circular base of a cone is 16π cm², and the slant height of the cone is 4 times the radius of the cone.
What is the approximate lateral area of the cone?
The approximate lateral area of the cone is equal to 200.96 cm².
How to calculate the lateral area of the cone?Mathematically, the lateral area of a cone can be calculated by using this mathematical expression:
Lateral surface area of a cone, LSA = πrl or πr√(r^2 + h^2)
Where
l represents the slant height of the cone.r represents the radius of the cone.h represents the height of the cone.How to calculate the area of a circle?Mathematically, the area of a circle can be calculated by using this formula:
Area of a circular base = πr²
16π = πr²
Radius, r = √16
Radius, r = 4 cm.
Substituting the given parameters into the lateral area of a cone formula, we have the following;
Lateral surface area of a cone, LSA = πrl = πr4(r)
Lateral surface area of a cone, LSA = 3.14 × 4 × 16
Lateral surface area of a cone, LSA = 200.96 cm².
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Answer:
201 beause you are rounding to the nearest whole number
Step-by-step explanation:
In your biology class, your final grade is based on several things: a lab score, scores on two major tests, and your score on the final exam. There are 100 points available for each score. However, the lab score is worth 23% of your total grade, each major test is worth 21.5%, and the final exam is worth 34%. Compute the weighted average for the following scores: 94 on the lab, 89 on the first major test, 63 on the second major test, and 73 on the final exam. Enter your answer as a whole number.
Answer: 79
Step-by-step explanation: The weighted average for the scores can be calculated as follows:
Lab score: 94 x 0.23 = 21.62
First major test: 89 x 0.215 = 19.135
Second major test: 63 x 0.215 = 13.495
Final exam: 73 x 0.34 = 24.82
Total weighted average: 21.62 + 19.135 + 13.495 + 24.82 = 78.976
Rounding to the nearest whole number, the weighted average is 79.
Question 9 find the height of the building
were going to need a lil more than that to answer :(
Sam is moving bags of soil from a loading dock into a storeroom. The topsoil
weighs 40 pounds per bag, and the mulch weighs 20 pounds per bag. The
cart Sam uses to move the bags can only carry up to 480 pounds.
Which graph represents the number of topsoil bags and mulch bags that Sam
can move in a single trip? Graphed
The inequality that can be used to represent the number of topsoil and mulch Sam can carry is, 40x + 20y ≤ 480
And, The graph which represents the number of topsoil bags and mulch bags that Sam can move in a single trip is shown in figure.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that:
Weight of top soil = 40 pounds
Weight of mulch = 20 pounds
Total weight Sam can carry = 480 pounds
Now, Let number of bags of top but soil = x
And, The number of weight of mulch = y
Hence, The inequality is,
⇒ 40x + 20y ≤ 480
Therefore, the inequality that can be used to represent the number of topsoil and mulch Sam can carry is 40x + 20y ≤ 480
And, The graph which represents the number of topsoil bags and mulch bags that Sam can move in a single trip is shown in figure.
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Please help me thank you so much!
Answer:
It's the second one because -3x3-5 equals -14
What is a number that when you multiply it by 7 and add 2 to the product, you get 30?
Answer:
4
7 * 4 = 28
28 + 2 = 30
Step-by-step explanation:
Hope it helps! =D
Solution is in the attachment!!
After a 75% reduction, you purchase a new dvd player on sale for $150. What was the original price of the dvd player ?
Step-by-step explanation:
The original price was 150 / (1 - 0.75) = $600.
x=√40-3x can someone help solve
The solution of the given equation is x= 5 and x = -8.
What is quadratic equation?An algebraic equation of the second degree in x is a quadratic equation. First, there must be a term other than zero in the coefficient of x^2 for an equation to be a quadratic equation. The x^2 term is written first when constructing a quadratic equation in standard form, then the x term, and finally the constant term.
The given equation is x = √40 - 3x.
Square on both sides of the equation:
x^2 = (√40 - 3x)²
x² = 40 - 3x
Regroup to one side of the equation:
x² + 3x - 40 = 0
x² + 8x - 5x - 40 = 0
x(x + 8) - 5 (x+8) = 0
(x - 5)(x + 8) = 0
Equate each term to 0:
x - 5 = 0
x= 5
x+ 8 = 0
x = -8
Hence, the solution of the given equation is x= 5 and x = -8.
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Ms. Pesko pulled 5 candy bars out of a bag. She pulled the following candies: Twix, Kit-Kat, Milky Way, Twix, Twix. What is the experimental probablity of getting a Twix?
Answer:
Step-by-step explanation:
The experimental probability of getting a Twix is 3/5 or 60%.
Assume an exponential function has a starting value of 14 and a decay rate of 42%. Write an equation to model the situation.
The equation is y=
The equation to model the situation will be written as y = 14 × (0.58)ˣ.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
y = a (1 ± r)ˣ
Assume an exponential function has a starting value of 14 and a decay rate of 42%. Then the equation is given as,
y = 14 × (1 - 0.42)ˣ
y = 14 × (0.58)ˣ
The equation to model the situation will be written as y = 14 × (0.58)ˣ.
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If a fair die is rolled 5 times what is the probability of rolling 3 sixes to the nearest thousandth
The probability of rolling 3 sixes to the nearest thousandth is 0.556.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Using binomial distribution.
[tex]^nC_r P^cQ^{n - r}[/tex]
Now,
Probability of getting a six = 1/6
P = 1/6
Probability of not getting a six = 5/6
Q = 5/6
Now,
n = 5 and r = 3
So,
[tex]^nC_r P^rQ^{n - r}[/tex]
= [tex]^5C_3(1/2)^3(5/6)^2[/tex]
= (5 x 4)/2 x (1/2) x (1/2) x (1/2) x (5/6) x (5/6)
= 10 x 1/8 x 25/36
= 5/9
= 0.556
Thus,
The probability of rolling 3 sixes is 0.556.
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How many degrees is the peripheral angle above the circular arc that represents 4/9 of the circle
The peripheral angle above the arc would be:
160 / 2 = 80 degrees.
Solution
The peripheral angle above a circular arc is equal to the central angle subtended by the arc divided by 2.
The central angle of a circle is 360 degrees, so if the arc represents 4/9 of the circle, the central angle subtended by the arc would be:
360 * (4/9) = 160 degrees
The peripheral angle above the arc would be:
160 / 2 = 80 degrees.
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