The product of equation (4y-3)(2y²+3y-5) is 8y³+6y²-29y+15.
According to the question,
The equation is = (4y-3)(2y²+3y-5)
A product is defined as the result of two or more numbers when multiplied together.In mathematics, a product is the result of multiplication or an expression that identifies objects ( variables) to be multiplied, called factors.First, let us start with "4y"
4y×2y² = 8y³
4y×3y = 12y²
4y×(-5 )= -20y
Next, let us multiply by "-3"
(-3)×(2y²) = -6y²
(-3)×3y = -9y
(-3)×(-5) = 15
Now, let us combine all of our values.
The product is = 8y³+12y²-6y²-20y-9y+15
= 8y³+6y²-29y+15 (apply BODMAS rule)
So, the product is 8y³+6y²-29y+15.
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A right triangle has side lengths measuring 5cm 12cm and 13 cm a similar triangle has a hypotenuse of 169cm what is the length of the shortest of the larger triangle
the answer should be B. 65cm
PLEASE HELP!!!
(05.05 MC)
Complete the frequency table.
What percentage of students age 15 and above travel to school by bus? Round to the nearest whole percent.
A.
36%
B.
26%
C.
45%
D.
50%
Answer:
b
Step-by-step explanation:
Classify this triangle by its sides and angles.
A.) right and scalene
B.) acute and scalene
C.) right and equilateral
D.) acute and equilateral
Answer: acute and scalene
Step-by-step explanation:
we can see from the figure that no side has an angle greater than 90°. Therefore triangle must be an acute angled triangle
Also given in the figure that no two or all sides are equal that is all sides are of different length which means it is a scalene triangle
Hence the answer is acute and
At a school play, 750 tickets were sold. Each adult paid $0.75 admission and each minor paid 50 cents. How many adults attended if the receipts were $437.50?
Answer:
583 adults.
437.50/.50 = 583.333333333
Step-by-step explanation:
Hope it helps! =D
Under what condition the ratio of sine of angle of incidence to the sine of angle of refraction is always a constant?.
The ratio of the sine of the angle of incidence to the sine of the angle of refraction is always a constant when the light is traveling from a denser medium to a rarer medium and the angle of incidence is greater than the critical angle.
The ratio of the sine of the angle of incidence to the sine of the angle of refraction is always a constant under the condition of total internal reflection.
This constant is known as the refractive index of the medium in which the light is traveling. When a beam of light passes from one medium to another, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is known as the refractive index of the second medium with respect to the first medium.
Total internal reflection occurs when a beam of light passes from a medium with a higher refractive index to a medium with a lower refractive index, and the angle of incidence exceeds the critical angle. Under this condition, the light is reflected back into the original medium, instead of passing into the second medium.
In short, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is always a constant when the light is traveling from a denser medium to a less dense medium and the angle of incidence is greater than the critical angle.
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For which value of k will the pair of linear equations 3x Y 1 and 3kx 5y 2 have no solution?.
The pair of linear equations does not have a solution when K is equal to 2.
We can solve this system of linear equations by using the process of elimination. This involves rearranging the equations to isolate one variable and then using that information to determine the values of the other variables.
The first equation should be multiplied by (k-1) and the second equation by 3.
3(3x+y)=3
(2k-1)(3x + y)=(2k-1)2k+1
Add the two equations
3(3x+y)+(2k-1)(3x+y)=(2k-1)2k+1 + 3
Simplify the equation
5kx+ (3+2k-1)y = (2k-1)2k+1 + 3
Further simplify the equation
5kx + (2k+2)y = (2k-1)2k+1 + 3
Rearrange the equation
5kx - (2k+2)y = (2k-1)2k+1 + 3 - (2k+2)
Simplify the equation
5kx - (2k+2)y = (2k-1)2k+1 -2
With the LHS set to 0 and the RHS set to a non-zero number, we can determine the value of k for which the equations cannot be solved.
5kx - (2k+2)y = 0
(2k-1)2k+1 -2 ≠ 0
Solve for k
5k = 2k +2
3k = 2
k=2
Therefore, K=2 is the value of k for which there is no solution to the pair of linear equations.
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They want the cones to hold 28. 26 cubic
inches of popcorn. If the height is 19 inches, what is the radius?
If the radius of the base of the cone is 2 inches the height of the cone should be 2.1485 inches.
The volume of the cone is the capacity occupied by this. It is given by the formula,
The volume of the cone = [tex]\frac{1}{3} \pi r^{2} h[/tex]
r is the radius of the base, and h is the height of a cone.
Now, it is stated that cones hold 9 cubic inches of popcorn. Hence, the volume of a cone can be noted as,
The volume of the cone = [tex]\frac{1}{3} \pi r^{2} h[/tex]
[tex]9 * 3 = \pi r^{2} h[/tex]
[tex]\frac{9 *3}{\pi } = r^{2}h[/tex]
[tex]r^{2}h = 8.5943[/tex]
Now, let the radius of the cone be 2 inches, hence, the height of the cone is,
[tex]8.5943 = r^{2}h[/tex]
[tex]8.5943 = 2^{2}h[/tex]
h = 2.1485 in
Hence, if the radius of the base of the cone is 2 inches the height of the cone should be 2.1485 inches.
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The complete question is:
Noah and Lin are making paper cones to hold popcorn to hand out at parent math night. They want the cones to hold 9 cubic inches of popcorn. What are two different possible values for height h and radius r for the cones?
How many domestic stamps do I need for an international letter?.
You need only Two stamp. If you are tranfering from the United States of America to the United States of America, you just have to pay $0.550 for a Domestic Forever Stamp. Your letter will reach the destination within 1 to 3 working days.
How cool is that? Just 50 cents for such quick delivery should be truly cherished
Carry in mind though, that this covers the first ounce. As soon as your wrapper goes over that weight, you need to add an extra 15-20 cents per ounce onto the price.
Do not stress, we’re going to know this in more detail
There are following requirements that your envelope must fit to be eligible for posting this way. These rules are as follows:
1. The envelope needs to be at least 4-5 inches by 3.5 inches but not much bigger than 11.5 inches by 6.125 inches, and no thicker than ¼ inches.
2. It needs to have a constant thickness.
3. It must be rectangular.
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The axis of symmetry line passes through which point?
A. Y-intercept
C. Any random point
B. Vertex
D. Symmetrical point on the vertex
The axis of symmetry line passes through the vertex of the parabola.
What is the line of symmetry?The term "line of symmetry" refers to the fictitious axis or line that can be used to fold a figure into symmetrical halves. The axis of symmetry is another name for it. Due to the fact that it displays two coincident reflections of the same image, the line symmetry is also known as a mirror line.Any combination of vertical, horizontal, and diagonal lines or axes may be used. However, there are essentially two different kinds of symmetry lines. They are: symmetry in the vertical direction. Transverse Line of SymmetryA line that splits a form exactly in half is known as a line of symmetry. This indicates that both half of the object would perfectly match if you folded it along the line.Learn more about symmetry line refer to ;
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The ratio of the measures of the three angles of a triangle is 4:5:6. Find the measure of each angle of the triangle in order from smallest to largest.
Smallest angle:?
Medium angle:?
Largest angle:?
Answer:
48, 60, 72
Step-by-step explanation:
4 + 5 + 6 = 15
The sum of interior triangles is 180
15/180 = 12
Multiply each part by 12
4 x 12 = 48
5 x 12 = 60
6 x 12 = 72
Use the graphs to evaluate the following:
1. f(1) =_
2.g (-5) =
3. f (g (1)) =
4. f(g(-1.5)) =
5.g (f(-4)) =
6. f(f(-1)) =
The value for f(1) is -2. The solution has been obtained by forming equations of graphs of functions.
What is equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
First let's find the equation f(x)
Vertex form of parabola is y = a(x-h)^2 + k
where (h,k) is the location of the vertex.
Here, h= -1 and k = -4
We get y = a(x+1)^2 -4
Now, the parabola passes through (-4,0.5)
So,
0.5 = a(-4+1)^2 -4
We get a=0.5
Thus, f(x) is 0.5(x+1)^2 - 4
So, f(1)= 0.5(1+1)^2 - 4
⇒f(1)= 0.5*4 - 4
⇒f(1)= 2 - 4
⇒f(1)= -2
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Since the question contains multiple questions, the question I answered is
Use the graphs to evaluate the following:
1. f(1) =_
Solve for j.
16j = 736
Answer:
j = 46
Step-by-step explanation:
16j = 736
---- -----
16 16
j = 46
Answer:
j = 46
I did 736 divided by 16 to find the answer.
Is proof by contrapositive direct or indirect?.
Contrapositive is an example for indirect proof.
Indirect proof;
When the conclusion from a hypothesis is taken to be false (or the opposite of what it states), indirect proof or proof by contradiction is achieved from the given or deduced statements.
Contrapositive method of proof;
Proof by contrapositive, also known as proof by contraposition, is an inference rule used in proofs in mathematics where a conditional statement is inferred from its contrapositive. To put it another way, the assertion "if B, then not A" is proven rather than the conclusion "if A, then B."
Proof by Contrapositive method is indirect.
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Proof by contrapositive is an indirect method of proof where we assume the negation of the conclusion and show that it leads to the negation of the hypothesis. It is a powerful tool in mathematical reasoning and can be used to prove various statements and theorems.
In mathematics, a direct proof is a method of proving a statement by providing a logical sequence of steps that directly leads from the given information to the desired conclusion. On the other hand, an indirect proof is a method of proving a statement by assuming the opposite of the desired conclusion and deriving a contradiction or an absurdity.
To prove a statement using the contrapositive, we start by assuming the negation of the conclusion. Then, we proceed to show that if the negation of the conclusion is true, then the negation of the hypothesis must also be true. In other words, we prove the contrapositive of the statement.
Here is an example to illustrate proof by contrapositive:
Statement: If a number is even, then its square is also even.
To prove this statement by contrapositive, we assume the negation of the conclusion: If a number's square is odd, then the number itself is odd.
We then proceed to show that if the negation of the conclusion is true, then the negation of the hypothesis is also true. In this case, if the square of a number is odd, then the number itself must be odd.
We can prove this by considering that any even number squared will always result in an even number. Therefore, the contrapositive of the original statement is true, which implies that the original statement is true as well.
In conclusion, proof by contrapositive is an indirect method of proof where we assume the negation of the conclusion and show that it leads to the negation of the hypothesis. It is a powerful tool in mathematical reasoning and can be used to prove various statements and theorems.
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Martin is building a fence around his rectangular garden. He has a 100 foot long roll of fencing he can use. The width of the garden is 10 feet
Answer:
Step-by-step explanation:
To find out how much of the 100 foot roll of fencing Martin will need to enclose the garden, you need to calculate the perimeter of the rectangular garden.
The perimeter is the total distance around the garden. To find the perimeter, you add up the lengths of all four sides of the rectangle.
The formula for the perimeter of a rectangle is: P = 2L + 2W
Where P is the perimeter, L is the length, and W is the width.
In this case:
P = 2 x 10 feet + 2 x 100 feet = 20 feet + 200 feet = 220 feet
Martin will need 220 feet of fencing to enclose his rectangular garden.
PLSSS HELP IF TURLY KNOW THISSS
To solve the expression 9 - 12 + 6/-3 + 3(-3) first do the operation of division, i.e. option B: 6/-3.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
The given expression is - 9 - 12 + 6/-3 + 3(-3)
Follow the BODMAS rule to solve the expression.
BODMAS = Bracket Of Division Multiplication Addition and Subtraction
The first step is to solve the bracket -
= 9 - 12 + 6/-3 + 3(-3)
= 9 - 12 + 6/-3 - 9
The next step is to solve the division -
= 9 - 12 + 6/-3 - 9
= 9 - 12 -2 - 9
The next step is to solve the addition and subtraction -
= 9 - 12 - 2 - 9
= 9 - 23
= -14
Therefore, the value of the expression is obtained as -14.
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In 2010, the population of a city was 220,000. From 2010 to 2015, the population grew by 6.2%. From 2015 to 2020, it fell by 4.5%. How much did the population grow from 2010 to 2015, to the nearest 100 people?
Answer: It grew by 13,640 people
Step-by-step explanation:
First, turn 6.2% into 0.062.
Next, multiply 0.062x220,000.
You get 13,640.
The rest of the information is unnecessary.
It takes a train going 50 mph approximately _____ to stop safely.
A. 100 ft B. 1/2 miles C. 1 1/2 miles D. 5 miles
It takes a train going 50 mph approximately 11/2 miles to stop safely.
The distance a train takes to come to a stop can be determined by several factors, including the speed of the train, the weight of the train, the condition of the brakes and the track, and the reaction time of the engineer.
In general, a train going 50 mph will take about 1 1/2 miles or 8,000 feet to stop safely. This is because a train moving at 50 mph is traveling at about 75 feet per second, and it takes a significant distance to slow down a heavy object moving at such a high speed. It's important to note that this is an estimation, and the actual stopping distance may vary depending on the specific conditions.
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Jada had 30 dollars to spend on 3 gifts. She spent 10
9
10
dollars on gift A and 4
3
5
dollars on gift B. How much money did she have left for gift C?
STUV is a parallelogram. Solve for SV:
S
19
4x1
2x + 3
U
The side length SV= 13 units
What is a parallelogram?
A parallelogram is the name given to a quadrilateral in geometry. In a parallelogram, the opposing sides are parallel and of equal length. The rhombus, rectangle, and square are just a few shapes that are parallelograms.
Having two sets of parallel sides makes a quadrilateral a parallelogram. A parallelogram has opposite sides that are the same length and angles that are the same size. Additionally, the internal angles on the same transverse side are supplementary. 360 degrees are equal to the total of all internal angles.
In a parallelogram, opposite sides are congruent.
ST=VU
=> 19=4x-1
=> 4x=19+1 = 20
=> x= 20/4 = 5
SV=2x+3
=> SV=2(5)+3 = 10+3 = 13
The side length SV= 13 units
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Write down in terms of n, an expression for the nth term
of the following sequences:
b) 9 11 13 15 17
i need help
The expression for the nth term of the sequences in terms of n is 2n + 7
How to write expression for nth term?9 11 13 15 17
Where,
First term, a = 9Common difference, d = 11 - 9 = 2nth term = number of termnth term = a + (n - 1)d
= 9 + (n - 1)2
= 9 + 2n - 2
nth term = 2n + 7
Therefore, 2n + 7 is the expression which represents the nth term of the given sequence.
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PLSsSS I NEED HELP (and pls give the right answer)
The volume of right prism is equal to 464 cubic inches.
How to determine the volume of a beam-like right prism
Volume of right prisms (V), in cubic inches, is equal to the product of cross area (A), in square inches, and height (h), in inches:
V = A · h
According to figure, cross area is the result of adding the areas of three rectangles. Area formula for rectangles is:
A' = w · l
Where:
w - Width, in inches.l - Length, in inches.First, determine the cross area of the prism:
A = 2 · (3 in) · (7 in) + (4 in)²
A = 42 in² + 16 in²
A = 58 in²
Second, calculate the volume of the right prism:
V = (58 in²) · (8 in)
V = 464 in³
The right prism has a volume of 464 cubic inches.
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Carter plays
5
8
5
8
of a basketball game. The basketball game is 40 minutes long. Which of the following shows how to find the number of minutes Carter plays?
A.
5
×
8
8
×
8
=
40
64
5
×
8
8
×
8
=
40
64
; 40 minutes
B.
5
×
7
8
×
7
=
35
56
5
×
7
8
×
7
=
35
56
; 35 minutes
C.
5
×
5
8
×
5
=
25
40
5
×
5
8
×
5
=
25
40
; 25 minutes
D.
5
×
4
8
×
5
=
20
40
5
×
4
8
×
5
=
20
40
; 20 minutes
The total number of minutes Carter played the basketball game is 25 minutes.
The correct answer choice is option C.
What is the total number of minutes Carter plays?Total minutes of the basketball game= 40 minutes
Minutes Carter played= 5/8 of Total minutes of the basketball game
= 5/8 × 40
= 0.625 × 40
= 25 minutes
Hence, Carter played the basketball game for 25 minutes.
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What does a basic log graph look like?.
A basic log graph is a line graph that plots logarithmic data points plotted on a logarithmic scale.
The x-axis of the graph is the logarithmic scale, and the y-axis is the data points.
The points are plotted in a straight line, making it easy to see how the data points change as the logarithmic scale increases or decreases.
On the exponential f, identify several locations (x). The graph will look better the more points we plot.
A two-dimensional graph of numerical data using logarithmic scales on both the horizontal and vertical axes is known as a log-log graph or log-log plot.
In order to obtain points on the inverse, swap the x and y variables. Discover the asymptote. The ensuing logarithmic functions should be plotted. the domain and the range.
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A local little league has a total of 70 players, of whom 80% are left-handed. How many left-handed players are there?
Answer:
56
Step-by-step explanation:
Take 70 and multiply 80%
70 × 80/100 = 56
A boat is traveling in a river with a current that has a speed of 1.5 km/h . in one hour the boat can travel twice the distance downstream as it can travel upstream . what is the boat speed in Stillwater ?
Answer:
To find the speed of the boat in still water, we can use the formula:
Speed in still water = (Downstream speed + Upstream speed) / 2
We know that the speed of the current is 1.5 km/h and the boat can travel twice the distance downstream as it can travel upstream. Therefore, if the boat travels x km downstream in one hour, it travels x/2 km upstream in one hour.
We can use this information to set up the following equation:
x + (x/2) = (x + x/2) = (3/2)x = Downstream speed
And the upstream speed is x/2
Now we can substitute this value into the formula for speed in still water:
Speed in still water = ( (3/2)x + (x/2) )/2 = (3x + x)/4 = x = (3+1) km/h = 4 km/h
So, the speed of the boat in stillwater is 4 km/h.
We don't know the exact distance that the boat travels downstream in one hour, so we can't calculate the speed in still water with the given information. To find the speed in still water we need to know the distance traveled downstream or upstream.
Tomo is making brownies.
He has 4/3 cups of sugar.
He needs 1/3 cup of sugar to make one whole batch of brownies.
Use the drop-down menus to complete the statements below about the brownies that Tomo can make.
Tomo can make more one whole batch of brownies. Tomo can make exactly four batch(es) of brownies with the sugar he has.
How to determine the true and complete statement?Based on the information provided, we can logically deduce the following parameters:
Number of cups of sugar is equal to 4/3 cups of sugar.
Number of cups of sugar to make one whole batch of brownies is equal to 1/3 cup of sugar.
In order to determine the exact batches of brownies which Tomo can make based on the number of cups of sugar he has, we would divide the number of cups of sugar by the number of cups of sugar that is required to make one whole batch of brownies as follows;
Batch of brownies = 4/3 ÷ 1/3
Batch of brownies = 4/3 × 3
Batch of brownies = 12/3
Batch of brownies = 4 batches of brownies.
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Complete Question:
Tomo is making brownies he has 4/3 cups of sugar. He needs 1/3 cup of sugar to make one whole batch of brownies. Tomo can make _____ one whole batch of brownies. Tomo can make exactly _____ batch(es) of brownies with the sugar he has.
Mario and Luigi are making pizza for their birthday party. They need to make 25 pizza. Mario i fat and ha already made 11 pizza. Luigi i lower and only ha made 3. Write an equation with the variable (p) and how your work to determine how many pizza they have left to make
The equation for the remaining work is given by the equation 25 - (x+y)
let x be the number of pizza made by Mario and y be the number of pizza made by luigi
let z be the pizza that still need to be made
so x+y+z=25
=> z = 25 - ( x + y )
so the total remaining pizza is given by 25 - (x+y) ---(i)
given that Mario had made 11 pizza so x = 11
and Luigi had made 3 pizza so y = 3
so total remaining work is found using equation (i)
so z = 25 - ( 11 + 3)
=> 11
so remaining work is 11
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What is the main difference between an expression and a polynomial class 8?.
Expression and polynomial are both mathematical terms that are used to represent mathematical equations.
An expression is any combination of symbols, numbers, and operations that represent a value or a quantity. Expressions can be represented as algebraic equations, numerical equations, or verbal phrases.
A polynomial is a specific type of expression that is composed of one or more terms with each term containing a power of a single variable. A polynomial can be represented with a single variable or multiple variables.
A formula is an expression or equation that represents an idea or a relationship between two or more variables. A calculation is the actual process of evaluating an expression or equation to determine a numerical value or answer.
In summary, an expression is any combination of symbols, numbers, and operations that represent a value or quantity, while a polynomial is a specific type of expression composed of one or more terms with each term containing a power of a single variable.
A formula is an expression or equation that represents an idea or relationship between two or more variables, while a calculation is the actual process of evaluating an expression or equation to determine a numerical value or answer.
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What is 1 4 equivalent to in fractions?.
Equivalent 1/4 is equals to 4/16 in fractions.
Equivalent fractions in mathematics are ones that have the same denominator but different numerators. For instance, 2/4 and 3/6 are equivalent fractions since they both equal 1. A fraction is a piece of the total. Equivalent fractions are used to indicate identical parts of the whole.
The equivalent fraction of each fraction can be calculated by multiplying the numerator and denominator by the same integer. Equivalent fractions are ones that denote the same value despite visual disparities. You will have devoured half of a cake, for example, if you take a piece, cut it into two equal pieces, and then eat one of them.
= 1/4 is equivalent to:
= 1/4 * 4/4
= 4/16
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Correct Question:
What is 1/4 equivalent to in fractions?.
What is the solution of the equations 8x +3y 5 and 3x 2y 5?.
The solution of the equation 8x + 3y = 5 and 3x + 2y = 5 is x = -5/7 and y = -7/24
In math the term called equation is defined as a mathematical statement that shows that two mathematical expressions are equal
Here we have given that the equation 8x + 3y = 5 and 3x + 2y = 5 and we need to solve the equation to find the values of x and y.
in order to solve the equation we have to multiply 2 with the equation (1), then we get,
=> 16x + 6y = 10
And then we have to multiply 3 with the equation (2), then we get,
=> 9x + 6y = 15
Now, we have to subtract these two equation then we get,
=> 7x = -5
=> x = -5/7
Then the value of y is calculated as,
=> 8(-5/7) + 3y = 5
=> -40/7 + 3y = 5
=> 3y = -35/40
=> 3y = -7/8
=> y = -7/24
Therefore, the solution is found.
Complete Question:
What is the solution of the equations 8x + 3y = 5 and 3x + 2y = 5?
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