Based on the given ratio of modern and classical songs learned, the number of modern songs learned if 9 classicals have been learned is 15
What is the number of modern songs learned?Number of modern songs they learn = 5Number of classical songs = 3If the choir has learned 9 classical songs;
Number of modern songs learnt = xEquate the ratio of the number of modern songs to the number of classical songs
5 : 3 = x : 9
5/3 = x/9
cross product5 × 9 = 3 × x
45 = 3x
divide both sides by 3
x = 45/3
x = 15
In conclusion, the number of modern songs they have learned if they learn 9 classical songs is 15
Complete question:
Raymond sings in a choir called the Seaville Songbirds. For every 5 modern songs they learn, the choir leader teaches them 3 classical songs.
If the choir has learned 9 classical songs, how many modern songs have they learned?
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help me on this math please!
The function rule for each are:
f(x) = -2x - 6
g(x) = 5x - 4
f(x) is less than g(x), in terms of slope, while in terms of y-intercept, f(x) is greater than g(x).
How to Write the Rule of a Function?The rule of a function can be written in slope intercept form as, f(x) = mx + b, where the slope is m and the y-intercept is the value of b.
To write the function rule for f(x), substitute m = -2 and b = -6 into f(x) = mx + b:
f(x) = -2x - 6
Find the slope of the function g(x) whose graph is given:
Slope of g(x) = rise/run = 5/1 = 5
m = 5
The y-intercept is at y = -4, therefore b = -4.
To write the function rule for g(x), substitute m = 5 and b = -4 into g(x) = mx + b:
g(x) = 5x - 4
In terms of slope, f(x) is less than g(x)
In terms of y-intercept, f(x) is greater than g(x).
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Write a polynomial of least degree with roots 1 and -9. un Write your answer using the variable x and in standard form with a leading coefficient of 1.
Answer:
y = x² +8x -9
Step-by-step explanation:
You want the least-degree polynomial with roots 1 and -9, written in standard form.
FactorsEach root p means there is a factor (x-p). The two roots make the factored form of the polynomial be ...
y = (x -1)(x +9)
Expanding this to standard form, we get ...
y = x² +8x -9
__
Additional comment
A quadratic that has two roots, p and q, will have the standard form ...
y = (x -p)(x -q) = x² -(p+q)x +pq
That is, the linear term coefficient is the opposite of the sum of the roots, and the constant is their product. This means you can write down the equation directly from the roots:
y = x² -(1-9)x +(1)(-9) = x² +8x -9
Norman wants to figure out how tall a light pole is. he uses his sextant to measure the angle of elevation to be 36 degree and he holding the sextant at his eye level, 5 feet from the ground.if he is 10 feet away from the light pole how tall is the light pole?
Norman will measure the light pole to be 12 feet tall
How to determine the height of the light poleInformation from the question
Norman uses his sextant to measure the angle of elevation to be 36
5 feet from the ground. if he is 10 feet away from the light pole
how tall is the light pole = ?
The height of the light pole is calculated using SOH CAH TOA
The direction of movements describes a right angle triangle of
opposite = height of the light pole
adjacent = 10 feet away from the light pole
The height is is calculated using tan, TOA let the angle be x = 36
tan x = Opposite / Adjacent
tan 36 = opposite / 10
opposite = tans 35 * 10
opposite = 7 feet
this is height 5 feet from the ground, so total height is calculated to be
5 + 7 = 12 feet
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A positive integer M divided by six gives a remainder of three. Another positive integer N divided by six gives a remainder of five. What is the remainder when the sum M+N is divided by six?
When the sum M+N is divided by 6 , the remainder is 8
What is Remainder?The remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient (integer division). We always have remainder when the denominator is a factor of numerator.
For example 5/2, diving 5 with 2, 2 is not a factor of 5,
There are 2 2s in 5 with remainder 1.
M/6= x y/6
where is the factor and y is the remainder
therefore m/6= (6x+y)/6
y= 3,. m/6= (6x+3)/6
N/6= (6x+5)/6
therefore dividing both sides by 6
m= 6x+3
n= 6x+5
adding m and n
m+n= 12x+8
dividing m+n by 6
(m+n)/6 = (12x+8)/6
relating (12x+8)/6 with (6x+y)/6
y = 8
Therefore the remainder is 8
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In ΔTUV, m∠T = 58° and m∠U = 97°. Which list has the sides of ΔTUV in order from longest to shortest?
The sides of ΔTUV in order from longest to shortest is as follows -
TV > TU > VU
What is triangle?A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
The sum of two sides of a triangle is greater then the third side. Mathematically -
a + b > c
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given is ΔTUV, m∠T = 58° and m∠U = 97°.
Refer to the image attached.
TV > VU
TU + VU > TV
TV > TU + VU
So we can arrange the sides as follows -
TV > TU > VU
Therefore, the sides of ΔTUV in order from longest to shortest is as follows -
TV > TU > VU
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To paint a house, a painting company charges
a flat rate of $500 for
supplies, plus $50 for each hour of labor.
a.
How much would the painting company charge to paint
a house that
needs 20 hours of labor? A house that needs 50 hours?
Call the number of hours of labor x.
A flat rate of $500 -> just $500.
$50 for each hour of labor -> 50x (for x hours)
Therefore, we can represent the amount needed for x hours of labor as the function : 500 + 50x.
We substitute :
20 hours of labor = 500 + 50 x 20 = $1500
50 hours of labor = 500 + 50 x 50 = $3000
Sandy bought an outboard motor for a total selling price of $420 in Maine, which has a 7% sales tax rate. Calculate the sales tax.
Answer
you do 420x0.7= 29.40
Answer:
The sales tax is 29.4
Step-by-step explanation:
Just divide in half until you reach 5 and then calculate the other 2 percent of it and add the 2 percent back onto it.
in a class of 20 students, there are two students a and b. what will be the probability of selecting these two students randomly?
The probability of selecting two students (a and b) randomly is found as 1/380.
What is referred as the word probability?The study of random experiments is what aids in determining the likelihood of an event.The study of probabilities, which are determined by the ratio of favorable cases to possible cases, is known as probability.The formula for evaluating the Probability is-
Probability = Favourable outcomes / Total outcomes.
As, per the given question.
Total number of students = 20.
The probability for selection of 'a' is 1/20.
Now, the total students left is 19.
Thus, the probability for selection of 'b' is 1/19.
The total probability for selection of both is -
Probability(a and b) = 1/20×1/19
Probability(a and b) = 1/380
Thus, the probability of selecting two students ( a and b) randomly is found as 1/380.
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raina swam 8 kilometers against the current in the same amount of time it took her to swim kilometers with the current. the rate of the current was kilometer per hour. how fast would raina swim if there were no current?
The speed at which raina can swim if there is no current is 3 km/hor 3 kilometers per hour.
Given that,
In the same length of time it took raina to swim kilometers with the river, she was able to swim 8 kilometers against it. The current flowed at a kilometer per hour rate.
Distance 1 * (Raina's velocity - current velocity) = Distance2 * (Raina's velocity + current velocity)
16 * (Raina's velocity - 1) = 8 * (Ivan's velocity + 1)
(16 * Raina's velocity) - 16 = (8 * Ivan's velocity) +8
8 * Raina's velocity = 24
Raina's velocity = 3 kilometers per hour
As a result, Raina can swim at a speed of 3 km/hr in the absence of a current.
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Pls solve this problem
Answer: -22/5 or -4.4
Step-by-step explanation:
Simplify so 2(22/7*10)(10+h)=352
Distribute so (2*22/7*10)(10) + (2*22/7*10)(h) = 352
Which would equal 4400/7 +440/7h=352
Subtract 4400/7 to both sides
That equals 440/7h=-1396/7
Multiply both sides by 7/440
h=-22/5
given that £1 = $1.62
how much is £650 in $
Answer:
$1053
Step-by-step explanation:
If we have that £1 = $1.62, then we can multiply both sides by 650 in order to get £650 on the left side of the equality. We must multiply the right side also by 650, and so we get £650=$1.62 * 650.
To do this multiplication, we can break 1.62 down simply into $1.00 +$0.6+$0.02
650*$1.00=$650, 650*$0.6=650*6/10=65*6=$390, and 650*$0.02=650*2/100=6.5*2=$13.
When we add these three products together, we get $650+$390+$13=$1053. And so, £650=$1053
Pls help me and give steps as to how to do it thank you
Answer: [tex]x=13, y=132[/tex]
Step-by-step explanation:
Using the same-side interior angles theorem, [tex]y=132[/tex].
Using the alternate interior angles theorem, [tex]5x-17=48 \implies x=13[/tex]
I need help asap please now please !!!!!!!!!!!
help meeeeeeeeeeeeeee pleaseee
The table of solutions for this quadratic equation (y = -2x²) include the following:
x y_
-2 -8
-1 -2
0 -0
1 -2
2 -8
A graph of the solution of the given quadratic equation has been plotted in the image attached below.
How to determine the solutions?In Mathematics, the graph of any quadratic equation or function always forms a parabola, which simply means a u-shaped curve. In order to determine the correct solutions to the given quadratic equation, we would have to substitute the x-values contained in the table into the quadratic equation.
At point x = -2, the y-value of this quadratic equation is given by:
y = -2x²
y = -2(-2)²
y = -2 × 4
y = -8
At point x = -1, the y-value for this quadratic equation is given by:
y = -2x²
y = -2(-1)²
y = -2 × 1
y = -2
At point x = 0, the y-value of this quadratic equation is given by:
y = -2x²
y = -2(0)²
y = -2 × 0
y = 0
At point x = 1, the y-value of this quadratic equation is given by:
y = -2x²
y = -2(1)²
y = -2 × 1
y = -2
At point x = 2, the y-value of this quadratic equation is given by:
y = -2x²
y = -2(2)²
y = -2 × 4
y = -8
In conclusion, we can logically deduce that the graph of this quadratic equation forms a downward parabola.
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please help ASAP
A toy cannon ball is launched from a cannon on top of a platform.
The function h(t) =-5+ 2 + 20+ + 4 gives the height, in meters, of the ball t seconds after it is launched.
Write and solve an inequality to find the times where the ball is more than 12 meters above the ground.
Round to the nearest hundredth.
Answer:
hello\\
Step-by-step explanation:
Find the number of square tiles of sides 6 cm needed to fit in a rectangular region whose length andbreadth are: a) 9 m and 12 m b) 8 m and 9 m
Number of square tiles that are needed to fit the rectangular region are
(a) 30000 tiles and (b) 20000 tiles .
In the question ,
it is given that
the side of the square tile is = 6 cm
so ,the area of the square tile = 6*6= 36 cm²
Part(a)
the length of the rectangular region = 9m = 900 cm
the breadth of the rectangular region = 12m = 1200 cm
So, the area of the rectangular region = 900 * 1200 = 1080000 cm²
the number of tiles required = (area of rectangular region)/(area of tile )
= 1080000/36
= 30000
hence , 30000 tiles are needed.
Part(b)
the length of the rectangular region = 8m = 800 cm
the breadth of the rectangular region = 9m = 900 cm
So, the area of the rectangular region = 800 * 900 = 720000 cm²
the number of tiles required = 720000/36
= 20000
hence , 20000 tiles are needed .
Therefore ,Number of square tiles that are needed to fit the rectangular region are
(a) 30000 tiles and (b) 20000 tiles .
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Please help, I'm struggling.
I think you would just add 8 + 5, because if NO is the same length as MN, then the length from MN is 5 and NP makes up the rest of the line.
Answer: MP = 13
Write equivalent fractions for 8/9 and 5/8 using the least common denominator.
Type the fractions, using a slash ( / ) to separate the numerator and denominator.
8/9 =
5/8 =
The equivalent fractions for 8/9 and 5/8 using the least common denominator are 8/9 = 64/72 and 5/8 = 45/72.
What is the Least Common Denominator?
The smallest number that can serve as a common denominator for a group of fractions is known as the least common denominator (LCD). The smallest number that may be used as the denominator to produce a group of comparable fractions that all have the same denominator is known as the lowest common denominator.
The given fractions are 8/9 and 5/8.
The denominators of these fractions are 8 and 9.
so Least Common Divisor(LCD) of 8 and 9 will be = 8 × 9
= 72.
so the equivalent fraction can be calculated as
for 8/9 = [tex]\frac{8*8}{9*8}[/tex]
= 64/72
and for 5/8 = [tex]\frac{5*9}{8*9}[/tex]
= 45/72
Hence, the equivalent fractions are 64/72 and 45/72.
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what is the sum between 6/9 and 3/6
Answer:
21/18 or 1 and 3/18
Step-by-step explanation:
6/9 = 12/18
3/6 = 9/18
12/18 + 9/18 = 21/18 or 1 3/18
Answer:
[tex] \frac{6}{9} + \frac{3}{6} \\ \\ = \frac{2 \times 6 + 3 \times 3}{18} = \frac{12 + 9}{18} = \frac{21}{18} = \frac{7}{6} = 1 \frac{1}{6} [/tex]Please answer this
This is very hard for me and my friend
The value of x is 10.6 which is equivalent to 11.
In the given triangle
the triangle is divided into two triangles which are both right angled
However in the bigger triangle
we would use the Pythagoras Theorem
( y + 6 )² = x² + 100 ---------- equation 1
In the smaller triangle;
x² = y² + 64 --------------equation 2
Thus substituting the value of x in equation 1
Thus the equation becomes
( y + 6 )² = y² + 64 + 100
y² + 36 + 12x = y² + 164
Cancelling y² on both sides we will get
36 + 12x = 164
12x = 164 - 36
this implies 12 x = 128
x = [tex]\frac{128}{12}[/tex]
x = 10.6 ≈ 11
Thus the required value of x is 10.6 or 11
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Mrs. Wong is researching what it would cost to order flower arrangements for a fancy party. She wants one large centerpiece for the head table, and smaller arrangements for the smaller tables. Lakeside Florist charges $19 for each smaller arrangement, plus $50 for the large centerpiece. Spencer's Flowers, in contrast, charges $42 for the large centerpiece and $23 per arrangement for the rest. If Mrs. Wong orders a certain number of small arrangements, the cost will be the same at either flower shop. How many small arrangements would that be? What would the total cost be?
Step-by-step explanation:
so, we have 2 cost functions. each consisting of 1 large centerpiece, and x smaller arrangements.
cost1(x) = 19x + 50
cost2(x) = 23x + 42
to get the value for x we know that the cost is the same either way.
that means
cost1(x) = cost2(x) = 19x + 50 = 23x + 42
19x + 50 = 23x + 42
50 = 4x + 42
8 = 4x
x = 2
so, she orders 2 small arrangements.
the total cost is
19×2 + 50 = 38 + 50 = $88
cross check with the other function :
23×2 + 42 = 46 + 42 = $88
correct
Complete the statement to describe the expression (a+b+c)(d+e+f)(a+b+c)(d+e+f). The expression consists of 3 factors, and each factor contains terms
The statement about the given expression is described below.
What is expression?A math expression consist numbers, variables and operators its operation addition, subtraction, multiplication, and division. The parts of the expression that are connected with addition and subtraction are considered as terms.
According to given data:Expression, (a+b+c)(d+e+f)(a+b+c)(d+e+f) = (a +b+c)^2(d+e+f)^2
It has factors two which consist of 3 termsEach factor has a multiplicity of 2terms in factor (a+b+c) are a, b, cTerms in factor (d+e+f) are d, e, fThus, given expression has two factors which consist 3 terms.
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3
3
Use exponent rules to explain why (√5)³ = √√5³.
Answer:
see image
Step-by-step explanation:
Use new exponent rules like:
A power raised to a power is the product of the powers. (power to a power, times the exponents)
and,
Square root is a half power. (Converting radicals to fractional exponents)
Also, you can multiply in any order, like since you learned multiplying (example: 2×6 is the same as 6×2)
see image.
Here's the plan:
Change the radical to a 1/2 exponent. Now 3 and 1/2 are both exponents. Rearrange the order. Rewrite in radical form again.
see image.
The proof of the equation (√5)³ = √(5³) is given below.
What is an exponent?Exponentiation is one of the mathematics operation.
Let mᵃ, where m and a are the real numbers.
And m is multiplied by a times to itself.
So, a is the exponent of m.
Given:
A radical equation,
(√5)³ = √(5³).
LHS = (√5)³
Simplifying,
(√5)³ = {(5[tex])^{1/2}[/tex]}³
= [tex]5^{3/2}[/tex]
= √(5³)
= RHS.
Therefore, (√5)³ = √(5³).
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The complete question:
Simplify and prove the equation (√5)³ = √(5³) by using exponent rules.
Paul is a keen cyclist. the chart shows the distance he cycled each day of last week. a)How much further did Paul cycle on Friday than on Monday? b)what is the total distance cycled by Paul on the three days he cycled the most?
Answer:
a) 6 km
b) 66 km
Step-by-step explanation:
a) According to the graph:
Paul cycled about 22 km on Friday.Paul cycled about 16 km on Monday.To find how much further, subtract the distance cycled those two days:
22 - 16 = 6 km
b) The three days he cycled the most are the three days with the highest lines on the graph, so that would be:
Saturday, about 24 km.Friday, about 22 km.Wednesday, about 20 km.Add them all up to find the total distance cycled:
24 + 22 + 20 = 66 km
HELP PLEASE QUICKLY THANKS
Graph will shift in both horizontal and vertical direction by 4 units.
What is straight line?
An unending, one-dimensional figure with no width is a straight line. It consists of an infinite number of points connected on either side of a point. There is no curvature in a straight line. It might be angled, vertical, or horizontal.
What is general equation of a Straight Line?
The general equation of a straight line can be given as ax + by + c = 0, where
a, b, c are constants, andx, y are variables.The slope is -a/bWhat do you mean by function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain. The usual way to refer to a function is as fn(x), where x is the input.
We have function,
fn(x) = x + 5
when the graph is translated by 4 units, we can write it as;
g(x) = fn(x) + 4
the graph will shift in both horizontal and vertical direction by 4 units as it can be seen in the graph.
Therefore, graph will shift in both horizontal and vertical direction by 4 units.
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Given the following list of axioms, draw a model to properly represent the information.
a. there exists five points
b. there exists two lines
c. each line consists of at least two points
d. each line contains only these five points.
The model which properly represent the information in given axioms is Cross geometry (+).
In the given question we have following information,
total number of points in model is 5total number of lines in model is 2each line consists atleast 2 pointseach line contains only these five pointsby using the above axioms we draw a geometry of Cross sign Geometry as seen above .
We can draw a line which contains three points and these points are only from given five points another line also follow this . this geometry follows all given axioms . The two lines intersect each other at a point . The point of intersection is one of point from five points . both of lines are linear and consists three points .
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each face of a cube is given a single narrow stripe painted from the center of one edge to the center of the opposite edge. the choice of the edge pairing is made at random and independently for each face. what is the probability that there is a continuous stripe encircling the cube?
The probability that there is a continuous stripe encircling the cube is 3/16.
A single, thin stripe is painted from the center of one edge to the center of the other edge on each face of a cube. Each face's edge pairing is selected independently and at random.
For each of the cube's six faces, there are two possible stripe orientations, resulting in a total of 2 x 6 = 64 possible stripe permutations. Since there are three sets of parallel faces, the stripe orientation for the remaining faces is determined uniquely by the pair of faces that does not contribute to the encircling stripe. Additionally, there are two possible orientations for the stripe on each face that is non-contributing.
A continuous stripe surrounds the cube as a consequence of a total of
3 * 2 * 2 = 12 stripe variations.
The necessary probability is 12/64, which equals 3/16.
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you have 100 feet of fence to make a rectangular play area alongside the wall of your house. the wall of the house bounds one side. what is the largest possible area (in square feet)?
The length and width of the rectangle are 50 feet and 25 feet respectively, the product of which gives the area of the rectangle which is 1250 feet.
Given, 100 feet of fence to make a rectangular play area that is side by side with the wall of your house.
The perimeter of the rectangle is = 2x+2y, since the wall bounds from one side as given in the question perimeter changes to = x+2y.
Perimeter = x+2y
100 = x+2y
100 = 50+2y
2y = 50
y = 25
Using this we found the length and width of the rectangle which is equal to 50 feet and 25 feet respectively. The area which is the final answer comes out to be 1250 feet.
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a column contains phone numbers such as (801)-555-1234. what function should you use to extract the last four digits?
RIGHT function should be used to extract the last four digits from a column containing phone numbers.
The Excel TEXT functions section includes the RIGHT Function[1]. A predetermined number of characters from the end of a provided text string will be returned by the function.
The RIGHT function can be helpful in the financial analysis if we want to extract characters from a text string's right side. It is typically used in conjunction with functions like VALUE, SUM, COUNT, DATE, DAY, etc.
Formula is=RIGHT(text,[num chars])
The following arguments are used by the RIGHT function:
Text is the original text string (mandatory argument).
The number of characters to be returned from the end of the provided text is specified by the optional argument Num chars. It specifies how many characters will be taken, beginning on the right side of the text. If the argument is omitted, the value of 1 by default is used.
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There are 11 counters in a bag.
8 of the counters are green.
3 of the counters are blue.
Sid takes at random two counters from the bag.
Work out the probability that Sid takes one counter of each colour
(Hint: Fractions can be written in the form a/b. eg [tex]\frac{5}{28}[/tex] would be written as 5/28)
The probability of Sid takes at random counters from the bag is 24/55
The total number of counters = 11
Total number of green counters = 8
Total number of blue counters = 3
Probability = Number of favorable outcomes / Total number of outcomes
Total number of outcome = 55
Number of outcome that Sid will get both green = 28
Number of outcome that Sid will get both blue = 3
Number of favorable outcome = 55 - 28 - 3
= 24
Probability = Number of favorable outcomes / Total number of outcomes
= 24/55
Hence, the probability of Sid takes at random counters from the bag is 24/55
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