Solution
Step 1:
Let the number of pupils = n
[tex]\begin{gathered} Number\text{ of boys = }\frac{2}{3}n \\ Number\text{ of girls = }\frac{2}{3}n\text{ - 15} \end{gathered}[/tex]Step 2:
Write an equation to find the value of n
[tex]\begin{gathered} \frac{2}{3}n\text{ + }\frac{2}{3}n\text{ - 15 = n} \\ \frac{4n}{3}\text{ - n = 15} \\ \frac{4n\text{ - 3n}}{3}\text{ = 15} \\ \frac{n}{3}\text{ = 15} \\ \text{n = 15 }\times\text{ 3} \\ \text{n = 45} \end{gathered}[/tex]Final answer
There are 45 pupils in the class.
linear equations in deletion method2x + 2y − z = 04y − z = 1−x − 2y + z = 2
The given system is:
[tex]\begin{gathered} 2x+2y-z=0\ldots(i) \\ 4y-z=1\ldots(ii) \\ -x-2y+z=2\ldots(iii) \end{gathered}[/tex]Multipliy (iii) by 2 to get:
[tex]-2x-4y+2z=4\ldots.(iv)[/tex]Add (i) and (iv)
[tex]\begin{gathered} 2x+2y-z=0 \\ + \\ -2x-4y+2z=4 \\ -2y+z=4\ldots(v) \end{gathered}[/tex]Add (ii) and (v) to get:
[tex]\begin{gathered} 4y-z=1 \\ + \\ -2y+z=4 \\ 2y=5 \\ y=\frac{5}{2} \end{gathered}[/tex]Put y=5/2 in (ii) to get:
[tex]\begin{gathered} 4(\frac{5}{2})-z=1 \\ 10-z=1 \\ -z=-9 \\ z=9 \end{gathered}[/tex]Put y=5/2 and z=9 in (i) to get:
[tex]\begin{gathered} 2x+2(\frac{5}{2})-9=0 \\ 2x+5-9=0 \\ 2x=4 \\ x=2 \end{gathered}[/tex]Hence x=2, y=5/2 and z=9.
which is the graph of f(x)=2(3)^2
You have the folowing function:
f(x) = 2(3)ˣ
In order to determine which of the given graph belongs to f(x), you verufy if the given points of the graphs correspond to f(x). You proceed as follow:
For first graph:
x = 1
f(x) = 2(3)¹ = 2(3) = 6
The point is (1,6)
The previous point is the same that the graph has, hence, the first graph belongs to f(x) = 2(3)ˣ
Then, it is not necessary to check the other points becasue they are not agree with f(x)
Which of the following graphs represents the equation 3x + 2y = 24?
Answer:
C
Step-by-step explanation:
if x=0
2y = 24
2/2 y = 24/2
y = 12
if y =0
3x = 24
3/3 x = 24/3
x = 8
Instructions: Find the missing angle. Round your answer to the nearesttenth.
ANSWER
[tex]x=65.9^o[/tex]EXPLANATION
We are given a right-angled triangle.
We have that the hypotenuse is 46.
The side opposite the given angle is 42.
The angle given is x.
To solve this, we can use trigonometric ratios SOHCAHTOA.
We will use the SOH part of it:
[tex]\sin (x)\text{ = }\frac{opposite}{hypotenuse}[/tex]So, we have that:
[tex]\begin{gathered} \sin (x)\text{ = }\frac{42}{46} \\ \sin (x)\text{ = 0.9130 } \\ \text{ Find the sine inverse (sin}^{-1})\text{ of 0.9130 to get x:} \\ x=sin^{-1}(0.9130) \\ x=65.9^o \end{gathered}[/tex]That is the value of the missing angle x.
2.2Determine the value of n for which (3k - 2) = 70
The value of k is 24.
From the question, we have
(3k - 2) = 70
(3k) = 72
k=24
Subtraction:
Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.
The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.
Complete question: Determine the value of k for which (3k - 2) = 70
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Find the speed of each train (set up a table )
We have two trains that leave Mexico City at the same time, one to the east and the other to the west. The train that travels to the west is 10 mph slower than the other train. The diagram of the problem is:
The combined velocity is:
[tex]V_T=v+v-4=2v-4[/tex]The equation that relates the distance D between the trains and the time after t hours is:
[tex]D=V_T\cdot t[/tex]If after 1.5 hours the trains are 171 miles apart, then using the equation above:
[tex]\begin{gathered} 171=V_T\cdot1.5 \\ V_T=\frac{171}{1.5} \\ V_T=114 \\ 2v-4=114 \\ 2v=118 \\ v=59\text{ mph} \end{gathered}[/tex]Now, the speeds are:
[tex]\begin{gathered} \text{East}\colon59\text{ mph} \\ \text{West}\colon55\text{ mph} \end{gathered}[/tex]In the year 2010, Xavier's car had a value of $22,000. When he bought the car in 2006 he paid $28,000. If the value of the cardepreciated linearly, what was the annual rate of change of the car's value? Round your answer to the nearest hundredth if necessary.
The annual rate of change is given by:
[tex]A\mathrm{}R\mathrm{}C=\frac{f(b)-f(a)}{b-a}[/tex][tex]\begin{gathered} A\mathrm{}R\mathrm{}C=\frac{22000-28000}{2010-2006} \\ A\mathrm{}R\mathrm{}C=\frac{-6000}{4}=-1500 \end{gathered}[/tex]Hence, the annual rate of change is -1500 dollars/year, meaning the car depreciates/loses value by an amount of 1500 dollars
The u.s system of weighs and measureenter the maximim number of whole feet and then the remaining inches. Simply your answer
One foot is 12 inches. So the maximum number of feet that fit into 78 inches is the quotient of the division of 78 by 12.
[tex]\frac{78}{12}[/tex]The above division gives us 6 whole feet and 6 inches.
Hence, the door is 6 feet and 6 inches high.
Solve the compound inequality.3x + 12 ≥ –9 and 9x – 3 ≤ 33 x ≥ –7 and x ≤ –4x ≥ 7 and x ≤ 4x ≥ 1 and x ≤ 4x ≥ –7 and x ≤ 4
To solve this problem, we will solve each inequality for x and the solution to the system will be the intersection of the solution sets.
1) Solving the first inequality for x we get:
[tex]\begin{gathered} 3x+12\ge-9, \\ 3x\ge-9-12, \\ 3x\ge-21, \\ x\ge-\frac{21}{3}, \\ x\ge-7. \end{gathered}[/tex]2) Solving the second inequality for x we get:
[tex]\begin{gathered} 9x-3\le33, \\ 9x\le33+3, \\ 9x\le36, \\ x\le\frac{36}{9}, \\ x\le4. \end{gathered}[/tex]Answer:
[tex]x\ge-7\text{ and x }\le4.[/tex]Julian has a hundred songs on his media player he knows that 1/4 of the song or Jazz and the rest are pop which statement correctly describes the song on Julian media player
100 songs
1/4 of those are Jazz songs and the rest 3/4 are Pop songs
1/4=0.25
3/4=0.75
To know how many Jazz songs are multiply 100*0.25= 25 Jazz songs
Pop songs: 100*0.75= 75 pop songs
jared has 12 coin 4th 75 cents. 3 of the coins are worth twice as much as tge rest. construct a math argument to justify the conjecture thqt jared has 9 nickels and 3 dimes
To solve this question, we proceed as follows:
Step 1: Let x be the worth of one of the type of coins Jared has, and let y be the worth of the other type of coin
Thus:
Since 3 of the coins are of a different type, we have that:
[tex]\begin{gathered} 3x+(12-3)y=75 \\ \Rightarrow3x+9y=75 \end{gathered}[/tex]Also, since 3 of the coins are worth twice as much as the rest, we have that:
[tex]x=2y[/tex]Now, substitute for x in the first equation:
[tex]\begin{gathered} 3x+9y=75 \\ \Rightarrow3(2y)+9y=75 \\ \Rightarrow6y+9y=75 \\ \Rightarrow15y=75 \\ \Rightarrow y=\frac{75}{15} \\ \Rightarrow y=5cents \end{gathered}[/tex]Since y = 5 cents, we have that:
[tex]\begin{gathered} x=2y \\ \Rightarrow x=2(5) \\ \Rightarrow x=10cents \end{gathered}[/tex]Now, since x = 10 cents (the equivalent worth of a dime), and y = 5 cents (the equivalent worth of a nickel), we have from the first equation that:
[tex]3x+9y=75\text{cents}[/tex]From the above equation, therefore, we can conclude that Jared has nine 10 cents coins (dimes), and three 5 cents coins (nickels)
MathTaAngel LoweA coin is tossed. What is the theoretical probability of the coin NOT showing tails?P(Not tails) =
Since is a theoretical probability, the probability of a coin showing heads (no tails) should be somewhere around 50%.
A coin toss has two possible results.
50% tails
50% heads
What is the acceleration of a 50 kg object pushed with a force of 500 newtons?10 m/s225,500 m/s2490 m/s225 m/s2
Let's use Newton's second law of motion:
F = m*a
Where:
F= Force = 500
m = mass = 50
a = acceleration
So:
500 = 50*a
Solve for a:
Divide both sides by 50:
500/50 = 50a/50
10 = a
a = 10m/s²
find the ratio of the primeter to the area of the square
Given data:
The given figure of square.
The perimeter of the square is,
[tex]P=4(x+3)[/tex]The area of the square is,
[tex]A=(x+3)\times(x+3)[/tex]The ratio of the perimeter to the area of the given square is,
[tex]\begin{gathered} \frac{P}{A}=\frac{4(x+3)}{(x+3)(x+3)} \\ =\frac{4}{x+3} \end{gathered}[/tex]Thus, the ratio of the perimeter to the area of the given square is 4/(x+3).
Find the distance between the points ( 3,1 ) and (9,9). Write answers as a whole number or a fully simplified radical expression. Do not round
The distance between two points (x1, y1) and (x2, y2) can be calculated as follows:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]The points are given: (3, 1) and (9, 9), thus:
[tex]d=\sqrt[]{(9-3)^2+(9-1)^2}[/tex]Operating:
[tex]\begin{gathered} d=\sqrt[]{6^2+8^2} \\ d=\sqrt[]{36+64} \\ d=\sqrt[]{100} \\ d=10 \end{gathered}[/tex]The distance is 10
kareem correctly answered 85% of the questions on his math test. He missed 6 questions. How many questions were on his test
Answer:
40 questions
Explanation:
The total number of questions on his test represents 100%.
So, If he correctly answered 85% of the questions, then he missed 15% of the questions because:
100% - 85% = 15%
Therefore, 15% of the questions are equivalent to 6 questions, then we need to find the number equivalent to 100%. So 100% is equivalent to:
[tex]100\text{ \% }\times\frac{6}{15\text{ \%}}=40[/tex]Then, there were 40 questions on his test.
Claire has 11/12pound of butter. She will use 5 /12 pound of butter to make cookies She estimates she will have 1 /2 pound of butter when she is finished. Is Claire correct?
Explanation:
We have to substract 5/12 from 11/12:
[tex]\frac{11}{12}-\frac{5}{12}=\frac{11-5}{12}=\frac{6}{12}[/tex]And simplify the fraction:
[tex]\frac{6}{12}=\frac{1}{2}[/tex]Answer:
Claire is correct, she'll have 1/2 pound of butter.
change the quadratic equation from standard from to vertex form
Answer:
[tex]y=\left[x-\left(-2\right)\right]^2+\left(-9\right)[/tex]Explanation:
Given the quadratic equation in standard form:
[tex]y=x^2+4x-5[/tex]1. Transpose the c-value to the left side of the equation.
[tex]y+5=x^2+4x[/tex]2. Complete the square of the expression on the right side of the equation to get a perfect square trinomial. Add the resulting term to both sides.
[tex]\begin{gathered} y+5+(\frac{4}{2})^2=x^2+4x+(\frac{4}{2})^2 \\ \implies y+5+(2)^2=x^2+4x+(2)^2 \end{gathered}[/tex]3. Add the numbers on the left and factor the trinomial on the right.
[tex]$ y+9=(x+2)^2 $[/tex]4. Transpose the number across to the right side to get the equation into the vertex form, y=a(x-h)²+k.
[tex]y=(x+2)^2-9[/tex]5. Make sure the addition and subtraction signs are correct to give the proper vertex form.
[tex]y=\left[x-\left(-2\right)\right]^2+\left(-9\right)[/tex]The vertex form of the given quadratic equation is:
[tex]y=\left[x-\left(-2\right)\right]^2+\left(-9\right)[/tex]
Ciara has a bag of 50 colored marbles. There are yellow, green, and white marbles. She empties the bag, sorts the marbles, and counts11 yellow marbles and 19 green marbles. She wants to write a ratio of the number of green marbles to the number of white marbles. How can she find the number ofwhite marbles without counting them?
The total number of marbles is, 50.
11 yellow marbles
19 green marbles
x be the number of white marbles.
Without counting, x can be calculated as,
[tex]\begin{gathered} 11+19+x=50 \\ x=50-11-19=20 \end{gathered}[/tex]Therefore the ratio of green marbles to white marbles is,
[tex]\frac{G}{W}=\frac{19}{20}[/tex]Thus option B is correct.
Find the area of the figure. Remember to label use ^2 for units squared.10 ft15 ftA=12 ft
Solution
Find the area of the figure.
Area of the figure : Area of a parallelogram = base x height
base = 15ft
height = 10ft
[tex]\begin{gathered} A=bh \\ A=(15\times10)ft^2 \\ A=150ft^2 \end{gathered}[/tex]Therefore the area of the figure = 150ft²
Area of a triangle = 16ft²B = 4ftH = ?
Given:
Area of a triangle, A = 16 ft²
Base of the triangle, b = 4 ft
Height of the triangle, h, is unknown.
To find the height of the triangle, h, apply the formula below:
[tex]A=\frac{1}{2}b\times h[/tex]Rewrite the formula for h.
Multiply both sides by 2:
[tex]\begin{gathered} 2A=\frac{1}{2}b\times h\times2 \\ \\ 2A=b\times h \end{gathered}[/tex]Divide both sides by b:
[tex]\begin{gathered} \frac{2A}{b}=\frac{b\times h}{b} \\ \\ \frac{2A}{b}=h \\ \\ h=\frac{2A}{b} \end{gathered}[/tex][tex]h=\frac{2A}{b}[/tex]Where,
A = 16 ft²
b = 4 ft
Substitute values into the formula and evaluate.
We have:
[tex]\begin{gathered} h=\frac{2A}{b} \\ \\ h=\frac{2(16)}{4} \\ \\ h=\frac{32}{4} \\ \\ h=8\text{ ft} \end{gathered}[/tex]Therefore, the value of h is 8 ft
ANSWER:
H = 8 ft
2b^2 (3a - 5b +8c)Multiply
Answer
2b² (3a - 5b + 8c)
= 6ab² - 10b³ + 16b²c
Explanation
We are told to multiply 2b² with (3a - 5b + 8c)
2b² (3a - 5b + 8c)
= 6ab² - 10b³ + 16b²c
Hope this Helps!!!
add.(7k + 3) + (3k + 2)
for the function what are the possible values for B if the function is an exponential decay function select the two right answers
In order for the function to represent an exponential decay, the value of b needs to be a value between 0 and 1.
So analysing each value, we have:
√(0.9)
Since 0.9 is lesser than 1, its square root is also lesser than 1, so this is a valid option.
1 1/5
This value is greater than 1, so it's not a valid option.
√e
The value of e is approximately 2.71, so its square root is greater than 1, so it's not a valid option.
2^-1
This value is equal to 1/2, that is, 0.5, so it's lesser than 1, therefore it's a valid option.
2-0.9999
This exp
write the equation of the line that is perpendicular to the graph of y=3/4x-3, and whose y-intercept is -8
write the equation of the line that is perpendicular to the graph of y=3/4x-3, and whose y-intercept is -8
step 1
Find the slope of the given line
y=(3/4)x-3
the slope is m=3/4
step 2
Find the slope of the perpendicular line
REmember that
If two lines are perpendicular, then the product of their slopes is equal to -1 (inverse reciprocal)
so
the slope of the perpendicular line is
m=-4/3
step 3
Find the equation of the line
we have
m=-4/3
y-intercept is -8
so
b=-8
y=mx+b
substitute
y=-(4/3)x-8Part 2
write an equation of the line that is parallel to the graph of y=-4x-9, and whose y-intercept is 3
step 1
Find the slope of the given line
y=-4x-9
the lope is m=-4
step 2
Find the slope of the parallel line
Remember that
If two lines are parallel, then their slopes are the same
so
the slope of the parallel line is m=-4
step 3
Find the equation of the line in slope intercept form
y=mx+b
we ahve
m=-4
b=3
substitute
y=-4x+31. Nasir had 2.45 inches of tape thatwill be divided into 3 pieces. What is the length of each piece round-ed to the nearest hundredth?a. .81b. .82c. 7.35d. 7.36
Answer:
b. 0.82
Explanation:
Nasir had 2.45 inches of tape
The tape will be divided into 3 pieces.
Therefore:
[tex]\text{Length of each piece}=2.45\div3[/tex]Now, we know that:
[tex]\begin{gathered} \frac{245}{3}=81\frac{2}{3} \\ \frac{2}{3}=0.667 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} 2.45\div3=0.81667 \\ \approx0.82\text{ }(to\text{ the nearest 100th}) \end{gathered}[/tex]The correct choice is B.
For each table below, describe whether the table represents a function that increasing or decreasing.
To determine the table that represents a function that is increasing, we check if the following holds.
• When x increases, f(x) increases.
In Options A, as x increases, f(x) increases.
In Options B, as x increases, g(x) decreases.
In Options C, as x increases, h(x) decreases.
In Options D, as x increases, z(x) increases.
Therefore, the table that
Figure ABCDE is similar to figure VWXYZ.Solve for the side length of WX.a 1/2b. 3c. 2.5 d 2
In similar figures the ratio of corresponding sides is the same:
Corresponding sides in given figure:
AB and VW
BC and WX
CD and XY
DE and YZ
EA and ZV
As you know the length of AE and ZV and need to find the value of WX taht is correspondig side of BC, you have the next:
[tex]\frac{ZV}{EA}=\frac{WX}{BC}[/tex][tex]\frac{4}{10}=\frac{WX}{5}[/tex]You use this equation to find the length of WX:
[tex]\begin{gathered} \frac{5\cdot4}{10}=WX \\ \\ \frac{20}{10}=WX \\ \\ \\ WX=2 \end{gathered}[/tex]Then, the length of WX is 2Hannah bought 3.8 pounds of tomatoes at a farmer's market for $1.45 per pound. How much did Hannah pay for the tomatoes?
Answer:
Hanna would pay $5.51 for the tomatoes.
Step-by-step explanation:
You can multiply 3.8 by 1.45 and that will get you 5.51.
Making 5.51 your total cost.
The amount for 3.8 pounds of tomato is given by the equation A = $ 5.51
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total amount for the tomatoes be represented as A
Now , the equation will be
The cost of 1 pound of tomatoes = $ 1.45
Now , Hannah bought 3.8 pounds of tomatoes
So , the amount for 3.8 pounds of tomatoes A = 3.8 x cost of 1 pound of tomatoes
Substituting the values in the equation , we get
The amount for 3.8 pounds of tomatoes A = 3.8 x 1.45
On simplifying the equation , we get
The amount for 3.8 pounds of tomatoes A = $ 5.51
Therefore , the value of A is $ 5.51
Hence , the amount is $ 5.51
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Helpppppppppppppppppp
Answer: The restaurant requires some additional forks in supply, there are currently 287 forks in the restaurant, and there should be at least 732.
The new forks come in sets of 10, the inequality which represents the number of sets that Peyton needs to buy is:
[tex]\begin{gathered} 10x+287\ge732\rightarrow(1) \\ \\ x\rightarrow\text{ Number of fork sets which contain 10 forks} \end{gathered}[/tex]Therefore the inequality (1) represents the number of sets of forks that Peyton needs to buy, the solution for this inequality is as follows:
[tex]\begin{gathered} 10x+287\geqslant732 \\ \\ \\ 10x\ge732-287 \\ \\ \\ 10x\ge445 \\ \\ \\ x\ge\frac{445}{10} \\ \\ \\ x\ge44.5 \end{gathered}[/tex]