1) Solving for y, the following expression
6y -4 = 3y +2 Add 4 to both sides
6y = 3y +2+4
6y = 3y +6 Subtract 3y from both sides
6y -3y = 6
3y = 6 Divide both sides by 3
y= 2
S={2}
2) So the solution for this is y=2
y varies directly as x. y =84 when x=6. Find y when x=12y= ?
If y varies directly as x, we have that
[tex]y\propto x[/tex]Then
[tex]y=kx(where\text{ k is a constant\rparen}[/tex][tex]\begin{gathered} When\text{ y=84 , x= 6} \\ y=kx \\ 84=6k \\ k=\frac{84}{6}=14 \end{gathered}[/tex]The relationship between x and y is given as
[tex]\begin{gathered} y=kx \\ y=14x \end{gathered}[/tex]Therefore when x= 12, y=?
[tex]\begin{gathered} y=14x \\ y=14\times12=168 \end{gathered}[/tex]Hence, the value of y when x = 12 is 168
Final answer: y = 168
In a isosceles triangle one angle is 57° greater than each of the other two equal angles. find a measure of all three angles
An Isosceles triangle has two sides and two angles to be congruent or equal.
Let the two congruent angles be x° degrees, then the third side which is 57° greater than the congruent angles would measure (x+57°).
SKETCH
The sum of angles in a triangle is 180°. Hence,
[tex]\begin{gathered} x+x+(x+57)=180^0 \\ 3x+57=180^0 \\ 3x=180-57 \\ 3x=123 \\ x=\frac{123}{3} \\ x=41^0 \\ \therefore(x+57)=41^0+57^0=98^0 \end{gathered}[/tex]Therefore, the measure of all three angles are: 41,⁰ 41⁰, and 98⁰
consider the relationship between f(x)=2^x and g(x)=log2 x.g is a reflection of f over the line y=x.True or False
the function
[tex]\log _2x[/tex]is the inverse function of
[tex]2^x^{}[/tex]On the graph, the inverse of a function is the reflection of the original function over the line y = x. Then, the statement is true
Lola has 8 bear figurines. These bear figurines make up 40% of her collection of animal figurines. Find the total number
Hence, the total number of bear figurines are 20
Find the solution for the given the system of equations:Y= (1/2)x - 1/2 and y=2^(x+3)
Answer:
This system has no solution.
Step-by-step explanation:
The solution of this system is the ordered pair that is the solution to both equations, we can solve this using the graphical method, which consists of graphing both equations in the same coordinate system.
The solution to the system will be at the point where the two functions intersect.
Since the functions do not intersect, this system has no solution.
Use elimination to solve eachsystem of equations3x - y = -56x - 2y = 8
Solution
We are given the pair of simultaneous equation
[tex]\begin{gathered} 3x-y=-5\ldots\ldots\ldots\ldots\ldots(1) \\ 6x-2y=8\ldots\ldots\ldots\ldots\ldots\ldots(2) \end{gathered}[/tex]we solve using elimination method
equation (1) x 2
[tex]\begin{gathered} 6x-2y=-10\ldots\ldots\ldots\ldots\ldots(1) \\ 6x-2y=8\ldots\ldots\ldots\ldots\ldots\ldots(2) \end{gathered}[/tex]Equation (2) - equation (1)
We have
[tex]\begin{gathered} (6x-6x)+(-2y+2y)=8-(-10) \\ 0=18 \end{gathered}[/tex]Which is impossible because 0 (zero) can never be equal to 18
Therefore, the simultaneous is not consistent or it degenerate and thus, there is no solution
The rectangular rug has side lengths of 3 and 4 ft. What is the length of the diagonal? Draw a picture of the problem and solve. Round to the nearest tenth
ANSWER
The length of the diagonal is 5 ft
EXPLANATION
The diagram of the rug with the diagonal is:
The diagonal and the sides form a right triangle, so we can use the Pythagorean theorem to find x, the length of the diagonal:
[tex]\begin{gathered} x^2=3^2+4^2 \\ x=\sqrt[]{9+16} \\ x=\sqrt[]{25} \\ x=5 \end{gathered}[/tex]The recommended daily allowance of niacin for adults is 20 mg. One serving of a certain breakfast cereal provides 8 mg of niacin, What percent of the recommendeddaily allowance of niacin does one serving of this cereal provide?
Given:
Total allowance = 20mg.
Used = 8 mg
Percentage of daily allowance is:
[tex]\begin{gathered} =\frac{8}{20}\times100 \\ =\frac{8}{2}\times10 \\ =8\times5 \\ =40 \end{gathered}[/tex]So 40% daily allowance .
simplify: 9x^4-27x^6/3x^3
simplify: 9x^4-27x^6/3x^3
we have the expression
[tex]\begin{gathered} 9x^4-\frac{27x^6}{3x^3} \\ \\ 9x^4-9x^{(6-3)} \\ 9x^4-9x^3 \end{gathered}[/tex]we have the expression
[tex]\begin{gathered} \frac{9x^4-27x^6}{3x^3} \\ \frac{9x^4}{3x^3}-\frac{27x^6}{3x^3} \\ 3x-9x^3 \end{gathered}[/tex]this is the answer
Write a equation of the line described
Passes through (4,8)
Parallel to the line y=-7/4x-4
Answer:
y=-7/4x+15
Step-by-step explanation:
Parallel line so has the same gradient:
y=-7/4x+c
Substitute (4,8) into above equation
8=(-7/4 x 4)+ c
rearrange to find c
8=-7+c
c=15
New equation: y=-7/4x+15
Hope this helps!
Find the volume of this cone.Use 3 for TT.V = Tigh3Hint: The radius (1) is1/2 of the diameter.6 ft6 ft-3V ~ [?]ft
ANSWER
[tex]54ft^3[/tex]EXPLANATION
The volume of a cone is given by:
[tex]V=\frac{\pi r^2h}{3}[/tex]where r = radius
h = height
The height of the given cone is 6 ft and its diameter is 6 ft. The radius of a cone is half its diameter, hence its radius is:
[tex]\begin{gathered} r=\frac{6}{2} \\ r=3ft \end{gathered}[/tex]Hence, the volume of the cone is:
[tex]\begin{gathered} V=\frac{3\cdot3^2\cdot6}{3} \\ V=54ft^3 \end{gathered}[/tex]That is the answer.
An employee makes $10.51 per hour but is getting a 3% increase. What is his new wage per hour to the nearest cent?
First, we find 3% of $10.51.
[tex]0.03\cdot10.51=0.32[/tex]Then, we add this increase to $10.51.
[tex]10.51+0.32=10.83[/tex]Hence, the new wage per hour is $10.83.write a part to part and a part to whole ratio for each problem situation of the 31 students surveyed 19 prefer white bread and the remaining students prefer wheat bread
Total number of students = 31
19 prefer white bread
31 - 19 prefer wheat bread ==> 31- 19 = 12 prefer wheat bread
Relations:
Part to part:
Relation between the number of students that prefer wheat bread to the number of students that prefer white bread:
Ratio: 12/19
Part to part:
Relation between the number of students that prefer white bread to the number of students that prefer white bread:
Ratio: 19/12
Part to whole:
Relation between the number of students that prefer wheat bread to the total number of students:
Ratio: 12/31
Part to whole:
Relation between the number of students that prefer white bread to the total number of students:
Ratio: 19/31
please help i dont know to do it please help
Given:
0.5
Let's write the decimal in form of a fraction a/b using integers.
To write the number in fractional form, we have:
[tex]0.5=5\times10^{-1}[/tex]Since the exponent is the negative of 1, using the definition of negative exponent, we have:
[tex]5\times10^{-1}=\frac{5}{10^1}=\frac{5}{10}[/tex]Therefore, the correct fraction is:
[tex]\frac{5}{10}[/tex]ANSWER:
[tex]\frac{5}{10}[/tex]Pls help now You play a game that requires rolling a 6 sided die then randomly choosing a colored card from a deck containing 5 red cards,4blue cards, and 8 yellow cards find the probability that you will roll 3 on the die and choose a yellow card
Find the probability that you will get a 3 on a roll of a die. Since there is only one 3 in a die and there are 6 sides in a die, divide 1 by 6.
[tex]P(3)=\frac{1}{3}[/tex]Find the probability that you will get a yellow card. Divide the number of yellow cards by the total number of cards.
[tex]\begin{gathered} P(y)=\frac{8}{5+4+8} \\ =\frac{8}{17} \end{gathered}[/tex]Since the two events are independent, multiply the obtained probabilities.
[tex]undefined[/tex]Han spent a total of $221.76, before tax, on bags of chips for the basketball team, and each bag cost $3.52. What is the total number of bags of chips that Han bought?
Given:
a.) Han spent a total of $221.76, before tax, on bags of chips for the basketball team.
b.) Each bag cost $3.52.
Let's determine the number of bags of chips bought.
[tex]\text{ No. of bags of chips bought = }\frac{\text{ Total cost}}{\text{ Price of each bag}}[/tex][tex]\text{ = }\frac{\text{ 221.76}}{\text{ 3.52}}[/tex][tex]\text{ = 63}[/tex]Therefore, Han bought 63 bags of chips for the basketball team.
The answer is 63.
Consider the following function. Complete parts (a) through (e) below.f(x)=x²-2x-8The vertex is.(Type an ordered pair.)c. Find the x-intercepts. The x-intercept(s) is/are(Type an integer or a fraction. Use a comma to separate answers as needed.)d. Find the y-intercept. The y-intercept is(Type an integer or a fraction.)e. Use the results from parts (a)-(d) to araph the quadratic function.
Given the function:
[tex]f(x)=x^2-2x-8[/tex]It is a quadratic function where:
a=1
b= -2
c= -8
The x-coordinate of the vertex is given by:
[tex]x=-\frac{b}{2a}[/tex]Substitute a and b:
[tex]x=-\frac{-2}{2(1)}=\frac{2}{2}=1[/tex]Substituting in the original equation to obtain the y-coordinate, we obtain:
[tex]y=(1)^2-2(1)-8=1-2-8=-9[/tex]So, the vertex is (0, -9)
c. For the intercept at x we make y = 0:
[tex]0=x^2-2x-8[/tex]And solve for x by factorization:
[tex]\begin{gathered} (x-4)(x+2)=0 \\ Separate\text{ the solutions} \\ x-4=0 \\ x-4+4=0+4 \\ x=4 \\ and \\ x+2=0 \\ x+2-2=0-2 \\ x=-2 \end{gathered}[/tex]So, the x-intercepts are:
(-2, 0) and (4,0)
Answer: (-2,0), (4,0)
d. For the intercept at y we make x = 0:
[tex]y=(0)^2-2(0)-8=-8[/tex]So the y-intercept is (0, -8)
Answer: (0, -8)
e. Graphing the function:
Classify the polynomial as constant, linear, quadratic, cubic, or quartic, anddetermine the leading term, the leading coefficient, and the degree of thepolynomial.g(x) = - 2x^4 - 6
Given:
[tex]g(x)=-2x^4-6[/tex]To classify: The polynomial name, degree, leading term, and leading coefficient
Explanation:
Since the degree of the polynomial is the highest or the greatest power of a variable in a polynomial equation.
Here, 4 is the greatest power of a variable x.
So, the degree of the polynomial is 4.
As we know,
The leading term is the term containing the highest power of the variable.
So, the leading term is,
[tex]-2x^4[/tex]Since the coefficient of the term of the highest degree in a given polynomial is -2.
So, the leading coefficient is -2.
Since the degree of the polynomial is 4.
So, the given polynomial is a quartic polynomial.
Final answer: Option C. Quartic polynomial.
Graph the line. I am only able to use 2 points on this graph.
In order to graph line first we need to calculate the equation of the line
[tex]y-y_1=m(x-x_1)[/tex]where m is the slope and (x1,y1) is a line where the line passing throught
in our case
m=3/4
(x1,y1)=(-4,5)
[tex]y-5=\frac{3}{4}(x+4)[/tex]Then we isolate the y
[tex]y=\frac{3}{4}x+3+5[/tex][tex]y=\frac{3}{4}x+8[/tex]We can calculate another point to obtain the graph in this case the y-intercept (0,8)
The points are
(-4,5) and (0,8)
the graph is
Use a properly of equality to solve this equation: 4.5x = 18
To solve the equation you can use the property of the multiplicative inverse, like this
[tex]\begin{gathered} 4.5x=18 \\ \frac{1}{4.5}\cdot4.5x=18\cdot\frac{1}{4.5} \end{gathered}[/tex]Dividing by 4.5 into both sides of the equation is the same as multiplying by the multiplicative inverse of 4.5 on both sides of the equation
[tex]x=\frac{18}{4.5}[/tex]Therefore,
[tex]x=4[/tex]What is the greatest common factor of the polynomial: 35y + 5y + 157 "
The greatest common factor of the expression is:
[tex]5y^3[/tex]This comes from the fact that 5 is the greatest common factor of the constants, whereas y^3 is the greatest common factor of the variable.
Which function is undefined for x = 0?O y=³√x-2Oy=√x-2O y=³√x+2Oy=√x+2
The above function is defined for (x=0)
From the question, we have
Function 1 - y = ∛x-2
Function 2 - y = √x-2
Function 3 - y = ∛x+2
Function 4 - y = √x+2
substituting (x = 0) to determine which function is undefined for (x = 0).
Function 1 - y = ∛x-2
substituting (x = 0), we get
y=∛-2
The above function is defined for (x=0).
Function 2 - y = √x-2
substituting (x = 0), we get
y = √-2
The above function is defined for (x=0).
Function 3 - y = ∛x+2
substituting (x = 0), we get
y = ∛2
The above function is defined for (x=0).
Function 4 - y = √x+2
substituting (x = 0), we get
y = √2
The above function is defined for (x=0).
Hence, it can be concluded that the above function is defined for (x=0)
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.
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You need to ride an average of at least 35 miles per day for five consecutive days toqualify for a cross-country biking expedition. The distances (in miles) of your rides in thefirst four days are 45, 33, 27, and 26. What distances on the fifth day will allow you toqualify for the competition?
We are to maintain a constant mean distance of ( d-avg ) to qualify for the cross-country biking expedition.
The qualification for the expedition is to rirde an average distance of:
[tex]d_{avg}\text{ }\ge\text{ 35 miles each for 5 consecutive day }[/tex]We are already on target for 4 days. For which we covered a distance ( d ) for each day:
[tex]\begin{gathered} \text{\textcolor{#FF7968}{Day 1:}}\text{ 45 miles} \\ \text{\textcolor{#FF7968}{Day 2:}}\text{ 33 miles} \\ \text{\textcolor{#FF7968}{Day 3:}}\text{ 27 miles} \\ \text{\textcolor{#FF7968}{Day 4: }}\text{26 miles} \end{gathered}[/tex]We are to project how much distance we must cover atleast on the fifth day ( Day 5 ) so that we can qualify for the expedition. The only condition for qualifying is given in terms of mean distance traveled over 5 days.
The mean value of the distance travelled over ( N ) days is expressed mathematically as follows:
[tex]d_{avg}\text{ =}\sum ^N_{i\mathop=1}\frac{d_i}{N}[/tex]Where,
[tex]\begin{gathered} d_i\colon Dis\tan ce\text{ travelled on ith day} \\ N\colon\text{ The total number of days in consideration} \end{gathered}[/tex]We have the data available for the distance travelled for each day ( di ) and the total number of days in consideration ( N = 5 days ). We will go ahead and used the standard mean formula:
[tex]d_{avg}\text{ = }\frac{d_1+d_2+d_3+d_4+d_5}{5}[/tex]Then we will apply the qualifying condtion to cover atleast 35 miles for each day for the course of 5 days.
[tex]\frac{45+33+27+26+d_5}{5}\ge\text{ 35}[/tex]Then we will solve the above inequality for Day 5 - (d5) as follows:
[tex]\begin{gathered} d_5+131\ge\text{ 35}\cdot5 \\ d_5\ge\text{ 175 - 131} \\ \textcolor{#FF7968}{d_5\ge}\text{\textcolor{#FF7968}{ 44 miles}} \end{gathered}[/tex]The result of the above manipulation shows that we must cover a distance of 44 miles on the 5th day so we can qualify for the expedition! So the range of distances that we should cover atleast to qualify is:
[tex]\textcolor{#FF7968}{d_5\ge}\text{\textcolor{#FF7968}{ 44 miles}}[/tex]All covered distances greater than or equal to 44 miles will get us qualified for the competition!
Factor the polynomial: s^2+ 12s + 32
SOLUTION
We want to factor the polynomial
[tex]s^2+12s+32[/tex]To do this we look for two values with s such that when we multiply them, we get 32 and when we add then we get the middle item 12s.
These are 8s and 4s because
[tex]\begin{gathered} 8s+4s=12s \\ 8s\times4s=32s^2 \end{gathered}[/tex]Now we replace 8s and 4s with the middle item and factorize, we have
[tex]\begin{gathered} s^2+12s+32 \\ s^2+8s+4s+32 \\ s(s+8)+4(s+8) \\ (s+4)(s+8) \end{gathered}[/tex]Hence the answer is
(s + 4) (s + 8)
On Monday, Freda spent $20 to buy 3 burgers and 4 orders of fries for her friends to share for lunch. Let r represent the cost of a burger and y represent the cost of an order of fries. What linear equation would model this?
Let:
r = Cost of a burger
y = Cost of an order of fries
Freda spent $20 to buy 3 burgers and 4 orders of fries for her friends to share for lunch, therefore:
[tex]3r+4y=20[/tex]I just need to know the answer to question 11
Answer:
A number line a closed circle on 8, shading to the left, and a closed circle on 11, shading to the right.
Explanation:
Given the compound inequalities:
[tex]x-1\le7\text{ or }2x\ge22[/tex]First, solve both inequalities:
[tex]\begin{gathered} x-1\le7\implies x\le7+1\implies x\le8 \\ 2x\ge22\implies x\ge\frac{22}{2}\implies x\ge11 \end{gathered}[/tex]Thus, the number line should be the one that represents the solution:
[tex]x\le8\text{ or }x\ge11[/tex]• For x≤8, there is a ,closed circle on 8, and ,shading to the left.
,• For x≥11, there is a ,closed circle on 11, and ,shading to the right.
Therefore, the correct description will be:
A number line a closed circle on 8, shading to the left, and a closed circle on 11, shading to the right.
The last option is correct.
The tables of ordered pairs represent some points on the graphs of Lines F and G.
Line F
x y
2 7
4 10.5
7 15.75
11 22.75
Line G
x y
-3 4
-2 0
1 -12
4 -24
Which system of equations represents Lines F and G?
1. y=1.75x+3.5
y=-4x-8
2. same as 1 but -8 is -2
3. 1.75 and 3.5 are switched
4. 2 and 3 combined
In linear equation, Equation for line F is y = 1.75x + 3.5 and equation for line G is y = -4x-8.
What is a linear equation example?
Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5.Finding both intercepts of an equation in this format is rather simple (x and y).y = 1.75x + 3.5 (For line F)
let's take the point (2,7) and put in the equation,
y = 1.75*2 + 3.5
= 3.5 +0.35
= 7
which is true.
Hence, (2,7) satisfies the equation.
y = -4x-8 (For line G)
lets take the point (-3,4) and put in the equation,
y = (-4)*(3) - 8
= 12 - 8
= 4
which is true.
Hence, (-3,4) satisfies the equation.
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Use the Pythagorean Theorem to find the length of the unknown side in the righttriangle shown below. (Round your answer to the nearest tenth.)817
pythagorean theorm is a^2 + b^2 = c^2
side lengths 8 and 17
8 is a base and 17 is the hypotenuse, the other side is 15
8 15 17 is one of the first 10 Pythagorean triples
8^2 + 15^2 = 17^2
64 + 225 = 289
289 = 289
slope is ___ of change in a relationship.
The slope is the rate of change of 2 variables associated.
Usually the rate of change of y with x.
But it can be of any 2 variables in the problem.
So, the slope is the rate.
The rate at which something is changing with respect to another thing.
Thus,
Answer:
slope is rate of change in a relationship.
Find the diameter of the circle with an area of 14π squared inches. Round to the nearest hundredths. Please solve using this formula: Area= πr^2r=radius
Given:
Area of the circle
[tex]A=14\pi\text{ in.}^2[/tex]Required:
To find the diameter of the circle.
Explanation:
The area of the circle is given by the formula:
[tex]A=\pi r^2[/tex]Where r = radius of the circle
Put the given value of A.
[tex]\begin{gathered} 14\pi=\pi r^2 \\ r^2=14 \end{gathered}[/tex]Take the square root on both sides.
[tex]\begin{gathered} r=\sqrt{14} \\ r=3.741\text{ in.} \end{gathered}[/tex]Now the diameter D= 2r
[tex]\begin{gathered} D=2\text{ }\times3.741 \\ D=7.482\text{ in.} \end{gathered}[/tex]Final answer:
The diameter of the circle D= 7.482 in,
