In general, a quadratic equation can be written in terms of its solutions:
[tex]y=(x-a)(x-b).[/tex]Now, notice that:
[tex]x+\frac{1}{2}=0\text{ }[/tex]when x= -1/2, and it is equivalent to:
[tex]2x+1=0.[/tex]Therefore, you can write the quadratic equation as:
[tex]y=(2x+1)(x-4).[/tex]Computing the above multiplication, you get:
[tex]y=2x^2-8x+x-4.[/tex]Simplifying the above equation you get:
[tex]y=2x^2-7x-4.[/tex]Answer: [tex]y=2x^{2}-7x-4[/tex]Plot the x-intercept and y-intercepts to graph the equationy = 1/3x - 1
The equation is written in the slope-intercept form:
[tex]y=mx+b[/tex]Where:
m = Slope
b = y-intercept
From the equation we can conclude that the y-intercept is:
[tex](0,-1)[/tex]We can find the x-intercept as follows:
[tex]\begin{gathered} y=0 \\ \frac{1}{3}x-1=0 \\ \frac{1}{3}x=1 \\ x=3 \end{gathered}[/tex]The x-intercept is:
(3,0)
The graph is:
[tex]undefined[/tex]Find the equation of the line passing through the points (3,-2) and (3, 4).The answer is x = 3. I'm just wondering how my textbook got to this solution.My work:y-y1=m(x-x1). m=y2-y1 / x2-x1. y=mx+bm=4--2 / 3-3 = 6/0 = 0. m=0.y--2=0(x-3) = y=0-2 y=-2 <<<
Given two points. we can find the equation of a line passing through the points
The formula to be used is:
[tex]\frac{y_2-y_1}{x_2-x_!}=\frac{y-y_1}{x-x_!}[/tex]where
[tex]x_1=3,y_!=-2,x_2=3,y_2=4[/tex][tex]\frac{4-(-2)}{3-3}=\frac{y-(-2)}{x-3}[/tex]=>
[tex]\frac{6}{0}=\frac{y+2}{x-3}[/tex]The next step is to cross multiply
[tex]6(x-3)=0(y+2)[/tex]=>
[tex]6(x-3)=0[/tex]Divide both sides by 6 and make x the subject
x=3
6. Tyrion's hourly rate is $16 an hour. He worked for 30 hours this week. 5 of those hours wereon a holiday, and his company pays twice the hourly rate for holidays. What was the total on hispaycheck? Show your calculations.
Factor Problem Completely 16n^3 - 56n^2 + 8n - 28
Given
The equation is given as
[tex]16n^3-56n^2+8n-28[/tex]Explanation
Factorisation the equation,
[tex]4(4n^3-14n^2+2n-7)[/tex]Factorise the polynomial.
[tex]4(2n-7)(2n^2+1)[/tex]AnswerHence the answer is
[tex]4(2n-7)(2n^2+1)[/tex]Solve for c.
6>c+8>5
Step-by-step explanation:
Solve for w. 3w + 2w - 3w = 8
Answer
w = 4
Explanation
We are asked to solve for w
3w + 2w - 3w = 8
5w - 3w = 8
2w = 8
Divide both sides by 2
(2w/2) = (8/2)
w = 4
Hope this Helps!!!
The domain of f(g(x)) is:
Answer:
x ≥ 0
Explanation:
Given the function f(x) and g(x) defined below:
[tex]f(x)=3x-1,g(x)=\sqrt{x}[/tex]The composite function f(g(x)) is:
[tex]f(g(x))=3\sqrt[]{x}-1[/tex]The domain of the function is the value at which the value under the square root sign is non-negative.
Therefore:
[tex]\text{Domain of f(g(x)): }x\ge0[/tex]The first option is correct.
Is the ratio 11/15 the same as 15/11 Choose the correct answer below A,B,C or D
Given,
The ratios are,
[tex]\frac{11}{15},\frac{15}{11}[/tex]The value of 11/15 is,
[tex]\frac{11}{15}=0.7333[/tex]The value of 15/11 is,
[tex]\frac{15}{11}=1.3636[/tex]Hence, option B is correct.
The table shows a proportional relationship.
x 12 8 24
y 3 2 6
Describe what the graph of the proportional relationship would look like.
A line passes through the point (0, 0) and continues through the point (3, 12).
A line passes through the point (0, 0) and continues through the point (2, 8).
A line passes through the point (0, 0) and continues through the point (6, 24).
A line passes through the point (0, 0) and continues through the point (12, 3).
The graph of the proportional relationship would look like A line passes through the point (0, 0) and continues through the point (12, 3).
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
A proportional relationship graph between two variables is a relationship where the ratio between the two variables is always the same.
The given table is
x 12 8 24
y 3 2 6
The graph of the proportional relationship would look like.
A line passes through the point (0, 0) and continues through the point (12, 3).
In the ordered pair the first value represents the x axis value and second value represents the y value. The ordered pair (12, 3) is coordinated with the values of x and y in the table.
Hence the graph of the proportional relationship would look like A line passes through the point (0, 0) and continues through the point (12, 3).
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why are integers rational numbers? give an example
Integers are rational numbers because it consists of zero, positive and negative numbers till infinity only.
What is Rational number?This is referred to as a number which can be expressed as the quotient p/q of two integers such that q ≠ 0 and they are present till infinity due to the large numbers and examples include 2000, 25 etc.
Integers are rational numbers because they contain zero, positive and negative numbers. Decimals and fractions are not included in this context and an example is 12, 100 etc which is why the aforementioned above was chosen as the correct choice.
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Write an expression to represent the area for figure in #4.Simplify the expression.Find the area when x=2.
Given: A figure is given.
Required: to determine the expression for the area of the figure. Also, determine the area when x=2.
Explanation: The area of the figure can be determined by dividing the figure as shown below-
Now, DEFG and ABCG represent rectangles. The dimensions of the rectangle DEFG is (2x+4) by (7x+2), and of the rectangle, ABCG is (4x+2) by BC where BC is-
[tex]\begin{gathered} BC=(3x+5)-(2x+4) \\ =x+1 \end{gathered}[/tex]Hence, the expression for the area is-
[tex]\begin{gathered} A=(2x+4)(7x+2)+(4x+2)(x+1) \\ A=(14x^2+4x+28x+8)+(4x^2+4x+2x+2) \end{gathered}[/tex]Further solving-
[tex]\begin{gathered} A=14x^2+32x+8+4x^2+6x+2 \\ =18x^2+38x+10\text{ sq units} \end{gathered}[/tex]Substituting x=2 as follows-
[tex]\begin{gathered} A=18(2^2)+38(2)+10 \\ =72+76+10 \\ =158\text{ sq units} \end{gathered}[/tex]Final Answer: The expression for the area of the figure is-
[tex]A=18x^2+38x+10\text{ sq un}\imaginaryI\text{ts}[/tex]The area when x=2 is 158 sq units.
The _________ is a point that is equidistant from all points on the perimeter of the circle.
The center is a point that is equidistant from all points on the perimeter of the circle, where this distance is the radius.
a horse race has 14 entries and one person owns 2 of those horses. assuming that there are no ties, what is the probability that those two horses finish first and second (regardless of order)
Answer:
1/91
Explanation:
Number of entries in the horse race = 14
• The probability that one of those 2 horses will be first = 2/14
,• The probability that the second horse will be second = 1/13
Therefore:
[tex]\begin{gathered} P(\text{those two horses finish first and second)} \\ =\frac{2}{14}\times\frac{1}{13} \\ =\frac{1}{91} \end{gathered}[/tex]The probability is 1/91.
Solve the equation using the justification given for each step.
Multiplicative property of equality
[tex]\begin{gathered} Multiply\text{ both sides by 3} \\ (5x+7)3=\frac{3(-15x-1)}{3}+3(\frac{4}{3}) \end{gathered}[/tex]Distributive property of equality
[tex]3(5x+7)=-15x-1+4[/tex]Associative property
[tex]\begin{gathered} 15x+21=-15x-1+4 \\ 15x+21=-15x+3 \end{gathered}[/tex]Subtraction property of equality
[tex]\begin{gathered} 15x+21-21=-15x+3-21 \\ 15x=-15x-18 \end{gathered}[/tex]Addition property of equality
[tex]\begin{gathered} 15x+15x=-15x+15x-18 \\ 30x=-18 \end{gathered}[/tex]Division property of inequality
[tex]\begin{gathered} \text{divide both sides by 30} \\ \frac{-18}{30}=\frac{30x}{30} \\ x=-\frac{18}{30}=-\frac{3}{5} \end{gathered}[/tex]What is the value of 9 − (−4)?
Answer:13
Step-by-step explanation:
Step-by-step explanation:
remember, when 2 signs and/operations come together, for addition/subtraction and multiplication/division it always applies :
+ + = +
- + = -
+ - = -
- - = +
and therefore,
9 - (-4) = 9 + 4 = 13
a minus meeting a minus always results in a plus.
Old-Tyme Fashions specializes in hats modelled after fashions from the past. It purchases these hats for $42 each. It can provide a custom service to print the new owner’s name on the hatband. The printing machine costs $243 per month to rent. If Old-Tyme sells the hats at a price of $69 each, how many does it need to sell to break even?
Old-Tyme Fashions needs to sell 9 hats to break even at a price of $69 each.
Given, Old-Tyme Fashions specializes in hats modelled after fashions from the past.
It purchases these hats for $42 each.
It can provide a custom service to print the new owner’s name on the hatband.
The printing machine costs $243 per month to rent. If Old-Tyme sells the hats at a price of $69 each, how many does it need to sell to break even=?
The cost function to make n hats is:
C(n) = 42*n + 243 dollars.
The revenue function is
R(n) = 69*n dollars.
The break event equation/inequality is
R(n) ≥ C(n), or
69*n ≥ 243 + 42*n.
Simplify and solve for n:
(69-42)*n ≥ 243
27n ≥ 243
n ≥ 243/27 = 9.
hence 9 hats should be sold to break even.
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f(x)=-17x+2 and g(x)=x^2+1 find f(-7) + g(-7)
Answer:
171
Explanation:
Given f(x) and g(x) defined below:
[tex]\begin{gathered} f\mleft(x\mright)=-17x+2 \\ g\mleft(x\mright)=x^2+1 \end{gathered}[/tex]To find the value of f(-7) + g(-7), substitute -7 for x in both functions:
[tex]\begin{gathered} f\mleft(-7\mright)=-17(-7)+2=121 \\ g\mleft(-7\mright)=(-7)^2+1=50 \\ \implies f\mleft(-7\mright)+g\mleft(-7\mright) \\ =121+50 \\ =171 \end{gathered}[/tex]
Determine whether the statement is true or false.
2E{x|XEN and x is odd}
Is the statement true or false?
O True
O False
The given statement exists as false. An expression, rule, or law in mathematics establishes the link between an independent variable and a dependent variable.
What is meant by function?An expression, rule, or law in mathematics establishes the link between an independent variable and a dependent variable (the dependent variable).
The characteristic that every input is associated with exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs.
A relation between a collection of inputs and outputs is known as a function. A function exists, to put it simply, a relationship between inputs in which each input exists connected to precisely one output.
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What is the simplified expression for the expression below?7(x - 4) - 3(x + 5) A. 4x - 43 B. 4x + 1C. 4x - 13D. 4x - 9
Answer:
4x - 43
Step-by-step explanation:
This Question requires the concept of solving algebraic expressions.
Algebraic ExpressionsAlgebraic Expressions are expressions made up of alphabet variables and numbers and can be simplified using order of operations just like numerical expressions.
Example: 8(4x-6) = 32x - 48
ApplicationFor this question, we will use the same concept as above to solve for the expression.
[tex]7(x - 4) - 3(x + 5) = 7x - 28 - (3x + 15) \\ = 7x - 28 - 3x - 15 \\ = 4x - 43[/tex]
Find the product.Simplify to lowest terms:[tex] \frac{9}{10} \times \frac{3}{8} [/tex]A. 5/18B. 1/3C. 2/3D. 27/80
Answer:
D. 27/80
Explanation:
Given the expression
[tex]\frac{9}{10}\times\frac{3}{8}[/tex]We can multiply the numerators together, (Do likewise for the denominators).
[tex]=\frac{27}{80}[/tex]We cannot simplify thi
Picture translating A ABC three units to the left and five units up.What are the coordinates of A'?A(2,-2)
The coordinates of point A are (2, -2)
If the picture is translated 3 units to the left, we need to subtract 3 units to the x coordinate as:
( 2 - 3, -2) = (-1, -2)
Then, if the picture is translated 5 units up, we need to sum 5 units to the y-coordinate as:
( -1 , -2 + 5) = (-1, 3)
So, the coordinates of A' are (-1, 3)
Answer: (-1, 3)
Question number 3: which of the following is equal to 18x*7 y*6?
Solution:
Given:
[tex]\sqrt{18x^7y^6}[/tex]Splitting the expressions further to get the perfect squares out:
[tex]\begin{gathered} \sqrt{18x^7y^6}=\sqrt{9\times2\times(x^6\cdot x)\times(y^3)^2} \\ =\sqrt{9\times2\times(x^3)^2\cdot x\times(y^3)^2} \end{gathered}[/tex][tex]\begin{gathered} \sqrt{18x^7y^6}=\sqrt{9\times2\times(x^3)^2\cdot x\times(y^3)^2} \\ =3x^3y^3\sqrt{2x} \end{gathered}[/tex]Therefore, the correct answer is:
[tex]3x^3y^3\sqrt{2x}[/tex]what is the probability that a student will be in both chemistry and math but not Spanish round to three decimal places
Answer :
3/13
Explanation :
The probablity of an event = favourable outcome / total outcomes
Now in our case,
favorable outcome = 60
Total number of outcomes = 5 + 70 + 5 + 85 + 60 + 15 + 3 + 17 = 260
Therefore,
probablity = 60 / 260
= 3 /13
What is the slope and y-intercept of the equation y = -2/3x + 1Group of answer choicesSlope = 2/3; y-intercept = 0Slope = 1; y-intercept = -2/3Slope = -2; y-intercept = 3Slope = -2/3; y-intercept = 1
The form of the linear equation is
[tex]y=mx+b[/tex]m is the slope
b is the y-intercept
The given equation is
[tex]y=-\frac{2}{3}x+1[/tex]Let us compare the given equation with the form above, then
[tex]m=-\frac{2}{3}[/tex]and the value of b is
[tex]b=1[/tex]The slope of the line is the coefficient of x
The y-intercept is the numerical term
The slope = -2/3
The y-intercept = 1
The right answer is D the last answer
In any question like that, put the equation in the form
y = m x + b
m is the slope
b is the y-intercept
428 x 35 using long multiplication .
Answer:
14980
Step-by-step explanation:
4 2 8
x
3 5
-----------
2 1 4 0 ---> 428 x 5
1 2 8 4 ---> 428 x 3 but since 3 is in the 10s place we shift by 1
--------------- to the left. You can think of that 1248 as 12480
1 4 9 8 0 --> add the two rows
Hope that helps. I tried my best to explain :)
Answer:
4 2 8
× 3 5
+ 2 1 4 0
+ 1 2 8 4
= 1 4 9 8 0
Step-by-step explanation:
A printer takes 5 seconds to print 3 pages. How many pages can it print in 125 seconds? Enter the answer in the box.
Answer: 75
Step-by-step explanation:
So first, we need to divide 125 by 5
125÷5=25
Next we need to multiply 3 by 25.
25×3=75
The printer can print 75 pages in 125 seconds.
find the following quantity. Do not round your answers 5.4% of 900
The question asks us to find 5.4% of 900.
Percentage is expressed in terms of 100.
5.4% of 900 would be written as
5.4/100 * 900
= 48.6
5.4% of 900 is 48.6
What is the equation of the line that passes through the point (-5, -2) and has aslope of -6/5
Answer:
The equation of the line is;
[tex]y=-\frac{6}{5}x-8[/tex]Explanation:
Given the slope of the line as;
[tex]m=-\frac{6}{5}[/tex]And passes through point;
[tex](-5,-2)[/tex]Using the Point-slope equation to derive the equation of the line;
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-2)=-\frac{6}{5}(x-(-5)) \\ y+2=-\frac{6}{5}(x+5) \end{gathered}[/tex]Simplifying;
[tex]\begin{gathered} y+2=-\frac{6}{5}x-\frac{6}{5}(5) \\ y+2=-\frac{6}{5}x-6 \\ y=-\frac{6}{5}x-6-2 \\ y=-\frac{6}{5}x-8 \end{gathered}[/tex]Therefore, the equation of the line is;
[tex]y=-\frac{6}{5}x-8[/tex]
Find the value of the variableу846v=
We are to find an unknown side in a case of a triangle bisected via one of its angles.
We therefore use the bisecting angle theorem:
Which in the case of our image:
can be written as the following proportion:
8 / 4 = y / 6
in order to solve for "y", we multiply both sides by 6:
(8 * 6) / 4 = y
48 / 4 = y
then y = 12
Use the given sets to find A∩B.A={2,4,6,8,10,12}B={7,9,11,13,14,15,16}
Recall that
[tex]A\cap B[/tex]is a set that consists of all the elements that are in both A and B.
From the given sets we get that the elements that are in both A and B are:
[tex]\text{None.}[/tex]Therefore, the intersection of the sets is the empty set.
Answer:
[tex]A\cap B=\emptyset.[/tex]