The leading coefficient of the quadratic equation f(x)= x² – 8x – 4 will be 1.
What is a quadratic equation?The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.
The quadratic function, of vertex (h, k), is given by:
y = a(x – h)² + k
where a is the leading coefficient.
Then we have the quadratic equation given below.
f(x)= x² – 8x – 4
f(x)= x² – 8x + 16 – 16 – 4
f(x)= (x – 4)² – 20
Then the leading coefficient will be 1.
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Lines l and m are parallel and intersect transversal p, as shown in the diagram below.
What is the value of n?
A 6
B 10
C 20
D 24
Terry brings home $14 per hour he works. When he started this job, he had
$40 in the bank. Write and graph the equation that would represent how
much money Terry has in the bank (y) after x hours of work. Identify the x-
and the y-intercepts. Do they make sense in this context. If so, what do they
tell us about Terry's situation? Find the point (3, 82) on the graph. What does
that point represent in the context of Terry's situation?
The point (3, 82) on the graph represents after Terry's hours his bank balance will be $82.
Given that, Terry brings home $14 per hour he works. When he started this job, he had $40 in the bank.
We need to write and graph the equation that would represent how much money Terry has in the bank (y) after x hours of work.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Now, y=40+14x
Graph the line using the slope and y-intercept, or two points.
Slope: 14
y-intercept: (0, 40)
The coordinates to plot the graph are (0, 40), (1, 54), (2, 68) and (3, 82).
The graph for the given equation is given below.
Therefore, the point (3, 82) on the graph represents after Terry's hours his bank balance will be $82.
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Circle G is shown. Line segment F G is a radius with length 3.
In circle G, r = 3 units. Maria draws a circle with double the area of circle G.
What is the area of Maria’s circle?
6Pi units squared
9Pi units squared
12Pi units squared
18Pi units squared
By definitions of the area of a circle and area ratios, we conclude that the area of the circle drawn by Maria is equal to a value of 18π units squared.
What is the area of the circle?
In this question we have a circle whose radius (r) is kwown. Besides, we know that Maria draws a circle with double the area of the prior circle. The area of the circle (A) is described by the following formula:
A = π · r² (1)
Then, we have that the area drawn by Maria is:
A = 2 · [π · 3²]
A = 18π
By definitions of the area of a circle and area ratios, we conclude that the area of the circle drawn by Maria is equal to a value of 18π units squared.
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Answer:
18π units squared
Step-by-step explanation:
On edge
Boxes of tins are delivered to a shop. There are 37 boxes. Each box contains 25 tins. How many tins are there?
Answer:
Step-by-step explanation:
it equal 925 tins in total when you multiply 37 times 25. Hope that helps
what is the median \
66, 51, 77, 68, 60, 75, 54, 80
Please help
Tell me the solution of this question .. if 7+9=254016 , 3+7=7779240 , 5+8=2496000 then 4+5=?
Based on the data given on the number pattern, 4 + 5 = 180
Number pattern7 + 9 = 254016
3 + 7 = 7779240
5 + 8 = 2496000
7 + 9 = (7 × 9)^|7-9| × (7 + 9) × |7 - 9)
= 69² × 16 × 2
= 4761 × 16 × 2
= 254,016
3 + 7 = (3×7)^|3-7| × (3+7) × |3-7|
= 21⁴ × 10 × 4
= 194,481 × 10 × 4
= 7,779,240
So,
4 + 5 = (4×5)^|4-5| × (4+5) × |4-5|
= 20¹ × 9 × 1
4 + 5 = 180
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Determine the number of zeros of the polynomial function. f(x) = x^3 + 7x^2 + 2
Answer:
3
Step-by-step explanation:
The fundamental theorem of algebra tells you the number of zeros is equal to the degree of the polynomial.
__
applicationThe given degree-3 polynomial has 3 zeros.
__
Additional comment
Descarte's rule of signs tells you the absence of sign changes among the coefficients means that there are no positive real roots. Changing the sign of the one odd-degree term gives one sign change, so there is one negative real root. The other two zeros are complex.
one negative real zero, and two complex zeros
A graph confirms that the only real zero is negative and irrational, about -7.04.
Evaluating a piece-wise function. 10 pts
Solve the following system of equations:
4x − 2y − z = −5
x − 3y + 2z = 3
3x + y − 2z = −5
(0, 1, 3)
(0, −1, 3)
(0, 1, −3)
(0, −1, −3)
Answer: (0, 1, 3)
Step-by-step explanation:
Adding the second and third equations, we get [tex]4x-2y=-2[/tex]Multiplying both sides of the first equation by 2, we get that [tex]8x-4y-2z=-10[/tex]. Adding this to the second equation, we get that [tex]9x-7y=-7[/tex].If we multiply both sides of the equation [tex]4x-2y=-2[/tex] by 7, we get [tex]28x-14y=-14[/tex].
If we multiply both sides of the equation [tex]9x-7y=-7[/tex] by 2, we get [tex]18x-14y=-14[/tex].
Subtracting the equation [tex]28x-14y=-14[/tex] from the equation [tex]18x-14y=-14[/tex], we get that [tex]-10x=0 \longrightarrow x=0[/tex].
This means that [tex]4(0)-2y=-2 \longrightarrow y=1[/tex]
And thus, [tex]4(0)-2(1)-z=-5 \longrightarrow -2-z=-5 \longrightarrow z=3[/tex].
So, the solution is (0, 1, 3).
Eli read 1 book in 5 months If he read constantly how many books did he read?
Answer:
(life span - age when he started reading)/5months =number of books he read
Step-by-step explanation:
(life span - age when he started reading)/5months =number of books he read
Given a_4=135\;and\;a_6=1215a
4
=135anda
6
=1215, find the explicit rule for the geometric sequence, given that the common ratio is positive.
Answer:
Step-by-step explanation:
let a be first term and r be c.r.
a_{n}=ar^{n-1}
a_{4}=ar^{4-1}=ar^3=135
a_{6}=ar^{6-1}=ar^5=1215a_{4}=1215 \times 135
divide
r^2=1215
r=√1215=35
a_{n}=35 a_{n-1}
the product of a quarter of 3 more than a number a and 2 times a number b
Answer:
[tex] \frac{1}{4} (3a + 2b)[/tex]
The expression from the given condition is 1/4(3a+4b).
We have given that,
The product of a quarter of 3 more than a number a and 2 times a number b.
What is the quarter?
The quarter means divided into four equal or corresponding parts.
Therefore we get the expression from the given condition is
1/4(3a+4b).
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The graph of a function is shown on the coordinate plane below.
Between which two values of x is the function nonlinear and increasing?
A -5 and -3
B -3 and 1
C 1 and 4
D 4 and 6
The answer to this question is choice B
Fill in the blank. In the triangle below, x=?. Round your answer to two decimal places.
Answer:
x = 31.5, y = 41.7, z = 48
Step-by-step explanation:
use the rule that cos (x) = adjacent/hypotenuse:
you know that x (the angle) = 42 and the adjacent side = 35, so:
cos (42) = 35/y
y = 35/cos(42)
y = 47.1
then, to find x:
use the fact that tan (x) = opposite side/adjacent side
so tan (42) = x/35
x = 35tan(42)
x = 31.5
finally, you know all 3 angles of the triangle have to add up to 180, so to find z you can do:
z + 90 + 42 = 180
z + 132 = 180
z = 48
Help !! I’ll mark brainliest !!
Answer:
9
Step-by-step explanation:
The opposite sides of a parallelogram are congruent.
Answer:
9
Step-by-step explanation:
Parallel sides are always equal. :)
Consider the function f(x)=3^x and the translation if f(x) named g(x). Janeen created a table for select values of x. What can be concluded about the relationship between two functions?
The conclusion about the relationship is
The functions have the same base.The functions have the same range.The functions have the same domain.g(x) is a translation left 1 unit.What is function?The complete question is:
Consider the function f(x) = 3x and a translation of f(x) named g(x). Janeen created a table for select values of x. Her table is shown below. What can be concluded about the relationship between the two functions? Check all that apply.
The functions have the same base.
The functions have the same range.
The functions have the same exponent.
The functions have the same domain.
g(x) is a translation left 1 unit.
g(x) is a translation right 2 units.
g(x) is a translation up 2 units.
Given function is:
f(x) = [tex]3^{x}[/tex]
g(x) = [tex]3^{x+1}[/tex]
Firstly, the functions have the same base i.e., base 3.
second, the functions have the same range.
As the range of f are all the values that f can assume. i.e., positive numbers and the range of g are all the values that g can assume. i.e., positive numbers.
third, both functions have the same domain as x = {0,1,2,3}.
Fourth, g(x) = f(x+1). So, g(x) is a translation left 1 unit.
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What is the inverse of p>q
Inequalities help us to compare two unequal expressions. The inverse of p>q is p<q.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
Given the inequality that p is greater than q, therefore, the inverse of it will be p smaller than q. Thus, The inverse of p>q is p<q.
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EAsy math challenge! Click me!
Answer:
the answer is 64
Step-by-step explanation:
now atleast mark me brainliest answer
Please help !!! I will give 20 points to correct answer !!!!
Answer:
the answer above the image
Answer:
a=-4/3, 14/3
Step-by-step explanation:
absolute value only makes the answer become positive whether the value inside is negative or positive.
so -3a+5=9 or -3a+5=-9 all works
-3a+5=9
-3a=4
a=-4/3
If -3a+5=-9
-3a=-14
a=14/3
The graph of the cube root parent function y = RootIndex 3 StartRoot x EndRoot is translated to form f(x) shown on the graph.
On a coordinate plane, a cube root function goes through (negative 7, 0), has an inflection point at (negative 6, 1), and goes through (2, 3).
Which equation represents f(x)?
f(x) = RootIndex 3 StartRoot x + 6 EndRoot + 1
f(x) = RootIndex 3 StartRoot x minus 6 EndRoot + 1
f(x) = RootIndex 3 StartRoot x + 6 EndRoot minus 1
f(x) = RootIndex 3 StartRoot x minus 6 EndRoot minus 1
Step-by-step explanation:
The graph of the cube root parent function y = RootIndex 3 StartRoot x EndRoot is translated to form f(x) shown on the graph.
On a coordinate plane, a cube root function goes through (negative 7, 0), has an inflection point at (negative 6, 1), and goes through (2, 3).
Which equation represents f(x)?
f(x) = RootIndex 3 StartRoot x + 6 EndRoot + 1
f(x) = RootIndex 3 StartRoot x minus 6 EndRoot + 1
f(x) = RootIndex 3 StartRoot x + 6 EndRoot minus 1
f(x) = RootIndex 3 StartRoot x minus 6 EndRoot minus 1
Answer:
Step-by-step explanation:
The translation of the parent function is:
g(x) = ∛(x + 6) + 1
How do translations work?
There are two types of translations, these are:
Horizontal translation:
For a function f(x), a horizontal translation of N units is written as:
g(x) = f(x + N)
If N is positive, the translation is to the left.
If N is negative, the translation is to the right.
Vertical translation:
For a function f(x), a vertical translation of N units is written as:
g(x) = f(x) + N
If N is positive the translation is upwards.
If N is negative the translation is downwards.
Here we start with the parent function:
f(x) = ∛x
And we apply two translations such that:
g(x) = ∛(x + a) + b
Such that:
g(-7) = 0
g(2) = 3
Then we have the system of equations:
∛(-7 + a) + b = 0
∛(2 + a) + b = 3
From the options, the only ones that make the first option true are:
g(x) = ∛(x + 6) + 1
Such that when evaluated in x = -7 we get:
g(-7) = ∛(-7 + 6) + 1 = ∛(-1) + 1 = 0
When evaluated in x = 2 it gives:
∛(2 + 6) + 1 = ∛(8) + 1 = 2+ 1 = 3
So the only option that meets these conditions is:
g(x) = ∛(x + 6) + 1
Which is a translation to the left of 6 units and up 1 unit.
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Determine the equation of the line with slope m=2/3, passing through the point (0,4)
Answer:
y = 2/3x + 4
Step-by-step explanation:
The slope-intercept form is y=mx+b. m (the slope) is equal to 2/3, so you can substitute that number in for m. B is the y value of the y-intercept. The y-intercept is (0,4) as given in the problem, so the value of b is 4. You can substitute that value into the equation as well.
g(x) f(x) = −6x − 3 cosine function with y intercept at 0, negative 3 h(x) = 2 cos(x + π) − 1 Using complete sentences, explain which function has the greatest y-intercept. (10 points)
full step by step process please.
A function assigns the values. The function that has the greatest y-intercept is h(x).
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
There are three function, g(x){given in the graph below}, f(x)= -6x-3, and -3h(x) = 2 cos(x + π) − 1, the y-intercept of the function is the point at which the graph intersects the y-axis. Therefore, the y-intercept are,
g(x) = -3
f(x) = -3
h(x) = 1
Hence, the function that has the greatest y-intercept is h(x).
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(5x+7)(8x+7) = 0
Find the two possible values.
[tex](5x + 7)(8x + 7) \\ \\ 5x + 7 = 0 \\ \\ 5x = - 7 \\ \\ x = \frac{ - 7}{5} \\ \\ 8x + 7 = 0 \\ \\ 8x = - 7 \\ \\ x = \frac{ - 7}{8} .[/tex]
the values of x are -7/5 and -7/8 .
Hi!
___________________________________________________________
[tex]\rightsquigarrow\circ\boldsymbol{Answer.}\circ\leftharpoonup[/tex]
[tex]\rightsquigarrow\circ\boldsymbol{Explanation}\circ\leftharpoonup[/tex]
Set each factor equal to 0.
[tex]\twoheadrightarrow\sf 5x+7=0[/tex]
[tex]\twoheadrightarrow\sf 8x+7=0[/tex]
[tex]\bullet[/tex] Solve each equation
[tex]\twoheadrightarrow\sf 5x+7=0[/tex]
[tex]\bullet[/tex] Subtract 7 from both sides
[tex]\twoheadrightarrow\sf 5x=-7[/tex]
[tex]\bullet[/tex] Divide both sides by 5
[tex]\underline{\twoheadrightarrow\sf x=-\cfrac{7}{5}}[/tex]
[tex]\bullet[/tex] Now let's solve the second equation
[tex]\twoheadrightarrow\sf 8x+7=0[/tex]
[tex]\bullet[/tex] Subtract 7 from both sides
[tex]\twoheadrightarrow\sf 8x=-7[/tex]
[tex]\bullet[/tex] Divide both sides by 8
[tex]\underline{\twoheadrightarrow\sf x=-\cfrac{7}{8}}[/tex]
[tex]\bullet[/tex] Great job, we found the two possible values
--
Hope that this helped! Best wishes.
[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]
--
factor completely
0.09y² - 0.81
Answer:
[tex]0.09y^2 - 0.81 = (0.3y+0.9)(0.3y-0.9)[/tex]
Step-by-step explanation:
The difference of squares formula gives us
[tex]a^2 - b^2 = (a+b)(a-b)[/tex]
(you can multiply this out to confirm)
[tex]0.09y^2 = (0.3y)^2[/tex]
and
[tex]0.81 = 0.9^2[/tex]
Thus, by the difference of squares formula
[tex]0.09y^2 - 0.81 = (0.3y+0.9)(0.3y-0.9)[/tex]
Examine the following three premises: i. All kids who have a smartphone play mobile legends.
ii. All people who play mobile legends enjoy life.
iii. Some college instructors enjoy life. Now consider each of the following six conclusions. For each conclusion, determine whether the argument formed by the three premises and the conclusion is valid or invalid.
1. Therefore, some college instructors have a smartphone.
2. Therefore, some college instructors play mobile legends.
3. Therefore, some kids who play mobile legends are college instructors. Examine the following three premises :
i . All kids who have a smartphone play mobile legends .
ii . All people who play mobile legends enjoy life .
iii . Some college instructors enjoy life . Now consider each of the following six conclusions . For each conclusion , determine whether the argument formed by the three premises and the conclusion is valid or invalid .
1. Therefore , some college instructors have a smartphone .
2. Therefore , some college instructors play mobile legends .
3. Therefore , some kids who play mobile legends are college instructors .
Answer:
The increasing number of students who are hooked on playing online mobile games (OMG) is alarming. As such, this study was realized to address the problem. This study assessed the gaming profile towards OMG and its relation to the academic performance of the engineering students of Eastern Visayas State University Tanauan Campus (EVSUTC). Specifically, the study investigated the correlation between student's number of hours spent on playing OMG (at school and home), commonly played OMG (at school and home), reasons for playing OMG and attitudes on playing OMG with academic performance utilizing Eta and Pearson r correlation analyses. A random sample of 134 student respondents were selected through purposive sampling of those who are playing OMG using their mobile phones. Descriptive correlational research design was utilized and a validated survey instrument was employed to gather the needed information. The findings revealed that majority of the students played mobile legends and spent mostly 2 hours playing OMG for a reason of boredom. The overall attitudes of the students on playing OMG were interpreted as Less Favorable (M=2.58, SD=1.13). Out of the independent variables being set in the study, the number of hours spent on playing OMG at home (r=-0.188, p=0.039) and commonly played OMG at school (r=0.203, p=0.045) were found significantly correlated with student's academic performance. Hence, the students' time spent on playing OMG at home and the type of games that students played at school have significant bearing to their academic performance. As such, delimiting student's usage of internet can be made to address the problem.
look at the picture
what is the ratio of the radius of circle a to the radius of circle b?
Answer:
3:1
Step-by-step explanation:
Assuming that the edges of the circle are supposed to line up with the dotted lines of the graph, all you have to do is count how many lines are between the middle of the circle and the edge (either directly vertical or horizontal due to the graph we are using). We can see that the radius of circle A is approximately 3 units, while the radius of circle B is approximately 1 unit. So the ratio of the radius of circle A to the radius of circle B is 3:1.
Answer:
3:1
Step-by-step explanation:
because once count the radius of the big circle that is 3 unit and the radius of small circle is 1 unit
Giraffe Jack is 19 feet tall, and Ostrich Jim is 9 feet tall. A) What percent of Jack's height is Jim's height? B)What percent of Jim's height is Jack's height?
A percentage is a way to describe a part of a whole. Jim's Height is 47.37% of Jack's height.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Giraffe Jack is 19 feet tall, and Ostrich Jim is 9 feet tall.
A.) The percent of Jack's height is Jim's height,
Percentage = (Height of Jack/Height of Jim) × 100%
= 19/9 × 100%
= 211.11%
Hence, Jack's Height is 211.11% of Jim's height.
B.) The percent of Jim's height is Jack's height,
Percentage = (Height of Jim/Height of Jack) × 100%
= 9/19 × 100%
= 47.37%
Hence, Jim's Height is 47.37% of Jack's height.
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Answer:
211.11%
Step-by-step explanation:
If f(x) = x², and
g(x) = x1, then
f(g(x)) = ?
will give brainliest answer !!
Answer: 1, -2, 1
Step-by-step explanation:
[tex]f(g(x))=f(x-1)=(x-1)^{2}=x^{2}-2x+1[/tex]
The Royal Fruit Company produces two types of fruit drinks. The first type is 35% pure fruit juice, and the second type is 60% pure fruit juice. The company is attempting to produce a fruit drink that contains 45% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 40 pints of a mixture that is 45% pure fruit juice?
32 pints of each of the two existing types of drink must be used to make 40 pints of a mixture that is 45% pure fruit juice.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let x be the pints of 60% pure fruit juice
0.60x + 0.35(40 - x) = 0.40(40)
x = 8
= 40 - 8 (pints of 35% juice)
= 32
Thus, 32 pints and 8 pints of each of the two existing types of drink must be used to make 40 pints of a mixture that is 45% pure fruit juice.
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