Answer: [tex]x=-\frac{5}{4}[/tex] and [tex]x=-2[/tex]
Step-by-step explanation:
To factor an equation in the form of [tex]ax^2+bx+c[/tex] you need to find the value of [tex]ac[/tex]. So first solve for that
[tex](4)(10) = 40[/tex]
Now we need to find two numbers that add up to b and multiply together to make ac. In this case those numbers are 5 and 8 since 5+8=13 and (5)(8)=40
Now split 13x into 5x+8x and solve by grouping
[tex]4x^2+5x+8x+10\\(4x^2+5x)+(8x+10)[/tex]
Factor out the GCF in each quantity
[tex](4x^2+5x)+(8x+10)\\x(4x+5)+2(4x+5)[/tex]
Now group x+2 together
[tex](x+2)(4x+5)[/tex]
Finally, set each factor equal to 0 and solve for x
[tex]x+2=0\\x+2-2=0-2\\x=-2\\\\\\4x+5=0\\4x+5-5=0-5\\4x=-5\\\frac{4x}{4} =\frac{-5}{4} \\x=-\frac{5}{4}[/tex]
Select all the correct answers.
Which expressions are equivalent to this exponential expression? Please help
An expression is defined as a set of numbers, variables, and mathematical operations. The correct options are A and C.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given exponential (6⁻¹⁰/6⁻⁴) function can be simplified as shown below,
(6⁻¹⁰/6⁻⁴)
= 6⁻¹⁰ × 6⁴
= 6⁽⁻¹⁰⁺⁴⁾
= 6⁻⁶
= 1/6⁶
Hence, the correct options are A and C.
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Please help!!
Construct the circle that circumscribes image DEF.
Answer:
See below
Step-by-step explanation:
General outlineConstruct the perpendicular bisectors of DE, EF, and DF.Identify the circumcenter. Draw the circumcircle.Circles & CircumcirclesTo construct a circle, one must know the center point of the circle, and the circle's radius.
The circle that circumscribes a triangle (called a circumcircle), has a circumcenter (center point) that is the point of concurrency (a point where more than two lines intersect at the same point) of all three perpendicular bisectors (perpendicular lines that happen to cut a given line segment exactly in half) of the sides of the triangle.
Construct the circle with a center at the circumcenter, and a radius out to any one of the vertices of the triangle. The circumcenter is equidistant from all three vertices, so the circle draw will contain all three vertices.
Constructing perpendicular bisectorsTo construct perpendicular a bisector, recall that a perpendicular bisector is a line containing all points that are equidistant the end points of a line segment (each point on the line is the same distance from both segment endpoints simultaneously).
So, if we can find two points that are the equidistant from the two segment endpoints, we'll have two points on the line, and to draw any line, one only needs two distinct points, and the straightedge.
Finding a point that is equidistant from two given points
Set the compass to any radius that is larger than half the distance between the two endpoints. If uncertain of a "good" choice, one can simply choose the length of the line segment itself as a radius.
Setting the center of the compass circle on one endpoint, draw an arc such that the arc will pass through the perpendicular line we're trying to construct twice. If uncertain, draw the entire circle. Keeping the radius saved.
With the same radius, setting the center of the compass circle to the second endpoint, draw and arc such that the arc intersects the first circle two times. If it doesn't intersect two times, the radius chosen at the beginning was too small. Start the entire process over with a larger radius.
These two points of intersection are equidistant from the two endpoints of the line segment, and thus, they are on the perpendicular bisector of the line segment.
Using those two points, and a straightedge, draw the line containing those two points, and extend it generously in both directions.
ProcessSteps 1-5 in pink; steps 6-10 in green; steps 11-15 in blue (see diagram):
Set compass radius to length DEDraw circle, centered at D, through E. Keep radius set.Draw circle, centered at E, through D.Identify points of intersection of the circles from steps 2 & 3, M & NDraw line MNSet compass radius to length EFDraw circle, centered at E, through F. Keep radius set.Draw circle, centered at F, through E.Identify points of intersection of the circles from steps 7 & 8, Q & RDraw line QRSet compass radius to length DFDraw circle, centered at D, through F. Keep radius set.Draw circle, centered at F, through D.Identify points of intersection of the circles from steps 12 & 13, S & TDraw line STIdentify point of concurrency of line MN, line QR, and line ST; label it point PSet compass radius to length DP (or EP, or FP)Draw circle, centered at P, through points D, E, and F.Note: Since all three perpendicular bisectors intersect at the same point, it is only necessary to find two of three, not all three. So, one could skip constructing one of those three perpendicular bisectors (either steps 1-5, 6-10, or 11-15), and still be able to construct the circumcircle correctly.
When planning road development, the road commission estimates the future population using the function represented in the table, where x is the time in years and f(x) is the total population.
What is the significance of 160,000 in the function?
the maximum population of the city
the expected population in 5 years
the initial population at the time of the estimation
the amount of increase in the popu
Considering that 160,000 is the y-intercept of the function, it's significance is given by:
the initial population at the time of the estimation.
What is the y-intercept of a function f(x)?The y-intercept is f(0), that is, the value of y when x = 0, which is interpreted as the initial value of the function.
Researching this problem on the internet, it is found that f(0) = 160,000, hence the significance of 160,000 in the function is given by:
the initial population at the time of the estimation.
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Janet solves this equation
log(x-3)+logx=1
She finds the two solutions; x=5 and x=-2
Of Janet’s two solutions, ____ correct because _____
A. Neither x=5 nor x=-2 is
B. Only x=5 is
C. Only x=-2 is
D. Both x=5 and x=-2 are
1. x=5 is an extraneous solution
2. Both x=-2 and x=5 are valid solutions
3. Both x=-2 and x=5 are extraneous solutions
4. x=-2 is an extraneous solution
(TWO DIFFERENT ANSWERS FILL IN THE BLANK)
Of Janet’s two solutions, both x=5 and x=-2 are correct because both x=-2 and x=5 are extraneous solutions
Logarithmic functionGiven the log function expressed as:
log(x-3) + logx=1
According to the law of logarithm, addition becomes product to have:
log x(x -3) = log₁₀10
x² - 3x = 10
x² - 3x -10 = 0
x² - 5x + 2x - 10 = 0
x(x-5) + 2(x-5) = 0
(x+2)(x-5)=0
x = -2 and 5
Of Janet’s two solutions, both x=5 and x=-2 are correct because both x=-2 and x=5 are extraneous solutions
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Help me show your work
The value of x should be greater than or equal to -2. The number line from -2 to the entire right till ∞ of the number line will satisfy this condition.
What is a number line?A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. It’s not a ruler, so the space between each number doesn’t matter, but the numbers included on the line determine how it’s meant to be used.
The value of x that will satisfy this condition can be found by simplifying the given inequality. Therefore, The given inequality can be simplified as,
4x + 1 - 1 ≥ -8
4x ≥ -8
x ≥ -2
Hence, the value of x should be greater than or equal to -2. The number line from -2 to the entire right till ∞ of the number line will satisfy this condition.
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Zippy company manufactured 10,000 units in december with a total product cost of $22,900 they had zero finished goods inventory at the start of december. in december zippy sold 7,796 units at a unit price of $5.54. period expenses were $4,723. what is the amount of zippy's gross profit (otherwise know as gross margin).? round any intermediate calculations to four decimal places
The amount of zippy's gross profit (otherwise know as gross margin) is: $25,337.
Gross profitSales revenue $43,189.84
(7,796 units × $5.54)
Less Cost of goods sold $17,852.84
[($22,900/10,000)×7,796]
Gross profit $25,337
( $43,189.84-$17,852.84)
Therefore the amount of zippy's gross profit (otherwise know as gross margin) is: $25,337.
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Select the correct answer. A linear function on a coordinate plane passes through (minus 3, 2), (0, 4), and (3, 6) Which equation describes the line graphed above? A. B. C. D.
Answer:
I don't see the equation options. See below for a predicted equation.
y= (2/3)x + 4
Step-by-step explanation:
The points are (-3,2), (0,4), and (3,6). I will assume they lie in a straight line.
Find an equation of the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0).
m, the slope, is also known as the "Rise/Run."
Pick any two points. I'll use (0,4) and 3,6)
Rise = (6-4) = 2
Run = (3-0) = 3
Slope = 2/3
The equation becomes y = (2/3)x + b
B is easy in this case. Point (0,4) tells us that y = 4 when x = 0 (the definition of b).
The equation is y= (2/3)x + 4
See the attached graph.
Which expression for YYY correctly outputs that x is between 50-100? if (YYY) { // Output "50, 51, ..., 99, 100" } Group of answer choices (x >= 50) || (x <= 100) 50 <= x <= 100 50 >= x <= 100 (x >= 50) && (x <= 100)
The expression for YYY is (d) (x >= 50) && (x <= 100)
How to determine the correct expression?The instruction is given as:
If (YYY) {
// Output "50, 51, ..., 99, 100"
}
The value of x is given as:
x = 50 to 100 (inclusive)
This means that:
x must be greater than or equal to 50 AND x cannot exceed 100
The keyword AND is represented as &&.
So, the condition is:
x >= 50 && x <= 100
Hence, the expression for YYY is (d) (x >= 50) && (x <= 100)
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what is the answer in system form
y=-2x
5x-7y=-38
Answer:
x = -2
y = 4
Step-by-step explanation:
To solve the system of equations, you want to plug one equation into the other and then simplify. You can do this by setting one equation equal to a variable (like in the first equation), and then substituting the function into the variable into the second equation.
First Equation: y = -2x
Second Equation: 5x - 7y = -38
5x - 7y = -38 <----- Second equation
5x - 7(-2x) = -38 <----- Plug first equation into "y"
5x + 14x = -38 <----- Multiply -7 and -2x
19x = -38 <----- Add 5x and 14x
x = -2 <----- Divide both sides by 19
Now that you know the value of one variable, you can use it to find the value of the second variable. This can be done by plugging x = -2 in to one of the equations.
y = -2x <----- First equation
y = -2(-2) <----- Plug -2 in "x"
y = 4 <----- Multiply -2 and -2
Match each pair of equivalent values.
1 .
1
square root of 16
2 .
12
square of 8
3 .
4
4 2
4 .
64
1 2
5 .
16
6 .
2
Answer:
1 - [tex]1^{2}[/tex]
12 - ?
4 - square root of 16
64 - [tex]8^{2}[/tex]
16 - [tex]4^{2}[/tex]
2.828 - square root of 8
Step-by-step explanation:
I need more terms to match
Square root of 16 is 4, square root of 8 is 2, but for an answer it would be , 4² is 16, 1² is 2, number 5 would be 64 and number 6 would be 12.
What are mathematical values?A mathematical value can generally be any specific mathematical object. This is most frequently a number in elementary mathematics, such as a real number like or an integer like 42. Every integer or even other mathematical object set to a variable or constant is that object's value.
A mathematical expression's value is the outcome of a computation it describes when its variables and constants are given values. The amount that the function assumes for these argument numbers is the result of a function, assuming the value(s) provided to its argument(s).
Square root of 16 is 4, square root of 8 is 2, but for an answer it would be , 4² is 16, 1² is 2, number 5 would be 64 and number 6 would be 12.
Therefore, Square root of 16 is 4, square root of 8 is 2, but for an answer it would be , 4² is 16, 1² is 2, number 5 would be 64 and number 6 would be 12.
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Emily works at a local restaurant. She made $200 in tips last night. She shared 15 percent of her tips with the crew that cleans the tables. How much did she give to the clean-up crew?
$
A percentage is a way to describe a part of a whole. The amount Emily shared is $30.
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.
Emily works at a local restaurant. She made $200 in tips last night. She shared 15% of her tips with the crew that cleans the tables. The amount Emily shared is,
15% of $200
= 0.15 × $200
= $30
The amount Emily shared is $30.
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How do you use the additive inverse to evaluate an expression that uses subtraction ?
To use the additive inverse to evaluate an expression that uses subtraction, change the sign of the number to positive
What is additive inverse?Additive inverse is simply changing the sign of a number and then adding it to the original number to get an answer that is equal to 0.
The additive inverse of a number is another number
The additive inverse of number 3 is - 3
For an expression that uses subtraction, to use the additive inverse, change the sign of the number to positive
Thus, to use the additive inverse to evaluate an expression that uses subtraction, change the sign of the number to positive
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Determine the linear function for a graph that is a line with a slope of 1/7
and contains the point
(−4, 1).
The linear equation is y = (1/7)*x + 11/7.
How to get the linear equation?
The general linear equation is:
y = a*x + b
Where a is the slope.
Here we know that a = (1/7), then the line is:
y = (1/7)*x + b
We also know that the line contains the point (-4, 1), this means that when x = -4, we must have y = 1.
Replacing that, we get:
1 = (1/7)*(-4) + b
1 + 4/7 = b
7/7 + 4/7 = b
11/7 = b
So the linear equation is:
y = (1/7)*x + 11/7.
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The equation of the linear function of the line is: y = 1/7x + 11/7.
What is a Linear Function Equation?A linear function equation is modelled as, y = mx + b, where m is the slope and b is the y-intercept.
Slope (m) = 1/7, and the line passes through (-4, 1), therefore, substitute (x, y) = (-4, 1) and m = 1/7 into y = mx + b:
1 = 1/7(-4) + b
1 = -4/7 + b
1 + 4/7 = b
11/7 = b
b = 11/7
Plug in the values of m and b into y = mx + b:
y = 1/7x + 11/7
The equation of the linear function is: y = 1/7x + 11/7
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Find the perimeter of the triangle.
23.
7 in.
(x + 4) in.
(4x + 1) in.
Answer:
17 in.
Step-by-step explanation:
There are two same angles shown, so two sides are equal. We can form an equation x+4=4x+1. Solution is x=1, then both unknown sides are 5 in. long. Given all side lengths we add them 7+5+5+15 getting the perimeter.
Sequence: 1,5,13,25
Find nth term (Equation/formula thingy)
Need answer ASAP
Answer:
Formula for a linear sequence is
Tn=a+(n-1)d
where Tn is the nth term
a is the first term
n is the number of term
d is common difference
please help and answer it in a sentence :)
Answer:
x = $1 & y = $2.
Each doughnut cost $1 and hot chocolate cost $2.
All of the details to the question are in the picture that is attached in this question, please help
Answer: 10
The arc length of the semicircle is
a+(a+1)+(a+2)+(a+3)+(a+4)=5a+10
As x = 42, this means a+4 is 42/180 of the arc length of the circle, 5a+10.
So,
(42/180)(5a+10)=a+4
42(5a+10)=180(a+4) [multiply both sides by 180]
210a+420=180a+720 [distributive property]
30a+420=720 [subtract 180a from both sides]
30a=300 [subtract 420 from both sides]
a=10 [divide both sides by 30]
What is the coefficient of the third term in the binomial expansion of (a b)6? 1 15 20 90
What is the range of the function y=-x² +1?
A) y≤ -1
B) y²-1
C) y≤ 1
D) y≥ 1
Answer:
Option (C)
Step-by-step explanation:
The minimum value of x² is 0, and the maximum value is unbounded, so therefore, the maximum value of -x² is 0, and the minimum value is unbounded.
So, this means that adding 1 to this, the range matches with option C.
PLEASE HELP I WILL GIVE 20 POINTS
Function g can be thought of as translated (shifted) version of f(x)=x^2
Jeremy is reading a 60-page book. He read the first 20 pages in 30 minutes. If Jeremy continues to read a the same rate, how long will it take him to finish the book?
It will take total 90 minutes to finish the book and 60 minutes to read the left 40 pages.
What is Ratio and Proportion ?When two numbers can be written as p/q is called a Ratio , and when two ratios are equal they are said to be in proportion .
It is given that
Jeremy is reading a 60-page book.
The time taken to read 20 pages is 30 minutes
Then it can be written as 20:30 = 2:3
The rate of reading is same so To read the rest 40 pages is given by
40:x
40: x = 2:3
40*3/2 = x
x = 60 minutes
Therefore it will take total 90 minutes to finish the book and 60 minutes to read the left 40 pages.
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Step 1: We know that Angle A B C Is-congruent-to Angle F G H because all right angles are congruent. Step 2: We know that Angle B A C Is-congruent-to Angle G F H because corresponding angles of parallel lines are congruent. Step 3: We know that Line segment B C is-congruent-to line segment G H because it is given. Step 4: Triangle A B C Is-congruent-to Triangle F G H because of the
Triangles FGH and ABC are congruent because of the: AAS congruence theorem.
What is the AAS Congruence Theorem?
The AAS congruence theorem states that when two angles and one non-included side in one triangle are congruent to corresponding two angles and one non-included side in another triangle, then both triangles are congruent.
In the proof given, it is established that both triangles have two corresponding congruent angles, and also, BC ≅ GH which are non-included sides.
Therefore, both triangles are congruent because of the AAS congruence theorem.
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write 9 430 049 in international number system
Step-by-step explanation:
9, 430, 049 = 9 million four hundred thirty thousand and fourtynine....
[tex]...[/tex] :)..
√2/√2+√3-√5 rationalise the denominator
What is the value of x?
to
x = [? ]°
36°
Enter
I will give you points
Answer:
54 degrees!
Step-by-step explanation:
its a right triangle so we know 2 out of the 3 angles
so 36 + 90 = 126
180 - 126 = 54!
hope this helps :)
(-3 +6 i )(-3 - 6 i )
Answer:
45
Step-by-step explanation:
Triangle A C D is shown. A line is drawn from point D to point B on side A C to form a right angle. Line A D is labeled s. The length of A B is 8, the length of B C is 5, and the length of B D is 15.
What is the value of s in units?
Answer:
s = 17units
Step-by-step explanation:
For this problem, we are trying to find a specific unknown side length.
We're actually given some extraneous information (information that is not needed to solve the problem): It isn't necessary to know that BC is 5.
If the side AD with the unknown length is part of a right triangle (the triangle in red in the attached diagram), we can use the Pythagorean Theorem to solve for AD.
It isn't clear if the diagram you were provided gives ∠ABD as a right angle, if it only gives ∠CBD as a right angle, or if it gives both as a right angle. Below, we prove that it doesn't matter, because regardless, both must be right angles.
Is Triangle ABD a "right triangle"?
Since B is between A and C, then the two angles ∠ABD & ∠CBD form a linear pair, and by the linear pair postulate are supplementary. Since they are supplementary, their measures add to 180°. Using the fact that all right angles are 90°, substitution, the subtraction property of equality, arithmetic, the measure of ∠ABD is also 90°, and thus must be a right angle. Thus, based on the given information, both ∠ABD & ∠CBD must be right angles.
Consequently, triangle ABD is a right triangle, by definition (it is a triangle that has a right angle).
Pythagorean Theorem
Since triangle ABD is a right triangle, the Pythagorean Theorem can be applied.
The Pythagorean Theorem states that [tex]a^{2} +b^{2} =c^{2}[/tex] where "c" is the hypotenuse (the side across from the right angle) and "a" and "b" the the lengths of the two other sides (called legs) of the right triangle. (Aside: Because of the commutative property of addition, it doesn't matter which of the two legs' lengths is used for a, and which is used for b. The only thing that is required is that "c" be the length of the hypotenuse)
In our triangle, side AD, with unknown length "s" is the length of our hypotenuse, and sides AB and BD are the two legs. Substituting values into the Pythagorean Theorem equation, we can solve for the unknown "s":
[tex]a^{2} +b^{2} =c^{2}[/tex]
[tex](8)^{2} +(15)^{2} =(s)^{2}[/tex]
[tex]64 +225 =s^{2}[/tex]
[tex]289 =s^{2}[/tex]
Applying the square root property...
[tex]\pm \sqrt{289} =\sqrt{s^{2}}[/tex]
[tex]s=17 \text{ or } s=-17[/tex]
Final Solution
We discard the negative solution we obtained, since s represents the length of the side of a triangle.
s = 17units
Answer:
17
Step-by-step explanation:
Let
f(x) = (x − 3)−2.
Find all values of c in (1, 4) such that
f(4) − f(1) = f '(c)(4 − 1).
(Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
c =
Based off of this information, what conclusions can be made about the Mean Value Theorem?
This contradicts the Mean Value Theorem since f satisfies the hypotheses on the given interval but there does not exist any c on (1, 4) such that
f '(c) =
f(4) − f(1)
4 − 1
.
This does not contradict the Mean Value Theorem since f is not continuous at x = 3.
This does not contradict the Mean Value Theorem since f is continuous on (1, 4), and there exists a c on (1, 4) such that
f '(c) =
f(4) − f(1)
4 − 1
.
This contradicts the Mean Value Theorem since there exists a c on (1, 4) such that
f '(c) =
f(4) − f(1)
4 − 1
,
but f is not continuous at x = 3.
Nothing can be concluded.
Answer:
3/4 = -3* 2*(c-
I hope it helps!
if it does pls mark me brainliest answer
Separating variable in the equation gives you the following equation:
Answer:
[tex]\textsf{E.} \quad y\:dy=xe^x\:dx[/tex]
Step-by-step explanation:
Given equation:
[tex]ye^{-x}\dfrac{dy}{dx}=x[/tex]
Divide both sides by [tex]e^{-x}[/tex]:
[tex]\implies \dfrac{ye^{-x}}{e^{-x}}\:\dfrac{dy}{dx}=\dfrac{x}{e^{-x}}[/tex]
[tex]\implies y\:\dfrac{dy}{dx}=\dfrac{x}{e^{-x}}[/tex]
Multiply both sides by [tex]dx[/tex] :
[tex]\implies y\:\dfrac{dy}{dx}\cdot dx=\dfrac{x}{e^{-x}}\cdot dx[/tex]
[tex]\implies y\:dy=\dfrac{x}{e^{-x}}\:dx[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{1}{a^{-n}}=a^n:[/tex]
[tex]\implies y\:dy=xe^x\:dx[/tex]
Answer: E
Step-by-step explanation:
[tex]ye^{-x} \frac{dy}{dx}=x\\\\y \frac{dy}{dx}=xe^{x} \\ \\ \boxed{y dy=xe^{x} dx}[/tex]
Triangle ABC is shown on the graph. What are the coordinates of the image of point B after the triangle is rotated 270° about the origin?
(4, 2)
(2, 4)
(–4, –2)
(–2, –4)
The coordinates of the image of point B after the triangle is rotated 270° about the origin is (4, 2)
How to determine the image of point B?The complete question is added as an attachment
From the attached image, we have the following coordinate
B = (-2, 4)
When the triangle is rotated by 270 degrees, the rule of rotation is:
(x, y) ⇒ (y, -x)
For point B, we have:
B' = (4, 2)
Hence, the coordinates of the image of point B after the triangle is rotated 270° about the origin is (4, 2)
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