Answer:
[tex]f(x) = -x^2 - 2x + 8[/tex]
y-intercept is when x = 0:
[tex]\implies f(0) = -(0)^2 - 2(0) + 8=8[/tex]
So the y-intercept is (0, 8)
x-intercepts are when f(x) = 0:
[tex]\implies f(x)=0[/tex]
[tex]\implies -x^2 - 2x + 8=0[/tex]
[tex]\implies x^2 + 2x - 8=0[/tex]
[tex]\implies x^2 - 2x + 4x - 8=0[/tex]
[tex]\implies x(x - 2) + 4(x-2)=0[/tex]
[tex]\implies (x+4)(x - 2)=0[/tex]
Therefore:
[tex]\implies (x+4)=0 \implies x=-4[/tex]
[tex]\implies (x-2)=0 \implies x=2[/tex]
So the x-intercepts are (-4, 0) and (2, 0)
The vertex is the turning point of the parabola. The x-value of the vertex is the x-value between the 2 zeros (x-intercepts).
Therefore, the x-value of the vertex is [tex]\sf \dfrac{x_1+x_2}{2}=\dfrac{-4+2}{2}=-1[/tex]
Substituting x = -1 into the function:
[tex]\implies f(-1) = -(-1)^2 - 2(-1) + 8=9[/tex]
So the vertex is (-1, 9)
The domain is the input values, so x = all real numbers.
The range is the output values, so the range is [tex]f(x)\leq 9[/tex]
Therefore, (-4, 0), (-1, 9), (0, 8) and (2, 0) are solutions of the function, HOWEVER they are not ALL the solutions.
All solutions of the function are:
[tex](x, -x^2 - 2x + 8)[/tex] for all real numbers of x
4.
Write an equation and solve it. Anything goes as long as you address the following points:
a. The equation must start with an 'x' variable in an exponent.
b. The equation must require logarithms to solve.
c. In the solution you must use the power rule, the product rule and the quotient rule at least once each.
d. Explain each step as you solve; which rules are you using and why?
e. What challenges did you face as you were writing your problem? Did you run into any dead ends?
My problem lies in finding an exponential equation [tex]N^x=N^x[/tex] (N being any positive number) that needs all 3 rules to solve. I can come up with an equation that uses 2 of the rules but I'm stuck on adding the third. Any suggestions would be nice. Thanks
Step-by-step explanation:
hope you understand. :)
The table shows selected values of a piecewise defined function f(x) that increases over the intervals (-∞, 3) and (3,∞). Which of the following statements are true? Select all that apply.
help pls
Answer: B D F
Step-by-step explanation:
The statement (B), statement (D), statement (F) are true if piecewise defined function f(x) that increases over the intervals (-∞, 3) and (3,∞).
What is piecewise function?A piecewise function is one that has several curve parts in its graph.
It means that, based on the value of the input, it has countless definitions.
A piecewise function, in other words, performs differently depending on the input.
We have given a data for a piecewise function.
From the data:
[tex]\rm \lim_{n \to 3^+} f(x) = 5[/tex]
[tex]\rm \lim_{n \to 3^-} f(x) = 6[/tex]
[tex]\rm \lim_{n \to 2^+} f(x)[/tex] Does not exist because [tex]\rm \lim_{n \to 3^+} f(x)[/tex] and [tex]\rm \lim_{n \to 3^-} f(x)[/tex] are not equal.
Thus, the statement (B), statement (D), statement (F) are true if piecewise defined function f(x) that increases over the intervals (-∞, 3) and (3,∞).
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4. Find the area of the triangle.
9 km
16 km
Answer:
72
Step-by-step explanation:
Triangle area formula: A = 1/2 (B) (H)
This means the area of a triangle is half of the base times the height.
So we can plug the numbers into the formula:
A = 1/2 (16) (9)
16 x 9 is 144, divided by 1/2 is 72.
Final answer 72.
help pls it’s due soon :/
Chord AB subtends two arcs with measures in the ratio of 1:5. Line PQ is tangent
to the circle at point B. Find the measure of the angle between the tangent and secant AB.
Answer:
acute: 30°obtuse: 150°Step-by-step explanation:
The angle between the secant and the tangent will be half the measure of the intercepted arc. The two intercepted arcs total 1+5=6 ratio units and 360°. That means each ratio unit represents 60° of arc. The two arcs are 60° and 300°.
Then the two angles at the tangent and secant are ...
60°/2 = 30° . . . . . . . the one marked in the attache drawing
300°/2 = 150°
For each value of x determine whether it is a solution
Hey !
Question :For each value of x determine whether it is a solution to 45 = -9 ( x + 5 )
Given :In the question we have given an equation i.e. :
45 = -9 ( x + 5 )In the question values of x are also given i.e. :
5-71-4To Determine :In this question we have to determine whether given value of x are solution fo the given equation or not .
How we have to solve this question :We are solving this question by substituting given value of x in the equation if equation satisfied then it means that the value for x is solution of the equation .
So Let's get started :1) Value of x as 5 :
45 = -9 ( x + 5 ) ( Given Equation )Now substituting value of x as 5 :
45 = -9 ( 5 + 5 )45 = -9 ( 10 )45 = -90But , 45 is not equal to -90Therefore , 5 is not the solution for equation .
2) Value of x as -7 :
45 = -9 ( x + 5 ) ( Given Equation )Now substituting value of x as -7 :
45 = -9 ( -7 + 5 )45 = -9 ( -2 )45 = 18But , 45 is not equal to 18Therefore , -7 is not the solution for equation .
3) Value of x as 1 :
45 = -9 ( x + 5 ) ( Given Equation )Now substituting value of x as 1 :
45 = -9 ( 1 + 5 )45 = -9 ( 6 )45 = -54But , 45 is not equal to -54Therefore , 1 is not the solution for equation .
4) Value of x as -4 :
45 = -9 ( x + 5 ) ( Given Equation )Now substituting value of x as -4 :
45 = -9 ( -4 + 5 )45 = -9 ( 1 )45 = -9But , 45 is not equal to -9Therefore , -4 is not the solution for equation .
So ,In there is no proper value of x that can be solution of the given equation .[tex] Keep \: Learning[/tex]
Convert (1, 1) to polar form.
OA (2, 45°)
OB. (1,45°)
OC. (2,225)
OD. (2.459)
[tex](\sqrt{2}{, 45^{\circ})[/tex]
============================================================
Explanation:
The original point is in cartesian form (x,y). We have x = 1 and y = 1 pair up together.
The radius is [tex]r = \sqrt{x^2+y^2} = \sqrt{1^2+1^2} = \sqrt{2}[/tex]
The angle theta is [tex]\theta = \tan^{-1}(y/x) = \tan^{-1}(1/1) = 45^{\circ}[/tex]
Therefore, the polar form is [tex](r, \theta) = (\sqrt{2}, 45^{\circ})[/tex]
The idea is to start at the origin while facing directly east at the angle 0 degrees. Then turn 45 degrees to the north (going counterclockwise) and then move [tex]\sqrt{2}[/tex] units away from the origin. Doing these steps will take you to the point (x,y) = (1,1)
100 points! Please help find the direction!
The direction will be resultant
A=11iB=20i+9√3jNow
R=√A²+B²+2ABcos60R=√(11i)²+(20i+9√3j)²+2(11i)(20+9√3j)(1/2)R=√1155.5R≈33.98°Write the point-slope form of a line that has slope −7 and passes through the point (4, 8)
Answer:
y = -7x + 36
Step-by-step explanation:
Point-slope form: y - y1 = m(x - x1)
y1 = y-value of a point on a linem = slopex1 = x-value of a point on a lineSubstitue 8 for y1, and 4 for x1, and -7 for m:
y - y1 = m(x - x1)
y - 8 = -7(x - 4)
Solve:
y - 8 = -7(x - 4) <== distribute -7
y - 8 = -7x + 28 <== add 8 to both sides
+ 8 + 8
y = -7x + 36
Therefore, the point-slope of the line is y = -7x + 36
Check your answer using (4, 8):
y = -7x + 36
8 = -7(4) + 36
8 = -28 + 36
8 = 8
This statement is correct
Hope this helps!
Find the degree of this polynomial. 19x^9-2x^6+9x^5
Answer:
Step-by-step explanation:
The degree of a polynomial is the variable (in this case 1 variable) raised to the highest power.
Look at the first term: 19x^9
The variable is x
The highest power is 9
So the answer is 9.
Find the volume of the prism please help and hurry
Answer:
volume is 360 i hope i uelped u
Kevin and Randy Muise have a jar containing 63 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $7.35. How many of each type of coin do they have?
Answer:
About 0.1
Step-by-step explanation:
If you divide 7.35 by 63, you get about 0.1.
⭐ Question
I have 30 red marbles, 28 blue marbles, 13 green marbles, and 6 magenta marbles.
What is the probability I pull 3 blue marbles? Write as a fraction, no need to simplify.
Answer:
im thinking that is 3/74 because i count them
Step-by-step explanation:
3/74 rhe answer but 3/77 are wrong he just thinking
Answer:
3 over 77, 3/77
Step-by-step explanation:
You add up all of the marbles. (including the blue ones)
30+28+13+6 = 77.
So. You have a 3/77 chance of pulling a blue marble.
A,B,C,D are points on the circumference of a circle centre o
ed is a tangent to the circle
angle odb = 25
work out angle bad
The points A,B,C,D make up the circumference of the circle
The measure of angle BAD is 65 degrees
How to determine the measure of angle BAD?The measure of angle ODB is given as:
ODB = 25 degrees
Considering the triangle BOD, we have:
ODB + BOD + DBO = 180
Where:
ODB = DBO = 25
So, we have:
25 + BOD + 25 = 180
Solve for BOD
BOD = 130 degrees
The angle at an arc is twice the angle at the circumference.
So, we have:
BOD = 2 * BAD
Substitute 130 for BOD
130 = 2 * BAD
Divide both sides by 2
65 = BAD
Hence, the measure of angle BAD is 65 degrees
Read more about angle measures at:
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Help please, not sure how to do this....
Answer:
[tex]4\sqrt{2b}[/tex]
Step-by-step explanation:
[tex]\sqrt{98b}-\sqrt{72b}+\sqrt{18b}[/tex]
Apply radical rule [tex]\sqrt{ab} =\sqrt{a} \sqrt{b}[/tex]:
[tex]\implies \sqrt{98}\sqrt{b} -\sqrt{72}\sqrt{b} +\sqrt{18}\sqrt{b}[/tex]
Factor out common term [tex]\sqrt{b}[/tex]:
[tex]\implies \sqrt{b}(\sqrt{98} -\sqrt{72}+\sqrt{18})[/tex]
Rewrite 98, 72 and 18:
[tex]\implies \sqrt{b}(\sqrt{49 \cdot 2} -\sqrt{36 \cdot 2}+\sqrt{9 \cdot 2})[/tex]
[tex]\implies \sqrt{b}(\sqrt{49}\sqrt{2} -\sqrt{36}\sqrt{2}+\sqrt{9}\sqrt{2})[/tex]
[tex]\implies \sqrt{b}(7\sqrt{2} -6\sqrt{2}+3\sqrt{2})[/tex]
Factor out common term [tex]\sqrt{2}[/tex]:
[tex]\implies \sqrt{b}\sqrt{2}(7 -6+3)[/tex]
[tex]\implies \sqrt{b}\sqrt{2}(4)[/tex]
[tex]\implies 4\sqrt{2b}[/tex]
help me help me me hel
NO LINKS!
Bob knew that he was standing 50 feet from the base of a flag pole and was looking up at a 25° angle. How tall the flag pole?
Perpendicular we need(Let it be P
Base=B=50ftSo
[tex]\\ \rm\Rrightarrow tan\theta=\dfrac{Perpendicular}{Base}[/tex]
[tex]\\ \rm\Rrightarrow tan25=\dfrac{P}{50}[/tex]
[tex]\\ \rm\Rrightarrow P=50tan25[/tex]
[tex]\\ \rm\Rrightarrow P=23.31ft[/tex]
Q
Match the definition on the left to its corresponding geometric figure on the right
A zero-dimensional object that defines a specific location on a plane
A one-dimensional figure, which extends without end in two
directions
A finite section of a line between any two points that lie on the line
A half-line that begins at one point and goes on forever in one
R
direction
A two-dimensional surface that continues infinitely
Point: is a zero-dimensional object that defines a specific location on a plane. Also, it's represented by using a small dot.
What is a geometric figure?A geometric figure can be defined as the forms of different dimensional objects that are formed through a combination of lines, planes or points.
In Geometry, the following terminologies and definitions are used to describe a geometric figure:
Point: is a zero-dimensional object that defines a specific location on a plane. Also, it's represented by using a small dot. ⇒Image 4.Line: is a one-dimensional figure which extends without end in two (2) directions. ⇒Image 5.Line segment: is a finite section of a line that exist between any two (2) points that lie on the line. ⇒Image 1.Ray: is a half-line that starts at one (1) point and goes on infinitely (forever) in one (1) direction. ⇒Image 3.Plane: is a two-dimensional surface that continues infinitely (forever). ⇒Image 2.Read more on lines here: https://brainly.com/question/1655368
Omar paid $23.60 for 29.5 centimeters of wire. Find unit price in dollars per centimeter
Answer:
$0.80
Step-by-step explanation:
$23.60 divided by 29.5cm = $0.80 per cm.
Can someone help me super fast? The answers are (m+5n) (m-n) and (a+4b) (a-3b) I just need to know how to get them cuz my calculations aren't working
Let's see
#1
(m+5n)(m-n)m(m-n)+5n(m-n)m²-mn+5nm-5n²m²+4n-5n²#2
(a+4b)(a-3b)a(a-3b)+4b(a-3b)a²-3ab+4ab-12b²a²+ab-12b²Please help for brainliest :(
Given the figure below, find the values of x and z.
Answer:
Below in bold.
Step-by-step explanation:
z = 87 degrees ( vertical angles)
9x - 87 = 180 - z ( adjacent angles are supplementary)
9x - 87 = 180 - 87
9x = 180
x = 20 degrees.
Amanda and her little brother each throw a model airplane at the same time, but from different heights on the playground. The functions h(x) = -16x2 + 24x + 40 and g(x) = -16x2 + 10x + 21 represent the heights of Amanda's plane and her brother's plane, respectively, x seconds after the planes are thrown.
Which of the following statements is true?
Amanda's brother's model airplane will stay in the air for 3 seconds longer than Amanda's model airplane.
Amanda's brother's model airplane will touch ground 2 seconds earlier than Amanda's model airplane.
Amanda's model airplane will touch ground 4 seconds earlier than Amanda's brother's model airplane.
Amanda's model airplane will stay in the air for 1 second longer than Amanda's brother's model airplane.
13. Use the graph of a piecewise function with three equations. 25,000 $21,197 20,000 15,000 Tax 10,000 $5.448 -5,000 $1,045. 0 80,000 20,000 $10,450 40,000 60,000 $39,800 Taxable Income 100,000 S102,800 a. A taxpayer has a taxable income of $39,800. What is her tax? b. A taxpayer will owe $21,197. What is his taxable income?
Answer:
A. $5,448
B. $102,800
If you need the rest of the parts:
C. $4,500
D. $20,500
E. $68,000
The income tax of $5,448.
The taxable income is $102,800
What is Income Tax?The tax that is imposed on all people and corporations is called income tax. The amount of individual income taxes is determined by the individual's income. Because the burden is assumed to fall on the payers, it is typically characterised as a direct tax. Corporate income tax is charged on net profits, which are determined as the difference between allowable costs and receipts.
From the graph,
it can be observed that the taxpayer who has the taxable income of $39,800 has to pay income tax of $5,448.
Also, a taxpayer owing $21,197 means that he has to pay income tax of $21,197.
His taxable income is $102,800 as shown in the graph below.
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order to estimate the average time spent on the computer terminals per student at a university, data were collected for a sample of 81 business students over a one week period. Assume the population standard deviation is 1.8 hours. With a 0.95 probability, the margin of error is approximately a. 0.20 b. 0.39 c. 1.96 d. 1.64
Using the z-distribution, as we have the standard deviation for the population, the margin of error is given by:
b. 0.39.
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the sample.The margin of error is given by:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
As for the other parameters, we have that [tex]\sigma = 1.8, n = 81[/tex].
Hence, the margin of error is given by:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]M = 1.96\frac{1.8}{\sqrt{81}}[/tex]
[tex]M = 0.39[/tex]
Hence option b is correct.
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HELPPP PLSSSS THE PYTHAGOREAN THEOREM
Answer:
Step-by-step explanation:
a²+b² = c² c is always the longest line thats opposite to the 90 degree angle
for 1
15² + b² = 17²
b² = 17² - 15²
b = √(17² - 15²)
b= 8
A babysitter charges a rate of $15 per hour. how long was the babysitter there if she makes 40
Answer:
2.7
Step-by-step explanation:
15/1 = 40/x
Cross multiply: 40/15
Divide: 2.66
Round up: 2.7
2.7 times 15= 40.5
Answer:
2hrs. 40mins.
Step-by-step explanation:
A babysitter charges a rate of $15 per hour. How long was the babysitter there if she makes $40?
x = hours she babysat
Equation:
15x = 40
Divide to isolate x:
15x = 40
/15 /15
x = 8/3 hrs.
Now, we convert into hours and minutes, since she did work for more than an hour, to earn the $15 each hour.
We know that there are 60 mins. in an hour
60 * 8/3
480/3
160 mins.
Convert into hour and mins:
1 hr. = 60 mins
160/60 = 2 40/60 ==> 2 2/3
Convert 2/3 into mins to add to the hours:
60 * 2/3
120/3 = 40
2hrs. + 40 mins.
2hrs. and 40mins
Therefore, the babysitter was there for 2hrs. 40mins.
Hope this helps!
6. Sam scored 12 points on a math quiz, and he scored 3 points fewer than Alicia. Write an
equation for this situation, and find Alicia's score.
Step 1: Determining and using scale factors The Empire State Building is just over 1,450 feet tall. In anticipation of visiting this landmark on your vacation, you create a model of it using blocks. b) Suppose you are making a model where one block represents 5 feet. About how many blocks tall is your model of the Empire State Building? What is the scale factor? (2 points) What is the scale factor? About how many blocks tall is your model of the Empire State Building?
(no joke answer and no links please)
Answer:
See below ↓↓
Step-by-step explanation:
About how many blocks tall is your model of the Empire State Building?
Divide the actual height by the unit height of a block⇒ 1,450 / 5⇒ 290 blocksWhat is the scale factor?
Height of block model = 5 ftHeight of empire state building (actual) = 1,450 ftScale factor = Actual : modelScale factor = 5 : 1,450 = 1 : 290. What is 1- 87+23
What is 5- 700÷7
Step-by-step explanation:
[tex]1 - 87 + 23 \\ = - 86 + 23 \\ = - 63 \\ \\ \\ \\ 5 - 700 \div 7 \\ = 5 - 100 \ \\ = - 95[/tex]
hope it helps ..
If your net pay, after a $142.00 automatic withdrawal, is $2,665.00, what percent of your net pay was withdrawn?
Answer:
Net pay = $142 + $2665 = $2807
Percent withdrawn = (withdrawal ÷ net pay) × 100%
= (142 ÷ 2807) × 100%
= 5.058781617...%
= 5.1% (nearest tenth)
The area of Elizabeth's garden is 60 square
7 feet. The garden has a width of 5 feet as
shown in the diagram.
?
5 feet
What is the length, in feet, of the garden?
205 ft as lenght
Step-by-step explanation:
First i multiplyed 60x7 nd got 420. Then i subtracted 10 from 420 and got 410. Next i divided 410 by 2 and got 205 ft.