Answer:
D
Step-by-step explanation:
It's d because it has the highest x value. The higher x value is the farther it is from the y-axis
MATHEMATICS
SECTION A (VERY SHORT ANSWERS)
1. Which of the following is irrational?
a V25
V12
b. Vs
c.
V3
2. V768 in its simplest form is:
dve
16
a.
16 V3
b. 64 V3 c.4 V3
d. 8 V3
3. The simplest rationalisation factor of 27 is:
a. b. 73
c. 27
d. 3
4. If x=2 and y = 3, then the value of xy + yt is:
a. 15
b. 17
c. 19
d. 21
a
2
5. The value of [ 8-43 + 22/12 is:
b. 2 ch d. 4
6. If p(x) = x2 – 3x + 2, then what is the value of p(0) + p(2).
7. Find the value of k, if (2x - 1) is a factor of the polynomial 6x2 + kx - 2.
8. Expand (x - y)
9. If x11 + 101 is divided by (x + 1), then what remainder do we get?
10. Find the value of x2 + 3, if(x - 5) = 13
SECTION B (SHORT ANSWERS
11. Express 0.123 in the form where p and q are integers and qf0
9
√7-√6
12. Rationalise the denominator of
√ + √6
13. Find the value of x if
&2x
14. If x2 + = 7 then find x3 +
15. If x + y + z = 10 and x2 + y2 + z = 40 find xy + y2 + zx and x3 + y + z3 - 3xyz
16. Factorize 8x3 - (2x - y)3
81
16
In 2008, golfer Annika Sornestam had a driving accuracy of 71%. That is, on par 4 and par 5 holes, her tee shot landed in the fairway 71% of the time. Explain how to use a spinner to simulate Sorenstam’s performance in a round of golf where she attempts 15 drives. (Hint: What type of chart is a spinner? What does each piece represent?)
Answer:
Ok, we know that the driving accuracy is of 71%.
Then the first step is to get a spinner that is enumerated from 1 to 100 (in such way that each number is equispaced)
Now, we can mark a section between numbers 1 and 71. (this regio represents the cases where the shot lands in the fairway) and the unmarked region represents the cases where the shot does not land in the fairway.
Now, for each shot, we can spin our spinner next to a fixed pencil, depending on the section of the spinner that is marked by the pencil when the spinner fully stops, we can guess if the shot landed or not in the fairway.
In this way the shot has the region from 1 to 71 (71%) to land in the fairway
and the region from 72 to 100 to not land in the fairway.
If you want to simulate Sorenstam’s performance in a round of golf where she attempts 15 drives, you need to spin the spinner 15 times, and record the oucomes.
The area of a square of side 2.4 cm is
Answer:
area of cube = a^2 ( a is side)
2.4^2 = 5.76 cm^2
Answer:
5.76 cm^2
Step-by-step explanation:
Hey there!
Well if the side length is 2.4 cm then the area would be,
A = l•l
A = 2.4 • 2.4
A = 5.76cm^2
Hope this helps :)
Claire and Richard are both artists who use square canvases. Claire
uses the polynomial 50%? + 250 to decide how much to charge for her paintings
and Richard uses the polynomial 40x² + 350 to decide how much to charge for
his paintings. In each polynomial, x is the height of the painting in feet.
a. How much does Claire charge for a 20-foot-tall painting?
b. How much does Richard charge for a 15-foot-tall painting?
c. To the nearest tenth, for what height will both Claire and Richard charge
the same amount for a painting? Explain how to find the answer.
d. When both Claire and Richard charge the same amount for a painting,
how much does each charge?
Answer:
A. [tex]Claire = 20250[/tex]
B. [tex]Richard = 9350[/tex]
C. Height = 3.2 feet
D. Charges = $760
Step-by-step explanation:
Given
[tex]Claire = 50x^2 + 250[/tex]
[tex]Richard = 40x^2 + 350[/tex]
Solving (a): Claire's 20ft charges
In this case, x = 20
Substitute 20 for x in [tex]Claire = 50x^2 + 250[/tex]
[tex]Claire = 50(20)^2 + 250[/tex]
[tex]Claire = 50(400) + 250[/tex]
[tex]Claire = 20000 + 250[/tex]
[tex]Claire = 20250[/tex]
Solving (b): Richard's 15ft charges
In this case, x = 15
Substitute 20 for x in [tex]Richard = 40x^2 + 350[/tex]
[tex]Richard = 40(15)^2 + 350[/tex]
[tex]Richard = 40(225) + 350[/tex]
[tex]Richard = 9000 + 350[/tex]
[tex]Richard = 9350[/tex]
Solving (c): Height which they both charge the same;
This implies that
[tex]50x^2 + 250 = 40x^2 + 350[/tex]
Solving for x [Collect Like Terms\
[tex]50x^2 - 40x^2 = 350 - 250[/tex]
[tex]10x^2 = 100[/tex]
Divide both sides by 10
[tex]x^2 = 10[/tex]
Take square roots of both sides
[tex]x = \sqrt{10}[/tex]
[tex]x = 3.2ft[/tex] (Approximated)
Hence; Height = 3.2 feet
Solving (d): How much they charge when the charge the same amount.
Substitute 3.2 for x in any of the given equation
[tex]Claire = 50x^2 + 250[/tex]
[tex]Claire = 50(3.2)^2 + 250[/tex]
[tex]Claire = 50*10.24 + 250[/tex]
[tex]Claire = 512 + 250[/tex]
[tex]Claire = 762[/tex]
[tex]Richard = 40x^2 + 350[/tex]
[tex]Richard = 40(3.2)^2 + 350[/tex]
[tex]Richard = 40 * 10.24 + 350[/tex]
[tex]Richard = 409.6 + 350[/tex]
[tex]Richard = 759.6[/tex]
The reason for the difference is due to approximation
Hence, they both charge approximately 760
Dante is baking two different recipes, cookies and brownies. The cookie recipe requires 1.5 cups of sugar, and the brownie recipe requires 1.25 cups of sugar. Write an addition equation to represent the total amount of sugar Dante needs. Enter your answer as an addition equation, like this: 42+(-53)=-11
Answer:
2.75 cups of sugar
Step-by-step explanation:
Hello!
To find the total amount of sugar Dante needs we need to add the amount need for each recipe
Cookie recipe needs 1.5 cups
Brownie recipe needs 1.25 cups
1.5 + 1.25 = 2.75 cups of sugar
The answer is 2.75 cups of sugar
Hope this helps!
Answer:
the answer is 1.5+1.25=1.75
Step-by-step explanation:
i just added them together
your welcome ( it also depends on how many times he uses the recipes)
what is the coefficient of x in the equation of 32+2x=10
solve after finding the coefficient
Answer:
x= -11
Step-by-step explanation:
the coefficient is variable that appears before a number . bearing this in mind, the coefficient of x is therefore 2 .
the value of x is:
>32+2x=10
>2x=10-32
>2x= -22
>x= -11
Answer:
Step-by-step explanation:
Coefficient of x = 2
32 + 2x = 10
Subtract 32 from both side
32 + 2x -32 = 10 - 32
2x = - 22
Divide both sides by 2
2x/2 = -22/2
x = -11
Hey there please help me with this question
Answer:
see explanation
Step-by-step explanation:
sum the parts of the ratio, 2 + 1 = 3 parts , thus
81 cm² ÷ 3 = 27 cm² ← value of 1 part of the ratio
2 parts = 2 × 27 = 54 cm²
Area of A = 54 cm² and area of B = 27 cm²
The side of the original square = [tex]\sqrt{81}[/tex] = 9 cm
The width of both rectangles is 9 cm ( width remains unchanged after cut )
Thus
Rectangle A
9 × length = 54 ( divide both sides by 9 )
length = 6 cm
Rectangle B
9 × length = 27 ( divide both sides by 9 )
length = 3 cm
Rectangle A → length = 6 cm, width = 9 cm
Rectangle B → length = 3 cm , width = 9 cm
Answer:
Rectangle A Rectangle B
length = 9 cm length = 9 cm
width = 6 cm width = 3 cm
Step-by-step explanation:
Area of square At = 81 cm²
Square is cut into two pieces = A + B
The ration of area A to B = 2:1
Find
Rect A Rect B
length length
width width
---------------------------------
first, get the side of the square = A = s²
81 = s²,
s = √81
s = 9 cm
since the ratio is 2:1, therefore the side can be divided into 3
9 ÷ 3 = 3 cm ----- take note of this to get the Width
Rectangle A
L = 9 cm (which is the s = 9 cm)
W = 3 cm (2 ratio) = 6 cm
Rectangle B
L = 9 cm (which is the s = 9 cm)
W = 3 cm (1 ratio) = 3 cm
Proof:
At = A + B
81 = (9x6) + (9x3)
81 = 54 + 27
81 = 81 ----- OK
Kim is y years old. Jasper is twice as old as Kim, or 2y years old. Lorenzo is 2 years older than Jasper, or (2y + 2) years old. Finally, Vinnie is 9 years old. The sum of their ages is y + 2y + (2y + 2) + 9. What is an equivalent way to write this expression?
Answer:
5y+11
Step-by-step explanation:
y+2y+2y+2+9
5y+11
An orchardist is to plant apple trees and pear trees in the ratio 3:11. If he intends to plant 150 apple trees, how many pear trees will he need to plant?
The ratio 2:11 means for every 3 apple trees they will plant 11 pear trees.
They are planting 150 apple trees. Divide total apple trees by the ratio: 150/3 = 50
Multiply that by the ratio of pear trees:
50 x 11 = 550
They need to plant 550 pear trees.
it a cycle is sold for rs 17250 there is again of rs 2250. what is the gain percentage
Answer:
15%
Step-by-step explanation:
profit=sp -cp
cp=sp-profit
=17250-2250
=15000
profit%= profit amount/cp *100%
=2250/15000×100
= 15
Answer:
[tex] \boxed{ \boxed{ \sf{ \bold{ \purple{15\%}}}}}[/tex]Step-by-step explanation:
Given,
SP ( Selling price ) = Rs 17250
Profit ( P ) = Rs 2250
CP ( Cost price ) = Rs 17250 - Rs 2250 = Rs 15000
Now, let's find the profit / gain percentage :
Profit % = [tex] \sf{ \frac{profit}{cost \: price} \times 100\%}[/tex]
plug the values
⇒[tex] \sf{ \frac{2250}{15000} \times 100\%}[/tex]
Calculate
⇒[tex] \sf{15\%}[/tex]
-----------------------------------------------------------------
▪[tex] \underline{ \underline{ \sf{ \blue{What \: is \: the \: formula \: to \: find \: profit \: percent \: and \: loss \: percent?}}}}[/tex]
We know that , profit and loss are calculated on cost price ( CP ). So, profit percent and loss percent can be calculated by using the following formula :
[tex] \boxed{ \sf{Loss\% \: = \frac{cp - sp}{cp} \times 100\%}}[/tex]
[tex] \boxed{ \sf{ \bold{Profit\% \: = \: \frac{sp \: - \: cp}{cp} \times 100}}}[/tex]
Hope I helped!
Best regards!!
HELP!!!
The solutions to (x + 3)^2- 4=0 are x = -1 and x = -5
True or false
Answer:
False
Step-by-step explanation:
We can simplify this equation and then solve for x.
[tex](x+3)^3-4=0\\\\x^2+6x+9-4=0\\\\x^2+6x+5=0\\\\(x+2)(x+3)=0\\\\x=-3\\x=-2[/tex]
As you can see, the solutions are not x=-1 and x=-5.
Therefore, the answer is false.
Answer:
True
Step-by-step explanation:
Given
(x + 3)² - 4 = 0 ( add 4 to both sides )
(x + 3)² = 4 ( take the square root of both sides )
x + 3 = ± [tex]\sqrt{4}[/tex] = ± 2 ( subtract 3 from both sides )
x = - 3 ± 2
Thus
x = - 3 - 2 = - 5
x = - 3 + 2 = - 1
On a coordinate plane, parallelogram H I J K is shown. Point H is at (negative 2, 2), point I is at (4, 3), point J is at (4, negative 2), and point K is at (negative 2, negative 3). HIJK is a parallelogram because the midpoint of both diagonals is __________, which means the diagonals bisect each other
Answer: HIJK is a parallelogram because the midpoint of both diagonals is (1,0) , which means the diagonals bisect each other.
Step-by-step explanation:
Given: The coordinates of parallelogram H I J K as
H is at (- 2, 2), point I is at (4, 3), point J is at (4, - 2), and point K is at (- 2, - 3).
Diagonals : HJ and IK [join opposite vertices]
Mid point of HJ = [tex](\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]
[tex]=(\dfrac{-2+4}{2},\dfrac{2+(-2)}{2})=(1,0)[/tex]
i.e. Mid point of HJ = (1,0)
Mid point of IK = [tex](\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]
[tex]=(\dfrac{4+(-2)}{2},\dfrac{3+(-3)}{2})=(1,0)[/tex]
i.e. Mid point of IK = (1,0) =Mid point of HJ
When mid points of both diagonals are equal then that means the diagonals bisect each other.
Thus, HIJK is a parallelogram because the midpoint of both diagonals is (1,0) , which means the diagonals bisect each other.
Answer:
(1,0)
Step-by-step explanation:
Solve the triangle. A = 51°, b = 14, c = 6, I'll give 20 points
Answer:
Step-by-step explanation:
We have that
A = 51°, b = 14, c = 6
step 1
find the value of a
Applying the law of cosines
a²=c²+b²-2*c*b*cos A
a²=6²+14²-2*6*14*cos 51-------> 126.27
a=11.2
we know that
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
we have
a=11.2
b=14
c=6
so
(a+b) > c-------------> (11.2+14)=25.2
25.2 > 6-----> is not correct
therefore
the answer is the option
a. No triangles possible
I don't know if i am right sorry if this is wrong
If L is the line having x -intercept of -1 and y -intercept of 3, complete the equation of L . y = -x + 3 y = -3x + 3 y = 3x + 3
Answer:
y = 3x + 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, 3) ← x and y- intercepts
m = [tex]\frac{3-0}{0+1}[/tex] = [tex]\frac{3}{1}[/tex] = 3
The line crosses the y- axis at (0, 3) ⇒ c = 3
y = 3x + 3 ← equation of line
An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 3028 feet and Plane B is at an altitude of 4000 feet. Plane A is gaining altitude at 55.75 feet per second and Plane B is gaining altitude at 35.5 feet per second. How many seconds will pass before the planes are at the same altitude? seconds What will their altitude be when they're at the same altitude? feet
Consider plane A with respect to B,
initial relative Altitude [tex] h_{a, b}=h_a-h_b=-972 [/tex]
relative rate of altitude(speed) $r_{a,b}= 55.75-35.5=20.25$
To get at same altitude, they'll take same time, and their relative height will be $0$ So,
$H_{a,b}=h_{a,b}+r_{a,b}t$
$0=-972+20.25t$
$t=48$
and altitude will be, $3028+55.75\cdot 48=5704$
Answer:
48 seconds5704 feetStep-by-step explanation:
We can write equations for the altitude of each plane:
A(t) = 3028 +55.75t . . . . . initially at 3028 ft; gaining at 55.75 ft/s
B(t) = 4000 +35.5t . . . . . initially at 4000 ft; gaining at 35.5 ft/s
The two altitudes will be equal when ...
A(t) = B(t)
3028 +55.75t = 4000 +35.5t . . . . substitute the expressions for A and B
20.25t = 972 . . . . . . subtract 3028+35.5t
t = 48 . . . . . . . . . . . . divide by 20.25
The common altitude will be ...
B(48) = 4000 +35.5(48) = 5704 . . . . feet
The planes will both be at an altitude of 5704 feet after 48 seconds.
ASAP!!! PLEASE help me solve this question! No nonsense answers, and solve with full solutions.
Answer:
Option (4)
Step-by-step explanation:
By the theorem of inscribed angles and the intercepted arc,
"In a circle, angles subtended by the same arc always measure the same and the arc measures the double of the inscribed angle."
If an inscribed angle in a circle measures 75° then all inscribed angles by the same arc will measure 75°.
In addition to this, measure of arc subtended by these inscribed angle will measure double of the inscribed angle (150°)
Therefore, Option (4) will be the answer.
The braking distance, D, of a car is directly proportional to the square of its speed, v. When d=5, v=10
Find d when v=70
Answer:
d = 245Step-by-step explanation:
d is directly proportional to the square of a speed v
d = av²
5 = a•10²
5 = 100a
a = 0.05
d = 0.05v²
d = 0.05•70²
d = 0.05•4900
d = 245
PLEASE help me solve this question! This is really URGENT! No nonsense answers please.
Answer:
[tex]\boxed{\sf 6.4 \ seconds}[/tex]
Step-by-step explanation:
t = time (s) ⇒ ?
d = distance falling (m) ⇒ 200 (m)
a = acceleration due to gravity ⇒ 9.8 (m/s²)
The time in seconds is not given. Solve for time using the formula.
[tex]t=\sqrt{\frac{2(200)}{9.8} }[/tex]
[tex]t=\sqrt{\frac{400}{9.8} }[/tex]
[tex]t= 6.388766...[/tex]
Round answer to nearest tenth of a second.
[tex]t \approx 6.4[/tex]
Point B lies between points A and C, and all three points lie on point AC, which of the following is not true? A. Point B lies on segment AC B. Point C lies on ray AB C. Point A lies on ray BC D. Point C lies on line AB
Answer:
C. Point A lies on ray BC
Step-by-step explanation:
Points A and C can be connected by a segment which would be a measure of the distance between the points. Locating point B between AC, makes the three points lying on segment AC.
A ray extends from a point to infinity, a line extend to infinity on both sides, while a segment is known to have two endpoints. Therefore, points AC are the end points of the segment AC, and point B between this segment confirms that point B lies on the segment AC. Therefore, Point A lies on ray BC is not correct.
11 Points Estimate the average by first rounding to the nearest 1,000: 1,000 2,300 2,600
Answer:
Average = 2000
Step-by-step explanation:
Given numbers are:
1,000 2,300 2,600
To find:
First round off the numbers to nearest 1000 and then find Average.
Solution:
1000 is already in thousands so no need to round off.
To round off a number to nearest thousand, we need check the digit on hundred's place.
If the hundred's digit is greater than 5, we increase the thousand's digit by 1 and make the hundred's digit as 0.If the hundred's digit is lesser than 5, the thousand's digit remains the same and we make the hundred's digit as 0.So, 2300 will be rounded off as 2000.
and 2600 will be rounded off as 3000.
Now, the numbers whose average is to be calculated are 1000, 2000, 3000.
Formula for average is given as:
[tex]Average = \dfrac{\text{Sum of all numbers}}{\text{Count of numbers}}[/tex]
applying the formula:
[tex]Average = \dfrac{1000+2000+3000}{3}\\\Rightarrow Average = \dfrac{6000}{3}\\\Rightarrow \bold{Average = 2000}[/tex]
So, the average after rounding off to nearest 1000 is 2000.
Find the length of AB
Answer:
AB = 3π
Step-by-step explanation:
The formula for the circumference of a circle is:
C = 2πr
By substituting 27 for r:
C = 2π(27)
C = 54π
The whole circumference is 54π. A circle is 360º around. We can set up a proportion to find the length of the 20º arc:
[tex]\frac{360}{54p}[/tex] = [tex]\frac{20}{x}[/tex]
Cross-multiply:
360x = 1080π
Divide both sides by 360:
x = 3π
AB = 3π
Answer:
AB = 3π
Step-by-step explanation:
The arc AB can be calculated as
AB = circumference of circle × fraction of circle
The central angle is equal to the measure of arc AB = 20° , thus
AB = 2πr × [tex]\frac{20}{360}[/tex]
= 2π × 27 × [tex]\frac{1}{18}[/tex] ( cancel 18 and 27 by 9 )
= 2π × 3 × [tex]\frac{1}{2}[/tex] = 6π × [tex]\frac{1}{2}[/tex] = 3π
Pluto is 2.7 times 10 to the power of 9 miles from the sun. Venus is 6.7 times 10 to the power of 7 miles from the sun. How mnay times greater is the distance of pluto to the sun than venus
Answer:here for the comments
Step-by-step explanation:
Answer:
The answer is 40.3 times greater
Step-by-step explanation:
If the Cost price of the an article is greater than the selling price, we have a ____?
Answer:
loss
Step-by-step explanation:
Selling an item for less than was paid gives a loss
Selling an item for more than was paid gives a profit
Solve: 3a^2-4b a= -6 b= -5 If you could also leave an explanation that would be great! Thank you for your time!
Answer:
128
Step-by-step explanation:
3a² - 4b
plug in values
3(-6)² - 4(-5)
use PEMDAS and simplify (-6)² first
3(36) -4(-5)
multiply
108 + 20
add
128
hope this helps :)
The figure below shows a parallelogram ABCD Side AB parallel to side DC and side AD is parallel to side BC A student wrote the following sentences to prove that parallelogram ABCD has two pairs of opposite sides equal For triangles and COB alternate interior angle ABD is congruent to angle CDB because AB and DC are parallel lines Similarly interior angle equal to angle CBD because AD and are parallel lines equal to DB by the reflexive property Therefore , triangles ABD and COB are congruent by the SAS postulate Therefore AB congruent to and AD congruent BC CPCTC Which statement best describes a flaw in the student's proof ?
Answer:
Second choice
Explanation :
The postulate that is used in order to prove the congruency of the triangles is the ASA which means (Angle – Side – Angle). The property that is applicable for the congruency of DB to itself is the reflexive property. Therefore, the answer to this item is the second choice.
Hope I helped! :)
If yes mark me BRAINLIEST!
Tysm!
Triangles ABD and CDB are congruent to each other by the ASA theorem. The student used SAS which is wrong. The answer is: D.
What is the ASA Theorem?The ASA theorem states that two triangles that have a pair of corresponding included congruent sides and two pairs of corresponding congruent angles are congruent triangles.
Based on the ASA theorem, triangles ABD and CDB are congruent to each other.
Therefore, the use of SAS theorem by the student is wrong.
Learn more about the ASA theorem on:
https://brainly.com/question/2102943
#SPJ6
S(t) = -105t + 945 to determine the salvage value, S(t), in dollars, of a table saw t years after its purchase. How long will it take the saw to depreciate completely? A. 11 years B. 8 years C. 7 years D. 9 years
Answer:
D
Step-by-step explanation:
When something depreciates completely, it will have a total value of 0 dollars. Therefore, set the equation to zero and solve for t to find the years.
[tex]S(t)=-105t+945\\0=-105t+945\\-105t=-945\\t=9[/tex]
Therefore, the table saw will completely depreciate after 9 years.
Answer:
[tex]\large \boxed{\sf \bold{D.} \ 9 \ years}[/tex]
Step-by-step explanation:
[tex]S(t) = -105t + 945[/tex]
For the value to depreciate completely, the amount has to be equal to 0 dollars.
Set S(t) to 0.
[tex]0 = -105t + 945[/tex]
Solve for the time t.
Subtract 945 from both sides.
[tex]0 -945= -105t + 945-945[/tex]
[tex]-945=-105t[/tex]
Divide both sides by -105.
[tex]\displaystyle \frac{-945}{-105}=\frac{-105t}{-105}[/tex]
[tex]9=t[/tex]
It will take 9 years for the saw to depreciate completely.
Factor completely x3 + 8x2 − 3x − 24. (x − 8)(x2 − 3) (x + 8)(x2 + 3) (x − 8)(x2 + 3) (x + 8)(x2 − 3)
Answer:
(x + 8) (x² - 3)
Step-by-step explanation:
Given:
x³ + 8x² - 3x - 24
Find:
Factors
Computation:
x³ + 8x² - 3x - 24
x²(x + 8) -3(x + 8)
(x + 8) (x² - 3)
Factor of the given equation is (x + 8) (x² - 3)
Answer:
(x + 8) (x² - 3)
Step-by-step explanation:
what is nine and forty-two hundredths
Answer:
9.42
Step-by-step explanation:
Breaking the phrase down:
'Nine' would be the number 9 in the ones place.
'And' represents the decimal in a number. ('.')
'Forty-Two Hundredths" is 0.42.
So, "nine and forty-two hundredths" would be 9.42.
Hope this helps.
Draw a line for the axis of symmetry of function f. Also mark the x-intercept(s), y-Intercept, and vertex of the function.
f(x)= x^2- 4x-5
+
10-
Line
8
6
4
2-
-10
-8
Answer:
1) Please find attached the graph sowing the line of symmetry
The symmetry line is a vertical line passing through (2, -9)
2) The x-intercept are (5, 0) and (-1, 0)
The y-intercept is (0, -5)
The vertex is (2, -9)
Step-by-step explanation:
The given function is;
f(x) = x² - 4·x - 5
The data values are generated as follows;
x, f(x)
-1, 0
-0.8, -1.16
-0.6, -2.24
-0.4, -3.24
-0.2, -4.16
0, -5
0.2, -5.76
0.4, -6.44
0.6, -7.04
0.8, -7.56
1, -8
1.2, -8.36
1.4, -8.64
1.6, -8.84
1.8, -8.96
2, -9
2.2, -8.96
2.4, -8.84
2.6, -8.64
2.8, -8.36
3, -8
3.2, -7.56
3.4, -7.04
3.6, 6.44
3.8, -5.76
4, -5
4.2, -4.16
4.4, -3.24
4.6, -2.24
4.8, -1.16
5, 0
The minimum is found from differentiating the function, f(x), with respect to x and looking for the zeros of the result as follows;
f'(x) = 2·x -4
f'(x) = 0 = 2·x -4
x = 2
The y-coordinate gives; f(2) = 2² - 4×2 - 5 = -9
Therefore, the symmetry line is a vertical line passing through (2, -9)
The x-intercept is the point at which y = 0, therefore, from f(x) = x² - 4·x - 5, we have;
0 = x² - 4·x - 5 = (x - 5)·(x + 1)
Therefore, the x-intercept are x = 5 or -1
The x-intercept are (5, 0) and (-1, 0)
The y-intercept occur at the point where the x value = 0, therefore, we have;
The y-intercept occur at y = f(0) = 0² - 4·0 - 5 = -5
The y-intercept is (0, -5)
Re-writing the equation in vertex form y = a(x - h)² + k gives;
f(x) = x² - 4·x - 5 = 1·(x - 2)² - 9
Therefore, the vertex is (2, -9)
Answer:
see attached graph
The x-intercept are (5, 0) and (-1, 0)
The y-intercept is (0, -5)
The vertex is (2, -9)
Step-by-step explanation:
Consider the following system of equations: y=2x−2 6x+3y=2 The graph of these equations consists of two lines that: 1. intersect at more than one point. 2. intersect in an infinite number of points. 3. intersect at exactly one point. 4. do not intersect.
Answer:
3. Intersect at exactly one point. ( (2/3), (-2/3) )
Step-by-step explanation:
To make the comparison of these lines easier, let's rewrite the 2nd equation into slope-intercept form, as the 1st equation is in slope-intercept form.
[1] y = 2x - 2
---------------------
[2] 6x + 3y = 2 ==> 3y = 2 - 6x ==> y = -2x + (2/3)
[2] y = -2x + (2/3)
So now that we have both equations in slope-intercept form, we can see that the two equations are both linear, have different slopes, and have different y-intercepts.
Since these equations have both different slopes and different y-intercepts, we know that the lines will cross at least one point. We can confirm that the lines only cross at a single point using the fact that both equations are linear, meaning there will only be one point of crossing. To find that point, we can simply set the equations equal to each other.
y = 2x - 2
y = -2x + (2/3)
2x - 2 = -2x + (2/3)
4x = (8/3)
x = (8/12) = (2/3)
And plug this x value back into one of the equations:
y = 2x - 2
y = 2(2/3) - 2
y = (4/3) - (6/3)
y = (-2/3)
Thus these lines only cross at the point ( (2/3), (-2/3) ).
Cheers.
Answer:
I don't understand the question
