y = -x² + 9
the x-intercepts are x = - 3 and x = 3 hence the factors are
(x + 3 ) and (x - 3 )
polynomial is the product of its factors
y = a(x - 3 )(x + 3) ← ( a is a multiplier )
from the end behaviour the parabola opens down and is a maximum and so the value of a is negative
y = -(x - 3)(x+3) = - (x² - 9 ) = - x² + 9
The polynomial function with the given features is f(x) = -(x + 3)(x - 3), which is a quadratic function with the required y-intercept, x-intercepts, and end behavior.
Explanation:The question involves finding a polynomial function given certain characteristics: a y-intercept of (0, 9), x-intercepts at (-3, 0) and (3, 0), a degree of 2, and specific end behavior.
Since the degree is 2, we are dealing with a quadratic function.
The x-intercepts tell us that the factors of the polynomial are (x + 3) and (x - 3).
The y-intercept indicates that when x is 0, the function equals 9.
The end behavior suggests that the leading coefficient is -1 because as x goes to infinity or negative infinity, f(x) goes to negative infinity.
Considering all the information, the function can be expressed as:
f(x) = -(x + 3)(x - 3)
To verify, expanding the factors gives:
f(x) = -(x^2 - 9)
f(x) = -x^2 + 9
This function has the required y-intercept of 9, x-intercepts of -3 and 3, and the correct end behavior.
A segment has endpoints (a,b) and (c,d). The segment is translated so that its image is 6 units up and 3 units left of the preimage. Are the two segments parallel, perpendicular, or neither? Also need a picture of the image and preimage, thanks!
Answer:
parallel
Step-by-step explanation:
Translation moves each point the same amount in the same direction. Essentially, the original segment becomes the side of a parallelogram, whose other side is the image, and whose ends are the vectors specifying the translation.
In the attachment, we have designated (a, b) as point A, and (c, d) as point B. We had to choose specific values for these in order to plot them, but the description of the effect of translation applies no matter what the point coordinates are chosen to be.
The price of a round trip ticket to San Francisco increases from $525.00 to $650.00. To the nearest whole percent, what is the percent of increase?
A) 18%
B) 24%
C) 28%
D) 30%
E) 34%
B
to calculate percent increase use
[tex]\frac{increase}{original}[/tex] × 100%
increase = $650 - $525 = $125
percent increase = [tex]\frac{125}{525}[/tex] × 100% = 24% → B
Answer:
The answer is B) 24%
Step-by-step explanation:
The formula for percentage increase is given as:-
Percentage Increase = ( New Price - Old Price ) /old price * 100
old price = $525
New Price = $650
Percentage Increase = 24%
Hence the price increases by 24%
what is 352 divided by 53 please reply to this within a hour im timed....
352 divided by 53 is 6.64150943
Hi TaeArmy23,
352 / 53
= 6.6415
= 6.6
Hope This Helps!
Jillian had
5
6
of a whole and took
3
6
away from it. How much does she have left?
2/6 is remaining from Jillian's whole.
[tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]
Since the denominators of both fractions are common , that is 6
To subtract, subtract the numerators leaving the denominator
[tex]\frac{5}{6}[/tex] - [tex]\frac{3}{6}[/tex] = [tex]\frac{5-3}{6}[/tex] = [tex]\frac{2}{6}[/tex]
This fraction may be simplified by dividing the numerator/ denominator by 2
[tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex] ← in simplest form
The bird population on an island is declining at a rate of 2.2% per year. The population was 3500 in the year 2009.
Which answer is the best prediction of the population in the year 2014?
A 2730
B 3062
C 3132
D 3423
The population is multiplied by 100% -2.2% = 97.8% each year. After 5 years, the population will have been multiplied by this value 5 times, so will be ...
... 3500×0.978⁵ ≈ 3132
The appropriate choice is ...
... C. 3132
Since it's Wednesday, Buy for Less gives a 5% discount for purchases. The items in Rhonda's cart total $53.75. She needs to know the cost of the items with the discount. So, she multiplies 5% times $53.75 and subtracts the amount from $53.75. Which expression would give Rhonda the same result in one step? A) .90(53.75) B) .95(53.75) C) 1.05(53.75) D) 53.75 - .05(53.75)
First we need to know how much the discount was so 5% is actually 0.05 then we need to multiply it by 53.75 which would equal 2.6875 then subtract it by 53.75 which would equal -51.0625.
B) .95(53.75)
This is a trick question because D) could also be correct if they said you could subtract it but it's not saying use the distributive property.
The answer would be B) .95(53.75)
given the function f(x)=3^x, find the value of f^-1(27)
This is asking you to solve the equation ...
... 27 = 3^x
You can use logarithms to find
... log(27) = x·log(3)
... log(27)/log(3) = x = 1.43136376.../0.47712125...
... x = 3
Or, you can use your knowledge of small cubes and match exponents.
... 3^3 = 3^x
... 3 = x
3 and 5 form what type of angle pair? A. corresponding angles B. alternate interior angles C. consecutive interior angles D. alternate exterior angles
Answer:
C. consecutive interior angles
Step-by-step explanation:
The subject angles are between lines a and b, so are interior (not exterior). They are on different corners of the intersection, so are not corresponding. They are on the same side of line c, so are not alternate. The share a side, but not a vertex, so they are consecutive. The appropriate choice is ...
... C. consecutive interior angles
Answer: C. consecutive interior angles
ANSWER = BRAINLIEST
Why does a = 8sin40?
look at the shaded right-angled triangle on the left
8 is the hypotenuse n a is opposite to the 40-degree angle
by definition, sin = opposite side / hypotenuse
so sin40=a/8
rearranging a=8sin40
Two right-angled triangles share a common side with length a.
For the inverted triangle on the left, a is the opposite side to the 40-deg angle.
Its longest side, hypotenuse, is 8cm.
Use the sine function, sin40 = opposite/hypotenuse = a/8
Multiply 8 on both sides, a = 8sin40
solve the system by graphing or using a table.
2x+4y=12
x+y=2
Answer: x = -2 and y = 4
Step-by-step explanation:
We have given a system of equations
2x + 4y =12 ...........(1)
and
x + y = 2 .............(2)
Now to plot them in graph we need to find the points of the above linear equations .
From equation 1 ,we get
[tex]4y=12-2x\\\Rightarrow\ y=\frac{12-2x}{4}\\ \Rightarrow\ y=3-\frac{x}{2}\\\text{Put x=0, then} \\y=3-\frac{0}{2}=3\\\Rightarrow\ \text{Put x=6}\\y=3-\frac{6}{2} =3-3=0[/tex]
So get the points (0,3) and (6,0).
From equation 2 ,we get
[tex]y=2-x\\\text{Put x=0}\\y=2-0=2\\\text{Put x=2}\\y=2-2=0[/tex]
So we get the points (0,2) and (2,0).
So after plotting these points we get two lines intersecting at (-2,4).
Therefore our solution is x=-2 and y= 4.
Answer:
(-2, 4)
Step-by-step explanation:
The straight line joining the points A(3,-5) and B(6,k) has a gradient of 4. Work out the value of k.
The straight line joining the points A(3,-5) and B(6,k) has a gradient of 4.
Gradient is the slope
So the slope of the line joining the points A(3,-5) and B(6,k) is 4
Slope of line joining two points = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
A(3,-5) and B(6,k) are (x1,y1) and (x2,y2)
slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
slope = [tex]\frac{k-(-5)}{6-3}=\frac{k+5)}{3}[/tex]
We know slope =4
[tex]\frac{k+5)}{3}=4[/tex]
Cross multiply and solve for k
k + 5 = 12
k = 7
The value of k = 7
please help!!!
The value of " X " is...
2x + y − z = 3
−x + y + 2z = 0
3x + 2y + z = 9
12
2
3
-4
x = 3
2x + y - z = 3 → (1)
- x + y + 2z = 0 → (2)
3x + 2y + z = 9 → (3)
we require to eliminate the y and z terms from the equations
(1) + (3) : 5x + 3y = 12 → (4)
multiply (1) by 2
4x +2y - 2z = 6 → (5)
(2) + (5) : 3x + 3y = 6 → (6)
(4) - (6) : 2x = 6 ⇒ x = 3
Q # 8 please I need your help
A. -2/3 because you would go down two and then to the right three. I hope that helps.
Solution :
Given ,line that passes through the pair of points (1,7) and (10,1)
The slope of the line passing through the points [tex](x_{1},y_{1} ) \:and \:(x_{2},y_{2})[/tex] is given by,
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Here, [tex](x_{1},y_{1} ) =(1,7)\:and \:(x_{2},y_{2})=(10,1).[/tex]
[tex]\Rightarrow m=\frac{1-7}{10-1} \\\Rightarrow m=\frac{-6}{9}=\frac{-2}{3}[/tex]
Hence , slope of the line passing through the pir of points (1,7) and (10,1) is [tex] \frac{-2}{3}[/tex] ( first option)
HURRYYY!!! 20 POINTS AND BRAINLIEST IF CORRECT.
Which represents where f(x) = g(x)?
f(2) = g(2) and f(0) = g(0)
f(2) = g(0) and f(0) = g(4)
f(2) = g(0) and f(4) = g(2)
f(2) = g(4) and f(1) = g(1)
Its A i did the test
__________ are pairs of angles formed when a third line (transversal) intersects two other lines. These angles are on the opposite sides of the transversal and are between the other two lines.
"Opposite sides of the transversal..." Alternate
"Between the other two lines." Interior
Alternate Interior angles.
If they were outside the two lines they would be alternate exterior angles and if they were on the same side of the transversal then they would be corresponding angles.
If (c) were f(k) = -3/k+2, what value of k would be excluded from the domain?
k = - 2 is excluded from the domain
the denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that k cannot be
solve k + 2 = 0 ⇒ k = - 2 ← excluded value
if 3x + 5y = 2 and 2x - 6y = 20 what is 5x - y
Hey!
We have:
... 3x + 5y = 2
... 2x - 6y = 20
In order to get 5x - y , we will need to add both the equations.
3x+5y=2
2x-6y=20
____________________________________________________
...5x - y = 22
Hence, the required answer is 22.
Hope it helps!
Linear equations in two variables are solved to obtain the values of variables. Thus, the value of the equation [tex]5x - y[/tex] is [tex]\bold{22}[/tex].
Given equations are mentioned below:
[tex]3x + 5y = 2\\2x - 6y = 20[/tex]
We need to determine the values of the expression [tex]5x - y[/tex].
For calculating the value of the above expression, first we need the value of the variables x and y.
How to calculate the values of the variables?The solution of linear equation in two variables can be calculated by different methods such as substitution, elimination and graphical methods.Here, in this question we used substitution method to calculate the desired value. Calculations:[tex]\begin {aligned}3x + 5y &= 2\\3x&=2-5y\\x&=\dfrac{2-5y}{3} \end{aligned}[/tex]
Now, substitute the value of the x in another expression and solve it further.
[tex]\begin{aligned}2 \times \dfrac{2-5y}{3} -6y&=20\\ \dfrac{4-10y}{3}-6y&=20\\4-10y-18y&=60\\28y&=-56\\y&=-2 \end{aligned}[/tex]
Now, calculate the value of x.
[tex]\begin{aligned}x&=\dfrac{2-5 \times -2}{3}\\&=\dfrac{12}{3}\\&=4 \end{aligned}[/tex]
Now, calculating the value of [tex]5x - y[/tex].
[tex]5\times4 - (-2)=22[/tex]
Hence, the value of the expression [tex]5x - y[/tex] is 22.
Learn more about the linear equations in two variables here:
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there is a photo attached
drop down 1:
161/289 -- incorrect
-161/289 -- CORRECT
64/289
-64/289
drop down 2:
-30/217 -- incorrect
-30/161 -- INCORRECT
-240/217 -- incorrect
-240/161
Your question answers itself.
You have shown the correct answer for the first drop-down: -161/289
You have shown the 3 incorrect answers out of the 4 choices for the second drop-down. The correct choice is the remaining one: -240/161.
_____
Even if all you know is that tan = sin/cos, you would suspect that answer choice based on the numerator of the cosine: 161. That value is likely the one in the denominator of the tangent value.
_____
cos(2θ) = 2cos(θ)² . . . . trig identity
... = 2(-8/17)² -1 = 128/289 -1 = -161/289
sin(2θ) = √(1-cos(2θ)²) . . . . trig identity
... = √(289² -161²)/289 = √57600/289 = 240/289
tan(2θ) = sin(2θ)/cos(2θ) . . . . trig identity
... = (240/289)/(-161/289) = -240/161
y = 12x2 - 9x + 4 how many real solution 10x + y = -x2 + 2 how many real solution(s) 4y - 7 = 5x2 - x + 2 + 3y how many real solution(s) y = (-x + 4)2 how many real solution(s)
Answer:
(a) 0
(b) 2
(c) 0
(d) 1
Step-by-step explanation:
All of these can be solved easily by a graphing calculator. The attached graphs show the real solutions of those equations that have them. Here, you can also answer the question from the sign of the discriminant.
For y = ax² +bx +c
the value of the discriminant is
... b² -4ac
When the discriminant is negative, both solutions are complex. When 0, there is one solution. When positive, there are two real solutions.
(a) The discriminant is ...
... (-9)² -4(12)(4), a negative number. There are no real solutions.
(b) This needs to be rearranged to ...
... y = -x² -10x +2
Then the discriminant is ...
... (-10)² -4(-1)(2), a positive number. There are 2 real solutions.
(c) This needs to be rearranged to ...
... y = 5x² -x +9 . . . . add 7-3y
Then the discriminant is ...
... (-1)² -4(5)(9), a negative number. There are no real solutions.
(d) This equation is in vertex form, and the vertex is (4, 0). Since the vertex is the only x-intercept, there is one real solution.
97 POINTS WILL MARK BRAINLESS
I need help with these i'm so confused could you show me on how you got the answers Thank you so much
Answer:
2.
x = 15∠1 = 45°1.
x = 5∠A = 85°Step-by-step explanation:
2.Angles 135° and (2x+15)° together make up a line (the transversal crossing m and n). Such angles are called a "linear pair" and their sum is always 180°. That means we can write the equation ...
... 135° + (2x+15)° = 180°
... 150 +2x = 180 . . . . . . . remove the degree symbol, combine terms
... 2x = 30 . . . . . . . . . . . . subtract 150
... x = 15 . . . . . . . . . . . . . . divide by 2
Angle 1 and angle (2x+15)° are on opposite sides of the transversal line, and are both between the parallel lines m and n. This makes them alternate interior angles. Such angles are congruent—they have the same measure. We know the measure of angle (2x+15)° is (2·15+15)° = 45°, so we know the measure of ∠1 is also 45°.
1.a) The sum of angles in a triangle is always 180°. This means ...
... (15x +10)° + (15x -10)° + (3x +15)° = 180°
... 33x +15 = 180 . . . . . . . drop the ° symbol, combine terms
... 33x = 165 . . . . . . . . . . subtract 15
... x = 5 . . . . . . . . . . . . . . . divide by 33
b) ∠A = (15x+10)° = (15·5 +10)°
... ∠A = 85°
(1)
(a)
the sum of the angles in a triangle = 180°, hence
3x + 15 + 15x - 10 + 15x + 10 = 180
33x + 15 = 180 ( subtract 15 from both sides )
33x = 165 ( divide both sides by 33 )
x = 5
(b) ∠A = 15x + 10 = (15 × 5 ) + 10 = 75 + 10 = 85°
(2)
2x + 15 + 135 = 180 ( straight angle )
2x + 150 = 180 ( subtract 150 from both sides )
2x = 30 ( divide both sides by 2 )
x = 15 ⇒ 2x + 15 = 45
∠1 = 45° ( alternate angles are congruent )
A pair of sneakers on sale for $51. This is 75% off the original price. How much less than the original price is the sales price?
75% of X = $51, thus x or the original price is $68 . Thus the sales price is $17 less.
Consider the following investment. (Round your answers to the nearest cent.)
$3,000 at 6% compounded annually for 15 years
(a) FIND the future value of the given amount.
(b) INTERPRET the future value of the given amount.
After 15 years, the investment is worth $?
(a) 6% of the value of the investment is added each year. This means the value of the investment is multiplied by 1.06 each year. After 15 multiplications, the value is ...
... $3000×1.06¹⁵ ≈ $7189.67
(b) The interpretation of this result is ...
... After 15 years, the investment is worth $7189.67.
The future value of a $3000 investment at an annual interest rate of 6%, compounded annually for 15 years, is approximately $8093.97. This means that the original sum will grow to this amount after the set period.
Explanation:To find the future value of an investment, we use the formula for compound interest which is A = P(1 + r/n)^(nt). Where:
A is the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount you borrowed or deposited). r is the annual interest rate (in decimal form). n is the number of times that interest is compounded per unit t. t is the time the money is invested for in years.Given are P = $3000, r = 6%/100 = 0.06 (annually), n = 1 (since it's compounded annually), and t = 15 years. Plugging these into the formula, we get A = $3000(1 + 0.06/1)^(1*15) = $3000(1.06)^15 = $8093.97.
Interpreting this, it means that investing $3000 at 6% compounded annually would grow to approximately $8093.97 after 15 years.
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13. Model the function rule y = -2x - 3 with a table of values. Show your work.
y = -2x - 3
To make a table, we assume any number for x and find out y
Lets assume x= -1
y = -2x - 3 = -2(-1) -3 = 2-3 = -1
Lets assume x= 0
y = -2x - 3 = -2(0) -3 = 0-3 = -3
Lets assume x= 1
y = -2x - 3 = -2(1) -3 = -2-3 = -5
Lets assume x= 2
y = -2x - 3 = -2(2) -3 = -4-3 = -7
Table is
x y = -2x-3
-1 -1
0 -3
1 -5
2 -7
Find the area of the sector of a circle with diameter 34 feet and an angle of π/5 radians. (Round your answer to four decimal places.)
The area of the sector of a circle with diameter 34 feet and an angle of π/5 radians is approximately 9.0095 square feet.
Explanation:To find the area of the sector of a circle, we need to use the formula A = πr2θ/360, where A is the area, r is the radius, and θ is the angle in radians. The given diameter is 34 feet, so the radius is 17 feet. The angle is π/5 radians. Plugging these values into the formula, we get A = π(17)2(π/5)/360. Simplifying, we find A = 9.0095 square feet. Rounded to four decimal places, the area of the sector is 9.0095 square feet.
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To find the area of the sector of a circle, you use the formula A = 0.5 * r² * θ where r is the radius (half of the diameter) and θ is the angle in radians. After plugging in the provided values, you calculate the area to four decimal points.
Explanation:The subject is related to finding the area of the sector of a circle. The formula to calculate the area of the sector is A = 0.5 * r² * θ, where r is the radius and θ is the angle in radians. In the given problem, the diameter of the circle is given as 34 feet, so the radius will be 17 feet, and the angle is given as π/5 radians.
Step 1: First, note down the radius from the given diameter, which would be 17 feet, as radius = diameter/2.
Step 2: Plug the value of the radius and the angle into the formula for the area of a sector. The calculation will look like this: A = 0.5 * (17)² * (π/5).
Step 3: Calculate the area by multiplying the values. The final answer will be rounded to four decimal places.
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Jon Ericson bought a home with a 11.5% adjustable rate mortgage for 20 years. He paid $10.67 monthly per thousand on his original loan.
At the end of 2 years he owes the bank $50,000. Now that interest rates have gone up to 13%, the bank will renew the mortgage at this rate or Jon can pay $50,000.
Jon decides to renew and will now pay $11.72 monthly per thousand on his loan. You can ignore the small amount of principal that has been paid.
What is the amount of the old monthly payment? $ ____
What is the amount of the new monthly payment? $ ____
What is the percent of increase in his new monthly payment? ____ %
You are told to ignore the amount of principal paid, so you are apparently to assume the loan amount was for $50 thousand.
a) The old monthly payment was $10.67×50 = $533.50
b) The new monthly payment is $11.72×50 = $586.00
c) The increase in monthly payment is figured in the usual way:
... (new/old -1)×100% = (1.0984-1)×100% = 9.84%
_____
In reality, about 3% of the loan will have been paid at the end of 2 years. Thus, the original loan amount may have been near $51,500. This problem is telling you to ignore the difference.
Remark
The first fact you need to know is that the bank has taken money from you and nothing has been reduced from the principle. Crafty people those bankers; you are going to pay off the interest before touching the principle. They're like you to refinance for the rest of your life at the rates you currently have.
Point. You started out with a 50k debt. You still have that same debt.
Solution
Givens
number of thousands (n) = 50000/1000 = 50
Amount paid per thousand (A) = 10.67
Total monthly payments (T) = ?
Part A
T = n * A
T = 50 * 10.67
T = 533.50 is the old monthly payment
Part B
T = n * A
T = 50 * 11.72
T = 586.00 new monthly payment.
Part C
This is a notes question. What have you been told in your notes on this question. You can find the raw amount just by subtracting 586 - 533.50 = 52.50
But how do you find the % increase. Which one of the payments do you use as your base?
In point of fact, you should be using the first number 533.5
What % will you get when you multiply that by 533.5 and get 52.50?
You are not trying to find 586. You are trying to find the number that you add to 533.5 to get to 586
The answer is (52.50 / 533.5)*100% = 9.84% is the % increase.
how many times larger is 9 X 10 to the 6 exponent than 3 x 10 to the 4th exponent
300
divide 9 × [tex]10^{6}[/tex] by 3 × [tex]10^{4}[/tex]
= [tex]\frac{9}{3}[/tex] × [tex]10^{6}[/tex] / [tex]10^{4}[/tex]
= 3 × [tex]10^{6-4}[/tex] = 3 × [tex]10^{2}[/tex] = 300
Help me please very confused
Read the problem and answer choices. You want to get from ABCD to EFGH, so you need to figure out how to do that with reflection, translation, and dilation—in that order.
The reflection part is fairly easy. ABC is a bottom-to-top order, and EFG is a top-to-bottom order, so the reflection is one that changes top to bottom. It must be reflection across a horizontal line. The only horizontal line offered in the answer choices is the x-axis. Selection B is indicated right away.
The dimensions of EFGH are 3 times those of ABCD, so the dilation scale factor is 3. This means that prior to dilation, the point H (for example), now at (-12, -3) would have been at (-4, -1), a factor of 3 closer to the origin. H corresponds to D in the original figure, which would be located at (0, -2) after reflection across the x-axis.
So, the translation from (0, -2) to (-4, -1) is 4 units left (0 to -4) and 1 unit up (-2 to -1).
The appropriate choice and fill-in would be ...
... B. Reflection across the x-axis, translation 4 units left and 1 unit up, dilation with center (0, 0) and scale factor 3.
_____
You can check to see that these transformations also map the other points appropriately. They do.
The princess traces one plant’s roots to discover that it has exactly 5 roots. One of the roots she can trace to 2−3√5. At least two of the roots are the same and labeled −4.
What conclusions can the princess draw about the other two roots?
There may be more than one correct answer. Select all correct answers.
-One of the other roots is 2+ 3√5
-One of the other roots could be another −4.
-One of the other roots could be another 2− 3√5
-One of the other roots is 3+ 2√5
-One of the other roots is 3− 2√5
complex roots occur in conjugate pairs
given 2 - 3√5 is a root then 2 + 3√5 is also a root
one of the other roots is 2 + 3√5
there are 2 roots of - 4
one of the other roots could be another - 4
Final answer:
The princess can conclude that one of the other roots is 2+ 3√5, one of the other roots could be another −4, and one of the other roots could be another 2− 3√5.
Explanation:
The princess can draw the following conclusions about the other two roots:
One of the other roots is 2+ 3√5.One of the other roots could be another −4.One of the other roots could be another 2− 3√5.These conclusions are based on the fact that the princess has already traced one root to be 2−3√5 and at least two roots are labeled −4.
What is the Equivalent ratio of 6:_= 9:12
[tex]\frac{6}{8}[/tex]
let x be the unknown value in the ratio, hence
[tex]\frac{6}{x}[/tex] = [tex]\frac{9}{12}[/tex] ( cross- multiply )
9x = 72 ( divide both sides by 9 )
x = 8
thus [tex]\frac{6}{8}[/tex] = [tex]\frac{9}{12}[/tex]
name a plane two different ways