Answer:
Smaller t = 2
Larger t = 5
Step-by-step explanation:
Given:
The given function is.
[tex]f(t)=-(t-2)(t-5)[/tex]
Find the zeros of the function.
Solution:
[tex]f(t)=-(t-2)(t-5)[/tex]
Simplify the equation above equation.
[tex]f(t)=-(t^{2}-5t-2t+10)[/tex]
[tex]f(t)=-(t^{2}-7t+10)[/tex]
[tex]f(t)=-t^{2}+7t-10[/tex]
Now, we first find the root of the above equation.
Use quadratic formula with [tex]a=-1, b=7, c=-10[/tex].
[tex]t=\frac{-b\pm \sqrt{(b)^{2}-4ac}}{2a}[/tex]
Put a, b and c value in above equation.
[tex]t=\frac{-7\pm \sqrt{(7)^{2}-4(-1)(-10)}}{2(-1)}[/tex]
[tex]t=\frac{-7\pm \sqrt{49-4\times 10}}{-2}[/tex]
[tex]t=\frac{-7\pm \sqrt{49-40}}{-2}[/tex]
[tex]t=\frac{-7\pm \sqrt{9}}{-2}[/tex]
[tex]t=\frac{-7\pm 3}{-2}[/tex]
For positive sign
[tex]t=\frac{-7 + 3}{-2}[/tex]
[tex]t=\frac{-4}{-2}[/tex]
t = 2
For negative sign
[tex]t=\frac{-7 - 3}{-2}[/tex]
[tex]t=\frac{-10}{-2}[/tex]
t = 5
Put t = 2 in given function.
[tex]f(t)=-(2-2)(2-5)=0[/tex]
Put t = 5 in given function.
[tex]f(t)=-(5-2)(5-5)=0[/tex]
So, the zeros of the function is t = 2 or 5
Therefore, the smaller value of t = 2 and larger value of t = 5.
Find the sum the interior angle angle measures of a 17-gon
Answer:
2700 degrees.
Step-by-step explanation:
The external angles add up to 360 degrees
So 1 external angle in a regular 17-gon = 360/17
= 21.176 degrees
The internal angle = 180 - 21.176
= 158.824 degrees
Sum of internal angles = 158.824 * 17
= 2700 degrees.
Answer:
Step-by-step explanation:
Every closed curve called a polygon can be separated into a specific number of triangles. Then, because the sum of the interior angles of a triangle is 180, you take the number of triangles and multiply by 180 to get the sum of the interior angles of the n-gon. To find the number of triangles that exist within an n-gon, subtract 2 from the number of sides. If our figure is a 17-sided polygon, then the number of triangles within it is 17 - 2 = 15. 15 triangles, each with a sum of 180 for its angles. 15 * 180 = 2700.
Each central angle is 360 divided by 17 to get 21°10'35"
Each interior angle is 2700 divided by 17 to get 158°49'24"
Willing to brainlist solve 16-17 please during this exam
Answer:
16. B
17. B
Step-by-step explanation:
16. The intercept form of the parabola is
[tex]y=a(x-x_1)(x-x_2),[/tex]
where [tex]x_1, x_2[/tex] are two x-intercepts.
In your case,
[tex]x_1=2\\ \\x_2=-8[/tex]
so
[tex]y=a(x-2)(x-(-8))\\ \\y=a(x-2)(x+8)[/tex]
To find a, substitute coordinates of the point (-6,-4) parabola is passing through
[tex]-4=a(-6-2)(-6+8)\\ \\-4=-16a\\ \\a=\dfrac{1}{4}[/tex]
and
[tex]y=\dfrac{1}{4}(x-2)(x+8)[/tex]
17. The vertex form of the parabola equation is
[tex]-2p(y-k)=(x-h)^2,[/tex]
where (h,k) are the coordinates of the vertex and sign "-" because parabola goes down.
In your case, vertex is (2,3), so
[tex]-2p(y-3)=(x-2)^2[/tex]
The vertex is 3 units from the focus, then
[tex]\dfrac{p}{2}=3\\ \\p=6[/tex]
The equation of the parabola is
[tex]-2\cdot 6(y-3)=(x-2)^2\\ \\y=-\dfrac{1}{12}(x-3)^2+3[/tex]
Olivia bought a piece of ribbon priced at $0.56 per yard. The total cost was $1.54. How many yards did she buy?
Answer:
2.75 or 2 3/4
Step-by-step explanation:
Divide the total cost by the price of each ribbon.
$1.54 ÷ $0.56/yard = 2.75 yards
If the answer needs to be in mixed fractional form, convert 0.75 to a fraction.
3/4 = 0.75
The fraction form of 2.75 is 2 3/4.
Therefore Olivia bought 2 3/4 yards of ribbon.
Which transformation describes the equation from its parent equation? f (x-9) Your answer: horizontal shift right 9 units vertical shift up 9 units vertical stretch by a factor of 9 horizontal shift left 9 units
Translate each sentence into an equation. Use x for the variable.
Three more than eight times a number is equal to 19.
3 + 8x = 19 is the equation for given sentence three more than eight times a number is equal to 19
Solution:
Given sentence is:
Three more than eight times a number is equal to 19.
We have to translate the sentence into an equation
Let us first break the sentence and find out the equation
Let "x" be the required number
Given that, Three more than eight times a number is equal to 19.
Here "more than" represents addition
"times" represents multiplication
eight times a number = [tex]8 \times x[/tex]
So the required equation is:
Three more than eight times a number is equal to 19
[tex]3 + 8 \times x = 19\\\\3 + 8x = 19[/tex]
Thus the required equation for given sentence is found
A book is on sale for $8.93. The sale price is 15% off the original price. What was the
original price?
Answer:
i think 10.30 according to my calculation
Answer:
10.30
Step-by-step explanation:
Solve the system of equations.
Step-by-step explanation:
Solve the system via elimination (add the equations):
-10y + 9x = -9
+ (10y + 5x = -5)
-----------------------
14x = -14
x = -1
Plug in the value for 'x' into the second equation:
-10y + 5(-1) = -5
Solve for y:
-10y - 5 = -5
--> -10y = 0
--> y = 0
x = -1
y = 0
Which number line represents the solution of 4 - 3x > 13?
Answer:
[tex]x<-3[/tex]
Step-by-step explanation:
Given inequality:
[tex]4-3x>13[/tex]
In order to represent the solution on the number line, we will first solve the given inequality.
We have
[tex]4-3x>13[/tex]
Subtracting both sides by 4.
[tex]4-3x-4>13-4[/tex]
[tex]-3x>9[/tex]
Dividing both sides by -3.
[tex]\frac{-3x}{-3}<\frac{9}{-3}[/tex] [On dividing both sides by a negative number the sign of the inequality reverses.]
[tex]x<-3[/tex]
So, solution of this inequality will range from -3 to -∞
The number line is represented below.
Adam writes 18y to simplify an expression with three like terms. What could the expression be?
Answer:
Step-by-step explanation:
5y + 6y + 7y = 18y......any numbers that add(or subtract) to equal 18, stick them before the y....
or it could be : 10y + 10y - 2y = 18y or 5y + 10y + 3y or 30y - 20y + 8y....I could go on forever...lol
Which of the following is the missing justification?
Step Justification
one fifth times x plus six equals five Given
x + 30 = 25
x = −5 Subtraction Property of Equality
A Multiplication Property of Equality
B Distributive Property
C Addition Property of Equality
D Division Property of Equality
Answer:
No idea what the other person who answered was trying to say since it has to be 1 answer but i think its multiplication because to get 1/5 to be 1 so x you multiply by 5 and it matches because to get 6 to be 30 you multiply by 5 and to get 5 to be 25 you multiply by 5
ANSWER A
Step-by-step explanation:
Riley’s Rug Warehouse purchases rugs from the manufacturer for $82.00 each. The manager marks the rugs up 150% and then includes a 10% sales tax. How much much does a customer pay for 1 rug?
A customer will pay $225.5 for one rug.
Step-by-step explanation:
Given,
Purchase price of rug = $82.00
Mark up = 150%
Amount of mark up = 150% of purchase price
Amount of mark up = [tex]\frac{150}{100}*82[/tex]
Amount of mark up = 1.5*82 = $123
Price of rug after mark up = Purchase price + Mark up
Price of rug after mark up = 82+123 = $205
Sales tax = 10%
Amount of sales tax = 10% of price after markup
Amount of sales tax = [tex]\frac{10}{100}*205=\$20.5[/tex]
Selling price = Price after markup + Amount of sales tax
Selling price = 205+20.5 = $225.5
A customer will pay $225.5 for one rug.
Keywords: percentage, markup
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A line containing the points (3,0) and (-2,-2) is graphed on a coordinate grid. Which of these
points is a solution to the equation that represents this line?
(-12,-6)
(-4,-3)
(0.5,-1)
(5,0.8)
(9,3)
(18,6)
Answer: (-12,-6)
Step-by-step explanation:
If we already have two points of the line, we can find its slope ([tex]m[/tex]), its intersection with the y-axis ([tex]b[/tex]), hence its equation:
Point 1: [tex](x_{1},y_{1})=(3,0)[/tex]
Point 2: [tex](x_{2},y_{2})=(-2,-2)[/tex]
Slope equation:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{-2-0}{-2-3}[/tex]
[tex]m=\frac{2}{5}[/tex] This is the slope of the line
Now, the equation of the line is:
[tex]y=mx+b[/tex]
We already know the slope, now we have to find [tex]b[/tex] with any of the given points. Let's choose Point 1: [tex](x_{1},y_{1})=(3,0)[/tex]
[tex]0=\frac{2}{5}(3)+b[/tex]
Isolating [tex]b[/tex]:
[tex]b=-\frac{6}{5}[/tex]
Then, the equation of the line is:
[tex]y=\frac{2}{5} x-\frac{6}{5}[/tex]
With this equation we can find which point is a solution. Let's begin with the first point (-12,-6):
[tex]-6=\frac{2}{5} (-12)-\frac{6}{5}[/tex]
[tex]-6=-\frac{24}{5} -\frac{6}{5}[/tex]
[tex]-6=-6[/tex] Since both sides of the equation are equal, (-12,-6) is the point that fulfills the solution of the equation.
Sandy makes $2 profit on every cup of lemonade that she sells and $1 on every cupcake that she sells.Sandy wants to sell at least 5 cups of lemonade and at least 5 cupcakes per day.She wants to earn at least $25 per day.Show and describe all the possible combinations of lemonade and cupcakes that sandy needs to sell to meet her goals.List two possible combinations.If you can please graph.Thank You
Answer:22
Step-by-step explanation:
Answer:maximize p = profit = 2 L + 1 C >/= 25
L >/= 5
C>/=5
start with L = 5
10+C >/= 25
C >/= 15
if L = 6
12 + C >/= 25
C >/= 13
so
L 7, C 11
L 8 ,C 9
L 9 , C 7
L 10, C 5
are your MINIMUM combinations. Of course you can always sell more
Step-by-step explanation:
Can u guys PLEASE answer this question 9 ASAP
Answer:
$ 9.99 almost $ 10 she would save every week.
Step-by-step explanation:
Weekly Salary = $ 628
Tax deduction= $149.8
Superannuation Fund = 4.5 % of $ 628= $28.26
Mortgage = 8 % of 628= $ 50.24
Income after deductions = $ 628- $ 149.8 - $ 28.26- $ 50.24= $ 399.7
10 % of $ 399.7 = $ 39.97 almost $ 40
In one week she would save $39.97/4= $ 9.99 = $ 10
David plans to cover the floor of his room with new material.
The floor is an isosceles trapezoid whose bases are 16 feet and 26 feet
and sides are 13 feet in length. Each piece of new material has an area of 2.5 square feet.
Assuming the pieces of new material can be cut as needed, how many pieces does
David need?
101
126
202
252
Answer:
[tex]\large \boxed{\text{101 pieces}}[/tex]
Step-by-step explanation:
1. Calculate the area of the floor
The formula for the area of a trapezoid is
A = ½(a + b)h,
where a and b are the lengths of the parallel sides and h is the distance between them.
However, we are not given the value of h, so we must use Brahmagupta's formula.
If the four sides are a, b, c, and d, the area A is
[tex]A = \sqrt{(s - a) (s - b) (s - c) (s - d)}[/tex]
where s is the semiperimeter
[tex]s = \frac{1}{2}(a + b + c + d)[/tex]
Data:
a = 13 ft
b = 16 ft
c = 13 ft
d = 26 ft
(a) Calculate the semiperimeter
[tex]\begin{array}{rcl}s & = & \sqrt{(s - a) (s - b) (s - c) (s - d)}\\\\ & = & \frac{1}{2}(13 + 16 + 13 + 26)\\\\ & = & \frac{1}{2}(68)\\\\ & = & 34\\\end{array}[/tex]
(b) Calculate the area
[tex]\begin{array}{rcl}A & = &\sqrt{(s - a) (s - b) (s - c) (s - d)}\\\\& = &\sqrt{(34 - 13) (34 - 16) (34 - 13) (34 - 26)}\\\\& = &\sqrt{21 \times 18 \times 21 \times 8}\\\\& = & \sqrt{63504}\\\\ & = & \mathbf{252}\\\end{array}[/tex]
The area of David's floor is 252 ft².
2. Calculate the number of pieces of material
[tex]\text{No. of pieces} = \text{252 ft}^{2} \times \dfrac{\text{1 piece}}{\text{2.5 ft}^{2}} = \textbf{100.8 pieces}\\\\\text{David can't buy a fraction of a piece, so he must buy $\large \boxed{\textbf{101 pieces}}$}[/tex]
What is 4 common multiples of 2 and 4
Answer:
Multiples of 2 are {2,4,6,8,10,12,14,16,...} Multiples of 4 are {4,8,12,16,.......) Hence common multiples are {4,8,12,16,...} and Lowest Common Multiple is 4 .
Step-by-step explanation:
To find common multiples of 2 and 4, list the multiples of each and identify the common elements. For 2 and 4, these are 4, 8, 12, and 16.
Finding Common Multiples of 2 and 4
To find common multiples of 2 and 4, we start by listing the multiples of each number.
→ Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ...
→ Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, ...
Next, we look for common multiples from these lists.
→ 4: divisible by 2 and 4
→ 8: divisible by 2 and 4
→ 12: divisible by 2 and 4
→ 16: divisible by 2 and 4
Therefore, four common multiples of 2 and 4 are 4, 8, 12, and 16.
PLEASE HELPP
Find the length of segment AB
I'm not sure, but I know that it is longer than 5
Answer:
5.5-6ish sorry its hard to tell
Happy Holidays!
When solving the equation, which is the best first step to begin to simplify the equation?
-2(x+3)=-10
Answer:
Step-by-step explanation:
-2(x+3)=-10
Open the bracket
-2x - 6 = -10
Collecting like terms
-2x = -10 + 6
-2x = -4
Dividing through by -2
x = -4/-2
x = 2
What is the equation of y=x^3 with the given transformations? Vertical stretch by a factor of 3, horizontal shift 4units to the right, vertical shift 3 units down
Answer:
y = 3(x -4)^3 -3
Step-by-step explanation:
As you know, the transformations are
g(x) = (vertical stretch factor) · f(x - (right shift)) +(vertical shift)
For the given transformations, the equation becomes ...
y = 3(x -4)^3 -3
The equation of y=x^3 with the given transformations is y = 3(x - 4)^3 - 3.
Explanation:The equation of y = x^3 after the given transformations is y = 3(x - 4)^3 - 3.
The vertical stretch by a factor of 3 means that all y-values will be multiplied by 3, so the equation becomes y = 3x^3.
The horizontal shift 4 units to the right means that x-values will be replaced by (x - 4), so the equation becomes y = 3(x - 4)^3.
The vertical shift 3 units down means that all y-values will be decreased by 3, so the equation becomes y = 3(x - 4)^3 - 3.
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[tex]f(x) = 3 \\ what \: is \: the \: domain \: and \: range \: of \: th \: function \: above.[/tex]
Answer:
Domain: (-∞,∞)
Range: {3}
Step-by-step explanation:
The domain is the x-values of the function, and the range is the y value of the function.
F(x)=3 is really just a fancy way of saying y=3. The range is 3.
Since the function makes a horizontal line, the domain is ∞.
i just need help at this point
16π
Step-by-step explanation:
The area within a circle is given by the formulae;
πr²
Since this circle is part of a full circle will multiply the area by teh appropriate fraction;
90/360 = ¼
¼ πr²
r = 8 according to the illustration
¼ π*8²
1/4 * π * 64
= 16π
Area = 16π
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after placing an equation into his calculator Rob got the following table. He then determine that X=6 when f (x) = -4 is he correct? explain
x | f(x)
——————
-4 | 6
——————
-2 | 3
——————
0 | -1
——————
2 | -4
Answer:
Step-by-step explanation:
No, unless the function decides to follow a different pattern. See more explanation below.
Step-by-step explanation:
He is wrong, the table doesn't tell us what happens at x=6.
It does tell us the following:
1) When x=-4, f(x)=6.
2) When x=-2, f(x)=3.
3) When x=0, f(x)=-1.
4) When x=2, f(x)=-4.
So maybe he got it the x and f(x) value switched in his brain.
Because according to 1) x=-4 when f(x)=6.
If the points keep having x increase while y decreases, then every x>2 will have a y less than -4 correspond to it.
Rob's determination that the function X = 6 when f(x) = -4 appears to be correct based on the provided data.
What is equation?An equation is a mathematical statement that shows that two expressions are equal.
It typically includes variables, constants, and mathematical operations and is used to solve for unknown values.
Rob seems to be correct. If you look at the table of values:
x | f(x)
-4 | 6
-2 | 3
0 | -1
2 | -4
When x = 6,
we find that the function f(x) = -4 (as indicated in the last row of the table).
So, Rob's determination that X = 6 when f(x) = -4 appears to be correct based on the provided data.
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Translate and solve eight more than the difference of-5s and -6s is equal to the sum of 3 and 7
Answer:
s=2
Step-by-step explanation:
-5s-(-6s)+8=3+7
-5s+6s+8=10
s+8=10
s=10-8
s=2
The word problem would be translated as s + 8 = 10.
The solution is: s = 2
First, let's translate the statement given to form an algebraic equation, then solve for the unknown variable.
The difference of -5s and -6s is translated as -5s - (-6s) = "s"8 more than the "difference of -5s and -6s" is: s + 8.sum of 3 and 7 = 3 + 7 = 10.Therefore, the equation would be:
s + 8 = 10
Solve for s by subtracting 8 from both sidess + 8 - 8 = 10 - 8
s = 2
Therefore, the word problem would be translated as s + 8 = 10.
The solution is: s = 2
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A parabolic arch needs to be 5m high and 2m wide at ground level. Find the quadratic equation which describes the arch.
Answer:
[tex]y=-5(x-0)^2+5[/tex]
Step-by-step explanation:
Given height of parabola is [tex]5\ m[/tex].
And [tex]2\ m[/tex] wide at ground level.
Also, the parabola opens down.
Let us assume the parabola is aligned on Y-axis
As the height of parabola is [tex]5\ m[/tex]. The maximum height of parabola is achieved when [tex]x=0[/tex].
So, the vertex of parabola is [tex](0,5)[/tex].
The equation of parabola having vertex [tex](h,k)[/tex] is.
[tex]y=a(x-h)^2+k[/tex].
Plugging the vertex of parabola
[tex](h,k)[/tex] [tex]=[/tex] [tex](0,5)[/tex].
[tex]h=0\ and\ k=5[/tex]
[tex]y=a(x-0)^2+5[/tex]
It is given that parabola is [tex]2\ m[/tex] wide at the ground.
As the parabola is aligned on Y-axis. So, distance between X-intercept is [tex]2\ m[/tex].
The X-intercept would be [tex](-1,0)\ and\ (1,0)[/tex]
Plugging [tex](1,0)[/tex] in the equation [tex]y=a(x-0)^2+5[/tex]
[tex]0=a(1-0)^2+5\\\\-5=a(1)^2\\\\-5=a[/tex]
Now, we get [tex]a=-5[/tex] and having vertex [tex]h=0\ and\ k=5[/tex].
So, the equation of parabola is
[tex]y=a(x-h)^2+k[/tex].
[tex]y=-5(x-0)^2+5[/tex]
Which expression is equivalent to 2(5m)+ m
Answer:
11m
Step-by-step explanation:
2(5m)+m=10m+m=11m
The polynomials that are given are P(x)=
[tex] {x}^{3} - {x}^{2} - 18[/tex]
and Q(x)= P (2x-1)
Show that the result of Q is going to be Q(x)=
[tex]8 {x}^{3} - 16 {x}^{2} + 10x - 20x[/tex]
Answer:
Step-by-step explanation:
P(x)= x³ - x² - 18
Q(x) = P(2x-1)
= (2x-1)³ - (2x-1)² -18
= (2x)³ - 3*(2x)² * 1 + 3*2x* 1² - 1³ - [ (2x)² - 2*2x*1 + 1 ] - 18
=8x³ - 12x² + 6x - 1 - [4x² - 4x +1 ] - 18
= 8x³ - 12x² + 6x - 1 - 4x² + 4x - 1 - 18
= 8x³ - 16x² + 10x - 20
Hint : (a-b)³ = a³-3a²b+3ab²-b³
(a-b)² = a² -2ab + b²
If F(x) = 2x-5 and G(x) = x + 1, what is G(F(x)) ?
CAN SOMEONE HELP ME PLEASE...ILL GIVE BRAINLEST AND EXTRA POINTS
Answer:
(- 2, - 7 )
Step-by-step explanation:
Under a reflection in the x- axis
a point (x, y ) → (x, - y ), thus
P(- 2, 7 ) → P'(- 2, - 7 )
Sovle: for n:3xn =2x9
A:2
B:5
Help asap
C:6
D:8
E:9
Answer:
n will be 6
Step-by-step explanation:
3×n=2×9
substitute n=6 in the above equation
3×6=2×9
18=18
N is 6
what is the x coordinate of the point of intersection for 2x+y=7 & 10x-7y=-1
The x-coordinate of the point of intersection for given equations is 2
Step-by-step explanation:
Given equations are:
[tex]2x+y = 7\ \ \ Eqn\ 1\\10x-7y = -1\ \ \ Eqn\ 2[/tex]
The point of intersection is the solution of the system of equations
as we have to find the x-coordinate we will use elimination method to eliminate y
So,
Multiplying equation 1 with 7
[tex]7(2x+y) = 7(7)\\14x+7y = 49\ \ \ \ Eqn\ 3[/tex]
Adding equation 2 and 3
[tex](14x+7y) + (10x-7y) = 49-1\\14x+10x+7y-7y = 48\\24x = 48[/tex]
Dividing both sides by 24
[tex]\frac{24x}{24} = \frac{48}{24}\\x = 2[/tex]
The x-coordinate of the point of intersection for given equations is 2
Keywords: Linear equations, simultaneous equations
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