Answer: 9
Step-by-step explanation:
Finding the zeros is the same as solving. Then, we will add the two solutions together.
Given:
y = x² - 9x - 10
Solving by Quadradic Formula:
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
[tex]\displaystyle x=\frac{-(-9)\pm\sqrt{(-9)^2-4(1)(-10)} }{2(1)}[/tex]
[tex]\displaystyle x=\frac{9\pm\sqrt{81+40} }{2}[/tex]
[tex]\displaystyle x=\frac{9\pm\sqrt{121} }{2}[/tex]
[tex]\displaystyle x=\frac{9+11}{2},\;\;x=\frac{9-11}{2}[/tex]
x = 10, -1
Adding them together:
10 + -1 = 9
solve the equation. justify each step
2(-x - 5) = 12
2(-x - 5) = 12
Step 1 : Expand the bracket.
=> -2x - 10 = 12
Step 2 :Add both side by 10.
=> -2x - 10 + 10 = 12 + 10
=> -2x = 22
Step 3 : Divide both side by -2.
=> -2x : (-2) = 22 : (-2)
=> x = -11
Therefore, x = -11.
Answer:
x = - 11
Step-by-step explanation:
2(- x - 5) = 12 ( divide both sides by 2 )
- x - 5 = 6 ( add 5 to both sides )
- x = 11 ( multiply both sides by - 1 )
x = - 11
a circular curve is to be constructed with a 225 ft radius and an interior angle of 55 degrees. the separation between the stakes along the arc is 50 ft. assuming the curve is laid out from point to point, what is the last deflection angle?
The curve is laid out from point to point, the last deflection angle of circular curve is 26.5°
In the given question we have,
Radius of circular curve (R) = 225 ft
intersection or central angle in circular curve (I or delta) = 55°
separtion between stakes alaong arc = 50 ft
Angle of deflection is measured from tangent at PC or PT to any point .
deflection angle formula
deflection angle = (Lc /L)(I/2)
where, Lc is long chord and L is lenth of arc , I is central angle
first we find out the value of Lc and L
using formula , R = Lc / 2sin(I/2)
Lc = 225× 2 sin(55°/2) = 208 ft
L = R × I ×π/180°
L = 225 × 3.14 ×55/180 = 215.8 ~ 216 ft
put all the vales in deflection angle formula we get ,
deflection angle= (208/216)(55°/2) = 26.48° ~ 26.5°
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help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The function f(x) = [tex]-3x^2[/tex] + 18x + 3 has the maximum value of 30 at x = 3
The quadratic function is
f(x) = [tex]-3x^2[/tex] + 18x + 3
The general form of the quadratic function is
y = [tex]ax^2[/tex] + bx + c
If a < 0, the quadratic function has maximum value
Here the value of a = -3
Therefore the function has maximum value.
Maximum value will be at x = -b / 2a
= -18 / 2(-3)
= -18 / -6
= 3
The maximum value of quadratic function will be (4ac - [tex]b^2[/tex]) /4a
Substitute the value in the equation
(4ac - [tex]b^2[/tex]) /4a = (4×-3×3 - 18×18) / 4×-3
= (-36 - 324 / -12
= -360 / -12
= 30
Hence, the function f(x) = [tex]-3x^2[/tex] + 18x + 3 has the maximum value of 30 at x = 3
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Solve for x.
9x3x36
0-6
O-4
O
4
6
Answer:
[tex]9x = 3x - 36 \\ 6x = - 36 \\ x = - 6[/tex]
hopefully this will u...^_^
Given Two Points: Write the equation of the line with the two given point
5. (1, 3) and (-3, -5)
6. (1, 4) and (6, -1)
7. (-12, 14) and (6, -1)
8. (-4,-2) and (4, 0)
Writing Parallel & Perpendicular Equations
9. Write an equation parallel to y = 3x + 6 that passes through the point (4, 7).
A car is moving north at 60km/h. The driver sees a sign beside the road ahead of him. What is the velocity of the sign relative to:
a) The car
b) The ground
*Please leave an explanation*
The velocity of the sign are given as follows:
a) Relative to the car: 60 kilometers an hour.
b) Relative to the ground: 0 kilometers an hour.
What is relative speed?The relative speed of one object towards another is given by the rate of change in the position of each these objects relative to each other in regard to time.
Relative to the car, the sign gets 60 kilometers closer every hour, hence the relative speed of the sign will be of 60 kilometers. an hour.
Now, for the ground, the distance between the sign and the ground will always be the same, that is, there is no change in the distance. Hence, the velocity of the sign relative to the ground is of 0 kilometers and hour.
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I need help I am very confused on this Thank you for your guys help!!
The measure of the side MK of the triangle is 109.6.
What is the scale factor?The scale factor is defined as the proportion of the new image's size to that of the previous image. The ratio of the scale of an original object to a new object that is a representation of it but is a different size is known as a scale factor.
For the triangles, the scale factor will be calculated as,
Scale factor = 57 /13
The measure of the side MK will be calculated as,
57 / 13 = MK / 25
MK = ( 57 x 25 ) / 13
MK = 1425 / 13
MK = 109.61
Therefore, the measure of the side MK of the triangle is 109.6.
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Please provide, with your answer, the steps taken.
The value of the given expression is 9/2 when substituting the values of m = -3, n = 2, and p = -1 in the expression.
The value of the given expression is 10/3 when substituting the values of x = 3, y = 2, and z = 4 in the expression.
Given that m = -3, n = 2, and p = -1
The expression is given in the question
⇒ m(p -n)²/ 3p +m
Substitute the values of m = -3, n = 2, and p = -1 in the expression
⇒ -3(-1 -2)²/( 3(-1) +(-3))
⇒ -3(-3)²/(-3-3)
⇒ -3(9)/(-6)
⇒ 27/6
⇒ 9/2
Given that x = 3, y = 2, and z = 4
The expression is given in the question
⇒ (3z + 2x + y)/(4y - 2x + z)
Substitute the values of x = 3, y = 2, and z = 4 in the expression
⇒ (3×4 + 2×3 + 2)/(4×2 - 2×3 + 4)
⇒ (12 + 6 + 2)/(8 - 6 + 4)
⇒ 20/6
⇒ 10/3
Thus, the value of the given expression is 10/3 when substituting the values of x = 3, y = 2, and z = 4 in the expression.
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Write and solve and equation for each scenario. Use x for the variable in your equation. Show your work by first writing an equation and then solving it. Put the solution of your equation in the answer box. If you multiply a number (x) by 5, the product is equal to the sum of 20 and 15.
Based on the calculations, the unknown number (x) is equal to 7.
How to determine the unknown number?In order to solve this word problem, we would assign a variable to the unknown number, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the unknown number. Therefore, translating the word problem into an algebraic equation, we have the following;
Multiply a number (x) by 5 = 5x
The product is equal to the sum of 20 and 15 = 20 + 15 = 35.
Combining the above information, we have:
5x = 20 + 15
5x = 35
Dividing both sides by 5, we have:
x = 35/5
x = 7.
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I need help please!!!!
=========================================================
Explanation:
x = number of weeks
y = height of the plant (inches)
The first sentence of "plant is 4 inches tall on week 8" gives us the point (x,y) = (8,4)
The second sentence gives us the point (32,16)
To find the growth rate, compute the slope.
[tex](x_1,y_1) = (8,4) \text{ and } (x_2,y_2) = (32,16)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{16 - 4}{32 - 8}\\\\m = \frac{12}{24}\\\\m = \frac{1}{2}\\\\m = 0.5\\\\[/tex]
The slope of 0.5 means the plant grows 0.5 inches per week.
Put another way, the plant grows 1 inch per every 2 weeks.
-----------------
Another approach:
The plant goes from 4 inches to 16 inches. It has grown 16-4 = 12 inches over the timespan of 24 weeks (since 32-8 = 24).
So its growth rate is 12/24 = 0.5 inches per week.
Notice how these values and calculations were mentioned in the previous section.
Bell Work
You Do
Camspite A is 5 miles north and 2 miles east of a ranger station.
Campsite B is 8 miles north and 6 miles east of the ranger station.
How far is Campsite A from Campsite B?
A 1 mi
B 5 mi
7 mi
25 mi
7 i do not feel like explaining tbh
M3L3
As Long, As Wide
David's kitchen has an area of 60 square feet. The kitchen is 6 times as many square feet as
David's pantry. If the pantry is 2 feet wide, what is the length of the pantry? ")
First find the area of the pantry.
Solve on paper and check you answer on Zearn. -->
The area of the pantry is square ft.
8
9
Enter ✓
The area of the David's pantry = 10 square feet.
The length of the pantry = 5 feet.
Define the term area of the rectangle?The territory inhabited by a rectangle inside its 4 sides or limits is known as its area. The area of such a rectangle is determined by its sides. Essentially, the formula calculating area is equivalent to the product of the rectangle's length and breadth.For the given question.
David's kitchen is 60 square feet in size. The kitchen is six times the size of the living room.Thus,
Area of kitchen = 6 x area of the pantry
60 = 6 x area of the pantry
area of the pantry = 60 / 6 = 10 square feet.
Area of the pantry = length x breadth
10 = length x 2
length = 10/2 = 5 feet.
Thus, the length of the pantry is found as the 5 feet.
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You and your friend went out to lunch and your total bill (before
taxes) was $36.50. You enjoyed your
service and want to leave a tip of $20%. What is your tip amount?
$7.30
$0.73
$20.00
$36.70
Answer: Your answer is $7.30
Step-by-step explanation:
Finding the amount for a tip is simple!
all that's required is multiplying the bill (36.50) by the amount you want to tip (.20, because 20% is equal to .20)
36.50×.2= $7.30
How do you use distributive property to express the expression as the multiple of a sum of two whole numbers with no common factor? 27 + 99, 99+36, 3+33, 33+27, 10+50
help help help help help help
When equation f(x) = 3x + 4 is transformed to h(x) = f(x + 3) and plotted on the graph, both the lines of the equations are parallel to each other.
What are graph equations?Equations with graphs as unknowns are known as graph equations in graph theory. The concept of isomorphism is one of the key issues in graph theory.Different graph equations may be used to express the aforementioned graphs.So, the equations are graphs are:
Given equation: f(x) = 3x + 4Which is transform to equation: h(x) = f(x + 3)Now, graph both equations as follows:
Both equations are parallel to each other.(Refer to the graph attached below)Therefore, when equation f(x) = 3x + 4 is transformed to h(x) = f(x + 3) and plotted on the graph, both the lines of the equations are parallel to each other.
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Shakira went bowling with her friends. She paid $3 to rent shoes and then $4.75 for each game of bowling. If she spent a total of $22, then how many games did Shakira bowl?
please show the work
Step-by-step explanation:
15t + 30 = 20t | -15t
30 = 5t
t = 30/5 = 6
20 + 5t = -6t + 86 | + 6t
20 + 11t = 86 | -20
11t = 66
t = 6
18t + 20 = 24t + 50 | -18t
20 = 6t + 50 | -50
-30 = 6t
t = -30/6 = -5
18t - 2 = 10t + 54 | -10t
8t - 2 = 54 | +2
8t = 56
t = 56/8 = 7
7t - 5 = 15t + 91 | -7t
-5 = 8t + 91 | -91
-96 = 8t
t = -96/8 = -12
One type of plant root splits 4 times while growing in the ground. The number of new roots after each split can be modeled by the function f(x)=3x, where x is the number of times the root splits. What is the domain of f(x)? CLEAR CHECK All positive integers All positive integers less than or equal to 4 All integers All positive integers greater than or equal to 4
The domain of the function f(x) = 3x is (b) All positive integers less than or equal to 4
How to determine the domain of the function?From the question, we have the following equation of the function that can be used in our computation:
f(x) = 3x
In this case, the notations are given as
x = Number of splits
f(x) = number of new roots in each split
From the question, we have
Splits = 4
This means that the maximum value of x is 4
The other values of x would be
x = 1, 2, 3, 4
This can be represented as
0 ≤ x ≤ 4
The interpretation of the above notation is all positive values less than or equal to 4
Hence, the domain value is option (b)
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Another thing you will need to know before you can perform a rotation is
direction of rotation
corresponding angles
corresponding sides
the angle measures
An angle is bisected. Each resulting angle is 78 degree. how is the original angle
Find the area of a regular hexagon
with a side length of 5 cm. Round to
the nearest tenth.
5 cm
[? ]cm²
Answer: 64.95
Step-by-step explanation: The formula is (3√3 s2)/2 so using that we can find the answer which is, 64.95
5a-2-3a+7 Simplify this expression.
Answer: 2a+5
5a-2-3a+7
First gather together the like terms
5a-3a and -2+7
then solve
5-3=2 and -2+7=5
answer = 2a+5
2015
The ratio of boys to girls in a class is 4:3. There are 35 students in the class. How many
students are boys?
Mrs. sisneros ran 3 miles in 27 minutes on monday. she ran 5 miles in 50 minutes on wednesday. on which day did mrs. sisneros run at a faster rate? what was that rate?
Friday hope that this helps
What are the roots of this polynomial? f(x) = (x+9)(x-9)(x+10)?
The solution for the given polynomial are x = -9, 9 and -10.
What is polynomial?
Polynomials are algebraic expressions that contain coefficients and variables. Variables are sometimes known as indeterminates. Mathematical operations like addition, subtraction, multiplication, and positive integer exponents can be performed on polynomial equations but division by variables cannot.
Given polynomial:
(x+9)(x-9)(x+10)
Equating it wit zero,
we get solutions as:
x = -9, 9, -10
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2x + y = 17 slope liner expression
Answer:
Step-by-step explanation:
Answer:
I don't know if this what you want but...
Step-by-step explanation:
2x+y=17
2x= 17-y
x= 17-y
2
Find the area of the square . Units required 18cm
Answer:
324 cm²
Step-by-step explanation:
area of a square = L x L = L²
L = 18cm
(18cm)² = 18cm x 18cm = 324 cm²
which of the following is a polynomial?
Answer:
Option D
Step-by-step explanation:
This is because it contains the sum of the same variable to different powers.
The function h is defined by h (x) = 2(x − 7).
What is the value of h (8) ?
2
23
30
9
Answer:
h(8) = 2
Step-by-step explanation:
substitute x = 8 into h(x) , that is
h(8) = 2(8 - 7) = 2(1) = 2
a survey of a congressional race finds 52 percent of voters supporting candidate a and 48 percent supporting candidate b, with a 5 percent margin of error. given this information, we can say that:
Answer:
When you round the number to 5
Step-by-step explanation: