solve w^2 + 7w - 18 = 0
with the steps pls
Answer:
w=2 w = -9
Step-by-step explanation:
w^2 + 7w - 18 = 0
We can factor this equation
What 2 numbers multiply to -18 and add to 7
9*-2 = -18
9+-2 = 7
(w-2) (w+9) = 0
Using the zero product property
w-2 = 0 w+9 =0
w=2 w = -9
Answer:
[tex]w_1=2\\w_2=-9[/tex]
Step-by-step explanation:
This is going to be solved using the quadratic formula.
1. Determine the quadratic equation’s coefficient [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex].
Use the standard form, [tex]ax^2+bx+c=0[/tex] , to find the coefficients of our equation,
[tex]w^2+7w-18=0[/tex]:
a = 1
b = 7
c = -18
2. Plug these coefficients into the quadratic formula
The quadratic formula gives us the roots for [tex]aw^2+bw+c=0[/tex] , in which [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are numbers (or coefficients), as follows:
[tex]w=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
7 additional steps:
a = 1
b = 7
c = -18
[tex]w=\frac{-7\pm\sqrt{7^2=4*1*-18} }{2*1}[/tex]
Simplify exponents and square roots
[tex]w=\frac{-7\pm\sqrt{49-4*1*-18} }{2*1}[/tex]
Perform any multiplication or division, from left to right:
[tex]w=\frac{-7\pm\sqrt{49-4*-18}}{2*1}\\w=\frac{-7\pm\sqrt{49--72}}{2*1}\\\\w=\frac{-7\pm\sqrt{49+72}}{2*1}\\w=\frac{-7\pm\sqrt{121}}{2*1}[/tex]
to get the result:
[tex]w=\frac{-7\pm\sqrt{49-4*-18}}{2}[/tex]
3. Simplify square root [tex]\sqrt{121}[/tex]
Simplify 121 by finding its prime factors:
121 ( 11 * 11)
The prime factorization of 121 is 11^2
Write the prime factors:
[tex]\sqrt{121}=\sqrt{11\cdot 11}[/tex]
Group the prime factors into pairs and rewrite them in exponent form:
'[tex]\sqrt{11\cdot 11}=\sqrt{11^2}[/tex]
Use the rule [tex]\sqrt{x^2=x}[/tex] to simplify further:
[tex]\sqrt{11^2}=11[/tex]
4. Solve the equation for w
[tex]w=\frac{-7\pm11}{2}[/tex]
The ± means two answers are possible.
Separate the equations:
[tex]w_1=\frac{(-7+11)}{2}[/tex] and [tex]w_2=\frac{-7-11}{2}[/tex]
[tex]w_1=\frac{-7+11}{2}[/tex]
[tex]w_1=\frac{4}{2}[/tex]
[tex]w_1=2[/tex]
[tex]w_2=\frac{-7-11}{2}[/tex]
[tex]w_2=\frac{-18}{2}[/tex]
[tex]w_2=-9[/tex]
---------------------
Why learn this
In their most basic function, quadratic equations define shapes like circles, ellipses and parabolas. These shapes can in turn be used to predict the curve of an object in motion, such as a ball kicked by football player or shot out of a cannon. When it comes to an object’s movement through space, what better place to start than space itself—with the revolution of planets around the sun in our solar system. The quadratic equation was used to establish that planets’ orbits are elliptical, not circular. Determining the path and speed an object travels through space is possible even after it has come to a stop: the quadratic equation can calculate how fast a vehicle was moving when it crashed. With information like this, the automotive industry can design brakes to prevent collisions in the future. Many industries use the quadratic equation to predict and thus improve their products’ lifespan and safety.---------------
Terms and topics
Solving quadratic equations using the quadratic formulaSimplifying radicalsFind prime factors-----------
Learn more:
https://brainly.com/question/1214333https://brainly.com/question/13603021Consider parallelogram △MNOP shown above.
Enter the length of each measurement, in units, in the table.
To find the length of the sides of this parallelogram, we just have to calculate the length of each side and then proceed to find the perimeter.
The perimeter of the parallelogram is 13 units.
Perimeter of a ParallelogramTo calculate the perimeter of a parallelogram, we need the values of the length of the sides. However, if we have the details of two opposite sides, we can find the perimeter of the parallelogram because opposite sides are equal.
Length of MN = 2unitsLength of MP = 4.5 unitsThe perimeter of MNOP can be calculated as
[tex]perimeter = 2(MP + MN)[/tex]
We can substitute the values into the equation and solve
[tex]perimeter = 2(MP + MN)\\perimeter = 2 * (4.5 + 2)\\perimeter = 2 * 6.5\\perimeter = 13[/tex]
The perimeter of the parallelogram is 13 units.
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the area of a square is 2116 CM square which is equal to the area of a rectangle whose length is 92 cm what is the perimeter of the rectangle
Answer:
Perimeter = 230 cm.Step-by-step explanation:
width of the rectangle = 2116 ÷ 92 = 23
Perimeter of the rectangle = 2×(23 + 92) = 230
Jason and his friend went to a restaurant for dinner. The food that they ordered cost $25. A 7% sales tax was applied to the total.
After the sales tax was applied, Jason paid a 15% tip on the total bill. How much did Jason pay at the restaurant?
OA. $30.76
OB. $28.75
OC. $30.50
OD. $26.75
Answer:
A. $30.76
Step-by-step explanation:
First find the amount of tax applied to the bill.
Change 7% to a decimal by moving the decimal point two places left.
7% = 0.07
Multiply
25 x 0.07 = 1.75
Add the amount of tax to the total cost.
25 + 1.75 = 26.75
Now find the amount of the tip.
Change 15% to a decimal by moving the decimal two places left.
15% = 0.15
Multiply
26.75 x 0.15 = 4.0125
Add the amount of the tip back into the cost.
26.75 + 4.0125 = 30.7625
Round
30.7625 = 30.76
What number is 278 less than 6,896?
Answer:
6618
Step-by-step explanation:
6896 - 278 = 6618
Hope this helps
Answer:It’s 6,618
Step-by-step explanation: Since it’s less you have to subtract, 6,896 - 278 = 6,618.
Hope this helped ya! :D
What is an equation parallel and perpendicular to the given line equation is y=2x - 5
Answer:
This should help.
Step-by-step explanation:
The attached image will help.
Trigonometry: "Find x, to the nearest tenth of a centimetre."
How and what formulas/etc. can I use to solve this?
Answer:
The rule to be use is
SOC CAH TOA
But in this we use d CAH cox there's adjacent and hypothenos here
Step-by-step explanation:
The first triangle
hyp²=opp.²+adj²
62²=x²+3.5²
x²=62²-3.5²
x²=3844-12.25
x²=3831.75
the radius of a circle is 5 in. Find its area in terms of pi.
Answer:
well the area of a circle is [tex]\pi r^{2}[/tex]
Step-by-step explanation:
since they want it in terms of pi
just say, 25[tex]\pi[/tex]
algebra 2 pls help ill give brainliest
Answer:
a = -2
p = 2
w = 3
Step-by-step explanation:
The degree of the polynomial is 6 as it has five turning points.
From inspection of the graph it appears that the curve touches
the x-axis at x = 1.
Therefore, a factor is (x - 1) with multiplicity of 2: (x - 1)²
The curve appears to cross the x-axis at x = 2.
Therefore, a factor is (x - 2), so p = 2
There appears to be a point of inflection at x = -1
Therefore, a factor is (x + 1)³, so w = 3
The y-intercept appears to be at (4, 0)
The product of the constants of the found factors is:
⇒ 1³ × (-1)² × (-2) = -2
Therefore, to find the value of a:
⇒ 4 = -2a
⇒ a = -2
Therefore, the polynomial function is:
f(x) = -2(x + 1)³ (x - 1)² (x - 2)
Which of the following are mathematical sentences? Check all that apply.
A. 5-v
B.7
C. 4+3=7
D. 2<3
Y. 5-re =0
O F. gram
Which inequality has a solid boundary line when graphed?
Y<-x-9
y<1/9x+9
y>-1/9x
y >9x+9
Inequalities are expression not separated by an equal sign. None of the inequality is correct since there is absence of equal sign.
Graph of inequalitiesInequalities are expression not separated by an equal sign. According to the question, we ned the inequality's graph that will have a dashed boundary line.
An inequality that will have solid boundary line must include only the less than or equal to sign < or greater than or equal to > sign.
From the option given, none of the inequality is correct since there is absence of equal sign.
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How do you write 6,920 in scientific notation
Answer:
6.92×10 to the power inverse eleven
A person standing close the the edge on the top of a 80 foot building throws a baseball vertically upward. the quadratic function h(t) = -8t^2 + 32t + 80 models the ball's height above the ground, h(t), in feet, t seconds after it was thrown.
How do I efficiently determine...
-- how many seconds it takes until the ball reaches max height
-- the maximum height
-- how many seconds it takes until the ball hits the ground
without graphing?
The number of seconds it takes until the ball reaches max height is 2 seconds and the maximum height is 112 feet, and the number of seconds it takes until the ball hits the ground will be 6.9 seconds.
What is a projectile motion?When a body is thrown in the air then the motion under the gravity is known as projectile motion.
A person standing close the the edge on the top of a 80 foot building throws a baseball vertically upward. the quadratic function
h(t) = -8t² + 32t + 80 models the ball's height above the ground, h(t), in feet, t seconds after it was thrown.
The number of second to reach at maximum height will be
We know that at maximum height, the rate will be zero. Then we have
h'(t) = 0
-16t + 32 = 0
t = 2 seconds
Then the maximum height will be
h(t) = -8(2)² + 32 x 2 + 80
h(t) = -32 + 64 +80
h(t) = -32 + 144
h(t) = 112 feet
Then the number of the seconds to reach at the ground will be
-8t² + 32t + 80 = -80
-8t² + 32t + 160 =0
t² - 4t - 20 = 0
Then t will be
[tex]\rm t = \dfrac{-(4) \pm \sqrt{(-4)^2 - 4 * 1 * -160}}{2*1}[/tex]
Then we have
t = 6.9 and -2.9
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A concert that features different singing groups will be held at a Municipal Hall. The concert will start with a solo performance, followed by a duet, then a trio, and so on with the last performance coming from a choir with 30 members. How many people will perform at the concert? (problem-solving)
Step-by-step explanation:
this is the problem to sum the numbers 1 ... n.
remember the old trick by adding
n + 1
n-1 + 2 = n + 1
n-2 + 3 = n + 1
...
and doing this n/2 times, giving us a sum
n×(n+1)/2
for n = 30 we get
30×31/2 = 15×31 = 465
so, 465 people will perform.
Aiden surveyed 300 of the students in his school about their favorite color. 85% said their favorite color was red. How many students' favorite color was red?
Answer:
255 students
Step-by-step explanation:
we can solve for the number of students who said their favorite color was red by setting up a cross-multiplication equation.
85% is nothing but 85/100
85/100 = ?/300
85 times 300 is 25500
25500/100 = 255
give brainliest, please!
hope this helps :)
The table represents a function.
X
-6
-2
6203
f(x)
3
1
4
-2
What is f(-2)?
0-3
O-1
0 1
0 3
Solve the proportion (write it as a whole number or decimal)
2/3 - 3/q
so q =__
A college basketball player is known to make 80% of his free throws. Over the course of the season, he will attempt 100 free throws. Assuming free-throw attempts are independent, what is the probability that the number of free throws he makes exceeds 80
The probability that the number of free throws he makes exceeds 80 is approximately 0.5000.
The complete question is as below:-
A college basketball player makes 80% of his free throws. Over the course of the season, he will attempt 100 free throws. Assuming free throw attempts are independent, the probability that the number of free throws he makes exceeds 80 is approximate:____________.
A) 0.2000
B) 0.2266
C) 0.5000
D) 0.7734
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Given that,
A college basketball player makes 80% of his free throws.
Over the course of the season, he will attempt 100 free throws.
Assuming free throw attempts are independent.
We have to determine,
The probability that the number of free throws he makes exceeds 80 is.
According to the question,
P(Make a Throw) = 80% = 0.80
number of free throws n = 100
Binomial distribution:
Mean: n x p = 0.80 x 100 = 80
Then, The standard deviation is determined by using the formula;
[tex]\sigma[/tex] = [tex]\sqrt{np(1-P)[/tex]
= [tex]\sqrt{80\TIMES (1-0.80)[/tex]
= [tex]\sqrt16[/tex]
= 4
Therefore,
To calculate the probability that the number of free throws he makes exceeds 80 we would have to make the following calculation:
P ( x> 80) = 1 - P ( x < 80)
To calculate this value via a normal distribution approximation:
P ( [tex]Z < \dfrac{80-80}{4})[/tex] = 1-P(Z < 0 ) = 1 - 0.50 = 0.500
Hence, The probability that the number of free throws he makes exceeds 80 is approximately 0.5000.
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The table represents the function f(x).
The value of f(3) is 9
How to determine the value of f(3)?The table that completes the question is added as an attachment.
From the complete table, we have:
When x = 3, the value of the function is 9
This means that:
f(3) = 9
Hence, the value of f(3) is 9
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Write in ascending order: 3 2 , 3 8 , 3 5 , 3 11 __________________
Answer:
3, 11, 32, 35, 38
Step-by-step explanation:
Ascending order means to place in order from smallest to largest.
Hope this helps!
If not, I am sorry.
The cost of a rice cooker with 13% VAT is Rs 4,068.
Answer:
0.319
Step-by-step explanation:
I have do 13/4068*100percent hope the answer that I have gave is correct
Triangle ABC is an isosceles triangle and gle B measures 28.5 degrees. What is measurement of the other two angles?
Answer:
angle c: 28.5°
angle a: 123°
Step-by-step explanation:
After a storm, a 36-foot tall tree is now leaning
towards a house, making an 87° angle with the
ground. If the angle of elevation from the base of
the house to the top of the tree is 38°, how far is the
tree from the house?
The distance of the tree from the house is: 45.99 feet
What is angle of elevation?Angle of elevation is the angle the horizontal makes with the line of sight.
Analysis:
The tree lean towards a house meaning it does not lean on the house but a distance away from the house.
let the distance away from the house be d.
The line of sight intersects the top of the tree at a point.
The height of the point from the horizontal ground is 36 sin 87 = 36(0.998) = 35.92 feet
to find distance of the tree from the house, we use the angle of elevation which is 38 degrees. so that tan 38 = 35.92/d
d = 35.92/0.781 = 45.9 feet
In conclusion, the distance of the tree from the house is 45.9 feet
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Monica earned twice as much Samuel walking dogs. The amount Samuel earned was $7 more than Kara earned. Suppose Monica earned $48.50. Write and solve an equation to find the amount Kara earned. What is the difference between the greatest amount earned and the least amount earned walking dogs?
Answer:
Always include the steps and/or background required to get to the final answer. Let’s help other people understand and solve future problems on their own.
Step-by-step explanation:
Select the correct answer from each drop-down menu. Segment AB has seven equally spaced points on it. Starting at A and moving left to right, the points are C, D, E, F, G, H, and I. In the diagram, is divided into equal parts. The coordinates of point A are (-3, 9), and the coordinates of point B are (9, 5). The coordinates of point C are . The coordinates of point E are . The coordinates of point H are .
The coordinates of points C, E and G are respectively; C = (-0.75, 8.5), E = (3.75, 7.5) and H= (7.5, 6)
What is the Coordinates of the Line Segment about?The question stated that the line AB is divided into 7 equally spaced points that are tagged as C, D, E, F, G, H and I.
Note that the coordinates of A and B are A(-3, 9) and B(9, 5) respectively and because they are known to be equally spaced, then it implies that point F is the midpoint of the line.
Thus (x, y) is said to be the coordinate of F. So;
x, y = (-3 + 9)/2, (9 + 5)/2
x, y = (6, 7)
Note also that H is the midpoint of FB. So,
H(x, y) = (6 + 9)/2, (5 + 7)/2
H(x, y) = (7.5, 6)
Since D is midpoint of A and F. therefore;
D(x, y) = (-3 + 6)/2, (9 + 7)/2
D(x, y) = (1.5, 8)
Since E is midpoint of F and D. So;
E(x, y) = (1.5 + 6)/2, (8 + 7)/2
E(x, y) = (3.75, 7.5)
C is midpoint of D and A. So;
C(x, y) = (-3 + 1.5)/2, (9 + 8)/2
C(x, y) = (-0.75, 8.5)
Therefore, we can say that the coordinates of points C, E and G are respectively; C = (-0.75, 8.5), E = (3.75, 7.5) and H= (7.5, 6).
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If \mathbf{9x+4y=3}9x+4y=3 is a true equation, what would be the value of \mathbf{4y+9x}4y+9x?
Answer:
3
Step-by-step explanation:
[tex]9x+4y = 4y+9x = 3[/tex]
If the factors of quadratic function g are (x − 7) and (x + 3), what are the zeros of function g?
A.
3 and 7
B.
-3 and 7
C.
-7 and -3
D.
-7 and 3
Answer: B. -3 and 7
Step-by-step explanation:
To find the zeros, just move the constants to the other side,
x - 7 ⇒ x = 7
x + 3 ⇒ x = -3
If the number is moved to the other side its sign becomes opposite
Hope it helps!
The circle below has a center D and its diameter is 10 feet. Given that m angle A D B equals 35 degree, find the length of major arc stack A C B with overparenthesis on top.
A circle with center D and points A B C on the circle. Angle A D B is 35 degrees formed by radius B D and A D.
Group of answer choices
35 over 36 straight pi feet
325 over 18 straight pi feet
325 over 36 straight pi feet
35 over 18 straight pi feet
The length of major arc ACB with angle measure of 325° and diameter of 10 feet is (325/36)π
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
angle of arc ACB = 360° - 35° = 325°
The length of major arc ACB = (325/360) * π * 10 = (325/36)π
The length of major arc ACB with angle measure of 325° and diameter of 10 feet is (325/36)π
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Mark is baking a pie that has a diameter of 10 inches. he wants to cover the top of the pie with a pie crust . what is the area of the crust that will cover the top of the pie?
Answer:
79 square inches.
Step-by-step explanation:
Mark is baking a pie that has a diameter of 10 inches. he wants to cover the top of the pie with a pie crust. what is the area of the crust that will cover the top of the pie?
Pie = circle (shape)
What is the area of a circle 10 inches in diameter? ≈ 79 square inches. and r denotes the radius. = 78.5 square inches. ≈ 79 square inches.
if a = 6, b = 3, and c = 7, evaluate the following expression (picture below)
A 84
B 147
C 3
D 1/3