Answer:
2
Step-by-step explanation:
[tex]5x^2 +3x +2 = 0\\\\\text{Apply the quadratic formula,}~ x=\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\\text{In this case,}~a= 5, ~ b = 3~ \text{and}~ c = 2\\\\ \\x=\dfrac{-3\pm \sqrt{3^2 -4\cdot 5 \cdot 2}}{2\cdot 5}\\\\~~~=\dfrac{-3 \pm \sqrt{9-40}}{10}\\\\~~~=\dfrac{-3 \pm \sqrt{-31}}{10}\\\\~~~=\dfrac{-3 \pm i\sqrt{31}}{10}\\\\\text{So, there are 2 solutions,}~ x=\dfrac{-3 + i\sqrt{31}}{10}~ \text{and} ~x=\dfrac{-3 -i\sqrt{31}}{10}[/tex]
Another way to find the number of solutions is by looking at the highest exponent(Degree), which indicates the number of solutions.
[tex]\\ \rm\rightarrowtail 5x^2+3x+2=0[/tex]
[tex]\\ \rm\rightarrowtail x=\dfrac{-3\pm \sqrt{9-40}}{10}[/tex]
[tex]\\ \rm\rightarrowtail x=\dfrac{-3\pm\sqrt{-31}}{10}[/tex]
[tex]\\ \rm\rightarrowtail x=\dfrac{-3\pm\sqrt{31}i}{10}[/tex]
A golfer hits from a tee for a 300-yard hole. Her drive carries 275 yards but it’s 13 degrees off the line from the hole. How much farther must the golfer now hit the ball to reach the hole?
By using the cosine rule, we will see that the distance between the golfer and the hole is 69.7 yd.
How to find the distance?Basically, we need to find the length of the missing side of the shown triangle.
So, one side measures 300yd, other side measures 275 yd, and the angle between these sides measures 13°.
Now we can use the cosine rule, where for sides a, b, and c, and angle A (A is the opposite angle to the side a) the rule says:
a^2 = b^2 + c^2 - 2bc*cos(A).
In this case we define:
b = 300ydc = 275 ydA = 13°Replacing that we get:
a^2 = (300yd)^2 + (275yd)^2 - 2*(300yd*275yd)*cos(13°) = 4,853.94 yd^2
a = √(4,853.94yd^2) = 69.7 yd
So the distance between the golfer and the hole is 69.7 yd.
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What is the solution set of the quadratic inequality f
Answer:
A quadratic inequality is an equation of second degree that uses an inequality sign instead of an equal sign. The solutions to quadratic inequality always give the two roots. The nature of the roots may differ and can be determined by discriminant (b2 – 4ac).
what are the possible values of remainder r, when a positive integer 'a' is divided by 3
Answer:
0, 1, 2
Step-by-step explanation:
Euclid's division Lemma states that for any two positive integers ‘a’ and ‘b’ there exist two unique whole numbers ‘q’ and ‘r’ such that , a = bq + r, where 0≤ r < b.
Here, a= Dividend, b= Divisor, q= quotient and r = Remainder.
According to Euclid's division lemma a 3q+r, where 0≤r≤3 and r is an integer.
Therefore, the values of r can be 0, 1 or 2.
The equation to model Exponential Decay is:
y = a[1 – r)
y= total amount
a= starting amount
r= the growth rate as a decimal
t= number of growth periods
Question 1 (1 point)
Sarah takes 550 mg of an antibiotic. Every hour,
her body breaks down 25% of the remaining drug.
How much will be left after 12 hours?
Guys help me please I really don’t understand this
I will give some hints. We know most values, we have to solve for y as that is the remaining amount.
y = We have to find.
a = 550 mg (She takes this much)
r = 0.25 (This is 25% as a decimal, don't forget to subtract 1)
t = 12 (This is because over the 12 hours, each hour it breaks down so (12 hours total * 1 hour periods) gives us 12 periods.
I hope this helps!
is this right? please tell me :) asap!!
Answer:
A
Step-by-step explanation:
calculate 20% of $88
[tex]\frac{20}{100}[/tex] × $88 = 0.2 × $88 = $17.60
The ratio of green marbles to yellow marbles is
4 green marbles to 6 yellow marbles.
If there are 2 green marbles,
how many yellow marbles are there?
Answer:
There are three yellow marbles.
Step-by-step explanation:
The way i figure it is since they are both even numbers divide them both by two and you have your answer.
Class
At the grand opening of a Cooper's department store, every sixth
customer to enter the store is given a free coffee cup and every ninth
customer is given a free tote bag. Which customer will receive both
gifts?
6RP
Answer:
Amy has $75 to buy 6 new books.If each book costs $5, which equation represents the amount of money ( m) Amy will have left? A. 75-11= m B. 75+15= m C. 75-30= m D.75+30= m
The area of the triangle is 22.4 cm2. Calculate the length, b, of the longest side of the triangle. 97° 3.7 cm a b
Answer:
Step-by-step explanation:
1. liola drives 130 m up a hill that has a slope of 7°. what horizontal distance, to the nearest hundredth of a
meter, has she covered?
o 129. 03 m
o 15. 84 m
o 15. 96 m
o 130. 97 m
The horizontal distance to the nearest hundredth of a meter, that Liola covered is 129.03 m (option A)
How to determine the horizontal distance?The following data were obtained from the question:
Hypotenuse = 130 mAngle (θ) = 7°Horizontal distance = Adjacent =?The horizontal distance Liola covered as she drives 130 m up the hill can be obtained as follow:
Cos θ = Adjacent / Hypotenuse
Cos 7 = Horizontal distance / 130
Cross multiply
Horizontal distance = 130 × Cos 7
= 130 × 0.9925
= 129.03 m
Thus, the horizontal distance Liola covered is 129.03 m (option A)
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Natalie surveyed 800 of the students in her school about their favorite color. Students could choose between blue and red. 77% said their favorite color was red. How many students' favorite color was blue?
The number of students whose favorite color was blue is 184.
WE are Given that the number of students surveyed by Natalie is 800 and that 77% of them chose red as their favorite color.
We can determine the number of students who chose blue by Finding the percentage of students who chose blue and then converting it to the actual number of students who chose blue.
Consider x be the number of students who chose blue as their favorite color.
Therefore, the number of students who chose red is;
77% of 800
= 77/100 × 800
= 616
To find the number of students who chose blue, we need to subtract the number of students who chose red from the total number of students surveyed.
Therefore:
x = Total number of students surveyed - Number of students who chose red
x = 800 - 616
x = 184
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Please Help! In a proof to show two triangles are congruent if a given is PR ⟂ CK, which of the following statements most likely will be used within the proof?
Answer: PR and CK form right angles.
Step-by-step explanation:
By definition, perpendicular lines form right angles, and vice versa (in other words, lines that form right angles are perpendicular). Since we need to show PR is perpendicular to CK, we must first show that PR and CK form right angles.
The experimental probability of a quarter landing on HEADS is 3/5 if the quarter landed on TAILS 36 times how many times tossed.
Answer:
90 times
Step-by-step explanation:
I don't rly know how to explain it but it's 90 and I hope this helps you at least know the answer if not then sorry for wasting your time and may God bless you:)
Find the AREA of the figure. (Sides meet at right angles.)
Answer:
47
Step-by-step explanation:
3 x 4 = 12
7 x 5 = 35
35 + 12 = 47
In creating a new scale for the mercury thermometer, anders celsius initially set the boiling point of water at _____. a. 0° b. 32° c. 100° d. 273°
Answer: 100 °
Step-by-step explanation:
t divided by 5 = 2.9
What step should be performed on both sides of this equation to find the solution?
Add 5.
Subtract 5.
Multiply by 5.
Divide by 5.
Answer:
multiply by 5
Step-by-step explanation:
Answer:
3 / C. Your answer is multiply by 5!!!!!
Step-by-step explanation:
Hope this helps!
BRAINLIEST FOR CORRECT ANSWER: What is the area of this figure?
Step-by-step explanation:
The answer should be 578mi²
Each of the two numbers were increased by 10. How did the average of the two numbers change?
Answer:
Average increased by 10
Step-by-step explanation:
Lets take 2 numbers - 10 and 12. The average of these two numbers is 11. By adding 10 to both of these numbers you get 20 and 22. The average of these numbers is 21. The average of the 2 numbers increased by 10
Which effect did World War II have on the United States?
a) The United States became the richest, most powerful nation in the world.
b) The war caused the United States to enter another severe depression.
c) The war had little effect on the United States.
d) The United States became second in power only to England.
Answer:
the anwer is A cause jobs and industials had 96 percent and corperate profits after taxes doubled
Answer:
a
Step-by-step explanation:
world War 2 did in fact cause the United States to become the richest and most powerful
Hannah travels 6 times as many minutes to work as Raoul does. Together,
they travel for 63 minutes. How many minutes does Hannah travel? Draw
a model and write an equation to solve.
Answer:
hannah 54
raoul 9
Step-by-step explanation:
hannah _ 6x
raoul _ x
6x+x=63
7x=63
x=9
hannah _ 6×9=54
raoul _ 9
A surveyor determines that the angle of elevation between herself and the top of an observation tower is 60^o. She determines that the distance between her position and the base of the tower is 20 meters. Approximately how tall is the tower?
Find the area. :)
please and thx
Answer:
132 cm²
Step-by-step explanation:
To find the area of the figure, start by dividing the figure into smaller rectangles.
Area of figure
= area of shaded rectangle +area of unshaded rectangle
[tex]\textcolor{steelblue}{\text{Area of rectangle= length ×breadth}}[/tex]
Shaded rectangle
Length= 4 cm
Breadth= 6 cm
Area
= 4(6)
= 24 cm²
Unshaded rectangle
Length= 9 cm
Breadth= 12 cm
Area
= 9(12)
= 108 cm²
After finding the area of each rectangle, we can add the two areas together to obtain the total area of the figure.
Area of figure
= 108 +24
= 132 cm²
how do you find the circumference, radius, and diameter in area?
Answer:
Sample Respond: Let's assume it's equal to 14 cm. Substitute this value to the formula for circumference: C = 2 * π * R = 2 * π * 14 = 87.9646 cm . You can also use it to find the area of a circle: A = π * R² = π * 14² = 615.752 cm² . Finally, you can find the diameter - it is simply double the radius: D = 2 * R = 2 * 14 = 28 cm .
Step-by-step explanation:
I got 100% on the quiz
let f(x)=3x+4 and g(x)=2x-5 find (f+g)(x)
Answer:
(f+g)(x) = 5x - 1
Step-by-step explanation:
Let f(x) = 3x + 4 and g(x) = 2x - 5 find (f+g)(x)
f(x) = 3x + 4 and g(x) = 2x - 5, find (f+g)(x)
(f+g)(x) =
f(x) + g(x)
3x + 4 + 2x - 5 (combine like terms)
5x - 1
Therefore, (f+g)(x) = 5x - 1
Hope this helps!
Answer:
5x -1
Step-by-step explanation:
(3x + 4) + (2x - 5) = 3x + 4 + 2x - 5 = 3x + 2x + 4 - 5
5x - 1
Problem 2
What is the probability of pulling a heart, replacing it, pulling a club, replacing it, pulling a diamond,
replacing it, then pulling a spade, all from a standard deck?.
Answer:
subtract one for heart drawn without replacement leaves 51 cards on which thirteen are clubs. probability of drawing club 13/51. After drawing a heart as first card there are 51 cards left and 13 of them are clubs. So the probability on drawing a club then equals 13/51
Which trig ratio will be helpful in finding the missing side length sin(24)
The sin ratio will be helpful in finding the missing side length and the missing side length is 29.50 units.
What is the trigonometric ratio?The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.
We have a right-angle triangle in the figure in which:
Length of the hypotenuse = x unit
Length of the side opposite to the angle = 12
And the angle is given between sides adjacent to the angle to the hypotenuse = 24°
We know the:
[tex]\rm sin\theta = \frac{Side \ opposite \ to \ the \ angle}{hypotenuse }[/tex]
[tex]\rm sin24 = \frac{12}{x}[/tex]
[tex]\rm x = \frac{12}{sin24}[/tex]
x = 29.50 units
Thus, the sin ratio will be helpful in finding the missing side length and the missing side length is 29.50 units.
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I need help on this question I’m confused I think a &b are the same and c &d are different but I’m not to sure !
====================================================
Reason:
[tex]2^6[/tex] means we have 6 copies of "2" multiplied out as shown in choice B. That explains how A and B are the same, and we can say
[tex]2^6 = (2*2*2)*(2*2*2)[/tex]
The parenthesis are optional, but I find they're handy to count the '2's easier.
----------------
Now notice that
[tex]2^3 = 2*2*2[/tex]
So,
[tex]2^6 = (2*2*2)*(2*2*2)\\\\2^6 = (2^3)*(2^3)\\\\2^6 = (2^3)^2\\\\[/tex]
The last step is possible because we have two copies of [tex]2^3[/tex] multiplied together.
This shows that choice C is equivalent to A and B.
-------------------
Lastly,
[tex]2^6 = (2*2*2)*(2*2*2)\\\\2^6 = (2*2)*(2*2)*(2*2)\\\\2^6 = (2^2)*(2^2)*(2^2)\\\\2^6 = (2^2)^3\\\\[/tex]
The jump to the last step is possible because we have three copies of [tex]2^2[/tex] multiplied together.
This shows choice D is equivalent to the others.
All four expressions are the same.
They represent different ways to say the same number. That number being 64.
How many solutions are there?
Answer:
no solution
Step-by-step explanation:
Solve:
6(2k + 1) = 12k + 1
Expand brackets:
⇒ 12k + 6 = 12k + 1
Subtract 12k from both sides:
⇒ 6 = 1
As 6 ≠ 1 there is no solution
Answer:
No solution
Step-by-step explanation:
Simplify the L.H.S and the R.H.S
⇒ [tex]6(2k + 1) = 12k + 1[/tex]
⇒ [tex]12k + 6 = 12k + 1[/tex]
Cancel out the "12k"
⇒ [tex]12k + 6 = 12k + 1[/tex]
⇒ [tex]6 = 1 (\text{False})[/tex]
Henceforth, this equation has no solution.
Find the distance between the two points in simplest radical form.
Answer:
13 units
Step-by-step explanation:
A right triangle can be drawn using the grid lines for legs and the line segment between the two points as the hypotenuse. You can count grid squares or subtract coordinates to find the vertical leg is 12 units and the horizontal leg is 5 units. The Pythagorean theorem tells you the length of the hypotenuse (distance between the points) is ...
d² = 12² +5² = 144 +25 = 169
d = √169 = 13
The distance between the two points is 13 units.
_____
Additional comment
This set of dimensions, {5, 12, 13}, is one of several "Pythagorean triples" that often show up in math problems. Other common triples are {3, 4, 5}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}, and multiples of these.
100 BRAINLY POINTS!!!!
The cost, y, in dollars, to purchase x school T-shirts includes a one-time setup fee, plus a charge per T-shirt. The cost is modeled with the linear function y = 6.67x + 35. What is the cost to purchase each T-shirt after the beginning setup cost is paid?
A. $41.67
B. $35.00
C. $28.33
D. $6.67
PLEASE HELP CUH
EXPLAIN YOUR ANSWER
SHOW YOUR WORK
Let's check our given function.
y=6.67x+35Compare to y=mx+b(Slope intercept)
Slope=m=6.67Y intercept=b=35So beginning set up is fixed i.e 35 .
per shirt cost the rate of change which is slope
option D is correct
ZA and ZB are vertical angles. If mA = (2x - 4)º and mZB = (4x - 30),
then find the value of x.
Answer:
x=13
Step-by-step explanation:
2x-4 = 4x - 30
-4 = 2x - 30
26 = 2x
x = 13