The solution of the given quadratic equation is x = -2.
What is a quadratic equation?A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.
Given is a quadratic equation x²+4x+4 = 0, we need to solve it using the Quadratic Formula:
The formula for the same is given by -
x = -b ± √b²-4ac / 2a
Here,
a = 1, b = 4 and c = 4
Put in the formula,
x = -4 ± √4²-4(1)(4) / 2
x = -4 ± √16-16 / 2
x = -4 ± √0 / 2
x = -4/2
x = -2
Hence, the solution of the given quadratic equation is x = -2.
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Divide. Write your answer as a fraction in simplest form. − 10 2/7÷(−4 4/11)=
Answer:
33/14
Step-by-step explanation:
[tex] - 10 \frac{2}{7} + ( - 4 \frac{4}{11} )[/tex]
[tex] = - \frac{72}{7} \div - ( \frac{48}{11} )[/tex]
[tex] = \frac{72}{7} \times \frac{11}{48} [/tex]
[tex] = \frac{3}{7} \times \frac{11}{2} [/tex]
[tex] = \frac{33}{14} [/tex]
stan dreamcatcher
find the mean value of the following. 5, 11, 4, 10, 8, 6
please help me guys its important
Answer:
1441.08in^3
Step-by-step explanation:
I don't understand need help?
9514 1404 393
Answer:
2. (only)
Step-by-step explanation:
The Pythagorean theorem tells you the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. To determine if these are right triangles, determine if that condition is met.
1. 3^2 +5^2 = 9 + 25 = 34 ≠ (√35)^2 . . . . not a right triangle
2. 5^2 +4^2 = 25 +16 = 41 = (√41)^2 . . . a right triangle
3. 6^2 +8^2 = 36 +64 = 100 ≠ (√10)^2 . . . . not a right triangle
4. 3^2 +3^2 = 9 +9 = 18 ≠ (3√3)^2 = 27 . . . . not a right triangle
An angle measures 73.6° more than the measure of its complementary angle. What is the measure of each angle?
PLEASE help, I'm struggling a lot!
Answer:
Let ABC = 73.6
Complement = ABD = 16.4
ABx = unknown angle
ABx + (ABx + 73.6) = 90
ABx = 16.4 / 2 = 8.2
The angles are 8.2 and (8.2 + 73.6) = 90
solve for w.
-9/7=-2/3w-1/2
Answer: [tex]w=\frac{33}{28}[/tex]
Step-by-step explanation:
To solve for w, we want to isolate w.
[tex]-\frac{9}{7}=-\frac{2}{3}w-\frac{1}{2}[/tex] [add both sides by 1/2]
[tex]-\frac{11}{14}=-\frac{2}{3}w[/tex] [multiply both sides by -3/2]
[tex]w=\frac{33}{28}[/tex]
Now we know that [tex]w=\frac{33}{28}[/tex].
Answer:
[tex]\sf w=\dfrac{33}{28} \\[/tex]
Step-by-step explanation:
[tex]\sf -\dfrac{9}{7} =-\dfrac{2w}{3} -\dfrac{1}{2}[/tex]
First, take -2w/3 to the left side.
[tex]\sf -\dfrac{9}{7}+\dfrac{2w}{3} = -\dfrac{1}{2}[/tex]
Then, add 9/7 to both sides.
[tex]\sf \dfrac{2w}{3} = -\dfrac{1}{2}+\dfrac{9}{7}[/tex]
Make the denominators the same and add the fractions.
[tex]\sf \dfrac{2w}{3} = -\dfrac{1*7}{2*7}+\dfrac{9*2}{7*2}\\\\\sf \dfrac{2w}{3} = -\dfrac{7}{14}+\dfrac{18}{14}\\\\\sf \dfrac{2w}{3} = \dfrac{-7+18}{14}\\\\\sf \dfrac{2w}{3} = \dfrac{11}{14}[/tex]
Use cross multiplication.
[tex]\sf 2w*14=11*3\\\\28w=33[/tex]
Divide both sides by 28.
[tex]\sf w=\dfrac{33}{28} \\[/tex]
SEE QUESTION IN IMAGE
Answer:
B. 48°Step-by-step explanation:
∠OST = 90° as ST ⊥ OS (tangent is perpendicular to radius at same point)
m∠OSP = 1/2(180° - m∠SOP) = 90° - 96°/2 = 42° (sum of interior angles of the triangle SOP)
m∠PST = 90° - m∠OSP = 90° - 42° = 48° (angle addition postulate)
Correct choice is B
Am I suppose to substitute the variables with random numbers in order to answer these questions???
Translation A maps (x, y) to (x + n, y + 1). Translation B maps (x, y) to (x +s, y + m).
1. Translate a point using Translation A, followed by Translation B. Write an algebraic rule for the final image of the point after this composition.
2. Translate a point using Translation B, followed by Translation A. Write an algebraic rule for the final image of the point after this composition.
3. Compare the rules you wrote for parts (a) and (b). Does it matter which translation you do first? Explain your reasoning.
9514 1404 393
Answer:
(x, y) ⇒ (x +n +s, y +1 +m)(x, y) ⇒ (x +s +n, y +m +1)they are identical in effect; order does not matterStep-by-step explanation:
Substitute the expressions.
A then BAfter the first translation, the value of x is (x+n). Put that as the value of x in the second translation.
x ⇒ x +s . . . . . . . . . the definition of the second translation
(x+n) ⇒ (x+n) +s . . . the result after both translations
The same thing goes for y. After the first translation, its new value is (y+1).
y ⇒ y +m . . . . . . . . the definition of the second translation
(y+1) ⇒ (y+1) +m . . . the result of both translations
Then the composition of A followed by B is (x, y) ⇒ (x +n +s, y +1 +m).
__
B then AThe same reasoning applies. After the B translation, the x-coordinate is (x+s) and the y-coordinate is (y+m). Then the A translation changes these to ...
x ⇒ x +n . . . . . . . . . . definition of translation A
(x+s) ⇒ (x+s) +n . . . . translation A operating on point translated by B
y ⇒ y +1 . . . . . . . . . . . definition of translation A
(y+m) ⇒ (y+m) +1 . . . . translation A operating on point translated by B
The composition of B followed by A is (x, y) ⇒ (x + s + n, y + m + 1).
__
You should recognize that the sums (x+n+s) and (x+s+n) are identical. The commutative and associative properties of addition let us rearrange the order of the terms with no effect on the outcome.
The two translations give the same result in either order.
If 75% is 10 days, how many days is the remaining 25%?
Answer:
10/3 days or 3 1/3 days
Step-by-step explanation:
Let d = number of days total
75% of the days is 10
.75 d = 10
d = 10/.75
d = 40/3 days
We want to know how man is 25% of d
d * 25%
(40/3) *.25
10/3 days
How many gallons equal 26 liters
Answer:
6.8 gallions i believe. im not quite sure
please help i need to finnish this!
Answer:
56
Step-by-step explanation:
f(x)=6*x^2+2 =6*3^2+2=56
Answer:
56
Step-by-step explanation:
6(x^2) + 2 = 0replace x = 3 => 6 x (3 ^ 2) + 2 = 56
Given: j(x) = x2 - 2x + 1
Which set of values represents the range of the function for the domain {0, 1, 5}?
Answer:
{1, 0, 16}
Step-by-step explanation:
given..
j(x) = x^2-2x+1
put all given values of domain (1,0 and 5 ) in the equation..
the values you get are range of the function
Answer: 1
Step-by-step explanation
0(2)-2(0)+1=0+0+1= 1
1(1)-(2)(1)+1=1-2+1= 1
(5)(2)-(2)(5)+1=10-10+1= 1
Is the following number rational or irrational?
-117
Choose 1 answer:
Rational
Irrational
Answer:
-117 is irrational number
Answer:
Irrational
Step-by-step explanation:
Irrational number can't be written as a faction, -11pie can't be written as a fraction. Therefore it is a irrational number.
help please ITS OF TRIGONOMETRY
PROVE
Answer:
The equation is true.
Step-by-step explanation:
In order to solve this problem, one must envision a right triangle. A diagram used to represent the imagined right triangle is included at the bottom of this explanation. Please note that each side is named with respect to the angle is it across from.
Right angle trigonometry is composed of a sequence of ratios that relate the sides and angles of a right triangle. These ratios are as follows,
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]
One is given the following equation,
[tex]\frac{sin(A)+sin(B)}{cos(A) +cos(B)}+\frac{cos(A)-cos(B)}{sin(A)-sin(B)}=0[/tex]
As per the attached reference image, one can state the following, using the right angle trigonometric ratios,
[tex]sin(A)=\frac{a}{c}\\\\sin(B)=\frac{b}{c}\\\\cos(A)=\frac{b}{c}\\\\cos(B)=\frac{a}{c}[/tex]
Substitute these values into the given equation. Then simplify the equation to prove the idenity,
[tex]\frac{sin(A)+sin(B)}{cos(A) +cos(B)}+\frac{cos(A)-cos(B)}{sin(A)-sin(B)}=0[/tex]
[tex]\frac{\frac{a}{c}+\frac{b}{c}}{\frac{b}{c}+\frac{a}{c}}+\frac{\frac{b}{c}-\frac{a}{c}}{\frac{a}{c}-\frac{b}{c}}=0[/tex]
[tex]\frac{\frac{a+b}{c}}{\frac{a+b}{c}}+\frac{\frac{b-a}{c}}{\frac{a-b}{c}}[/tex]
Remember, any number over itself equals one, this holds true even for fractions with fractions in the numerator (value on top of the fraction bar) and denominator (value under the fraction bar).
[tex]\frac{\frac{a+b}{c}}{\frac{a+b}{c}}+\frac{\frac{b-a}{c}}{\frac{a-b}{c}}[/tex]
[tex]\frac{\frac{a+b}{c}}{\frac{a+b}{c}}+\frac{\frac{-(a-b)}{c}}{\frac{a-b}{c}}[/tex]
[tex]1+(-1)=0[/tex]
[tex]1-1=0[/tex]
[tex]0=0[/tex]
a sum of money Doubles itself in 5 years what is rate of simple interest
Step-by-step explanationIf you are reading this say
thank u
I need help ASAP!!! Please help me FInd the missing side
Answer:
Step-by-step explanation:
Tan 22 = [tex]\frac{opposite \ side}{adjacent \ side}[/tex]
[tex]tan \ 22 = \frac{30}{x}\\\\0.4040 = \frac{30}{x}\\\\0.4040*x = 30\\\\x = \frac{30}{0.4040}\\\\x = 74.25\\\\x = 74.3[/tex]
Answer:
Sin= opp/hyp
Sin22= 30/x
0.3746=30/x
cross multiply
0.3746x=30
make x the subject of the formula
x= 30/0.3746
x=80
Trigonometric ratios
class 9
please answer my questions
Step-by-step explanation:
Hi there!
Please see the answer in the picture.
Hope it helps!
1. Approach
One is given a trigonometric equation with and one is asked to prove that it is true. Using the attached image, combined with the knowledge of trigonometry, one can evaluate each trigonometric function. Then one can simplify each ratio to solve. To yield the most accurate result, one has to each of the ratios in a fractional form, rather than simplifying it into a decimal form. Remember the right angle trigonometric ratios, these ratios describe the relationship between the sides and angles in a right triangle. Such ratios are as follows,
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}\\\\csc(\theta)=\frac{hypotenuse}{opposite}\\\\sec(\theta)=\frac{hypotenuse}{adjacent}\\\\cot(\theta)=\frac{adjacent}{opposite}[/tex]
Please note that the terms (opposite) and (adjacent) are relative to the angle uses in the ratio, however the term (hypotenuse) refers to the side opposite the right angle, this side never changes its name. Use these ratios to evaluate the trigonometric functions. Then simplify to prove the identity.
2. Problem (9)
[tex]\frac{sin(60)+cos(30)}{1+sin(30)+cos(60)}=sin(60)[/tex]
As per the attached image, the following statements regarding the value of each ratio can be made:
[tex]sin(60)=\frac{\sqrt{3}}{2}\\\\cos(30)=\frac{\sqrt{3}}{2}\\\\sin(30)=\frac{1}{2}\\\\cos(60)=\frac{1}{2}[/tex]
Substitute,
[tex]\frac{sin(60)+cos(30)}{1+sin(30)+cos(60)}=sin(60)[/tex]
[tex]\frac{\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]
Simplify,
[tex]\frac{\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\frac{2\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\frac{2\sqrt{3}}{2}}{1+1}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\sqrt{3}}{1+1}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{\sqrt{3}}{2}[/tex]
Thus, this equation is true.
2. Problem (10)
Use a similar strategy to evaluate this equation,
[tex]\frac{1-cos(30)}{sin(30)}=\frac{1-cot(60)}{1+cot(60)}[/tex]
Use the attached image to evaluate the ratios.
[tex]cos(30)=\frac{\sqrt{3}}{2}\\\\sin(30)=\frac{1}{2}\\\\cot(60)=\frac{1}{\sqrt{3}}[/tex]
Substitute,
[tex]\frac{1-cos(30)}{sin(30)}=\frac{1-cot(60)}{1+cot(60)}[/tex]
[tex]\frac{1-\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
Simplify,
[tex]\frac{1-\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{\frac{\sqrt{3}+1}{\sqrt{3}}}[/tex]
[tex]2-\sqrt{3}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{\frac{\sqrt{3}+1}{\sqrt{3}}}[/tex]
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}}*\frac{\sqrt{3}}{\sqrt{3}+1}}[/tex]
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}[/tex]
Rationalize the denominator,
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}[/tex]
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}*\frac{\sqrt{3}-1}{\sqrt{3}-1}[/tex]
[tex]2-\sqrt{3}=\frac{(\sqrt{3}-1)^2}{3-1}[/tex]
[tex]2-\sqrt{3}=\frac{3-2\sqrt{3}+1}{2}[/tex]
[tex]2-\sqrt{3}=\frac{4-2\sqrt{3}}{2}[/tex]
[tex]2-\sqrt{3}=2-\sqrt{3}[/tex]
Therefore, this equation is also true.
A recipe requires 500 mL of milk. You will make the recipe once a month for the next 4 months. You do not use milk other than for cooking. Which container of milk should you buy? (1L=1000 mL) *
Answer: 1 month = 500ml
4 month = 500ml × 4 = 2000ml = 2L
you should use the 2L container
Step-by-step explanation:
The circumference of a circle is 20π. What is the area of the circle?
Answer:
The area of the circle is 100 square units.
Step-by-step explanation:
We are given that the circumference of a circle is 20π, and we want to determine its area.
Recall that the circumference of a circle is given by the formula:
[tex]\displaystyle C = 2\pi r[/tex]
Substitute:
[tex]20 \pi = 2 \pi r[/tex]
Solve for the radius:
[tex]\displaystyle r = \frac{20\pi}{2\pi} = 10[/tex]
The area of a circle is given by:
[tex]\displaystyle A = \pi r^2[/tex]
Since the radius is 10 units:
[tex]\displaystyle A = \pi (10)^2[/tex]
Evaluate:
[tex]\displaystyle A = 100\pi\text{ units}^2[/tex]
In conclusion, the area of the circle is 100 square units.
Which is the graph of y = [x]-2?
PLEASE HELP TIMED PLEASE
Answer:
3rd graph
Step-by-step explanation:
if A ={1,2,3,4} and B={3,4,5,6} find A-B.
Answer: {1,2} is the answer.
Step-by-step explanation:
A-B
{1,2,3,4}-{3,4,5,6)
= {1,2}
Add.
(3x2 – 2x) + (4x-3)
O A. 7x2- 5x
O B. 12x3 - 14x2 + 6x
O C. 3x2 - 6x + 3
O D. 3x2 + 2x-3
Answer:
O D. 3x2 + 2x-3
Answer:
A.7x2-5x questions 2of 20
helpppppppppppppp meeeeeeeeeeeeeeeee plsssssssssssssssss!!!!!!!!!!!!!
Answer:
a=13
Step-by-step explanation:
-90=-6a-12
-6a=-78
a=13
Answer:
a=13 well as u can see the other comment already gave an explanation of y it is a=13 and i completely agree with it have a nice afternoon,night,or day to u
Step-by-step explanation:
I need help please help me
Answer:
I found x for you, right there.
Answer: x is 12 and y is 5
Step-by-step explanation:
Find the first three terms of the sequence given by the following.
a
n = 25-3(n − 1), n= 1, 2, 3, ...
A. 28, 25, 22
B. 25, 22, 19
C. 25, 28, 31
D. 28, 31, 34
the answer is
A. 28, 25, 22
Can some help please
Answer:
Step-by-step explanation:
2 * 10^7 You are to use a single digit. That's the 2 on the left. Then count what it takes to get the decimal between the 2 and the 3. It's 7
0.000136
Count the number of zeros. Add a minus 1. You want the number to be counted until you get minus 1 which is the number of powers after the 1.
1 * 10^-4
26837 becomes 2 * 10^4. 4 is the number of digits you have before you get to a number between 1 and 10.
0.0302 becomes 3 * 10^-(1 + 1) = 3 * 10^-2
HELP ITS DUE IN THE MORNING AND ITS 3:57
Answer:
A " (1,-2)
B " (4,0)
C " (6,-3)
Step-by-step explanation:
Hope it helped.
° ° °
Find the surface area of the triangular prism
Which segment is parallel to ED?
Answer:
AB
Step-by-step explanation:
The segments that are parallel need to be in the same direction ( up and down)
The segments that are parallel are FH, AB, GC
Answer:
AB
Step-by-step explanation:
since is a cube all of the angles are 90 degees and this only possibel whn the line That a vertical a parrelllt to each other
u4gent help needed
help me with the question of o.math
Answer:
1≤f(x)≤5
Step-by-step explanation:
-1≤x≤1
-2≤2x≤2 (Multiplied by 2 both side)
-2+3≤2x+3≤2+3 (Adding three both sides)
1≤f(x)≤5
