[tex]2 \sec^2 x = 3- \tan x \\\\\implies 2(1 +\tan^2 x) = 3- \tan x \\\\\implies 2 + 2 \tan^2 x +\tan x -3 =0\\\\\implies 2 \tan^2 x + \tan x -1 =0\\\\\implies 2u^2 + u -1 =0~~~ ;[\text{set} \tan x = u]\\\\\implies u = \dfrac{-1\pm \sqrt{1-4\cdot 2 \cdot (-1)}}{2(2)}\\\\\implies u =\dfrac{-1 \pm\sqrt{9}}{4}\\\\\implies u = \dfrac{-1 \pm 3}{4}\\\\\implies u = \dfrac{2}{4}=\dfrac 12~~ \text{or} ~~u =\dfrac{-4}{4} =-1\\\\[/tex]
[tex]\implies \tan x = \dfrac 12 ~~ \text{or} ~~ \tan x =-1~~~ ;[\text{Substitute back u =tan x}]\\\\\text{Now,}~ \\\\\tan x = -1,\\\\\implies x = n\pi - \dfrac{\pi}4\\\\\\\text{For interval,}~ [0,2\pi) \\\\x = \dfrac{3\pi}4, \dfrac{7\pi}4\\\\\text{In degrees,}~ x = 135^{\circ}, x =315^{\circ}\\\\\tan x = \dfrac 12\\\\\implies x = n\pi + \tan^{-1} \left(\dfrac 12 \right)\\\\\text{For interval} ~[0,2\pi),\\\\[/tex]
[tex]x=\tan^{-1} \left(\dfrac 12 \right), \left[\pi +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\text{in degrees,} ~~x=\tan^{-1} \left(\dfrac 12 \right), \left[180^{\circ} +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\\\\\text{Combine all solutions:}\\\\x=\dfrac{3\pi}4, \dfrac{7\pi}4, \tan^{-1} \left(\dfrac 12 \right), \left[\pi +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\\[/tex]
[tex]\text{In degrees,}~ x = 135^{\circ},~315^{\circ},~\tan^{-1} \left(\dfrac 12 \right), \left[180^{\circ} +\tan^{-1} \left( \dfrac 12 \right)\right][/tex]
Identify the equation of the circle that has its center at (7, -24)
and passes through the origin.
Answer:
(x-7)²+(y+24)² = 625
Step-by-step explanation:
A circle with center (h, k) and radius r can be represented as
(x-h)²+(y-k)² = r²
We know the center and one point, and need to find the radius. The radius is equal to the distance from the center to any point on the circle. Therefore, we need to find the distance from the center to the point on the circle (in this case, the origin) to obtain the radius.
The distance formula for points (x₁, y₁) and (x₂, y₂) is √((x₁-x₂)²+(y₁-y₂)²). Note that x₁ and x₂ (as well as y₁ and y₂) are interchangeable but x₁ and y₁ or x₂ and y₂ are not.
Our distance between (7, -24) and the origin is
√((x₁-x₂)²+(y₁-y₂)²) = √((7-0)²+(-24-0)²)
= √625
= 25
Therefore, the radius is 25 and our equation is
(x-7)²+(y-(-24))² = (x-7)²+(y+24)² = 25² = 625
Which of the following budgets is in surplus?
o Income $500, Fixed Exp. $100, Living Expenses $300
o Income $300, Fixed Exp. $100, Living Expenses $300
o Income $400, Fixed Exp. $100, Living Expenses $300
Answer:
Income $500, Fixed exp. $100, Living Expenses $300
What is the equation of the line?
Translate the following into an expression 45% of a
Answer:
Step-by-step explanation:
ok so this is pretty simple,
Imagine a was the number 1
45% of 1, which would obviously be
45/100 * 1
Same thing here but for the variable a.
45/100 * a!
That would be the algebraic expression for 45% of a!
Cheers! I hope you can understand the problem better now.
Describe the symmetry of the figure. Identify lines of symmetry, if any. Find the angle and the order of any
rotational symmetry.
Answer:
No symmetry
Step-by-step explanation:
The shape cannot be folded over any line to be equally matched up to the other side
Several days after a wedding, an outbreak of cyclosporiasis occurred among attendees. Of the 108 guests at the wedding, 76 were ill and met the case definition. 50 of the 76 who were ill ate the wedding cake. Three of those who were well ate the wedding cake. What is the attack rate for those who ate the wedding cake
Answer:
The answer is "94.3".
Step-by-step explanation:
Calculating the total numbers of cake eaters[tex]=50+3=53\\\\[/tex]
Calculating the total numbers of ill among them[tex]=50\\\\[/tex]
[tex]\therefore[/tex]
The attack rate for those who ate cake[tex]=\frac{50}{53}\times 100\%=94.3[/tex]
Write the solution set of the inequality graphed below as a com-
pound inequality using the variable g.
Answer:
-17 < g [tex]\leq[/tex] 8
Step-by-step explanation:
'g' is within the range of numbers that are greater than -17 and less than or equal to 8. we know that it is less than or equal to because the circle is closed or filled in, at 8.
can you help me find the slope intercept on the second one?
Answer:
y= 8x + 5
Step-by-step explanation:
y = 8x + b
5 = 8(0)+b
b = 5
Help me pleaseee i could really use it
Answer:
20 and 42
Step-by-step explanation:
Let the greater number be x and the smaller number be y.
3(x +y)= 186
x +y= 186 ÷3
x +y= 62 -----(1)
x -y= 22
x= y +22 -----(2)
Substitute (2) into (1):
y +22 +y= 62
2y= 62 -22 (-22 on both sides)
2y= 40
y= 40 ÷2
y= 20
Substitute y= 20 into (2):
x= 20 +22
x= 44
Thus, the two numbers are 20 and 42.
The line plot below shows the amount of time Jason spent practicing
his soccer skills on six separate days. How much time did he spend on
all six days?
х
X
х
+
3
х
+
1
х
1
Times (hour)
Please help me I will give brainliest!!!!
The total amount of time spent on practicing is 3 minutes
To obtain the total practice time, we multiply the time taken by its respective frequency as seen on the plot.
From the plot:
([tex](1 * 0) + (1 * 1/4) + (2 * 1/2) + (1 * 3/4) + (1 * 1)\\(0 + 1/4 + 1 + 3/4 + 1)\\= 3[/tex]
Hence, the total amount of time spent is 3 minutes as obtained from the dot plot given.
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The circumference of a circle is 257 cm. What is the area,
in
square
centimeters
Answer:
[tex]2\pi \times r = c[/tex]
[tex]\pi \times {r}^{2} = a[/tex]
A=5257.76
Step-by-step explanation:
Or use a calculator online.
How do I do this? I don’t understand it
Answer:
Step-by-step explanation:
x+65 = 180 Consecutive angles in llgm are supplementary
x = 180-65 Subtract equal amounts from both sides.
x = 115
y + 65 = 90 This hard to explain without letters. The lines are parallel. The right angle is an extension of the right vertical parallel line. So the left two angles are 90 degrees because of the perpendicular angles.
y = 90 - 65
y = 25
Factorize:
a)(a+b) (a-b)-a+b
b)a²-(b-3)a-3b
c) ax²-bx²-ax+bx+a-b
help Me these questions I will mark u as brainliest
Answer:
Step-by-step explanation:
which statement is true
pls pls pls pls help
Step-by-step explanation:
[tex]s = \pi \times {r}^{2} = \pi \times {6}^{2} = 36\pi[/tex]
[tex]h = 18 \times \sin(60) = 9 \sqrt{3} [/tex]
[tex]v = s \times h = 36\pi \times 9 \sqrt{3} = 324 \sqrt{3} \pi[/tex]
Instructions: Find the missing side. Round your answer to the nearest tenth
Answer:
x≈64.3
Step-by-step explanation:
since we already know the measures of 2 of the 3 angles in the triangle, we can find the 3rd angle:
180°-90°-25°=65°
now, we can use the law of sines to find the missing side:
sin25°/30=sin65°/x
x sin25°=30sin65°
x=(30sin65°/sin25°)
x≈64.33520762
rounded to the nearest 10th:
x≈64.3
How many significant digits are there in the number 1.00250? OA) 7 OB) 6 OC) 5 OD) 4
Answer:
OB
Step-by-step explanation:
start counting from 1
Then your significant digit is 6
fill in the blanks □+0=3/4.also mention the property used.
plz answer fastly and give correct answer and I can understand .
Answer:
3/4 + 0 = 3/4 Additive Neutral Property
Step-by-step explanation:
Given: overline LM cong overline ON and overline LO cong overline MN Prove : LMNO is a parallelogram
[tex]\overline {LM} \parallel \overline {ON} \ and \ \overline {LO} \parallel \overline {MN}[/tex] because they form congruent alternate interior angles with a common transversal, therefore, LMNO is a parallelogram because the opposite sides are parallel
The reason the above statement are correct is presented as follows:
The given parameters are;
[tex]\overline {LM}[/tex] is congruent to [tex]\overline {ON}[/tex] and [tex]\overline {LO}[/tex] is congruent to [tex]\overline {MN}[/tex]
Required:
To prove that LMNO (quadrilateral) is a parallelogram
Solution:
The two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
[tex]\overline {LM} \cong \overline {ON}[/tex] [tex]{}[/tex] Given
[tex]\overline {LM} = \overline {ON}[/tex] [tex]{}[/tex] Definition of congruency
[tex]\overline {LO}[/tex] ≅ [tex]\overline {MN}[/tex] [tex]{}[/tex] Given
[tex]\overline {LO}[/tex] = [tex]\overline {MN}[/tex] [tex]{}[/tex] Definition of congruency
[tex]\overline{LN}[/tex] ≅
[tex]\overline{LN}[/tex] =
ΔLNO ≅ ΔLMN [tex]{}[/tex] Side Side Side (SSS) congruency postulate
∠NLM ≅ ∠LNO [tex]{}[/tex] Cong. Parts of Cong. Triangles are Cong. CPCTC
∠NLM and ∠LNO are alternate interior angles
[tex]\mathbf{\overline {LM} \parallel \overline {ON}}[/tex] [tex]{}[/tex] Alternate interior angles between parallel lines are congruent
∠MNL ≅ ∠NLO [tex]{}[/tex] CPCTC
∠MNL and ∠NLO are alternate interior angles
[tex]\mathbf{\overline {LO} \parallel \overline {MN}}[/tex] [tex]{}[/tex] Alternate interior angles formed between parallel lines are congruent
LMNO is a parallelogram because the opposite sides, [tex]\overline {LM} \parallel \overline {ON}[/tex] and [tex]\overline {LO} \parallel \overline {MN}[/tex] are parallel
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LMNO is a plane shape which has the properties of a parallelogram. The the explanations below, it has been proven to be a parallelogram.
A parallelogram is a quadrilateral which has some unique properties. These properties can be used to prove if a given shape is a parallelogram or not.
To prove that LMNO as given in the question is a parallelogram:
The opposite sides of a parallelogram are congruent.Thus,
/LM/ ≅ /ON/ (opposite side property)
/LO/ ≅ /MN/ (opposite side property)
The opposite sides are parallel to each other.i.e LM || ON and LO || MN
Consecutive angles are supplementary.i.e <MLO + <LMN = [tex]180^{o}[/tex]
also
<LON + <MNO = [tex]180^{o}[/tex]
The diagonals are at right angles to each other.LN ⊥ MO
Opposite angles are congruent.<LMN ≅ <LON and <MLO ≅ <MNO
Therefore the given quadrilateral LMNO has all the properties described above, then it is a parallelogram.
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In a survey of 850 students in a school, 90% reported having pets at home. If the margin of error is 3.4%, what is the interval that is likely to contain the exact percent of all people who have pets at home?
Between 3.4% and 90%
Between 90% and 93.4%
Between 86.6% and 90%
Between 86.6% and 93.4%
Answer:
Between 86.6% and 93.4%Step-by-step explanation:
To obtain the population proportion from the sample, we calculate the confidence interval ; Confidence interval = phat ± margin of error Phat = 90% ; margin of error = +3.4% 90% ± 3.4% (90 - 3.4)% ; (90 + 3.4)% 86.6% ; 93.4%Given m|n, find the value of x.
(6x-5)
(6x+5)
Answer:
Submit Answer
attempt
PLSSSS HELP
Answer:
x = 15
Step-by-step explanation:
The two angles form a straight line so they add to 180
6x-5+6x+5 = 180
Combine like terms
12x= 180
Divide by 12
12x/12 =180/12
x = 15
there are 32 students in a class and 20 of them own at least one pet what fraction of the class own pets
HOPE IT HELPS
PLEASE MARK BRAINLIEST
The fraction of the class that owns pets is 20/32, which can be simplified to 5/8.
To find the fraction of the class that owns pets, we divide the number of students who own pets by the total number of students in the class.
A fraction is a mathematical representation of a part-to-whole relationship. It is expressed as a numerical quantity written in the form of one number (the numerator) divided by another number (the denominator), separated by a horizontal line or slash (/).
The numerator represents the number of parts being considered or counted, while the denominator represents the total number of equal parts that make up the whole. Fractions can be used to describe a portion or share of something, as well as to compare quantities or perform mathematical operations.
Number of students who own pets: 20
Total number of students in the class: 32
Therefore, the fraction of the class that owns pets is 20/32, which can be simplified to 5/8.
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find the measure of x and y
Answer:
x = 94, y = 76
Step-by-step explanation:
The opposite angles of a cyclic quadrilateral sum to 180° , then
x + 86 = 180 ( subtract 86 from both sides )
x = 94
and
y + 104 = 180 ( subtract 104 from both sides )
y = 76
What is the length of line segment SA
Answer:
slalalallalalalalalalalalallapapapqpqpq
8x+4=3(x-1) +7 solve
Answer:
x = 0
Step-by-step explanation:
8x + 4 = 3(x − 1) + 7
Simplify both sides of the equation:
8x + 4 = (3)(x)+ (3)(−1) + 7
8x + 4 = 3x + (−3) +7
Combine like terms:
8x + 4 = (3x) + (−3+7)
8x + 4 = 3x + 4
Subtract 3x from both sides:
8x + 4 − 3x = 3x + 4 − 3x
5x + 4 = 4
Subtract 4 from both sides:
5x + 4 − 4 = 4 − 4
5x =0
Divide both sides by 5:
5x/5 = 0/5
x = 0
The lengths of the sides of a triangle are 4,5 and 6 if the length of the longest side of a similar triangle is 15,what is the length of the shortest side of the triangle
Answer:
The length of the shortest side of the triangle is 10.
Step-by-step explanation:
Given that the lengths of the sides of a triangle are 4, 5 and 6, if the length of the longest side of a similar triangle is 15, to determine what is the length of the shortest side of the triangle, the following calculation must be performed :
6 = 15
4 = X
4 x 15/6 = X
10 = X
Therefore, the length of the shortest side of the triangle is 10.
Martina is recording the percentages she earned on each quiz in her math class. Here are her results for the last 7 quizzes.
74, 64, 90, 74, 92, 68, 71
Find the range of the data set.
=___
Answer:
28
Step-by-step explanation:
Subtract highest number from lowest.
92-64 = 28
The diagram above shows a plan for a park. ABCD is a rectangle.
APB and DQC are semicircles centred at X and Y.
Given AB = 7 cm and AC = 25 cm.
Calculate the perimeter of the park in cm.
Answer:
Perimeter of the park = 70 cm
Step-by-step explanation:
Perimeter of the park = perimeter of the 2 semicircles + 2(length of the rectangle)
Perimeter = 2πr + 2(BC)
✔️Perimeter of the 2 semicircles = 2πr
Where,
radius (r) = ½(AB) = ½(7)
r = 3.5 cm
Perimeter = 2*π*3.5 = 7*π
Perimeter of the two semicircles = 21.9911486 ≈ 22 cm
✔️Find BC using Pythagorean theorem:
Thus,
BC = √(AC² - AB²)
AC = 25
AB = 7
BC = √(25² - 7²) = √576
BC = 24
✔️Perimeter of the park = perimeter of the 2 semicircles + 2(length of the rectangle)
Perimeter of the park = 22 + 2(24)
= 22 + 48
= 70 cm
Roger bought some tins and decided to fill them with brownies to give to his friends. Roger baked 278 brownies. He put 4 brownies in each tin and made sure to fill as many tins as he could. How many brownies did Roger have left over?
Answer:
Divide 278 by 4 and the remainder value is the amount of leftover brownies.
278 ÷ 4 = 69, remainder of 2
Therefore, he had 2 brownies left.
9. Calculate the perimeter and the perimeter of a quadrant of a circle with radius 7 cm
correct to 3 significant figures.
Answer:
Circumference is 43.982 cm
Step-by-step explanation:
[tex]circumference = 2\pi r \\ = (2 \times 3.14 \times 7) \\ = 43.982 \: cm[/tex]
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