Answer:
x = -2
Step-by-step explanation:
1. Square both sides
x^2 +3x + 6 = x^2
2. Subtract x^2 from both sides
3x + 6 = 0
3. Subtract 6 from both sides and divide by 3
x = -2
Terry wants to pour cement around the edge of the circular patio in her backyard.The patio has a radius of 5 feet.What is the distance,in feet,around the edge of the patio?Use 3.14 for Pi.PLEASE EXPLAIN
E.15.7
F.31.4
G.49.3
H.78.5
Answer:
F. 31.4 ft
Step-by-step explanation:
The distance around the edge of a circle is called the circumference.
Formula for the circumference of a circle
[tex]\sf Circumference\:of\:a\:circle=2 \pi r[/tex]
(where r is the radius)
Given values:
radius = 5 ftπ = 3.14Substitute the given values into the formula:
[tex]\begin{aligned}\implies \sf circumference & = \sf 2 \cdot 3.14 \cdot 5\\ & = \sf 31.4\:ft \end{aligned}[/tex]
Therefore, the distance around the edge of the circular patio is 31.4 ft.
The distance around the edge of the patio is 31.4 feet, which is determined by the circumference of a circle. The correct answer is option (F).
To find the distance around the edge of the circular patio, we need to calculate the circumference of the circle.
The formula for the circumference of a circle is given by:
Circumference = 2 × π × radius
Given that the radius of the patio is 5 feet and using the approximate value of π as 3.14, we can now calculate the circumference:
Circumference = 2 × 3.14 × 5
Circumference = 31.4 feet
Therefore, the distance around the edge of the patio is 31.4 feet.
Hence, the correct answer is option (F).
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Find x and y please help
Answer:
x is 130°,y is 60°
Step-by-step explanation:
x is corresponding to 130° therefore they are equal to find y since the angle on a straight line is 180° you subtract 180 from 130 and get 50 then you have gotten the other interior angle then add both interior angles and subtract by180 then you get the y
Answer:
X = 130° Y = 60°both the lines are parallel
therefore, X= 130° ( if two lines are parallel their corresponding angles are equal)
Y + 70° = X ( sum of tow interior angle is equal to exterior)
Y + 70= 130
Y = 130 - 70
Y = 60°
Prove: An odd number squared is
an odd number.
(2n + 1)² = [?]n² + [ ]n +
=
[](2n² + 2n) + [ ]
= an odd
Considering the result of the expression of the square of the sum, 2(2n² + 2) is always an even number, then when 1 is added it will always be an odd number.
What is the square of the sum notable product?It is given as follows:
(a + b)² = a² + 2ab + b².
In this problem, the expression is:
(2n + 1)² = (2n)² + 2(2n)(1) + 1²
= 4n² + 4n + 1
= 2(2n² + 2) + 1
The term 2(2n² + 2) will always be even(multiplication by 2), and when 1 is added to an even number it will always be odd, hence it is proved that an odd number squared is an odd number.
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Which of the following is the best buy?
a 6 oz box of rice for $0.90
a 12 oz box of rice for $1.93
a 16 oz bag of rice for $2.42
a 9 oz box of rice $1.25
The best buy is (d) a 9 oz box of rice $1.25
How to determine the best buy?The best buy is the product that has the least unit rate.
The unit rate is calculated as:
Unit = Price/Weight
So, we have:
Box 1:
Unit rate = $0.90/6 oz = $0.150 per oz
Box 2:
Unit rate = $1.93/12 oz = $0.161 per oz
Box 3:
Unit rate = $2.42/16 oz = $0.151 per oz
Box 4:
Unit rate = $1.25/9 oz = $0.139 per oz
The least unit price is $0.139 per oz for box 4
Hence, the best buy is (d) a 9 oz box of rice $1.25
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Factor the quadratic equation of y= 4x^2 + 16x -48
Answer:
y = 4(x+6)(x-2)
Step-by-step explanation:
y = 4x² + 16x - 48, factor out the 4
y = 4(x² + 4x - 12), find factors of 12
Factors of 12:
1*12, 2*6, 3*4; find a pair that sums to 4x or 4
6-2 = 4, since 12 is a negative number, a number in the factor must be negative, in this case, making 2 negative, would make 6-2 = 4
y = 4(x+6)(x-2)
Shashi has a rectangular garden. The length of the garden is 4 feet less than twice the width. The area of the garden is 448 square feet. What is the length of the garden?
Answer:
28 feet
Step-by-step explanation:
Area of a rectangle is :
A = L × W
We are given A and a expression for L, so let's substitute :
448 = (2W-4) × W
Now we expand the left side :
2W²-4w = 448
Subtract 448 from both sides :
2W²-4W-448 = 0
Divide everything by 2 :
W²-2W-224 = 0
Now we factorise :
Find 2 numbers that multiply to give -224 and add to give -2 :
-16 and 14
Rewrite -2W with -16W and +14W :
W² - 16W + 14W -224 = 0
W(W-16) +14(W-16) = 0
(W+14)(W-16) = 0
W = -14 , W = 16
Only take positive value since this is lengths :
W = 16
Now we substitute W into the expression to find L :
L = (2W -4)
L = 2(16) - 4
L = 32 - 4
L = 28
Units will be feet since it is a length
Hope this helped and have a good day
Find the domain and range of the function graphed below. Answer in interval notation.
Answer:
Domain: [tex](-\infty, 8)[/tex]Range: [tex](-\infty, -3)[/tex]Step-by-step explanation:
The domain is the set of x values, and the range is the set of y values.
Question 6 of 10
sin 30º = √3/2 and cos 30º = 1/2
O A. True
OB. False
Jack and Susan bought together 28 books. Susan bought 11 books. Which one of the
following equations represents the number of books bought by Jack? Let x be the
number of books bought by Jack.
Answer:
11 + x = 28
Step-by-step explanation:
The number of books they bought must add to 28.
I should have payed more attention but can someone please guide me through this and build me up an answer.
Answer:
arc QM = 38°
Step-by-step explanation:
the inscribed angle NQM is half the measure of its intercepted arc NM , so
arc NM = 2 × 90° = 180°
the sum of the arcs in a circle = 360° , then
QN + NM + MQ = 360° , that is
142° + 180° + QM = 360°
322° + QM = 360° ( subtract 322° from both sides )
QM = 38°
What are the solution(s) to the quadratic equation x² - 25 = 0?
h
O x=5 and x =
-5
−5
x = 25 and x = -25
x = 125 and x = -125
Ono real solution’s
Answer:
x = ±5
Step-by-step explanation:
x² - 25 = 0
x² = 25
√x² = √25
x = ±5
Check:
5² - 25 = 0
-5² - 25 = 0
25 - 25 = 0
Given a regular 26 sided polygon, complete the following statements.
Answers:
Sum of the interior angles = 4320One interior angle = 166.15=======================================================
Work Shown:
n = number of sides = 26
S = sum of the interior angles of a polygon with n sides
S = 180(n-2)
S = 180(26-2)
S = 180(24)
S = 4320 degrees is the sum of the interior angles.
i = measure of one interior angle of a regular polygon
i = S/n
i = 4320/26
i = 166.1538 approximately
i = 166.15 degrees is the approximate measure of each interior angle.
Side note: The formula to determine the interior angle i only works for regular polygons. This is because each angle is the same measure.
If f(x) = x² - 2x, find:
f(6) = [?]
will give brainliest answer !!
Answer:
[tex] \boxed{f(6) =2 4}[/tex]
Step-by-step explanation:
Given function:
[tex]f(x) = x² - 2x[/tex]
Solution:
ATP,it is that x = 6. So substitute 6 on the function.
[tex]f(6) = 6 {}^{2} - 2(6)[/tex]
Simplifying using PEMDAS,we obtain:
[tex]f(6) = 6 \times 6- 12[/tex]
[tex]f(6) = 36 - 12[/tex]
[tex] \boxed{f(6) =2 4}[/tex]
Hence,f(6) = 24.
In one month, a farmer produces 300 pounds of corn. In the
following month he produces 35% more. How many pounds of corn
does he produce in the second month?
The pounds of corn in the second month is 390
How to determine the amount?We have:
First month, a = 300
Rate, r = 35%
The pounds of corn in the second month is calculated using:
Pound = a * (1 + r)
So, we have:
Pound = 300 * (1 + 30%)
Evaluate the sum
Pound = 300 * 1.3
Evaluate the product
Pound = 390
Hence, the pounds of corn in the second month is 390
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Considering only the values of β for which sinβtanβsecβcotβ is defined, which of the following expressions is equivalent to sinβtanβsecβcotβ?
Select the correct answer below:
secβcotβ
tanβ
cotβtanβ
tanβcscβsecβ
Answer:
[tex]\tan(\beta)[/tex]
Step-by-step explanation:
For many of these identities, it is helpful to convert everything to sine and cosine, see what cancels, and then work to build out to something. If you have options that you're building toward, aim toward one of them.
[tex]{\tan(\theta)}={\dfrac{\sin(\theta)}{\cos(\theta)}[/tex] and [tex]{\sec(\theta)}={\dfrac{1}{\cos(\theta)}[/tex]
Recall the following reciprocal identity:
[tex]\cot(\theta)=\dfrac{1}{\tan(\theta)}=\dfrac{1}{ \left ( \dfrac{\sin(\theta)}{\cos(\theta)} \right )} =\dfrac{\cos(\theta)}{\sin(\theta)}[/tex]
So, the original expression can be written in terms of only sines and cosines:
[tex]\sin(\beta)\tan(\beta)\sec(\beta)\cot(\beta)[/tex]
[tex]\sin(\beta) * \dfrac{\sin(\beta) }{\cos(\beta) } * \dfrac{1 }{\cos(\beta) } * \dfrac{\cos(\beta) } {\sin(\beta) }[/tex]
[tex]\sin(\beta) * \dfrac{\sin(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}}{\cos(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}} * \dfrac{1 }{\cos(\beta) } * \dfrac{\cos(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}} {\sin(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}}[/tex]
[tex]\sin(\beta) *\dfrac{1 }{\cos(\beta) }[/tex]
[tex]\dfrac{\sin(\beta)}{\cos(\beta) }[/tex]
Working toward one of the answers provided, this is the tangent function.
The one caveat is that the original expression also was undefined for values of beta that caused the sine function to be zero, whereas this simplified function is only undefined for values of beta where the cosine is equal to zero. However, the questions states that we are only considering values for which the original expression is defined, so, excluding those values of beta, the original expression is equivalent to [tex]\tan(\beta)[/tex].
Find the compound interest on $4000 for 2 years and 3months at 2% per annum,
compounded annually.
Answer:
CI = $182.25
Step-by-step explanation:
Compound interest formula:
[tex]Compound \space\ Interest= P(1 + \frac{r}{100})^{n} - P[/tex] ,
where P is the principal amount ($4000), r is the interest rate (2%), and n is the time period (2 years and 3 months = 2.25 years).
Using formula:
CI = [tex]4000(1 + \frac{2}{100} )^{2.25} - 4000[/tex]
CI = $182.25
Use the graph of the parabola to fill in the table
(a) The parabola opens downward.
(b) The axis of symmetry is at x = -2.
(c) The vertex is at (-2,0).
(d) The x-intercepts is (-2,0), and the y-intercept is at (0,-1).
Line AB and line BC form a right angle at point B with points A (2,5) and B(8,3). what is the equation of line BC?
Answer:
y=3x-21
Step-by-step explanation:
General outlineFind equation for line ABFind equation for perpendicular line BCStep 1. Find equation for line ABGiven points A(2,5) and B(8,3), line AB must contain them.
To calculate the slope, [tex]m_{\text{AB}}[/tex], of line AB, use the slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m_{\text{AB}}=\dfrac{(3)-(5)}{(8)-(2)}[/tex]
[tex]m_{\text{AB}}=\dfrac{-2}{6}[/tex]
[tex]m_{\text{AB}}=-\frac{1}{3}[/tex]
Since the slope isn't undefined, line AB must cross the y-axis somewhere. To find the y-intercept, build and equation in slope-intercept form:
[tex]y=m_{\text{AB}}x+b_{\text{AB}}[/tex]
[tex]y=\left(-\frac{1}{3} \right) x+b_{\text{AB}}[/tex]
Substituting values for a known point (point A) on line AB...
[tex](5)=\left(-\frac{1}{3} \right) (2)+b_{\text{AB}}[/tex]
[tex]5=-\frac{2}{3} +b_{\text{AB}}[/tex]
[tex](5)+\frac{2}{3} =(-\frac{2}{3} +b_{\text{AB}})+\frac{2}{3}[/tex]
Finding a common denominator...
[tex]\frac{3}{3}*5+\frac{2}{3} =b_{\text{AB}}[/tex]
[tex]\frac{15}{3}+\frac{2}{3} =b_{\text{AB}}[/tex]
[tex]\frac{17}{3}=b_{\text{AB}}[/tex]
So, the equation for line AB is [tex]y=-\frac{1}{3} x +\frac{17}{3}[/tex]
Step 2. Find equation for line BCSince line AB and line BC form a right angle, they are perpendicular. Perpendicular lines have slopes that are opposite (opposite sign) reciprocals (fraction flipped upside-down) of each other. Stated another way, the slopes multiply to make negative 1.
[tex]m_{\text{AB}}*m_{\text{BC}}=-1[/tex]
[tex]\left( -\frac{1}{3} \right) *m_{\text{BC}}=-1[/tex]
[tex]-3*\left( -\frac{1}{3} *m_{\text{BC}} \right) =-3*(-1)[/tex]
[tex]m_{\text{BC}} =3[/tex]
Since the slope isn't undefined, line BC must also cross the y-axis somewhere. To find the y-intercept, build and equation in slope-intercept form:
[tex]y=m_{\text{BC}}x+b_{\text{BC}}[/tex]
[tex]y=(3) x+b_{\text{BC}}[/tex]
Substituting values for a known point (point B) on line BC...
[tex](3)=3 * (8)+b_{\text{BC}}[/tex]
[tex]3=24+b_{\text{BC}}[/tex]
[tex](3)-24=(24+b_{\text{BC}})-24[/tex]
[tex]-21=b_{\text{BC}}[/tex]
So, the equation for line BC is [tex]y=3 x -21[/tex]
If you subtract 0. 3 from a certain number, add 0. 4 times the original number to the result, and then add another 2. 78, you'll get 25. What was the original number?
After all the conditions you applied from the statement given you will get the original number as 16.08.
What is the algebraic equation?An algebraic equation is when two expressions are set equal to each other, and at least one variable is included.
Given that, if you subtract 0.3 from a certain number, add 0.4 times the original number to the result and then add another 2.78, you'll get 25.
We need to find the original number.
Let us take the original number as x.
Now, subtract 0.3 from the original number.
That is x-0.3.
0.4 times the original number is 0.4x.
Add 0.4 times the original number to the result.
That is, x-0.3+0.4x=1.4x-0.3
Now, add 2.78 to the result. That is 1.4x-0.3+2.78=1.4x+2.48.
As a result, you'll get 25. That is 1.4x+2.48=25
⇒1.4x=22.52
⇒x=16.08
There, the original number is 16.08.
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which of the following are identities? check all that apply A. cot^2x+1=csc^2x B.tan^2=1-sec^2x C.sin2^x=1=cos^2x D.sin^2x+cos^2x=1
What is the measure of complemnt angle
a)42° b) 35°
Answer:
90°
Step-by-step explanation:
A complement angle is the same as a right angle
Hii!
___________________________________________________________
Answer:
[tex]\sf 48\textdegree[/tex][tex]\sf 55\textdegree[/tex]Step-by-step explanation:
The sum of complementary angles is always 90 degrees.
We can find the complements of these two angles by setting up an equation.
x+42=90
Subtract 42 from both sides
x=48
This problem can be solved the same way!
x+35=90
Subtract 35 from both sides
x=55
--
Hope that this helped! Best wishes.
--
I keep putting in the formula but I keep getting the answer wrong
Answer:
314 in² (nearest whole number)
Step-by-step explanation:
Radius of a regular polygon: The distance from the center of the polygon to any vertex. The radius of a hexagon is equal to the length of one side.
Therefore, from inspection of the given diagram:
radius = 11 in ⇒ side length = 11 inTo find the area of a regular polygon, we first need to calculate the apothem. The apothem is the line drawn from the center of the polygon to the midpoint of one of its sides.
[tex]\textsf{Length of apothem (a)}=\dfrac{s}{2 \tan\left(\frac{180^{\circ}}{n}\right)}[/tex]
where:
s = length of one siden = number of sidesGiven:
s = 11 inn = 6Substitute the given values into the formula and solve for a:
[tex]\implies \textsf{a}=\dfrac{11}{2 \tan\left(\frac{180^{\circ}}{6}\right)}=\dfrac{11\sqrt{3}}{2}[/tex]
Area of a Regular Polygon
[tex]\textsf{A}=\dfrac{n\:s\:a}{2}[/tex]
where:
n = number of sidess = length of one sidea = apothemGiven:
n = 6s = 11[tex]\textsf{a}=\dfrac{11\sqrt{3}}{2}[/tex]Substitute the given values into the formula and solve for A:
[tex]\implies \sf A=\dfrac{6 \cdot 11 \cdot \dfrac{11\sqrt{3}}{2}}{2}[/tex]
[tex]\implies \sf A=314.3672216...[/tex]
[tex]\implies \sf A=314\:\:in^2\:\:(nearest\:whole\:number)[/tex]
BRAIN WARM UP MATHS?
We can make 64 different equations using the power of ten.
What is the power of a number?The power of a number identifies how many times that particular number is multiplied by itself.
Here, let us assume that the different equations = x
Using a power of 10, we have 10x making a total of 640.
10x = 640Divide both sides by 10
10x/10 = 640/10
x = 64
Therefore, we can conclude that we can make 64 different equations using the power of ten.
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Which of the following is a correctly written algebraic equation?
2 + 0.2x
5b - 5x + 2
a - 3x=0
3(x/5)
height of 24cm with a radius of 7cm. What is the total surface area of the cone?
Answer:
the answer to this problem is 703.7 in^2
The ratio of the number of laps Andy swam to the number of laps Ben swam
on the first day of a swimming lesson was 5: 6. The ratio of the number of
laps Andy swam to the number of laps Ben swam on the second day of the
swimming lesson was 9: 5. If Ben swam 33 laps on both days, how many laps
did Andy swim on the second day of the swimming lesson?
Answer:
10
Step-by-step explanation:
function F(x)=x+1 and g(x)=5x+1 find the f(4)=g(x+1)
The function of f(4) = g(x+1) gives the value of x that is -1/5.
What is the function addition?It is the addition of two functions similar to the addition of any two polynomial functions.
Given;
F(x)=x+1
g(x)=5x+1
We need to find f(4)=g(x+1)
First substitute x = 4 in f(x)
F(x)=x+1
F(4) = 4 + 1
F(4) = 5
Now substitute x = x + 1 in g(x)
g(x)=5x+1
g(x + 1) = 5(x + 1) + 1
g(x + 1) = 5(x + 1) + 1
g(x + 1) = 5x + 5 + 1
g(x + 1) = 5x + 6
Then ,
F(4) = g(x + 1)
5 = 5x + 6
5x = 5 - 6
5x = -1
x = -1/5.
The function of f(4) = g(x+1) gives the value of x that is -1/5.
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Consider this quotient.
3x²-27 3x
-------------- ÷ --------------
2x² +13x -7 4x²-1
100 points (08 03)Consider the following set of equations: Equation A: y = 2x + 4 Equation B: y = 3x + 1 Which of the following is a step that can be used to find the solution to the set of equations? 08 03 ) Consider the following set of equations : Equation A : y = 2x + 4 Equation B : y = 3x + 1 Which of the following is a step that can be used to find the solution to the set of equations ?
Answer:the equations are
y = x + 4 and y = 3x + 6
Now we can use substitution method to solve the system
So we can substitute value of y from one equation into other
So we get
x+4 = 3x+6
So Option B is correct
Step-by-step explanation:
Answer:
2x + 4 = 3x + 1
Explanation:
Equation A: y = 2x + 4
Equation B: y = 3x + 1
Simultaneously solving :
⇒ y = y
⇒ 2x + 4 = 3x + 1
⇒ 2x - 3x = 1 - 4
⇒ -x = -3
⇒ x = 3
Solve for y :
⇒ y = 2x + 4
⇒ y = 2(3) + 4
⇒ y = 10
Use the Pythagorean Theorem to find the length of the leg in the triangle shown below.
The figure shows a right triangle with one leg marked 12. The hypotenuse is marked 15.
Answer:
9
Step-by-step explanation:
The Pythagorean Theorem is a² + b² = c². c² is the hypotenuse while a² and b² are the legs.
So plugging it into the equation,
a² + 12² = 15²
a² + 144 = 225
a² = 81
a = 9
steps:
1. square the values
2. isolate the missing value
3. take the square root of both sides