Answer:
w = -11
Step-by-step explanation:
[tex]\sqrt{3 - 2w} = w + 6[/tex]
[tex](\sqrt{3 - 2w})^2 = (w + 6)^2[/tex]
[tex] 3 - 2w = w^2 + 12w + 36 [/tex]
[tex] w^2 + 14w + 33 = 0 [/tex]
[tex] (w + 11)(w + 3) = 0 [/tex]
[tex] w + 11 = 0 [/tex] or [tex] w + 3 = 0 [/tex]
[tex] w = -11 [/tex] or [tex] w = -3 [/tex]
When you square both sides of an equation, you must check all solutions for extraneous solutions.
Check w = -11.
[tex]\sqrt{3 - 2w} = w + 6[/tex]
[tex] \sqrt{3 - 2(-11)} = -11 + 6 [/tex]
[tex] \sqrt{3 + 22} = -5 [/tex]
[tex] \sqrt{25} = -5 [/tex]
[tex] 5 = -5 [/tex]
This is a false statement, so the solution w = -11 is extraneous since it does not satisfy the original equation.
Check w = -3.
[tex]\sqrt{3 - 2w} = w + 6[/tex]
[tex] \sqrt{3 - 2(-3)} = -3 + 6 [/tex]
[tex] \sqrt{3 + 6} = 3 [/tex]
[tex] \sqrt{9} = 3 [/tex]
[tex] 3 = 3 [/tex]
This is a true statement, so the solution w = -3 is valid.
Answer: w = -11
The square below has an area of 1+ 2x + x² square meters.
What expression represents the length of one side of the square?
Side length
1+2x+x²
Side length
www
meters
Answer:
1 + x meters.
Step-by-step explanation:
A square has 4 equal sides so each side will have a length equal to the square root of the area.
Side length = √(1 + 2x + x^2)
= √(1 + x)(1 + x)
= 1 + x.
Jack wants to plant a border of flowers in the shape of an arc along the edge of a circular walkway. if the circle has a radius of 5 yards and the angle subtended by the arc measures 1.5 radians, what is the length of the curved border?
[tex]5(1.5)=\boxed{7.5 \text{ yd}}[/tex]
The length of the curved border or arc is 7.5 yards.
the length of the arc = [tex]\theta \times r[/tex]
given that [tex]\theta[/tex] = 1.5 radian
radius = 5 yards
then the length of arc from the above formula
[tex]l = \theta \times r\\l = 1.5 \times 5 = 7.5[/tex] yards
What is arc?A circle's arc is referred to as a portion or section of its circumference.A chord of a circle is a straight line that might be created by joining the arc's two ends.A semicircular arc is one whose length is exactly half that of a circle.To know more about arc with the given
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Type SSS, SAS, ASA, AAS, or HL to justify why AABC = ADEF.
AC FD and AB = DE
The theorem that justifies why triangles ABC and DEF are congruent is: HL.
What is the Hypotenuse-Leg Congruence Theorem (HL)?The hypotenuse-leg congruence theorem (HL) states that if two triangles that are right triangles have a pair of congruent hypotenuse and a pair of corresponding congruent legs, then both right triangles are proven to be congruent to each other. This means both right triangles are have the same shape and size.
Given that:
angle ABC = angle DEF = 90° (congruent right angles, this means both triangles are right triangles)
AC = FD (a pair of congruent hypotenuse)
AB = DE (a pair of congruent legs)
Thus, we can conclude that since triangle ABC and triangle DEF have a pair of congruent hypotenuses and a pair of congruent legs, therefore, the two right triangles, triangle ABC and triangle DEF are congruent to each other by the HL congruent theorem.
Thus, the theorem that justifies why both triangles are congruent is: HL.
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What is the equation of the line that passes through the point (-6,8) and has a slope of -5/3?
Answer:
y = -5/3 - 8
Step-by-step explanation:
We want to write this in the form y = mx + b. We need to find the m (slope) and the b (y-intercept) , Whew, they already gave us the slope, so we are have way there. I will plug in the x and y that we are given from the point (-6, 8) to solve for b.
y = mx + b
8 = -5/3(-6) + b Multiply the fraction by -6
8 = 30/3 + b I can make 6 a fraction by writing it 6/1 and then just multiply straight across. A negative times a negative is a positive.
8 = 10 + b 30/3 is equal to 10. Now subtract 10 from both sides to get b
-8 = b
I can now write the equations since I now know m and b.
y = -5/3 + (-8) which is the same as y = -5/3 - 8. Adding a negative is the same as subtracting a positive.
LOTS OF POUNT PLS HELP
Answer:
Option 2
Step-by-step explanation:
Using the quadrstic formula,
[tex]\tan \theta=\frac{-2 \pm \sqrt{2^2 - 4(\sqrt{3})(-\sqrt{3})}}{2\sqrt{3}} \\ \\ =\frac{-2 \pm 4}{2\sqrt{3}} \\ \\ =\frac{-1 \pm 2}{\sqrt{3}} \\ \\ = -\sqrt{3}, \frac{1}{\sqrt{3}}[/tex]
Case 1
[tex]\tan \theta=-\sqrt{3} \implies \theta=\frac{2\pi}{3}, \frac{5\pi}{3}[/tex]
Case 2
[tex]\tan \theta=\frac{1}{\sqrt{3}} \implies \theta=\frac{\pi}{6}, \frac{7\pi}{6}[/tex]
4 pounds of oranges cost $12. what is the unit price per pound ?
$ 1 per 3 pounds
$ 3 per 1 pound
$6 per 2 pounds
$12 per 4 pounds
the unit price is $3 per pound, the correct option is the second one.
How to get the unit price of the oranges?
The unit price for the oranges is just the price for one pound of oranges.
Here we know that the price of 4 lb of oranges is $12, with that we want to get the cost of a single lb of oranges, so we can write:
4lb = $12
If we divide both sides by 4, then we get:
4lb/4 = $12/4
1lb = $3
This means that the price of 1 pound of oranges is $3, then the unit price is $3 per pound, the correct option is the second one.
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Solve 2tan(x)cos^2(x)=1 algebraically
On June 10, Bertha Wooten deposited $8,241.78 in a savings account that pays 5.5% interest compounded
daily. How much interest will the money earn in 31 days?
The amount of interest that Bertha Wooten's deposit will earn in 31 days is $38.59, which is the difference between the future value and the present value.
What is the future value?The future value represents the amount that will be in the account after the present value investment is compounded at an interest rate periodically.
The future value of an investment can be calculated using the future value formula, A = P (1 + i)^n.
Where:
A = future value
P = Present value of investment
i = interest rate
n = number of periods.
The future value of the investment can also be determined using an online finance calculator, as follows.
Then the interest is the difference between the future value and the present value.
Data and Calculations:Initial deposit = $8,241.78
Interest rate = 5.5% compounded daily
Investment period = 31 days
N (# of periods) = 31 days
I/Y (Interest per year) = 5.5%
PV (Present Value) = $8,241.78
PMT (Periodic Payment) = $0
Results:
FV = $8,280.37
Total Interest $38.59 ($8,280.37 - $8,241.78)
Thus, the amount of interest that Bertha Wooten's deposit will earn in 31 days is $38.59.
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Given that xy=3/2 and both x and y are nonnegative real numbers, find the minimum value of 10x (3y/5)
The munimum value is, at x = 3/10, y = 5 and 10x+3y/5 = 6.
What are nonnegative real numbers?Non-negative real numbers are the set of positive real numbers that are bigger than 0 (zero). That is, the true values are either positive or negative. The collection will include numbers such as 0, 1, 2, 3, 4, 5, and so on.To find the minimum value of 10x (3y/5):
Given - y = 3/(2x)
So, we want the bare minimum of,
= 10x + 3/5 × 3/(2x)= 10x + 9/(10x)Take the derivative to obtain:
= 10 - 9/(10x^2)When you set it to zero, you get:
= 100x^2 - 9 = 0= (10x-3)(10x+3) = 0= x = ± 3/10So, at x = 3/10, y = 5 and 10x + 3y/5 = 3 + 3 = 6.
Therefore, the munimum value is, at x = 3/10, y = 5 and 10x+3y/5 = 6.
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Please help me 18 points
City B had the highest noon temperature, Interquartile Range, Larger Median temperature while City A had smaller range of temperature.
A box and whisker plot, also known as a box plot, shows a five-number summary of a set of data. The minimum, first quartile, median, third quartile, and maximum are the five-number summary. A box plot is created by drawing a box from the first to third quartiles. At the median, a vertical line runs through the box. The whiskers move from the lowest to the highest quartile.
From the figure:-
City B has the highest noon temperature with 86FCity B has the highest Interquartile RangeCity B has the highest median noon temperature with 79F City A has smaller range of temperatureLearn more about Statistics here :
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Answer:
(a) B
(b) B
(c) B
(d) B
Step-by-step explanation:
The following are the ages of 13 history teachers in a school district. 24, 27, 29, 29, 35, 39, 43, 45, 46, 49, 51, 51, 56 Notice that the ages are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum: Interquartile range:
The Five number summary for the given data:
Minimum: 24
Lower quartile: Q1 = 29
Median: 43
Upper quartile: Q3 = 50
Maximum: 56
Interquartile range: IQR = 21
What is the interquartile range?The interquartile range is calculated by
IQR = Q3 - Q1
Where Q3 - upper quartile and Q1 - lower quartile
Q3 = 3/4(n + 1) th term
Q1 = 1/4(n + 1) th term
Calculation:The given data points are
24, 27, 29, 29, 35, 39, 43, 45, 46, 49, 51, 51, 56
where n = 13
Maximum data value = 56
Minimum data value = 24
Calculating Median:
Median = (n+1)/2 th term
⇒ Median = (13 + 1)/2 = 7th term
∴ Median = 43
Calculating the quartiles:
Upper quartile Q3 = 3/4(n + 1)th term
⇒ Q3 = 3/4(13 + 1) = 10.5
⇒ Q3 = 10th term + 1/2(11th term - 10th term)
⇒ Q3 = 49 + 1/2(51 - 49)
⇒ Q3 = 49 + 1
∴ Q = 50
Lower quartile Q1 = 1/4(n + 1)th term
⇒ Q1 = 1/4(13 + 1) = 3.5
⇒ Q1 = 3rd term + 1/2(4th term - 3rd term)
⇒ Q1 = 29 + 1/2(29 - 29)
∴ Q1 = 29
Calculating the IQR:
IQR = Q3 - Q1
= 50 - 29
= 21
Thus, the interquartile range is 21.
Therefore, the five-number summary for the given data:
Minimum: 24
Lower quartile: Q1 = 29
Median: 43
Upper quartile: Q3 = 50
Maximum: 56
Interquartile range: IQR = 21
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Geometry: complete this proof of theorem 14, ASAP!
(Theorem 14: if a transversal intersects two lines so that corresponding angles are congruent, then the lines are parallel.)
Answer:
1. Transversal y intersects lines m and n; <1 ~= <2 (Given)
2. <1 ~= <3 (Vertical Angles Theorem)
3. <2 ~= <3 (Transitive Property of Congruence)
4. m || n (Converse of Alternate Interior Angles Theorem)
A triangle has side lengths of (2b + 5c) centimeters, (10b + 7d) centimeters, and
(4d-3c) centimeters. Which expression represents the perimeter, in centimeters,
of the triangle?
The perimeter of the triangle can be express as follows:
12b + 11d + 2c
How to find perimeter of a triangle?The perimeter of a figure is the sum of the whole sides of the figure.
A triangle has three sides. Therefore, the perimeter of a triangle is the sum of the three sides.
Therefore, the sides of the triangle are of lengths (2b + 5c) centimetres, (10b + 7d) centimetres, and (4d-3c) centimetres.
Hence, the perimeter of the triangle can be represented as follows:
Perimeter of the triangle = 2b + 5c + 10b + 7d + 4d - 3c
Perimeter of the triangle = 2b + 10b + 7d + 4d + 5c - 3c
Perimeter of the triangle = 12b + 11d + 2c
Therefore, the perimeter of the triangle can be express as follows:
12b + 11d + 2c
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Match the values associated with this data set to their correct descriptions. {6, 47, 49, 15, 43, 41, 7, 36}
1st quartile: 11
median: 38.50000
3rd quartile: 45
According to the given information:Order these numbers in increasing order: 6, 7, 15, 36, 41, 43, 47, 49There is a 38.5 median (it is the mean of 36 and 41 - the pair of middle entries).6,7,15,36, or the left-most half of the data, make up the sample.The median of the lower half is 11, which is the first quartile (it is the mean of 7 and 15 - the pair of middle entries).41, 43, 47, and 49, which are the data points in the upper half, are to the right of the median.The median of the upper half is 45 in the third quartile (it is the mean of 43 and 47 - the pair of middle entries).The biggest value deviates 10.5 from the median (49-38.5)Measure descriptive statistics
1st quartile: 11
median: 38.50000
3rd quartile: 45
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I understand that the question you are looking for is :
2 Drag the tiles to the boxes to form correct pairs. Match the values associated with this data set to their correct descriptions. {6, 47, 49, 15, 43, 41, 7, 36} first quartile 38.5 median 11 third quartile 10.5 the difference of the largest value and the median 45
Which combination of shapes can be used to create the 3-D figure?
Two regular octagons and eight congruent rectangles are perfect for the creation of 3-D figures.
According to the statement
we have to tell and explain about the types of shapes which are required for the creations of 3-D figure.
For this purpose, Firstly we have to know about the 3-D figures.
So,
A shape is a graphical representation of an object or its external boundary and outline, as opposed to other properties such as color, texture, or material type.
A plane shape is constrained to lie on a plane, in contrast to solid 3-D shapes.
After that we know that the
When the all dimensions of a given shape can be observed at the same time, then its is said to be in a 3-D. However, polygons are shapes which has 3 or mores sides. Examples are: trigon, hexagon, octagon etc.
Thus, since the in the 3-D figure have 8 sides connected which is greater than their width.
This confirms that the sides of the figure made up of eight congruent rectangles, because the 3-D figure has eight regular sides. Then, the height of the figure would be the length of the rectangles.
After that all this condition, Two regular octagons and eight congruent rectangles are perfect for the creation of 3-D figures.
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If 8x + 6y = 24, what is y in terms of x ?
Step-by-step explanation:
8x+6y=24
6y=24-8x
y=24/6 - 8/6x
y=4-4/3x
A 2-quart carton of non-dairy creamer costs $1.04. What is the price per cup?
If ₹405 is to be divided among three persons A, B, C in the ratio of 3:5:7, how much money does each one get? Express them in percentages.
I will mark the first answerer as Brainliest.
Answer:
A = 20%
B = 33.33%
C = 46.67%
Step-by-step explanation:
Ok we need to add up 3, 5, and 7
3+5+7 = 15
405/15 = 27.
27*3 = A
27*5 = B
27*7 = C
A = 81 / 20%
B = 135 / 33.33%
C = 189 / 46.67%
PLEASE HELP IM STUCK ONLY 3 MORE QUESTIJONS
Answer:
y = - 2x + 8
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{1}{2}[/tex] x - 9 ← is in slope- intercept form
with m = [tex]\frac{1}{2}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{2} }[/tex] = - 2
y = - 2x + c ← is the partial equation
to find c substitute (3, 2 ) into the partial equation
2 = - 6 + c ⇒ c = 2 + 6 = 8
y = - 2x + 8 ← equation of perpendicular line
Study island surface area
Answer:
C. 206 unit^2.
Step-by-step explanation:
Area = 2*11*5 + 2*11*3 + 2*3*5
= 110 + 66 + 30
= 206.
during the drive from the church to the graveyard , you cover 16,4 km in 1,5 hours . calculate your average speed
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
Avg. speed = 11 km/h[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
Average speed (v) :
[tex]\qquad❖ \: \sf \:v = \cfrac{total \: \: distance \: \: covered}{total \: \: time \: \: taken} [/tex]
[tex]\qquad❖ \: \sf \:v = \dfrac{16.4}{1.5} [/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex]\qquad❖ \: \sf \:v = 11 \: \: kmph[/tex]
The following figure is made of 2 triangles.
9
5
A
Figure
Triangle A
Triangle B
Whole figure
7
B
Find the area of each part of the figure and the whole figure.
Area (square units)
area is 1/2 times base times height
triangle A
1/2 times 7 times 9
answer 31.5
Triangle B
1/2 times 7 times 5
answer 17.5
Allen wants to buy colored pencils that cost $3.50. He has 2 dollars, 5 quarters, 2 dimes, and 7 pennies. Does he have enough money to buy the colored pencils
Answer:
Yes
Step-by-step explanation:
First we need to determine how much money Allen has
2 dollars = 2.00
5 quarters = 5 * .25 = 1.25
2 dimes = 2 * .10 = .20
7 pennies = 7 * .01 = .07
Add this together
2.00 + 1.25+.20+.07 =3.52
3.52 > 3.50
This is more than 3.50 so he has enough money to buy the pencils
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
Bottom left
Step-by-step explanation:
Since the slope has to be positive it can't be the ones on the right side since both of them are negative. And the bottom left one is rising 3 and running 4. (formula = rise/run). See image.
Show your work and hurry please
Answer:
15
Step-by-step explanation:
Note: Take note , absolute value will give the magnitude of the value. (Which means ignoring the + / - signs.)
Eg. | - 19 | = 19
Therefore,
[tex] \frac{12(30 - (9 + {4}^{2})) }{10 - | - 6| } \\ = \frac{12(30 - (9 + 16))}{10 - 6} \\ = \frac{12(30 - 25)}{4} \\ = \frac{12(5)}{4} \\ = \frac{60}{4} \\ = 15[/tex]
Express 16% percent as a fraction in the simplest form
Find the least number should 2028 be multiplied so that the product is a perfect
square?
Thus, 2028 needs to be multiplied by 3 to become a perfect square. Therefore, the number 6084 has 3 pairs of equal prime factors . Hence, the smallest number by which 2028 must be multiplied so that the product is a perfect square is 7
Enter the correct answer in the box. solve the equation x2 − 16x 54 = 0 by completing the square. fill in the values of a and b to complete the solutions.
The roots of the given polynomials exist [tex]$x=8+\sqrt{10}$[/tex], and [tex]$x=8-\sqrt{10}$[/tex].
What is the formula of the quadratic equation?For a quadratic equation of the form [tex]$a x^{2}+b x+c=0$[/tex] the solutions are
[tex]$x_{1,2}=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$[/tex]
Therefore by using the formula we have
[tex]$x^{2}-16 x+54=0$$[/tex]
Let, a = 1, b = -16 and c = 54
Substitute the values in the above equation, and we get
[tex]$x_{1,2}=\frac{-(-16) \pm \sqrt{(-16)^{2}-4 \cdot 1 \cdot 54}}{2 \cdot 1}$$[/tex]
simplifying the equation, we get
[tex]$&x_{1,2}=\frac{-(-16) \pm 2 \sqrt{10}}{2 \cdot 1} \\[/tex]
[tex]$&x_{1}=\frac{-(-16)+2 \sqrt{10}}{2 \cdot 1}, x_{2}=\frac{-(-16)-2 \sqrt{10}}{2 \cdot 1} \\[/tex]
[tex]$&x=8+\sqrt{10}, x=8-\sqrt{10}[/tex]
Therefore, the roots of the given polynomials are [tex]$x=8+\sqrt{10}$[/tex], and
[tex]$x=8-\sqrt{10}$[/tex].
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Answer:
x=8-[tex]\sqrt{10}[/tex] and x=8+[tex]\sqrt{10}[/tex]
Step-by-step explanation:
It was right for me
9. Safa is a resident of UAE where mobile numbers consist of 7 digits. She tells her friend that her mother's mobile number is the smallest number and father's is the greatest number that can be formed by using the digits 5,7,9,8. Help her friend to find her parents numbers. Each digit must be used at least once.
Answer:
Smallest number: 5555789
Largest number: 9999875
Step-by-step explanation:
Since each digit must be used at least once, the smallest number that can be formed with the digits 5, 7, 8 and 9 is 5555789 (ascending order of digits with smallest digit used four times
The largest number is 9999875 (descending order of digits with largest digit used four times)
If 12 men are needed to run 4 machines. How many men are needed to run 20
Answer:
60Step-by-step explanation:
If 12 men are needed to run 4 machines. How many men are needed to run 20
we can solve with an equation
12 : 4 = x : 20
x = 12 * 20 : 4
x = 240 : 4
x = 60
----------------------------
check
12 : 4 = 60 : 20
3 = 3
the answer is good
