Answer:
The rectangular coordinates of the point with polar coordinates (7, 2·π/3) is (-3.5, 3.5·√3)
Step-by-step explanation:
The given polar coordinates is (7, 2·π/3)
Where, the 7 represent the distance, r, from the point of reference and 2·π/3, the angle, θ, from the reference point.
Polar coordinates are represented in rectangular form by the equivalence transformation equation given as follows;
The x-coordinate = Radius, r × cos(θ), which gives
We note that 2·π/3 radians = 2 × 180/3 = 120°
x = 7 × cos(2·π/3) = 7 × cos(120°) = 7 × (-0.5) = -3.5
x = -3.5
The y-coordinate = Radius, r × sin(θ), which gives
x = 7 × sin(2·π/3) = 7 × sin(120°) = 7 × (√3)/2 = 3.5·√3
y = 3.5·√3
Therefore, the rectangular coordinates of the point with polar coordinates (7, 2·π/3) is (-3.5, 3.5·√3).
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QS=
Answer:
[tex]\boxed{\sf QS = 98}[/tex]
Step-by-step explanation:
QP = PS [Diagonals are bisected(Divided into two equal parts) by the other diagonal of parallelogram]
So,
3x - 11 = 2x + 9
3x - 2x = 9 + 11
x = 20
Now,
QS = QP + PS
QS = 3x-11+2x+9
QS = 3(20)-11+2(20)+9
QS = 60 - 11 + 40 + 9
QS = 49 + 49
QS = 98
Answer: QS=98
Step-by-step explanation: diagonals are bisected by the other diagonal parallelogram
Which equivalent expression will be generated by applying the distributive property and combing like terms in the expression 11+ 4(x + 2y + 4)
Answer:
Below
Step-by-step explanation:
● 11 + 4(x+ 2y + 4)
● 11 + 4x + 8y + 16
● 27 + 4x + 8y
Mikayla has $32 in her piggy bank. Her sister, Jessica, has $21. Mikayla earns $10 a week by doing chores for her grandparents, while Jessica earns $12 a week by mowing lawns. Which expressions give how much more or less money Mikayla has compared to Jessica after x weeks? Check all that apply. 11 – 2x ,2x – 11, 11 + 22x ,32 + 10x – (21 + 12x) 32 – 21 + 10x – 12x
Answer:
Hey There!! The answer to this is: 32+10x-(21+12x) We are given that:
Amount MIkayla has in here piggy bank initially = $32
Money earned by Mikayla per week = $10
Money earned by Mikayla in x weeks = 10x
Total money MIkayla has after x weeks = 32+10x
Amount Jessica has in here piggy bank initially = $21
Money earned by Jessica per week = $12
Money earned by Jessica in x weeks = 12x
Total money Jessica has after x weeks = 21+12x
Comparing,
In order to compare, we subtract the money earned by Jessica from that earned by MIkalya,
The final expression would be:
32+10x-(21+12x
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ItsNobody~ ☆
Answer:
1
4
5
Step-by-step explanation:
Isabelle bought some stationery. 1/3 of them were pencils. 5/8 of the remainder were erasers and the rest were ruler.The cost of the stationery is ,Pencil: $1.20 ,Eraser :$1 ,Ruler: $0.50 She spent a total of $169.50 on all the stationery. How much more did she spend on erasers than rulers.
Answer:
She spend[tex]\frac{7}{24}[/tex] more on erasers than rulers.
Step-by-step explanation:
We are given that Isabelle bought some stationery.
Fraction of pencil = [tex]\frac{1}{3}[/tex]
Remaining stationary =[tex]1-\frac{1}{3}=\frac{2}{3}[/tex]
5/8 of the remainder were erasers
So, part of eraser in stationary=[tex]\frac{5}{8} \times \frac{2}{3}=\frac{5}{12}[/tex]
Remaining stationary(rulers)=[tex]\frac{2}{3}-\frac{5}{12}=\frac{1}{4}[/tex]
Cost of ruler = $0.50
Cost of [tex]\frac{1}{4}[/tex]rulers =[tex]0.50 \times \frac{1}{4}=\frac{1}{8}[/tex]
Cost of eraser=$1
Cost of [tex]\frac{5}{12}[/tex] eraser=[tex]\frac{5}{12}[/tex]
Difference in cost of eraser and rulers =[tex]\frac{5}{12}-\frac{1}{8}=\frac{7}{24}[/tex]
Hence She spend[tex]\frac{7}{24}[/tex] more on erasers than rulers.
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In a circle whose center is O, arc AB contaisn 100 degrees. Find the number of degrees in angle ABO?
Answer:
40
Step-by-step explanation:
Angles ABO, BAO, and AOB are the angles of isosceles triangle AOB. The angles at A and B are equal, so we have ...
AOB +2ABO = 180° . . . . . sum of angles in the triangle
100° +2ABO = 180° . . . . . . use the given value
50° +ABO = 90° . . . . . . . . divide by 2; next, subtract 50°
∠ABO = 40°
11. House Prices In 1985, the median selling price of an
existing single-family home in Atlanta, Georgia, was
$66,200. Between 1985 and 1990, the average price in-
creased by 30%. Between 1990 and 2005, the average
price increased again, this time by 15%. What was the
median house price in Atlanta in 2005? -
Answer:
$98,969Step-by-step explanation:
$66,200 - the median selling price of a home in 1985
and the price increased by 30%:
66,200•30% = 66,200•0.3 = 19,860
66,200 + 19,860 = 86,060
$86,060 - the median selling price of a home in 1990
and the price increased by 15%
86,060•15% = 86,060•0.15 = 12,909
86,060 + 12,909 = 98,969
$98,969 - the median house price in Atlanta in 2005
simpily 2^3×3^2=6^5
Answer:
2^3×3^2=6^5 equation is wrong because
2×2×2×3×3=72
6^5=6×6×6×6×6=36×36×6=7776
the two numbers are not equal
Mate, I think your question is wrong ! ;(
[tex]Corrected \\ Question...\\[/tex] (2^3)^2*(3^2)^3=6^5
What is the result when the number 90 is decreased by 10%
Answer:
81
Step-by-step explanation:
First find the amount decrease
90 * 10 %
90 * .10
9
90 decreased by 9
90 -9
81
Answer:
81
Step-by-step explanation:
Turn into decimal.
10% = 0.1
Multiply
90 * 0.1 = 9
Subtract
90 - 9 = 81
Best of Luck!
6 sqrt (x-2) +4 < 28
How do you solve? Btw.. x-2 is under sqrt sign.
Answer:
Step-by-step explanation:
[tex]6\sqrt{x-2}+4<28\\6\sqrt{x-2}<28-4\\\sqrt{x-2}<\frac{24}{6}\\\sqrt{x-2}<4\\\\x-2 <16\\x<16-2\\x<14x-2 \geq 0\\x\geq 2\\so~2 \leq x < 14[/tex]
5/6 = b/12 help please
Answer:
[tex]b = 10[/tex]
Step-by-step explanation:
We can use the cross products property and solve for b.
[tex]\frac{5}{6} = \frac{b}{12}\\\\\\b=(12\cdot5)\div6\\b=60\div6\\b=10[/tex]
Hope this helped!
Answer:
The answer is b=10
Step-by-step explanation:
All you need to do is think 12/6 is what, the answer would be 2, then you would multiply the numerator by 2, which would be 5*2 which is 10.
Thank you, Hope this helps you.
The solutions to \[2x^2 - 10x + 13 = 0\]are $a+bi$ and $a-bi,$ where $a$ and $b$ are positive. What is $a\cdot b?$[tex]The solutions to\[2x^2 - 10x + 13 = 0\]are $a+bi$ and $a-bi,$ where $a$ and $b$ are positive. What is $a\cdot b?$[/tex]
In decimal form, this is equivalent to 1.25
=============================================
Work Shown:
The given equation 2x^2-10x+13 = 0 matches the form ax^2+bx+c = 0
We see that a = 2, b = -10, c = 13. Plug those values into the quadratic formula to solve for x.
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-10)\pm\sqrt{(-10)^2-4(2)(13)}}{2(2)}\\\\x = \frac{10\pm\sqrt{-4}}{4}\\\\x = \frac{10\pm2i}{4}\\\\x = \frac{2(5\pm i)}{2*2}\\\\x = \frac{5\pm i}{2}\\\\x = \frac{5}{2} \pm \frac{1}{2}i\\\\x = \frac{5}{2} + \frac{1}{2}i \ \text{ or } \ x = \frac{5}{2} - \frac{1}{2}i\\\\[/tex]
The two solutions are in the form [tex]a \pm bi[/tex] where a = 5/2 and b = 1/2
Therefore a*b = (5/2)*(1/2) = 5/4 = 1.25
The sum of two consecutive cube numbers is 341.
Work out the two numbers.
Answer:
see attachement
Step-by-step explanation:
Use the measure of the sides of triangle ABC to classify the triangle by its sides A(-1,3) B(-3,5) C(3,2)
Answer:
The triangle is a scalene triangle that has all three sides having different lengths
Step-by-step explanation:
The given vertices (and their coordinates) of the triangle are;
A(-1, 3)
B(-3, 5)
C(3, 2)
The equation for finding the lengths of a segment, l, given the coordinates, x, y is presented as follows;
[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
For segment AB, when, (x₁, y₁) = A(-1, 3) and (x₂, y₂) = B(-3, 5), we have;
[tex]l = \sqrt{\left (5-3 \right )^{2}+\left (-3-(-1) \right )^{2}} = 2\cdot\sqrt{2}[/tex]
Length of segment AB = 2·√2
For segment AC, when, (x₁, y₁) = A(-1, 3) and (x₂, y₂) = C(3, 2), we have;
[tex]l = \sqrt{\left (2-3 \right )^{2}+\left (3-(-1) \right )^{2}} = \sqrt{17}[/tex]
Length of segment AC = √17
For segment BC, when, (x₁, y₁) = B(-3, 5) and (x₂, y₂) = C(3, 2), we have;
[tex]l = \sqrt{\left (2-5 \right )^{2}+\left (3-(-3) \right )^{2}} = 3 \cdot \sqrt{5}[/tex]
Length of segment AC = 3·√5
The triangle is a scalene triangle that has all three sides having different lengths.
ASAP!!!!!!!!! PLEASE help me with this question! This is really urgent! No nonsense answers please.
Answer:
196 degrees
Step-by-step explanation:
360-164=196 degrees
the arch CDF=2*82=164
so the arch CGF =360-164=196 degrees
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Answer:
I will assume that ABCD is a parallelogram.
1. In a parallelogram, opposite sides are congruent so 3x = 18 which means x = 6.
2. The diagonals of a parallelogram bisect each other so BE is half of BD, therefore, BD = 7.5.
3. Consecutive angles of a parallelogram are supplementary so m∠ADC = 180° - 135° = 45°.
4. Consecutive angles of parallelograms are supplementary so 2x + 10 + 135 = 180 → 2x + 145 = 180 → 2x = 35 → x = 17.5°.
5. Again, the diagonals bisect each other so -6 + 8v = 9v - 10 → v = 4.
6. DA || BC so ∠DAC and ∠ACB are (congruent) alternate interior angles, therefore, m∠DAC = 37°.
7. The area of a parallelogram is base * height; we know base = 18 and height = 21 u so area = 378 u.
Help please will give brainiest if correct
Answer:
(x + 1)^2 + (y - 1)^2 = (8.5)^2
Step-by-step explanation:
Consider the general equation of a circle:
(x - h)^2 + (y - k)^2 = (r)^2
Where (h,k) represent the center point of the circle, and r represents the radius of the circle.
For this circle, our center point appears to be at (-1,1) and the circle has a radius of 8.5.
Using this information, we simply plug these values into the general equation to get the following:
(x + 1)^2 + (y - 1)^2 = (8.5)^2
Cheers.
What is the square root of 100?
Answer:
10
Step-by-step explanation:
Square root of 100 is 10
Answer:
10
Step-by-step explanation:
The square root of 100 is written as 2√100=√100=±10.
So it is 10. Also, 10 times 10 equals 100, so it checks out.
A square root is just two of the same numbers added together to equal a specific number.
A rhombus that is a rectangle is called
square ?
although this statement doesn't make any sense.
Answer:
Square!
Step-by-step explanation:
A rectangle is a parallelogram with all its interior angles being 90 degrees. A rhombus is a parallelogram with all its sides equal. This means that for a rectangle to be a rhombus, its sides must be equal. When this is satisfied, we have a square.
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Chris had $4 in cash, with which he purchased coffee for $0.79, a bag of chips for $1.69 and a lottery ticket for $1.00. If he does not have to pay sales tax, how much change should he receive?
Answer:
£0.79 add £1.69 add £1.00 equals £ 3. 4 8
Take away £4.00 and change is 52p
Step-by-step explanation:
An equation is formed of two equal expressions. The change that Chris would receive is $0.52.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='. while an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Given that Chris had $4 in cash. Also, he purchased coffee for $0.79, a bag of chips for $1.69 and a lottery ticket for $1.00. Therefore, the change he would receive is,
Change = Cash Chris has - Cost of coffee - Cost of chips - Cost of lottery
= $4 - $0.79 - $1.69 - $1.00
= $0.52
Hence, the change that Chris would receive is $0.52.
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The password for a certain safe is indicated by multiplying (x^2-16)/(x-1) with 1 / ((x ^ 2 + 6x + 8) / (x ^ 2 + 2x-3)) . Knowing that the value of X = 9. What is the numeric value of the password.
Answer:
5.455Step-by-step explanation:
If the password for a certain safe is indicated by multiplying (x^2-16)/(x-1) with 1 / ((x ^ 2 + 6x + 8) / (x ^ 2 + 2x-3))
Simplify the expression in its lowest term first
[tex]= \dfrac{x^2-16}{x-1} * \dfrac{1}{\dfrac{x ^ 2 + 6x + 8}{x ^ 2 + 2x-3} } \\\\= \dfrac{x^2-16}{x-1} * }{\dfrac{x ^ 2 + 2x - 3}{x ^ 2 + 6x + 8} }\\\\= \dfrac{ (x+4)(x-4)}{x-1} * \dfrac{(x+3)(x-1)}{(x+4)(x+2)}\\\\= \dfrac{x-4}{1} * \dfrac{x+3}{x+2}\\[/tex]
If the value of x = 9, to get the numeric value of the password, we will substitute x = 9 into the resulting function as shown;
[tex]= \dfrac{x-4}{1} * \dfrac{x+3}{x+2}\\\\= \dfrac{9-4}{1} * \dfrac{9+3}{9+2}\\\\= \frac{5}{1} * \frac{12}{11}\\\\= \frac{60}{11}\\ \\= 5.455[/tex]
Hence the numeric value of the password is 5.455
Weight of Sea Glass in Jars
2 2 2 1 11 12 12 2 24 22 24 3 37 22
Weight in Pounds
Mason loves collecting sea glass from the beach. He recorded the weight of
each jar full of sea glass. If he decided to distribute the sea glass equally among
the jars, how much would each Jar weigh?
pounds
(Write mixed numbers as x y/z.)
Answer:
[tex]Average = 12\frac{4}{7}\ lb[/tex]
Step-by-step explanation:
Given
Number of jars = 14
Weights = 2, 2, 2, 1, 11, 12, 12, 2, 24, 22, 24, 3, 37, 22 in pounds
Required
What is the weight of each jar if the sea glass is evenly distributed
What this question implies is that, the average weight of the sea glass is calculated;
[tex]Average = \frac{Sum\ of\ weights}{Number\ of\ jars}[/tex]
[tex]Average = \frac{2+ 2+ 2+ 1+ 11+ 12+ 12+ 2+ 24+ 22+ 24+ 3+ 37+ 22}{14}[/tex]
[tex]Average = \frac{176}{14}[/tex]
[tex]Average = 12\frac{8}{14}[/tex]
Divide the numerator and denominator by 2
[tex]Average = 12\frac{4}{7}[/tex]
Hence, the weight of each jar would be [tex]12\frac{4}{7}\ lb[/tex]
38. What is the solution to 2(x - 6) = 14?
40. Simplify: 8(2x - 2)
HELP! answer if you can there's two questions
Answer:
x=13, 16(x-1)
Step-by-step explanation:
For 38, you have to first divide both sides by 2.
This becomes, x-6=7
Add 6 to both sides
x=13.
For 40. You can can distribute the 8.
This makes it 16x-16.
With this you can than, factor out the 16.
16(x-1).
Answer:
x =1316x-16Step-by-step explanation:
38.
[tex]2(x - 6) = 14\\\\\mathrm{Divide\:both\:sides\:by\:}2\\\\\frac{2\left(x-6\right)}{2}=\frac{14}{2}\\\mathrm{Simplify}\\x-6=7\\\mathrm{Add\:}6\mathrm{\:to\:both\:sides}\\\\x-6+6=7+6\\\\x=13[/tex]
40.
[tex]8(2x - 2)\\\mathrm{Apply\:the\:distributive\:law}:\\\quad \:a\left(b-c\right)=ab-ac\\\\a=8,\:b=2x,\:c=2\\\\=8\times \:2x-8\times \:2\\\\=16x-16[/tex]
19 x97 find the product using suitable properties
Answer:
19 x 97 = 1843
whats the answer to this problem/how to figure it out?!
6x^2+4x+8
6x7^2+4x+8
blah blah blah
ANSWER
330
pls say if im right
Answer:
330Step-by-step explanation:
[tex]6x^2 +4x +8\\x =7\\\\6(7)^2 +4(7) +8\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Calculate\:exponents}\:\left(7\right)^2\::\quad 49\\\\=6\cdot \:49+4\left(7\right)+8\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:6\cdot \:49\::\quad 294\\\\=294+4\left(7\right)+8\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:4\left(7\right)\::\quad 28\\\\=294+28+8\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:294+28+8\:\\:\quad 330[/tex]
m +2p; use m = 2, and p = 4
Answer:
10
Step-by-step explanation:
m + 2p
2 + 2(4)
= 2 + 8
= 10
Answer:
10
Step-by-step explanation:
m +2p;
let m = 2, and p = 4
2+2*4
2+8
10
What is the area of a circle with a diameter of 29 centimeters?
cm2
(Use 3.14 for Pi.)
Answer:
Step-by-step explanation:
AREA OF CIRCLE = 660.185CM^2
HOPE IT HELPS
how do you solve 2m-10=44+8m
Answer:
m = -9
Step-by-step explanation:
2m-10=44+8m
Subtract 2m from each side
2m-2m-10=44+8m-2m
-10 = 44+6m
Subtract 44 from each side
-10-44 = 44-44+6m
-54 = 6m
Divide by 6
-54/6 = 6m/6
-9 = m
Answer:
solve by solving the salvation for equation don't be a slave get educated from what's gave
What is the product? One-fourth times three and two-thirds
Answer:
11/12
Step-by-step explanation:
The product of One-fourth times three and two-thirds will be 1 / 2.
What is multiplication?Multiplication is the process of determining the product of two or more numbers in mathematics. A product, or an expression that specifies factors to be multiplied, is what happens when you multiply two numbers in mathematics.
Given that, the numbers are one-fourth times three and two-thirds. The product of the numbers will be calculated as,
Product = ( 1 / 4 ) x ( 3 ) x ( 2 / 3 )
Product = 6 / 12
Product = 1 / 2
Therefore, the product of One-fourth times three and two-thirds will be 1 / 2.
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Follow the process of completing the square to solve x2 = -4x + 3
Answer:
x1 = 0.64575
x2 = -4.64574
Step-by-step explanation:
Step 1: We want to rearrange the equation so all the variables are on one side
0 = -x² - 4x + 3
Step 2: We take out -1 in the first 2 terms so a = 1
0 = -(x² + 4x) + 3
Step 3: Force a square, take the 'b' value and divide it by 2 and square the result. Add it and subtract it from the inside of the brackets
b = 4
4/2 = 2
2² = 4
0 = -(x² + 4x + 4 - 4) + 3
Step 4: Move the -4 out remembering to apply the -
= -(x² + 4x + 4) + 4 + 3
Step 5: We notice is inside the brackets is a perfect square
0 = -(x + 2)² + 7
Therefore the vertex form of the equation is
y = -(x + 2)² + 7
Step 6: We want to solve the equation (find the x intercepts) so we set y to 0 and solve for x
0 = -(x + 2)² + 7
-7 = -(x + 2)²
7 = (x + 2)²
[tex] \sqrt{7 } = x + 2 [/tex]
[tex]x = \sqrt{7} - 2[/tex]
1st Solution:
x = +2.64575 - 2
x = 0.64575
2nd Solution:
x = -2.64575 - 2
x = -4.64574
BRAINLIEST AND 25 POINTS THIS IS ONLY ONE QUESTION SUPER EASY AND I NEED IT IN 5 MINUTES IM SO TIRED AND STRESSED HELP
Answer:
52°
Step-by-step explanation:
360 - 33 - 165 - 20 - 90 = x
x = 52
Answer:
[tex] \boxed{52}[/tex]Step-by-step explanation:
Let's find the size of angle x
The angle in a complete turn add up to 360°
[tex] \mathsf{x + 20 + 165 + 33 + 90 = 360}[/tex]
Add the numbers
[tex] \mathsf{x + 308 = 360}[/tex]
Move constant to R.H.S and change it's sign
[tex] \mathsf{x = 360 - 308}[/tex]
Calculate the difference
[tex] \mathsf{x = 52}[/tex] °
Hope I helped!
Best regards!
