Answer: 35
Step-by-step explanation:
If you take the three angles shown, it's total is 180
So take the two angles you know, and subtract them from 180
Now we have 100 left, and we can subtract 30 to be left with 2x.
Now divide what is left by two, which is 70
70/2=35
Answer:
x = 35
Step-by-step explanation:
So we know that a straight line is equal to 180 degrees. So from there we can add the two 40 degrees to get 80 degrees. Now we can solve for x. So 180 - 80 = 100
2x + 30 = 100
Subtract 30 from both sides
2x = 70
Divide both sides by 2
x = 35
If $a>0$ and $b>0$, a new operation $\nabla$ is defined as follows:$$a \nabla b = \dfrac{a + b}{1 + ab}.$$For example,$$3 \nabla 6 = \dfrac{3 + 6}{1 + 3 \times 6} = \dfrac{9}{19}.$$For some values of $x$ and $y$, the value of $x \nabla y$ is equal to $\dfrac{x + y}{17}$. How many possible ordered pairs of positive integers $x$ and $y$ are there for which this is true?
This happens when
1 + a b = 17 ==> a b = 16
With a and b both positive integers, and 16 = 2^4, we can have
• a = 1 and b = 16
• a = 2 and b = 8
• a = b = 4
and vice versa. So there are 5 possible ordered pairs.
Point R is on line segment QS. Given RS=11 and QS=19, determine the length QR.
================================================
Explanation:
R is between Q and S and on segment QS, allowing us to say
QR + RS = QS
because of the segment addition postulate.
-------
Use substitution and solve for QR
QR + RS = QS
QR + 11 = 19
QR = 19 - 11 .... subtracting 11 from both sides
QR = 8
Write in point-slope form an equation of the line that passes through the point (8, 9) with slope 7.
Answer:
y=7x-47Step-by-step explanation:
[tex](8,9)=(x1,y1) \\ m=7 \\ y−y1=m(x−x1) \\ y−9=7(x−8)
[/tex]
[tex]y - 9 = 7x - 56 \\ y = 7x - 56 + 9 \\ y = 7x - 47[/tex]
5 * 10^6 is how many times larger as 5 * 10^4
[tex]\dfrac{5\cdot10^6}{5\cdot10^4}=10^{6-4}=10^2=100[/tex]
Answer:
100 times more
Step-by-step explanation:
5*10^4 over 5*10^6 is 1/100
Anyone who answers will be marked brainiest answer. If u don't understand anything just ask.
Answer:
7/2 pi
or approximately 10.99557429
Step-by-step explanation:
2 pi sqrt( a/b)
let a = 49 and b = 16
2 pi sqrt( 49/16)
We know that sqrt( a/b) = sqrt(a) /sqrt(b)
2 pi sqrt(49) / sqrt(16)
2pi ( 7) / (16)
2 pi ( 7/4)
7/2 pi
This is the exact answer
We can make an approximation for pi
Using the pi button on the calculator
10.99557429
12. Explain why is (+5) + (-7) = -2.
Let's use a number line to help us visualize what's going on.
Starting at 0, +5 takes us 5 units to the right.
From there, -7 moves us 7 units back to the left and we end up at -2.
So (+5) + (-7) simplifies to -2.
Take a look at the image below.
Let P (2,-3), Q (-2, 1) be the vertices of the triangle PQR. If the centroid of ΔPQR lies on the line 2x +3y = 1, then the locus of R is a. 2x + 3y = 9 b. 2x - 3y = 9 c. 3x + 2y = 5 d. 3x - 2y = 5
Answer:
Correct answer is a. 2x + 3 y = 9.
Step-by-step explanation:
Let the coordinates of centroid be (h,k)
{h/3 , (-2+k)/3}
h = (2 – 2 + a)/3 = a/3 ---eqn 1
k= ( - 3+ 1 + b )/3 = (-2 + b)/3 -----eqn 2
Where (x,y) are any point on the line 2x+3y=1
3h = a and 3k + 2 = b
From 2x +3y = 1,
Then, 2h +3k = 1, 3k = 1 - 2h -----eqn 3
b = 1 - 2h + 2 = 3 - 2h
also b = 3 - 2a/3
b = (9 -2a)/3
3b = 9 - 2a
3b + 2a = 9
Now (x,y) satisfy the point on the line 2x+3y=9
So the locus is 2x + 3 y = 9.
The weights of ice cream cartons are normally distributed with a mean weight of ounces and a standard deviation of ounce. (a) What is the probability that a randomly selected carton has a weight greater than ounces? (b) A sample of cartons is randomly selected. What is the probability that their mean weight is greater than ounces? (a) The probability is nothing. (Round to four decimal places as needed.) (b) The probability is nothing. (Round to four decimal places as needed.)
Answer:
The answer is below
Step-by-step explanation:
The weights of ice cream cartons produced by a manufacturer are normally distributed with a mean weight of 10 ounces and a standard deviation of 0.5 ounce. (a) What is the probability that a randomly selected carton has a weight greater than 10.21 ounces? (b) You randomly select 25 cartons. What is the probability that their mean weight is greater than 10.21 ounces
Answer:
Given that:
Mean (μ) = 10 ounces, standard deviation (σ) = 0.5 ounces.
The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score (z) is given by:
[tex]z=\frac{x-\mu}{\sigma} \\\\For\ a\ sample\ size(n):\\\\z=\frac{x-\mu}{\sigma/\sqrt{n} }[/tex]
a) For x = 10.21:
[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{10.21-10}{0.5}=0.42[/tex]
From the normal distribution table, probability that a randomly selected carton has a weight greater than 10.21 ounces = P(x > 10.21) = P(z > 0.42) = 1 - P(z < 0.42) = 1 - 0.6628 = 0.3372
b ) For x = 10.21 and n = 25
[tex]\sqrt{x} \sqrt{x} z=\frac{x-\mu}{\sigma/\sqrt{n} }\\\\z=\frac{10.21-10}{0.5/\sqrt{25 } }=2.1[/tex]
From the normal distribution table, probability that a randomly selected carton has a weight greater than 10.21 ounces = P(x > 10.21) = P(z > 2.1) = 1 - P(z < 2.1) = 1 - 0.9826 = 0.0174
Drag each label to the correct location on the table. Each label can be used more than once. A cross country coach records the number of miles his athletes on the Junior Varsity and Varsity teams ran today and displays the data in the provided dot plots. Given the shape of each distribution, determine which measures of center and spread are appropriate for him to use to summarize the data from each team. mean mean interquartile range interquartile range standard deviation standard deviation median median
Answer:
a.) For the Junior Varsity Team, mean would be the appropriate measure of center since the data is symmetric or well-proportioned while we should use standard deviation for getting the measure of spread since it also measures the center and how far the values are from the mean.
b.) For the Varsity Team, the median would be the appropriate measure of the center since the data is skewed left and not evenly distributed so median could be used since it does not account for outliers while we use IQR or interquartile range in measuring the spread of data since IQR does not account for the data that is skewed.
For the Junior Varsity Team, the mean would be the appropriate measure of the center since the data is symmetric or well-proportioned .
What is median?Median represents the middle value of the given data when arranged in a particular order.
Since the data for the Junior Varsity Team is symmetric or well-proportioned, the mean would be the best way to determine the center, and standard deviation, which also measures the center and how far the values deviate from the mean, should be used to determine the spread.
The median could be utilized for the Varsity Team since the data is not evenly distributed and skewed to the left, and it does not take into account outliers.
We can use the interquartile range (IQR) to quantify the spread of the data because IQR does not take into account the skewed data.
Therefore, the varsity squad competes in intercollegiate or international competitions on behalf of the high school or institution while we should use standard deviation for getting the measure of spread since it also measures the center and how far the values are from the mean.
Learn more about the Varsity team here
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[tex] \frac{5 + n}{4} = - 1[/tex]
What is n?
Answer:
n= -9
Step-by-step explanation:
Answer:
-9
Step-by-step explanation:
5 + n
==== = -1
4
Multiply both sides by 4
5 + n = - 1 * 4
5 + n = - 4
Subtract 5 from both sides
5-5 + n = - 4 - 5
n = - 9
Congratulations on being able to use latex.
Find the value of x.
76
Solve for x in the equation x squared + 11 x + StartFraction 121 Over 4 EndFraction = StartFraction 125 Over 4 EndFraction.
Answer:
Below
Step-by-step explanation:
● x^2 + 11x + 121/4 = 125/4
Substract 125/4 from both sides:
● x^2 + 11x + 121/4-125/4= 125/4 -125/4
● x^2 + 11x - (-4/4) = 0
● x^2 +11x -(-1) = 0
● x^2 + 11 x + 1 = 0
This is a quadratic equation so we will use the determinanant (b^2-4ac)
● a = 1
● b = 11
● c = 1
● b^2-4ac = 11^2-4*1*1 = 117
So this equation has two solutions:
● x = (-b -/+ √(b^2-4ac) ) / 2a
● x = (-11 -/+ √(117) ) / 2
● x = (-11 -/+ 3√(13))/ 2
● x = -0.91 or x = -10.9
Round to the nearest unit
● x = -1 or x = -11
The solutions are { -1,-11}
The solution of the equation x² + 11x + (121/4) = 125/4 will be 0.09 and negative 11.09.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
The equation is given below.
x² + 11x + (121/4) = 125/4
Simplify the equation, then the equation will be
4x² + 44x + 121 = 125
4x² + 44x + 121 - 125 = 0
4x² + 44x - 4 = 0
x² + 11x - 1 = 0
We know that the formula, then we have
[tex]\rm x = \dfrac{-b \pm \sqrt {b^2 - 4ac}}{2a}[/tex]
The value of a = 1, b = 11, and c = -1. Then we have
[tex]\rm x = \dfrac{-11 \pm \sqrt {11^2 - 4 \times 1 \times (-1)}}{2 \times 1}\\\rm x = \dfrac{-11 \pm \sqrt {121 +4}}{2 }\\x = \dfrac{-11 \pm \sqrt {125}}{2 }[/tex]
Simplify the equation, then we have
x = (- 11 ± 11.18) / 2
x = (-11 - 11.18) / 2, (-11 + 11.18) / 2
x = -11.09, 0.09
The solution of the equation will be 0.09 and negative 11.09.
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slope of (-2,2) and (3,4)
Answer:
2/5
Step-by-step explanation:
Good luck!
What the correct answer now
Answer:
1001.66 in²
Step-by-step explanation:
The following data were obtained from the question:
Pi (π) = 3.14
Slant height (l) = 18 in
Diameter (d) = 22 in
Surface Area (SA) =.?
Next, we shall determine the radius of the cone. This can be obtained as follow:
Diameter (d) = 22 in
Radius (r) =.?
Radius = diameter /2
Radius = 22/2
Radius (r) = 11 in.
Finally, we determined the surface area of the cone as follow:
Pi (π) = 3.14
Slant height (l) = 18 in
Radius (r) = 11 in.
Surface Area (SA) =.?
SA = πr² + πrl
SA = (3.14 × 11²)+ (3.14 × 11 × 18)
SA = (3.14 × 121) + 621.72
SA = 379.94 + 621.72
SA = 1001.66 in²
Therefore, the surface area of the cone is 1001.66 in²
Rick is driving to his uncle's house in Greensville, which is 120 miles from Rick's town. After covering x miles, Rick sees a sign stating that Greensville is 20 miles away. Which equation, when solved, will give the value of x?
Answer:
The equation which will give the value of x when solved is C. x + 20 = 120
x=100
Step-by-step explanation:
Total distance=120 miles
Distance covered=x miles
Distance remaining=20 miles
The equation is
Total distance=Distance covered + distance remaining
120 miles= x miles + 20 miles
120 miles - 20 miles = x miles
100 miles =x miles
Check:
Total distance=Distance covered + distance remaining
120 miles = 100 miles + 20 miles
120 miles =120 miles
The equation which will give the value of x when solved is C. x+20=120
Please answer this question now
Answer:
m∠C = 102°
Step-by-step explanation:
The above diagram is a cyclic quadrilateral
Step 1
First we find m∠B
The sum of opposite angles in a cyclic quadrilateral is equal to 180°
m∠D + m∠B = 180°
m∠B = 180° - m∠D
m∠B = 180° - 80°
m∠B = 100°
Step 2
Since we have found m∠B
We can proceed to find the Angle outside to circle
m∠CDA = 2 × m∠B
m∠CDA = 2 × 100°
m∠CDA = 200°
m∠CDA = m∠CD + m∠DA
m∠DA = m∠CDA - m∠CD
m∠DA = 200° - 116°
m∠DA = 84°
Step 3
Find m∠DAB
m∠DAB = m∠DA + m∠AB
m∠DAB = 84° + 120°
m∠DAB = 204°
Step 4
Find m∠C
It you look at the cyclic quadrilateral properly,
m∠DAB is Opposite m∠C
Hence
m∠C = 1/2 × m∠DAB
m∠C = 1/2 × 204
m∠C = 102°
Therefore ,m∠C = 102°
Tammy got a new credit card with an APR of 21% a month ago, and she just
got her first credit card statement. She charged a bracelet for $17, a purse for
$36, and some sunglasses for $11. If her credit card charges interest on the
previous monthly balance, how much should Tammy pay now so that she
doesn't have any interest charged to her on next month's statement?
Answer:
$64
Step-by-step explanation:
She should pay the entire amount which is $17 + $36 + $11 = $64
Answer:
64
Step-by-step explanation:
yezzir
Can u guys answer my question 13 and 14 pls
Answer:
√2=1.414
then :√8 +2√32 +3√128+4√50
√8=√2³ =2√2
2√32=√2^5 = 4*2√2 = 8√2
3√128 = 3√2^6*2=8*3√2 =24√2
4√50 =4√5²*2= 20√2
add results : 2√2+8√2 +24√2+20√2=54√2
54√2=54×1.414=76.356 ( it is not in the options)x=7-4√3
√x+ 1/√x
√(7-4√3) +1/√(7-4√3) =
(8-4√3)/√(7-4√3)
(8-6.93)/√(7-6.93) = 4 ( after rounded to the nearest whole number)
4 is your answer
El Pirata Barba Plata ha llegado a la isla del Coral para buscar un tesoro. En el mapa pone que, desde la orilla, debe recorrer 37 hm a la pata coja hacia el centro de la isla, y después otros 85 dam dando volteretas en la misma dirección. ¿Cuántos metros recorrerá en total desde la orilla hasta el tesoro? Expresa el resultado también en kilómetros.
Answer:
4550m ; 4
Step-by-step explanation:
Recall
1 hectometre = 100m
1 decameter = 10m
Distance from shore to center of island = 37hm
Another 85 decameter toward stge se direction
Therefore total metres it will travel in other to get to the treasure :
37 hectometre + 85 decameter
(37 * 100)m + (85 * 10)m
3700m + 850m = 4550m
In kilometers :
1000 meters = 1 kilometers
4550 meters =
(4550 / 1000)meters
= 4.55km
How many faces does a dodecahedron have?
Answer:
A dodecahedron has 12 faces
Answer:
Answer is
Step-by-step explanation:
A dodecahedron has 12 faces.
Hope this helps....
Have a nice day!!!!
ochieng had sh 250 as pocket money at the begining of the term.in the middle of the term he was left with 2 over five of this amount .how much did she spend
Answer:
625
Step-by-step explanation:
250 × X = 2
X = 5
250 × 5 = 2
1250 = 2 after this step u divided it by 2
1250 ÷ 2
= 625
What is the 8th term of the sequence? −16, 24, −36, 54, ... −729/8 2187/8 −2187/8 729/8
Answer:
The answer is
[tex] \frac{2187}{8} [/tex]Step-by-step explanation:
The sequence above is a geometric sequence
For an nth term in a geometric sequence
[tex]A(n) = a ({r})^{n - 1} [/tex]
where n is the number of terms
r is the common ratio
a is the first term
From the question
a = - 16
To find the common ratio divide the previous term by the next term
That's
r = 24/-16 = -3/2 or -36/24 = - 3/2
Since we are finding the 8th term
n = 8
Substitute the values into the above formula
That's
[tex]A(8) = - 16 ({ - \frac{3}{2} })^{8 - 1} [/tex][tex]A(8) = - 16 ({ - \frac{3}{2} })^{7} [/tex][tex]A(8) = - 16( - \frac{2187}{128} )[/tex]We have the final answer as
[tex]A(8) = \frac{2187}{8} [/tex]Hope this helps you
Please answer quick Find the standard form of the equation of the parabola with a focus at (-2, 0) and a directrix at x = 2. (5 points) y^2 = 4x 8y = x^2 x = 1 divided by 8 y^2 y = 1 divided by 8 x^2
Answer:
Step-by-step explanation:
If you plot the focus and the directrix on a coordinate plane, because the parabola wraps itself around the focus away from the directrix, we know that this parabola opens to the left. That means its general form is
[tex]4p(x-h)=-(y-k)^2[/tex] where h and k are the coordinates of the vertex and p is the distance between the vertex and either the focus or the directrix because both distances are the same. Knowing that both distances are the same, it logically follows that the vertex is directly in between the focus and the directrix. So the vertex is at the origin, (0, 0). p is 2 because the vertex is at an x value of 0 and the directrix is at the x value of 2, and because the focus is at an x value of -2. Filling in the equation, then:
[tex]4(2)(x-0)=-(y-0)^2[/tex] which simplifies to
[tex]8x=-y^2[/tex] and, solving for x:
[tex]x=-\frac{1}{8}y^2[/tex]
factor the polynomial by it's greatest common monomial factor 6x^3+8x^2-4x Help asap please
Answer:
Step-by-step explanation:
Hello,
First term is 2 * 3 * x * x * x
Second term is 2 * 2 * 2 * x * x
Last term is 2 * 2 * x
So we can factorise it as below.
[tex]\boxed{6x^3+8x^2-4x=2x(3x^2+4x-2)}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
The factor should be [tex]2x ( 3x^2 +4x -2 )[/tex]
Given that,
The equation is [tex] 6x^3+8x^2-4x[/tex]Based on the above information, the calculation is as follows:
[tex] 6x^3+8x^2-4x[/tex]
[tex]2x ( 3x^2 +4x -2 )[/tex]
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what is the square root of 450
Answer:
[tex]15\sqrt{2}[/tex] or 21.2132
Step-by-step explanation:
[tex]\sqrt{450}[/tex]
[tex]\sqrt{15^{2} }[/tex] (root of a product is equal to the product of the roots of each factor)
[tex]\sqrt{15^{2} } \sqrt{2}[/tex] (simplify)
[tex]15\sqrt{2}[/tex] or ≈ 21.2132
Answer:
[tex]15\sqrt{2}[/tex] or 21.213
Step-by-step explanation:
For radical form: think of multiples of 450. Think of a pair that contains one perfect square, particularly the higher, the better . These 2 numbers are 25 and 18. 25 is the perfect square number since the two numbers that multiply to be 25 is 5 and 5.
Now take the perfect square of 25 and put it outside of the radical. The 18 remains inside: [tex]5\sqrt{18}[/tex]
Now, since 18 is a high number that needs to get reduced, do the same for 18 as we did for 450--find two numbers, one of which is a perfect square. These two numbers are 9 and 2.
Now take the perfect square of 9. This is 3. Take it out of the radical so that only the two remains inside. The 3 will now multiply with the 5: [tex]5*3\sqrt{2}[/tex]
Multiply 5 and 3 to get 15. The 15 stays outside the radical. Your answer is:
[tex]15\sqrt{2}[/tex]
Complete the conditional statement. If 2 > -a, then _____.
Well, in this case we can take a as the protagonist.
We can, for example, take the a in the first member of the disequation, the 2 in the second one, changing the signs
so
+ 2 > - a
a > - 2
In fact,
"If 2 > - a, then a > -2."
I need help with this please :(
Answer:
4¹⁸
Step-by-step explanation:
(4⁻³)⁻⁶
= 4⁽⁻³⁾⁽⁻⁶⁾
= 4¹⁸
Answer:
[tex]\large \boxed{4^{18}}[/tex]
Step-by-step explanation:
When a base with an exponent has an whole exponent outside the parenthesis, we multiply the exponents.
[tex](4^{-3})^{-6}[/tex]
[tex]4^{-3 \times -6}[/tex]
[tex]4^{18}[/tex]
find the perimeter of a square of length of 5cm
Answer:
20cm
Step-by-step explanation:
If each side of the square = 5 cm, 5 cm times 4 sides = 20 cm.
Answer:
P=20cm
Step-by-step explanation:
To find the perimeter of a square, you just add all the four sides.
Because it says the sides are 5cm, and squares always have the same length, you just:
5+5+5+6=20cm
So, the perimeter of this square is 20cm.
Hope this helps, and have a nice day:)
I don’t understand how to solve this. Please help!
Answer:
GH = 16; CH = 12
Step-by-step explanation:
First of all, you need to understand the meaning of "perpendicular bisector." It means that GH is divided into two equal parts by line AC, and that AC makes a right angle to GH.
The right angle is marked.
(a) The length of one of the halves of GH is marked as being 8 units long, so the other half will also be 8 units long. Of course, the length of GH is the sum of its two halves:
GH = GB +BH = 8 + 8
GH = 16
__
(b) Triangles CBG and CBH share side CB, so have that length in common. They have equal lengths BG and BH because BC bisects GH. They have a right-angle at B in common, so can be considered congruent by SAS, the fact that two congruent sides have a congruent angle between them.
Since triangles CBG and CBH are congruent, their corresponding sides CG and CH are also congruent. Side CG is marked 12 units long, so CH will be 12 units long, also.
CH = 12
You could shortcut all of the congruent triangle logic by recognizing that an altitude (CB) is a perpendicular bisector of the base (GH) if and only if the triangle is isosceles. The sides of an isosceles triangle are always congruent, so CG = CH = 12.
__
In part (c), you're supposed to choose possible theorems for demonstrating the congruence of the triangles we described above.
What characteristics do similar triangles share? a They have the same sides and angles. b They have the same sides but different angles. c They have the same ratios for the sides. d They are the exact same.
Answer:
b. they have the same sides but different angles
Step-by-step explanation:
this answer makes the most sense
Answer:
C they have the same ratios for the sides
Step-by-step explanation:
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion. In other words, similar triangles are the same shape, but not necessarily the same size. The triangles are congruent if, in addition to this, their corresponding sides are of equal length.