The given equation rearranged so that the variable q is the independent variable is 12r + 4r = 3q + 7q OR 16r = 10q
Rearranging equationsFrom the question, we are to rearrange the given equation so that the variable q is the independent variable
From the given information,
The give equation is
−7q + 12r = 3q − 4r
Add 7q to both sides of the equation
−7q + 7q + 12r = 3q + 7q − 4r
12r = 3q + 7q − 4r
Add 4r to both sides of the equation
12r + 4r = 3q + 7q − 4r + 4r
12r + 4r = 3q + 7q
Simplifying
16r = 10q
The equation rearranged is 12r + 4r = 3q + 7q OR 16r = 10q
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How long will it take the highway crew to pave 1 mile?
Answer:
Eight workers can pave a 1-mile stretch of road in 6 hours.
Step-by-step explanation:
a researcher plans to use a random sample of families to estimate the mean monthly family income for a large population. the researcher is deciding between a 95% confidence level and a 99% confidence level. compared to a 95% confidence interval, a 99% confidence interval will be...
Compared to a 95% confidence interval, a 99% confidence interval will be wider.
A confidence interval is a range of values that is likely to contain the true population mean, with a certain level of confidence.
The level of confidence is usually represented as a percentage, such as 95% or 99%. The higher the level of confidence, the wider the confidence interval will be. This is because a higher level of confidence means that the researcher wants to be more certain that the true population mean falls within the interval, so they will make the interval wider to increase the chances of this happening.
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What is the measure of angle x?
Answer:
[tex]67^{\circ}[/tex]
Step-by-step explanation:
Angles that form a linear pair add to [tex]180^{\circ}[/tex].
Answer:
Step-by-step explanation:
Since angles x and 113° all lie on a straight line,
x + 113° = 180° (angles on a straight line add up to 180°)
therefore, x = 180°-113°
x = 67°
turner made spiced apple cider for a holiday party and divide it evenly among 12 mugs. each mug had more than 10 fluid ounces of apple cider. let x represent how much apple cider turner made. which inequality describes the problem?
x/12 > 10 is the inequality that describes the problem. This inequality represents the fact that Turner made more than 10 fluid ounces of apple cider, and that he divided that amount evenly among 12 mugs.
Algebra is a discipline of mathematics where abstract symbols rather than concrete numbers are subjected to arithmetic operations and formal transformations. The idea that there is such a separate branch of mathematics, as well as the term algebra to identify it, came about gradually through time. This article traces the development of the equation notion, number systems, symbols for representing and modifying mathematical claims, and the contemporary abstract structural perspective of algebra.
The order in which you perform operations in arithmetic and algebra is governed by a number of laws. The Commutative, Associative, and Distributive Laws are the three that receive the most attention.
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Please answer all of these. Thank you :)
Answer:
a.x²+4x+4
=x²+2x+2x+4
=X(X+2)+2(X+2)
=(X+2)(X+2)
=(X+2)²
b.x²-12x+27
=x²-9x-3x+27
=X(x-9)-3(x-9)
=(x-9)(x-3)
c.x²-x-42
=x²-7x+6x-42
=X(x-7)+6(x-7)
=(X+6)(x-7)
d.x²+8x-9
=x²+9x-x-9
=X(X+9)-1(X+9)
=(x-1)(X+9)
*Mark me brainliest*_*
can someone answer this q for my mock rev xx
Answer:
Step-by-step explanation:
(a) 10p = 3p - 5
7p = - 5
p = -5/7
(b) a^0 = 1 no matter what a is.
(c) 0.5 y²/x
(d) 5cd²(2c² + 3d²)
solving for a variable:
isolate so that the desired variable is alone on one side of the equationperform inverse operationsa)
[tex]10p=3p-5[/tex]
[tex]7p=-5[/tex]
[tex]p=\frac{-5}{7}[/tex]
b) A simple rule to follow is that any number raised to the exponent of 0 is equal to 1
[tex]a^0=1[/tex]
c)
cancel out common factorswhen multiplying exponents with the same base add the exponentswhen dividing exponents with the same base subtract the exponents[tex]\frac{xy^3}{2x^2y}[/tex] cancelled out the common factor of 3
[tex]\frac{y^2}{2x}[/tex] note that [tex]a^-^y=\frac{1}{a^y}[/tex]
d)
find what is in common between the two terms both have a CF of 5cd^2[tex]5cd^2(2c^2+3d^2)[/tex]
HELP ASAP! 30 POINTS!
What is the equation for the line in slope-intercept form?
A regular octagon $ABCDEFGH$ has an area of one square unit. What is the area of the rectangle $ABEF$
The area of the rectangle ABEF = 2sa = 2ss/(2*tan(180/8)) = s^2/(tan(180/8)).
What is an octagon?
An octagon is a polygon with eight straight sides and eight angles. It is a closed two-dimensional shape with eight sides of equal length. A regular octagon is an octagon in which all sides and angles are equal.
When it comes to the area of a regular octagon, the area of a regular polygon can be calculated using the formula
A = (ns^2)/(4tan(180/n)) where A is the area, n is the number of sides and s is the length of each side.
In case of a regular octagon, the area of an octagon is (8s^2)/(4tan(180/8))
A rectangle ABEF is made up of two congruent sides with the length of the side of the octagon, and two congruent sides with the length of the apothem of the octagon.
An apothem of a regular polygon is the distance from the center of the polygon to the midpoint of any side. The apothem of a regular octagon can be calculated by using the formula
a = s/(2*tan(180/8)) where a is the apothem and s is the side of the octagon.
Hence, the area of the rectangle ABEF = 2sa = 2ss/(2*tan(180/8)) = s^2/(tan(180/8)).
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Subtract 9x+2 from 2x−7
Answer:
(2x-7)(9x+2)
Step-by-step explanation:
Find The Least Common Multiplier of 9x+2, 2x-7
Help me please thx sm
Answer:
yes to all 3
Step-by-step explanation:
A
3z = 21 ( isolate z by dividing both sides by 3 )
z = 7
B
n + 14 = 36 ( subtract 14 from both sides )
n = 22
C
[tex]\frac{3}{4}[/tex] v = 12 ( multiply both sides by 4 to clear the fraction )
3v = 48 ( divide both sides by 3 )
v = 16
Suppose $a$ and $b$ are positive integers such that $\gcd(a,b)$ is divisible by exactly $7$ distinct primes and $\mathop{\text{lcm}}[a,b]$ is divisible by exactly $28$ distinct primes. If $a$ has fewer distinct prime factors than $b$, then $a$ has at most how many distinct prime factors
The number of distinct prime factors are 17
The term prime factors in math is defined as a method to find the prime factors of a given number and it can be said a composite number.
As per the definition of prime factor here we have know that a and b have 7 prime factors in common.
Then it can be written as a*b has 28 prime factors
And here we also know that the number of prime factors of a or b that are not common to both is 21
Here we have also know that a has less prime factors than b so at most 10 of these 21 extra prime factors belong to a
Then the the most prime factors that a can have is calculated as
=> 7 + 10 = 17
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An Isosceles triangle and a square have the same perimeter. Find the side lengths of the triangle.
triangle base: 3x
triangle height: 2x+1
square length: 4
Answer: 5, 5, 6
How you get this answer?
Answer:
In isosceles triangle two sides are equal,
So,
3x-1=2x+2
x=3
Perimeter=sum of all sides
=3x-1+2x+2+2x
=7x+1
Substituting value of x
Perimeter=7(3)+1
=21+1
=22
Thus x=3
:. Perimeter of a triangle=22 square units
Forgotten completely how to do this
Would love an explanation too
Answer:
Step-by-step explanation:
s the orthocenter for an obtuse traingle always outside the circumcircle which the obtuse triangle is drawn in?
The orthocenter for an obtuse triangle is always outside the circumcircle in which the obtuse triangle is drawn.
What is the Orthocenter Of A Triangle?In geometry, each triangle has a few highly significant points that go along with it. One such point is the triangle's orthocenter, which is identified as the location where the triangle's altitudes cross.
An altitude of a triangle is a line segment that extends perpendicularly from one of its vertices to the side opposite that vertex. A triangle with an angle larger than 90° is said to have an obtuse angle. The heights of the vertices of the acute angles of an obtuse triangle reside outside of the triangle due to the way the triangle is constructed. The orthocenter, or the location where the three elevations intersect, must therefore be outside of the circumcircle in which the triangle is inscribed.To learn more about Orthocenter visit:
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The orthocenter for an obtuse triangle is always outside the circumcircle in which the obtuse triangle is drawn.
What is the Orthocenter of a triangle?In geometry, each triangle has a few highly significant points that go along with it. One such point is the triangle's orthocenter, which is identified as the location where the triangle's altitudes cross.
An altitude of a triangle is a line segment that extends perpendicularly from one of its vertices to the side opposite that vertex. A triangle with an angle larger than 90° is said to have an obtuse angle. The heights of the vertices of the acute angles of an obtuse triangle reside outside of the triangle due to the way the triangle is constructed.
The orthocenter, or the location where the three elevations intersect, must therefore be outside of the circumcircle in which the triangle is inscribed.
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The complete question is as follows:
Is the orthocenter for an obtuse triangle always outside the circumcircle which the obtuse triangle is drawn in?
An arcade sells game cards that customers can use to play the arcade games. A game card
comes stocked with credits, and each game costs 5 credits to play. Shivani was able to play
16 games before her card ran out of credits.
Graph the function that models the relationship between the number of games Shivani
played, n, and the number of credits remaining on her card, C(n).
Select points on the graph to plot them.
Answer: The function that models the relationship between the number of games played (n) and the number of credits remaining on the card (C(n)) is C(n) = 5n.
Step-by-step explanation: This function can be derived by realizing that each game costs 5 credits to play, so as the number of games played (n) increases, the number of credits remaining on the card (C(n)) decreases by 5 for each game played.
For example, if Shivani played 16 games before her card ran out of credits, we can substitute n = 16 into the function to find that C(16) = 5(16) = 80 credits. This means that her card had 80 credits on it before she started playing games.
To plot points on the graph, we can select a few different values of n and substitute them into the function to find the corresponding values of C(n). Here are a few examples:
When n = 0, C(n) = 5(0) = 0. This represents the case when Shivani has not played any games yet and has no remaining credits on her card.
When n = 8, C(n) = 5(8) = 40. This represents the case when Shivani has played 8 games and has 40 credits remaining on her card.
When n = 16, C(n) = 5(16) = 80. This represents the case when Shivani has played 16 games and her card has no remaining credits.
We can plot these points on the graph and label them (0,0), (8,40), (16,0) respectively.
Note that the y-intercept is (0,0) and the x-intercept is (16,0)
Graph:
n C(n)
0 0
8 40
16 0
The graph is a straight line starting from (0,0) and going down till (16,0) with a slope of -5.
(2a−13)÷b15 when a=−35 and b=−6.75
Please and Thank You! :)
Answer:
-.56296296296...
Step-by-step explanation:
[tex]\frac{(2)(-35)-13}{(-6.75)(15)}[/tex]
[tex]\frac{70-13}{-101.25}[/tex]
[tex]\frac{57}{-101.25}[/tex]
-.56296296296... The 296 is repeating
Directions: Use the Law of Sines to find each missing side or angle. Round to the nearest tenth.
Question 5
The remaining interior angle is [tex]135^{\circ}[/tex].
[tex]\frac{x}{\sin 19^{\circ}}=\frac{32}{\sin 135^{\circ}}\\ \\ x=\frac{32 \sin 19^{\circ}}{\sin 135^{\circ}} \\ \\ x \approx 14.7[/tex]
Question 6
The remaining interior angle is [tex]27^{\circ}[/tex].
[tex]\frac{x}{\sin 27^{\circ}}=\frac{28}{\sin 75^{\circ}}\\\\x=\frac{28\sin 27^{\circ}}{\sin 75^{\circ}}\\\\x \approx 13.2[/tex]
Question 7
The remaining interior angle is [tex]59^{\circ}[/tex].
[tex]\frac{x}{\sin 59^{\circ}}=\frac{9}{\sin 70^{\circ}}\\\\x=\frac{9\sin 59^{\circ}}{\sin 70^{\circ}}\\\\x \approx 8.2[/tex]
Question 8
The remaining interior angle is [tex]95^{\circ}[/tex].
[tex]\frac{x}{\sin 33^{\circ}}=\frac{16}{\sin 95^{\circ}}\\\\x=\frac{16 \sin 33^{\circ}}{\sin 95^{\circ}}\\\\x \approx 8.7[/tex]
For the data set shown, find the median, the 1st quartile, and the 3rd quartile. Drag the correct values into the table.
The median and the quartiles of the data-set are given as follows:
First quartile: 13.Median: 22.Third quartile: 29.How to obtain the median and the quartiles of the data-set?The median of a data-set is the middle value of the data-set, that is, the value of which 50% of the data-set is less than and 50% of the data-set is greater than.
The data-set is composed by 16 elements, which is an even cardinality, hence the median is the mean of the 8th and of the 9th elements, as follows:
Median = (20 + 24)/2
Median = 22.
Then the first quartile is the median of the first seven elements of the data-set, which is the fourth element, hence it is of 13.
The third quartile is the median of the last seven elements of the data-set, hence it assumes a value of 29.
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Answer: first quartile is 14 , the median is 22 , and the third quartile is 28
Step-by-step explanation:because I answered that on my homework and it worked.Take words from people who have tried it before!!!
One day eleven babies are born at a hospital. assuming each baby has an equal chance of being boy or girl, what is the probability that exactly eight of the eleven babies are girls?
The probability of getting exactly 8 girls out of 11 births is 21.9%.
The binomial probability formula is used to calculate the probability of getting a certain number of successes (in this case, girls) out of a fixed number of trials (in this case, 11 births).
The first part of the formula (11 choose 8) is the number of ways to choose 8 girls out of 11 births, which is 330.
i.e; (11 choose 8) * (0.5)^8 * (0.5)^3 = 330
The second part of the formula (0.5)^8 represents the probability of getting 8 girls out of 11 births assuming each birth has a probability of 0.5 of being a girl.
The third part of the formula (0.5)^3 represents the probability of getting 3 boys out of 11 births assuming each birth has a probability of 0.5 of being a boy.
i.e; (11 choose 8) * (0.5)^8 * (0.5)^3 = 330 * 0.00390625 * 0.125 = 0.21875
When we multiply all of these values together we get the final probability of getting exactly 8 girls out of 11 births, which is approximately 0.21875 or about 21.9%.
Therefore, the probability of getting exactly 8 girls out of 11 births is given by the binomial probability formula: (11 choose 8) * (0.5)^8 * (0.5)^3 = 330 * 0.00390625 * 0.125 = 0.21875 or about 21.9%.
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Can someone please solve this
Answer:
Step-by-step explanation:
Let, f(x) = y
y = 5 + √(5x - 3)
((y - 5)² = 5x + 3
y² - 10y + 25 - 3 = 5x
x = (y² - 10y +22)/5
so, [tex]f^{-1} (y)[/tex] = (y² - 10y +22)/5
[tex]f^{-1} x[/tex] = (x² - 10x + 22)/5
A survey of 481 of your customers shows that 79% of them like the recent changes to the product. Is this percentage a parameter or a statistic and why?Statistic as it represents the populationParameter as it represents the populationParameter as it represents the sampleStatistic as it represents the sample
In this case, the proportion (79%) only applies to the sample of 481 consumers and thus it is a statistic because it represents the sample.
The distinction between a parameter and a statistic is that a parameter refers to a sample property, but a statistic is referred to as a population distribution characteristic.
For instance, a population mean is a parameter, but a sample mean is a statistic.
Although we can use it to draw conclusions about the population, in this case, the proportion (79%) only applies to the sample of 481 consumers and is thus only a statistic.
Therefore, This percentage is a statistic because it represents the sample.
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Help me pleaseeeeeeeeeee
The absolute value graph shifted to the right 5 units is
A |x - 5|What is transformation?Transformation is a term used in mathematics to refer to the movements made by objects.
Translation refers to a type of transformation that involve a linear movement.
Translation has to do with the following movements
leftrightupdownThe up and down movements are on the vertical direction controlled by the y coordinate.
While the left and right movements are on the horizontal direction controlled by the x coordinate.
The movement represented by the absolute value equation |x - 5| is is translation 5 units right
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|
Evaluate.
[2−∣∣−14−2(−35)∣∣]÷(−6)
What is the value of the expression?
Enter your answer as a simplified fraction in the box.
GIVING 100
Answer:
The solution of the mathematical expressions will be 0.175.
Step-by-step explanation:
Given that;
The mathematical expressions are,
⇒ [ 2 - | - 1/4 - 2 (-3/5) | ] ÷ -6
Now,
Solve the mathematical expression as;
⇒ [ 2 - | - 1/4 - 2 (-3/5) | ] ÷ -6
Using the BODMAS rule to solve the expressions as;
⇒ [ 2 - | - 1/4 - 2 (-3/5) | ] ÷ -6
⇒ [ 2 - | - 1/4 + 6/5 | ÷ -6
⇒ [ 2 - 19/20 ] ÷ -6
⇒ [ 21/20] ÷ -6
⇒ 21/20 x 1/-6
⇒ - 7 / 40
Therefore,
The solution of the mathematical expressions will be 0.175.
But you didn't have to cut me off
Make out like it never happened and that we were nothing (aah-ooh)
And I don't even need your love (ooh)
But you treat me like a stranger, and that feels so rough (aah)
No, you didn't have to stoop so low (ooh)
Have your friends collect your records and then change your number (aah)
I guess that I don't need that, though
Now you're just somebody that I used to know
Answer:
[tex]-\dfrac{7}{40}[/tex]
Step-by-step explanation:
Given expression:
[tex]\left[2-\left|-\dfrac{1}{4}-2\left(-\dfrac{3}{5}\right)\right|\right] \div (-6)[/tex]
Carry out the operations inside the absolute value bars (following the order of operations):
[tex]\implies \left[2-\left|-\dfrac{1}{4}+\dfrac{6}{5}\right|\right] \div (-6)[/tex]
[tex]\implies \left[2-\left|\dfrac{19}{20}\right|\right] \div (-6)[/tex]
As the fraction inside the absolute value bars is already positive, we can simply remove the bars:
[tex]\implies \left[2-\dfrac{19}{20}\right] \div (-6)[/tex]
Rewrite 2 as 40/20 and carry out the subtraction inside the square brackets:
[tex]\implies \left[\dfrac{40}{20}-\dfrac{19}{20}\right] \div (-6)[/tex]
[tex]\implies \left[\dfrac{40-19}{20}\right] \div (-6)[/tex]
[tex]\implies \left[\dfrac{21}{20}\right] \div (-6)[/tex]
Rewrite -6 as a fraction:
[tex]\implies \dfrac{21}{20} \div -\dfrac{6}{1}[/tex]
When dividing fractions, multiply the first fraction by the reciprocal of the second fraction:
[tex]\implies \dfrac{21}{20} \times-\dfrac{1}{6}[/tex]
[tex]\implies \dfrac{21 \times (-1)}{20 \times 6}[/tex]
[tex]\implies -\dfrac{21}{120}[/tex]
Reduce the fraction to its simplest form by dividing the numerator and denominator by the highest common factor, 3:
[tex]\implies -\dfrac{21 \div 3}{120 \div 3}[/tex]
[tex]\implies -\dfrac{7}{40}[/tex]
Megan and Paula decided to shoot arrows at a simple target with a large outer ring and a
smaller bull's-eye. Megan went first and landed 3 arrows in the outer ring and 4 arrows in
the bull's-eye, for a total of 390 points. Paula went second and got 4 arrows in the outer
ring and 5 arrows in the bull's-eye, earning a total of 492 points. How many points is each
region of the target worth?
The number of points in a large outer ring and a smaller bull's-eye are 18 points and 84 points respectively.
How to write a system of equations to describe the situation?In order to write a system of equations that model this situation, we would assign variables to the large outer ring and the smaller bull's-eye respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the large outer ring.Let the variable y represent the smaller bull's-eye.Next, we would translate the word problem into algebraic equation as follows for both Megan and Paula:
3x + 4y = 390
4x + 5y = 492
In this scenario, we would use an online graphing calculator to plot and solve the above system of equations graphically, with a point of intersection at (18, 84) as shown in the image attached below.
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When Alan Sheperd hit the golf ball on the moon, it traveled in a projectile arc and
eventually sailed to the ground. If Alan was to do the same shot on earth, how would the golf
ball's height and distance compare to the shot on the moon?
more height and less distance
more height and more distance
O less height and less distance
less height and more distance
On Earth, the golf ball would travel much farther and higher than on the moon due to the difference in gravity. On the moon, the gravity is only 1/6th the strength of Earth's, making it much easier for the golf ball to travel farther and higher. On Earth, the golf ball would travel farther and higher due to the stronger gravitational pull.
You and your friends earn (14h+5c) dollars for washing h houses and c cars last month you washed 10 houses and your friend washed 28 cars who earned more money you,your friend, or neither
Step-by-step explanation:
first
for washing 10 houses we get (14*10) dollars which is 140
now for washing cars ur frirnd gets (28*5) which is also 140
so u both earn the same amount
hence the answer is neither.
Find the missing lengths of the sides.
a = 3 in., b = 3v2 in.
6 a = 3 in., b = 3v3 in
a = 3 in., b = 9 in
a = 3v3 in., b = 3 v3 in.
The missing lengths of the sides a = 3 inches , b = 3√3 inches .
90 -60 -30 triangle .
We have given 90 -60 -30 triangle with hypotenuses = 6 in.
By the 90 -60 -30 triangle rule : The hypotenuse is equal to twice the length of the shorter leg, which is the side across from the 30 degree angle and the length of the longer leg is 3√ times the length of the shorter leg.
Then Shorter leg = a longer leg = b.
Hypotenuse = 2 * Shorter leg .
Plug the values.
6 = 2 * Shorter leg .
On dividing both sides by 2
Shorter leg (a) = 3 inches .
Then by the rule : longer leg is 3√ times the length of the shorter leg.
Longer leg = 3√Shorter .
Longer leg (b) = 3√3 inches .
Therefore, a = 3 inches , b = 3√3 inches .
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find a unit vector normal to the surface cos(xy) = ez − 2 at (1, π, 0).
The given surface is [tex]\cos(xy) = e^z-2[/tex]. The unit vector normal to this surface at the point (1, π, 0) is[tex]\vec{n}=\langle 0, 0, 1\rangle[/tex].
A vector with a magnitude of one is termed a unit vector. To determine a unit normal vector for the given surface, start by describing the surface as a function of form F(x, y, z). Next, calculate this function's gradient and then normalize the outcomes.
Consider the normal vector [tex]\vec{n}=\langle a, b, c\rangle[/tex] to the plane ax + by + cz = d. Given [tex]\cos(xy) = e^z-2[/tex] then, z = ln(2+cos(xy)).
At point (x₀,y₀,z₀), the equation for the tangent plane to z = f(x,y) is written as, [tex]z-z_0 = f_x(x_0,y_0)(x-x_0) + f_y(x_0,y_0)(y-y_0)[/tex]. The value of [tex]f_x[/tex] and [tex]f_y[/tex] are
[tex]f_x = \frac{-y \sin(xy)}{(2+\cos(xy))}[/tex] and [tex]f_y =\frac{ -x \sin(xy) }{ (2+\cos(xy))}[/tex].
At *x, y) = (1, π), the value of [tex]f_x[/tex] and [tex]f_y[/tex] is zero. Then, the equation of the tangent plane is given as z-0=0+0 ⇒ z=0.
Then, the resulting unit normal vector is [tex]\vec{n}=\langle 0, 0, 1\rangle[/tex].
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(03.06 LC)
Which is the standard equation of the hyperbola centered at the origin, with a vertical transverse axis and values of a = 7 and b = 10?
On solving the the provided question we can say that - in the equation we have 12a - 3b = 84 - 30 = 54
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
here, we have
a = 7 and b = 10
so, 12a - 3b
84 - 30 = 54
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HELP ME ASAP ILL MARK BRAINLIEST!! HELP ME NOW!!!!!!
Answer:
P is equal to or greater than 27
(c)
Step-by-step explanation:
