Simplify 4 p + 3 q − 3 p − 3 q

The lengths of LV and OE are 15cm, and the lengths of LD and EV are 3√7 cm and 9/√7 cm, respectively.

Since LOVE is a kite, LV and OE are perpendicular bisectors of each other. Let the length of LD be x, and the length of EV be y. Then, we can use the Pythagorean theorem and the fact that the diagonals bisect each other to set up two equations:

x² + (LV/2)² = DV²/4

y² + (OE/2)² = LE²/4

Simplifying each equation and substituting the given values, we get:

x² + (LV/2)² = 81/4

y² + (OE/2)² = 225/4

We also know that the diagonals bisect each other, so we can set up another equation:

LV/2 + OE/2 = LO = VE

Substituting the given value for LE, we get:

LV/2 + OE/2 = 15

Solving this equation for one of the variables, we get:

LV = 30 - OE

Substituting this expression into the first equation above, we get:

x² + ((30 - OE)/2)² = 81/4

Simplifying and rearranging, we get:

OE² - 60OE + 675 = 0

Using the quadratic formula, we get:

OE = (60 ± √(3600 - 2700)) / 2

OE = 15 or 45

If OE = 15, then LV = 30 - 15 = 15, and we can solve for x and y:

x² + 7.5² = 81/4

y² + 7.5² = 225/4

Solving these equations, we get:

x = 3√7

y = 9/√7

If OE = 45, then LV = 30 - 45 = -15, which is impossible for a length. Therefore, the solution is:

LV = OE = 15

x = 3√7

y = 9/√7

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Complete question:

LOVE is a kite. LV and OE are diagonals. The segments DV = 9cm and LE = 15cm are given. Find the lengths of the other segments of the diagonals, DV, OE, and LV.

Answer: -6

Step-by-step explanation:

Let x= the number

2x-4=x-10 ⇔ according to the statement

  x-4=-10 ⇔ subtraction property of equality (subtract x from both sides)

     x=-6 ⇔ addition property of equality (add 4 on both sides)

Hope this helps!! :)

Please let me know if you have any question

Answer:

n = -6

Step-by-step explanation:

Alright so this can be solved by using variables. Let's say n = number.

4 subtracted from twice a number can be represented as 2n - 4.

10 less than the number can be represented as n - 10.

Since the outcome of the first expression is equal to the second, we can set them equal to each other to solve:

2n - 4 = n - 10.

Then you isolate n by adding 4 to both sides...

2n = n - 6,

... then subtracting n from both sides:

n = -6

There you go!

Answer:

315cm^3

Step-by-step explanation:

multiply 15cm×6cm×3.5cm=

315cm^3

There are 55 ways to form a train consisting of tank cars, boxcars, and flatcars by using concept of combinations.

If there are t tank cars, b boxcars, and f flatcars in the train yard, then the number of ways to form a train by selecting some of these cars is the same as the number of ways to distribute n = t + b + f identical objects into three distinct boxes, such that each box may receive any number of objects (including zero). The solution is given by the combination formula:

C(n + k - 1, k - 1)

where k is the number of boxes (in this case, k = 3). Therefore, the number of ways to form a train from t tank cars, b boxcars, and f flatcars is:

C(t + b + f + 3 - 1, 3 - 1) = C(t + b + f + 2, 2) = (t + b + f + 2)! / ((t + b + f)! * 2!)

There are 4 tank cars, 3 boxcars, and 2 flatcars in the train yard, then the number of ways to form a train is:

C(4 + 3 + 2 + 2, 2) = C(11, 2) = 55

Therefore, there are 55 ways to form a train consisting of tank cars, boxcars, and flatcars

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Answer:

Answer Expert Verified

Given; prove; statements; and reasons. Explanation: The given is important information we are given at the beginning of the proof that we will use in constructing the proof. The "prove" is the statement we are trying to prove

Answer:

Sample Response: Proofs contain given information and a statement to be proven. You use deductive reasoning to create an argument with justification of steps using theorems, postulates, and definitions. Then you arrive at a conclusion.

Step-by-step explanation:

Have the day you deserve :)

Answer:

5 marbles

Step-by-step explanation:

A bag contains

8 white marbles

6 red marbles

4 blue marbles.

Total number of marbles is :

8 + 6 + 4

= 18 marbles

Based on this current proportion

The Probability of choosing a blue marble = Number of blue marbles/ Total number of marbles

In order for the Probability of choosing a blue marble to be 1/2

The number of blue marbles has to be:

= 18 marbles × 1/2

= 9 blue marbles

From the question we have 4 blue marbles, hence:

9 blue marbles - 4 blue marbles

= 5 blue marbles

Therefore, 5 blue marbles must be added to the bag so that the probability of choosing a blue marble is 1/2.

Answer:

The actual answer would be 10 marbles.

Step-by-step explanation:

1. we had started off by adding 8+4+6 to get the total number of marbles. If we do that, we will get that there are 18 marbles in total.

2. here is where the others went wrong. If we say that we need 5 blue marbles to get 9/18 blue marbles, you are wrong. This is because we have to add 5 to the total number of marbles as well. Then we get 9/23 marbles. which is clearly not 1/2,

3. However, if we multiply 5 by 2, we get 10 blue marbles. if we add 10 to the original 18, we get 28 total marbles. Now if we add 10 to 4 we get 14 blue marbles.

SUCCESS!!!

14/28 blue marbles is 1/2, therefore we must add 10 blue marbles.

Answer:

Step-by-step explanation:

boody boody

Answer:

4th answer

Step-by-step explanation:

g(h(x)) means to put the formula for h(x) into the formula for g(  ).

\(g(h(x))=g(2x-2)=-3(2x-2)^3-2(2x-2)^2\\=-3(8x^3-24x^2+24x-8)-2(4x^2-8x+4)\\=-24x^3+72x^2-72x+24-8x^2+16x-8\\=-24x^3+64x^2-56x+16\)

Cubing the binomial 2x - 2 can take some time!

=======================================================

Reason:

The first marble was replaced, so the original state of the bag hasn't changed overall. The probability isn't changed either. We can treat the second selection entirely independent of the first one.

If the first marble wasn't replaced, then the marble count of course goes down by 1. That affects the probability of the second selection and we'd consider these events to be dependent.

---------

An example:

Consider a bag with 4 red marbles and 6 green ones. The chances of picking red on the first try are 4/10 = 2/5. The chances of picking red again would be 2/5 assuming we put that red marble back. We can see the second selection is independent of the first.

If the marble wasn't put back, then the chances of picking a 2nd red marble would be 3/9 = 1/3. I subtracted 1 from the numerator and denominator of 4/10 to get to 3/9. In this case, the 2nd selection's probability depends on the first event (whether red was picked or not).

Congruency is a type of equivalence relation that states that two geometric figures are the same size and shape. In other words, if two figures are congruent, then all of their corresponding parts are the same size and shape. Therefore, if ⊙a ≅ ⊙v, then it can be concluded that a is congruent to v, and the congruency statements that can be made are a ≅ v, a ≅ ⊙v, and ⊙a ≅ v.

A. a ≅ v

D. a ≅ ⊙v

E. ⊙a ≅ v

Since the symbol ⊙ represents congruency, ⊙a ≅ ⊙v implies that a is congruent to v. Therefore, the congruency statements that can be made are a ≅ v, a ≅ ⊙v, and ⊙a ≅ v.

Congruency is a type of equivalence relation that states that two geometric figures are the same size and shape. In other words, if two figures are congruent, then all of their corresponding parts are the same size and shape. Therefore, if ⊙a ≅ ⊙v, then it can be concluded that a is congruent to v, and the congruency statements that can be made are a ≅ v, a ≅ ⊙v, and ⊙a ≅ v.

The complete question is :

Given , ⊙a ≅ ⊙v, what congruency statements can you make? Check all that apply.

A. a ≅ v

B. a ~ v

C. ⊙a ~ ⊙v

D. a ≅ ⊙v

E. ⊙a ≅ v

The correct answers are: A. a ≅ v, D. a ≅ ⊙v, and E. ⊙a ≅ v.

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Upon simplifying the expressions on each side of an equation, I noticed that the coefficients of x and the constants on each side of the equal sign were zero.

When simplifying expressions in an equation, we aim to rearrange and combine like terms to simplify the equation. In this particular scenario, after performing the simplification, it became apparent that the coefficients of x, which represent the numerical factors multiplying x, were equal to zero on both sides of the equation. Similarly, the constants, which are the terms without variables, were also zero on both sides.

An equation where the coefficients of x and the constants are zero on each side is known as a trivial equation. In this case, the equation doesn't contain any variables or unknowns, as both sides reduce to zero. Consequently, the equation holds true for all values of x since any value substituted for x will result in zero on both sides of the equation, making it an identity.

Trivial equations are distinct from other types of equations because they don't involve any variable-dependent relationships or solutions. While they may not have any practical significance in most situations, they can arise in mathematical manipulations or as special cases in certain mathematical contexts. It is crucial to recognize and differentiate trivial equations from other types of equations to ensure accurate problem-solving and analysis.

To summarize, upon simplifying the expressions on each side of an equation, I observed that the coefficients of x and the constants were zero on both sides. This leads to a trivial equation, where the equation holds true for all values of x. Trivial equations lack variable-dependent relationships and have no practical significance in most cases, but they are important to recognize in mathematical contexts.

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Step-by-step explanation:

\( \because \angle JKM \) is the exterior angle of \( \triangle KLM \)

\( \therefore \) by remote interior angle theorem of a triangle, we have:

\( m\angle L + m\angle M = m\angle JKL \\\\

(18z + 3)\degree + (5z - 3)\degree = 161\degree \\\\

(18z + 3+5z - 3)\degree = 161\degree \\\\

(23z)\degree = 161\degree \\\\

23z = 161\\\\

z = \frac{161}{23} \\\\

\huge \red {\boxed {z = 7}} \\\\

\because \measuredangle L = (18z +3)\degree \\\\

\therefore \measuredangle L = (18\times 7+3)\degree \\\\

\therefore \measuredangle L = (126+3)\degree \\\\

\huge\purple {\boxed {\therefore \measuredangle L = 129\degree}} \\\\

\because \measuredangle M = (5z - 3)\degree \\\\

\therefore \measuredangle M= (5\times 7-3)\degree \\\\

\therefore \measuredangle M = (35-3)\degree \\\\

\huge\orange {\boxed {\therefore \measuredangle M = 32\degree}} \\\\\)

Step by step solution is above

Answer:

Is that 12

12+x+3

x = 12-3

x = 9

To determine the number of ways the little league manager can form a 9-player batting order from a team of 12 children, we can use the concept of permutations.

Since the order of the players in the batting order matters, we need to calculate the number of permutations of selecting 9 players from a pool of 12.

The formula to calculate permutations is:

P(n, r) = n! / (n - r)!

where:

In this case, we want to find P(12, 9), which represents the number of permutations of selecting 9 players from a pool of 12.

P(12, 9) = 12! / (12 - 9)!

= 12! / 3!

Calculating the factorials:

12! = 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

3! = 3 * 2 * 1

Simplifying the calculation:

P(12, 9) = (12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (3 * 2 * 1)

= 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4

= 199,584,000

Therefore, the little league manager can form a 9-player batting order in 199,584,000 different ways.

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Answer:

2.625

Step-by-step explanation:

258=2.625

Solution by Separating the Parts

258=2+58

We know that

58

is the same as

5÷8

Therefore:

258=2+(5÷8)

Then using

Long Division for 5 divided by 8

we have

=2+0.625=2.625

Rounded to a Max of 3 Decimal Places.

Solution by Converting to Improper Fraction

258=2+58

=21+58

=(21×88)+58

=168+58=218

We know that

218

is the same as

21÷8

Answer:

Your answer is D 2 and 82/100

If a significant result is yielded by a repeated-measures analysis of variance, post - hoc tests would be used to determine which levels of the independent variable significantly differ from each other.

What is the purpose of a post hoc test?

When an analysis of variance (ANOVA) F test indicates that there are significant differences between three or more group means, post hoc (Latin for "after this") tests are employed to identify the precise discrepancies.

When an experiment's findings show that the dependent variable has a substantial effect size You can infer it from this, right?

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Answer: 4, 4, 6, 7, 14

Step-by-step explanation:

There is only one possible way to do this because 6 has to be the median (middle value), 4 has to repeat twice as the lowest numbers, and the highest number has to be 14 to fit the range of 10. Because the mean is 7, the fourth number has to be 7 so that they all average to 7. There is no other way to do this.

Answer:

4,4,6,7,14

Step-by-step explanation:

median means middle number which is 6

mean means average. there are 5 numbers with a mean of 7 so all 5 numbers added up are 35

range is 10 which means the last number minus the first number is 10

mode is 4 means that the number 4 occurs more than once

so 4,4,6,

the last number must be 14

so 4,4,6,x,14

so 4+4+6+14 = 28. 35-28 = 7

so x is 7

so its 4,4,6,7,14

Tijani Gali quora

Answer: what does this say please help

Step-by-step explanation:

===================================================

Explanations:

Answer:

A, B, D

Step-by-step explanation:

Right on edge 22

a.....9.000%

b.....5575.28 cm³

c...... 17.446%.

a)Maximum error in the calculated surface area. The formula to calculate the surface area of a sphere is given by the equation; SA = 4πr²where r is the radius of the sphere. Differentiating this equation with respect to r, we get: dSA/dr = 8πr. The maximum error in the calculated surface area is given by: Maximum error = dSA/dr * maximum error in radius (Δr)Using the value of Δr = 0.5, we get: Maximum error = dSA/dr * Δr = 8πr * Δr. For the given value of the circumference, we can find the radius using the formula: C = 2πr88 = 2πr4r = 88/πr ≈ 11.122Maximum error = 8πr * Δr = 8π * 11.122 * 0.5 ≈ 139Maximum error in the calculated surface area ≈ 139 cm²Relative error. Relative error is given by the formula: Relative error = (Maximum error in the calculated quantity / Calculated quantity) * 100. For surface area: Calculated surface area = 4πr². Calculated surface area ≈ 1540.48 cm²Relative error = (139 / 1540.48) * 100Relative error ≈ 9.000%

b)Maximum error in the calculated volume. The formula to calculate the volume of a sphere is given by the equation: V = 4/3 * πr³Differentiating this equation with respect to r, we get: dV/dr = 4πr²The maximum error in the calculated volume is given by: Maximum error = dV/dr * maximum error in radius (Δr)Using the value of Δr = 0.5, we get: Maximum error = dV/dr * Δr = 4πr² * ΔrFor the given value of the circumference, we can find the radius using the formula: C = 2πr88 = 2πr4r = 88/πr ≈ 11.122Maximum error = 4πr² * Δr = 4π * 11.122² * 0.5 ≈ 973Maximum error in the calculated volume ≈ 973 cm³Relative error. For volume: Calculated volume = 4/3 * πr³Calculated volume ≈ 5575.28 cm³. Relative error = (Maximum error in the calculated quantity / Calculated quantity) * 100Relative error ≈ 17.446%Therefore, the maximum error in the calculated surface area ≈ 139 cm² and the relative error ≈ 9.000%. The maximum error in the calculated volume ≈ 973 cm³ and the relative error ≈ 17.446%.

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Happy Pride Month!

Answer:

320m

Step-by-step explanation:

let the two runners be A and B

with Va and Vb as their velocities

velocity=distance/time

Va=720/4*60

=3m/s

Vb=720/5*60

=2.4m/s

Let the 2 runners start from a common position X and meet at Y

so the 2 consecutive meetings happen at X and Y

so we have to find time of meeting at Y as we know that of X (which is t=0)

720=Va*t+Vb*t

t(5.4)=720

t=133.33 or t=720/5.4

therefore distance travelled by B =Vb*t

=2.4*720/5.4

=319.99m

=320m

Han's retirement account earns $247,163.25 in simple interest.

To find the simplest interest, we need to use the formula:

Simple Interest = Principal × Rate × Time

In this case, the Principal is $410,000 and the Rate is $15,785 per year. We don't know the time period, but we can solve for it using the formula:

Time = Simple Interest ÷ (Principal × Rate)

Plugging in the values, we get:

Time = $15,785 ÷ ($410,000 × 1) = 0.0385 years

Therefore, the simplest interest is:

Simple Interest = $410,000 × $15,785 × 0.0385 = $247,163.25

So Han's retirement account earns $247,163.25 in simple interest.

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The arc measures on the given circle are as follows, using theorems:

1. Arc CE: 148º.

2. Arc BD: 6º.

The measure of Arc CE is found applying the central angle theorem, which states that the measure in degrees of the arc is twice the measure of the inscribed angle from these points.

The measure of the inscribed angle is of m<1 = 74º, hence the measure of the arc is given as follows:

m<Arc CE = 2 x 74º = 148º.

The measure of arc BD is found applying the outside angle theorem, which states that the measure of the arc formed by two secants of the circle is half the difference of the measures of the intercepts arcs.

Hence, in the context of this problem, the measure of arc BD is obtained as follows:

34 = (74 - BD)/2

74 - BD = 68

BD = 6º.

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By conducting mathematical operations, we know that the group of friends will order 6 pizzas.

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.

The operation's arity is determined by the number of operands.

Mathematical operations include addition, subtraction, multiplication, division, and finding the root.

So, a number of pizzas the friends should buy:

We know that a group is of 15 people.

They are ordering a pizza which have also 15 slices in each.

And each person wants 2 slices: That is

Then, the number of pizzas they have to order will be:

1 pizza (15 slices) * 2 = 2 pizza (30 slices)

Therefore, by conducting mathematical operations, we know that the group of friends will order 6 pizzas.

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Answer: n=-2

Step-by-step explanation:

Given

The length of the football field is  \(300\ ft\)

In the mile, it can be expressed as \(5.7\times 10^n\ mile\)

Also, \(5280\ ft=1\ mile\) or

\(1\ ft=\dfrac{1}{5280}\ miles\\\\1\ ft=1.893\times 10^{-4}\ miles\)

converting \(300\ ft\) to miles

\(\Rightarrow 300\times 1.893\times 10^{-4}\\\Rightarrow 5.68\times 10^{-2}\approx 5.7\times 10^{-2}\)

Comparing it with the given value \(5.7\times 10^n\ mile\)

we get \(n=-2\)