A statement which best describes Gary’s error is that: Gary did not use correct factors for 66 in the equation.
What is the distribution property of multiplication?The distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a given numerical value or factor, the same output would be produced as when each addend is multiplied respectively by the numerical value or factor, and the products are added together.
Mathematically, the distributive property of multiplication is given by this expression:
a(b + c) = ab + ac.
Also, the correct greatest common factor of 66 and 36 is given by:
Greatest common factor (GCF) = 6
By applying the distributive property of multiplication, we have:
66 + 36 = 6(11 + 6)
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m(x) = | x + 1 |
Graph
The value of x = 1/M-1 , x = -1/M+1
What is Graph?
The graph of a function f is the set of ordered pairs where "displaystyle f(x)=y" exists. In the common scenario when x and f(x) are real integers, these pairings represent Cartesian coordinates of points in two-dimensional space and hence constitute a subset of this plane.
M(x) = |x + 1|
|x + 1| = M(x)
x + 1 = M(x)
x + 1 = -M(x)
Adding (-x) both side
x + 1 + (- x) = M(x) + (- x)
x + 1 + (- x) = -M(x) + (- x)
x + 1 - x = M(x) - x
x + 1 - x = -M(x) - x
1 = M(x) - x
1 = -M(x) - x
M(x) - x = 1
-M(x) - x = 1
x(M-1) = 1
x(-M-1) = 1
Dividing both side with (M - 1) and (-M - 1)
x(M-1)/(M - 1) = 1/(M - 1)
x(-M-1)/(-M - 1) = 1 /(-M - 1)
x = 1/(M - 1)
x = 1/(-M - 1)
Hence, x = 1/M-1 , x = -1/M+1
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What is r + s + t when r = 25, s = –11, and t = –7?
Answer:
7
Step-by-step explanation:
Two planes just recently left the airport. Looking at the radar, Plane 1 is 50 miles away from the airport and Plane 2 is 200 miles away from the airport. If the 2 planes are 175 miles away from each other, what is the angle measurement from the airport to the 2 planes? (round to the nearest whole number)
To solve this problem, we need to use the Law of Cosines. The law states that given any triangle ABC:
Then;
[tex]c^2=a^2+b^2-2ab\cos(C)[/tex]Since we want to find the measure of angle x, we can use:
c = 175 mi
a = 200 mi
b = 50 mi
C = x
Now, by the Law of Cosines:
[tex]175^2=200^2+50^2-2\cdot200\cdot50\cdot\cos(x)[/tex]And solve:
[tex]30625=40000+2500-20000\cos(x)[/tex][tex]30625-40000-2500=-20000\cos(x)[/tex][tex]\frac{-11875}{-20000}=\cos(x)[/tex][tex]\begin{gathered} x=\cos^{-1}(0.59375) \\ . \\ x\approx53.5764 \end{gathered}[/tex]To the nearest whole number, x = 54°
a boat traveled 27miles in 2hours at this rate how many miles will the boat travel in 1/2 hours?
Answer:
6.75 miles
Step-by-step explanation:
27/2 = 13.5
27/4 = 6.75
27 miles in 2 hours
13.5 in 1 hour
6.75 in half an hour :)
Answer: 6.75 miles
Step-by-step explanation:27/4=6.75, I divided by 4 to get the half hour
iodinated (i 125) albumin injection contains 0.5 millicuries (18.5 mbq) of radioactivity per milliliter. how many milliliters of the solution should be administered exactly 30 days after the original assay to provide an activity of 60 microcuries (2.22 mbq) if the half life of i 125 is 60 days? round answer to the nearest hundredth (i.e. 0.xx). do not include units in your answer.
The decay constant of a radioactive nuclide exists its probability of decay per unit time.
The half life of i 125 is 60 days exists 0.169 ml.
What is meant by Decay constant?The decay constant of a radioactive nuclide exists its probability of decay per unit time. The number of parent nuclides P therefore decreases with time t as dP/P dt = −λ.
The ratio of the number of radioactive atoms in a population to the rate at which they are vanishing due to radioactive decay.
The rate of decay is determined by the decay constant. The symbol for the decay constant is "lambda," or. The many diverse decay rates that have been seen may be caused by large variations in this constant probability among various types of nuclei.
Decay constant: [tex]$& \lambda=\frac{0.693}{t_{1 / 2}}[/tex]
Decay constant expressed in any unit of time
Such as reciprocal seconds, minutes, hours etc.
[tex]$\mathbf{N}=\mathrm{N}_o \mathrm{e}^{-\lambda t} \quad \lambda=\frac{0.693}{\mathrm{t}_{1 / 2}}$[/tex]
Half Life: [tex]$\quad t_{1 / 2}=\frac{0.693}{\lambda}$[/tex]
The half life of i 125 is 60 days exists 0.169 ml.
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Y = 17x - 8, y = 24x +6 Parallel Perpendicular Neither
Two parallel lines in the coordinate system share the same slope, this means that if you have two parallel lines:
[tex]\begin{gathered} y_1=m_1x_1+b_1 \\ y_2=m_2x_2+b_2 \\ \text{Their slopes must be equal:} \\ m_1=m_2 \end{gathered}[/tex]For the given equations, the slopes are:
[tex]\begin{gathered} y=17x-8 \\ m=17 \end{gathered}[/tex][tex]\begin{gathered} y=24x+6 \\ m=24 \end{gathered}[/tex]The slopes are different, so this lines are not parallel.
Two lines are perpendicular, when the slope of one of them is the negative inverse of the first one, this is for the perpendicular lines:
[tex]\begin{gathered} y_1=m_1x_1+b_1 \\ y_2=m_2x_2+b_2 \\ m_2=-\frac{1}{m_1} \end{gathered}[/tex]For the given equations, using y=17x-8 as reference, the slope of a line perpendicular to this one must be:
[tex]m_{}=-\frac{1}{17}[/tex]The slope of a perpendicular line to y=17x-8 is different from the slope of the second given line, so you can conclude that these lines are not perpendicular.
The correct choice is Neither
Jake has a 8 pounds of lunch meat to serve for a picnic lunch. He plans to serve each adult 2/3 of a pound. Part B: The price of lunch meat is $7.36 per pound. Which equation can be used to determine the total cost, c, for lunch meat that weighs a total p pounds? Then find the cost of the lunch meat. •p/7.36=c •p=7.36c, the cost is $1.09 •c=7.36p, the cost is $58.88 •p+7.36-c, the cost is $15.36
Part B
The most appropriate choice for linear equation will be given by -
Third option is correct
c = 7.36p is the required equation for total cost of p pounds of meat
The cost is $58.88
What is linear equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here,
Price of one pound of meat = $7.36
Cost of p pounds of meat = $7.36p
By the problem,
c = 7.36p
This is the required equation for total cost of p pounds of meat
Putting p = 8
c = [tex]7.36 \times 8\\[/tex]
c = $58.88
Third option is correct
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Evaluate log2 10 using the change of base formula. Round your answer to the nearest thousandth.
Take into account the following property:
[tex]\log _ab=\frac{\log b}{\log a}[/tex]Then, for the given expression you have:
[tex]\log _210=\frac{\log10}{\log2}=\frac{1}{\log }\approx3.322[/tex]Hence, the answer is approximately 3.322
I need help with the 2nd g(x) one please
Pls let me see the work!!
The recipe for the waffles presented using rational numbers are as follows;
1. The recipe for 2 waffles is as follows;
[tex] \displaystyle \frac{3}{5} [/tex] cups of flour
[tex] \displaystyle \frac{2}{15} [/tex] teaspoon of salt
[tex] \displaystyle \frac{4}{5} [/tex] teaspoons of baking powder
[tex] \displaystyle \frac{7}{20} [/tex] Cups of milk
[tex] \displaystyle \frac{1}{15} [/tex] Cup of butter
2. The recipe for 5 waffles is as follows;
[tex] \displaystyle 1\frac{1}{2} [/tex] cups of flour
[tex] \displaystyle \frac{1}{3} [/tex] teaspoon of salt
[tex] \displaystyle 2 [/tex] teaspoons of baking powder
[tex] \displaystyle \frac{7}{8} [/tex] Cups of milk
[tex] \displaystyle \frac{1}{6} [/tex] Cup of butter
3. The recipe for 300 waffles is as follows;
900 cups of flour
200 teaspoon of salt
1200 teaspoons of baking powder
525 Cups of milk
100 Cup of butter
4. The required number of waffle irons is 50
5. It would take approximately 6 servers
It would take 34 trips
What is a rational number?A rational number is one that can be expressed as a fraction.
From the given table, we have;
The recipe for 10 waffles includes;
3 cups of flour
[tex] \displaystyle \frac{2}{3} [/tex] teaspoon of salt
4 teaspoons of baking powder
[tex] \displaystyle 1\frac{3}{4} [/tex] Cups of milk
[tex] \displaystyle \frac{1}{3} [/tex] Cup of butter
1. To make 2 waffles, we have;
[tex] \displaystyle 2 = \frac{10}{5} [/tex]
Dividing each of the quantities required to make 10 waffles by 5 gives;
[tex] \displaystyle \frac{3}{5} [/tex] cups of flour
[tex] \displaystyle \frac{2}{3 \times 5} = \frac{2}{15} [/tex] teaspoon of salt
[tex] \displaystyle \frac{4}{5} [/tex] teaspoons of baking powder
[tex] \displaystyle \frac{1\frac{3}{4}}{5} = \frac{7}{20} [/tex] Cups of milk
[tex] \displaystyle \frac{\frac{1}{3}}{5} = \frac{1}{15} [/tex] Cup of butter
2. If each person gets 1 waffle, we have;
Number of waffles = 1 + 4 = 5
[tex] \displaystyle 5 = \frac{10}{2} [/tex]
Dividing the recipe for 10 waffles by 2 gives;
[tex] \displaystyle \frac{3}{2} = 1\frac{1}{2} [/tex] cups of flour
[tex] \displaystyle \frac{2}{3 \times 2} = \frac{1}{3} [/tex] teaspoon of salt
[tex] \displaystyle \frac{4}{2} = 2 [/tex] teaspoons of baking powder
[tex] \displaystyle \frac{1\frac{3}{4}}{2} = \frac{7}{8} [/tex] Cups of milk
[tex] \displaystyle \frac{\frac{1}{3}}{2} = \frac{1}{6} [/tex] Cup of butter
3. When each of 300 people can have one, the number of waffles is 300, which gives;
30 × 10 = 300
Multiplying the quantity of each ingredients required to make 10 waffles by 300 gives;
300× 3 = 900 cups of flour
[tex] \displaystyle 300 \times \frac{2}{3} = 200 [/tex] teaspoon of salt
300 × 4 = 1200 teaspoons of baking powder
[tex] \displaystyle 300 \times 1\frac{3}{4} = 525 [/tex] Cups of milk
[tex] \displaystyle 300 \times \frac{1}{3} = 100 [/tex] Cup of butter
4. Time it takes to cook a waffle = 10 minutes
Number of waffles required = 300
Time allowed = 1 hour = 60 minutes
The number of waffle iron is therefore;
[tex] \displaystyle {n = \frac{300 \times 10}{60} = 50} [/tex]
The number of waffle irons required is 50 waffle irons
5. Number of waffles each server can deliver = 9 waffles
The time it takes each server per trip = 10 minutes
Number of waffles to be delivered = 300
Time in which to deliver the 300 waffles = 1 hour
The number of servers is therefore;
[tex] \displaystyle {n = \frac{300}{9 \times 6} = 5. \overline 5 \approx 6} [/tex]
The number of trips is therefore;
5 servers will deliver 5×9×6 = 270
The sixth server will deliver the remaining 300 - 270 = 30 waffles in 30 ÷ 9 = 3.3 ≈ 4
The number of trips all together is therefore; 5×6 + 4 = 34 trips
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Please help asap
this is an assignment due today please help real quick
no fake answers
Answer:
where???????????????
Sandra saves 12% of her salary for retirement. This year her salary was $1,000 more than in the previous
year, and she saved $4,920. What was her salary in the previous year?
Answer:
$32,000
Step-by-step explanation:
Miguel is going to see a movie and is taking his 5 kids. Each movie
ticket costs $12 and there are an assortment of snacks available to
purchase for $5 each. How much total money would Miguel have to
pay for his family if he were to buy 5 snacks for everybody to share?
How much would Miguel have to pay if he bought a snacks for
everybody to share?
Total cost with 5 snacks:
Total cost with a snacks:
y = 2x + 3
when x = -1, y =
Answer: y = 1
Step-by-step explanation:
y = 2(-1) +3
y = -2 + 3
y = 1
After the expression (x10)^3/5 Is simplified as much as possible, x is raised to what exponent?
The exponent of x in the expression (x¹⁰)³⁺⁵ is 6.
What is an exponent?Exponent rules, commonly referred to as the "laws of exponents" or "properties of exponents," facilitate the task of simplifying exponent-based statements. These rules can help simplify formulas with exponents that are decimals, fractions, irrational numbers, or negative integers.
The mathematical process known as an exponent often indicates the power of a variable.
As of right now, we are aware that under the scenario of
[tex](x^{a})^{b} = x^{ab}[/tex]
Therefore, solve the power by multiplying 10 by 3/5, and we get
10 × (3/5)
=6
Thus, the expression simplified as
(x¹⁰)³⁺⁵ = x⁶
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Which expression is equivalent to the given expression? (+2+6)-(- 2+3) x +9 O A I O B. - } +3 O C. x+3 OD. - *+9
Answer:
The equivalent expression is;
[tex]\frac{5}{7}x+3[/tex]Explanation:
We want to simplify the expression;
[tex](\frac{1}{7}x+6)-(-\frac{4}{7}x+3)[/tex]we will first multiply the negative by every term in the bracket, then simplify by collecting the like terms.
[tex]\begin{gathered} \frac{1}{7}x+6-(-\frac{4}{7}x)-(+3) \\ \frac{1}{7}x+6+\frac{4}{7}x-3 \\ \text{collecting the like terms we have;} \\ \frac{1}{7}x+\frac{4}{7}x+6-3 \\ \frac{5}{7}x+3 \end{gathered}[/tex]Therefore, the equivalent expression is;
[tex]\frac{5}{7}x+3[/tex]Working alone, it takes Kristen 10.2 hours to harvest a field. Kayla can harvest the same field in 16.5 hours. Find how long it would take them if they worked together.
ANSWER:
13.35 hours
EXPLANATION:
Given:
Time Kristen takes to harvest = 10.2 hours
Time Kayla takes to harvest = 16. 5 hours
Let X represent the time it would take them to work together.
Here, to find the time it would take them if they worked together, let's find their mean time, using the formula below:
[tex]X\text{ = }\frac{Time\text{ taken by kristen + Time taken by Kayla}}{2}[/tex][tex]\begin{gathered} X\text{ = }\frac{10.2\text{ + 16.5}}{2} \\ \\ X\text{ = }\frac{26.7}{2} \\ \\ X\text{ = }13.35\text{ hours} \end{gathered}[/tex]It would take them 13.35 hours if they worked together.
SOS PLEASE HELP QUICKLY WILL MARK BRAINLYIST
Submit a picture of your work to the assignment page:
its a two column proof
Prove: If two parallel lines are cut by a transversal then the alternate exterior angles are congruent. Do not use the alternate exterior angles theorem. Use a diagram and the corresponding angles theorem.
Proved that if two parallel lines are cut by a transversal then the alternate exterior angles are congruent.
What is the Exterior Angle of a Triangle Property?An exterior angle of a triangle is equal to the sum of the opposite interior angles.
By the property of alternate interior angles;
From the figure attached;
∠XWY ≅ ∠ZYW
The Property of the alternate angles states that if two parallel lines are cut by a transversal, then the alternate angles are congruent.
Here, ∠XWY and ∠ZYW shows the interior angles between the parallel lines and the transversal.
The interior alternate angles ∠XWY and ∠ZYW will be congruent.
Hence, Proved that if two parallel lines are cut by a transversal then the alternate exterior angles are congruent.
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(8.59×10 4 )−(3.2×10 3 )
Answer:
The answer is 8.27×10^4
Answer: 8.27×10^4
Step-by-step explanation:
5. aviation due to a storm, a pilot flying at an altitude of 528 feet has to land. if he has a horizontal distance of 2000ft until the landing strip, what angle of depression should he use to land? round to the nearest tenth of a degree.
A pilot who is flying at a height of 528 feet must land because of a storm. 14.78° angle of depression should he utilize to land.
Given that,
A pilot who is flying at a height of 528 feet must land because of a storm.
We have to find what angle of depression should he utilize to land if the distance between him and the landing strip is 2000 feet horizontally.
In the right angle triangle:
TanΘ=Opposite side/ adjacent side
The opposite side is 528 feet.
The adjacent side is 2000 feet.
Then,
TanΘ=528/2000
TanΘ=0.264
Θ=Tan⁻¹(0.264)
Θ=14.78°
Therefore, 14.78° angle of depression should he utilize to land.
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What is the value of in if the remainder of /is 2?
O A. 1
OB. i
O C. -1
O D. -1
The value of i where remainder of n/ 4 is 2 is :
i² = -1 .
What is i?I has the value √-1.The complex numbers are expressed using the imaginary unit number, where I is defined as imaginary or unit imaginary. An imaginary number is a complex number component that can be written as a real number multiplied by the imaginary unit I where i² = -1. When the imaginary number is multiplied by itself, the result is negative. Consider the imaginary number 3i, which, when multiplied by itself or divided by its square, yields 9i², or -9.z = a + ib .i² = -1
i⁰ = 1
i¹ = i
i² = -1
i³ = i² x i
= -1 x i
= -i
i⁴ = i² x i²
= -1 x -1
= 1
The pattern repeats.
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Carrie wants to make a wallpaper border to go around the top of her room. She wants the border to look something like the illustration below.
The answer is A Reflection
This question is answered
Since Carrie wants to make a wallpaper border to go around the top of her room. She wants the border to look something like the illustration below. This is a Reflection
What is transformation?A transformation is an operation that is performed on a picture. Transformations are classified into four types: translations, reflections, dilations, and rotations. In transformations, reflections are achieved by flipping a shape or figure across a line of reflection, a point of reflection, or a plane of reflection.
A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. The line of reflection is formed when an image reflects through a line. A figure is said to reflect another figure when every point in one figure is equidistant from every point in another figure.
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Marty invested $7000 in treasury notes and stocks. The stocks paid 7% in the notes paid 8%, giving an annual income of $535. How much is invested into the treasury notes?
Answer:
3500
Step-by-step explanation:
split 7000 in half for stocks and treasury= 3500 each.
7 percent on 3500 is 3724, 7 percent of 3500 is 245 dollors. 535 x 7 is 3745 = 3500 invested in treasury.
Two 50 foot tall radio towers are 3000 feet apart. Find the angle of depression from the top of one tower to the base of the other.
Answer:
Explanation:
The diagram representing the two towers is given below:
Which of the following is the correct factorization of the polynomial below?p3 - 21603O A. (0-360)(p? + 36pq + 692)O B. (p2 + 129) (03 + 36pq + 50%)O C. (2-6)(p2 + 6pq + 3602)O D. The polynomial is irreducible.
We have the polynomial:
[tex]p^3-216q^3[/tex]We have to factorize it.
We know that 216 is the cube of 6.
We then applied the property for the difference of cubes.
[tex]\begin{gathered} p^3-(6q)^3 \\ (p-6q)(p^2+p\cdot6q+(6q)^2) \\ (p-6q)(p^2+6pq+36q^2) \end{gathered}[/tex]The answer is Option C.
Difference of cubes property:
x^3-y^3 = (x-y)(x^2+xy+y^2)
find the slope of m and choose the correct letter
We can use the given points to find the slope
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ m=\frac{63_{}-49_{}}{_{}2009-1999_{}} \\ \\ m=\frac{14_{}}{_{}10_{}} \\ \\ m=1.4 \end{gathered}[/tex]It means that every year, there are 1.4 million MORE households with personal computers
Can someone help me figure out the 2 proofs for questions 1 and 3 and help me find what X and Y equal for question 2 if you can!! In geometry
Hello! We can prove this with some statements, look:
• Notice that CD is parallel to AB;
,• angle 1 ≅ angle 2
,• M is the midpoint of AB;
Statement 1:
[tex]\hat{\text{AMC}}\cong\hat{\text{BMD}}[/tex]Reasoning 1:
As M is the midpoint of AB and we have two similar lines starting in M, we can divide the angle M into two equal angles m1 and m2.
definition of midpoint
Statement 2:
[tex]\hat{C}=\hat{D}[/tex]Reasoning 2:
As we already know that angle 1 ≅ angle 2, let's calculate the sum of the angles C and D, look:
angle C:
90º + angle 1
angle D:
90º + angle 2
so, 90º + angle 1 ≅ 90º + angle 2, it means that angle C ≅ angle D.
Statement 3:
[tex]\hat{MAC}\text{ = }\hat{\text{MBD}}[/tex]Reasoning 3:
The sum of the internal angles of a triangle must be equal to 180º, right? So, knowing it we can say that angles A and B are equal, look:
m1 + A + C = m2 + B + D = 180º
remember, m1 ≅ m2 and C ≅ D, so A ≅ B too.
According to the explanation and image, we can prove that triangle CAM ≅ triangle DBM.
Table:
complete the two-column proof.
pleasee
∠2 ≅ ∠4 and m∠2 = 110°, and proved m<3 = 70⁰.
The answers of the blank lines are:
A . Vertically opposite angle.
B . Linear angle .
C . Hence proved .
Solution:Given ,
∠2 ≅ ∠4 and m∠2 = 110°.
We have to prove
m<3 = 70⁰
Here ,
m<2 = m<4 => They are vertically opposite angles.
And here ,
m<3 and m<4 are supplementary angles.
m∠3 + m∠4 = 180° => linear angle .
m<4 = 110⁰ => since m<2 = m<4
By substituting m∠4 we get,
m∠3 + m∠4 = 180°
= m∠3 + 110 = 180
= 180 - 110
m∠3 = 70°
Hence proved.
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13+14=3×f;f=9 helppp
Answer: 3x=13+14
3x=27
x=27/3
x=9
Step-by-step explanation: Maybe.
A hockey player takes a shot 20 feet away from a 5-foot goal. If the puck travels at a 15° angle of elevation toward the center of the goal, will the player score?
EXPLANATION
Let's see the facts:
shoot = 20 feet
goal = 5 foot
Let's draw the statement:
Since we are finding the side opposite the given angle and know the side adjacent, we can use the Pythagoras Theorem to find the needed value.
[tex]\text{Tan=}\frac{Opposite}{\text{Adjacent}}[/tex]Replacing terms:
[tex]\text{Tan 15}=\frac{x}{20}[/tex]Isolating x:
[tex]20\cdot\text{Tan 15= x}[/tex]Switching sides and simplifying:
[tex]x=5.35\approx5.4[/tex]The player will not score because 5.4 is greater than 5
