The given expression is,
[tex]\lvert n\rvert=3.5[/tex]So we know that, the absolute value of a number is its distance from the origin, say 0. SInce the distance cannot be expressed in negative values, absolute values are always expressed as positive numbers. FOr example,
[tex]\lvert-x\rvert=\lvert x\rvert=x[/tex]Therefore, the values that make the given expression true can be,
[tex]\lvert n\rvert=3.5\Rightarrow n=-3.5\text{ or n=3.5}[/tex]Dado la siguiente información de un triángulo, encuentre B,C y cB=_______. A = 36° , a = 8 , b = 5C=_______c=_______
Usa la ley de seno para hallar la medida del angulo B:
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}[/tex][tex]\begin{gathered} \sin B(\frac{a}{\sin A})=b \\ \\ \sin B=b\cdot\frac{\sin A}{a} \\ \\ B=\sin ^{-1}(b\cdot\frac{\sin A}{a}) \\ \\ B=\sin ^{-1}(5\cdot\frac{\sin 36}{8}) \\ \\ B\approx21.55 \end{gathered}[/tex]Como la suma de los angulos interiores de un triangulo siempre es 180°, usa la medida del angulo A y angulo B para hallar la medida del angulo C:
[tex]\begin{gathered} A+B+C=180 \\ C=180-A-B \\ C=180-36-21.55 \\ C=122.45 \end{gathered}[/tex]Usa la ley de seno para hallar la medida del lado c:
[tex]\begin{gathered} \frac{c}{\sin C}=\frac{a}{\sin A} \\ \\ c=\frac{a}{\sin A}\cdot\sin C \\ \\ c=\frac{8}{\sin36}\cdot\sin 122.45 \\ \\ c\approx11.48 \end{gathered}[/tex]Entonces, las medidas que tenias que hallar so;
B=21.55°
C=122.45°
c=11.48
Solve x^2+5x=-6
A)x=5 and x=1
B)x=-5 and x=-1
C)x=3 and x =2
D)x=-3 and x=-2
Answer:
C
Step-by-step explanation:
x²+5x=-6
Collect like terms
x²+5x+6=0
Factors that when multiplied will give us 6 and when added will give us 5 are 2 and 3.
Therefore,
x²+5x+6=0
x²+2x+3x+6=0
Factorizing;
x(x+2)+3(x+2)=0
Pick one (x+2)
(x+2)(x+3)=0
x+2=0 x+3=0
x=2 and x=3
What is the measure of each interior angle of the regular polygon picture below ?if necessary, round to the nearest tenth
Our figure is a regular polygon. A polygon is regular when all angles are equal and all sides are equal. The measure of each inside angle of a regular polygon is given by the following expression
[tex]\frac{180^o\times(n-2)}{n}[/tex]Where n represents the amount of sides.
Since our polygon is a regular hexagon, we have n = 6. Using this value on the expression, we have
[tex]\frac{180^o\times(6-2)}{6}=\frac{180^o\times4}{6}=\frac{720^o}{6}=120^o[/tex]The measure of each interior angle a regular hexagon is 120º.
what was the initial amount of water in a barrel, in liters, if x liters remain after y liters were spilled and 6 were added?
Let's call A the initial amount of water, in liters, in that barrel.
After y liters were spilled, the amount left was
A - y
Then, after 6 liters were added, the final remaining amount was given by:
A - y + 6
Now, since x liters remain, we have:
x = A - y + 6
Therefore, if we can find the expression for the initial amount of water, in liters, by isolating A in that equation:
x = A - y + 6
x + y = A + 6
x + y - 6 = A
A = x + y - 6
Thus, the initial amount of water was (x + y - 6) liters.
<1 and <2 form a linear pair. If m<1
= (18r - 1)° and m<2 = (23r + 17)°. find m<2.
The measure of angle m<2 for the given linear pair is found as 109°.
What is meant by the term linear pair?Once two lines intersect at a single point, a linear pair of angles is formed. If the angles are adjacent to one another after the two lines intersect, they are referred to as linear. The sum of the angles of a linear pair has always been 180°.For the given question;
<1 and <2 form a linear pair.
m<1 = (18r - 1)° and m<2 = (23r + 17)°
Thus, from the property of the linear pair;
m<1 +m<2 = 180
Put the values;
(18r - 1)° + (23r + 17)° = 180
Simplify the expression.
18r - 1 + 23r + 17 = 180
41r = 180 - 16
r = 4
m<2 = (23r + 17)°
m<2 = (23×4 + 17)°
m<2 = 109°
Thus, the measure of angle m<2 for the given linear pair is found as 109°.
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the price of a computer component is decreasing at a rate of 9% per year. if the component costs $60today ,what will it cost in there years ?
The exponential decay formula is:
[tex]y=a(1-r)^t[/tex]where y is the final cost, a is the initial cost, r is the annual decreasing rate (as a decimal), and t is the time in years.
Substituting with a = $60, r = 0.09, and t = 3 years, we get:
[tex]\begin{gathered} y=60\cdot(1-0.09)^3 \\ y=60\cdot(0.91)^3 \\ y=60\cdot0.75 \\ y=45.21 \end{gathered}[/tex]It will cost $45.21 in 3 years
Select all units that can be used for surface area. Explain why the others cannot be
used for surface area.
motera
A square meters
B. feet
C. centimeters
D. cubic inches
E.square inches
F. square feet
Answer: A, E, F
Step-by-step explanation:
The area answers always need to have a square in the unit so B & C are wrong.
D is wrong because it is a unit for volume. So A, E, and F are the right answers.
Khan Academy
Graph the equation.
y = 2(x-4)² + 5
Answer: 4,5
Step-by-step explanation
A diagram is shown, where kill and Move statements and reasons to the table to provem is a transversal.that 21 25.mReasonsStatements1. kl-K2.1. Given2. Corresponding anglesare congruent.3.253763.4. 215 254.A <10 -2 B-1u23C218 24 D-2013E-2014 F-2025 G229 26 1723324I 23:25 J24325 R-4826L_Transitive property Msymmetric propertyN Vertical angles are congruent.Straight angles form a linear pair.P Corresponding angles are congruent.Q Alternate exterior angles are congruent.
Given:- The triangle with dimensions in it.
To find:- Which triangle is congruent to triangle MNO.
Solution:-
As we know that two triangles are congruent only when they satisfy one of the given rules.
1. SSS (Side-side-side) congruency rule.
2. SAS (side-angle-side) congruency rule.
3. ASA (Angle-Side-Angle) congruency rule.
4. AAS (Angle-Angle-Side) congruency rule
5. RHS (Right angle-Hypotenuse-Side) congruency rule.
So, check one by one option.
Option A:-
One side is 4.6 cm, another side is 4.99 cm and one angle is 60 degrees.
But it does not satisfy any of the congruency rules because there are 2 sides and then one angle.
So, option A is incorrect.
Option B:-
In option B there are three angles given 70 degrees, 60 degrees and 50 degrees. But to prove that the triangle is congruent we need at least one side.
So, Option B is incorrect.
Option C:-
In option C, there are only two sides given as 4.07 cm and 4.99 cm and to prove that the triangles are congruent we need at least three measurements of the triangle.
So, option C is incorrect.
Option D:-
In option D, there is one side of 4.07 cm, then one angle of 60 degrees and then one side of 4.99 cm. And we can observe that there is an angle between the two sides.
So, it follows SAS (side-angle-side) congruency rule.
So, Option D is correct.
Final answer:-
Therefore, the answer is option D.
A boat heading out to sea starts out at Point A, at a horizontal distance of 1083 feet
from a lighthouse/the shore. From that point, the boat's crew measures the angle of
elevation to the lighthouse's beacon-light from that point to be 8°.At some later
time, the crew measures the angle of elevation from point B to be 4°. Find
distance from point A to point B. Round your answer to the nearest
the
tenth of a foot if
necessary.
The distance between point A and point B is 75.6 feet.
Let's set up a right triangle with the lighthouse at the top and the boat at points A and B at the bottom, with the base of the triangle being the horizontal distance between the two points.
We can then use the trigonometric function tangent to solve for the vertical distance between points A and B, which is given by the formula:
tan(angle of elevation) = vertical distance / horizontal distance
For point A, the angle of elevation is 8° and the horizontal distance is 1083 feet. So, the vertical distance from point A to the lighthouse is given by:
tan(8°) = vertical distance / 1083 feet
Solving for the vertical distance gives us:
vertical distance = tan(8°) * 1083 feet
For point B, the angle of elevation is 4° and the horizontal distance is still 1083 feet. So, the vertical distance from point B to the lighthouse is given by:
tan(4°) = vertical distance / 1083 feet
Solving for the vertical distance gives us:
vertical distance = tan(4°) * 1083 feet
Now we can find the distance between points A and B by subtracting the vertical distance from point A to the lighthouse from the vertical distance from point B to the lighthouse. This gives us:
distance between point A and point B = (tan(8°) * 1083 feet) - (tan(4°) * 1083 feet)
Plugging in the numerical values, we get:
Distance between point A and point B = (0.1403 * 1083 feet) - (0.0698 * 1083 feet)
Simplifying, we get: distance between point A and point B = 75.6083 feet
Therefore, the distance between point A and point B is 75.6 feet.
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Which segment is a reflection of segment AB over the line x=1? X CD O EF O GA O IJ
Since the line on which segment AB is reflected is x = 1 then the rule for this reflection will be
[tex](x,y)\rightarrow(-x+2\cdot1,y)=(-x+2,y)[/tex]Then, the coordinates of the segment that is reflections of segment AB with respect to the line x = 1 will be
[tex]\begin{gathered} A(-4,3)\rightarrow(-(-4)+2,3)=(4+2,3)=(6,3) \\ B(-1,1)\rightarrow(-(-1)+2,1)=(1+2,1)=(3,1) \end{gathered}[/tex]And the segment with these coordinates is EF
[tex]\begin{gathered} E(6,3) \\ F(3,1) \end{gathered}[/tex]Therefore, the correct answer is b. EF.
A population of values has a normal distribution with μ = 159.8 and σ = 59.5 . If a random sample of size n = 13 is selected, Find the probability that a single randomly selected value is greater than 156.5. Round your answer to four decimals. P(X > 156.5) = Find the probability that a sample of size n = 13 is randomly selected with a mean greater than 156.5. Round your answer to four decimals. P(M > 156.5) =
In a population of values having a normal distribution with (μ = 159.8) and (σ = 59.5), if a random sample of size (n = 13) is selected, then the probability that a single randomly selected value is greater than 156.5 will be 0.52.
As per the question statement, a population of values has a normal distribution with (μ = 159.8) and (σ = 59.5) and a random sample of size (n = 13) is selected,
Then we are required to calculate the probability that a single randomly selected value is greater than 156.5.
To solve this question, let us assume that, a random variable "X" follows normal distribution with mean (μ = 159.8), standard deviation (σ = 59.5) and a sample size of (n = 13).
Then the probability that a single randomly selected value is greater than 156.5 can be calculated as follows:
P (X > 156.5) = [1 - P(X < 156.5)]
= [1 - P{(X - μ)/σ < (156.5- 159.8)/59.5}]
= [1 - P{Z < (-0.0554)}]
= (1 - 0.477885127828 )...[Using Excel Function "NORMSDIST (-0.0554)]
= 0.522114872172
≈ 0.52
Probability: Probability is the branch of mathematics that deals with the numerical descriptions on the extent to which an event is likely to occur, or how likely it is, that a proposition is true, being calculated by the ratio of the favorable cases to the total number of cases possible.To learn more about Samples and Probability, click on the link below.
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15x -2 = 3 ( 5x + 7)
We have the following:
[tex]15x-2=3\cdot(5x+7)[/tex]solving for x:
[tex]\begin{gathered} 15x-2=15x+7 \\ 15x-15x=2+7 \\ 0=9 \end{gathered}[/tex]Therefore, the system has no solution
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Several bakeries in a town were asked the price for different amounts of donuts at their shop. The scatter plot with a line of best fit was created from the data gathered.
Part A: Estimate the correlation coefficient. Explain your reasoning for the given value. (4 points)
Part B: How many positive and negative residuals are there? Explain your reasoning. (3 points)
Part C: State the point with the largest absolute value residual and interpret the point in terms of the context of the data. (3 points)
Considering the given scatter plot, it is found that:
a. The correlation coefficient is of 0.303.
b. Regarding the residuals, there are six positive and four negative.
c. The point with the largest residual is (6,2), which is the point in which the largest difference between the predicted and the actual value were found.
How to find the correlation coefficient of a scatter plot?The correlation coefficient is gotten by selecting the points (x,y) from the scatter plot, and inserting them into a calculator.
The coordinates of these points from the given plot are;
(1,2), (1,3), (2,4), (3,4), (3,5), (4,3), (4,5), (5,5), (5,6), (6,2).
Punching these points into a calculator, gives the coefficient as 0.303.
A residual is calculated as the difference that is gotten between the observed value and the predicted value. Thus;
The positive residuals are defined as the points that exists above the line and in this given plot we have six positive residuals.
The negative residuals are the points that exists below the line, and in this plot, we have four negative residuals.
Hence the largest residual, with the aid of absolute value, is at the point:
(6,2).
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What is the maximum value of this function on the interval [-2,0]
Answer:
2,0?
Step-by-step explanation:
To do this, find your first derivative and then find where it is equal to zero. Because we are only concerned about the interval from -5 to 0, we only need to test points on that interval. (i really don't know hot to explain)
Three Albany Middle Schools raised money to buy new computers.EON raised $286.00 Hackett raised $192.84 Myers raised $113.25 more than Hackett. What is the total amount of money raised by all three schools
We have to find the amount of money raised by all three schools.
The first school: EON, raised $286.00
The second school: Hackett raised $192.84
The third school: Myers raised $113.25 more than Hackett
To calculate the amount that the third school raised, we add $113.25 to the amount that the second school raised $192.84:
[tex]192.84+113.25=306.09[/tex]Myers raised $306.09
Finally, we add the money that the three schools raised to find the total:
[tex]286.00192.84+306.09=784.93[/tex]The total amount of money raised was $784.93
Answer:
$784.93
If a watch costs $40 and you must pay 6.5 % sales tax, how much will the tax be?
Write 2 proportions so that the product of the means equal 27
Two proportions that has a product of 27 are
first proportion is 27 = 2/3 * 81/2second proportion is, 27 = 4/7 * 189/4What is proportion as used in math?Proportion as used in math refer to the condition when two ratios are equal.
Let the two proportions be x and y
say 2/3 * x = 27
x = 27 / 2/3
x = 81/2
4/7 * y = 27
y = 27 / 4/7
y = 189/4
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Melina is hiking and is at en elevation of 2000 feet. If she descends by 500 feet. What is her elevation now?
Please help! I need this asap. P.S.- I'm in class. Thanks!
The elevation of Melina when she descends by 500 feet is 1500 feet.
What is an elevation?An elevation simply means the height above a particular place. It is usually referenced as the sea level.
In this situation, Melina is hiking and is at en elevation of 2000 feet. If she descends by 500 feet. It should be noted that since she descend, we will have to subtract 500 from the initial value that was given as 2000. feet.
Therefore, the calculation will be illustrated through subtraction. This will be:
= 2000 - 500
= 1500 feet.
This implies that when Melina descends, the elevation that she'll be at that point in time is 1500 feet.
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Determine if it’s true or false based on the figure shown
Answer:
True is the correct answer for this
A quarter weights approximately 5.7 grams and dimes weights approximately 2.3 grams. a bag of 18 quarters and some dimes weights 141.7 grams. how many dimes are in the bag?
No. of dimes in the bag will be = 17
What is linear equation ?In the algebraic form y=mx+b, where m denotes the slope and b the y-intercept, a linear equation is defined as a first-order (linear) term plus a constant. When x and y are the variables, the previous statement is occasionally referred to as a "linear equation of two variables."
Calculation5.7 grams -------> one quarter
2.3 grams -------> one dimes
5.7 q + 2.3 d = 141.7
given q = 18
5.7 * 18 + 2.3 d = 141 .7
2.3d = 141.7 - 102.6
2.3 d = 39.1
d = 39.1 / 2.3
d = 17
therefore , no. of dimes in the bag will be = 17
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The population of rabbits on an island is growing exponentially. In the year
2010, the population of rabbits was 9400, and by 2012 the population had
grown to 11500. Predict the population of rabbits in the year 2021, to the
nearest whole number.
The population of the rabbit in 2009
Given that the population of rabbits on an island which is growing exponentially
So let the population be as P = P₀ [tex]e^{bt}[/tex]
where P₀ and b are constants and t = current year - 1994
In 1994, time is equal to 0
the population of rabbit , P = 9,600
so thus the expression becomes
P₀ = 9,600
and in 2000 , t = 2000 - 1994 thus time = 6 years and population of the rabbit is 18,400
[tex]18400 = 9600[/tex] × [tex]e^{b 6}[/tex]
18400 / 9600 = [tex]e^{b 6}[/tex]
23/ 12 = [tex]e^{b 6}[/tex]
Taking log on both sides
ln 1.92/ 6 = b
b = 0.109
On putting the value of P₀ and b the population of the rabbit after t years from 1994 is
P = 9600 × [tex]e^{0.109}[/tex] [tex]^{t}[/tex]
In 2009, t = 2009 - 1994 = 15 years
So, the population of the rabbit in 2009
thus P= 49243
Hence we can say that the population of the rabbit in 2009
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Answer:
It's 28495
Step-by-step explanation:
I'm having a problem with logarithms I will upload a photo
SOLUTION:
Step 1 :
In this question, we are asked to solve the equation:
[tex]In\text{ ( 4 x + 4 ) = 2}[/tex]Step 2 :
Now, taking the exponents of both sides, we have that:
[tex]\begin{gathered} e^{In\text{ ( 4 x + 4 ) }}=e^2 \\ 4x+4=e^2 \\ \text{But e}^2\text{ = 7.3891 ( to 4 decimal places )} \\ 4\text{ x + 4 = 7. 3891} \\ \text{ 4 x = 7. 3891 - 4} \\ \text{4 x = 3.3891} \\ \text{Divide both sides by 4 , we have that:} \\ x\text{ = }\frac{3.3891}{4} \\ x\text{ = 0.847275} \\ \text{x = 0.8473( to 4 decimal places)} \end{gathered}[/tex]Principal Phillips asked 150 sixth graders to vote on their end-of-year trip. 120 sixth graders voted for a trip to the water park. What percent of sixth graders voted for a trip to the water park?
Answer:
80%
Step-by-step explanation:
A school's administration needs to buy benches and chairs for the gymnasium. They have a total budget of $1,500 and each bench, x, costs $100 while each chair, y, costs $50. Which graph shows an inequality that describes the possible number of benches and chairs the administration can buy?
The required graph shows the inequality that describes the possible number of benches and chairs the administration can buy is graph A. Option A is correct.
Here,
According to the question,
cost of the benches = 100x
cost of the chairs = 50y,
the total cost would exceed $1500
So,
the inequality can be formed,
100x + 50y ≤ 1500
Graph A shows the above inequality.
Thus, the required graph shows the inequality that describes the possible number of benches and chairs the administration can buy is graph A. Option A is correct.
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c to the fifth power squared
Answer: c to the power of 25
Step-by-step explanation: c can stay on its on 5 squared is 25 so the answer is c *25
Which expression is equivalent to -2(5x + 3y)?
A. 3y(5x - 2)
B. 5x(-2 + 3y)
C. -10x - 6y
D. -10x + 3y
Answer:
C. -10x - 6yStep-by-step explanation:
[tex]\sf -2(5x + 3y)[/tex]
Apply the Distributive Property:-
[tex]\sf -2\left(5x+3y\right)[/tex]
[tex]\sf -2\times\:5x-2\times\:3y[/tex]
[tex]\sf -2\times\:5x=\bf -10x[/tex]
[tex]\sf 2\times\:3y=\bf 6y[/tex]
[tex]\sf -10x-6y[/tex]
Therefore, your answer is C. -10x - 6y!!
_______________________
Hope this helps you!
Have a great day!
I can enter the problem here so ill add a picture, sorry for the inconvenience
Given two numbers a and b
Their Arithmetic mean (A), Geometric mean (G) and Harmonic mean (H) are given below,
[tex]\begin{gathered} A=\frac{a+b}{2} \\ G=\sqrt[]{ab} \\ G=\sqrt[]{AH} \end{gathered}[/tex]To find the formula that correctly relates H, a and b,
Relating the last two equations, i.e the geometric and harmonic mean below,
[tex]\begin{gathered} G=\sqrt[]{ab} \\ G=\sqrt[]{AH} \\ \text{relating both equations} \\ \sqrt[]{ab}=\sqrt[]{AH} \\ \text{Square both sides } \\ (\sqrt[]{AH})^2=(\sqrt[]{ab})^2 \\ AH=ab \\ \text{Make H the subject},\text{ by dividing both sides by A} \\ \frac{AH}{A}=\frac{ab}{A} \\ H=\frac{ab}{A} \end{gathered}[/tex]Substituting for A into the above expression,
[tex]\begin{gathered} \text{recall A=}\frac{a+b}{2} \\ H=\frac{ab}{A}=\frac{ab}{\frac{a+b}{2}} \\ H=(2\times\frac{ab}{a+b})=\frac{2ab}{a+b} \\ H=\frac{2ab}{a+b} \end{gathered}[/tex]Hence, A is the correct option.
help please tyyyyyyyyy
Answer: 5 tadoples
Step-by-step explanation:
Please get me the Braniliest award, thanks!
Answer:
30
Step-by-step explanation:
If there are 18 swans in the ratio of 3
you divide 18 by 3 = 6
So you times 5 by 6 to get 30 as your answer
3.13 Which triangle congruence postulate or theorem proves that these triangles are congruent?
The SAS triangle congruence postulate proves that these triangles are congruent .
Given,
In the figure,
There are two triangles ABC and Triangle XYZ
Now, According to the question:
Consider the triangle ABC and triangle XYZ .
we can see that
(i) angle C = angle Z .....given in the figure
(iii) side AC = side XZ .... given in the figure
(ii) side BC = side ZY ....given in the figure
From the above three statements we conclude that
ΔABC ≅ ΔXYZ
both the triangles ABC and XYZ are congruent by SAS Congruence Postulate .
Therefore , The SAS triangle congruence postulate proves that these triangles are congruent .
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