linear pair theorem
ZADCZBDC
given
2m BDC=180°
definition of supplementary
mzADC-mzBDC
definition of
congruence
m *ADC +
m BDC=180°
ADC is complementary
to BDC
substitution property of
equality
m BDC=180°
ADC is supplementary
to BDC
⠀⠀
m BDC=90°
division property of
equality
What the given proof is trying to show us is that; ∠3 = 126°
How to prove supplementary angles?From the attached line, we see that angle 1 and angle 3 form a straight line. Now, since we know that angles on a straight line sum up to 180°, then it means that they are supplementary.
We are given;
1) ∠1 and ∠2 are supplementary
2) ∠1 = 36°
Thus from definition of complementary angles, we can say that;
36° + ∠2 = 90°
Subtraction property of equality when applied gives;
∠2 = 54°
We are told that ∠2 and ∠3 are linear pairs and as such;
∠2 + ∠3 = 180° from linear pairs theorem.
By substitution property of equality we have;
54° + ∠3 = 180°
Solving gives ∠3 = 126°
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2 and 3/4 plus 3 and 2/4
Answer:
6 1/4
Step-by-step explanation:
ad 2 and 3 get 5 ad 3 and 2 get five now u have 5/4 uh oh the 4 is full
take 1 from the 5 over 4 and turn that one into 6 and turn the 4/4 to 1/4
boom 6 1/4
In the following exercises, multiply the binomials. Use any method.
266. (3rs − 7)(3rs − 4)
Answer:
Hence the expression [tex]$$(3rs-7)(3rs-4)=9r^2s^2-33rs+28$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (3rs-7)(3rs-4).We have to multiply the given expression.Multiply the (3rs-7) by -4, multiply the (3rs-7) by 3rs then add like terms.[tex]$$\begin{matrix}{} & {} & {} & {} & 3rs & - & 7 \\ \times & {} & {} & {} & 3rs & - & 4 \\ \end{matrix}$$[/tex]
_________________
[tex]$$\begin{matrix}{} & {} & {} & - & 12rs & + & 28 \\ {} & {} & 9{{r}^2}{{s}^2} & - & 21rs & {} & {} \\ \end{matrix}$$[/tex]
________________
[tex]$$\begin{matrix}{} & {} & 9{{r}^2}{{s}^2} & - & 33rs & + & 28 \\ \end{matrix}$$[/tex]
The cube of the sum of a number and 3.
The word expression the cube of the sum of a number and 3 can be written as (x + 3)³ or x³ + 9x² + 27x + 27.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that:
Let x be the number:
The word expression is:
The cube of the sum of a number and 3.
The sum of a number x and 3 is:
x + 3
The cube of the number (x + 3)
= (x + 3)³
After expanding the cube of (a + b)
(a + b)³ = a³ + 3a²b + 3ab² + b³
Similarly,
(x + 3)³ = x³ + 3x²(3) + 3(x)(3)² + (3)³
(x + 3)³ = x³ + 9x² + 27x + 27
Thus, the word expression the cube of the sum of a number and 3 can be written as (x + 3)³ or x³ + 9x² + 27x + 27.
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The graph represents the heights of two climbers on a climbing wall over a 12-minute time period.
A graph titled The Climbing Wall where the horizontal axis shows time (minutes), numbered 1 to 12, and the vertical axis shows height (feet) numbered 2 to 24. The line labeled Brynn's climb begins at 0 feet in 0 minutes, to 15 feet from 5 to 7 minutes, to 0 feet in 10 minutes. The line labeled Abby's climb begins at 4 feet in 0 minutes, to 14 feet from 4 to 6 minutes, to 22 feet in 8 minutes, to 0 feet in 12 minutes.
Which statement is true about the climbers’ heights?
Brynn was resting at a constant climbing height when Abby’s climbing height was decreasing.
Abby’s climbing height was decreasing when Brynn’s climbing height was increasing.
The heights of both climbers increased, then decreased, with no rest at a constant height.
Both climbers rested on the wall at a constant height for 2 minutes.
Both climbers rested on the wall at a constant height for 2 minutes.
How to determine the true statement?The illustrative graph that represents the climbers' movement is added as an attachment
From the attached graph, we have the following observation
The line of Abby's movement is horizontal from x = 4 to x = 6The line of Brynn's movement is horizontal from x = 5 to x = 7The difference between the endpoints of both horizontal line is
Difference = 6- 4 = 2
Difference = 7 - 5 = 2
This means that both Brynn and Abby stopped for 2 minutes
Hence, the true statement about is that (d) Both climbers rested on the wall at a constant height for 2 minutes.
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Make sure your answer is in
degrees. You should be able to
find this without a calculator.
-1
12/1/= = [?]°
sin-1
Answer:
210° , 330°
Step-by-step explanation:
using the sides of the 30- 60- 90 triangle
with legs 1, [tex]\sqrt{3}[/tex] and hypotenuse 2 , then
[tex]sin^{-1}[/tex] [tex]\frac{1}{2}[/tex] = 30° ← related acute angle
since [tex]sin^{-1}[/tex] - [tex]\frac{1}{2}[/tex]
then angle is in third / fourth quadrants , then required angles are
180° + 30° = 210° ← in third quadrant
360° - 30° = 330° ← in fourth quadrant
If 16g if a radioactive substance are present initially and 5yr later only 8g remain how much substance will be present after 5yr
4.59 g will be the amount of substance that will be present after 5 year.
Given: 16g of radioactive substance
8g left after 8 year
Concept: In a chemical reaction, the half-life of a species is the time it takes for the concentration of that substance to drop to half its original value. In a first-order reaction, the half-life of the reactant is ln(2)/λ, where λ (also referred to as k) is the reaction rate constant.
The half-life is given as 5 years, so the amount remaining after 9 years will be found by using the steps done below:
Remaining amount of radioactive substance = initial × (1/2)^(t/(half-life))
Remaining substance = (16 g)×(1/2)^(9/5) ≈ 4.59 g
After 9 years i.e., after 8 years have passed
About 4.59 g of the substance remains.
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PLEASE HELP
Triangle not drawn to scale
Given: measure of angle A = 51 degrees, b = 12, and c = 8. What is the length of a to the nearest tenth?
Eisha swims 18 ft from one side of her circular pool to the other, swimming straight through the center. she then swims one time around the entire edge of her swimming pool.
Answer: 74.52 if the question is how far she swims
Step-by-step explanation:
Complete the following proof.
Given: SW is diameter of R
m = 30°
Prove: m RTW = 15°
Using the circle theorems, we have proven that m ∠RTW = 15°
Circle theoremsFrom the question, we are to prove that m ∠RTW = 15°
In the given diagram,
measure of arc ST = 30°
∴ m ∠SRT = 30°
m ∠SRT = ∠T + ∠W ( Exterior angle of a triangle equals the sum of the two remote angles)
Also,
∠T = ∠W (Radii of the same circle)
∴ m ∠SRT = ∠T + ∠T
m ∠SRT = 2 × ∠T
30° = 2 × ∠T
∠T = 30° /2
∠T = 15°
∴ m ∠RTW = 15°
Hence, we have proven that m ∠RTW = 15°
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A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 450 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.03 cents per square centimeter. The top will be made of glued paper, costing 0.08 cents per square centimeter. Find the dimensions for the package that will minimize production cost.
The dimensions of the microwave cup-of-soup package are:
Radius = 3.39cm, and Height = 9.27cm.
Computed using differentiation.
The microwave cup-of-soup package is in the shape of a cylinder.
Thus, its volume can be shown as, V = πr²h, where r is its radius in cm and h is its height in cm.
The volume is given to be 450 cm³.
Thus, we can say that,
πr²h = 450,
or, h = 450/(πr²) ... (i).
The cost of the microwaveable cup-of-soup package is given as:
The bottom is made of styrofoam at 0.03 cents/cm².
The area of the bottom = πr².
Therefore, the cost of the bottom = πr²(0.03) cents.
The side is made of styrofoam at the rate of 0.03 cents/cm².
The area of the side = 2πrh = 2πr{450/(πr²)}. {Taking h = 450/(πr²) from (i)}.
Therefore, the cost of the side = 2πr{450/(πr²)}(0.03) cents.
The top is made of glued paper at the rate of 0.08 cents/cm².
The area of the top = πr².
Therefore, the cost of the top = πr²(0.08) cents.
Therefore the total production cost function can be written as:
C = πr²(0.03) + 2πr{450/(πr²)}(0.03) + πr²(0.08) cents,
or, C = 0.03πr² + 0.08πr² + 27/r cents,
or, C = 0.11πr² + 27/r cents ... (ii).
We are asked to minimize the cost function.
To minimize it, we follow these steps:
Differentiating both sides in (ii) with respect to the radius,
dC/dr = 0.22πr - 27/r² ... (iii).
To get the points of inflections, we equate this to zero, to get,
dC/dr = 0.22πr - 27/r² = 0,
or, 0.22πr - 27/r² = 0,
or, 0.22πr = 27/r²,
or, r³ = 27/0.22π,
or, r = ∛(27/0.22π) = 3.393 cm.
To check whether the cost C, is minimum or maximum at the point, we calculate the second order differential, and if it's greater than 0, then we get a minimum and vice-versa.
Thus, differentiating both sides of (iii), with respect to the radius r, we get:
d²C/dr² = 0.22π + 54/r³.
0.22π + 54/r³ is greater than 0, for all values of r, since r is always greater than 0 {radius of an object cannot be negative}.
Thus, the radius at which the cost is minimized is 3.393 cm.
The corresponding height will be 450/(πr²) = 9.274 cm.
Thus, the dimensions of the microwave cup-of-soup package are:
Radius = 3.39cm, and Height = 9.27cm.
Computed using differentiation.
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PLEASE HELP QUICK!!
Question 1: About 80% of the packages on a delivery truck are internet orders. The driver delivered 644 packages that were internet orders. About how many total packages did the driver deliver that day?
Question 2: A librarian estimated that 60% of the books in the local library were fiction. She counted 8556 fiction books. About how many books are in the local library?
The total packages the driver delivered is 805.
The total number of books in the local library is 14,260.
What is the total packages delivered?Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred.
Total packages delivered = total number of internet orders / percentage of internet orders
644 / 80%
644 / 0.8 = 805
Total number of books = total number of fiction books / percentage of fiction books
8556 / 60%
8556 / 0.6 = 14,260
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3. Try It #3 Write the point-slope form of an equation of a line with a slope of -2 that passes through the point (-2,2). Then rewrite it in the slope-intercept form.
Answer:
Point-slope form of equation given as [tex]$y-2=-2(x+2)$[/tex].
Slope-intercept form of equation is given as [tex]$y=-2 x-2$[/tex].
Step-by-step explanation:
In the question, it is given that the slope of a line is -2 and it passes from (-2,2).
It is asked to write the point-slope form of the equation and rewrite it as slope-intercept form.
To do so, first find the values which are given in the question and put it in the formula of point-slope form. Simplify the equation to rewrite as slope-intercept form.
Step 1 of 2
Passing point of the line is (-2,2).
Hence, [tex]$x_{1}=-2$[/tex] and
[tex]$$y_{1}=2 \text {. }$$[/tex]
Also, the slope of the line is -2.
Hence, m=-2
Substitute the above values in point-slope form of equation given by [tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex]
[tex]$$\begin{aligned}&y-y_{1}=m\left(x-x_{1}\right) \\&y-2=-2(x-(-2) \\&y-2=-2(x+2)\end{aligned}$$[/tex]
Hence, point-slope form of equation given as y-2=-2(x+2).
Step 2 of 2
Solve y-2=-2(x+2) to write it as slope-intercept form given by y=mx+c.
[tex]$$\begin{aligned}&y-2=-2(x+2) \\&y-2=-2 x-4 \\&y=-2 x-4+2 \\&y=-2 x-2\end{aligned}$$[/tex]
Hence, slope-intercept form of equation is given as y=-2x-2.
how to convert whole number as fraction
To convert an integer to a fraction you must choose an expression that does not alter the numerical value. You can do this with multiples of the number, for example, for 100:
100/1 = 200/2 = 300/3 = 400/4 = 100
The numerical value is not altered and the result will always be 100
Another example, for 500:
500 = 500/1 = 1000/2 = 1500/3 = 2000/4
{ Pisces04 }Answer:
Step-by-step explanation:I actually depends on what your solving like if you are solving a question is says solving 16 times a random fraction, you just simply add one under 16. And it will make it 16/1
there are 4 people at a party. each person brings one gift for each other person . what is the total number of gifts at the party
Answer:
4 gifts
Step-by-step explanation:
4÷4=0
so you get each other a gift so there none to spare
Answer:
12 gifts
Step-by-step explanation:
If there are 4 people, and each person brings a gift for each of the other three people, that means that there are 12 gifts at the party. Let's say there are four people: A, B, C, and D. Person A would have to bring 3 gifts to give B, C, and D. Similarly, B would bring a gift each for A, C, D. C would bring a gift for A, B, D. Lastly, D would bring a gift for A, B, and C. Each person brings three gifts to give to the other three people at the party, and 3*4 people is 12. I hope that makes sense.
Greg walks 1/3 mile in 10 minutes
Answer:
Greg will walk 1 mile in 30 minutes, or 2 miles per hour.
Explanation:
Multiply the ratio of miles to minutes:
1/3 mi : 10 min
1 mi : 30 min
2 mi : 1 hr
Which property was applied to create this equivalent expression? 7 x (5 6 x) right-arrow (7 x 5) 6 x the commutative property only the associative property only the distributive property only both the commutative property and the associative property
Step-by-step explanation:
7×5×6×x
7×5×6×392
210×392
82320
The option (B) is correct. Associative property was applied to create the given expression.
Given expression is 7x+(5+6x) rightarrow (7x+5)+6x.
Firstly, check the given expression by commutative property.
The commutative property of addition is a+b=b+a and the commutative property of multiplication is a×b=b×a.
The commutative property didn't satisfy the given expression.
Now, check the given expression by associative property.
The associative property of addition is (a+b)+c=a+(b+c) and the commutative property of multiplication is (a×b)×c=a×(b×c).
The associative property of addition satisfy the given expression.
Further, check the given expression by distributive property.
The distributive property is a×(b+c)=ab+bc.
The distributive property didn't satisfy the given expression.
Hence, the given expression 7x+(5+6x) rightarrow (7x+5)+5x s created by the associative property.
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Please help me with Algebra 2 problems.
Answer:
[tex]5)\ \ \left( x^{8}y^{4}\right)^{\frac{1}{10} } +3\left( x^{\frac{1}{5}}y^{\frac{1}{10} \right)^4=4x^{\frac{4}{5}}y^{\frac{2}{5}}[/tex]
[tex]6)\ \ \frac{2\sqrt{9^{5}} +7\sqrt{9^{5}} }{\sqrt{9^{7}} }=1[/tex]
Step-by-step explanation:
[tex]\left( x^{8}y^{4}\right)^{\frac{1}{10} } +3\left( x^{\frac{1}{5}}y^{\frac{1}{10} \right)^4[/tex]
[tex]=x^{\frac{8}{10}}y^{\frac{4}{10}} +3x^{\frac{4}{5}}y^{\frac{4}{10} }[/tex]
[tex]=x^{\frac{4}{5}}y^{\frac{2}{5}} +3x^{\frac{4}{5}}y^{\frac{2}{5} }[/tex]
[tex]=x^{\frac{4}{5}}y^{\frac{2}{5}}\times(1+3)[/tex]
[tex]=4x^{\frac{4}{5}}y^{\frac{2}{5}}[/tex]
……………………………………
[tex]\frac{2\sqrt{9^{5}} +7\sqrt{9^{5}} }{\sqrt{9^{7}} }[/tex]
[tex]=\frac{(2+7) \times\sqrt{9^{5}} }{\sqrt{9^{2}} \times \sqrt{9^{5}} }[/tex]
[tex]=\frac{9 \times\sqrt{9^{5}} }{9 \times \sqrt{9^{5}} }[/tex]
[tex]=1[/tex]
The sum of ages Kate and Gift is 38 years now.What was the sum of their ages five years ago
Answer:
28
Step-by-step explanation:
Simple solution:
Each one was 5 years younger 5 years ago, so subtract 5 from 38 for each one.
38 - 5 - 5 = 28
The sum of their ages was 28.
Algebra solution:
Kate is x years old now.
Gift is y years old now.
The sum of their ages now is x + y.
The sum of their ages is 38, so x + y = 38.
5 years ago:
Kate was x - 5 years old.
Gift was y - 5 years old.
The sum of their ages 5 years ago was x - 5 + y - 5 = x + y - 10.
Substitute 38 for x + y.
The sum of their ages was 38 - 10 = 28
Assume that all conditions are met. The mean of the differences was 1. 33 and the standard deviation of those differences was 2. 90. What is the test statistic for this procedure?.
The test statistic for this procedure is using two sample T-test is 0.458.
Definition of Two Sample T-test
A variation of the Student's t-test used to determine if two sample means are substantially different is known as the two sample T-test (also known as Welch's t-test, Welch's adjusted T, or unequal variances t-test). The test's degrees of freedom have been changed, which generally boosts the test's power for samples with unequal variance.
T-Test Statistic for The Procedure
It is given that mean of the differences = 1.33
And, the standard deviation of the differences, standard error = 2.90
The test static formula is given as,
t = (estimate - hypothized value) / standard error
Here, t is the t- test statistic, and estimate is the mean of the differences.
Since it is given that all conditions are met, the hypothized value can be taken as 0
Substituting substituting estimate = 1.33 and standard error = 2.90 in the t-test statistic formula, we get,
t = (1.33-0)/2.90
or t = 0.458
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The graph below shows the solution set of a certain inequality. State one solution represented by the graph.
Answer:
(1,3)
Step-by-step explanation:
since they are open circles they will not have brackets instead they will have parentheses.
one answer for this number line (graph) is (1,3)
Select the correct answer.
This system of equations is shown on the graph:
2y - 4x = 6
y = 2x + 3
The equations are both the same with a slope of 2 and y-intercept of 3.
Solution to system of equationA line is the distance between two points. Given the equations below;
2y - 4x = 6
y = 2x + 3
___________
y - 2x = 3
y = 2x + 3
The equations are both the same with a slope of 2 and y-intercept of 3. The graph of the equation is plotted below.
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Given: x//y
w is a transversal of x and y.
Prove: ∠4 ≅ ∠5
3) Vertical angles are congruent.
4) Corresponding angles tehorem
5) Transitive property of congruence
20 POINTS!!! PLEASE HELP
Find the logarithm base 10 of each number:
10
Please show work. Thanks!!
The logarithm of 10 to base 10 is 1
How to determine the logarithm?The given parameters are:
Base = 10Number = 10So, the logarithm expression can be represented as:
[tex]\log_{10}10[/tex]
The law of logarithm states that:
[tex]\log_{x}x = 1[/tex]
The above means that;
When the base and the number are the same, the logarithm is 1
So, we have:
[tex]\log_{10}10 = 1[/tex]
Hence, the logarithmic value is 1
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Pls help me with my hw.
I'm having difficulty in adjusting bases.
find x, here e is natural logarithm.
Answer:
See below
Step-by-step explanation:
7 + 15 e^(1-3x) = 10 start by subtracting 7 from both sides
15 e^(1-3x) = 3 now divide both sides by 15
e ^(1-3x) = .2 now take the ln of both sides
1-3x = -1.6094379 subtract 1 from both sides
-3x = = 2.6094379 divide both sides by -3
x = .869813
Can someone help me out and show work please
The function is assigning to each element of one set exactly one element from the other set.
First table represent a function.
Second table not represent a function (for -1 are four different numbers).
Third table represent a function.
Fourth table not represent a function (for -6 are two differen numbers 5 and 9)
What is the polynomial function of lowest degree with lead coefficient 1 and roots 1 and 1 i?
Answer:
C
Step-by-step explanation:
on edge
two numbers add up to 30, and one of them is greater than the other by 8. what are these numbers?
Answer:
11 and 19
Step-by-step explanation:
X + (X+8) = 30
Open bracket
X plus X + 8 = 30
2x + 8= 30
Collect like terms
2x = 30 - 8
2x = 22
X=11
And x + 8 = 11 + 8= 19
I need someone to solve this
The value of ? and X are 12 and 24 respectively
Similarity theorem of a triangleA triangles is 2D shape with three sides and angles.
From the given diagram, the ratio of similar sides is equal to a constant as shown;
15/20 = 9+15/20+x
Cross multiply
15/9+15 = 20/20+x
15/24 = 20/20+x
Comparing with the given ratio
? = 24
X = 20+x
Find x
15(20+x) = 480
300 + 15x = 480
15x = 180
x =12
Fro the given expression
x/32 = 9/?
12/32 = 9/?
12 ? = 32 * 9
? = 24
Hence the value of ?and x from the given diagram is 12 and 24 respectively
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Let a=3/5 and let b=2/3. Compute a^2b^-3.
Answer: 81/100
Step-by-step explanation:
I don't guarantee you I am right but..
first, solve for the exponents after substituting the numbers in
3/5 x 3/5 is 9/25
since b's exponent is negative, you change the fraction into its reciprocal and then do it with the exponent but positive
2/3^-3 to 3/2^3 and 3/2 x 3/2 is 9/4
then you mutiply both numbers to get 9/4 x 9/25 is 81/100