Use the diagram below for questions 15-17.
15. If m/1 = (7x-19), and m/2 = (x + 5)°, find m/2.
16. If m/1 = (6x + 25)°, and m/4= (10x - 11)°, find m/1.
17. If m/4= (3x + 7)°, and m25= (9x - 43)°, find m/UPS
18. If ZW and ZV are supplementary angles and m/V = 49°, find m/W.
S
19. If 21 and 22 are vertical angles, <2 and <3 are complementary angles,
and m/3 = 56°, find m/1.
20. If 21 and 22 form a linear pair and m/1 is 18 degrees less than fives
times the measure of 22, find m/1.
Gina Wilson (All Things
Answers
The angle measures for this problem are given as follows:
15. m<2 = 18º.
16. m<1 = 79º.
17. m<UPS = 151º.
18. m<W = 131º.
19. m<1 = 34º.
20. m<1 = 147º.
Item 15Using the angle addition postulate, we have that an angle of 90º is split into two angles, angle 1 and angle 2, hence:
m<1 + m<2 = 90º.
We use this equation to solve for x as follows:
7x - 19 + x + 5 = 90
8x - 14 = 90
8x = 104
x = 104/8
x = 13º.
Hence the measure of angle 2 is given as follows:
m<2 = x + 15 = 18º.
Item 161 and 4 are vertical angles, meaning that they are congruent, hence we can solve for x as follows:
6x + 25 = 10x - 11
4x = 36
x = 9º.
Hence the measure of angle 1 is given as follows:
m<1 = 6(9) + 25 = 79º.
Item 17Angles 4 and 5 are supplementary, meaning that the sum of their measures is of 180º, hence we solve for x as follows:
3x + 7 + 9x - 43 = 180
12x = 216
x = 216/12
x = 18.
The measure of angle UPS is:
m<UPS = m<4 + 90º = 3(18) + 7 + 90 = 151º.
Item 18From the explanation of supplementary angles in item 17, we have that:
m<W + 49º = 180º
m<W = 131º.
Item 19Complementary angles are angles whose sum of the measures is of 90º, hence:
m<2 + m<3 = 90º
m<2 + 56 = 90
m<2 = 34º.
Vertical angles are congruent, hence:
m<2 = m<1 = 34º.
Item 20The measures of the angles are:
m<1 = 5x - 18.m<2 = x.Angles that form a linear pair are supplementary, hence:
m<1 + m<2 = 180
5x - 18 + x = 180
6x = 198
x = 198/6
x = 33.
Then the measure of angle 1 is given by:
m<1 = 5(33) - 18 = 147º.
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Related Questions
Choose the expression that is equivalent to (6^-3/3^-2x6^2)to the 3rd
Answers
The required expression that is equivalent to (6^-3/3^-2x6^2) to the 3rd power is 3^3/2^3.
What is an expression?An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
Now the given expression is,
(6^-3/3^-2x6^2)to the 3rd power
or, we can write
(6^-3/3^-2x6^2)^3
Since, a^-1 = /a
Therefore we have
6^-3 = 1/6^3
3^-2 = 1/3^2
Therefore we get,
{(1/6^3)/(1/3^2) x 6^2}^3
Simplifying we get
{(3^2/6^3) x 6^2}^3
or, {(3^2 x 6^2)/6^3}^3
Solving we get
(3^2/6)^3
Now since,
3^2 = 9
Put in expression we get
(9/6)^3
or, (3/2)^3
therefore we get,
3^3/2^3
this is the required expression that is equivalent.
Thus, the required expression that is equivalent to (6^-3/3^-2x6^2) to the 3rd power is 3^3/2^3.
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PLEASE HELP ASAP!!!
Answers
Answer: y = x + 4.
Reason: -2 + 4 = 2 and -1 + 4 = 3 so, any equation added with 4 would be y or x + 4 = y.
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Can someone please describe the domain and range in these sets?
Answers
Answer:
a.
D=[-6,4)
R=(-3,4]
b.
D=[-6,7)
R=[-1,6)
Step-by-step explanation:
[,] <-- used for when the point is included in the answer (closed circle or greater than/less than or equal to sign)
(,) <-- used for when the answer does not include point (open circle or greater than/less than sign not equal to)
Plug in the points where shown on each line.
Hey again! Just answered your last domain and range question so I hope I helped again!
Use a table to solve each equation. Round to the nearest hundredth.
6²x=10
Answers
[tex]6^{2x} = 10[/tex] => x = 0.642, by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Given: [tex]6^{2x} = 10[/tex]
Taking logarithm on both sides:
=> log ([tex]6^{2x}[/tex]) = log 10
=> 2x (log 6) = log 10 ( as [tex]log_b(a)^m = m (log_b(a))[/tex])
=> 2x = [tex]\frac{log10}{log6}[/tex]
=> 2x = [tex]\frac{1}{0.778}[/tex]
=> 2x = 1.285
=> x = 0.642
Hence, [tex]6^{2x} = 10[/tex] => x = 0.642, by properties of logarithm.
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The velocity v of an object dropped from a tall building is given by the formula v=√64d , where d is the distance the object has dropped. Solve the formula for d .
Answers
The distance, d = v²/64.
Let 'v' denote the velocity of an object dropped from a tall building.
Let 'd' be the distance the object has dropped.
Given that the relation between v and d is, v =√(64d)
This equation gives 'v' in terms of 'd'.
We need to solve this formula for d.
For this, consider v =√(64d)
We square on both sides to get rid of the square root.
⇒ v² = 64d
Now isolating d to one side of the equation,
⇒ d = v²/64 is the formula for d
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Simplify each expression.
3¹/₄+27¹/₄
Answers
The expression has to be written in it's prime factor form. 27 = 3x3x3 = 3^3 in index form. 3=3^1 . By power rule (a^m)^n = a^mn.
(3^1)^1/4+(3^3)^1/4
3^1/4 + (3^2x3^1)^1/4
3^1/4+3^2/4x3^1/4
3^1/4(1+3^1/2)
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Pls help me urgently with all the questions!!! It's really important! Its all attached!!
Answers
The radius of the new parking area is 71cm. (option b)
The liters of sporting drinks they have with them is 30 liters (option d).
What is the area of the new parking area?A circle is a bounded figure which points from its center to its circumference is equidistant. The area of a circle is the area that is bounded in a circle.
Area of a circle = πr²
Where :
π = pi = 22/7R = radius22/7 x 123² = 47,548.286 m²
When the parking area is reduced by 1/3. its new area is: 1/3 x 47,548.286 m² = 15,849.429 m²
The radius of the reduced parking lot:√ (7/22 x 15,849.429 m²) = 71m
How many liters of sports drink do they have with them?The first step is to determine the volume of one of the packages.
Volume of a rectangular prism = length x width x height
6 x 4 x 10.5 = 252 cm³
Now, the volume of the 120 packs of sports drinks have to be determined:
120 x 252 cm³ = 30,240cm³
The last step is to convert cm to liters
1 cm = 1 /1000 liters
30,240 / 1000 = 30 liters
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Aya bought a pair of shoes that was on sale for $30 off. The original price of the shoes was $75. Find the sale price.
Answers
Suppose that x and y vary inversely. Write a function that models each inverse variation and find y when x=-5 . x=12 when y=4
Answers
Using inverse variation, the function model will be y = 48. 1/x and the value of y at x = -5 will be -48/5
What precisely is the inverse of a function?Those with inverse properties cancel each other out. In other words, f(g(x)) = g(f(x)) = x if g(x) is f's inverse (x). We have a great approach we can use to achieve this given an equation for which we desire the inverse.
Not every action has an equivalent. It is obvious that f(x) will never again have the same value if it has an inverse. We designate a unique name for this resource.
Inverse variation is y = k. 1/x
given y = 4
x = 12
So, 4 = k. 1/12
So, the value of k = 48
We can conclude that the value of constant variation is 48
when x = -5, the value of y will be -
y = k.1/x
y = 48 . 1/-5
y = -48/5
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What is the arithmetic mean between 5 and 19
Answers
Answer:
the arithmatic mean of 5 and 19 is: 5,7,9,11,13,15,17,19.
Step-by-step explanation:
hope this helps
In triangle RST, m∠R > m∠S + m∠T. Which must be true of triangle RST? Check all that apply.
m∠R > 90°
m∠S + m∠T < 90°
m∠S = m∠T
m∠R > m∠T
m∠R > m∠S
m∠S > m∠T
Answers
The statements which must be true of triangle RST are;
m∠R > 90°m∠S + m∠T < 90°m∠R > m∠Tm∠R > m∠SWhich must be true of triangle RST?According to the stated premises;
m∠R > m∠S + m∠T
This in turn means that the angle measure of ∠R > angle measure of ∠S and ∠T.
Therefore, we can conclude that; m∠R > 90° and m∠S + m∠T < 90°
As such, certainly, m∠R > m∠T and m∠R > m∠S
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Find the distance from point A(−14, 5) to the line −x+2y = 14. Round your answer to the nearest tenth.
Answers
Approximately 1.7 units separate A(-1/4, 5) from the line -x + 2y = 14.
The perpendicular line to a point is the path that travels the shortest distance between them.
The equation for the indicated line is -x + 2y = 14, which can be expressed as the following in slope and intercept form:
-x + 2·y = 142·y = 14 + xy = 14/2 + x/2 = x/2 + 7y = x/2 + 7The y-intercept is 7, and the slope, m1, is 1/2.
As a result, the slope, m2, of the line perpendicular to the line y = x/2 + 7 (y = -x + 2y = 14) is m2 = -1/m1 = -1/(1/2) = -2.As a result, we know that the line from A(-1/4, 5) to the line -x + 2y = 14 has a slope of -2.Consequently, the line's equation is:
y - 5 = -2(x - (-1/4))y - 5 = -2·x - 1/2y = -2·x - 1/2 + 5 = -2·x + 9/2y = -2·x + 9/2Therefore, the coordinates of the point on line A(-1/4, 5) that coincides with the perpendicular from the line -x + 2y = 14 (y = x/2 + 7) are as follows:
-2·x + 9/2 = x/2 + 79/2 - 7= x/2 + 2·x-2.5 = 2.5·xx = -2.5/2.5 = -1x = -1y = x/2 + 7 = -1/2 + 7 = 6.5y = 6.5The location on the line -x + 2y = 14 (y = x/2 + 7) that is perpendicular to the point A(-1/4, 5) has the coordinates: (-1, 6.5)
The following formula is used to calculate the distance between points A and B:
[tex]l=\sqrt{\left(y_2-y_1\right)^2+\left(x_2-x_1\right)^2}[/tex]Where: (x₁, y₁) = (-1/4, 5), and (x₂, y₂) = B(-1, 6.5)
Using the values as plug-ins, we have;
[tex]\begin{aligned}&I_{A B}=\sqrt{(6.5-5)^2+((-1)-(-1 / 4))^2}=\sqrt{(-0.75)^2+(1.5)^2}=\sqrt{\frac{45}{16}}=\frac{3}{4} \cdot \sqrt{5} \\&l_{A B}=\frac{3}{4} \cdot \sqrt{5} \approx 1.677\end{aligned}[/tex]
Therefore, approximately 1.7 units separate A(-1/4, 5) from the line -x + 2y = 14.
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Solve the formula for the indicated varible.
G= h-p/f for h
Answers
Answer:
[tex]h = G + \frac pf[/tex]
Step-by-step explanation:
[tex]G = h - \frac pf \text{ / Add }\frac pf \text{ to both sides}\\\\G + \frac pf = h - \frac pf + \frac pf\\\\G + \frac pf = h[/tex]
Simplify each expression.
ln e⁸³
Answers
ln e⁸³ = 83, by definition and properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Now,
As seen by the definition of logarithms, [tex]log_b(a)=x[/tex]In case of natural logarithm, b = e, i.e., [tex]log_e(a)=x[/tex] = ln (a) = xIn the question, ln (e)⁸³, a = e
By property of logarithms, [tex]log_b(a)^{m}=m(log_b(a))[/tex],
=> 83 (ln (e)) = 83 [tex]log_e(e)[/tex]
Since, [tex]log_e(e)[/tex] = 1, ln (e)⁸³ = 83 (1) = 83.
Hence, ln e⁸³ = 83, by definition and properties of logarithm.
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In figures, ____ matching marks show that line segments have the same length. (Fill in the blank)
Answers
Answer:
hatch
Step-by-step explanation:
the hatch marks on the triangle represent the same length
if a side has one hatch mark it has the same length as the other side with one hatch mask
the same goes for the one with two hatch marks
Mr. Smith's water bill for this month is $5988, how many units does he use if the cost per unit is $41? (show working)
Answers
5988 divided by 41.
Nicole and Kiri are evaluating the conditional If 15 is a prime number, then 20 is divisible by 4. Both think that the conditional is true, but their reasoning differs. Is either of them correct? Explain.
Answers
Neither of Nicole and Kiri are correct that evaluating the conditional If 15 is a prime number, then 20 is divisible by 4.
Nicole reasoning is incorrect because despite the fact that 20 is divisible by 4, it does not mean the conditional is true. The conditional states that “15 is a prime number”- this is incorrect. Because this is incorrect the validity of the conclusion does not justify the validity of the hypothesis. Kiri’s reasoning is inaccurate despite the fact that his explanation of the hypothesis is correct, the hypothesis has no direct implication on the conclusion.
Hence, their belief that the conditional is true are both wrong. A conditional is only true if the premise for that conditional is first true in itself and also directly affects the conclusion.
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. The perimeter of a rectangular pool is 74 feet. The width
is 9 feet shorter than the length. What is the length and
width of the pool?
Answers
Answer: the length is 23 feet the width is 14 feet
Step-by-step explanation:
Let the length is x feet
Hence, the width is (x-9) feet
The perimeter of a rectangular pool is:
P=(2)(x+(x-9))
74=(2)*(2x-9)
74=(2)(2x)-(2)(9)
74=4x-18
74+18=4x-18+18
92=4x
(4)(23)=(4)(x)
Divide both parts of the equation by 4:
23 feet=x
23-9=x-9
14 feet=x-9
Multiply and simplify. √5 x³ . √40 x y⁷
Answers
On simplifying the expression √5 x³ . √40 x y⁷ we get 10√2 x⁴y⁷
How do we multiply numbers?Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The components in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the result is the number 54.
Given,
√5 x³ . √40 x y⁷
⇒ √5 × √40 × x⁴ × y⁷
⇒ √200 × x⁴y⁷
⇒ 10√2 x⁴y⁷
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Twelve boxes each containing 8 packets of sweets is redistributed into 4 larger boxes. How many packets are there in each of the larger boxes if the sweets were evenly distributed?
Answers
Answer:
24
Step-by-step explanation:
8 * 12 = 96
96 / 4 = 24
Have a great night! :D
Hope this helps.
Factor each expression. 2 x²-19 x+24
Answers
The factors of 2 x²-19 x+24 are x = 3/2 and x = 8
What is Factorization?Factorization in mathematics is the process of dividing a large number into smaller ones that, when multiplied together, give you the original number. Factorization is the division of a number into its factors or divisors. The factorization of the integer 12, for instance, may appear as 3 times 4.
Given,
2 x²-19 x+24
By factorization,
⇒ 2x² - 16 x - 3x + 24
⇒ 2x (x-8) - 3 (x - 8)
⇒ (2x - 3) (x-8)
⇒ x = 3/2 and x = 8
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Solve the equation −128 = 4x for x.
Answers
The solution for x in the equation -128 = 4x is -32
The collection of values used to replace the unknowns in an equation to make it true is known as the solution. Two fundamental algebraic laws, the additive property and the multiplicative property, are utilized to find the solutions to equations with a single unknown raised to a single power.
Given that,
The equation: -128 = 4x
We have to find x:
That is:
-128 = 4x
x = ( -128 / 4 )
x = -32.
Therefore, the solution for the given equation -128 = 4x is -32.
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Mannn can someone help me please
Answers
5. 8
6. 5
hope this helps ♡
What is the difference between −125 and 18?
Answers
Please help me please help me I’m being timed
Answers
Answer:
use an app for it.
which expressions is equivilant too 0.7590.753
Answers
The equivalent expression of the expression given as 0.75/9 * 0.75/3 is 1/48
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the equivalent expression?The expression is given as
0.75/9 * 0.75/3
Evaluate the product of the numerators
So, we have
0.75/9 * 0.75/3 = 0.5625/9 * 1/3
Evaluate the product of the denominators
So, we have
0.75/9 * 0.75/3 = 0.5625/27
Simplify the fraction
So, we have
0.75/9 * 0.75/3 = 0.0625/3
Further simplify
So, we have
0.75/9 * 0.75/3 = 625/30000
Further simplify
So, we have
0.75/9 * 0.75/3 = 1/48
Hence, the equivalent expression of the expression given as 0.75/9 * 0.75/3 is 1/48
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Find the new given amount given the original amount and the percent of change
$7; 20% increase
The new amount is $ __
Answers
Answer:
8.4
Step-by-step explanation:
7 x .2 is the increase 1.4
Add 1.4 to 7 to get 8.4
Each pair of values is from an inverse variation. Find the missing value. (x, 12),(4,1.5)
Answers
The missing value of inverse variation is 0.5
What is inverse variation ?The inverse variation property states that , whenever the product of values of two quantities is a constant value then there is opposite variation between these two corresponding values. Or we can also say that if the productive nature of two corresponding values is constant, then one quantity is inversely varies with second quantity.
Let say if x and y are two values and k is a constant value, then
According to inverse variation
k = xy or y = k/x
In the given question,
Take the order pair (4,1.5)
As it is an inverse variation, we can substitute it
y=k/x
1.5=k/4
K=6
Now find the inverse variation equation
y=k/x
Also, k=6
Solve this equation for the second pair (x,12)
As, y=6/x
x = 6/12 = 1/2 = 0.5
Therefore, missing value is 0.5
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when you add 2+2 is it fish?
Answers
Answer:
So when you add 2 plus to it equals 2 adrew tates kissing.
Step-by-step explanation:
Solve each equation. Check your answers.
log 2 x=-1
Answers
log (2x) = -1 => x = 0.05, by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Given: log (2x) = -1
Raising both sides to 10, in order to remove the logarithm:
=> [tex]10^{log_{10}(2x)} = 10^{-1}[/tex]
=> 2x = [tex]\frac{1}{10}[/tex] ( as [tex]a^{log_a(x)} = x[/tex])
=> x = [tex]\frac{1}{20} =[/tex] 0.05
Hence, log (2x) = -1 => x = 0.05, by properties of logarithm.
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