Answers
Step-by-step explanation:
due to the principle of identical angles on parallel lines when intersected by an inclined line, x is equal to the angle at B on the other side of AB.
in other words it is the supplementary angle to 150° at B.
that means together they are 180°. that is because the sum of all angles around a single point on one side of a line is 180° (because that line can be seen as the diameter of a circle, the point as the center of that circle, and one side of the diameter is a half-circle, which represents 180°).
so,
x = 180 - 150 = 30°
now, for the same principle,
x + y = 70
y = 70 - x = 70 - 30 = 40°
Related Questions
6x - 5y = 8
-12x + 2y = 0
Answers
Answer:
the answer is in picture
Step-by-step explanation:
hope it will help you
What is the value of x in the equation 1/5x-2/3y = 30, when y = 15?
Answers
Answer:
x = 200
Step-by-step explanation:
Given equation:
[tex]\sf \dfrac{1}{5}x-\dfrac{2}{3}y=30[/tex]
Steps:
1. Substitute 15 as the value of y in the equation:
[tex]\sf \dfrac{1}{5}x-\dfrac{2}{3}(15)=30\ \textsf{[ multiply ]}\\\\\Rightarrow \dfrac{1}{5}x-\dfrac{30}{3}=30\ \textsf{[ simplify ]}\\\\\Rightarrow \dfrac{1}{5}x-10=30[/tex]
2. Add 10 to both sides:
[tex]\sf \dfrac{1}{5}x-10+10=30+10\\\\\Rightarrow \dfrac{1}{5}x=40[/tex]
3. Multiply both sides by 5 to isolate x:
[tex]\sf 5\left(\dfrac{1}{5}\right)x=5(40)\\\\\Rightarrow x=200[/tex]
4. Check your work:
[tex]\sf \dfrac{1}{5}x-\dfrac{2}{3}y=30\ \textsf{[ substitute 200 for x, and 15 for y ]}\\\\\dfrac{1}{5}(200)-\dfrac{2}{3}(15)=30\ \textsf{[ multiply ]}\\\\\dfrac{200}{5}-\dfrac{30}{3}=30\ \textsf{[ divide ]}\\\\40-10=30\ \textsf{[ subtract ]}\\\\30=30\ \checkmark[/tex]
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Hey there!
Answer :[tex] \boxed{\bold{\green{ x = 200}}} [/tex]
[tex] \\ [/tex]
Explanation:Given expression :
[tex] \sf{ \frac{1}{5} \green{x} - \frac{2}{3} \orange{y} = 30 } [/tex]
1) Substitue 15 for [tex] \sf{\orange{y}} [/tex] :
[tex] \sf{ \frac{1}{5} \green{x} - \frac{2}{3} \orange{ \times 15} = 30 } \\ \\ \implies\sf{ \frac{1}{5} \green{x} - \frac{30}{3} = 30 } \\ \\ \implies\sf{ \frac{1}{5} \green{x} - 10= 30 } [/tex]
[tex] \\ [/tex]
2) Solve for x :
[tex]\sf{ \frac{1}{5} \green{x} - 10= 30 } [/tex]
⇢Add 10 to both sides of the equation :
[tex]\sf{ \frac{1}{5} \green{x} - 10 \: \bold{+ \: 10}= 30 \: \bold{+ \: 10 }} \\ \\ \implies \sf{\frac{1}{5} \green{x} \: = 40 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
⇢Multiply both sides of the equation by 5:
[tex] \Big( \dfrac{1}{5} \green{x}\Big) \: \bold{ \times \: 5}=40 \: \bold{ \times \: 5} \\ \\ \implies \sf{\dfrac{5}{5} \green{x} \: = 200} \\ \\ \implies \green{ \boxed{\sf{x = 200}}}[/tex]
[tex] \\ [/tex]
3) Let's check our answer by replacing [tex] \green{x} [/tex] with 200 and [tex] \orange{y} [/tex] with 15 :
[tex] \sf{\dfrac{1}{5}\overbrace{\green{\times \: 200}}^{\green{x}} - \dfrac{2}{3}\underbrace{\orange{\times \:15}}_{\orange{y}}= \dfrac{200}{5} - \dfrac{30}{30} = 40 - 10 = \boxed{ 30} } [/tex]
[tex] \\ \\ [/tex]
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Charlotte recorded the number of minutes she spent exercising in the past ten days: 12, 4, 5, 6, 8, 7, 9, 8, 2, 1. Find the median of the data.
Answers
Answer:
6.5
Step-by-step explanation:
Median is always the middle number of the set of data, so lets re order the numbers least to greatest
1,2,4,5,6,7,8,8,9,12
Since there's an even amount there wont be an exact middle number, however we know its in-between 6 and 7. So we can do 6+7 = 13 and then 13/2 = 6.5 to get the middle number or median.
A timer is started and a few moments later a swimmer dives into the water and then comes back up. The swimmer's depth (in feet) as a function of time (in seconds after the timer was started) is given by the equation h(t)=t2−12t+27
Rewrite the formula in factored form and select each true statement below.
The swimmer dives into the water 3 seconds after the timer was started.
The swimmer comes back up 9 seconds after the timer was started.
The swimmer is underwater for 12 seconds.
The swimmer dives into the water 12 seconds after the timer was started.
The swimmer dives to a maximum depth of 27 feet.
Answers
The correct true statement is: b. The swimmer comes back up 9 seconds after the timer was started.
The swimmer's maximum depth (in feet)Given:
h(t)=t^2−12t+27
Let velocity of the function= 0
h(t) = 2t - 12
0 = 2t - 12
2t = 12
Divide both side by 2t
t=12/2
t = 6secs
Substitution
h(6) = 6²-12(6)+27
h(6) = 36 - 72 + 27
h(6) = -36 + 27
h(6) = -9 feet
The correct statement is b.
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This graph talks about supply and demand can I get some help with it?
Answers
well that's Economics not Mathematics
5 feet to 31 inches write the ratio of the first measurement to the second measurement compare in inches
Answers
Answer:
60:31
Step-by-step explanation:
Suzie's Slushes has increasing profits each week during the hot summer months. Suzie finds that each week during the summer her profits increase by 30% over what they were the previous week. In her first week of business, her profits were $300. How much money will she make in all over 4 weeks
Answers
The amount of money that Suzie will make over the four weeks is; $1856
How to find amount of profit made?
Suzie will make a profit of:
The first week = $300
The second week = (300 * 30%) + 300 = $390
The third week = 390 * (1430%) = $507
The fourth week: 507 × (1430%) = $659.1
Thus, Sum of profit = $300 + $390 + $507 + $659.1
Sum of Profit = $1856.1 ≈ $1856
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asap need help quick
Answers
Answer:
Answer:11
Step-by-Step Answer:
When we multiply 11 with 1\2 then thier answer will be 11\2
ACTIVITY #1
Try It!
A. Write the definition, property, postulate or theorem that will prove each of the given statements.
Answers
What completes the proof are:
1. LC ≅ CU; CU ≅ UK
2. Given
3. Unequal angle theorem (Aa → Ss)
What is the Unequal Angle Theorem?The unequal angle theorem states that the longer side of a triangle will always be directly opposite the largest angle measure. This implies that, if an angle that is opposite a side is greater than another another, the side it is opposite will also be longer than the side opposite the other angle (Aa → Ss).
From the image given, statement 1 was given as well as statement 2.
Statement 1 would be: LC ≅ CU; CU ≅ UK.
The reason for statement 2 will also be "given".
Then, UL > CK using the unequal angle theorem (Aa → Ss).
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A ser of esta consists of four scores…
Answers
Answer:
x4 = 8
Step-by-step explanation:
To find the mean, add the values and divide by the number of values.
mean = (x1 + x2 + x3 + x4)/4
(3 + 12 + 7 + x4)/4 = 8
x4 + 22 = 32
x4 = 10
Answer:
x4 = 8
Step-by-step explanation:
Find Measure of angle B (m18. a = 7 m, b = 5 m, m∠A = 45°
Answers
Answer:
30.34 degree
Step-by-step explanation:
Apply sine formula
[tex]\frac{sin\left(A\right)}{a}=\frac{sin\left(B\right)}{b}[/tex]
[tex]\frac{\sin \left(45^{\circ \:}\right)}{7}=\frac{\sin \left(b\right)}{5}[/tex]
->simplify
[tex]\frac{\sin \left(b\right)}{5}=\frac{\frac{\sqrt{2}}{2}}{7}[/tex]
you will get
[tex]\sin \left(b\right)=\frac{5\sqrt{2}}{14}[/tex]
which
sin b is about 0.50507
[tex]sin^{-1}\left(0.50507\right)[/tex]
->arc sine in degree mode
the answer is 30.34
WILL GIVE 100 POINTS PLS HELP RN EVEN IF ITS JUST A FEW
In order to determine the best fit undergraduate program, a high school senior researches the majors offered at the universities he is considering for admissions. The internet search reports that Arizona State University lists nine of their most popular majors and the percent of student population enrolled in the programs.
Popular Majors Percent of Student Body
Biology 8%
Business Marketing 20%
Communications/Journali 6%
Education 5%
Engineering 7%
Interdisciplinary Studies 6%
Psychology 6%
Social Sciences 10%
Visual and Performing Arts 8%
The university’s enrollment is expected to reach at least 20,000 students for the fall semester.
1. The minimum number of students who are expected to be working towards a Social Sciences degree is ???
2. The university requires that any student who is studying Visual and Performing Arts or Communications Journalism must perform in one of the student productions before graduation. At least ??? of the 20,000 students will be performing in the university’s student productions before graduation.
3.
In the fall semester, ???% of the student population will be enrolled in a degree program not listed as one of the university’s most popular.
The most popular degree offered at Arizona State University is ???
4. The most popular degree offered at Arizona State University is ???
5. For the fall semester, the university should expect that ??? students will enroll in one of the two most popular degree programs.
Answers
1. 20,000×10%=2,000
2. 20,000×14%=2,800
3. 20,000×5%=1,000
4. Business Marketing
5. 20,000×30%=6,000
(c) If f(x) = a^x , then show that f(m +n + p) = f(m). f(x). f(p)
Answers
[tex]\text{Given that,}~\\\\f(x) =a^x\\\\\text{L.H.S}\\\\=f(m+n+p)\\\\=a^{m+n+p}\\\\\text{R.H.S}\\\\=f(m) \cdot f(n) \cdot f(p)\\\\=a^m \cdot a^n \cdot a^p\\\\=a^{m+n+p}\\\\ \text{L.H.S} = \text{R.H.S}\\\\\text{Proved.}[/tex]
the radius of the bigger circle is 9cm and the area of the shaded region is twice that of the smaller circle then how long is the radius of the smaller circle ?
Answers
Given the dimensions of the composite figure, formed by two concentric circles, we conclude that the radius of the smaller circle is approximately 3.728 centimeters.
How to determine the radius of the smaller circle
In this situation we have a composite figure formed by two concentric circles, whose area ratio is presented below, in which the area is directly proportional to the square of radius:
[tex]\frac{A'}{A} = \frac{(R-r)^{2}}{r^{2}}[/tex]
2 · r² = (9-r)²
2 · r² = 81 - 18 · r + r²
r² + 18 · r - 81 = 0
The roots of the second order polynomial are r₁ = -9 + 9√2 and r₂ = -9 - 9√2. As radius is a non-negative number, the only root that is reasonable is r₁ = -9 + 9√2 (r₁ ≈ 3.728).
Given the dimensions of the composite figure, formed by two concentric circles, we conclude that the radius of the smaller circle is approximately 3.728 centimeters.
Remark
The image is missing and is thus included in the figure attached below.
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The equation of line A is y = 5 - 2x Line B is parallel to line A. Line B passes through the point (-3,7)
Work out the coordinates of the point where line B intersects the x-axis.
Answers
Answer:
The answer is (0.5, 0)
Step-by-step explanation:
Find the midpoint of the line segment with end coordinates of:
(-4,-4) and (-4,-8)
Answers
Answer:
(-4, -6)
Step-by-step explanation:
(x,y) = ((x1+x2)/2 , (y1+y2)/2)
[substitute the values given]
(x,y) = ((-4+-4)/2 , (-4+-8)/2)
[solve]
(x,y) = (-8/2 , -12/2)
[simplify]
(x,y) = (-4, -6)
THE ANSWER IS (-4, -6) HOPE IT HALP'S MARK IT AS BRAILY.
pls help me answer thiss. I really really need help! thank u
Answers
Answer:
see explanation
Step-by-step explanation:
the centroid is where the medians intersect.
On each median the distance from the vertex to the centroid is twice as long as the distance from the centroid to the midpoint.
(3)
GF = [tex]\frac{1}{2}[/tex] CG = [tex]\frac{1}{2}[/tex] × 14 = 7
CF = CG + GF = 14 + 7 = 21
(4)
GD = [tex]\frac{1}{3}[/tex] AD = [tex]\frac{1}{3}[/tex] × 45 = 15
AG = 2 × GD = 2 × 15 = 30
(5)
GE = 2 × BG , that is
9x = 2(3x + 6) = 6x + 12 ( subtract 6x from both sides )
3x = 12 ( divide both sides by 3 )
x = 4
A comparson of two or more quantities of the same kind is called a
Answers
It’s known as a ratio
This chart shows the result of an experiment conducted to see the effect of different brands of fertilizers on the growth of a bean plant.
Which of the following ranges would be appropriate to use in order to represent the numerical data in centimeters on the vertical axis of a Line Graph?
A. 0.0 to 26.0
B. 0.0 to 25.0
C. 14.0 to 25.2
D. 0.0 to 20.0
Answers
The range that is appropriate to use to represent the numerical data is 0.0 to 26.0.
What is a line graph?
A line graph is a graph that is used to represent numerical data. It shows the changes in the data with the passage of time. There are two axes on a line graph, the vertical axis and the horizontal axis. The range of the vertical axis should start from 0 and end at the largest number of data set.
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Pre Calc question, thanks for the help! Question linked in photo below.
Answers
The valid solution for the positive demand is (6,3)
How to determine the valid solutions?The equation of the function is given as:
[tex]C(t) = -\sqrt{t^2 - 4t - 12} + 3[/tex]
Next, we test the options::
Option (a): (t, C(t)) = (2,3)
This gives
[tex]-\sqrt{2^2 - 4*2 - 12} + 3 = 3[/tex]
Evaluate the radicand
[tex]-\sqrt{-16} + 3 = 3[/tex] ---- this is not true (square root of -16 is a complex number)
Option (b): (t, C(t)) = (6,3)
This gives
[tex]-\sqrt{6^2 - 4*6 - 12} + 3 = 3[/tex]
Evaluate the radicand
[tex]-\sqrt{0} + 3 = 3[/tex]
Evaluate the root
0 + 3 = 3
Evaluate the sum
3 = 3 ---- this is true
Hence, the valid solution for the positive demand is (6,3)
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(3x+43)^((2)/(3))+22=38
Answers
Answer:
X = 7 and -35.6666
Step-by-step explanation:
Which number produces a rational answer when added to 0.85
Answers
The number that produces a rational answer when added to 0.85 is; 193/180
How to identify rational numbers?A rational number is an algebraic term expressed as a fraction. The fraction can also be in decimals but only if the decimal places are not repeating or not infinitely long. If they aren't, then these are called irrational numbers.
Now, let us convert 0.85 to a fraction. Thus;
0.85 = 85/100 = 17/20
From the given options, the only one that when added to 0.85 will yield a rational number is 2/9. This is because;
17/20 + 2/9 = 193/180
193/180 is a rational number.
The missing options are;
A. 2/9
B. 0.2645751311...
C. √2
D.
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What is startfraction 3 pi over 4 endfraction radians converted to degrees? if necessary, round your answer to the nearest degree.
Answers
Unit conversion is a way of converting some common units into another without changing their real value. The value of (3π/4) radian converted to a degree is 135°.
What is unit conversion?Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimeter is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.
Since π radian is equal to 180°. Therefore, the value of (3π/4) radian is equal to,
1 radian = 180°/π
(3π/4) radian = (3π/4) × (180°/π) = 135°
Hence, the value of (3π/4) radian converted to a degree is 135°.
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Answer:
option 2
Step-by-step explanation:
If $3840 is deposited into a bank account at a 5% interest rate how long will it take the account to make $960 in interest?
Answers
assuming is simple interest
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$960\\ P=\textit{original amount deposited}\dotfill & \$3840\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years \end{cases} \\\\\\ 960 = (3840)(0.05)(t)\implies \cfrac{960}{(3840)(0.05)}=t\implies 5=t[/tex]
Solve for the h in the triangle below. Round to the nearest tenth. 90⁰ 6.0 Oh-13.3 Oh 5.5 Oh 8.0 53%
Answers
Answer:
h=8.0
Step-by-step explanation:
law of sines
sinA/a=sinB/b
b/a=sinB/sinA
b = a times sinB/sinA
b = 10 times sin53/sin90
on a calculator type sin53 in degrees
b = 10 times 0.7986/1
b = 7.986
Consider the expression below.
9 + 4(x + 2) – 3x
Select the term that best describes "3" in the given expression.
A.
exponent
B.
variable
C.
coefficient
D.
constant
Answers
Answer:
the term that best describes 3 is a coefficient because a
Step-by-step explanation:
Coefficient is a number that is being multiplied by the variable.
The table below represents the closing prices of stock ABC for the last five
days. Using your calculator, what is the equation of linear regression that fits
these data?
Day
Value
1
20.71
2
19.69
3
19.61
4
19.64
5
19.26
OA. y = 0.289x + 21.459
OB. y=-0.311x + 19.213
O C. y=-0.295x+20.667
D. y=-0.272x+22.319
Answers
Using a calculator, it is found that the equation of linear regression that fits the data is given by:
C. y=-0.295x+20.667
How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
In this problem, the points are given as follows: (1, 20.71), (2, 19.69), (3, 19.61), (4, 19.64), (5, 19.26). Hence the equation is:
Doing this, the equation is:
y = -0.295x + 20.667.
Hence option C is correct.
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- Write the inequality that shows how much money you can spend on the booth.
Answers
The inequality x + 10(5) ≤ 1000 shows how much money you can spend on the booth if you have $1000 and need to buy 10 chairs worth $5.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let us assume that you have $1000 and need to buy 10 chairs worth $5. Let x represent the money that can be spent on the booth, hence:
x + 10(5) ≤ 1000
The inequality x + 10(5) ≤ 1000 shows how much money you can spend on the booth, if you have $1000 and need to buy 10 chairs worth $5.
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The length of a reclangle can be represented by the expression 2x - 1. The width of the same rectangle can be represented by the expression x^2 - x + 3. Which of the following expressions can represent the area of the rectangle?
Answers
Answer:
2x^3 - 3x^2 + 7x - 3
Step-by-step explanation:
Area = length * width
= (2x - 1)(x^2 - x + 3)
= 2x(x^2 - x + 3) - 1(x^2 - x + 3)
= 2x^3 - 2x^2 + 6x - x^2 + x - 3
= 2x^3 - 3x^2 + 7x - 3
Rational and irrational numbers
Answers
Answer:
Rational numbers is a ratio (i.e., P/Q and Q≠0)
Irrational numbers cannot be expressed as a fraction.
so a
Rational numbers can show a Fraction
Irrational numbers can not show a Fraction
Hope This Helped
Answer:
Rational numbers are any infinite number or ratio that goes on and on and represents such mathematical values, e.g five-over-twelve is a rational number because it is a fraction.
Irrational numbers are squares of a number or any number that does not include a comparison(e.g division, fraction, ratio, etcetera) of a value. For instance, the square root of 2 is an irrational number because it does not go on indefinitely.