In a triangle, the measure of the first angle is twice the measure of the second angle. The measure of the third angle is 80° more than the measure of the second angle. Use the fact that the sum of the measures of the three angles of a triangle is 180° to find the measure of each angle. what is the measure of the first angle?
Answer:
The measure of the first angle is 50°.
Step-by-step explanation:
Let the three angles be a, b, and c.
The measure of the first angle is twice the measure of the second angle. In other words:
[tex]a=2b[/tex]
The measure of the third angle is 80° more than the measure of the second angle. In other words:
[tex]c=b+80[/tex]
And since the interior angles of a triangle must equal 180°:
[tex]a+b+c=180[/tex]
Substitute a and c:
[tex](2b)+b+(b+80)=180[/tex]
Combine like terms:
[tex]4b+80=180[/tex]
Subtract 80 from both sides:
[tex]4b=100[/tex]
And divide both sides by four:
[tex]b=25^\circ[/tex]
So, the measure of the second angle is 25°.
Since the measure of the first is twice the second, the measure of the first angle is 50°.
(And since the measure of the third is 80° than the second, the measure of the third angle is 105°.)
Researchers at a medical school conducted a study to test the effectiveness of a new drug for lowering cholesterol. The 52 subjects who volunteered for the study were each given a randomly generated number. Subjects with an odd number were given the new drug, while those with an even number were given a placebo. Cholesterol levels before and after the treatment were measured for each subject, and the differences were computed.
This study is an example of ______________ study. The difference in cholesterol level is _____________ the variable. The treatment with drug or placebo is the ____________ variable.
Answer:
1. An Experimental
2. Dependent
3. Independent
Step-by-step explanation:
Considering the description of how the research was carried out, it can be concluded that This study is an example of AN EXPERIMENTAL study. This because the researcher is trying to study the effectiveness of a new drug for lowering cholesterol
The difference in cholesterol level is the DEPENDENT variable. This is because the difference in cholesterol level is what the researcher wants to determine.
The treatment with a drug or placebo is the INDEPENDENT variable. This is because this is what the researcher manipulates to determine the difference in cholesterol level which is the dependent variable in this experimental study.
what that two numbers when multiplied give 600 and when added give 59
Answer:
Step-by-step explanation:
Let the 2 numbers be x and y
From the problem we have that
x * y = 600 and x + y = 59
From x + y = 59 -> x = 59 - y
Plug x = 59 - y to x * y = 600 we have
(59 - y) * y = 600
-> 59y - y^2 = 600
-> -y^2 + 59y - 600 = 0
-> y = [tex](59 - \sqrt{1081})/2[/tex] or [tex](59 + \sqrt{1081})/2[/tex]
Then we could plug the answers in and find x because x = 59 - y
What is the solution of the equation, 8y = 4?
A. y = 1/2
B. y = 2
c. y = 12
D. y = 32
Answer: A, which is y = 1/2
Step-by-step explanation: To find the value of y, you would need to divide both of the sides by 8. This makes it so that 8y turns into just y. After you do this, you would find an answer of y = 1/2. Hope this was helpful! :)
Answer:
y = 1/2
Step-by-step explanation:
8y = 4
Divide each side by 8
8y/8 = 4/8
y = 1/2
Find the point on the terminal side of θ = three pi divided by four that has a y coordinate of 1. Show your work for full credit.
Answer:
Remember that tan=y/x from your notes from module 4.
Step-by-step explanation:
Refer to the unit circle to see the relationship between x and y at that angle, it is -1. Now you can set up your equation of tan=1/x and solve for x.
For all the problems in this section you can set up an equation where tan=y/x, sin = y/h, and cos=x/h. Then using your equation you can solve for whatever number is missing.
Answer:
-1/1
Step-by-step explanation:
Graph the line.
y=3x
Answer:
desmos(dot)com/calculator/gv8jsoui4w
Step-by-step explanation:
Create a table of appropriate x values e.g. x = 2 and substitute into y=3x which will be y=3*2 meaning y=6 at the point x=2. Repeat with different x values until you have enough points to draw a straight line.
The sky ride at an amusement park spans 2,715 feet. Over the course of the day,
Anna rode the sky ride 7 times. How many feet did she ride?
A. 14,025 feet
B. 15,500 feet
C. 19,005 feet
D. 21,000 feet
Whoever answers this then there gonna get Branliest
Answer:
C. 19,005 feet
Step-by-step explanation:
[tex] \begin{array}{ccc} \rm 1 \: time \: ride \implies \: 2175 \: feet\\ \rm 7 \: times \: ride \implies 2175 \times 7 = 19005 \: feet\end{array}[/tex]
hence,
our answer is C)
Answer:
Solution given:
1times ride[tex]\rightarrow: [/tex]2715ft
7 times ride[tex]\rightarrow:[/tex]2715*7=19005ft
Option C 15,500 feet
Jeff can build 7 birdhouses in 5 hours. Use a
proportion to find out how long it would take
him to build 30 birdhouses. (Round answer to
nearest whole number)
Answer:
21 hours
Step-by-step explanation:
We can use a ratio to solve
7 houses 30 houses
------------- = --------------
5 hours x hours
Using cross products
7x = 5*30
7x = 150
Divide by 7
7x/7 =150/7
x =21.42857143
Rounding to the nearest whole number
x = 21 hours
Identify which shapes are similar to shape A and which are not.
Answer: Shape 3 and Shape 2
Hope this helps...
Have a great day.
Is my answer correct?
9514 1404 393
Answer:
yes
Step-by-step explanation:
By the "rule of 72", the amount will be doubled in 72/I years, where I is the annual interest rate in percent. That is, it can be estimated to take 72/4 = 18 years to double the $240 investment to $480. It would take another 18 years to double it again to $960. So, to achieve a balance of $1500 will be expected to take more than 36 years. The only reasonable answer choice is the one you have selected.
__
The exact solution is ...
log (1500/240)/log(1 +0.04) ≈ 46.72 years ≈ 47 years.
Three relatives will share an inheritance of 196,800 in the ratio of 3 to 7 to 2. How many dollars of the inheritance will each of the relatives receive?
Answer:
49200
114800
32800
Step-by-step explanation:
196800/12=ans
ans * 3
ans * 7
ans * 2
What is the first term in the sequence for which d = -2 and a7 = 3?
A. -6
B. 12
C. 15
D. -12
Answer:
First term is 15
Step-by-step explanation:
Given data:
[tex]a_{7} =3\\d=-2[/tex]
Now,
[tex]a+6d=3.....(1)\\a_{n} =a+(n-1)d\\\\\\From equation (1)\\a+6(-2)=3\\a-12=3\\a=12+3\\a=15[/tex]
Therefore first term a =15
Correct option is (c)
Which is the decimal expansion of the following 1/5
Answer:
Decimal expansion of 1/5 = 0.2
An object dropped from a height of 500 feet has a height, h(t), in feet after t seconds have elapsed, such that h(t)=500−16t^2. Express t as a function of height h, and find the time to reach a height of 100 feet
Step-by-step explanation:
the answer is in the above image
What is the image point of (1,-7) after the transformation T-3,-1 degrees R180 degrees?
Answer:
first hust rotate 180 and next reflect it over x axis.
the given point (-7,3) id in second quadrant but after rotation it will be in fourth quadrant.
afterwards you have to refect that point over x-axis which gives you the image of the points on first quadrant ie. (7,1).
Which measure of central tendency best describes the data set below?
{0, 80, 85, 88, 90, 95}
A. the mean, 73
B. the mode, none
C. the range, 95
D. the median, 86.5
Answer:
The correct answer would be D, the median 86.5. In this set of data most of the values are in the 80's or 90's.
Step-by-step explanation:
d point is the answer
Answer:
D) The median, 86.5
Step-by-step explanation:
Most of the data is clustered in the 80s. Therefore, D is correct.
definition of descartes
Answer:
French philosopher and mathematician; developed dualistic theory of mind and matter; introduced the use of coordinates to locate a point in two or three dimensions (1596-1650)
Help me fast 50 points!!!!!!!!
Answer:
30
Step-by-step explanation:
There are 14 data points on the plot
The median is the middle value, which is between the 7th and 8th data points
Since it is even, we find the average of the 7th and 8th data points
Add the 7th and 8Th data points values and divide by 2
( 30+30)/2 = 60/2 = 30
The median is 30
Answer:
30
Step-by-step explanation:
Middle numbers are 30 and 30 so you add them and then divide by two:
[tex]\frac{30 + 30}{2}[/tex] = [tex]\frac{60}{2}[/tex]= 30
Plzzz help I don’t have a lot of time
Answer:
7
Step-by-step explanation:
It’s a right angle, so you can add the two expressions togther to get 90, then isolate x.
(8r-6)+(5r+5)=90
13r-1=90 (combine like terms)
13r-1+1=90+1 (add 1, addition property of equality)
13r=91
13r/13=91/13
r=7
Can any one help?
Solve the following equations:
Answer:
2- x=16/3 or 5.3
4- x=8
Step-by-step explanation:
yeah
how do i solve this problem
Answer:
5 sqrt(2) =x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hypotenuse
sin 45 = x / 10
10 sin 45 = x
10 ( sqrt(2)/2) =x
5 sqrt(2) =x
I need help finding the answer. Would appreciate some help
Answer:
a = 153.5 yd²
Step-by-step explanation:
horizontally divide the figure into a tringle and a trapezoid
triangle
a = (1/2)bh
a = (1/2)(19)(7)
a = 66.5
trapezoid
a = (b₁ + b₂)/2 * h
a = (19 + 10)/2 * (13 - 7)
a = 87
Combined
a = 66.5 + 87
a = 153.5
Please help me with my math question?
Answer:
150 mL
Step-by-step explanation:
270 - 120 = 150
Hope this helps!
Which algebraic expression has a term with a coefficient of 9? O A. 6(x + 5) O B. 6x - 9 O C. 6+ x - 9 O D. 9x=6
Answer:
D is the answer to your question
Estimate: 4/5 - 1/2
Answer:
Need help ASAP..
Answer:
3/10
Step-by-step explanation:
Find the LCM of 5 and 2.
LCM = 10
[tex]\frac{4}{5} - \frac{1}{2} = \frac{8 - 5}{10} = \frac{3}{10}[/tex]
Answer:
[tex]\frac{3}{10}[/tex]
Step-by-step explanation:
5 = 5 × 1
2 = 2 × 1
LCM = 2 × 5
10
[tex]\frac{2(4)}{2(5)} -\frac{5(1)}{5(2)}[/tex]
[tex]\frac{8}{10} -\frac{5}{10}[/tex]
[tex]\frac{3}{10}[/tex]
Please I need help in finding the diameter
Answer:
im pretty sure its 152, im sorry if im wrong, i took 180 and subtracted 180 - 16 - 12 and got that soooo
Step-by-step explanation:
Please help it’s not hard
Answer:
H
Step-by-step explanation:
y= (1)x-3
Positive gradient, and the y intercept for the graph is -3, F is not the answer, the Y intercept is not -3.
How many different ways may a set of 4 books be arraged side by side on a shell?
Answer:
24
Step-by-step explanation:
4 * 3 * 2 * 1 = 24
Use the data in the table to complete the sentence. x y –2 7 –1 6 0 5 1 4 The function has an average rate of change of __________.
Answer: -1
Step-by-step explanation:
Just took the test
,and the equation is y=-1x+5, so the change of x is -1
Answer:
The answer is -1
Step-by-step explanation:
Which sequence is an example of an arithmetic sequence? A) –8, –4, –2, –1, . . . B) –4, –2, 0, 2, 4, . . . C) –1, –7, –49, –343, . . . D) 2, 4, 8, 16, 32, . . .
i dont have the membership.
Answer:
Answer- D)2,4,8,16,32, . . .
Answer:
b. -4,-2,0,2,4,...
Step-by-step explanation:
