Answer:
7(3+2x)
Step-by-step explanation:
An architect designs two similar triangular patios. The first patio has angle measures of (x + 10)°, (y + 15)°, and 70°. The second patio has angle measures of (x + 20)°, 50°, and 60°. Find the values of x and y.
Given:
An architect designs two similar triangular patios.
The first patio has angle measures of (x + 10)°, (y + 15)°, and 70°.
The second patio has angle measures of (x + 20)°, 50°, and 60°.
To find:
The values of x and y.
Solution:
We know that, corresponding angles of similar triangles are equal. So, the value of (x + 20)° must be 70°.
[tex]x+20=70[/tex]
[tex]x=70-20[/tex]
[tex]x=50[/tex]
The value of x is 50.
Now,
[tex](x+10)^\circ=(50+10)^\circ[/tex]
[tex](x+10)^\circ=(60)^\circ[/tex]
So, remaining angles must be equal, i.e., (y + 15)° and 50° are equal.
[tex]y+15=50[/tex]
[tex]y=50-15[/tex]
[tex]y=35[/tex]
Therefore, the values of x and y are 50 and 35 respectively.
The values of x and y are 50 and 35 respectively.
The corresponding angles of similar triangles are equal. Therefore,
The first patio angles are:
x + 10
y + 15
70°
The second patio angles are ;
x + 20
50°
60°
Therefore,
x + 20 = 70
x = 70 - 20
x = 50
y + 15 = 50
y = 50 - 15
y = 35
read more: https://brainly.com/question/19297980?referrer=searchResults
1000 branilys Determine the coordinates of the point shown.
A coordinate grid shown. There are increments of 0.5 for each grid line on each of the two axes. A point is located at 3 grid lines to the right and 1 grid line down from the origin.
(1.5, −0.5)
(−0.5, 1.5)
(3, −1)
(1, −1)
Answer:
Its A ( 1.05, -0.5)
Step-by-step explanation:
Complete the statement. Round to the nearest hundredth if necessary.
14 m to ft
(the answer is not 45.93)
In Last Lecture, which person does Randy Pausch connect to the idea of always encouraging his students to strive for higher goals?
Answer:
C
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
It is correct
Can someone please help?
What property goes on the right side?
example: addition, subtraction, etc.
Answer:
3. definiton of angle bisector
4. substitution property (of equality)
5. 2x+14=34
5. subtraction property of equality
6. 2x = 20
6. subtraction property of equality
Draw the image of ABC under a translation by 2 units down.
I need help please !!!
Answer:
Please find attached drawing created with Microsoft word, that shows the image of of the triangle ΔABC. with coordinates of the vertices as, A(2, -4), B(0, -5), and C(6, 2), translated down 2 units to give the triangle ΔA prime B prime C prime , with coordinates of the vertices as A prime (2, -6), B prime (0, -7), and C prime (6, 0)
Step-by-step explanation:
Answer:
Here u go
Step-by-step explanation:
Because yeah
Hi. I need help with these questions.
See image for question.
Answer 23 , 24,25,26
Answer:
23) 4x² - 8k²x + k⁴ = 024) (i) 2, (ii) 725) (i) 11/8, (ii) -81/826) (a³ + b³ + c³ + 3abc)/a³Step-by-step explanation:
23..............................
GivenEquation 2x(x - k) = k² with the roots α and βTo findThe equation with roots α² and β²Solution2x(x - k) = k²2x² - 2kx - k² = 0The sum and the product of the roots
α + β = - (-2k)/2 = kαβ = - k²/2The equation with roots α² and β² is:
(x - α²)(x - β²) = 0x² - (α² + β²)x + α²β²= 0x² - ((α + β)² - 2αβ)x + (αβ)² = 0x² - (k² - 2( -k²/2))x + (- k²/2)² = 0x² - (k² + k²)x + k⁴/4 = 04x² - 8k²x + k⁴ = 024..............................
GivenEquation 3x² - 9x + 2 = 0 with the roots α and βTo findThe values of
αβ² + α²βα² - αβ + β² SolutionThe sum and the product of the roots
α + β = - (-9)/3 = 3αβ = 2/3(i)
αβ² + α²β =αβ(α + β) =2/3(3) =2(ii)
α² - αβ + β² = α² + 2αβ + β² - 3αβ =(α + β)² - 3αβ =3² - 3(2/3) =9 - 2 =725..............................
GivenEquation 2x² + 9x + 12 = 0 with the roots α and βTo find(a) show that the quadratic equation whose roots are (α - 1/α) and (β - 1/β) is 24x² + 90x + 115 = 0The values of
(i) αβ (1/α² + 1/β²)(ii) α³ + β³SolutionThe sum and the product of the roots
α + β = - 9/2αβ = 12/2 = 6a) The quadratic equation whose roots are (α - 1/α) and (β - 1/β) is:
(x - (α - 1/α))(x - (β - 1/β)) = 0x² - (α - 1/α + β - 1/β)x + (α - 1/α)(β - 1/β) = 0x² - ((α + β) - (α + β)/αβ)x + αβ + 1/(αβ) - (α/β + β/α) = 0x² - ((α + β) - (α + β)/αβ)x + αβ + 1/(αβ) - ((α+β)² - 2αβ)/(αβ)= 0x² - (-9/2 - (-9/2)/6)x + 6 + 1/6 - ((-9/2)² - 2(6))/6 = 0x² - ( -9/2 + 3/4)x + 37/6 - (81/4 - 12)/6 = 0x² + 15/4x + 37/6 - 33/24 = 0x² + 90/24x + 148/24 - 33/24 = 024x² + 90x + 115 = 0Proven(i)
αβ (1/α² + 1/β²) =αβ(α² + β²)/(α²β²) =((α + β)² -2αβ)/(αβ) =((-9/2)² - 2(6))/6 =(81/4 - 12)/6 =81/24 - 2 =33/24 =11/8(ii)
α³ + β³ =(α + β)(α² - αβ + β²) = (α + β)(α² + 2αβ + β² - 3αβ) =(α + β)((α + β)² - 3αβ) =(-9/2)((-9/2)² - 3(6)) =-9/2(81/4 - 18) =-9/2(9/4) =-81/826..............................
GivenEquation ax² + bx + c = 0 with the roots α and βTo findExpress (1 - α³)(1 - β³) in terms of a, b and cSolutionThe sum and the product of the roots
α + β = - b/aαβ = c/aThe expression is evaluated as follows:
(1 - α³)(1 - β³) = 1 - (α³ + β³) + α³β³ =1 - (α + β)((α + β)² - 3αβ) + (αβ)³ =1 - (-b/a)((-b/a)² - 3c/a) + (c/a)³ =1 + (b/a)³ + 3bc/a² + c³/a³ =1 + (b³ + c³ + 3abc)/a³ =(a³ + b³ + c³ + 3abc)/a³BRAINLY PLS I NEED HELP WITH THE RIGHT ANSWER APS !HELP!!
Answer:
The measurement of angle 3 is 45.
Step-by-step explanation:
It said line q is perpendicular. Then line m bisects that 90 degree angle and 90/2=45. Does this help?
HELP PLEASE
The sum of three numbers is 19. The third number is eleven less than five times the second number. If the first number is quadruple the amount of the second number, what is the value of the third number? (may I have the equation please)
Answer:
third number = 4,
equation of y, y = 5x - 11
equation of n, n = 4x
equation of x, n + x + y =19
Step-by-step explanation:
so lets write evertything as a n equation. n + x + y =19. N is the first number, x is the second number, and y is the third number. We will write the equation for y as follows 5x - 11. N will be four times the second number, so 4x. If substitute the values for out equation for x we will find what x equals to. So (4x) + x + (5x - 11) = 19
10x = 30
x = 3.
Then you substiute the answer for x in the equation for y. This will get you 5(3) - 11
15 - 11
4 = third number
Michelle has a balance of $950 in a savings account that pays 3% interest compounded annually. If Michelle makes no deposits or withdrawals, how much money will be in her savings account after 2 years?
Answer:
She will save by borrowing from Bank B.
Step-by-step explanation:
Michelle needs to calculate the interest for the length of each loan. Bank A will charge $2430 in interest and Bank B will charge $1980 in interest. She will save by borrowing from Bank B.
Sample answer on edge ;)
Stanley is running a 5 mile race. He runs 1 mile every 6 minutes. Stanley's distance from the finish line after x minutes is represented by the function x+6y=30
Answer:
Suppose you earned extra money by having a part-time job. You open up a bank account in order to save your money. Your body acts similar to a bank account—you can “deposit” and “store” energy.
Step-by-step explanation:
5x+x=-18
solve for x
Answer:
x=-3
Step-by-step explanation:
5x+x=-18 Combine like terms.
6x=-18 Divide by 6 on both sides.
/6 /6
x=-3
Hope this helps...have an amazing day Σ(っ °w °;)っ
Order the 9 ( yes 9 including Pluto )planets from smallest to biggest according to volume
Answer:
Pluto has a density of 1.86 grams per cubic centimeter
Mercury has a mass of 3375.9 kilograms
Mars has a volume of 1.6318 x 10¹¹ km³
The volume of Venus is 9.38 x 1011 km3
The Earth has a volume of about 1,083,206,916,846 cubic kilometers
volume of 15 trillion cubic miles which is 62 trillion cubic kilometers
The planet has a volume of 6.83x1013 cubic kilometers
The volume of Saturn is about 8.27 x 10 cubic kilometers.
The volume of Jupiter is 1,431,281,810,739,360 cubic kilometers
hope this helps and feel free to give brainiest
A logo in an advertisement is an equilateral triangle with a side length of 7 centimeters. Give the measure of each side. From least to greatest, the measure of each side is centimeters, centimeters, and centimeters.
Answer:
The measure of the least side of the logo = The measure of the greatest side of the triangular = 7 cm
Step-by-step explanation:
The measure of all the sides of an equilateral triangle are equal
Therefore, the measure of each side of the logo are equal to the length of the given side length of 7 centimeters
The measure of the least side of the logo = The measure of the greatest side of the triangular = 7 cm
16 17 18
Select True or False for each statement.
Point A(5,-5) is to the right of the y-axis and below the x-axis.
7
Point B(-3, 2) is to the left of the y-axis and below the x-axis.
7
Point C(2, 2) is to the right of the y-axis and above the x-axis.
?
V
Point D(-4, 4) is to the left of the y-axis and below the x-axis.
?
Answer:
true, false, true, false
The weight of an object on the moon is one-sixth its weight on earth.If an object weighs 48 pounds in the moon how much does it weigh on earth
Answer:
288 lbs
Step-by-step explanation:
since it is 1/6 of the amount on the moon compare to the earth
take 48 and multiply it by 6
48x6=288
Which correctly explains how to estimate 55 percent of 64? A. Round 55 percent to 40 percent and 64 to 60. Think of 40 percent as 1/4 so 1/4 of 60 is 15 B. Round 55 percent to 60 percent and 64 to 70. Think of 60 percent as 1/3 so 1/3 of 70 is 23.3 C. Round 55 percent to 50 percent and 64 and 70. Think of 50 percent as 1/5 so 1/5 of 60 is 12 or D. Round 55 percent to 50 percent and 64 to 60. Think of 50 percent as 1/2 so 1/2 of 60 is 30
Answer: Choice D
Round 55 percent to 50 percent and 64 to 60. Think of 50 percent as 1/2 so 1/2 of 60 is 30.
===================================================
Explanation:
There are many ways to estimate, but this is probably the easiest since 1/2 = 0.50 = 50%, and taking half of something is fairly straightforward and quick.
Taking half of 60 is like taking half of 6, except we stick at 0 at the end.
Half of 6 is 3
Half of 60 is 30
The estimate of 55% of 64 is 30
The actual value is
55% of 64 = 0.55*64 = 35.2
which isn't too far off.
-------------------------
Extra info:
Choice A is false because 40% is not equal to 1/4. Instead 1/4 = 0.25 = 25%Choice B is false because 1/3 = 0.333 = 33.3% approximately, so 1/3 is not equal to 60%Choice C is false because 1/5 = 0.20 = 20% and not 50%Donald Duck has the option of being paid biweekly or weekly? He chooses
weekly because he tells you, more paychecks means more money. What
would you tell him?
A. Donald you are wrong. You get more money if you get paid biweekly, the checks are
double
B. not enough information
C. Donald you are wrong. Its the same amount of money in a year.
D. Donald you are right. I am changing to weekly paychekcs.
Answer:
b
Step-by-step explanation:
doesn't tell the amount of money each check he gets
Answer:
answer is C
C. Donald you are wrong it's the same amount of money in a year
Does someone know the answer?
Answer:
i do not
know the awnser but c would be 720 multiplied by its self 3 times the converted
Step-by-step explanation:
which shows the best use of the associative and communitive properties to make simplifying 3/4 - 5 + 9 - 2/4 + 2 easier?
a.) [2 + 3/4 + (-5)] + [(2/4) + 9]
b.) [3/4 + 9 + (-5) + [2 + (-2/4)]
c.) [3/4 + (-2/4)] + [9 + 2 + (-5)]
d.) [3/4 + (-5)] + [9 + (-2/4) + 2]
Please post a real answer.
Answer:
The Answers A.
Step-by-step explanation:
Meredith deposits $1,400 into an account that earns 3% annual simple interest. How many years will it take Meredth to earn $294 in simple interest on the account?
Answer:
21 years
Step-by-step explanation:
Help me solve this please
Answer:
180 - 90 - 41 = 49
Step-by-step explanation:
Have a great day :)
Answer: 49
Step-by-step explanation:
90 + 41 + G = 180
131 + G = 180
G = 49
In which quadrant does the point (-8 , -18) lie?
Answer:
Quadrant 3
Step-by-step explanation:
Quadrant 1- (Positive,Positive)
Quadrant 2- (Negative Positive)
Quadrant 3- (Negative,Negative)
Quadrant 4- (Positive,Negative)
Solve the equation for all real solutions 4z^2-8z+5=2
Answer:
z=1/2 and z=3/2
Step-by-step explanation:
A rectangular is completety filled with dice.Each dice has volume of 2cm³.The length of the box is 5cm grater than its width and its height is 5cm.Suppose the box holds at most 150dice.What are the posibble dimensions of the box
Answer:
length = 10.64 cm, width = 5.64 cm, and height = 5 cm.
Step-by-step explanation:
Total volume of dice that filled the box = (150 x 2) cm³
= 300 cm³
Let the length, width and height of the box be represented by l, w and h respectively.
So that;
l = (w + 5) cm
w = w
h = 5 cm
volume of the box = length x width x height
= (w + 5) x w x 5
= (w + 5) x 5w
= 5[tex]w^{2}[/tex] + 25w
volume of the box = 5[tex]w^{2}[/tex] + 25w
Since the box was completely filled by 150 dice, then;
total volume of dice = volume of the box
300 = 5[tex]w^{2}[/tex] + 25w
5[tex]w^{2}[/tex] + 25w - 300 = 0
Divide through by 5 to have;
[tex]w^{2}[/tex] + 5w - 60 = 0
Applying the quadratic expression,
w = (-b ± [tex]\sqrt{b^{2} - 4ac}[/tex]) ÷ 2a
where: a = 1, b = 5 and c = -60
(-5 ± [tex]\sqrt{5^{2} - 4(1*-60)}[/tex] ) ÷ 2
(-5 ± [tex]\sqrt{265}[/tex]) ÷ 2
(-5 ± 16.28) ÷ 2
(-5 + 16.28) ÷ 2 OR (-5 - 16.28) ÷ 2
5.64 OR -10.64
Thus, w = 5.64 cm
So that, l = (w + 5) = 10.64 cm
The possible dimensions of the box are: length = 10.64 cm, width = 5.64 cm and height = 5 cm.
can you guys help me please ?
Answer:
4x + 12 = -4
4x = -16
x = -4
Step-by-step explanation:
Have a great day :)
Nathaly is twice as old as her little sister. The sum of their ages is 24. Letting
the age of Nathaly's little sister be N, write an equation for the problem and
then solve it. Then state how old Nathaly and her little sister are.
Answer:
AN equation would be N=x•2x
Nathaly would be 16 and her little sister would be 8
May I have brainliest please? :)
Can someone help me solve for y. Please make sure to explain how you got that answer. THANKS<3
Answer:
7. y=42
8. y=58
If we could call on discord, zoom or anything like that i could easily explain. To type out the whole process would take all night
Step-by-step explanation:
Answer:
7. 42 degrees
8. 58 degrees
Step-by-step explanation:
Question 7
The three angles on the bottom line add up to 180.
65 + 31 + 2y = 180
2y = 84
So y = 42
Question 8
Let's start with the triangle with the 27 degree angle.
We have 27 + 90 + z = 180 (z is the top right angle)
z = 63 (which is also the bottom left angle of the triangle with the 32 degree angle).
63 + 32 + x = 180
x = 85 degrees
Now we look at the bottom polygon with the y degree angle we're trying to find.
We have one angle opposite x and another opposite z.
The angle opposite x + x = 180
The angle opposite x + 85 = 180
The angle opposite x = 95
The angle opposite z + z = 180
The angle opposite z + 63 = 180
The angle opposite z = 117
The sum of the interior angles of a polygon equals the number of sides less 2 * 180. We have four sides, so the interior angles add up to 360.
90 + 95 + 117 + y = 360
Therefore y = 58 degrees
Which equation represents the horizontal line passing through (9,-7)?
O y = 9
O x = -7
O x = 9
O y = -7
Answer:
y = -7
General Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptHorizontal lines have a slope of 0.
Step-by-step explanation:
Step 1: Identify
Point (9, -7)
Horizontal line
We know that a horizontal line will always have the same y values.
Step 2: Write equation
y = -7
Consider the graph representing the cans of soda in a refrigerator at a birthday party.
Which statement describes the graph? Select all that apply.
the y intercept is 50
the y intercept is 100
it decreases as 2 sodas per trip
it decreases every 10 sodas per 20 trips
the y intercept is 0 and the rate of change is 50
Answer:
B/ C
Step-by-step explanation:
because it starts at 100 - the y intercept
and because it goes down 2