The value of x is 15.
What is parallelogram?"It is a quadrilateral with opposite sides parallel.""The opposite angles of parallelogram are equal. "For given question,
Two of the angles in a parallelogram measure 5x° and 7x°
The measure of an angle opposite to 5x° is also 5x°
Similarly the measure of an angle opposite to 7x° is also 7x°
So, we have the four angles of parallelogram as 5x°, 7x°, 5x°, 7x°
We know, the sum of all angles of quadrilateral is 360°
⇒ 5x° + 7x° + 5x° + 7x° = 360°
⇒ (5 + 7 + 5 + 7) x = 360
⇒ 24x = 360
⇒ x = 15
Therefore, the value of x is 15.
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How to find equation of axis of symmetry when given 2 points?
the volume of the sphere is increased by 72.8%. what is the percentage increase in the radius?
Final answer:
The volume of a sphere increases by 72.8%, which after calculations, results in a 20% increase in the radius of the sphere.
Explanation:
The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere. An increase in volume by 72.8% implies that the new volume V' is equal to 1.728 times the original volume V. To find the percentage increase in the radius, we use the relationship between volume and radius:
V' = (4/3)πr'^3, where r' is the new radius after increase. Since V' = 1.728V, we have:
1.728 (4/3)πr³ = (4/3)π[tex]r'^3[/tex]Therefore, [tex]r'^3[/tex] = 1.728r³.After taking the cube root of both sides, we obtain:
r' = ∛1.728 * r ≈ 1.200 * rThus, the new radius is approximately 120% of the original radius, which means there is a 20% increase in the radius.
Final answer:
To calculate the percentage increase in the radius of the sphere when the volume is increased by 72.8%, we can use the formula for volume and solve for the new radius in terms of the original radius. The percentage increase in radius is then calculated by comparing the new and original radius.
Explanation:
The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere. If the volume of the sphere is increased by 72.8%, we can calculate the new volume by multiplying the original volume by 1 + 0.728. Let's denote the original radius as r1 and the new radius as r2.
The formula for volume can be written as V = (4/3)πr³. Substituting r1 and r2 into the formula, we get:
Original volume: V1 = (4/3)πr1³New volume: V2 = (4/3)πr2³Since the two volumes are related by the percentage increase (1 + 0.728), we can write the equation:
(1 + 0.728)V1 = V2
Now, let's solve for r2 in terms of r1:
(1 + 0.728)V1 = (4/3)πr2³
r2 = ([(1 + 0.728)V1] * (3/4π))^(1/3)
Finally, we can calculate the percentage increase in the radius by comparing r2 to r1:
Percentage increase in radius = (r2 - r1) / r1 × 100%
Triangle XYZ is located at X (−2, 1), Y (−4, −3), and Z (0, −2). The triangle is then transformed using the rule (x−1, y+3) to form the image X'Y'Z'. What are the new coordinates of X', Y', and Z'?
Please Help Me
The area of a round mat is 64 pi square inches. what is the diameter of the mat
ab is tangent to the circle ad=4 and bc=3 solve for x
Answer:
Step-by-step explanation:
alright, lets get started.
bc and cd will be same as both are radius of the circle.
[tex]bc=cd=3[/tex]
[tex]ac=ad+cd[/tex]
[tex]ac=4+3[/tex]
[tex]ac=7[/tex]
as we know ab is tangent to the circle so, triangle abc will be a right triangle.
Using Pythagorean theorem
[tex]a^2+b^2=c^2[/tex]
[tex]3^2+x^2=7^2[/tex]
[tex]9+x^2=49[/tex]
Subtracting 9 from both sides
[tex]x^2=49-9=40[/tex]
[tex]x=\sqrt{40} =2\sqrt{10}[/tex]
So, the answer is [tex]2\sqrt{10}[/tex] : answer
Hope it will help. :)
If s = -5 and t = 3, find the value of s^2t.
225
75
30
-75
Answer:
75
Step-by-step explanation:
If a solid has faces that consist of 2 equilateral triangles and 3 congruent rectangles, what type of solid is it?
A. regular hexagonal prism
B. right rectangular prism
C. right triangular prism
D. triangular pyramid
How many yards equals 765 inches?
1 yard = 3 feet
1 foot = 12 inches
so 36 inches = 1 yard
765 / 36 = 21.25 yards
Chad owns twice as many cds as carlin owns. if you add 6 to the number of cds chad owns and then divide by 7, you get the number of cds bryce owns. bryce owns 30 cds. how many cds does carlin own?
An equation is formed of two equal expressions. The number of CDs owned by Carlin is 102.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given the following points:
Chad owns twice as many CDs as Carlin owns. if you add 6 to the number of CDs chad owns and then divide by 7, you get the number of CDs Bryce owns. Bryce owns 30 CDs.Let the variables represent the following numbers as shown,
CDs owned by Chad = M.Cds owned by Carlin = NCDs owned by Bryce = OThe number of CDs owned by Chad.
M = 2N ______(1)
The number of CDs owned by Carlin.
= N ________(2)
The number of CDs owned by Bryce.
O = (6+2N) / 7
And O = 30
30 = (6 + 2N) / 7 ________(3)
From (3), the value of N can be written as,
30 = (6 + 2N) / 7
Multiply both sides by 7
30 x 7 = 6 + 2N
210 = 6 + 2N
Subtract 6 on both sides.
210 - 6 = 6 + 2N - 6
204 = 2N
Divide both sides by 2.
102 = N
N = 102
Thus, the number of CDs owned by Carlin is 102.
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When you sign up for a movie service, you get three free months of movies. Then you are charged $15 per month to rent movies. If you pay $90, how many months of use do you get?
I need help figuring this out, I think X is 61 but I'm not sure
Give an example of a linear equation perpendicular to y=5
Final answer:
A linear equation perpendicular to y=5 is a vertical line, expressed as x=c, where c is any real number. For instance, x=2 is perpendicular to y=5.
Explanation:
A linear equation perpendicular to y=5 would need to have an undefined slope, meaning it's a vertical line. Since y=5 is a horizontal line, a perpendicular line will have no slope value that we can put in terms of y=mx+b, where m represents the slope and b represents the y-intercept. Thus, the equation will be of the form x=c, where c is any real number. This represents a vertical line that crosses the x-axis at the point (c,0).
For example, the linear equation x=2 is perpendicular to y=5 and crosses the x-axis at the point (2,0).
f(x)=2x + 1 and g(x) = -3x+4. Find f(x) + g(x)
Gerald bought a home for $300,000. His largest up–front cost is 10 percent, or $30,000. What is this cost called?
Answer:
The answer is down payment.
Step-by-step explanation:
Gerald bought a home for $300,000. His largest up–front cost is 10 percent, or $30,000.
This cost is called down payment.
Down payment is an amount in cash that is given while purchasing a home. This lies between 5% to 20% of the purchase price.
This payment reduces the amount of money you will have to borrow from banks. Each loan requires some sort of down payment.
Solve this Multi-Step Equation: (Show your work)
-3(t + 5) + (4t + 2) = 8
I have a math question
For
the first question; we have a problem dealing with translations.
Our goal is to translate
the word problem into an algebraic one. So our numbers are
60, 2, and 5. Our variable, or the letter holding the unknown
number's place
value, is
N.
The
problem states that 60 is MORE THAN the PRODUCT of 5 and N. Focus
on the words I bolded and capitalized. These are your key words that
tells you what operations
you need to use. Note that 'product' signals the operation of
multiplication (Since the answer you get from multiplying numbers is
called the 'product'.) and
'more than' signals the operation of addition (Because you are left
off with more than you originally had before adding).
Now
that we know that our algebraic expression contains multiplication,
addition, letter N and the numbers 2 and 5; we can start plugging the
numbers in.
60
= 2 (more than) + (product of) 5N. The answer for the first
attachment is
B.
_____________________________________________________________
All
we need to do for the AB problem (Question 25 on your material) is
solve AB.
Note
1: When a problem has no operation separating two letters or numbers,
this means multiplication.
Note
2: A and B are variables. Variables are letters that stand for and
hold the place of our unknown quantities. However, the values are not
unknown anymore given the fact that the question tells us that A= 42
and B = 2. Thus we substitute A with 42 and B with 2, then work from
there. 42 * 2 =84. Answer = A.
____________________________________________________________________
And
finally, for question 26, we use PEMDAS. P = parenthesis (), E =
exponent x^2, M/D = x or /, A/S means + or subtraction.
According to PEMDAS, we first solve what's parenthesis, which is 77 – 32. Using mental math, 77 – 32 = 45. ( 7 – 3 = 4 and 7 – 2 = 5.). 5/9 * 45 is what we have left. 5 divided by 9 =0.5555555555555556. 0.5555555555555556 * 45 = 25. Answer is D.
Write down in the terms of n, an expression for the nth term of the following sequences:
a.) 23, 20, 17, 14, 11
b.) 36, 30 24, 18, 12
Suppose an investment of $500 doubles in value every 15 years. How much is the investment after 30 years? 45 years?
During summer months, one ice cream trucks come 4 days another 5 days. If both trucks came today, when is the next time both would be here on the same day?
A negatively skewed curve represents a distribution in which there are very few scores on the right side of the distribution.
Which of the following shows the length of the third side, in inches, of the triangle below?
A right triangle is shown. One side of the triangle is labeled shown as 97 inches. The height of the triangle is labeled as 65 inches.
Square root of 32
72
Square root of 13634
16
97^2 = 65^2 +x^2
9409 = 4225 +x^2
9409 -4225 = 5184
Sqrt(5184) = 72
length of missing side = 72 inches
i think of a number, multiply it by 3 and add 4 and i get 22
form an equation, using x for the unknown number and then solve it
The student's clues form the equation 3x + 4 = 22. When solved, this equation reveals that the original number x is 6.
Explanation:The student is creating an algebraic equation to find an unknown number. Starting with the clues given:
They think of a number (which we represent with x)Multiply the number by 3 (3x)Add 4 (3x + 4)The result is 22 (3x + 4 = 22)Now, we can solve this equation to find x:
Start by subtracting 4 from both sides of the equation (3x + 4 - 4 = 22 - 4)Simplify to get 3x = 18Then divide both sides by 3 (x = 18/3)This gives us x = 6 as the unknown numberLearn more about Algebra here:https://brainly.com/question/24875240
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7. What is the value of x?
6
6√3
12
12√3
8. What is the value of x?
7
7√2
14
14√2
9.What is the area of this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
cm²
10. In △ABC, AC=12 in., BC=1.5 in., and m∠C=63°.
What is the area of △ABC?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
11. The relative locations of Pedro's house, the grocery store, and the bank are shown in the diagram.
What is the distance between the grocery store and the bank?
Enter your answer in the box. Round your final answer to the nearest mile.
mi
12. Marco, Garret, and Dino are hiding during a game of hide-and-seek. Their relative locations are shown in the diagram.
What is the distance between Garret and Dino?
Enter your answer in the box. Round your final answer to the nearest yard.
The solution to the parts is given below.
What is Trigonometry?Trigonometry is a discipline of mathematics that studies the relationship between the sides of a triangle (right triangle) and their angles. There are six trigonometric functions that define the relationship between sides and angles.
1. Using Trigonometry
sin 60 = P/H
√3/2 = x/ 12
x = 12√3 / 2
x= 6√3
2. Using Trigonometry
sin 60 = P/H
1/√2 = 7√2 / x
x/√2 = 7√2
x = 14 unit
3. Using sine law
sin 75 /11 = sin 54 / x
0.965 / 11 = 0.809 / x
0.0877 = 0.809 / x
x = 9.224 miles
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Problem 4 the measure of the largest angle of a triangle is 90◦ more than the measure of the smallest angle, and the measure of the remaining angle is 30◦ more than the measure of the smallest angle. find the measure of each angle. showyourwork in obtaining your answe
1. What point is the image of (4,5) with a translation of right 2 and down 3?
2. Find B' in a reflection of Triangle ABC when A(3,6), B(-4,2), C(-1,-3) over the y axis.
3. Which axis is (0,7) on?
A. X axis
B. Y axis
please show me how to solve ... -12x - 17 = -89
Plz help with math. will reward.
A meteor crater is 3000 feet in diameter. Approximate the distance around the crater use 3.14 for pi
which number is a solution of the inequality 12 < y(8-y)
The solution to the inequality 12 < y(8 - y) is y such that 2 < y < 6.
The solution of the inequality 12 < y(8 - y), you can start by simplifying the expression on the right side: y(8 - y)
Distribute the y on the right side: 8y - [tex]y^2[/tex]
Now, substitute this expression back into the original inequality: [tex]12 < 8y - y^2[/tex]
Rearrange the terms to form a quadratic inequality: [tex]y^2 - 8y + 12 > 0[/tex]
Now, factor the quadratic expression: (y - 2)(y - 6) > 0
To solve for y, set each factor equal to zero and find the critical points: y - 2 = 0 or y - 6 = 0
Solving these equations gives y = 2 and y = 6.
Now, create intervals using these critical points and test a value in each interval:
1. Test y = 1: (1 - 2)(1 - 6) = (-1)(-5) = 5 > 0
2. Test y = 3: (3 - 2)(3 - 6) = (1)(-3) = -3 < 0
3. Test y = 7: (7 - 2)(7 - 6) = (5)(1) = 5 > 0
The solution is y such that 2 < y < 6
What is the perimeter of the rectangle shown on the coordinate plane, to the nearest tenth of a unit?
13.4 units
17.9 units
26.8 units
40.0 units