Answer:
Let's mark Pat's age is x. Then Mattie's age is 2x and Jon's age is 4x.
So (x + 4) + (2x + 4) + (4x + 4) = 61.
7x + 12 = 61 => 7x = 49 => x = 7.
So the answer is
Pat = 7
Mattie = 14
Jon = 28
The ages of Pat, Mattie, and Jon are as follows: 7 years, 14 years & 28 years.
If we take Pat's age as = 'x' years,
so, Mattie's age will be = '2x' years.
and then, Jon would be = 2(2x)
= '4x' years.
Now, the sum of their ages after 4 years =
=> (x+4) + (2x+4) + (4x+4) = 61
=> 7x+12 = 61
=> 7x= 61-12
=> 7x= 49
=> x= 49/7
=> x = 7
Therefore, Pat's age is = 7 years.
Mattie's age is = 14 years (2×7).
Jon's age is = 28 years (4×7).
To learn more about the Sum of ages, refer to:
https://brainly.com/question/11282363
Find the area of the shaded region in terms of pi.
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Let’s find the area of the circle.
A = 3.14(7)^2 = 153.86
Now the area of the square:
14•14=196
Now we find the area of the shaded region:
196 - 153.86 = 42.14
the shaded region is 42.14 cm
The blue shape is a dilation of the black shape. What is the scale factor of the dilation?
Answer:
x and y values are doubled; scale factor is 2
Step-by-step explanation:
(4,5) becomes (8,10)
(2,5) becomes (4,10)
(1,4) becomes (2,8)
What are the 3 names of angles?
Angles are classified into three. They are acute angles, obtuse angle and right angle.
Therefore the three names of angles are - acute angles, obtuse angle and right angle.
Acute angles are angles that measure less than 90 degrees. They are smaller than a right angle and are often described as "sharp."
Right angles are angles that measure exactly 90 degrees. They are often represented by a square corner or the letter "L" shape.
Obtuse angles are angles that measure greater than 90 degrees but less than 180 degrees. They are larger than a right angle and are often described as "blunt."
To know more on angles
https://brainly.com/question/19247815
#SPJ4
Please help!!!!!!!!!!!
Answer:
9/4 *(x-2)
Step-by-step explanation:
Replace xa and y in the given function then solve for y
A waiter in a restaurant has eight booths in his station. How many different arrangements are possible for the hostess to seat customers at the waiter’s booths if order is important?
Answer:
8 seats
Step-by-step explanation:
n = 8 ---booths
r = 1 --- hostess
Order is required
Important Order? We solve using permutation.
nPr = n!/(n - r)!
So we have:
8p1 = 8!/(8 - 1)!
IF we do the math correctly, we get this:
8p1 = 8/7!
Finally let's expand to come up with the solution.
8p1 = 8 x 7/7
8p1 = 8
So the answer is 8!
I hope this helps! Have a good day (PLS GIVE BRAINLIEST)
There are 8 types of different arrangements possible for the hostess to seat customers at the waiter’s booths if order is important.
What is Permutation and Combination ?
The various ways in which objects from a set may be selected, generally without replacement, to form subsets. This selection of subsets is called a permutation when the order of selection is a factor, a combination when order is not a factor.
Total number of booths = 8
To determine we will use the generalized expression
How many ways can you arrange 'r' from a set of 'n' if the order matters
P(n,r) = n! / (n-r)!
P(8,1) = 8!/ (8-1)!
= 8!/7!
= 8
So there are 8 types of different arrangements possible for the hostess to seat customers at the waiter’s booths if order is important.
To know more about Permutation and Combination
https://brainly.com/question/9283678
#SPJ2
please help please please please please
Explanation is[tex]^{}[/tex] in a file
bit.[tex]^{}[/tex]ly/3gVQKw3
For the initial 90 miles of a flight, the pilot heads 8° off course in order to avoid a storm. The pilot then changes direction to head toward the destination for the remainder of the flight, making a 157° angle to the first flight course. Determine the total distance of the flight
A. 48.4
B. 135.9
C. 138.4
D. 228.4
In the above scenario, note that the total distance of the flight is given as: 48.4 miles (approximately). This is solved using the law of Sines to find x.
What is the law of Sines?The connection between the sides and angles of non-right (oblique) triangles is defined by the Law of Sines. Simply put, it asserts that the ratio of the length of a triangle's side to the sine of the angle opposite that side is the same for all triangle sides and angles.
Thus, with regard to the problem modeled in the attached triangle, because two angles are given, the missing angle is 180° − (157° + 8°) or 15°. Use the Law of Sines to find x.
Using the law of ins we can state that:
Sin 8°/x = sin 15°/90
90 (Sin 8°) /x = Sin 15°
90 Sin 8° = x Sin 15°
90 Sin 8° / Sin 15° = x
90 (0.13917310096)/ 0.2588190451 = x
Thus,
x = 48.3951213156
x [tex]\approx[/tex] 48.4
Thus, the distance of the flight is approximately 48.4 miles.
Learn more about the law of Sines:
https://brainly.com/question/17289163
#SPJ1
Is 0 in a closed interval?
So the only boundary point of [0,∞) and (0,∞) is 0 itself. It is in [0,∞), so that set is closed. It is not in (0,∞), so that set is open.
In mathematics, a (real) interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0, 1, and all numbers in between. Other examples of intervals are the set of numbers such that 0 < x < 1, the set of all real numbers
the set of nonnegative real numbers, the set of positive real numbers, the empty set, and any singleton (set of one element).
Real intervals play an important role in the theory of integration, because they are the simplest sets whose "length" (or "measure" or "size") is easy to define. The concept of measure can then be extended to more complicated sets of real numbers, leading to the Borel measure and eventually to the Lebesgue measure.
Intervals are central to interval arithmetic, a general numerical computing technique that automatically provides guaranteed enclosures for arbitrary formulas, even in the presence of uncertainties, mathematical approximations, and arithmetic roundoff.
So the only boundary point of [0,∞) and (0,∞) is 0 itself. It is in [0,∞), so that set is closed. It is not in (0,∞), so that set is open.
To learn more about intervals:
https://brainly.com/question/13708942
#SPJ4
Sienna goes to the mall with $56. She spends $13 on food and $24 on a book. How much money does Sienna have left?
Answer: 19
Step-by-step explanation:
56-13=43
43-24=19
Answer: 19
Step-by-step explanation: 13 + 24 = 37
so (56 - 37 = 19)
For the rhombus below, find the measures
Angle 1 and Angle 4 are alternate internal angles, Angle 1 also equals 51.Angles 1 and 2 of the rhombus are bisector by 51 and 2, respectively.
what is rhombus ?A parallelogram has a unique variation known as a rhombus. A rhombus has opposing sides that are parallel and opposing angles that are equal. A rhombus also has equal-length sides and diagonals that are at right angles to one another. The term "rhombus" can also refer to a diamond or rhombus. A rhombus has equal opposite angles. At a 90° angle, the diagonals split in half. 180 degrees is the sum of adjacent angles.
given
There is a line that passes through the parallel line; the alternate interior angles are 3 and 39.
The alternative interior angles are similar, hence Angle 3 = 39.
Since the upper left triangle is a triangle, angles 3, 4, and the center angle all add up to 180 degrees. The angle in the middle is 90 degrees. hence, we may locate angle 4.
angle 4=51.
Since Angle 1 and Angle 4 are alternate internal angles, Angle 1 also equals 51.Angles 1 and 2 of the rhombus are bisector by 51 and 2, respectively.
To know more about rhombus visit :-
https://brainly.com/question/27870968
#SPJ1
(10 POINTS) ATTENTION! PLEASE HELP! WILL GIVE BRANLIEST TO ACCURATE ANSWER
Answer:
c. 9ft
Step-by-step explanation:
[tex]x^{2} + 12^{2} = 15^{2}[/tex]
[tex]x^{2}[/tex] + 144 = 225
[tex]x^{2}[/tex] = 81
x = 9
This question has two parts. First, answer Part A. Then answer part B. Part A Based on the text what inference can be made about laughter? Part B Drag "yes" or "no" to each box to show whether or not the piece of evidence supports the answer to part A
Part A: Based on the text, an inference that can be made about laughter is that it can be a positive response to a situation or a way of expressing joy.
What is inference?Inference is the process of drawing conclusions from given facts or evidence. It involves making a logical guess or assumption based on the available information. Inference requires the use of critical thinking to draw conclusions that are most likely to be accurate.
Part B:
Yes - Laughter is described as a response to a situation and can be a way of expressing joy.
No - There is no evidence that laughter is a negative response to a situation.
To learn more about inference
https://brainly.com/question/30142576
#SPJ4
Can someone tell me what this is?
Answer:
there's one solution bc the lines have one point in common
PLS HELP MY WHOLE GRADE IS DEPENDING ON THIS QUESTION
A table with a round top is cut in half so that it can be used against a wall. After it is cut, the edge along the
wall is 6 feet.
What is the area A of the table after it is cut in half?
Give your answer in terms of pi.
А=____feet2
Answer:
4.5π ft.^2
Step-by-step explanation:
Please see the attached image.
The area of a circle is the radius of the circle squared times pi.
The diameter of the round top is 6.
The radius of a circle is equal to half the diameter, so 6/2=3.
Knowing the radius of the table is 3, we can find the area by doing
3^2π=9π
9π is the area of the table, so to get half of that, simply divide by 2.
9π/2=4.5π
Answer: 4.5π ft.^2
Answer:
14.1 ft^2 or In terms of pi: A = (1/2)(π)(3 ft)^2 = (9/2)π ft%2
Step-by-step explanation:
We're talking about a semicircle here. "semi-" indicates "half."
Here the cut edge along the wall is 6 ft, so the radius of the semicircle is half that, or 3 ft.
The area of the semicircle is A = (1/2)(pi)(3 ft)^2 = 14.1 ft^2
In terms of pi: A = (1/2)(π)(3 ft)^2 = (9/2)π ft%2
Hint: your answer will be a fraction or decimal. ex: 3/5 or 0.6 *
Find the probability that a point chosen at random on the part of the number line shown will lie
between points B and C.
On solving the provided question we can say that - the probability of the event will be there are two red sides, thus multiplying 16.6667 by two results in 33.3333%.
What is probability?A branch of mathematics known as probability measures the possibility of an event happening or a proposition being true. The probability of an occurrence is a number between 0 and 1, where roughly 0 denotes the event's improbability and 1 denotes certainty. A probability is a numerical representation of the possibility or probability that a specific event will take place. Probabilities can alternatively be stated as percentages ranging from 0% to 100%, or as percentages from 0 to 1. the proportion between the number of events in a comprehensive collection of equally likely outcomes that lead to a certain occurrence and the entire number of outcomes.
Each side would be 50%, and if one side were divided among three people, it would equal 16.6667 per person.
Given that there are two red sides, you can multiply 16.6667 by 2 to get 33.3333%.
To know more about probability visit:
https://brainly.com/question/11234923
#SPJ1
write down the value of 10^-3
Answer:
value of 10^-3= 0.001
hope it helps.
Answer:
Step-by-step explanation:
10^(-3) is equivalent to
1
--------- which in turn is equivalent to 1/1000, or 0.001.
10^3
What number would you multiply the second equation by in order to eliminate the x terms when adding the first equation?
Multiplying the second equation by -4 eliminates the x terms when adding the first equation.The second equation is 4x + 5y = -8
In order to eliminate the x terms when adding the first equation, you need to multiply the second equation by -4. The formula and calculation steps are as follows:
Formula:
Equation 1 + (-4 x Equation 2)
4x + 5y = -8
-4(4x + 5y) = -4(-8)
-16x -20y = 32
Adding the two equations together gives:
0x + 25y = 24
Therefore, multiplying the second equation by -4 eliminates the x terms when adding the first equation.
Learn more about equation here:
https://brainly.com/question/29657983
#SPJ4
What kind of triangle has 65 65 50?
Isosceles Triangle has 50°, 65°, 65°
An isosceles triangle is a triangle that has two sides of equal length. The two equal sides are called the legs and the third side is called the base of the triangle.
Properties of Isosceles Triangle:
The two equal sides of an isosceles triangle are known as ‘legs’, and the angle between them is called the vertex angle or apex angle.In an isosceles triangle, if two sides are equal, then the angles opposite to the two sides correspond to each other and are also always equal.The isosceles triangle has three acute angles, meaning that the angles are less than 90°.The sum of three angles of an isosceles triangle is always 180°. The side opposite the vertex angle is called the base and the base angles are equal, and perpendicular to the apex angle bisecting the base and the apex angle.To know more about Isosceles Triangle:
https://brainly.com/question/29793403
#SPJ4
x=
Length=
Width=
WILL GIVE BRAINLIEST + 5 star
Answer:
x = 20
Length = 20ft
Width = 12ft
Step-by-step explanation:
A = 240
x^2 - 8x = 240
x^2 - 8x - 240 = 0
x^2 - 20x + 12x - 240 = 0
x(x-20) + 12(x-20) = 0
(x+12)(x-20) = 0
x = 20
x = -12 (which we discard since x is a length)
So the dimensions are 20ft and 20-8 = 12ft
I just need somebody to explain how to do it step by step
Given m||n, find the value of x.
Answer:
x = 102°
Reason
They're both Alternate Exterior angles
ALTERNATE EXTERIOR ANGLES ARE EQUAL.
May someone please help me with this :) I have to find the value of x
Answer:
the answer is 50 are you trying to find the answer
Use complete sentences to explain why .
Answer:
answer what
Step-by-step explanation:
1. Combine the like like terms
14 + 8x + 2y -5x - 2
Answer:
12 + 3x + 2y
Step-by-step explanation:
14 + 8x + 2y -5x - 2
14 + -2 + 8x -5x + 2y
12 + 3x + 2y
Answer:
3x + 2y + 12
Step-by-step explanation:
In the photo.
HELp meh with this question it very hard
Answer:
AB = 7 cmStep-by-step explanation:
Use the law of cosines to find the side AB:
[tex]AB = \sqrt{(x + 3)^2+x^2-2x(x+3)cos (60)} =[/tex] [tex]\sqrt{x^2+6x+9+x^2-x^2-3x} = \sqrt{x^2+3x+9}[/tex]Use the Heron's area formula next:
[tex]A = \sqrt{s(s - a)(s-b)(s-c)}[/tex], where s- semi perimeters = 1/2[x + x + 3 + [tex]\sqrt{x^2+3x+9}[/tex]) = 1/2 (2x + 3 + [tex]\sqrt{x^2+3x+9}[/tex])s - a = 1/2 (2x + 3 + [tex]\sqrt{x^2+3x+9}[/tex] - 2x - 6) = 1/2 ([tex]\sqrt{x^2+3x+9 }[/tex] - 3)s - b = 1/2 (2x + 3 + [tex]\sqrt{x^2+3x+9}[/tex] - 2x) = 1/2 ([tex]\sqrt{x^2+3x+9}[/tex] + 3)s - c = 1/2 (2x + 3 + [tex]\sqrt{x^2+3x+9}[/tex] - 2[tex]\sqrt{x^2+3x+9}[/tex]) = 1/2 (2x + 3 - [tex]\sqrt{x^2+3x+9}[/tex])Now
(s - a)(s - b) = 1/4 [(x²+3x+9) - 9] = 1/4 (x² + 3x)s(s - c) = 1/4 [(2x + 3)² - (x² + 3x + 9)] = 1/4 (3x²+ 9x) = 3/4(x² + 3x)Next
A² = 3/16(x² + 3x)(x² + 3x)300 = 3/16(x² + 3x)²1600 = (x² + 3x)²x² + 3x = 40Substitute this into the first equation:
[tex]AB = \sqrt{40 + 9} = 7 cm[/tex]Answer:
AB = 7 cm
Step-by-step explanation:
Sine Rule for Area
[tex]\sf Area =\dfrac{1}{2}ab \sin C[/tex]
where:
a, b and c are the sides opposite angles A, B and Ca and b are the sides and C is the included angleGiven:
Area = √(300) cm²a = (x + 3) cmb = x cmC = 60°Substitute the given values into the formula and solve for x:
[tex]\begin{aligned} \sf Area & = \dfrac{1}{2}ab \sin C \\\\\implies \sqrt{300} & = \dfrac{1}{2}(x+3)x \sin 60^{\circ}\\\\\sqrt{300} & = \dfrac{\sqrt{3}}{4}(x+3)x\\\\\dfrac{4\sqrt{300}}{\sqrt{3}} & = x^2+3x\\\\40 & = x^2+3x\\\\x^2+3x-40 & = 0\\\\ (x-5)(x+8)& = 0\\\\ \implies x & = 5, -8\end{aligned}[/tex]
As length is positive, x = 5 only.
Substitute the found value of x into the expressions for the side lengths:
a = 5 + 3 = 8 cmb = 5 cmCosine rule
[tex]c^2=a^2+b^2-2ab \cos C[/tex]
(where a, b and c are the sides and C is the angle opposite side c)
Substitute the found values into the formula and solve for AB:
[tex]\begin{aligned}c^2 & =a^2+b^2-2ab \cos C\\\implies AB^2 & =8^2+5^2-2(8)(5) \cos 60^{\circ}\\AB^2 & =89-40\\AB^2 & =49\\AB & =\sqrt{49}\\AB & = \pm 7\end{aligned}[/tex]
As length is positive, AB = 7 cm.
Learn more about the sine rule for area here:
https://brainly.com/question/27088353
A certain psychological test measures empathy and
emotional intelligence. The score, S, of a randomly
selected senior student at a large university has a mean
of 123 and a standard deviation of 29. The score, F, of a
randomly selected first-year student at a large university
has a mean of 104 and a standard deviation of 34.
Suppose we randomly select one senior student and one
first-year student. We can consider Sand F to be
independent random variables.
As per the given standard deviation, the probability that the first-year student shows a higher emotional intelligence test score in a randomly selected senior/first-year pair is 0.72
Here we have given that the score, S, of a randomly selected senior student at a large university has a mean of 123 and a standard deviation of 29.
And the score, F, of a randomly selected first-year student at a large university has a mean of 104 and a standard deviation of 34.
Then the probability is calculated as,
=> 123/104
=> 1.182
Where as the based on the standard deviation, the value is calculated as
=> 29/34
=> 0.852
Then the total probability of the given situation is calculated as,
=> 0.852/1.182
=> 0.72
To know more about Standard deviation here.
https://brainly.com/question/16555520
#SPJ4
The staff at Larry's Lawns spends their workday mowing lawns, raking, and bagging leaves. They work an average of six hours per day. The mowing and raking typically takes four hours and an average of twenty-four bags of leaves are filled. Assuming the bags are filled at a constant rate, what is the average time it takes to fill one bag of leaves
Assuming the bags are filled at a constant rate, the average time it takes to fill one bag of leaves is 5 minutes.
To calculate the average time it takes to fill one bag of leaves, we need to know the total amount of time spent filling bags and divide that by the number of bags filled.
First, we know that the staff works an average of six hours per day. Since mowing and raking typically take four hours, we can assume that the remaining two hours are spent filling bags.
To find out how long it takes to fill one bag, we divide the total time spent filling bags by the number of bags filled. In this case, it would be:
(2 hours) / (24 bags) = 0.083 hours (or 5 minutes)
So the average time it takes to fill one bag of leaves is 5 minutes.
It's important to note that this is an average time and may not reflect the exact time it takes for each bag to be filled. Factors such as the size of the bag, the type of leaves being filled, and the skill level of the staff could all affect the time it takes to fill a bag.
To learn more about the average, visit:
brainly.com/question/14402983
#SPJ4
I'll mark you the brainliest
plzzzz help asap❤❤
if x+y+z=1 and 1/x+1/y+1/z=0
what is x²+y²+z²=?
A) 0
B) 1
C) 2
D) 3
and please tell me why?
if f(x)= mx+ c , f (1)=5 and f(-2)=-1
Answer:
[tex]y = 2x + 3[/tex]
Step-by-step explanation:
We can find the slope.
[tex] \frac{ 5 + 1}{1 + 2 } = 2[/tex]
so m is 2
[tex]y = 2x + c[/tex]
Plug one the equations in to find c.
[tex] - 1 = 2( - 2) + c[/tex]
[tex] - 1 = - 4 + c[/tex]
[tex]3 = c[/tex]
so the equation is
[tex]y = 2x + 3[/tex]
Please help! No links please! Will give brainliest to correct person!!
Answer:
About 50.14 Centimeters
Step-by-step explanation:
The formula for the volume of a cylinder is:
[tex]\pi(r^2)h[/tex]
Now, let's plug in the values. (We'll use 3.14 for pi.)
[tex]3.14(r^2)76 = 600,000[/tex]
All we do now, is solve for r. Divide 76 on both sides...
[tex]3.14(r^2) = 7894.74[/tex]
Divide 3.14 on both sides...
[tex]r^2 = 2514.25[/tex]
Lastly, find the square root on both sides.
[tex]\sqrt{r^2} = \sqrt{2514.25}[/tex]
[tex]r = 50.14[/tex]
Therefore, the r, or the radius, is around 50.14 centimeters. Hope this helps!
help me find the measure
Answer:
the value of x is 40 degree and the value of (2x+11) is 91 degree.
Step-by-step explanation:
hope it helps you.