Answer:
B
Step-by-step explanation:
To calculate the area of this triangle we can use the Heron’s formula
Mathematically we have the Heron’s formula as;
A = √s(s-a)(s-b)(s-c)
where s = (a + b + c)/2
Thus, s = (15 + 12+ 10)/2 = 18.5
a = 15, b = 12 and c = 10
Plugging these values into the equation, we have
√18.5(18.5-15)(18.5-12)(18.5-10)
= √18.5(3.5)(6.5)(8.5)
= √ 3,577.4375
A = 59.8116
which is approximately 59.8 square units
2. What is the formula for circumference of a circle (using radius instead
of diameter)?
How to do this question
Answer:
Length of the shorter diagonal is 8.68 cm.
Step-by-step explanation:
Length of the side AB = 11 cm
Length of side BC = 5 cm
Angle between these sides, m∠ABC = 50°
By cosine rule in ΔABC,
AC² = AB² + BC² - 2AB.BC.cos B
AC² = (11)² + 5² - 2(11)(5)cos50°
AC² = 121 + 25 - 70.71
AC = √(75.29)
AC = 8.68 cm
By the property of parallelogram,
m∠B + m∠C = 180° [Interior consecutive angles]
50° + m∠C = 180°
m∠C = 130°
Similarly, In ΔBCD,
BD² = BC² + CD² - 2BC.CD.cos130°
BD² = (5)² + (11)² - 2(5)(11)cos130°
BD² = 25 + 121 + 70.71
BD² = 216.71
BD = 14.72 cm
Therefore, length of the shorter diagonal will be 14.72 cm.
Lincoln and Natalie are workers in a factory making widgets. Lincoln can make 25 widgets per day in the factory. Natalie is able to produce 8% more widgets per day than Lincoln. How many widgets can Natalie make per day?
Answer:
27 widgets
Step-by-step explanation:
25÷100=0.25=1%
0.25×8=2=8%
25+2=17
What is the probability of rolling an EVEN number on a 6 sided cube (die) with the numbers 1-6 on the six sides?
Answer:
The probability is 1/2 because 3/6 numbers are even.
Step-by-step explanation:
The following list gives the number of public libraries in each of 11 cities.
6, 6, 4, 5, 4, 6, 8, 4, 5, 5, 7
Find the modes of this data set.
If there is more than one mode, write them separated by commas.
If there is no mode, put "No mode."
Answer:
mode is 6
Step-by-step explanation:
it appears four times whereas no other number appears more than three times
Which number is farthest from 1 on the number line?
start root 1.2 EndRoot
start root 1.3 EndRoot
start root 1.4 EndRoot
start root 1.5 EndRoot
Answer:
start root 1.5 EndRoot
Answer:
d
Step-by-step explanation:
In which figure is point G an orthocenter? Triangle A B C is a right triangle. Lines are drawn from each point to the opposite side and intersect at point G. Triangle F D E is shown. Lines are drawn from each point to the opposite side and intersect at point G. The lines cut each side into 2 equal parts. Triangle L M N is shown. Lines are drawn from each point to the opposite side and intersect at point G. Each angle has a different measure. Triangle H J K is shown. Lines are drawn from each point to the opposite side to form right angles and the lines intersect at point G.
Answer:
the Answer is D just got it right hope this help you
Step-by-step explanation:
The 4th figure is the correct option, i.e. triangle H J K, in which lines are drawn from each point to the opposite side to form right angles and the lines intersect at point G with G is an orthocentre.
What is orthocentre?The orthocenter denotes the intersection of all right angles extending from the vertices to the opposite sides, i.e. the altitudes. The term ortho means "right," and it is defined as the point at which three altitudes are drawn from the three vertices of a triangle intersect.
How to solve this problem?From the definition, it is clear that the lines must make right angles and intersect at G. The first three figures do not meet the criteria of orthocentre.
Therefore the 4th figure is the correct option, i.e. triangle H J K, in which lines are drawn from each point to the opposite side to form right angles and the lines intersect at point G with G is an orthocentre.
Learn more about orthocentre here -
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In a group of 35 pupils, 11 play the flute only. 8 play the piano only. 15 play neither instrument. A student is selected at random. What is the probability the student plays both instruments?
Answer: 1/35
Step-by-step explanation:
From the question, in a group that has 35 pupils, 11 of the pupils play flute only, 8 play the piano only and 15 play neither instrument.
The probability that a student plays both instruments will be:
Since a third instrument is not mentioned, P(a randomly selected student plays the flute and the piano)
35-15=20,
This is the total students minus the students that play neither instruments.
We then subtract those that play flute only and those that plays piano only from 20. This will be:
20-11-8 = 1
Probability (a student plays both instrument) = 1/35
What is 30% as a decimal
Kala needs to memorize words on a vocabulary list for German class. She has memorized 15 of the words, which is three-fifths of the list. How many words are on the list?
Answer: there is 25 in total
Answer:
25
Step-by-step explanation:
3/5 of the list is 15
So the whole list, by proportion, is 15 * 5/3
= 5 * 5
= 25.
What is the expression of 3/4 percent divided between 7/4 and 2/4?
Answer:
85.714285 reapeating
Step-by-step explanation:
The volume of box A is 60, and the volume of box B is half the volume of box A. What is the height of box B, a?
Answer: The box measurements are as follows: Box A: height = 5 inches, length = 18 inches, width = 10. Box B: height = 8 inches, length = 10 inches, ..
Step-by-step explanation:
Because the Texas Constitution does not have a "necessary and proper" clause, _________. a. government powers are almost unlimited b. much of what is included in the constitution is improper c. the governor has to make the laws d. government is limited to what is in the constitution Please select the best answer from the choices provided A B C D
Answer:
The answer is D.
Step-by-step explanation:
Edge
Bethany finished her math homework at 4:20 P.M. She did 10 multiplication problems in all. If each problem took her 3 minutes to do, at what time did Bethany start her math homework? Bethany started her math homework at :
Answer:
3:50 P.M.
Step-by-step explanation: 3 * 10 = 30 minutes
4:20 - 30 = 3:50
Find the volume of the composite figure round to the nearest tenth
Answer: [tex]1460.96ft^3[/tex]
Step-by-step explanation:
You have a cylinder and a cuboid. Find each of these figures' volume individually and add them together.
Cylinder:
height = 4ft
radius = 4ft
[tex]Formula: V=\pi r^2h[/tex]
[tex]V=(3.14)(4ft)^2(4ft)\\V=(3.14)(16ft^2)(4ft)\\V=(3.14)(64ft^3)\\V=200.96ft^3[/tex]
---------------------------------------------------------------------------------------------------
Cuboid:
[tex]Formula: V = l*w*h[/tex]
[tex]V=(15ft)(7ft)(12ft)\\V=1260ft^3[/tex]
------------------------------------------------------------------------------------------------------
Add these two volumes together.
[tex]200.96ft^3+1260ft^3=1460.96ft^3[/tex]
If tangents PA and PB from a point P to a circle with centre O are inclined to each other at an angle of 100°, then ∟BOA is equal to ____________
pls answer fast
Answer:
[tex] m\angle BOA = 80\degree[/tex]
Step-by-step explanation:
PA and PB are tangents to the circle with center O at points A and B respectively.
[tex]\therefore OA \perp PA\:\: \& OB \perp PB....(\because tangent\perp radius)\\\therefore m\angle OAP=m\angle OBP = 90\degree\\m\angle APB = 100\degree\\OAPB \: is \: a\: quadrilateral\\\therefore m\angle APB+m\angle OAP+m\angle OBP+m\angle BOA = 360\degree\\\therefore 100\degree + 90\degree+ 90\degree+ m\angle BOA = 360\degree\\\therefore 280\degree + m\angle BOA = 360\degree\\\therefore m\angle BOA = 360\degree-280\degree \\\huge\red{\boxed{\therefore m\angle BOA = 80\degree}}[/tex]
Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y =
64(0.97)x
Hello there!
Using the given exponential function of y = 64(0.97)^x, we can tell that it is a decaying exponential function since the rate is less than 1.
The percent of decrease is 3% since 97% of the value is retained per x time.
5 friends plan to split a restaurant Bill evenly. The total cost of the meal is $89.75, and they want to leave a 20% tip. what amount should each friend pay?
Answer:
£17.51
i used try and error
Au dépanneur, six conserves de maïs et deux boîtes de pâtes coûtent au plus 15,75 $. Indiquez le prix possible de la boîte de pâtes si une conserve de maïs coûte 0,50 $ de plus que la moitié du prix d’une boîte de pâtes.
Answer:
$ 2.55 or less
Step-by-step explanation:
We have if they buy 6 cans of corn and 2 boxes of pasta are priced at $ 15.75 or less, they also tell us that the price of a can of corn is $ 0.50 + half the price of a box of pasta. Let's formulate the equation, let "x" be the cost of the can of corn and "y" be the cost of the box of pasta.
6 * x + 2 * y <= 15.75
x = 0.5 + y / 2
replacing:
6 * (0.5 + y / 2) + 2 * y <= 15.75
3 + 3 * y + 2 * y <= 15.75
5 * and <= 15.75-3
y <= 12.75 / 5
y <= 2.55
replacing in x:
x = 0.5 + 2.55 / 2 = 1.775
Which means that the price of a can of corn is $ 1,775 and for the box of pasta it is $ 2.55 or less.
Answer:
The answer is 2.55
Step-by-step explanation:
hope this helps
Enfachadadeunacatedralpone:FechadeconstrucciónMCDLXXIX.¿Cuántosañoshaceque se construyó? Expresa el resultado con nuestros números y también en números romanos.
Answer:
Step-by-step explanation:
18 – 21 ft.
Determine whether each set of side lengths could be the sides of a right triangle. Drag and drop each set of side lengths to the correct box. Right Triangle Not a Right Triangle 10.5 cm, 20.8 cm, 23.3 cm6 cm, 22.9 cm, 20.1 cm
Answer:
Right Triangle-10.5 cm, 20.8 cm, 23.3 cmNot a Right Triangle-6 cm, 22.9 cm, 20.1 cmStep-by-step explanation:
Given the sets of side lengths of a triangle:
10.5 cm, 20.8 cm, 23.3 cm6 cm, 22.9 cm, 20.1 cmTo verify whether each set of side lengths could be the sides of a right triangle, we use the Pythagorean Theorem. Note that the longest side is always taken as the hypotenuse.
Pythagoras Theorem: [tex]Hypotenuse^2=Opposite^2+Adjacent^2[/tex]In the set of side lengths 10.5 cm, 20.8 cm, 23.3 cm
[tex]23.3^2=20.8^2+10.5^2\\542.89=432.64+110.25\\542.89=542.89[/tex]
Clearly these satisfies the required theorem and thus are side lengths of a right triangle.
In the set of side lengths 6 cm, 22.9 cm, 20.1 cm
[tex]22.9^2=20.1^2+6^2\\524.41\neq 440.01[/tex]
Clearly these does not satisfy the required theorem and thus are not side lengths of a right triangle.
To the nearest tenth, which is the perimeter of △ABC?
Answer:
30
Step-by-step explanation:
correct me if I'm wrong
But i believe adding up the sides will give you 30
Answer:
23.6
Step-by-step explanation:
23.6
The product of two binomials, u(x) and v(x), is a binomial of degree 8 with a positive leading coefficient. What must be true about the sum of u(x) and v(x)?
Answer:
From the above conclusion, it can be inferred that sum of u(x) and v(x) is a binomial of degree 4 with a positive or negative leading coefficient depending on the value of the constant 'a'Step-by-step explanation:
If the product of two binomials, u(x) and v(x)has a binomial of degree 8, then the individual binomial will have a binomial of degree 4. For example, lets assume u(x) = ax⁴ + bx and v(x) ax⁴+cx. Note that they are both functions of x and contain only two terms since they are binomial.
Taking their product we have;
u(x)*v(x) = (ax⁴ + bx)*(ax⁴+cx)
u(x)*v(x) = a²x⁸+acx⁵+abx⁵+bcx²
it can be seen that the higest power of x is 8 which gives the degree of the product.
Taking their sum;
u(x)+v(x) = (ax⁴ + bx)+(ax⁴+cx)
u(x)+v(x) = ax⁴ + ax⁴+ bx +cx
u(x)+v(x) = 2ax⁴ + bx +cx
It can be seen that the digest power of x is 4 which gives the degree of the sum of the binomial.
From the above conclusion, it can be inferred that sum of u(x) and v(x) is a binomial of degree 4 with a positive or negative leading coefficient depending on the value of the constant 'a'
PLs ANSWER EASY 10 points
Answer:
2 2/5 miles^2
Step-by-step explanation:
For this you have to times the mixed fractions
So....
1 1/5 x 1 1/5
Rewrite it as this 1 + 1/5 + 1 + 1/5
Add the two whole numbers:
1 + 1 = 2
Now the fractions:
1/5 + 1/5 = 2/5
Then:
2 + 2/5 = 2 2/5
The perimeter of the semicircle is 25.71 cm. Calculate the value of radius x. Take pi to be 3.142
Answer:
5 cm
Step-by-step explanation:
[tex]Perimeter of semicircle = \frac{1}{2} \times 2\pi \: x +2x\\ 25.71 = 3.14 2\times x+ 2x\\ 25.71 = 5.14 2 x\\ x = \frac{25.71}{5.142} \\ x = 5 \: cm[/tex]
Math question need help
Answers and Step-by-step explanations:
(a)
We need to figure out the amount (or total cost) for each size candy given that they sell a certain number of each box. For the small box, we're given the cost is $4.70, while the large box is $7.00.
We buy x of the small box, so the total amount should be 4.70 * x, or just 4.70x. We buy y of the large box, so the total amount should be 7.00 * y, or just 7y.
So on the table, the top value should be 4.70x, and the bottom value should be 7y.
(b)
The total number of boxes sold was 45 boxes. Remember that x boxes were small and y boxes were large. Since the number of small boxes plus the number of large boxes is equal to the total of 45, we can write:
x + y = 45
(c)
The total cost was $269, so we can write this as the sum of the amounts that we found in part (a):
4.70x + 7y = 269
PLEASE HELP! URGENT!
Which of the following functions shows the absolute value parent function, F(x) = |x|, vertically stretched?
A. G(x) = |x| + 9
B. G(x) = 3|x|
C. G(x) = |x + 14|
D. G(x) = 1/2|x|
Answer:
C, I believe!
The functions shows the absolute value parent function, F(x) = |x|, vertically stretched is C. G(x) = |x + 14|
What is the absolute value function?The absolute value function is defined by the following piecewise rule, depending on the input of the function:
|x| = x, x ≥ 0.
|x| = -x, x < 0.
This can be measures the distance of a point x to the origin, hence, for example, |-2| = |2| = 0, and has vertex(turning point) at (0,0). The range is from the y-coordinate of the vertex to positive infinity.
Vertex (2, 0), Range: {y | 0 ≤ y < ∞}
The parent absolute value function is F(x) = |x|,
If this function is stretched vertically, then the stretched function is of the form.
G(x) = |x + a|
where 0<a<1
Therefore the correct option is C. G(x) = |x + 14|
More can be learned about functions a;
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What is the correct equation for the line in slope-intercept form?
Answer:
y = -5x + 35
Step-by-step explanation:
You have two points: (0, 35) and (7, 0).
The slope is [tex]\frac{0-35}{7-0}=-5[/tex]
The y intercept is 35.
y = -5x + 35
Answer
Step-by-step explanat
2. How many times smaller is the surface area of a sphere if the radius is multiplied by 1/2?
If a number is multiplied by 1/2, this means that it strinks 2 times.
For example, we have the radius of 4.
If multipled by 1/2, we get 2.
So, the radius is now 2 times smaller than the original radius.
So, the radius of the sphere will be 2 times smaller than what it originally was.
Best of Luck!
solve for x x-1 ≥8
please help
Steps to solve:
x - 1 ≥ 8
~Add 1 to both sides
x - 1 + 1 ≥ 8 + 1
~Simplify
x ≥ 9
Best of Luck!