D is point lies between A and B.
Triangle △ABC has an altitude CD.
angles A and B are both acute.
Altitude is perpendicular bisector to side of triangle from opposite vertex of triangle.
Since △ABC
A and B are acute angles, and that altitude CD has one vertex at c and other is between A and B i.e. D
Thus, the required point of Altitude CD D lies between A and B.
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What is the surface area of a can that has radius of 9 ft. and height of 3 ft.? SA = __________ ft.2. Use 3.14 for pi. A. 678.2 B. 458.6 C. 354.3 D. 292.0
Answer:
678.2
Step-by-step explanation:
To find the surface area you need to use the expression [tex]2\pi rh + 2\pi r^2[/tex]
When you substitute the numbers in you get 678.24
The surface are of the can that has radius of 9 ft. and height of 3 ft is 678.2 ft².
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
The surface area of the can is the sum of the area of the bases of the can and the lateral surface area of the can. Therefore, the total surface area of the can is,
The surface area of can = 2(Area of base) + Lateral surface area of can
= 2(πr²) + 2πrh
= 2[π×(9 ft)²] + (2 × π × 9ft × 3ft)
= 508.8 ft² + 169.4 ft²
= 678.2 ft²
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h(t)=-16t^{2}+100t+10 find the domain and range. please
Answer:
Step-by-step explanation:
The graph of this function is that of a parabola that opens down (due to the negative coefficient of t^2). The axis of symmetry is
-b -100
x = --------- = ----------- = 50/16 = 25/8.
2a 2(-16)
The y value of the vertex is h(25/8) = -16(25/8)^2 + 100(25/8) + 10, or 166/25.
The largest value this function can take on is 166/25. Thus, the range is
(-infinity, 166/25).
Since the given function is a polynomial, the domain consists of all real numbers.
A principle of $2400 is invested at 7.5% interest, compounded annually. How many years will it take to accumulate $6000 or more in the account? Write the smallest possible whole number answer.
Step-by-step explanation:To find the interest accumulated over a period of time you use:
A = P [1 + (r/n)]^(nt)
with A = new amount in the account, P = principal, r = percent rate as a decimal, n = how many times you compound during one year, t = time in years.
A = 2000
P = 1500
r = 0.035
n=1
Thus you get:
2000 = 1500 (1+0.035)^t
Divide by 1500:
(4/3) = (1.035)^t
Apply "ln" on both sides:
ln(4/3) = t*ln(1.035)
Calculate the logarithms:
0.28768 = t*0.03440
Divide by 0.03440 on both sides:
t = 8.36 years
So after approximately 8 years and 5 month you will have $2000 or more in the account.
The least of 3 consecutive integers is a, and the greatest is z. What is the value of a + 2z/ 2 in terms of a?
Answer:
The value of a + 2z/ 2 in terms of a is (3a+4)/2
Step-by-step explanation:
least of 3 consecutive integers is a, and the greatest is z
if a is the least one
we know that integers differ by value of 1.
example -2, -1, 0, 1,2
they all differ by
then next consecutive integer will be a+1
third integer will be second integer +1 = a+1 + 1 = a+2
Thus, 3 consecutive integer
a , a+1, a+2
but given that greatest is z
thus, a+2 is greatest and hence
a+2 = z
we have to find value of a + 2z/ 2 in terms of a
a + 2z/ 2 = a + 2(a+2)/2 = (a+ 2a +4)/2 = (3a+4)/2.
The value of a + 2z/ 2 in terms of a is (3a+4)/2
Which description is paired with its correct expression? seven less than the quotient of two and a number squared, increased by six; 7 minus StartFraction 2 Over n squared EndFraction + 6 nine times the difference of a number cubed and three; 9 (n cubed minus 3) eight more than the quotient of a number squared and four, decreased by seven; 8 + StartFraction 4 Over n squared EndFraction minus 7 twice the difference of a number cubed and eight; 2 n cubed minus 8
Answer:
the second description and and expression is correct
Step-by-step explanation:
the first one is wrong because it says 7 minus while it should be minus 7
nine times the difference of a number cubed and three; 9(n³-3)
Paired data in statistics, often referred to the ordered pairs, refers to 2 variables in the individuals of the population that are linked together in the order to determine correlation between them.
Given :
7 less than the quotient of two and a number squared increased by six
7 - (2/n²) + 6
9 times the difference of a number cubed and three; 9(n³-3)
8 more than the quotient of a number squared and four, decreased by seven; 8 + (4 /n²) - 7
twice the difference of a number cubed and eight; 2 n³- 8
To Find: Which description is paired with its correct expression
Solution:
7 less than the quotient of two and a number squared increased by six
7 - (2/n²) + 6
Correct Expression is -7 + (2/n²) + 6
nine times the difference of a number cubed and three; 9(n³-3)
Expression is Correct
8 more than the quotient of a number squared and four, decreased by seven; 8 + (4 /n²) - 7
Correct Expression is 8 + (n²/4) - 7
twice the difference of a number cubed and eight; 2 n³- 8
The correct expression is 2( n³- 8)
Hence the correct answer is :
nine times the difference of a number cubed and three; 9(n³-3)
Statistics is a mathematical body of the science that pertains by the collection or analysis, or interpretation and explanation, or presentation of data, and as a branch of mathematics. Some consider statistics to be the distinct mathematical science rather than a branch of mathematics.
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Week 3 Day 14 – POD
On Friday, Mica has $22.50 in her bank account. Mica goes to the market to get
groceries for the week and ends up spending more than planned. When Mica checks
her account, she now has a balance of $-48.15. How much money did Mica spend at
the market?
Show or explain your work in the space below:
Can u plz help me create a model to solve the math problem plz?
Answer: Mica spent $70.65
Step-by-step explanation:
Mica's bank balance before shopping = $22.50
Mica's bank balance after shopping = - $48.15
Mica's spending could be calculated by:
Difference between initial and final bank balance.
Hence,
[(Bank balance before shopping - (bank balance after shopping)]
[$22.50 - (-$48.15)]
= $22.50 + 48.15
= $70.65
A cube has an edge length of 13 feet. What is its volume, in cubic feet?
Answer:
V =2197 ft^3
Step-by-step explanation:
The volume of a cube is given by
V = s^3 where s is the length of a side
V = 13^3
V =2197 ft^3
Answer:
Volume = 2197ft³
Which inequality is equivalent to \-41 <9?
0-9 > X-4 < 9
-9 < x-4 < 9
O X-4<-9 or x – 4 < 9
hry 4 > -9 or x - 4<9
PLEASE HELP GUYS ILL REWARD BRAINLIEST
Answer:
Step-by-step explanation:
(2,6)
Answer:
The solution of the two equations is where both lines intersect
From the graph they intersect at point
(6,2)
So the solution is x = 6 y = 2
Hope this helps you
65.
Evaluate a-b+c for?
Answer:
From the problem, the answer to the equation is 5 1/10
Step-by-step explanation:
First, let's gather the information from the problem.
a = 4 1/5 (also can be turned into 21/5)
b = 2 7/20 (also can be turned into 47/20)
c = 3 1/4 (also can be turned into 13/4)
Now, plug in the numbers using the improper fractions.
21/5 - 47/20 + 13/4
Turn the denominators into the same number.
84/20 - 47/20 + 65/20
Subtract 84/20 and 47/20.
37/20 + 65/20
Add 37/20 and 65/20.
102/20 or 5 1/10
So, your answer to this equation is 5 1/10.
Miracle Maid Service charges a $30 house visit fee plus $5 per room to clean a house. What is the independent variable? A) The price per room B) The number of rooms C) The house visit fee D) The Miracle Maid Service
Answer:
B
Step-by-step explanation:
The independent variable is the variable who's variation doesn't depend on the other. Therefore the answer is B because the amount of rooms doesn't depend on the charge, the charge depends of the amount of rooms.
Use the following data set to find the sample statistics for the following data set. 1. (N) or (n) 2. (x-bar) or (μ) 3. (σ) or (s) Thanks!
Answer:
(1) N or n = 20
(2) [tex]\bar X \text{ or } \mu[/tex] = 43.4
(3) σ = 9.78 and s = 10.04.
Step-by-step explanation:
We are given with the following data set below;
{51, 48, 42, 43, 48, 48, 46, 15, 29, 45, 47, 55, 46, 35, 47, 48, 54, 26, 53, 42}
(1) As we can see in the above data that there are 20 data values in our data set which means that the value of N or n (numner of observations) is 20.
(2) The formula for calculating Mean of the data, i.e. [tex]\bar X \text{ or } \mu[/tex] is given by;
Mean = [tex]\frac{\sum X}{n}[/tex]
= [tex]\frac{51 +48+ 42+ 43+48+48+ 46+ 15+ 29+ 45+ 47+ 55+ 46+ 35+ 47+ 48+ 54+ 26+ 53+ 42}{20}[/tex]
= [tex]\frac{868}{20}[/tex] = 43.4
So, the value of [tex]\bar X \text{ or } \mu[/tex] is 43.4.
(3) The formula for calculating population standard deviation ([tex]\sigma[/tex]) is given by;
Standard deviation, [tex]\sigma[/tex] = [tex]\sqrt{\frac{\sum (X - \bar X)^{2} }{N} }[/tex]
= [tex]\sqrt{\frac{(51-43.4)^{2}+(48-43.4)^{2}+.......+(42-43.4)^{2} }{20} }[/tex]
= 9.78
Similarly, the formula for calculating sample standard deviation (s) is given by;
Sample Standard deviation, s = [tex]\sqrt{\frac{\sum (X - \bar X)^{2} }{n-1} }[/tex]
= [tex]\sqrt{\frac{(51-43.4)^{2}+(48-43.4)^{2}+.......+(42-43.4)^{2} }{20-1} }[/tex]
= 10.04
This rectangular frame is made from 5 straight pieces of metal.
5 m
12 m
The weight of the metal is 1.5 kg per metre.
Work out the total weight of the metal in the frame.
Answer:
Total weight = 70.5 kg
Step-by-step explanation:
Rectangular frame is made from 5 straight pieces of metal. One of them goes through the diagonal of the rectangle.
2 pieces form the length of the rectangular frame, hence, they have a length of 12 m each
2 pieces from the width of the rectangular frame, hence, they a length of 5 m each
To find the length of the diagonal, we can use Pythagoras Theorem:
Hypotenuse² = Base² + Perpendicular²
Hypotenuse² = 5² + 12²
Hypotenuse² = 169²
Hypotenuse = 13
Hence, the length of the piece of metal placed at the diagonal is 13cm
Find the sum of all lengths of the metal pieces.
Total length = 12 + 12 + 5 + 5 + 13
Total length = 47 m
Total weight = 1.5 × Total length
Total weight = 1.5 kg/m × 47m
Total weight = 70.5 kg
The total weight of the metal in the frame is 70.5 kg
If a rectangular frame is made from 5 straight pieces of metal, with a length of 5m and a width of 12m
Get the diagonal
[tex]d^2= 5^2 + 12^2\\d^2 = 25 + 144\\d^2 = 169\\d= 13m[/tex]
Get the perimeter of the rectangular frame:
Perimeter of the frame = 2(5 + 12) + 13
Perimeter of the frame = 2(17) + 13
Perimeter of the frame = 34 + 13
Perimeter of the frame = 47m
If the weight of the metal is 1.5 kg per metre, the total weight will be expressed as:
Total weight = 47 * 1.5
Total weight = 70.5kg
Hence the total weight of the metal in the frame is 70.5 kg
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On which number line do the points represent negative seven and one over two and +1? Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed in between the 7th and 8th tick marks to the left of 0. A point labeled T is placed in between the 6th and 7th tick marks to the left of 0. Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed in between the 7th and 8th tick marks to the left of 0. A point labeled T is placed on the 1st tick mark to the right of 0 Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed on the 1st tick mark to the left of 0. A point labeled T is placed in between the 7th and 8th tick marks to the right of 0. Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed is placed on the 1st tick mark to the left of 0. A point labeled T is placed between the 6th and 7th tick marks to the right of 0.
Answer:
A number line is used in the mathematical positioning of real numbers that include the numbers from positive infinity to negative infinity. This includes rational, irrational, fractions, and whole numbers. In this case, we are given with an expression that we have to reduce to lowest terms: negative seven and one over two and +1. The first one is equal to -7.5 while the other one is equal to +1. Positive numbers lie on the right side of zero (center of the line) while negative numbers lie on the left on the other hand. -7.5 lies between -8 and -7 while +1 lies exactly between 0 and 2. Both of which are positive numbers
I hope that is what your asking...
Answer:
On which number line do the points represent negative seven and one over two and +1? The Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed in between the 7th and 8th tick marks to the left of 0. A point labeled T is placed in between the 6th and 7th tick marks to the left of 0. The Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed in between the 7th and 8th tick marks to the left of 0. A point labeled T is placed on the 1st tick mark to the right of 0 Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed on the 1st tick mark to the left of 0. A point labeled T is placed in between the 7th and 8th tick marks to the right of 0. The Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed on the 1st tick mark to the left of 0. A point labeled T is placed between the 6th and 7th tick marks to the right of
Step-by-step explanation:
The perpendicular bisector of the line segment connecting the points (-3,8) and (-5,4) has an equation of the form y = mx + b. Find m+b. BTW, the answer is not 16...
Answer:
Step-by-step explanation:
find the slope
[tex]\frac{4-8}{-5-(-3)} =\frac{-4}{-2} \\\\slope=2\\y=mx+b\\y=2x+b\\[/tex]
take a coordinate to fill in
[tex](-5,4)\\y=-5\\x=4\\-5=2(4)+b\\-5=8+b-8 -8\\-13=b\\[/tex]
this means that the equation is y=2x-13
and if you add m and b
you get :-11
I HOPE THIS HELPS
Answer:
7/2
Step-by-step explanation:
Let $A = (-3,8)$ and $B = (-5,4)$. The midpoint of $\overline{AB}$ is $\left( \frac{(-3) + (-5)}{2}, \frac{8 + 4}{2} \right) = (-4,6)$.
The slope of $\overline{AB}$ is $\frac{8 - 4}{(-3) - (-5)} = 2$, so the slope of the perpendicular bisector of $\overline{AB}$ is $-\frac{1}{2}$. Therefore, the equation of the perpendicular bisector is given by
\[y - 6 = -\frac{1}{2} (x + 4).\]Isolating $y,$ we find
\[y = -\frac{1}{2} x + 4.\]
Question 4 Select Prism from the list of shapes. Set the number of lateral faces to five, and explore the cross sections of a pentagonal prism. Move the intersecting plane, and vary the angle between the intersecting plane and the vertical axis to identify the shapes of different types of cross sections. Part A Note all the types of cross sections you observe. In the table, describe the shape of the cross section formed when a particular plane passes through the prism.
Answer:
Step-by-step explanation:
Answer:
Plato
Step-by-step explanation:
rectangle
pentagon
pentagon
pentagon, hexagon ,heptagon
pentagon, quadrilateral, or triangle
What are the first three terms of the Arithmetic Sequence an=11-3(n-1)?
a. 1, 2, 3
b. 0, 8, 16
c. 8, 5, 2
d. 11, 8, 5
Answer:
11,8,5
Step-by-step explanation:
an=11-3(n-1)
Let n=1
a1 = 11 - 3(1-1)
= 11 -0
=11
Let n=2
a2 = 11-3(2-1)
= 11 -3(1)
= 8
Let n=3
a3 = 11-3(3-1)
= 11 -3(2)
= 11 -6
=5
Answer:
The answer is 11,8,5
Step-by-step explanation:
that's the correct answer
Christina's family is building a house. On the blueprint, Christina's rectangular room measures 10cm by 12cm. The map has a scale of 1 cm=1.5 ft. What is the actual area of Christina's room?
Answer:
270 ft square
Step-by-step explanation:
10cm * 1.5ft = 15 ft
12cm * 1.5ft = 18ft
18ft * 15ft = 270ft square
Answer:
270 sq ft
Step-by-step explanation:
Which expression shows the simplified form of (8 r Superscript negative 5 Baseline) Superscript negative 3? 8 r Superscript 15 StartFraction 8 Over r Superscript 15 Baseline EndFraction 512 r Superscript 15 StartFraction r Superscript 15 Baseline Over 512 EndFraction
Answer:
[tex]\frac{r^{15}}{512}[/tex]
Step-by-step explanation:
Given
[tex](8r^{-5})^{-3}[/tex]
Required
Simplify
This can be simplified using the following law of indices;
[tex](ab)^n = a^{n}b^{n}[/tex]
The equation becomes
[tex](8^{-3})(r^{-5})^{-3}[/tex]
Express [tex]8^{-3}[/tex] as a fraction
[tex](\frac{1}{8^{3}})(r^{-5})^{-3}[/tex]
Simplify [tex]8^3[/tex]
[tex](\frac{1}{8*8*8})(r^{-5})^{-3}[/tex]
[tex](\frac{1}{512})(r^{-5})^{-3}[/tex]
The expression can further be simplified using the following law of indices;
[tex](a^m)^n = a^{mn}[/tex]
[tex](\frac{1}{512})(r^{-5})^{-3}[/tex] becomes
[tex](\frac{1}{512})(r^{-5*-3})[/tex]
[tex](\frac{1}{512})(r^{15})[/tex]
[tex]\frac{r^{15}}{512}[/tex]
Hence, the solution to [tex](8r^{-5})^{-3}[/tex] is [tex]\frac{r^{15}}{512}[/tex]
Answer:
D
Step-by-step explanation:
Which set of ordered pairs below is a function?
I.{(3,3),(6,1),(2,3)} .................. II.{(4,7),(2,8),(4,2)} .............. III.{(9,6),(3,1),(7,3)}
(((((((A I only )))))))) ((((( B II only ))))))) ((((((( C III only)))))) (((D I and III))))
Answer:
C
Step-by-step explanation:
How many solutions does this equation have?
x=y - 3
2x - 2y = - 6
1. NO SOLUTION
2. ONE SOLUTION
3. INFINITE NUMBER OF SOLUTIONS
Answer:
option 2 is correct ans. it can be solved by substitution method.
Simplify:$$\sqrt{2\sqrt{8^2+15^2}+\sqrt{9^2+40^2}}$$
Answer:
[tex]5\sqrt{3}[/tex]
Step-by-step explanation:
[tex]\sqrt{2\sqrt{8^2+15^2}+\sqrt{9^2+40^2}}=?\\\\1)\sqrt{8^2+15^2}=\sqrt{289}=17\\2)\sqrt{9^2+40^2}=\sqrt{1681}=41\\3)2\times17=34\\4)\sqrt{34+41}=5\sqrt{3}[/tex]
All Done!
Answer:
Your correct answer is 8.660254
Step-by-step explanation:
√2√82 + 152 + √92 + 402 = 8.660254
solve:
|3x+ 2| > 14
show work
Answer:
x < -16/3 or x > 4
Step-by-step explanation:
This is split into two inequalities: 3x + 2 > 14 and -(3x + 2) > 14.
3x + 2 > 14
3x > 12
x > 4
-(3x + 2) > 14
3x + 2 < -14
3x < -16
x < -16/3
Answer:
[tex]x > 4[/tex]
Step-by-step explanation:
Move the constant to the right-hand and change its sign:
[tex]3x > 14 - 2[/tex]
Subtract the number:
[tex]3x > 12[/tex]
Divide both sides of the inequality by 3:
[tex]3 \div 12 = 4[/tex]
Therefore, the answer will be x > 4.
Determine the slope of the following equation: 2y -4x = 9
I only need help step by step solution for question#40 and #44
the link is not working :(
Lines AB and CD (if present in the picture) are straight lines. Find x. Give reasons to justify your solutions.
Answer:
WORDS: The value of x is 15.
EQUATION: x = 15
Step-by-step explanation:
1. AB is a straight line therefore angles AOF, FOG, and GOB total 180º
2. If ∠FOG = 90º, AOF + GOB = 90º by subtraction & substitution property
3. 5x - 15 + 2x = 90 (now solve) --> by substitution
4. 7x - 15 = 90 --> by C.L.T. or Combine Like Terms
5. 7x = 105 --> by C.L.T. or Combine Like Terms
6. x = 15 --> by inverse operations (division)
Hope this helps!
How is the graph of y = 2 (3)^x+1 -4 translated from the graph of y = 2(3)^x
Answer:
f(x - n) - shift the graph n units right
f(x + n) - shift the graph n units left
f(x) - n - shift the graph n units down
f(x) + n - shift the graph n units up ----------------------------------------------------------------------------
Answer: shift the graph of y = 2(3)ˣ one unit right and four units up.
if the first and third of three consecutive odd integers are added, the result is 75 less than five times the second integers. find the third integer. please show work
Answer:
The third integer is 27
Step-by-step explanation:
Given
Represent the consecutive odd numbers with [tex]T_1, T_2; and\ T_3[/tex]
Since they are consecutive odds, then
[tex]T_2 = 2 + T_1[/tex]
[tex]T_3 = 2 + T_2[/tex]
From the first statement in the question, we have that
[tex]T_1 + T_3 = 5 T_2 - 75[/tex]
Required
Find the third integer
Recall that
Substitute [tex]T_2 = 2 + T_1[/tex] in [tex]T_3 = 2 + T_2[/tex]
[tex]T_3 = 2 + 2 + T_1[/tex]
[tex]T_3 = 4 + T_1[/tex]
Substitute [tex]T_3 = 4 + T_1[/tex] and [tex]T_2 = 2 + T_1[/tex] in [tex]T_1 + T_3 = 5 T_2 - 75[/tex]
[tex]T_1 + 4 + T_1 = 5(2 + T_1) - 75[/tex]
Open Brackets
[tex]T_1 + 4 + T_1 = 10 + 5T_1 - 75[/tex]
Collect like terms
[tex]T_1 + T_1 + 4 = 5T_1 - 75 + 10[/tex]
[tex]2T_1 + 4 = 5T_1 - 65[/tex]
Collect like terms
[tex]2T_1 - 5T_1 = - 65 - 4[/tex]
[tex]-3T_1 = - 69[/tex]
Divide both sides by -3
[tex]\frac{-3T_1}{-3} = \frac{- 69}{-3}[/tex]
[tex]T_1 = 23[/tex]
Recall that [tex]T_3 = 4 + T_1[/tex]
[tex]T_3 = 4 + 23[/tex]
[tex]T_3 = 27[/tex]
The third integer is 27
Every day you collect 3 pennies and keep them in a jar. So the first day you have 3, the second day you have 6, the third day you have 9, etc. How many do you have on the 13th day?
Answer: 39 Pennies
Step-by-step explanation: You can think about this question as a multiplication problem. When you look at the pattern of the the other days you notice that they are all mulitples of 3. So when you want to find the number of pennies on the 13th day. You can do 3*13 = 39.
Mr. Maddox asked four students to create a number line to help find the sum of the fractions. Negative StartFraction 7 over 10 EndFraction + StartFraction 4 over 10 EndFraction Which number line would be best to find this sum?
Answer:
First choice
Step-by-step explanation:
Sum of fractions:
-7/10 + 4/10= - 3/10
the interval required on the line from the left of - 7/10 to the right of -3/10
Which number line would be best to find this sum?
-8/10 to 0
yes, this is good as covers the interval from -7/10 to - 3/10
-3/10 to 3/10
no, it doesn't include the left half of required section
4/10 to 11/10
no, it doesn't include the required interval
0 to 15/10
no, it doesn't include the required interval
Answer:
A
Step-by-step explanation: