Answer:
E. 12
Step-by-step explanation:
The ratio of the lengths of the sides of a 30-60-90 triangle is
short leg : long leg : hypotenuse
1 : √3 : 2
The short leg is 4√3.
The long leg is √3 times the short leg.
a = 4√3 * √3 = 4 * √9 = 4 * 3 = 12
Answer: E. 12
8x+4=3(x-1) +7 solve
Answer:
x = 0
Step-by-step explanation:
8x + 4 = 3(x − 1) + 7
Simplify both sides of the equation:
8x + 4 = (3)(x)+ (3)(−1) + 7
8x + 4 = 3x + (−3) +7
Combine like terms:
8x + 4 = (3x) + (−3+7)
8x + 4 = 3x + 4
Subtract 3x from both sides:
8x + 4 − 3x = 3x + 4 − 3x
5x + 4 = 4
Subtract 4 from both sides:
5x + 4 − 4 = 4 − 4
5x =0
Divide both sides by 5:
5x/5 = 0/5
x = 0
I really need these answered!
Answer:
Step-by-step explanation:
#1) [tex]\arcsin \left(0.64958\right)=0.70703\dots \quad \begin{pmatrix}\mathrm{Degrees:}&40.51^{\circ \:}\end{pmatrix}[/tex]
∡C =62.49
[tex]\frac{\left(\sin \left(27^{\circ \:}\right)\right)}{3}=\frac{\sin \left(54^{\circ \:}\right)}{x}\quad :\quad x=\frac{3\left(\sqrt{5}+1\right)}{\sin \left(27^{\circ \:}\right)\cdot \:4}\quad \left(\mathrm{Decimal}:\quad x=5.34603\dots \right)[/tex]
Question 7 of 10
A construction worker needs to put a rectangular window in the side of a
building. He knows from measuring that the top and bottom of the window
have a width of 5 feet and the sides have a length of 12 feet. He also
measured one diagonal to be 13 feet. What is the length of the other
diagonal?
O A. 12 feet
B. 13 feet
O C. 5 feet
O D. 17 feet
Answer:
13
Step-by-step explanation:
The diagonals of rectangle are equal in length.
Monica took a survey of her classmates' hair and eye color. The results are in the table below.
What is the conditional relative frequency that a participant has red hair, given that he/she has green eyes.
0.5
0.13
5
0.38
Answer:
let R represent red hair
let G represent green eyes
from Baye's theorem:
[tex]P( \frac{R}{G} ) = \frac{P(RnG)}{P(G)} [/tex]
P(RnG) = 5
[tex]P(G) = { \sum}(green \: hair) \\ = (3 + 5 + 5) \\ = 13[/tex]
Therefore:
[tex]P( \frac{R}{G} ) = \frac{5}{13} \\ = 0.385[/tex]
The conditional relative frequency = 0.385
The conditional relative frequency will be 0.385
What is Baye's theorem?It is a theorem showing how to compute the conditional probability of each of a set of possible causes for a given observed outcome using knowledge about the probability of each cause and the conditional probability of each cause's outcome.
let R represent red hair
let G represent green eyes
from Baye's theorem:
[tex]P=\dfrac{R}{G}=\dfrac{P(R\cap G)}{P(G)}[/tex]
P(RnG) = 5
P(G) = ∑(Green hairs)
P(G)= 13+5+5 = 13
Therefore:
[tex]P(\dfrac{R}{G})= \dfrac{5}{13}=0.385[/tex]
The conditional relative frequency = 0.385
Hence the conditional relative frequency will be 0.385
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Penny attended a four year state college. She took out a student loan to pay for her tuition and room & board for the four years she was attending the college. Her tuition fees were $6,970 per year, and the cost of her room and board was $11,320 per year. Now that she has graduated, she will have to start paying back her loan. Fortunately, Penny has a grace period of one year before she has to start paying back the loan. Her loan details are as follows: there is a fixed-rate interest of 4.5% and the interest compounds each month. During her one year grace period, interest will accrue on the loan, so that when she has to start paying the loan back she will owe more than what she owes now. Her goal is to be able to payoff the loan in 10 years.
Given all of this information, answer the following questions:
1. What is the original loan amount, i.e. how much were the total costs for tuition plus room & board for the four years that Penny attended the college?
2. What is the new loan amount after the one-year grace period (remember that interest will accrue on the loan during this initial 12-month period that she is not paying anything back on the loan)? This is the amount that she will be responsible for paying back. (Round your answer to the nearest whole dollar)
3. Given that she can pay back the loan in full after 10 years of payments, what is the total amount she will end up paying back (both principal and interest that has accrued over the 10 years)? And how much will her monthly payments on the loan be for those 10 years? (Round your answers to the nearest whole dollar)
Answer:
27,880 for tutitions + 45,280 for room and board= 73,160 total
Rodney and their roommates are making homemade pizza for dinner. Rodney tells his roommates that he would like for his slice to be cut at a 100 degree angle. The pizza has a diameter of 20 inches. To the nearest tenth of an inch, find the area of Rodney's slice of pizza. Approximate pi at 3.14.
Answer:
Area of pizza slice = 87 inches² (Approx.)
Step-by-step explanation:
Given:
Angle cut of pizza = 100°
Diameter of pizza = 20 inches
Find:
Area of pizza slice
Computation:
Area of sector = [Ф / 360][π][r²]
Area of pizza slice = [100/360][3.14][(20/2)²]
Area of pizza slice = [100/360][3.14][(10)²]
Area of pizza slice = [100/360][3.14][100]
Area of pizza slice = [0.2778][3.14][100]
Area of pizza slice = 87.2292
Area of pizza slice = 87 inches² (Approx.)
assume abc=def. if ab=5, ac=9 and ef=7, what is the length of bc?
Answer:
bc= 7
Step-by-step explanation:
Please help im stuck on this pls help ( i have to sort the cubes some how) i will give brainliest to who gets it right
Answer:
see image
three groups of 4 means 12 / 4 = 3
Step-by-step explanation:
Tyrone measured the floor of his rectangular storage unit. It is 3 feet wide and 8 feet from one corner to the opposite corner. How long is the storage unit? If necessary, round to the nearest tenth.
Answer:
Rounded to the nearest tenth, 7.4 feet long.
Step-by-step explanation:
Tyrone has a rectangular storage unit. We are given the width and the diagonal length.
So we can use Pythagorean Theorem.
3^2 + b^2 = 8^2
9 + b^2 = 64
subtract 9 from both sides
b^2 = 55
b = sqrt55
b is around 7.4161984871, so b rounded to the nearest tenth is 7.4 feet long.
x^2= 14x +11
------------
Answer:
[tex]x=7+2\sqrt{5} ,7-2\sqrt{5}[/tex]
Step-by-step explanation:
[tex]x^{2} =14x+11[/tex]
[tex]x^{2} -14x-11=0[/tex]
[tex]x\frac{-b\pm\sqrt{b^{2} -4ac} }{2(a)}[/tex]
[tex]x=\frac{14\pm\sqrt{(-14)^{2} -4(1)(-11)} }{2(1)}[/tex]
[tex]x=\frac{14\pm\sqrt{240} }{2}[/tex]
[tex]x=\frac{14\pm4\sqrt{15} }{2}[/tex]
[tex]x=7+2\sqrt{5} ,7-2\sqrt{5}[/tex]
------------------------
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-----------------------
Answer:
Solution given:
x²=14x+11
keeping all term on same side
x²-14x-11=0
trying to make it a perfect square
x²-2*7*x+7²-7²-11=0
By using formula of (x-y)²=x²-2xy+y²we get
(x-7)²-60=0
keeping 60 in right side
(x-7)²=60
doing square root on both side
[tex]\frac{(x-7)²}=\sqrt{60}[/tex]
we get
x-7=[tex]\sqrt{5*3*2*2}[/tex]
x-7=±2[tex]\sqrt{15}[/tex]
So
x=7±2[tex]\sqrt{15}[/tex]
Either
x=7+2[tex]\sqrt{15}[/tex]or
x=7-2[tex]\sqrt{15}[/tex]A car starts from rest. if the velocity of car become 15m/s after 20s calculate the acceleration of the car.
Answer:
[tex]0.75 {ms}^{ - 2} [/tex]
Step-by-step explanation:
[tex]acceleration = \frac{velocity}{time} \\ = \frac{15ms ^{ - 1} }{20s} \\ = \frac{3}{4} ms ^{ - 2} \\ = 0.75 {ms}^{ - 2} [/tex]
[tex]\Large\rm{\underbrace{\green{ \: Acceleration \: = \: \ \frac{v}{t} \: }}}[/tex]
V denotes rate of change in Velocityt denotes time taken[tex] \bf \large \implies \: Acceleration \: = \: \frac{15}{20} \\ [/tex]
[tex]\bf \large \implies \: Acceleration \: = \: \cancel\frac{15 \: \small \: m /s }{20 \: s} \: = \: \frac{3}{4} \: m /s ^{ - 1} \\ [/tex]
[tex]\bf \large \implies \: Acceleration \: = \: \cancel\frac{3}{4} \:m /s ^{ - 1} \: = \: 0.75 \: \: m /s ^{ - 1} \\ [/tex]
[tex] \bf \large \implies \: \: Acceleration \: = \: 0.75 \: \: m /s ^{ - 1} \\ [/tex]
HELP!!!
I need to know if this is Function or not a function.
Answer:
Not a function
Step-by-step explanation:
Since x = 1 produces y = 3 and y = 4 , the relation is not a function.
( − 2 , − 5) , ( − 1 , − 3 ) , ( 0 , 0 ) , ( 1 , 3 ) , ( 1 , 4 )
The domain cannot be the same value.
equation of the line which passes through point (0,5) at gradient of - 1
Answer:
y = - x + 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here gradient (slope) = - 1 and (0, 5) ⇒ c = 5
y = - x + 5 ← equation of line
The distance AB rounded to the nearest tenth = [?]
Answer:
4.5 units
Step-by-step explanation:
Use the distance formula
[tex]\sqrt{(-1-3)^{2}+(-1-1)^{2} }[/tex]
[tex]\sqrt{16+4}=\sqrt{20}[/tex]
The distance AB on the diagram rounded to the nearest tenth is: 4.5 units
Meaning of DistanceDistance can me defined as a measure that tells us how far apart two objects or individual are to each other.
Distance is very important as it helps us know where exactly things are located and whether they are close or far apart
In conclusion, The distance AB on the diagram rounded to the nearest tenth is: 4.5 units
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help me please it's important!!
Answer:
Does the answer help you?
Answer:
102 cm³
Step-by-step explanation:
Volume of R1:
length = 7 cm
Width = 3 cm
Height = 2 cm
Volume = 7* 3 * 2 = 42 cm³
Volume of R2:
length = 5 cm
Width = 4 cm
Height = 3 cm
Volume = 5 * 4 * 3= 60 cm³
Volume of the figure = 42 + 60 = 102 cm³
Find the length of UC? Please help
Answer:
The choose C. 18
Step-by-step explanation:
UC —> 105+82=187 —> 96+22+51=169 —> 187–169=18
I hope I helped you^_^
use the prime factors of 3136 and 2744 to evaluate:✓3136/3✓2744
Answer:
3136 = 2^6 × 7^2
2744 = 2^3 x 7^3
✓3136/3✓2744 = ✓(2^6 × 7^2)/3✓(2^3 x 7^3) = (2^3 x 7)/3 x 14(✓14) = 56/42✓14 =4/3✓14
Find the square root of 7250 by prime factorisation.
Answer:
The square root of 7250 is 85.15
Step-by-step explanation:
[tex]{ \boxed{ \sf{7250}}} \\ ↓ \div 2 \\ { \boxed{ \sf{3625}}} \\ ↓ \div 5 \\ { \boxed{ \sf{725}}} \\ ↓ \div 5 \\ { \boxed{ \sf{145}}} \\ ↓ \div 5 \\ { \boxed{ \sf{29}}}[/tex]
Find square roots of divisors:
[tex]{ \sf{ = \sqrt{2} \times \sqrt{5 \times 5 \times 5} \times \sqrt{29} }} \\ = { \sf{ \sqrt{2} \times \sqrt{125} \times \sqrt{29} }} \\ = { \sf{85.15}}[/tex]
[tex]{ \underline{ \sf{ \blue{christ \:† \: alone }}}}[/tex]
Help me please Will give brainlist
Answer:
Step-by-step explanation:
These are geometric means problems. In the top one, a is the geometric mean as the height for both the smaller triangles inside the big one. Therefore,
[tex]\frac{4}{a} =\frac{a}{25\\}\\a^2=100\\a=10[/tex]
The next one has the geometric mean of b, being a part of the smaller triangle on the left and the big triangle as a whole:
[tex]\frac{4}{b} =\frac{b}{29}\\b^2=116\\b=10.77[/tex]
PLEASE HELP ASAP!!
Find the surface area of the regular pyramid shown in the accompanying diagram. If necessary, express your answer in simplest radical form.
A. 146.85 units²
B. 45+9√3 units²
C. 36+9√3 units²
D. 36+3√3 units²
The total surface area of the pyramid is 52 square units
The formula for calculating the area of the triangular based pyramid is expressed as;
[tex]TSA=Base \ Area+\frac{1}{2}ps[/tex] where;
p is the perimeter of the base
s is the slant height
Get the Base area
[tex]Base \ Area = \frac{1}{2}bh\\Base \ Area = \frac{1}{2}*6*\sqrt{5^2-3^2} \\ Base \ Area = \frac{1}{2}*6*\sqrt{25-9} \\ Base \ Area = \frac{1}{2}*6*\sqrt{16} \\ Base \ Area = \frac{1}{2}*6*4 \\ Base \ Area = \frac{24}{2} \\Base \ Area = 12 units^2[/tex]
Get the perimeter
Perimeter = 5 + 5 + 6
Perimeter = 16 units
Slant height = 5units
Substitute the given values into the formula above as shown;
[tex]TSA=12+\frac{1}{2}*16*5\\TSA=12+(8*5)\\\\TSA = 12 + 40\\TSA = 52 units ^2[/tex]
Hence the total surface area of the pyramid is 52 square units
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Answer:
52squnits
Step-by-step explanation:
Ethan sells e candy bars for $2.50 apiece and Chloe sells c candy bars for $2.00 apiece to raise
money for a school trip. Ethan sold 15 fewer candy bars than Chloe, but he also got a $6.00
donation. If Chloe and Ethan raised the same amount of money, which of the following systems
could be used to find how many candy bars each sold?
The system that could be used to find how many candy bars each sold is given is option B.
What is the candy bar about?Since Ethan sold 15 fewer candy bars than Chloe, as portrayed in the question, so:
e = C - 15
Based on the fact that Chloe and Ethan raised the same amount of money, the equation will be:
2C: 2.5e + 6
Therefore, The system that could be used to find how many candy bars each sold is given is option B.
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what is the answer to -3/7 x -1 2/3
Answer:
-9x-35/21
Step-by-step explanation:
Answer:
[tex]\frac{5}{7}[/tex]
Step-by-step explanation:
[tex]\frac{-3}{7}* (-1\frac{2}{3})=\frac{-3}{7}*\frac{-5}{3}\\\\= \frac{5}{7}[/tex]
Which figure is described below?
The locus of points in a plane
equidistant between
(-5, -6) and (-5, 7).
Answer:
A.Line
Step-by-step explanation:
The locus of points in a plane equidistant between (-5, -6) and (-5, 7) is describe by the Line. so option A is correct.
What is a line segment?A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).
We know that the graph of x = 5 is the vertical line through 5 on the x-axis. Two points on this line are (-5, -6) and (-5, 7).
We form a horizontal line through (0,1) and (1,1). This is the locus of points equidistant between (-5, -6) and (-5, 7)
We have parallel lines like this, the locus of points equidistant from the two lines is always one single line, and it's the middle line as described above.
This applies to diagonal parallel lines as well, and vertical parallel lines.
Hence, The locus of points in a plane equidistant between (-5, -6) and (-5, 7) is describe by the Line. so option A is correct.
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THIS IS TIMED! Find the equation of the graphed line.
On a coordinate plane, a line goes through (negative 6, 0) and (0, negative 7).
a.
y = negative 6 x minus 7
c.
y = negative StartFraction 6 Over 7 EndFraction x minus 6
b.
y = 6 x minus 7
d.
y = negative StartFraction 7 Over 6 EndFraction x minus 7
Please select the best answer from the choices provided
A
B
C
D
Answer:
D
Step-by-step explanation:
x/(-6)+y/(-7)=1
7x+6y=-42
7x+6y+42=0
y=(-7/6)x-7
Answer these questions about finding the missing
angle measures.
What is the measure of
What is the measure of
What can be concluded about these triangles?
Answer choices/:
what can be concluded?
1.corresponding angles are proportional
2.The triangles are congruent
3.The triangles are similar
Answer:
Answer number one the
Step-by-step explanation:
the unequal triangles. If measured by angle, they are equivalent.
HELP PLEASE 100 POINTS
Answer:
Step-by-step explanation:
That's an awful lot of points. You don't have to give that many. 10 or 15 points would be more than enough.
The graph touches the x axis at 1 point. That means its basic formula is y = (x - a)^2
Since it upside down, the formula is y = -(x - a)^2. A couple of other things are true.
a = 1 because that's where the graph touches the x axis. y = - x^2 has shifted 1 unit to the right.
Finally the y intercept is -4 which means that the final equation is y = -4(x-1)^2
That's all preliminary. The actual question is, what does the discriminate look like?
y = -4(x^2 - 2x + 1)
y = -4x^2 + 8x - 4
a = - 4
b = 8
c = - 4
sqrt(b^2 - 4ac)
sqrt(8^2 - 4(-4)(-4) )
sqrt(64 - 64) = 0
The answer is the third one. The answer will always be 0 when the graph touches the x axis and does not go through it.
Put the steps In order
The path from the subway station to the art museum is three blocks to the north then four blocks to the west.
What is the straight-line distance in blocks from the subway station to the art museum?
Answer:
7 block s
Step-by-step explanation:
3 from North plus
4 from West
4+3=7
which has a steeper slope y-1/2x or y=2/3x?
Answer:
y=2/3x
Step-by-step explanation:
2/3 is greater than 1/2. It doesn't matter if one of the slopes are negative.
1. Determine the measure of the unknown angles indicated by letters. Justify your answers with
the properties or theorems you used.
Answer:
110
Step-by-step explanation:
we use the sum of 3 angles in a triangle is 180
and sum of 2 adjacent angles is 180 too
180= (180-d)+)+(180-85)+(180-165)
so d=110
Step-by-step explanation:
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