Answer:
1 year and a half or 18 months
Step-by-step explanation:
ABC is a right triangle at B such that
AB = 8 cm and AC = 10 cm.
1° Calculate BC
2º Consider a point M of the segment [AB]
The line passing through M and parallel to the
line (AC) cuts the line (BC) in N.
Supposing that AM = x, calculate MB and BN in
5
terms of x. then verify that MN (8 - x).
4
3° Let D be the fourth vertex of rectangle
ABCD.
The parallel to (BD) passing through M.cuts the
line (AD) at P
Calculate AP and MP in terms of x
4° Prove that the perimeter of the polygon
MNCDP is independent from x
Answer:
Question 1
Pythagoras' Theorem: a² + b² = c²
(where a and b are the legs, and c is the hypotenuse, or a right triangle)
Given:
a = BCb = AB = 8cmc = AC = 10 cm⇒ BC² + 8² = 10²
⇒ BC² = 36
⇒ BC = 6 cm
Question 2
Given:
AB = 8 cmAM = x⇒ MB = AB - AM = 8 - x
As ΔABC ~ ΔMBN
⇒ AB : AC = MB : MN
⇒ 8 : 10 = (8 - x) : MN
[tex]\sf \implies \dfrac{8}{10}=\dfrac{(8-x)}{MN}[/tex]
[tex]\sf \implies \dfrac45=\dfrac{(8-x)}{MN}[/tex]
[tex]\sf \implies MN=\dfrac54(8-x)[/tex]
Question 3
D = (6, 8)
As ΔBAD ~ ΔMAP
⇒ AB : AD : BD = AM : AP : MP
⇒ 8 : 6 : 10 = x : AP : MP
[tex]\sf \implies \dfrac{8}{6}=\dfrac{x}{AP}[/tex]
[tex]\sf \implies AP=\dfrac34x[/tex]
[tex]\sf \implies \dfrac{8}{10}=\dfrac{x}{MP}[/tex]
[tex]\sf \implies MP=\dfrac54x[/tex]
Question 4
Perimeter of MNCDP = MN + NC + CD + PD + MP
As ΔABC ~ ΔMBN
⇒ AB : BC : AC = MB : BN : MN
⇒ 8 : 6 = (8 - x) : BN
[tex]\sf \implies \dfrac86=\dfrac{(8-x)}{BN}[/tex]
[tex]\sf \implies BN=\dfrac34(8-x)[/tex]
NC = BC - BN
[tex]\sf \implies NC=6-\dfrac34(8-x)[/tex]
PD = 6 - AP
[tex]\sf \implies PD=6-\dfrac34x[/tex]
Perimeter of MNCDP = MN + NC + CD + PD + MP
[tex]\sf \implies perimeter=\dfrac54(8-x)+6-\dfrac34(8-x)+8+6-\dfrac34x+\dfrac54x[/tex]
[tex]\sf \implies perimeter=10-\dfrac54x+6-6+\dfrac34x+8+6-\dfrac34x+\dfrac54x[/tex]
[tex]\sf \implies perimeter=10+8+6=24[/tex]
Answer 1-3 please. Thank you.
Answer:
If we look at this spinner, we first need to find out how many letters there are in total.
There are 12 letters in total.
1.
For this question, they want us to find the probability of getting the letter 'R'.
We need to find how many letter 'R's there are.
There are 2 lettered 'R', out of the 12 letters.
So the probability of getting the letter 'R' is 2/12 which simplifies to 1/6.
2.
For this question, they want us to find the probability of getting the letter 'L'.
We need to find how many letter 'L's there are.
There are 3 lettered 'L's, out of the 12 letters.
So the probability of selecting the letter 'L' is 3/12 which simplifies to 1/4.
3.
For this question, they want us to find the probability of getting the letter 'B'.
We need to find how many letter 'B's there are.
There are 0 lettered 'B's, out of the 12 letters.
Therefore the probability of selecting the letter 'B' is impossible.
4.
For this question, they want us to find out which letter has the most likely chance of getting landed on.
In order to find this, we need to find one letter that is repeated a lot in this spinner, that way it is more likelier of getting that letter.
Let's look at each individual letter keeping the letters we've found so far to the side.
P(Z) = 4/12, which simplifies to 1/3.
P(S) = 1/12, which is already in simplest form.
P(F) = 2/12, which simplifies to 1/6.
Now let's compare all the probabilities for selecting each letter.
P(R) = 1/6
P(L) = 1/4
P(B) = impossible ← immediately eliminate this choice
P(Z) = 1/3
P(S) = 1/12
P(F) = 1/6
Now out of all of these probabilities, we can infer that the chances of getting the letter 'Z' is the most likeliest.
Write the absolute value equations in the form |x-b|=c (where b is a number and c can be either a number or an expression) that have the following solution sets. Two solutions: x=2, x=14
Answer:
|x - 8| = 6
Step-by-step explanation:
|x - b| = c
⇒ (x - b)² = c²
Given:
x = 2x = 14Substitute the values of x into (x - b)² = c²:
(2 - b)² = c²
(14 - b)² = c²
Equate and solve for b:
(2 - b)² = (14 - b)²
⇒ 4 - 4b + b² = 196 - 28b + b²
⇒ 4 - 4b = 196 - 28b
⇒ 24b = 192
⇒ b = 8
Substitute b = 8 into the equations to find c:
x = 2 ⇒ |2 - 8| = 6
x = 14 ⇒ |14 - 8| = 6
Therefore, c = 6
Final equation: |x - 8| = 6
John is solving x^2 + 4x + 8=0 by completing the square. Which step would be part of John's solution.?
(x + 4)^2 = - 4
(x+2)^2 = - 4
(x+4)^2 = - 8
(x + 2)^2 = - 8
Answer:
[tex](x + 2) ^{2} = - 8[/tex]
Step-by-step explanation:
[tex] {x}^{2} + 4x + 8 = 0 \\ {x }^{2} + 4x = - 8 \\ {x}^{2} + 4x + 4 = - 8 + 4 \\ ( x + 2)^{2} = - 4[/tex]
Please help with my homework. I will give a brainlist out. Only solve 27 please.
Now
Base×Height=8517H=85H=85/17H=5ftDoes this table represent a function?
Answer:
Yes it does!
Have an amazing day!!
Please rate and mark brainliest!
Finn removes the plug from a trough to drain the water. the volume, in gallons, in the trough after it has been unplugged can be modeled by the expression 12x2 −13x 3, where x is the time in minutes. choose the appropriate form of the expression that would reveal the time in minutes when the trough is empty. 12(0)2 − 13(0) 3 (3x − 1)(4x − 3) 12(x − 3)2 − 1 12(x − 1)2 − 3
The given expression [tex]\rm 12x^2-13x+3[/tex]equivalent to (3x - 1)(4x - 3) option second is correct.
What is a quadratic expression?A quadratic expression is a second-degree algebraic expression represented by the:
[tex]\rm f(x)=ax^2+bx+c[/tex] ........(1)
Where a, b, and c are the constants and
We have the quadratic expression:
[tex]\rm f(x)=12x^2-13x+3[/tex]
[tex]\rm f(x)=12x^2-9x-4x+3[/tex] (we can write -13x as a sum of -9x and -4x)
After taking common term, we get:
[tex]\rm f(x)=3x(4x-3)-(4x-3)[/tex]
[tex]\rm f(x)=(4x-3)(3x-1)[/tex] or
[tex]\rm f(x)=(3x-1)(4x-3)[/tex]
Thus, the given expression [tex]\rm 12x^2-13x+3[/tex] is equivalent to (3x - 1)(4x - 3).
Learn more about quadratic equations here:
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The box plots summarize the attendance for the spring musical and fall musical. Each musical was performed for six evenings. Which statement best describes the data represented in the box plots? (6.13A)
Answer:
B
Step-by-step explanation:
The 1st quartile is 135. The 3rd quartile is 195. To find the interquartile, you would subtract the 3rd quartile from the 1st quartile. 195-135=60. The interquartile range for the spring musical is 60
A cylinder with a height of 8 inches and a radius of 4 inches what is the volume?
Answer:
Formula for volume of cylinder;
V = π[tex]r^{2}[/tex]h
Where 'π' is pi(22/7 or 3.14), 'r' is the radius which is being squared, and 'h' represents the height.
Plug in your values given that;
8 in. = height
4 in. = radius
V = π[tex]r^{2}[/tex]h
V = 3.14(4^2) x 8
V = 3.14(16) x 8
V = 50.24 x 8
V = 401.92 cubic inches or [tex]401.92^{3}[/tex] inches is the volume.
Hiroko is trying to find the value of d in 10d + 490 = 2,500. he starts by correctly rewriting the equation as 10(d + 49) = 10(250). How could this help Hiroko figure out the value of d?
Answer:
Hiroko removed common factors, which leads to smaller numbers, which can be easier to work with.
Step-by-step explanation:
However, this step is not entirely needed in the grand scheme of solving the problem. It simply uses smaller numbers to digest.
Do the opposite of PEMDAS when isolating the variable, d. Note the equal sign, what you do to one side of the equal sign, you do to the other.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction.
First, subtract 490 from both sides of the equation:
10d + 490 (-490) = 2500 (-490)
10d = 2500 - 490
10d = 2010
Next, divide 10 from both sides of the equation:
(10d)/10 = (2010)/10
d = 2010/10
d = 201
201 is your value for d.
~
Scaling factors! Help please!
Answer:
x=3
y=12
Step-by-step explanation:
The scale factor is 1:4
we divide 12 by 4 to get 3
if we multiply 3 by 4 it is 12 so y=12
We have a shape that has an area of 112 inches squared. Convert the units to centimeters squared. (HINT: Perform multiple conversions). Don’t forget to show your work.
Answer:
722.5792 cm²
Step-by-step explanation:
1 in ≈ 2.54 cm
Squaring both sides:
⇒ (1 in)² ≈ (2.54 cm)²
Apply exponent rule (ab)² = a²b²
⇒ (1)² in² ≈ (2.54)² cm²
⇒ 1 in² ≈ 6.4516 cm²
Therefore, to convert an area measured in inches squared to centimeters squared, multiply by 6.4516:
⇒ 112 in² ≈ (112 × 6.4516) cm²
= 722.5792 cm²
Given m
|| n, find the value of x and y.
Answer:
55 degrees
Step-by-step explanation:
well, x is on the same line as 125, and a line is always a straight 180 degrees, so you subtract 180-125=55, and angle x and angle y are corrisponding angles, so y also equals 55 degrees.
hope that helps!
What is Earth's diameter, rounded to the nearest whole number?
Answer:
7918
Step-by-step explanation:
If you round Earth's diameter, I believe that it is 7,918 miles.
Find the area of the figure in the picture below
Answer:
183 cm^2
Step-by-step explanation:
the line through the shape line means that they are equivalent meaning the side that is empty not making the trapezoid would be 9 as well. moving the 3 over since it is right next to it. 3 times 9 equal 27cm^2. later we are gonna use this number to subtract
then make a different equation with 3+9 to the the full height of the trapezoid pretending it is not missing anything. 3+9=12
then use the formula to find the area of the trapezoid which is 1/2(h)(b1+b2)
add the 2 bases together to get 35. how did i get 35. 12+14=26 yes then include the 9 to get 35.
1/2(height=12)(35)=6(35)=210cm^2
then you used 210-27 to get 183cm^2
Are the expressions 5(3a+2) and 15a+2 equivalent? Justify your answer.
SOLVE equations, SHOW WORK, AND EXPLAIN
Find the surface area - PLSS HELPP AND HURRY PLS
Answer:
A = 390
Step-by-step explanation:
l=14
w= 3
h= 9
A= 2 (wl+hl+hw) = 2 (3.14+9.14+9.3) = 390
Answer: 390in^2
Step-by-step explanation:
2(14 x 3) + 2(9 x 3) + 2(14 x 9)
84 + 54 + 252 = 390 in^2
I need help with D, i’m confused on it.
Answer:
Step-by-step explanation:
[tex]A=P(1+\frac{r}{n})^{nt[/tex]
A = future value ($)
P = principal (orignal amount - $400)
R = rate (written as a decimal - 3%/100= 0.03)
N = compound (yearly - 1)
T = number of years (0, 5, 10, 15)
Now, substitute each number into the formula and record them in the table.
0 years:
[tex]A=P(1+\frac{r}{n})^{nt}\\\\A=400(1+\frac{0.03}{1})^{1*0}\\\\A=400(1+\frac{0.03}{1})^0 < ==any\ number\ raised\ to\ zero=1\\\\A=400(1)\\\\A=\$400[/tex]
5 years:
[tex]A=P(1+\frac{r}{n})^{nt}\\\\A=400(1+\frac{0.03}{1})^{1*5}\\\\A=400(1+\frac{0.03}{1})^{5}\\\\A=400(1+{0.03})^{5}\\\\A=400({2.03})^{5}\\\\A=400({1.1593})\\\\A=\$463.72 < ==round\ to\ the\ nearest\ dollar\\\\A=\$464[/tex]
10 years:
[tex]A=P(1+\frac{r}{n})^{nt}\\\\A=400(1+\frac{0.03}{1})^{1*10}\\\\A=400(1+\frac{0.03}{1})^{10}\\\\A=400(1+{0.03})^{10}\\\\A=400({1.03})^{10}\\\\A=400({1.3439})\\\\A=\$537.56 < ==round\ to\ the\ nearest\ dollar\\\\A=\$538[/tex]
15 years:
[tex]A=P(1+\frac{r}{n})^{nt}\\\\A=400(1+\frac{0.03}{1})^{1*15}\\\\A=400(1+\frac{0.03}{1})^{15}\\\\A=400(1+{0.03})^{15}\\\\A=400({1.03})^{15}\\\\A=400({1.5579})\\\\A=623.16 < ==round\ to\ the\ nearest\ dollar\\\\A=\$623[/tex]
20 years:
[tex]A=P(1+\frac{r}{n})^{nt}\\\\A=400(1+\frac{0.03}{1})^{1*20}\\\\A=400(1+\frac{0.03}{1})^{20}\\\\A=400(1+{0.03})^{20}\\\\A=400({1.03})^{20}\\\\A=400({1.8061})\\\\A=722.44 < ==round\ to\ the\ nearest\ dollar\\\\A=\$722[/tex]
Note that since we are rounding, answers may vary by a dollar or two.
Hope this helps!
3. 9, 11, 33, N, 105.
Answer:
N = 35
Step-by-step explanation:
The pattern in this sequence is x3, +2.
3 * 3 = 9
9 + 2 = 11
11 * 3 = 33
33 + 2 = N
N * 3 = 105
N = 33 + 2 = 105/3 = 35
Apples cost $1.99 per pound how much do 3 1/4 pounds of apples cost
Answer:
6.47
Step-by-step explanation:
1.99/1 lb= x/3.25lb
3 1/4=3.25
Cross multiply
X=(1.99)(3.25)=6.47
Employee identification codes at a company contain 2 letters followed by 4 digits. Assume that all codes are equally likely. Identify the probability that an ID code does not contain the letter I.
A. 0.9246
B. 0.6567
C. 0.7493
D. 0.8321
Using it's concept, it is found that the probability that an ID code does not contain the letter I is given by:
A. 0.9246
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Considering that for each letter there are 26 possible outcomes and for each digit there are 10 possible outcomes, the total number of outcomes is given by:
T = 26 x 26 x 10 x 10 x 10 x 10 = 6,760,000.
Without the letter "l", the desired number is given by:
D = 25 x 25 x 10 x 10 x 10 x 10 = 6,250,000.
Hence, the probability is given by:
p = 6,250,000/6,760,000 = 0.9246.
Which means that option A is correct.
More can be learned about probabilities at https://brainly.com/question/14398287
The circumference of the Earth is 2.4x10^4 miles. If you traveled at an average of 8.5x10 miles per hour, how long would it take for you to go around the Earth? Round your answer to the nearest whole number.
It will take approximately 282.352 hours for one to go round the earth, this is equivalent to 11.764 days
Speed, Distance and TimeGiven Data
Circumference of Earth = 2.4x10^4 milesDistance round the earth = 2.4x10^4 milesSpeed = 8.5x10 miles per hourWe know that the relationship between speed, distance and time is given as
Speed = Distance/Time
Hence,
Time = Distance/Speed
Substituting our given data into the expression we have
Time = 2.4x10^4/8.5x10
Time = 2.4x10^3/8.5
Time = 282.352 hours
Learn more about speed, distance and time here:
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What is the area of this rectangle?
42 sq ft
17 ft
34 ft
52 sq ft
Answer:
42 ft²
Step-by-step explanation:
→ State the area of the formula of rectangle
Length × Width
→ Substitute in the numbers
14 × 3 = 42 ft²
Answer:
42 sq ft
Step-by-step explanation:
L*W=A
14*3=42
What is the lowest common denominator of 6,4,3,42?
Answer: 1
Step-by-step explanation: the lowest number they divide into evenly is 1
Lana does yard work. The information below shows the approximate time for each job:
Mow small lawn - 1/2hr
Mow large lawn - 3/4hr
Tidy yard - 1 1/2hr
Plant annuals - 2 1/2hrs
For one Saturday, Lana needs to mow 3 small lawns, mow 1 large lawn, tidy 2 yards, and plant annuals once. She needs travel time between jobs, and a break for lunch. Do you think she will be able to complete all of the jobs in one day? Justify your answer.
Answer:
No, not enough timeStep-by-step explanation:
Time to complete each of jobs
1/2 * 3 = 1 1/2 hrs3/4 * 1 = 3/4 hr1 1/2 * 2 = 3 hrs2 1/2 * 1 = 2 1/2 hrsTotal time at job
1 1/2 + 3/4 + 3 + 2 1/2 = 7 3/4 hrsIf the work day lasts for 8 hours, then Lana has only 1/4 hr to travel between jobs and a lunch break.
This time is not sufficient so she can't complete all the jobs.
Answer:
No (see explanation below)
Step-by-step explanation:
Approximate times to carry out each job:
Mow small lawn = 1/2 hrMow large lawn = 3/4 hrTidy yard = 1 1/2 hrPlant annuals = 2 1/2 hrsFor one Saturday, Lana needs to:
mow 3 small lawnsmow 1 large lawntidy 2 yardsplant annuals onceTherefore, the total time for the jobs is:
[tex]\begin{aligned}\sf Total\:time & = \sf 3\:small\:lawns+1\:large\:lawn+2\:tidy\:yards+1\:plant\:annuals\\\\& = \sf 3 \cdot \dfrac{1}{2}+\dfrac{3}{4}+2 \cdot 1 \frac{1}{2}+2\frac{1}{2}\\\\& = \sf 1 \frac{1}{2}+\dfrac{3}{4}+3+2\frac{1}{2}\\\\& =\sf 7 \frac{3}{4}\: hours\end{aligned}[/tex]
The likelihood of Lana being able to complete all the jobs in one day is dependent on how far she needs to travel between jobs and how long she wishes to break for lunch. A typical working day is around 8 hours. Therefore, unless Lana wishes to work for a longer day, it is unlikely she will be able to complete all of the jobs in one day as there is only 15 minutes available for traveling and lunch, which is likely not enough.
screenshot :D will award brainliest
Answer:
9 cm²
Step-by-step explanation:
Sometimes these inscribed polygon problems respond nicely to a little geometrical thinking. The figure is symmetrical about the vertical line through the center of the square(s).
__
AnalysisThat line of symmetry divides the figure into halves that are twice as tall as wide. That same ratio applies to both the outer square and the inner (blue shaded) square.
In other words, a line from the center of the top segment through either bottom corner of the figure will pass through the corners of both squares. That line will have a slope of ±2, making it easy to find the coordinates of one of the lower corners of the shaded square.
__
System of EquationsAnalytically, we can write the equation of the right circle shown in the attachment as ...
x² +y² = 5²
and the equation of the line as ...
y = 2x +5
__
Solution of EquationsThen the x-value of the lower left corner will be found where these intersect.
x² +(2x +5)² = 25 . . . . . . substitute for y
x² +4x² +20x +25 25 . . . . eliminate parentheses
5x² +20x = 0 . . . . . . . . . . . . subtract 25
5x(x +4) = 0 . . . . . . factor
x = -4 or 0 . . . . . the x-coordinates of the points of intersection
The y-coordinate of the lower left point is ...
y = 2(-4) +5 = -3
__
Area of the SquareSince the top edge of the blue square has a y-coordinate of 0, this means the square is 3 cm on a side. Its area is ...
A = s² = (3 cm)² = 9 cm² . . . . area of the blue shaded square
Plis somebody help me with this
Which table represents a relationship that is not a function?
Answer:
T is not a function.
Step-by-step explanation:
The definition of a function is a relationship where only one x value has a specific y value. So if an x-value has more than one y value, it is not a function due to its rule. This can also be checked by using a graph, graphing the function, and checking if it fits the vertical line test.
We see all of them work except T, where 2 x values are stated that are the same but have different y values.
So T is not a function.
I hope this helped!
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Which equation has a graph that is a parabola with a vertex at (–2, 0)?
y = –2x2
y = (x + 2)2
y = (x – 2)2
y = x2 – 2
Comparing to the standard equation, the parabola with a vertex at (-2,0) is given by:
y = (x + 2)²
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
In this problem, we have that h = -2 and k = 0, and all the options have leading coefficient a = 1, hence the equation is:
y = (x + 2)²
More can be learned about the equation of a parabola at https://brainly.com/question/17987697
Answer:
B. y = (x + 2)2the measure of an angle is 65 what is the measure of its complementary angle
Answer:
25 degrees
Step-by-step explanation:
complementary angles are 90 degrees
90-65=25 degrees
Question five What is the perimeter? Use 3.14 for pi. Please Show Work! I Will Mark As Brainlest!!
Answer:
73.81
Step-by-step explanation:
You know that the formula for circumeference is 2(pi)r.
2x3.14x11=69.08;
However, a part of the circle is cut off, leaving 3/4 of it.
3/4x69.08=51.81.
However, you add the 11+11 to it because of the slice.
22+51.81=73.81