Answer: 5;12;13
Step-by-step explanation:
let's call the shortest leg
[tex]x[/tex]
and then the longer leg and the hypotenuse
[tex]2x + 2[/tex]
[tex]2x + 3[/tex]
respectively, and then apply pythagorean theorem to the triangle:
[tex]x^2+(2x+2)^2=(2x+3)^2[/tex] at this point is simple number crunching;
[tex] x^2+4x^2+8x+4=4x^2+12x+9 \\ x^2-4x-5=0 \rightarrow (x-5)(x+1)=0[/tex]
the only valid solution is obviously x=5 since its a length of a segment.
During the year 2011 season a quarterback passed for 302 yd per game he played on my 16 regular season game for that year for how many total yards did the quarterback pass
Answer:
4,832 yards
Step-by-step explanation:
302x16=
The table shows the mass of a substance decreasing over a period of time during a chemical experiment.
Identify a quadratic model for the mass M, given the time t. Then use the model to predict the mass at t = 11
seconds
Time (s) Mass (g)
2
94.8
5
87.9
8
81.3
B
O M(x) = -0.02x2 - 2.42x + 99.57
M(11) - 75 g
O M(x) = 0.02x2 - 2.42x + 99.57
M(11) - 1299
O M(x) = -0.02x2 - 2.42X + 99.57
M(11) = 129 g
O M(x) = 0.02x2 - 2.42x + 99.57
M(11) = 75 g
So from a table, we want to find an equation that models the mass as a function of time, we will get the equation:
M(t) = 0.02*t^2 - 2.42*t + 99.57
And with that equation, we will find that the mass after 11 seconds is 75 grams.
From the table we have the points:
(2, 94.8)
(5, 87.9)
(8, 81.3)
And we know that this follows a quadratic model, then we have:
M(t) = a*t^2 + b*t + c
Notice that from the known points, we have 3 equations:
94.8 = a*2^2 + b*2 + c
87.9 = a*5^2 + b*5 + c
81.3 = a*8^2 + b*8 + c
So we have a system of equations, we can simplify the equations to get:
94.8 = a*4 + b*2 + c
87.9 = a*25 + b*5 + c
81.3 = a*64 + b*8 + c
To solve this, we start by isolating one of the variables in one of the equations, let's isolate c in the first one.
c = 94.8 - a*4 - b*2
now we replace this in the other two equations to get:
87.9 = a*25 + b*5 + (94.8 - a*4 - b*2)
81.3 = a*64 + b*8 + ( 94.8 - a*4 - b*2)
Now we simplify these two equations to get:
-6.9 = a*21 + b*3
-13.5 = a*60 + b*6
Now we do the same thing, I will isolate b in the first equation:
b = (-6.9 - a*21)/3 = -2.3 - a*7
Now we replace this in the other equation:
-13.5 = a*60 + (-2.3 - a*7)*6
Now we can just solve this for a:
-13.5 = a*(60 - 7*6) - 2.3*6
0.3 = a*18
0.3/18 = a = 0.016
Wich can be rounded to:
a = 0.02
Then the value of b is:
b = -2.3 - a*7 = -2.3 - 0.016*7 = -2.42
And the value of c is:
c = 94.8 - a*4 - b*2 = 94.8 - 0.016*4 - (-2.42)*2 = 99.57
So the equation is:
M(t) = 0.02*t^2 - 2.42*t + 99.57
Now we can evaluate this in t = 11s to get:
M(11) = 0.02*11^2 - 2.42*11 + 99.57 = 75.37
Wich can be rounded to 75 grams.
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i need help with 32
Answer: See the drawing below
Explanation:
The region to the left of x = -3 has f(x) > 0, aka f(x) is positive. This is due to the sign chart indicating this with a + sign. The same applies from the region between x = -3 and x = -2. The graph will show f(x) above the x axis for these two regions.
When -2 < x < 0, f(x) is now negative and below the x axis. It goes above the x axis for the interval 0 < x < 2. Then it dips back down below the x axis again once it passes x = 2.
The graph below visually summarizes everything talked about. Keep in mind that there are infinitely many ways to draw a graph like this. There's not enough info to pin down one exact answer.
The point (5 5/8, 2 1/4) lies on a line that represents a proportional relationship between two units of measure.
a. What is the constant of proportionality, or the unit rate (Leave answer as a fraction)?
b. Write an equation to represent this relationship (write rate as a fraction).
c. If point (6 1/2, y) also lies on this same line, what the value value of y, (otherwise, the y coordinate point?(Write point as a mixed fraction).
9514 1404 393
Answer:
a) k = 2/5
b) y = 2/5x
c) y = 2 3/5
Step-by-step explanation:
a)The proportional relation is described by the equation ...
y = kx . . . . . . k is the constant of proportionality
The value of k can be found by dividing the equation by x:
y/x = k = (2 1/4)/(5 5/8) = (9/4)/(45/8) = 18/45
k = 2/5
__
b)As above, the equation is ...
y = kx
y = 2/5x
__
c)Using 6.5 for x, we have ...
y = (2/5)(6.5) = 2.6 = 2 3/5
Write the equation of the line graphed below
Answer:
y= -1
Step-by-step explanation:
I think mainly because it's on the Y axis (horizontal line) on the negative so it would be ethical for that to be the answer
write the solution in interval notation: 1/4x−3≥−1 and −3(x−2)≥2
Answer:Mark me as Brainliest please
Step-by-step explanation:
Let's solve your inequality step-by-step.
[tex]\frac{1}{4}x-3\geq -1[/tex]
Step 1: Add 3 to both sides.
[tex]\frac{1}{4} x-3+3\geq -1+3[/tex]
[tex]\frac{1}{4} x\geq 2[/tex]
Step 2: Multiply both sides by 4.
[tex]4*(\frac{1}{4} x)\geq (4)*(2)[/tex]
Answer:x≥8
Let's solve your inequality step-by-step.
−3(x−2)≥2
Step 1: Simplify both sides of the inequality.
−3x+6≥2
Step 2: Subtract 6 from both sides.
−3x+6−6≥2−6
−3x≥−4
Step 3: Divide both sides by -3.
[tex]\frac{-3x}{-3} \geq \frac{-4}{-3}[/tex]
Answer:=[tex]x\leq \frac{4}{3}[/tex]Doing Test Corrections
A. 5
B. 4
C.6
D. 9
The ratio of the number of Marbles zali had to the number of marbles muthu had was 3 : 4 muthu gave half of his marbles to zali what was the new ratio of the number of marbles zali had to the number of marbles muthu had ?
Using the given ratio 3:4, Zali has 3 marbles and Muthu has 4 marbles.
If Muthu gives half of his marbles to Zali, Muthu would have 2 marbles (4/2 = 2) and Zali would have 5 ( 3+2 = 5). The ratio would now be 5:2
Answer: 5:2
Check for reasonableness 643 + 282
need help rn please?/..Thank you. Multiple step equation
Answer:
The answer (using BEDMAS) is 27
Step-by-step explanation:
The equation 9 x [(18+2) ÷ 5 - 1] is solved using BEDMAS or PEDMAS
First solve the smaller bracket
18 + 2 = 20
So then it becomes 9 x [20 ÷ 5 - 1]
Do the division inside the bracket next
20 ÷ 5 = 4
Then it becomes 9 x [4 - 1]
Do then subtraction within the bracket
4 - 1 = 3
Then it becomes 9 x 3
Finally solve 9 x 3 which equals 27
I forgot how to do this n they didn’t put an example help me lol
Answer:
60[tex]m^2[/tex]
Step-by-step explanation:
First, find the area of the square as it the missing piece wasn't missing.
8 x 9 = 72[tex]m^2[/tex]
Then, find the area of the missing section.
3 x 4 = 12[tex]m^2[/tex]
Finally, subtract 12[tex]m^2[/tex] from 72[tex]m^2[/tex] and you get 60[tex]m^2[/tex]
Find the sum of the next two numbers in the series below
20,24,33,49,_,_
A.74. B.36
C.184. D.110
Answer:
74 and 110
Step-by-step explanation:
lay out the numbers and the difference between the numbers:
20,24,33,49
+4 +9 +16
and notice the different between the amount added between the numbers
4,9,16
+5 +7
It seems the amount added to the amount added increases by 2 each time
the next two numbers in the sequence above is 9 and 11.
From that we can try to figure out what will be added to the original number by adding 9 and 11 to the difference list.
4, 9, 16, 25(added 9), 36(added 11)
and we can test those values
20,24,33,49,74(added 25),110(added 36)
which prime number is found in between 70 and 80 and is made up of two odd digits which add up to 10
Answer:71
71, 73 and 79
Step-by-step explanation:
A prime number is a number that can only be divided by 1 or itself. Otherwise, it is a composite numbers.
There are three numbers between
70
and
80
that fit this criteria,
71
,
73
, and
79
Determine the slope of the line in the graph below.
8
6
4
2
1
- 10 -8
-6
2
4
6
5
8
10
-4 --2
-2
-4
-6
-81
The slope is 1/2.
If you pick two points and count the rise over run (see picture below), you might get 1/2 or 2/4 or 3/6. But 3/6 and 2/4 reduce down to 1/2.
Given the perimeter P and the side B on the following rectangle are as indicated, find the side.
Answer:
a=7.6
Step-by-step explanation:
Since the perimeter is the length of the circumference, P=2a+2b=2(a+b)
We know b and P and if we do the math we get the answer
A chemical company makes two brands of antifreeze. The first brand is 40% pure antifreeze, and the second brand is 60% pure antifreeze. In order to obtain 180 gallons of a mixture that contains 55% pure antifreeze, how many gallons of each brand of antifreeze must be used?
First brand =
Second Brand=
Answer:
Step-by-step explanation:
Let x be the portion of 60%
180 - x is the portion of 40%
0.60x + 0.40(180 - x) = 0.55(180)
0.60x + 72 - 0.40x = 99
0.20x = 27
x = 135
180 - 135 = 45
First brand = 45 gallons of 40%
Second Brand = 135 gallons of 60%
What is the slope of the line on the graph? Enter your answer in the box.
Myra incorrectly factors 15 a-20ab as 5a( 3-4ab).
Factor the expression correctly.
15a - 20ab
Here, '5' & 'a' are the common factors. So factor them out.
=》15a - 20ab
=》5a (3 - 4b)
Myra incorrectly put 'a' inside the bracket which is wrong because 'a' is a common factor too along with 5.
_____
RainbowSalt2222 ☔
A quality-conscious disk manufacturer wishes to know the fraction of disks his company makes which are defective.
Step 1 of 2: Suppose a sample of 1221 floppy disks is drawn. Of these disks, 61 were defective. Using the data, estimate the proportion of disks which are defective.
Enter your answer as a fraction or a decimal number rounded to three decimal places.
Answer:
a
Step-by-step explanation:
a
If one inch is equivalent to 2.54 cm, then how many inches are there in 20.8 cm?
Answer:
8.18897637795
Step-by-step explanation:
20.8 divided by 2.54 equals 8.2. So 8.2 inches is you answer.
Answer:
1 inch =2.54cm
number of inches in 20.8 = 20.8/2.54 = 8.1889 inches
hope this will help you
b. During two years of college, a student earned $12,000. The second year she earned $500
more than twice the amount she earned the first year. How much did she earn the first
year?
Answer:
6000 dollars duhhhhhhhhhhhh
Question 4 of 17
Rewrite 50.82 : 1.1 to make the divisor a whole number. Select the answer
choice that shows the correct setup for long division and answer.
O A. 11)50.82 = 46.2
B. 11)508 2 = 42.6
O C. 11)508.2 = 46.2
D. 11)50.82 = 4.62
Help
Answer:
I think it is A OR D
$120; Markup: 35%
What's the final price? pls show how u got the answer...
Answer: 162
Step-by-step explanation:
So you will need to find the Markup. The original cost is $120.
Divide the number by 100 is 1.2. $1.2 is 1% of the $120.Now times the number by 35. $1.2 x 35 is $42.Finally, add the number. 120 + 42 = 162.I hope this is the answer you are looking for.
Is this a linear function?
5/6x = y − 4
Answer:
yes
Step-by-step explanation:
yes if you put -4 to the other side
i think so
What are the slope and y-intercept of the line?
slope = -170. y-intercept = 1020
Step-by-step explanation:
Let [tex]P_1(0, 1020)[/tex] and [tex]P_2(6, 0).[/tex] The slope can be calculated as
[tex]m = \dfrac{0 - 1020}{6 - 0} = -170\:\text{m/hr}[/tex]
So the equation can be written as
[tex]y = -170x + b[/tex]
To solve for b, let's use the values for P2:
[tex]0 = -170(6) + b \Rightarrow b = 1020[/tex]
Therefore,
[tex]y = -170x + 1020[/tex]
To find the y-intercept, let x = 0. then the y-intercept is
[tex]y = -170(0) + 1020[/tex]
or
[tex](0, 1020).[/tex]
Is 1.572735 rational?
Answer:
yes
Step-by-step explanation:
it is rational
Answer:
Yes
Step-by-step explanation:
To write 1.572735 as a fraction you have to write 1.572735 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.
1.572735 = 1.572735/1 = 15.72735/10 = 157.2735/100 = 1572.735/1000 = 15727.35/10000 = 157273.5/100000 = 1572735/1000000
And finally we have:
1.572735 as a fraction equals 1572735/1000000
And since there is a ratio (a proper fraction) number, it is rational.
Find the area of a rectangle that is 5 meters by 15 meters.
Show work
This diagram shows a pre image triangle ABC and its image triangle A'B'C' , after a series of transformations. Select from the drop down menu to correctly complete the statements.
Answer:
Step-by-step explanation:
ABC is translated right 4 units to become A'B'C'
which is then
Mirrored over the x axis to become A"B"C"
no idea what the last two might be because we don't know the options.
Could be "similar" "magnification of 1" "congruent"
Find the volume of the following cone.
Round your answer to the nearest integer
Check the picture below.
[tex]\textit{volume of a cone}\\ V = \cfrac{\pi r^2 h}{3}~~ \begin{cases} r = \stackrel{radius}{12}\\ h = \stackrel{height}{5} \end{cases} \\\\\\ V = \cfrac{\pi \cdot 144\cdot 5}{3}\implies V = 240\pi \implies V\approx 753.98\implies V = \stackrel{\textit{rounded up}}{754}[/tex]
The fraction 1/16 can correctly be read as
Question 5 options:
one divided by sixteen.
sixteen divided by 1.
one sixth.
one and one sixth.
The given fraction [tex](\frac{1}{16} )[/tex] can correctly be read as one divided by sixteen.
A fraction can be defined as a numerical quantity that isn't a whole number and as such has two (2) parts.
Hence, a fraction is simply a part of a whole number.
Generally, a fraction comprises two (2) main parts and these include:
Denominator: this refers to the lower part of a fraction.Numerator: this is the upper part of a fraction.Mathematically, a fraction is represented as:
[tex]Fraction \;A = \frac{1}{16}[/tex]In order to read a fraction, you will start by naming the numerator (upper part) followed by the denominator (lower part).
In this scenario, the given fraction [tex](\frac{1}{16} )[/tex] can correctly be read as one divided by sixteen.
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