A carpenter is creating two new templates for his designs. One template will be in the shape of a right triangle, where the longer leg is 4 inches more than six times the shorter leg.
The second template will be in the shape of a rectangle, where the width is 5 inches more than the triangle’s shorter leg, and the length is 3 inches.
The carpenter needs the areas of the two templates to be the same. Write a system of equations to represent this situation, where y is the area, and x is the length of the shorter leg of the triangle. Which statement describes the number and viability of the system’s solutions?
A.
The system has two solutions, but only one is viable because the other results in negative side lengths.
B.
The system has two solutions, and both are viable because they result in positive side lengths.
C.
The system has only one solution, but it is not viable because it results in negative side lengths.
D.
The system has only one solution, and it is viable because it results in positive side lengths.
Answers
Answer:
this is correct on plato/edmentum
Step-by-step explanation:
For an equation to be viable, the result of the equation must be positive (i.e. greater than 1).
The 2 templates, the farmer created have two solutions, but only one of the solutions are viable.
For the first template, we have:
[tex]x \to[/tex] length of the shorter leg of the triangle
[tex]z \to[/tex] length of the longer leg of the triangle
From the question, we have:
[tex]z = 4 + 6x[/tex]
The area (y) of the first template is:
[tex]y = \frac{1}{2}xz[/tex] --- area of a triangle
So, we have:
[tex]y = \frac{1}{2}x(4 + 6x)[/tex]
Open bracket
[tex]y = 2x + 3x^2[/tex]
For the second template, we have:
[tex]Width = 5 + x[/tex]
[tex]Length = 3[/tex]
So, the area (y) of the second template is:
[tex]y = Length \times Width[/tex] --- area of a rectangle
This gives:
[tex]y = 3 \times (5 + x)[/tex]
[tex]y = 3(5 + x)[/tex]
[tex]y = 15 + 3x[/tex]
So, the expression for both areas are:
[tex]y = 2x + 3x^2[/tex] --- template 1
[tex]y = 15 + 3x[/tex] --- template 2
Both areas must be equal. This is represented as:
[tex]2x + 3x^2 = 15 + 3x[/tex]
Collect like terms
[tex]3x^2 +2x - 3x - 15 = 0[/tex]
[tex]3x^2 - x - 15 = 0[/tex]
Solve for x using quadratic formula, we have:
[tex]x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]
Where:
[tex]a = 3; b =-1; c=-15[/tex]
So, we have:
[tex]x = \frac{-(-1) \± \sqrt{(-1)^2 - 4\times 3 \times -15}}{2 \times 3}[/tex]
[tex]x = \frac{1 \± \sqrt{181}}{6}[/tex]
[tex]x = \frac{1 \± 13.5}{6}[/tex]
Split
[tex]x = \frac{1 + 13.5}{6} \ or \ x = \frac{1 + 13.5}{6}[/tex]
[tex]x = \frac{-12.5}{6} \ or \ x = \frac{14.5}{6}[/tex]
[tex]x = -2.08 \ or \ x = 2.42[/tex]
We can see that x has 2 solutions, but only 1 of the solutions is viable because the other is negative.
Hence, option (a) is correct
Read more about viable and non-viable solutions at:
https://brainly.com/question/10558256
Related Questions
What is the measure of n?
Please help!!
Answers
Answer:
70°
Step-by-step explanation:
n+20=90° [being a right angelled triangle]
or, n=90°-20°
therefore n=70°
I guess this is the answer but please confirm first.
please help me:(*********
Answers
Answer:
x = 16
Step-by-step explanation:
I could be wrong so sorry in advance lol but this is what I did:
I made the equation 3x + 3 = ((7x-10)/2)
I divided the 2nd equation by 2 so that it would be the same length as RZ.
after that, I got: 3x + 3 = 3.5x - 5
from there, i did basic algebra to get the answer 16
hope this helps!
Hypotheses: p=.5 vs p NE .5 ; Sample data: p=28/40= .70 with n=40 Round the p-value to three decimal places.
Answers
Answer:
hahahahahaha yes hnjoo
Which of these choices are square roots of 144? Check all that apply.
Answers
Answer:
E
Step-by-step explanation:
The average monthly mortgage payment for all homeowners in a city is $2870. Suppose that the distribution of monthly mortgages paid by homeowners in this city follow an approximate normal distribution with a mean of $2870 and a standard deviation of $470. Find to 4 decimal places the probability that the monthly mortgage paid by a randomly selected homeowner from this city is
Answers
Answer:
The probability that the monthly mortgage is between 2300 and 3140 is: 0.23167
Step-by-step explanation:
Given
[tex]\mu = 2870[/tex] --- the average
[tex]\sigma = 470[/tex] --- the standard deviation
Required [Missing from the question]
Monthly mortgage is between 2300 and 3140
This is represented as:
[tex]P(2300 < x < 3140)[/tex]
This is calculated as:
[tex]P(a< x < b) = P(z_a < Z < z_b)[/tex]
[tex]P(2300< x < 3140) = P(z_b < Z < z_a)[/tex]
Calculate the z scores
[tex]x = 3140[/tex]
[tex]z = \frac{3140 - 2850}{470}[/tex]
[tex]z = \frac{290}{470}[/tex]
[tex]z = 0.6170[/tex]
[tex]x = 2300[/tex]
[tex]z = \frac{3140 - 2300}{470}[/tex]
[tex]z = \frac{840}{470}[/tex]
[tex]z = 1.7872[/tex]
So, we have;
[tex]P(2300< x < 3140) = P(1.1787 < Z < 0.6170)[/tex]
This is then calculated as:
[tex]P(a < Z < b) = P(Z < a) - P(Z <b)[/tex]
[tex]P(a < Z < b) = P(Z < 1.1782) - P(Z <0.6170)[/tex]
[tex]P(2300< x < 3140) = P(Z < 1.1782) - P(Z <0.6170)[/tex]
Using the z table:
[tex]P(Z<0.6170) =0.73138[/tex]
[tex]P(Z<1.7872) =0.96305[/tex]
[tex]P(2300< x < 3140) = 0.96305 - 0.73138[/tex]
[tex]P(2300< x < 3140) = 0.23167[/tex]
PLS HELP !!
G -9 < x < 2
F -9 < x < 2
H -6 < g (x) < 3
J -6 < g (x) < 3
Answers
Answer:
-6 <= g < 3
Step-by-step explanation:
-6 <= g < 3
Classify ∠1 and ∠2 using all names that apply
Answers
Step-by-step explanation:
complementry
since the angle 1 and 2 both measures 90⁰
Answer: Choice 2 Adjacent and Choice 4 Supplementary
Step-by-step explanation:
Here, we are given four choices, and I will be defining each of them.
Vertical angles: two angles that are opposite to each other which was formed by two intersecting lines.Adjacent angles: two angles that share one common vertex and "arm"Complementary angles: two angles that add up to 90°Supplementary angles: two angles that add up to 180°-----------------------------------------------------------------------------------------------
We can see from the figure given
Both angles are 90°, so ∠1+∠2=90+90=180°
Which is supplementary.
We can see from the figure given
Both angles share a common arm and vertex
Which is adjacent
Hope this helps!! :)
Please let me know if you have any questions
Find the probability of exactly two
successes in five trials of a binomial
experiment in which the probability of
success is 50%.
Round to the nearest tenth of a
percent.
[? ]%
Answers
Answer:
31.3%
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Five trials, probability of a success is 50%.
This means that [tex]n = 5, p = 0.5[/tex]
Probability of exactly two successes
This is P(X = 2). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{5,2}.(0.5)^{2}.(0.5)^{3} = 0.313[/tex]
0.313*100% = 31.3%
2. Amita decides that she wants the molds to have a
of the possible molds
square base. How many
can she use?
Answers
Answer:
amita can only use and it is only 2
2
Explain how 17.526 could be rounded to both 18 and 17.5.
Answers
Answer:
Step-by-step explanation:
If you round it to the nearest whole number, then 17.526 becomes 18 because if the first digit after the decimal(in this case,5) is 5 or greater you round to the next whole number.
If you round it to the nearest tenth, it would result in 17.5, because if the second digit after the decimal (in this case, 2) is 5 or greater you round to the next tenth of decimal.
Hope this helps!
Answer:
Step-by-step explanation:
It can be rounded down to 17.5 if rounding to 1 decimal place. If you are rounding to the nearest whole number, you would round to 18.
Hope this helps :)
Find the quotient using long division
6x2 - 8x + 5/
X-2
Answers
Step-by-step explanation:
hope this helps have a great day!
The length of a rectangle is five times its width.
If the perimeter of the rectangle is 60 cm, find its length and width.
length: 7 cm
Х
?
width: 1
cm
Answers
Answer:
The length of the rectangle is 25 cm, while the width is 5 cm.
Step-by-step explanation:
Given that the length of a rectangle is five times its width, to find its length and width, knowing that the perimeter of the rectangle is 60 cm, the following calculation must be performed:
(5X x 2) + (X x 2) = 60
10X + 2X = 60
12X = 60
X = 60/12
X = 5
5x5 = 25
Thus, the length of the rectangle is 25 cm, while the width is 5 cm.
Please help it’s due tonight. Your help will be greatly appreciated.There is also a graph. WILL PUT YOU AS BRAINLY!!!!!!
Answers
Answer: see below
Step-by-step explanation:
The shape is a trapezoid
Base 1 (BH) is 10
Base 2 (QA) is 14
Height is 5
Area
[tex]A=\frac{base_{1} +base_{2} }{2} h[/tex]
[tex]A=\frac{10+14}{2} *5\\A=12*5\\A=60[/tex]
Find distance between QB and HA
[tex]D=\sqrt{(x_{2} -x_{1}) ^{2}+(y_{2}-y_{1}) ^{2}[/tex]
Q( -4,4) B (-2,9)
[tex]D=\sqrt{(-2--4)^{2}+(9-4)^{2} } \\D=\sqrt{2^{2} +5^{2} } \\D=\sqrt{29}[/tex]
Perimeter
[tex]P=10+14+2\sqrt{29} \\P=24 +2\sqrt{29} \\P= 24+10.77\\P=34.77[/tex]
The following data table represents the total cost of a monthly cell phone bill as a function of the number of minutes that the phone is used each month. Minutes 500 750 1,000 1,250 1,500 Total Monthly Cost (in dollars) $62 $77 $92 $107 $122Choose the correct linear model that represents the total monthly cost as a function of time. y = 0.06 x + 500 y = 16 x + 32 y = 62 x + 16 y = 0.06 x + 32
Answers
Answer:
the answere is y=543.2
Step-by-step explanation:
thats it
Your mom asked you to frame an 8x10
picture with a piece of yarn. What is the
minimum length of yarn you need to buy to
frame the picture?
Answers
Answer:
80
Step-by-step explanation:
Evaluate 2w2+8, when w=−4.
HELP ASAP
Answers
Answer:
-8
Step-by-step explanation:
Plug in -4 for w, 2(-4)2+8 (2x-4x2+8)
2 x -4 x 2 =-16
-16+8= -8
A gum ball machine has 25 red gum balls, 30 green gum balls, 15 yellow gum balls, and 20 blue gum balls. If Peter puts 1 coin in the machine and gets 1 gum ball, what is the probabllity that the gum ball will not be red?
Answers
Answer:
It should be 13/18
Step-by-step explanation:
Find the solution set for this inequality. SHOW YOUR WORK OR NO CREDIT
-2x+4>-4x+8
Answers
Answer:
Below
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form: x >2
Interval Notation: ( 2, ∞)
Hope this helps:)
-2x+4x>8-4
2x>4
X>4/2
X>2
Find the area of the parallelogram shown below.
Answers
Answer:
120 square unitsStep-by-step explanation:
Given,
Base of the parallelogram = 10
Height of the parallelogram = 12
Therefore,
Area of the parallelogram = base × height
= 10 × 12
= 120
Hence,
Area of the parallelogram is 120 square units (Ans)
Please answer asap please take a look at the question explain and please be quick
Answers
Answer:
Step-by-step explanation:
52*3:4+1=40 There are 52 weeks in a year, 3/4 of 52= 39 , 1 week longer than it 39+1=40
Hailey made the following statement
"It is impossible to build a rectangular prism with a volume of 40 units it one side measures 5 units."
Key
represents
1 cubic unit
Select the two figures below that prove Hailey's statement is false
Answers
Answer:
D
Step-by-step explanation:
A mid-size city must decide whether or not to build a new combined bus and train station. To build the new station will require an increase in city taxes. According to a city politician, 70% of all city residents support the tax increase to build a combined bus and train station. An opinion poll of 400 city residents will ask whether they favor a rise in taxes to pay for a combined bus and train station. What is the standard deviation of the distribution of sample proportions?
Answers
Answer:
The standard deviation of the distribution of sample proportions is 0.0229.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
70% of all city residents support the tax increase to build a combined bus and train station.
This means that [tex]p = 0.7[/tex]
400 city residents
This means that [tex]n = 400[/tex]
What is the standard deviation of the distribution of sample proportions?
By the Central Limit Theorem:
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.7*0.3}{400}} = 0.0229[/tex]
The standard deviation of the distribution of sample proportions is 0.0229.
help with math please:)
Answers
Answer: ben
Step-by-step explanation:
How many lines of symmetry does the figure below have?
Answers
Answer:
4
Step-by-step explanation:
straight (1)
horizontal (1)
both diagonals (2)
Decrease $260 in the ratio 3:5
Answers
32.5 x 3= $97.50
32.5 x 5 = $162.50
$97.50:$162.50
Please help me! NO sites or links please!
Answers
Step-by-step explanation:
it's 13/16
I have done the processs:))
Answer:
D. 13/16
Step-by-step explanation:
D is the correct answer. hope this helps
HELP PLEASE NO LINKS OR FILES THEY WILL BE REPORTED
Answers
Answer:
One of the possible dimensions of the full trailer could be 5 by 12 by 3.
Step-by-step explanation:
Volume = weight times height times length = 12 times 5 times 3 = 180.
The diameter of a circle is 8 centimeters. What is the circle's circumference?
Answers
Answer:
25.13 centimeters
Step-by-step explanation:
PLEASE HELP !! ILL GIVE BRAINLIEST !!
Answers
Answer:
∠TUX and ∠WXU
Step-by-step explanation:
Alternate interior angles are angles that lie on the inside of the parallel lines, but different sides.
∠TUX is on the left side.
∠YXU is on the right side.
Therefore, ∠TXU and ∠WXU are alternate interior angles.
In a recent survey of 645 working Americans ages 25-34, the average weekly amount spent on lunch as $44.02 with standard deviation $2.81. The weekly amounts are approximately bell-shaped.
a. Estimate the percentage of amounts that were less than $38.40. Round the answer to one decimal place. Approximately % of the amounts were less than $38.40.
b. Estimate the percentage of amounts that are between $41.79 and $47.41.
c. Estimate the percentage of amounts that are at least $38.98.
d. Between what two values will approximately 95% of the amounts be?
Answers
Answer:
use photo math it's great and free