I need all of them answered they all have the same question. Use function notation to write the equation of the line.
The equation of each line using function notation is:
1. C. f(x) = 3x - 1.
2. D. f(x) = x.
3. D. f(x) = 4x + 4.
4. B. f(x) = -3/2x - 2
How to Write the Equation of a Line Using Function Notation?To use function notation, substitute the value of the slope (m) and the value of the y-intercept (b) into f(x) = mx + b.
Slope (m) = rise/run.
Y-intercept (b) is the point on the y-axis when the line intercepts the y-axis.
1. Slope (m) = rise/run = 3/1
Slope (m) = 3
Y-intercept (b) of the line = -1.
Substitute m = 3, and b = -1 into f(x) = mx + b:
f(x) = 3x - 1
The equation is: C. f(x) = 3x - 1.
2. Slope (m) = rise/run = 2/2
Slope (m) = 1
Y-intercept (b) of the line = 0.
Substitute m = 1, and b = 0 into f(x) = mx + b:
f(x) = (1)x + 0
f(x) = x
The equation is: D. f(x) = x.
3. Slope (m) = rise/run = 4/1
Slope (m) = 4
Y-intercept (b) of the line = 4.
Substitute m = 4 and b = 4 into f(x) = mx + b:
f(x) = 4x + 4
The equation is: D. f(x) = 4x + 4.
4. Slope (m) = rise/run = -3/2
Slope (m) = -3/2
Y-intercept (b) of the line = -2.
Substitute m = -3/2 and b = -2 into f(x) = mx + b:
f(x) = -3/2x - 2
The equation is: B. f(x) = -3/2x - 2
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Describe or show how to determine the average rate of change between x = 2 and x = 4 for the function f(x) = 2x3 + 1. Include the average rate of change you found in your answer.
The average rate of change on the interval [2, 4] is 56
How to find the average rate of change on the given interval?
Here we have the function:
f(x) = 2x^3 + 1
And we want to find the rate of change on the interval [2, 4].
Remember that for a function f(x) the rate of change on an interval [a, b] is.
R = ( f(b) - f(a))/(b - a)
Then in this case, the rate of change is:
R = [ f(4) - f(2)]/[4 - 2] = ( 2*4^3 + 1 - 2*2^3 - 1)/2 = (4^3 - 2^3) = 56
So the rate is 56.
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James has 6 stamps in his stamp collection. Roy has 12 stamps in his stamp collection. James adds 2 stamps to his stamp collection. After James adds these stamps, what is the ratio of the number of stamps in James's collection to the number of stamps in Roy’s collection? A. 1 : 2 B. 2 : 1 C. 3 : 2 D. 2 : 3James has 6 stamps in his stamp collection. Roy has 12 stamps in his stamp collection. James adds 2 stamps to his stamp collection. After James adds these stamps, what is the ratio of the number of stamps in James's collection to the number of stamps in Roy’s collection? A. 1 : 2 B. 2 : 1 C. 3 : 2 D. 2 : 3
After James adds stamps , the ratio of number of stamps in James's collection to the number of stamps in Roy's collection is 2:3 , the correct option is (D) 2:3 .
In the question ,
it is given that
Number of stamps that James has = 6 stamps
Number of stamps Roy has = 12 stamps
also , James adds 2 stamp to his collection ,
So number of stamps in James collection become = 8 stamps
So the ratio of number of stamps in James's collection to the number of stamps in Roy's collection is given by
= (number of stamps in James's collection)/(umber of stamps in Roy's collection)
Substituting the values , we get
= 8/12
Simplifying , we get
=2/3
Therefore , After James adds stamps , the ratio of number of stamps in James's collection to the number of stamps in Roy's collection is 2:3 , the correct option is (D) 2:3 .
The given question is incomplete , the complete question is
James has 6 stamps in his stamp collection. Roy has 12 stamps in his stamp collection. James adds 2 stamps to his stamp collection. After James adds these stamps, what is the ratio of the number of stamps in James's collection to the number of stamps in Roy’s collection?
(A) 1 : 2
(B) 2 : 1
(C) 3 : 2
(D) 2 : 3
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A trampoline park costs $12 for the first hour and $6 for each additional hour. Flynn pays $30 at the trampoline park. Select the equation that represents the given situation and find the number of additional hours Flynn stays at the trampoline park after the first hour.
Answer:
Flynn stays at the trampoline park for an additional 3 hours.
Step-by-step explanation:
30 - 12 = 18
18 / 6 = 3
As for the "Select the equation that represents the given situation" I don't know what this really means so I didn't do that. Sorry.
Solve 3x2 4x = 2. quantity of 2 plus or minus square root of 10 all over 6 quantity of negative 2 plus or minus 2 square root of 10 all over 3 quantity of negative 2 plus or minus square root of 10 all over 3 quantity of negative 4 plus or minus square root of 10 all over 3
Main Answer:
[tex]x=\frac{-2\±\sqrt{10}}{3}[/tex]
Explanation:
The given equation is,
[tex]3x^{2} +4x=2[/tex]
The
The quadratic formula to find the value of x for the equation [tex]ax^{2} +bx+c=0[/tex] is,
[tex]x=\frac{-b\±\sqrt{b^{2}-4ac}}{2a}[/tex]
The values are,
a = 3, b = 4, c = -2
Now, substitute the values of a, b and c
[tex]x=\frac{-4\±\sqrt{(4)^{2}-4(3)(-2)}}{2(3)}[/tex]
[tex]x=\frac{-4\±\sqrt{16-12(-2)}}{6}[/tex]
[tex]x=\frac{-4\±\sqrt{40}}{6}[/tex]
[tex]x=\frac{-4\±2\sqrt{10}}{6}[/tex]
[tex]x=\frac{2(-2\±\sqrt{10})}{6}[/tex]
[tex]x=\frac{-2\±\sqrt{10}}{3}[/tex]
A ball's position, in meters, as it travels every
second is represented by the position function
s(t) = 2.3t² + 225. What is the velocity of the
ball after 5 seconds?
A ball's position, in meters, as it travels every second is 282.5 sec.
What is addition?Combining things and counting them as one big group is done through addition. In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation. The sum is the entire value, and the addends are the integers that are being added. The mathematical operation of addition is the process of adding two or more numbers together to determine the total, or sum.
Given that,
The position function s(t) = 2.3t² + 225.
The velocity of the ball after 5 seconds is
s(t) = 2.3t² + 225.
t= 5
s(5) = 2.3(5)² + 225.
s(5) = 2.3(25) + 225.
s(5)= 57.5+ 225
s(5)= 282.5
Therefore, it travels every second is 282.5 sec.
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solve this please. i have no idea what to do
-3/2<h<0 is the answer.
How to simplify it?Given,
1+5h <h+1 <7+5h
Solution:
1+5h <h+1 <7+5h
If a < u <b, then a<u , u<b
Therefore,
1+5h <h+1 and h+1 <7+5h
1+5h <h+1
1+5h= h+1
4h = 0
h = 0
Therefore,
h<0
h+1 <7+5h
h+1 = 7+5h
4h = -6
h = -3/2
h > -3/2
Combine the intervals
h<0 and h> -3/2
By combining the above two, we get
-3/2<h<0
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last week, 3/4 of the students in Mr. Zanker's class went on a field trip. 5/8 of the students in Mr. Haynes's went. What is the average fraction of students in the two classes who went on the field trip?
The average fraction of students in Mr. Zanker's class and Mr. Haynes who went on the field trip is 11/8.
How can the fraction be calculated?From the question, the fraction of the students in Mr. Zanker's class that attended the field trip is 3/4.
The fraction of the students in Mr. Haynes class that attended the field trip is 5/8 .
Then the we can calculate the average fraction of student in the class of the two teacher is
= (3/4 + 5/8) = 11/8.
Therefore, the average fraction of the number of the student can be calculated as 11/8.
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What is the value of angle x?
A. 28 degrees
B. 67 degrees
C. 113 degrees
D. 152 degrees
Answer: b 67
Step-by-step explanation:
180-152 is 28
28+85=113
180-113=67
Answer:
B) 67°
Step-by-step explanation:
Exterior angle property:The exterior angle of a triangle equals the sum of opposite interior angles.
85 + x = 152
Subtract 85 from both sides,
x = 152 - 85
x = 67°
What is the slope equation for (1,-1) and (5,-17)
Answer:
slope(m) is -4
Step-by-step explanation:
[tex]m=\frac{-17-(-1)}{5-1} \\\\m=\frac{-16}{4} \\\\m=\frac{-4}{1} \\\\m=-4[/tex]
now substitute with one of the points
y=mx+b
-1=-4+b
+4 +4
3=b
now you have both m and b
y=-4x+3
what is the equation of the least squares regression line that describes the rela- tionship between operating cost per hour and number of passenger seats in the
The relationship between operating cost per hour and the number of passenger seats is shown by the equation of the least squares regression line, where y=1136+14.673x is the expected operating cost per hour and x is the number of passenger seats.
Why do you use the word "square"?a plane figure in geometry with four equal sides and four right angles of 90 degrees. A square is both an equilateral rectangle and a special kind of parallelogram (an equilateral and equiangular one).
the parallelogram in detail.In Euclidean geometry, a parallelogram is a simple quadrilateral having two sets of parallel sides. The confronting or opposed sides and the opposing angles of a parallelogram are of equal length.
based on the available facts;
y=1136+14.673x
where
x= number of passenger seat
y=predicted operating cost per hour.
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write the absolute deviation inequality for the following. Six students measure the acceleration of an object in free fall. The measured values are shown below. The students want to state that the absolute deviation for each measured value x from the mean is at most d. Find the value of d. 0.56, 9.52, 9.73, 9.80, 9.78, 10.91
Six students measure the acceleration of an object in free fall. The students want to state that the absolute deviation for each measured value x from the mean is at most d is 0.86.
What is an absolute deviation?The average of absolute deviations from a central point makes up the average absolute deviation (AAD) of a data collection. It is a statistical summary of the statistical variability or dispersion. A mean, median, mode, or the result of any other central tendency measure or any reference value associated with the specified data set can all serve as the central point in the general form. The mean absolute deviation and the median absolute deviation are part of AAD (both abbreviated as MAD).
Find the mean of the data set first, then use that value to calculate the mean absolute deviation of the data. Divide the total number of data values by the sum of the individual data values. Assess the magnitude of the absolute difference between each data point and and the mean.
The measured data is
x = [10.56, 9.52, 9.73, 9.80, 9.78, 10.91]
There are 6 measurements.
Calculate the mean.
m = (10.56+9.52+9.73+9.80+9.78+10.91)/6 = 10.05
Calculate deviations from the mean.
y = |x - m|
= [0.51, 0.53, 0.32, 0.25, 0.27, 0.86]
The greatest deviation from mean is d = 0.86.
Calculate the average absolute deviation.
(0.51+0.53+0.32+0.25+0.27+0.86)/6 = 0.4567
The answer is: d = 0.86
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I need help Asap What is the expression form of 8 more than the qoutient of a number times itself and 5 minus 3
Answer:
Step-by-step explanation:
[tex]\displaystyle\\8 > \frac{x}{4}(x+5)-3[/tex]
How do properties of integer exponents help you write equivalent expressions.
This is page 42 lesson 1-6 in the 8th grade math book.
By combining numerical or algebraic expressions that share a basis, distributing exponents among products and quotients, and simplifying powers of powers, one can exploit the properties of integer exponents to create similar expressions.
What is the explanation about the integer about?Based on the information, it's important to simply transfer the base and exponent to the other side of the fraction line, change the exponent to positive, and you have an analogous expression.
For example, the expression 2/3² can be illustrated to an equivalent expression as:
2/3² = 2 / (3 × 3)
= 2/9
This shows how the exponent has been used to form the new value.
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Debnil has 6 teaspoons of salt. The ratio of teaspoons to tablespoons is 3 : 1.
How many tablespoons of salt does Debnil have?
Answer:
lol
Step-by-step explanation:
I dunno my brain isn't braining
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=8800(1.573)^x
y=8800(1.573)
x
The given exponential function represents the growth in function with a percentage increase as 57.3%.
Given we have the exponential function as :
y=8800(1.573)ˣ
it is in the form of: y=k.aˣ
therefore, if a>2 then the function represents growth.
and if a<1 then the function represents decay.
now, x=1.573
1.573 > 1
so, the function represents change in growth.
therefore, 1.573 - 1
= 0.573
= 57.3%
hence the change in growth of the function is increased by 57.3%.
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there is a jar containing 27 black and 33 gold jelly beans. you will get a chance to draw 10 jelly beans at random from the jar. on each draw, what is probability of drawing a gold jelly bean
there is a jar containing 27 black and 33 gold jelly beans. you will get a chance to draw 10 jelly beans at random from the jar. on each draw, 0.5 is the probability of drawing a gold jelly bean
How can I find the probability?
The probability of an event can be calculated by probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes.
there is a jar containing 27 black
and 33 gold jelly beans.
you will get a chance to draw 10 jellybeans at random from the jar.
on each draw, what is probability of drawing a gold jelly bean
Add up the total number of jellybeans, 27 + 33 = 60
Divide the number of gold jellybeans by the total: 33/60 and reduce the fraction to 11/20
=0.55
Hence, there is a jar containing 27 black and 33 gold jelly beans. you will get a chance to draw 10 jelly beans at random from the jar. on each draw, 0.5 is the probability of drawing a gold jelly bean
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Please help!!! .The HCF of 90 and another number is 30. If the LCM of the number is 360, find the other number
The most appropriate choice for HCF and LCM will be given by
The other number is 120
What is HCF and LCM?
HCF of two numbers A and B is the highest common factor of A and B. HCF is the highest number which divides both A and B.
LCM of two numbers A and B is the lowest common multiple of A and B. LCM is the least number which is divided by both A and B.
Here,
Let the other number be [tex]x[/tex]
HCF of 90 and [tex]x[/tex] = 30
LCM of 90 and [tex]x[/tex] = 360
Product of HCF and LCM = 30 [tex]\times[/tex] 360
Product of 90 and [tex]x[/tex] = 90 [tex]\times[/tex] [tex]x[/tex]
By the problem,
90 [tex]\times[/tex] [tex]x[/tex] = 30 [tex]\times[/tex] 360
[tex]x = \frac{360 \times 30}{90}[/tex]
[tex]x = 120[/tex]
The other number is 120
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What is (3x2.05)+(_x1.09)+(2x_)+(_x_) I NEED HELP PLEASE SOMBODY
(MATH) (WILL MARK BRAINLIST)
The value of the expression given as (3x + 2.05) + (-x + 1.09) + (2x) + (x) is 5x + 3.14
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to solve the expression?The expression is given as
(3x + 2.05) + (-x + 1.09) + (2x) + (x)
Start by opening the brackets
(3x + 2.05) + (-x + 1.09) + (2x) + (x) = 3x + 2.05 - x + 1.09 + 2x + x
Next, we collect the like terms
(3x + 2.05) + (-x + 1.09) + (2x) + (x) = 3x - x + 2x + x + 2.05 + 1.09
Next, we evaluate the like terms
(3x + 2.05) + (-x + 1.09) + (2x) + (x) = 5x + 3.14
Hence, the value of the expression is 5x + 3.14
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Possible question
What is (3x + 2.05) + (-x + 1.09) + (2x) + (x)
Find the zeros of the quadratic equation: y = x^2 + 64
Answer: X=-8
Step-by-step explanation:
(x+8)(x+8)= 0
x=-8
Foster is centering a photo that is 7 1/5 inches wide on a scrapbook page that is 16 inches wide
The distance that's required to be kept geo either side will be 4.258 inches.
How to calculate the value?From the information, Foster is centering a photo that is 7 1/5 inches wide on a scrapbook page that is 16 inches wide.
It should be noted that 7 1/2 is the same as 7.5. Therefore,we can subtract and this will be:
= 16 - 7.5
= 8.5
Since we know that the scrapbook is 8.5 inches wider,we will divide the width by 2 to get the distance of either side and this will be:
= 8.5 / 2
= 4.25
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Foster is centering a photo that is 7 1/5 inches wide on a scrapbook page that is 16 inches wide. How far from each side go the page did he put the picture?
what is the GCF of 18a^4b^9c^2 and 34a^6b^5 and 22a^8bc^7
The greatest common factor, GCF, of the given terms is 2a⁴b
Determining Greatest Common Factor (GCF)From the question, we are to determine the GCF of the given expressions. GCF means Greatest common factor
The given expressions are 18a^4b^9c^2 and 34a^6b^5 and 22a^8bc^7
First, we will write the expressions properly
The given expressions are 18a⁴b⁹c² and 34a⁶b⁵ and 22a⁸bc⁷
To determine the GCF of the expressions, we will express each one of them as a product of their factors
That is,
18a⁴b⁹c² = 2 × 3 × 3 × a × a × a × a × b × b × b × b × b × b × b × b × b × c × c
34a⁶b⁵ = 2 × 17 × a × a × a × a × a × a × b × b × b × b × b
22a⁸bc⁷ = 2 × 11 × a × a × a × a × a × a × a × a × b × c × c × c × c × c × c × c
Hence, the GCF is 2 × a × a × a × a × b = 2a⁴b
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Find f(g(x)) and g(f(x)) and determine whether the pair of functions f and g are inverses of each other.
f(x)=6x+5 and g(x)= x-5/6
a. f(g(x))= (Simplify your answer.)
b. g(f(x))= (Simplify your answer.)
Part a
[tex]f(g(x))=6\left(x-\frac{5}{6})+5=6x-5+5=6x[/tex]
Part b
[tex]g(f(x))=g(6x+5)=(6x+5)-\frac{5}{6}=6x+\frac{25}{6}[/tex]
Therefore, the functions are not inverses of each other since [tex](f(g(x)) \neq x[/tex].
Please show work so I can better understand.
The probability of happening of the events either B or C is [tex]\frac{2}{3}[/tex]
What is Addition Rule in Probability?The probability that event A or event B happens is equal to the
probability that A happens plus the probability that B happens minus the probability that both happen. If events A and B are mutually exclusive, then the probability that event A or B happens is simply the sum of the probabilities. Given that
A = rolling a number greater than four
B = rolling an even number
C = rolling a multiple of 3
So,
P(A) = [tex]\frac{2}{6} =\frac{1}{3}[/tex]
P(B)=[tex]\frac{3}{6} =\frac{1}{2}[/tex]
P(C) = [tex]\frac{2}{6} =\frac{1}{3}[/tex]
Now, We have to find the probability of occurence of either event B or C
So, We know that
P(B or C ) = P(B) + P(C) + P(B or C)
P(B or C )= [tex]\frac{3}{6} +\frac{2}{6} -\frac{1}{6} =\frac{4}{6}[/tex]
P(BorC)= [tex]\frac{2}{3}[/tex]
Therefore, the probability of occurence of either event B or C is [tex]\frac{2}{3}[/tex].
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Show all work to identify the asymptotes and state the end behavior of the function
The horizontal asymptote of the function is y=36 and vertical asymptote is x = 6 and its end behavior is f(x)→6.
As the independent variable approaches a certain value, the function approaches asymptotes, but does not cross them. They could be angled, vertical, or horizontal.
ascending asymptotes
There will be a vertical asymptote at x=a if the denominator factor of a rational function, (x - a), is not matched by the same factor in the numerator.
horizontal asymptotes:
When x is large, the value of a rational function approaches the ratio of the highest-degree terms in the numerator and denominator.
Given the function is f(x) = 6x/x-36
limx→±∞ 6x/x-36
= limx→±∞ 6/1-36/x
= 6 ⇒ horizontal asymptote: y = 6
Consider denominator = 0 ↔ x-36 = 0 ↔ x=36
limx→₊₂₅ 6x/x-36
= 6×36/0⁺ = ∞ ⇒ vertical asymptote: x = 36
End behavior of f(x):
As x → -∞ or x → ∞, f(x) → 6.
Hence we get the asymptote and the end behavior of the function.
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2/3 x ___ = -1
what’s the blank ?
By doing multiply of = [tex]\frac{2}{3}[/tex] with =[tex]\frac{-3}{2}[/tex] we get -1 .
What is basic algebra ?Algebra is one of the areas of mathematics where mathematical expressions can be used to represent situations or problems. In order for a mathematical statement to make sense, it must have mathematical operations like addition, subtraction, multiplication, and division as well as variables like x, y, and z. Every branch of mathematics, including calculus, trigonometry, and coordinate geometry, uses algebra. The equation 2x + 4 = 8 is a simple algebraic formula.Mathematical branch known as algebra deals with symbols and arithmetic operations on them. These symbols are referred to be variables since they lack set values. We frequently observe specific values that change in our day-to-day situations. However, there is a continuing need to depict these shifting values. These values are frequently represented in algebra by symbols, which are known as variables, such as x, y, z, p, or q. In order to determine the values, additional arithmetic operations such as addition, subtraction, multiplication, and division are performed on these symbols.
Given that : = [tex]\frac{2}{3}[/tex] x ___ = -1
[tex]\frac{2}{3}[/tex] ×[tex]\frac{-3}{2}[/tex]
=-1
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In the diagram below, AB || CD, AD || BC, DEL CE, m/DCE = 30°
and m/ADE = 59°. Find m/ECB.
Answer: m/ECB
59°
=
You may assume lines that appear straight are straight, but the figure is not otherwise drawn to scale.
||
E
O
B
Submit Answer
30°
attempt 6 out of 10
Answer:
Angle EDC = 180 - 90 - 30 = 60° (sum of angles in triangle add up to 180°)
Angle ADC + angle DCB = 180° (interior angles, AB//CD)
59 + 60 + 30 + angle ECB = 180
Angle ECB = 180 - 59 - 60 - 30 = 31°
The shape of a water tower can partially be modeled by a sphere in which the diameter is 30 feet. A painter needs to calculate the surface area of this part of the water tower to accurately estimate the amount of paint needed for the job. What is the surface area of this portion of the water tower to the nearest square foot? Surface area: square feet
Answer: i believe the answer is 113.1 square feet
Step-by-step explanation: pi times 30
Lowes carries 3 types of plants. 1/10 of the plants are fruit bearing 1/2 of the plants are flower bearing, the rest are vegetable bearing plants. How many are vegetable bearing plants?
The number of vegetable bearing plants are : 0.45x, where x is the total number of plants.
A fraction in mathematics represents a portion or element of the whole. It represents the appropriate parts of the totality. A fraction is made up of two parts: the numerator and the denominator. The number at the top is the numerator, and the number at the bottom is the denominator. The numerator indicates the number of equal parts that were actually taken, whereas the denominator shows the total number of equal parts in the whole.
Let x be the initial plant population.
Now that 1/10 of plants bear fruit, the quantity of fruit-bearing plants is equal to 0.1x.
Plants remaining then equal x - 0.1x = 0.9x.
Once more, because half of the remaining plants give flowers, the number of flower-bearing plants is equal to 0.5(0.9x) = 0.45x.
As a result, the number of plants left is equal to 0.9x - 0.45x = 0.45x.
Given that all remaining plants produce veggies, the number of plants that do so is equal to 0.45.
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A triangle has angles that measure x, (x + 10), and (2x - 6). Solve for x to find the value of each angle, and determine what type of triangle it is.
Group of answer choices
60, 60, 60. Equilateral
40, 40, 100. Obtuse
44, 46, 90. Right
44, 54, 82. Acute
Answer:
44, 54, 82. Acute
Step-by-step explanation:
x + x + 10 + 2x - 6 = 180 (Triangle Sum Theorem)
4x + 4 = 180 (Combine Like Terms)
4x = 176 (Subtraction Property of Equality)
x = 44 (Division Property of Equality)
Now that we have found the value of x, we need to substitute it with the provided angles.
∡1 = x = 44°
∡2 = x + 10 = 54°
∡3 = 2x - 6 = 2(44) - 6 = 82°
So, the answer is an Acute triangle (Option 4).