Answer:
x = 26
Step-by-step explanation:
Since s║t and r is a transversal, consecutive interior angles add to 180
⇒ 2(x + 15) + (3x + 20) = 180
⇒ 2x + 30 + 3x + 20 = 180
⇒ 5x + 50 = 180
⇒ 5x = 180 - 50
⇒ 5x = 130
⇒ x = 130/5
⇒ x = 26
Answer:
x=26
Step-by-step explanation:
Given:
s || t
2(x+15) + (3x+20) = 180°
Since the sum of co interior angle is 180°
Opening bracket
2x + 30 + 3x + 20 =180
Solving like terms
5x+50= 180
subtracting both side by 50
5x=180-50
5x = 130
dividing both side by 5.
[tex]\tt x=\frac{130}{5}[/tex]
x = 26
Therefore value of x is 26.
Pls help with my homeworkkkkk
Answer: A= -1, B= -3,C=-4.D=3 i think
Which variation is represented by this situation:
A building that is 6 stories tall has a shadow that is 22 meters long. How many stories tall is a building with a shadow that is 40 meters long?
Answer:
The answer is approximately 11 stories
Step-by-step explanation:
6 stories------->22 meters
x stories---------->40 meters
[tex]x = \frac{6 \times 40}{22} [/tex]
x≈11 stories
given ac and bd bisect each other at O prove
HELP ASAP
The equality of angle A and angle C is proved by Side-Angle-Side theorem (SAS).
What is the proof of the similar triangles?The proof of similarity of the triangles is determined by applying angle - angle (AA) theorem as shown below.
angle A will be equal to angle C if the following condition is met;
triangle BAG ≅ triangle DCG
From the given diagram, by reflexive similarity;
line BG = line DG
line BA = line DC
line GA = line GC
Since all the side lengths are congruent to each other and ΔBGA is equal to ΔDGC, then angle A must be equal to angle C.
Thus, the equality of angle A and angle C is proved by Side-Angle-Side theorem.
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solve the exponential equation for x. 2^9x+2 = 16^5x-2
The value of is 2/11
How to determine the valueTo determine the value, we have;
Index forms are mathematical forms used to represent numbers or values that are too large or too small in more convenient forms.
From the information given, we have the expression written as;
2⁹ˣ+2 = 16⁵ˣ -2
Put all the terms in one base form, we have;
2⁹ˣ + 2¹ = 2²⁰ˣ - 2¹
equate the exponents, we have;
9x + 1 = 20x - 1
collect the like terms, we have;
9x - 20x = -2
-11x = -2
Make 'x' the subject of formula, we have;
x = 2/11
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O
Problem !. Draw the Logic Circuit for:
BD + BE + D'F
Problem 2. What is the boolean Expression of F5?
B
X
Y
Z
F5
The simplified boolean expression for F5 is F5 = P OR (NOT R). In this expression, P represents one boolean variable, and (NOT R) represents the negation of another boolean variable R. The OR operator combines the two variables, resulting in the final boolean expression F5.
To simplify the boolean expression F5 = (P AND Q) OR (R AND NOT P), we can apply Boolean algebra rules to reduce it to its simplest form.
Step 1: Apply De Morgan's laws
NOT (R AND NOT P) can be simplified as (NOT R) OR P.
Step 2: Distributive property
F5 = (P AND Q) OR ((NOT R) OR P)
Step 3: Apply associative property
F5 = (P AND Q) OR (P OR (NOT R))
Step 4: Apply absorption law
F5 = P OR (P OR (NOT R))
Step 5: Apply idempotent law
F5 = P OR (NOT R)
By simplifying the expression, we have reduced it to its simplest form while preserving its logical meaning. The simplified expression can be used to analyze and evaluate logical circuits or systems where the variables P and R are used.
Remember, boolean algebra allows us to manipulate and simplify complex logical expressions by applying various rules and properties. These simplifications help in understanding and analyzing logical operations in digital systems and circuits.
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The question probable may be:
Consider the boolean variables P, Q, and R. Determine the boolean expression for the variable F5 using the given variables:
F5 = (P AND Q) OR (R AND NOT P)
Using the boolean variables P, Q, and R, can you simplify the expression F5 to its simplest form by applying Boolean algebra rules?
Miguel deposited a certain amount of money in the bank. The bank paid him interest after one year at which point he had $757.12. After the next year he had $787.40. How much money did Miguel originally put into the bank? (Answer to the nearest dollar.)
The amount that Miguel originally put into the bank is given as follows:
$728.
How to obtain the balance using simple interest?The equation that gives the balance of an account after t years, considering simple interest, is modeled as follows:
A(t) = P(1 + rt).
Then the interest accrued is given as follows:
I(t) = Prt.
In which the parameters of the equation are listed and explained as follows:
A(t) is the final balance.P is the value of the initial deposit.r is the interest rate, as a decimal.t is the time in years.The interest accrued from the first year to the second year is of $30.28, hence the rate is given as follows:
30.28 = 757.12r
r = 30.28/757.12
r = 0.04.
Then the principal is obtained as follows:
1.04P = 757.12
P = 757.12/1.04
P = $728.
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which one of the following general term of sequence is arithmetic?
The options that represent arithmetic sequences are A) 2n - 1, C) 3n + 4, and D) 5n - 2.
To determine which of the given general terms represents an arithmetic sequence, we need to check if the difference between consecutive terms is constant. Let's evaluate each option:
A) 2n - 1
To find the difference between consecutive terms, we subtract the general term for the (n+1)th position from the general term for the nth position:
[(2(n+1)) - 1] - (2n - 1) = 2n + 2 - 1 - 2n + 1 = 2
Since the difference between consecutive terms is 2, option A) 2n - 1 represents an arithmetic sequence with a common difference of 2.
B) n^2 + 3
Let's calculate the difference between consecutive terms:
[(n+1)^2 + 3] - (n^2 + 3) = n^2 + 2n + 1 + 3 - n^2 - 3 = 2n + 1
The difference between consecutive terms is 2n + 1, which is not a constant value. Therefore, option B) n^2 + 3 does not represent an arithmetic sequence.
C) 3n + 4
Calculating the difference between consecutive terms:
[(3(n+1)) + 4] - (3n + 4) = 3n + 3 + 4 - 3n - 4 = 3
The difference between consecutive terms is 3, which is a constant value. Therefore, option C) 3n + 4 represents an arithmetic sequence with a common difference of 3.
D) 5n - 2
Finding the difference between consecutive terms:
[(5(n+1)) - 2] - (5n - 2) = 5n + 5 - 2 - 5n + 2 = 3
The difference between consecutive terms is 3, which is a constant value. Therefore, option D) 5n - 2 represents an arithmetic sequence with a common difference of 3.
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Question
which one of the following general term of sequence is arithmetic?
A) 2n - 1
B) n^2 + 3
C) 3n + 4
D) 5n - 2
Select the correct answer from each drop-down menu.
Given:
∠
BON
≅
∠
NOC
Prove:
∠
AOM
≅
∠
MOD
Three line segments AC, BD, and MN are intersecting each other at mid-point O
Statements Reasons
1.
AC
―
,
MN
―
, and
DB
―
intersect at O 1. given
2.
∠
AOM
≅
∠
NOC
2. vertical angles theorem
3.
∠
MOD
≅
∠
BON
3. vertical angles theorem
4.
∠
BON
≅
∠
NOC
4. given
5.
∠
AOM
≅
∠
MOD
5. transitive property of congruence
Convert the proof to the paragraph format.
Since
AC
―
,
MN
―
, and
DB
―
intersect at O,
∠
AOM
≅
∠
NOC
and
∠
MOD
≅
∠
BON
by the . It is given that
∠
BON
≅
∠
NOC
, so by the ,
∠
AOM
≅
∠
MOD
.
We can conclude that ∠AOM ≅ ∠MOD.
Given that AC, MN, and DB intersect at point O, we can prove that ∠AOM ≅ ∠NOC and ∠MOD ≅ ∠BON. This can be shown using the vertical angles theorem.
By the given information, we know that ∠BON ≅ ∠NOC. Using the transitive property of congruence, we can conclude that ∠AOM ≅ ∠MOD.
In other words, since AC, MN, and DB intersect at point O, we have the following angle relationships: ∠BON ≅ ∠NOC and ∠AOM ≅ ∠MOD.
The given information states that ∠BON ≅ ∠NOC. Using the vertical angles theorem, we can infer that ∠AOM ≅ ∠NOC. Furthermore, since ∠AOM ≅ ∠NOC and ∠BON ≅ ∠NOC, we can apply the transitive property of congruence to conclude that ∠AOM ≅ ∠MOD.
Therefore, we have successfully proved that ∠AOM ≅ ∠MOD based on the given intersecting line segments and angle relationships.
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John is a furniture maker. The graph shows the number of chairs John makes and the time it takes to make those chairs. Based on the graph, how many chairs can John make in 5 hours?
A.
55
B.
50
C.
45
D.
40
The correct answer is Option B. 50 chairs can John make in 5 hours from the graph.
John is a furniture maker and the graph shows the number of chairs John makes and the time it takes to make those chairs.
Based on the graph, the number of chairs John can make in 5 hours can be found by following the given steps:
Step 1: Look for the point on the graph where the line intersects the vertical line marking 5 hours.
Step 2: From the point on the graph found in step 1, read the horizontal line and find the point at which it intersects the y-axis.
This point will give us the number of chairs John can make in 5 hours.
According to the graph, John makes 50 chairs in 5 hours.
Therefore, the correct answer is option (B) 50.
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in your view support the method that you find important to enhance the strong number sense. Provides appropriate examples for chosen method
The method that you find important to enhance the strong number sense is the use of manipulatives and hands-on activities.
Example:
Illustrating numbers and executing mathematical operations through block representations can assist students in visualizing addition, subtraction, and multiplication.
How to determine the methodUsing manipulatives and interactive activities, numerical concepts can be grasped more tangibly, as learners physically engage with these objects, thereby developing a concrete understanding of mathematics.
Students can enhance their comprehension of measurement and units by employing measurement instruments such as rulers and measuring tapes.
Through participation in these tasks, students cultivate a profound sense of intuition in regard to numbers, operations, and their interconnections, thereby establishing a firm groundwork.
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If the time is between 8:00 a.m. and 3:00 p.m., then the bank is open.
If the bank is open, then people may make withdrawals or deposits.
Therefore, if …
Therefore, if the time is between 8:00 a.m. and 3:00 p.m., then people may make withdrawals or deposits.
How to find complete the statementBased on the given statements, we can make the following inference:
If the time is between 8:00 a.m. and 3:00 p.m., then the bank is open.
If the bank is open, then people may make withdrawals or deposits.
Therefore, if the time is between 8:00 a.m. and 3:00 p.m., then people may make withdrawals or deposits.
The inference follows the logical flow of the given statements.
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solve it pls fast
.........................
The solution to this integral [tex]\int\limits^{\infty} _{-\infty} e^{-x^{2} } \, dx =\sqrt{\pi}[/tex] is equal to √π.
How to integrate the given function?In Mathematics, the Gaussian integral is sometimes referred to as the probability integral, and it highly related to the erf function, which represents the integral of the one-dimensional Gaussian function over the interval [-∞, ∞].
Generally speaking, the given integral can be computed by using the advanced techniques of combining two one-dimensional Gaussians and converting into polar coordinates;
[tex]I^2 =\int\int e^{(-(x^2 +y^2))}dxdy\\\\I^2 =\int\int e^{-r^2}rdr d\theta[/tex]
In this context, we would use these integration limits [0, ∞) with respect to "r" and [0, 2π] with respect to "θ" as follows:
[tex]I^2 =\int\limits^{2 \pi}_{0} \int \limits^{\infty}_{0} e^{-r^2}rdr d\theta\\\\I^2 =\int\limits^{2 \pi}_{0} \int \limits^{\infty}_{0}\frac{1}{2} e^{-u}du d\theta\\\\I^2 =\int\limits^{2 \pi}_{0} [\frac{1}{2} e^{-u}]\limits^{\infty}_{0}d\theta\\\\I^2 =\int\limits^{2 \pi}_{0} (\frac{1}{2} )d\theta\\\\I^2=\frac{1}{2}[\theta]\limits^{2 \pi}_{0}\\\\I^2=\frac{1}{2}(2 \pi)-\frac{1}{2}(0)\\\\I^2=\frac{2 \pi}{2}[/tex]
I² = π
I = √π
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Selena and Drake are evaluating the expression (StartFraction r s Superscript negative 2 Baseline Over r squared s Superscript negative 3 Baseline EndFraction) Superscript negative 1, when r = negative 1 and s = negative 2.
Selena’s Work
Drake’s Work
(StartFraction r s Superscript negative 2 Baseline Over r squared s Superscript negative 3 Baseline EndFraction) Superscript negative 1 Baseline = (r Superscript negative 1 Baseline s) Superscript negative 1 Baseline = StartFraction r Over s EndFraction = StartFraction negative 1 Over negative 2 EndFraction = one-half
(StartFraction (negative 1) (negative 2) Superscript negative 2 Baseline Over (negative 1) squared (negative 2) Superscript negative 3 EndFraction) Superscript negative 1 = (StartFraction (negative 1) (negative 2) cubed Over (negative 1) squared (negative 2) squared EndFraction) Superscript negative 1 = (StartFraction negative 8 Over 4 Endfraction) Superscript negative 1 Baseline = StartFraction 4 Over negative 8 EndFraction = negative one-half
Who is correct and why?
Selena is incorrect because she should have substituted the values for the variables first, and then simplifed.
Selena is correct because she simplified correctly and then evaluated correctly after substituting the values for the variables.
Drake is incorrect because he should have simplified first, before substituting the values for the variables.
Drake is correct because he substituted the values for the variables first, and simplified correctly.
Drake is correct, and Selena is incorrect in this scenario.Option D.
Selena's Work:
Selena substituted the values for the variables r = -1 and s = -2 directly into the expression before simplifying. She then simplified the expression and evaluated it.
However, this approach is incorrect because the order of operations requires simplification before substitution. Selena should have simplified the expression first and then substituted the values of r and s.
Drake's Work:
Drake followed the correct order of operations. He simplified the expression first and then substituted the values of r = -1 and s = -2. By simplifying the expression, Drake obtained (-1/-2), which simplifies to 1/2. After substituting the values, Drake evaluated the expression correctly and arrived at the final result of 1/2.
Since Drake followed the correct order of operations and obtained the correct result, he is the one who is correct. Selena's mistake was in not simplifying the expression before substituting the values for r and s.
In mathematical operations, it is important to follow the order of operations (PEMDAS/BODMAS) to ensure accurate results. The correct order is to simplify the expression first, and then substitute the given values for the variables. So Option D is correct.
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Lucy buys a silver coat rack priced at $69.If the sales tax is 3%, how much tax will Lucy pay?
Answer:
ok, here is your answer
Step-by-step explanation:
If the sales tax is 3%, then the tax amount Lucy will pay on the silver coat rack priced at $69 would be:
Tax amount = 3% of $69
Tax amount = (3/100) * $69
Tax amount = $2.07
Therefore, Lucy will pay $2.07 in tax.
mark me as brainliestAnswer:
The final purchase price is 71.07
Step-by-step explanation:
First step is to determine the amount of tax:
69*3%
69 * .03
2.07
Now add the tax to the purchase price:
69+2.07
71.07
The final purchase price is 71.07
Which image shows a pair of similar polygons? A. Graphic Image showing a pair of similar polygons. The X-axis shows the Value range from 0 to 16 and the Y-axis values from 0 to 16. B. An image showing pair of Similar Polygons with an X-axis showing the Value range from 0 to 16 and Y-axis values from 0 to 16. C. Graph showing a pair of similar polygons. The X-axis shows the Value range from 0 to 16 and the Y-axis values from 0 to 16. D. Graph showing a pair of similar polygons. The X-axis shows the Value range from 0 to 16 and the Y-axis values from 0 to 16.
The polygons that can be regarded as similar polygons are A and D.
What are similar polygons?Similar polygons are those whose sizes may vary but whose shapes are the same. To put it another way, they have proportional sides and corresponding angles that are equivalent. The geometric likeness or resemblance between them is referred to as being "similar".
Similar polygons have corresponding angles with the same measurements. For instance, if a right angle exists in one polygon, another polygon with a comparable angle will likewise have a right angle. Similar to this, if an angle in one polygon is 60 degrees, the comparable angle in a related polygon will also be 60 degrees.
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Geometry
Solve both and show work
Answer:
For both problems, the correct equation of the line will be presented in three forms.
14)
y - 4 = -5(x + 1)---point-slope form
y - 4 = -5x - 5
y = -5x + 1---slope-intercept form
5x + y = 1---standard form
15)
y + 3x = 13
y = -3x + 13
y - 10 = (1/3)(x - 6)---point-slope form
y - 10 = (1/3)x - 2
y = (1/3)x + 8---slope-intercept form
3y = x + 24
-x + 3y = 24---standard form
x - 3y = -24
The graph represents a functional relationship.
The value that is the input of the function is 4.
How to represent a function?A function relates input and output. In other words, a function defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
The independent variable is the x values or the input value while the dependent variable is the y values of the output values.
Hence, the values of the input(x) of the function are 4, 6, 8, 10. 12 etc.
Therefore, base on the option, the input of the function is 4.
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Solve for the value of c.
(2c-3)°
97°
Answer:
c = 50
Step-by-step explanation:
2c - 3 = 97
2c = 100
c = 50
help me with math pls
Answer:
V = 1/3 π r^2 h
Step-by-step explanation:
V = 1/3 area base*height
1. work out the area
2. base*height
3. area*answer
4. you get full answer
Please help with an explanation my brain isn’t working
Answer:
h=1.8 cm
Step-by-step explanation:
Solution Given:
Volume of triangular prism= Area of base * length
Here
Volume of traingular Prism= 63 cm³
base =7 cm
length =10 cm
Area of base = Area of triangle=½*base*height=½*7*h
Now
substituting value in the formula:
63= ½*7*h*10
63=35*h
h=63/35
h=1.8 cm
Therefore, height of the triangular cross section is 1.8 cm.
Use the graph to determine a. the function's domain; b. the function's range; c. the x-intercepts, if
any; d. the y-intercept, if any; and e. the missing function value, indicated by the question mark
below.
f(9) = ?
a. Domain - [0, 20]
b. Range - [8, ∞)
c. X-intercepts - undefined.
d. Y-intercept - 8
e. Missing function value f(9) = 11
What is the explanation for the above ?a. The function's domain is the range of x-values over which the graph is defined. In this case, the domain is from 0 to 20, inclusive - [0, 20].
b. The function's range is the set of all possible y-values that the function takes. Since the graph starts from unit 8 on the y-axis, the range would be from 8 to positive infinity - [8, ∞).
c. since the graph does not touch the x- axis at any point, we can state that the there is no x-intercept orthat the x -intercept is undefined.
d. The y-intercept is the point where the graph intersects the y-axis. In this case, the y-intercept is at unit 8 on the y-axis.
e. Based on the graph the point (9, 11) corresponds to the value of y when x is 9, then f(9) would be equal to 11.
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There are 50 animals in a shelter. Sixty percent of the animals are dogs. Which equation can be used to find the number of dogs in the shelter?
StartFraction 60 divided by 2 Over 100 divided by 2 EndFraction = StartFraction 30 Over 50 EndFraction
StartFraction 100 times 2 Over 50 times 2 EndFraction = StartFraction 200 Over 100 EndFraction
StartFraction 50 divided by 1 Over 60 divided by 1 EndFraction = StartFraction 50 Over 60 EndFraction
StartFraction 60 times 2 Over 50 times 2 EndFraction = StartFraction 120 Over 100 EndFraction
The correct Option is A. Equation that can be used to find the number of dogs in the shelter is StartFraction 60 divided by 2 Over 100 divided by 2 EndFraction = StartFraction 30 Over 50 EndFraction.
In order to do that, we first need to determine the number of dogs in the shelter.
We can do that by multiplying the total number of animals by 60% (0.60):60% of 50 = (60/100) × 50 = 30
Therefore, there are 30 dogs in the shelter.
Now, we can look at the answer choices to see which equation can be used to find the number of dogs in the shelter.
A. (60/2 ÷ 100/2) = 30/50This equation simplifies to (30 ÷ 50) = 0.6, which is the decimal equivalent of 60%. T
his equation is correct.
B. (100 × 2 ÷ 50 × 2) = 200/100
This equation simplifies to 1, which is not the correct answer.
C. (50 ÷ 1 ÷ 60 ÷ 1) = 50/60
This equation simplifies to 5/6, which is not the correct answer.
D. (60 × 2 ÷ 50 × 2) = 120/100
This equation simplifies to 6/5, which is not the correct answer.
Therefore, the equation that can be used to find the number of dogs in the shelter is A. (60/2 ÷ 100/2) = 30/50.
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The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 120.5° is added to the data, how does the mean change and by how much?
The mean stays at 83.5°.
The mean increases by 3.1°.
The mean increases by 3.5°.
The means stays at 80.4°.
Answer:
The mean increases by 3.5°.
Step-by-step explanation:
To determine how the mean changes when a value of 120.5° is added to the data, we need to recalculate the mean before and after the addition.
Given the average high temperatures:
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
To find the original mean, we sum up all the temperatures and divide by the number of data points:
(58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57) / 12 = 904 / 12 = 75.33°
Now, let's add the value of 120.5° to the data:
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57, 120.5
To find the new mean, we sum up all the temperatures (including the added value) and divide by the number of data points:
(58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57 + 120.5) / 13 = 1025.5 / 13 ≈ 78.88°
The mean has increased from 75.33° to 78.88°.
Therefore, the mean increases by approximately 3.55° (rounded to the nearest tenth).
The correct answer is: The mean increases by 3.5°.
Answer:
The mean increases by 3.5°.
Step-by-step explanation:
Which set of ordered pairs represents a function?
{
(
−
5
,
−
9
)
,
(
−
7
,
−
9
)
,
(
−
5
,
−
7
)
,
(
−
8
,
6
)
}
{(−5,−9),(−7,−9),(−5,−7),(−8,6)}
{
(
−
1
,
6
)
,
(
0
,
−
3
)
,
(
5
,
−
9
)
,
(
−
1
,
3
)
}
{(−1,6),(0,−3),(5,−9),(−1,3)}
{
(
1
,
2
)
,
(
−
6
,
2
)
,
(
3
,
9
)
,
(
5
,
3
)
}
{(1,2),(−6,2),(3,9),(5,3)}
{
(
−
3
,
9
)
,
(
2
,
7
)
,
(
2
,
−
4
)
,
(
1
,
5
)
}
{(−3,9),(2,7),(2,−4),(1,5)}
The set of ordered pairs that represents a function is:
{(−1,6),(0,−3),(5,−9),(−1,3)}
In a function, each input value (x-coordinate) must be paired with only one output value (y-coordinate). In the given set, there are no repeated x-coordinates, meaning that each input value is associated with only one output value. Therefore, it satisfies the definition of a function.
Solve for the measure of the indicated arc.
O Saved 41°
O
49°
45°
51⁰
131
M
?
K
45°
The calculated measure of x in the circle is 2
How to calculate the measure of x in the circleFrom the question, we have the following parameters that can be used in our computation:
The circle
The measure of x in the circle can be calculated using the angle intersected by arc theorem
So, we have
1/2(69x + 2) = 70
Multiply both sides by 2
69x + 2 = 140
So, we have
69x = 138
Divide both sides by 69
x = 2
Hence, the measure of x in the circle is 2
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Please help me with this problem
Answer:
x = 5-------------------------
Solve the given equation in below steps:
[tex]\sqrt{2^{x+3}} =16[/tex][tex]2^{(x+3)/2} =2^4[/tex][tex](x+3)/2=4[/tex][tex]x+3=8[/tex][tex]x=5[/tex]
HELP FAST PLEASE!!!!!!!!!!!!!!!!!!!!
Answer: First row: 6,12,15
Second row: 15
Step-by-step explanation:
For first row: 3*1, 3*2, 3*3, 3*4, 3*5
Second row: 5*1, 5*2, 5*3, 5*4, 5*5
Helpppp it’s for my homework
Answer:
A = -5
B = -2
C = 3
Step-by-step explanation:
[tex](A) = (-3)^{2} +4(-3)-2\\(A) = 9+(-12)-2\\(A) = -5\\\\\\(B) = (0)^{2} +4(0)-2\\(B)=0+0-2\\(B)=-2\\\\\\(C)=(1)^{2} +4(1)-2\\(C)=1+4-2\\(C)=3[/tex]
Which graph represents h(x)?
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The graph that represents the piecewise function, h(x) is the second option
Please find attached the graph that represents h(x) created with MS Excel
What is a piecewise function?A piecewise function comprises of two or more functions, which are defined based on specified intervals of the input variable.
The possible piecewise function that is represented by h(x), obtained from a similar question on the site can be presented as follows;
[tex]h(x) \begin{cases} \frac{1}{4}\cdot x-4, & \text{ } x\leq0 \\\frac{1}{3}\cdot x - 3, & \text{ } 0 < x \leq 3 \\\frac{1}{2}\cdot x-2, & \text{ } x\geq4\end{cases}[/tex]
Therefore, at x ≤ 0, the y-intercept is -4, for h(x) = (1/4)·x - 4, which corresponds to the second graph.
The range for h(x) at 0 < x ≤ 3 is; h(0) = (1/3)×0 - 3 < h(x) ≤ (1/3)×3 - 3, which can be expressed as; (-3, -2], also corresponding to the second graph
The value of x-intercept of h(x) in the interval x ≥ 4 can be found from the equation; h(x) = (1/2)·x - 2 = 0
(1/2)·x = 2
x = 2 × 2 = 4
The x-intercept, (4, 0), corresponds to the second graph, therefore, the graph that represents h(x) is the second graph
Please find attached the graph that represents the piecewise function, h(x), created with MS Excel
Learn more on piecewise functions here: https://brainly.com/question/29192595
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Find BE, if DC is equal to 27 and FA is equal to 46.
Considering the triangles, the value of BE is 27
What are similar triangles?This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
In the figure, BE is solved using the following ratio
FD / FA = DC / AE
1 / 2 = 27 / AE
AE = 27 * 2
AE = 54
BE = 1/2 AE
BE = 27
hence BE = 27
Learn more about similar triangles here:
https://brainly.com/question/29333623
https://brainly.com/question/29333623
#SPJ1