Evaluate the function
g(x) = 2x2 + 3x – 5 for the input values -2, 0, and 3.
This is tedious math work but necessary to sharpen your skills.
Let x = -2
g(-2) = 2(-2)^2 + 3(-2) – 5
g(-2) = 2(4) - 6 - 5
g(-2) = 8 - 11
g(-2) = -3
Now let x = 0 and repeat the process.
g(0) = 2(0)^2 + 3(0) - 5
g(0) = 0 + 0 - 5
g(0) = -5
Lastly, let x = 3.
g(3) = 2(3)^2 + 3(3) - 5
g(3) = 2(9) + 9 - 5
g(3) = 18 + 9 - 5
g(3) = 27 - 5
g(3) = 22
Did you follow through each step?
Answer:
-19
-5
-14
Step-by-step explanation:
Which of the following equations is of the parabola whose vertex is at (4, 3), axis of symmetry parallel to the y-axis and focus at (4, -3)?
A.) y+3=1/24 (x+4)^2
B.)y-3=-1/24 (x-4)^2
C.)x-4=-1/24 (y-3)^2
Answer:
B.
Step-by-step explanation:
First thing to determine is how this parabola opens. Up or down? Or left or right?
*We see that the axis of symmetry is a line parallel to the y-axis; therefore, the axis of symmetry is an x = line, making this an up or down parabola. Now we need to determine how everything else all fits in.
The standard form of this type of parabola is
[tex]4p(y-k)=-(x-h)^2[/tex]
where p is the distance between the vertex and the focus. If the vertex has a y coordinate of 3, and the focus has a y coordinate of -3, the vertical distance between those 2 numbers is 6. Therefore, p = 6. Filling in then:
[tex]4(6)(y-3)=-(x-4)^2[/tex]
and [tex]24(y-3)=-(x-4)^2[/tex]
Dividing both sides by 24 gives you what you are looking for:
[tex]y-3=-\frac{1}{24}(x-4)^2[/tex]
The equation of the parabola is:
⇒ y - 3 = -(1/24)(x - 4)²
What is Parabola?A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line, which is known as the directrix.
We can use the standard form of the equation of a parabola with vertex (h, k) and axis of symmetry parallel to the y-axis, which is given by:
(x - h)² = 4p(y - k)
where (h, k) is the vertex and p is the distance between the vertex and the focus.
In this case, the vertex is (4, 3) and the focus is (4, -3).
Therefore, We get;
p = 3 - (-3)
p = 6.
Substituting the values of h, k, and p, we get:
(x - 4)² = 4(6)(y - 3)
Simplifying, we get:
(x - 4)² = 24(y - 3)
Now, we can simplify the equation to match it with the given options:
(x - 4)² = 24y - 72
(x - 4)² + 72 = 24y
y = (1/24)(x - 4)² + 3
Therefore, the equation of the parabola is:
B.) y - 3 = -(1/24)(x - 4)²
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Twenty-five blue and twenty-five yellow marbles are placed in a jar. Thirty-four marbles are removed from the jar and put in a second jar. What is the positive difference between the number of blue marbles in the second jar and the number of yellow marbles remaining in the first jar?
Answer:
a) Let b represent the number of blue marbles placed in the second jar. Then 34-b is the number of yellow marbles in the second jar, and 25 - (34-b) is the number of yellow marbles remaining in the first jar. That value simplifies to b-9. The positive difference between b and (b-9) is 9.
b) Let n, d, p represent the numbers of nickels, dimes, and pennies, respectively.
.. (5n + 10d + p)/(n + d + p) = 7 ... the average value of the collection is 7 cents per coin
.. (5(n-1) + 10d + (p+5))/((n-1) + d + (p+5)) = 6 ... replacing one nickel with pennies changes the average to 6 cents per coin
Multiplying by the denominator and subtracting the right side of each resulting equation gives
.. 10d + 5n + p = 7d + 7n + 7p
.. 10d + 5n + p = 6d + 6n + 6p + 24
Subtracting the second equation from the first gives
.. 0 = d + n + p - 24 ... tells us the total number of coins is 24. This tells us the total value is $1.68 = 24*$0.07.
This sum will consist of at least 3 pennies. If that is all the pennies, then the remaining 21 nickels and dimes must add to $1.65. If all were nickels, the value of the 21 coins would be $1.05. We have $0.60 more than that. For each nickel traded for a dime, we gain $.05, so 12 of the 21 nickels must be traded for dimes to raise the total coin value to $1.65.
Alternatively, you can write two equations in the two unknowns:
.. d + n = 21
.. 10d + 5n = 165
Subtracting 5 times the first equation from the second gives
.. 5d = 60 ... which gives the same answer as reasoned above.
There are 3 pennies, 9 nickels, 12 dimes. (If there are 8 pennies to start, then the number of nickels is zero, so it is impossible to trade one for 5 pennies. The solution shown is the only one.)
What is the solution to this system of equations?
x + 2y = 4
2x + 4z = 8
3y − z= 10
A. (-6, 5, 5)
B. (2, -4, 1)
C. no solutions
D. (1, 8, -2)
E. infinite solutions
Answer:
A. (-6, 5, 5)
Step-by-step explanation:
A suitable calculator can reduce the augmented matrix for the system.
Analyze the zeros of f(x) =x^4 - 3x^3 - 2x^2 + 3x + 5.
Determine the number of possible positive real zeros and the number of possible negative real zeros
a. positive 1; negative 3 or 1
b. positive 1; negative 2 or 1
c. positive 3 or 1; negative 1
d. positive 2 or 1; negative 1
Answer:
c
Step-by-step explanation:
c. positive 3 or 1; negative 1
What is the equation of the line best fit for the following data? Round the slope and y-intercept of the line to three decimal places. X=4,7,10,12,13 y= 5,7,12,14,18
Answer:
y = 1.383x - 1.526
Step-by-step explanation:
Intercept- -1.526
Slope- 1.383
Line of best fit- y = 1.383x - 1.526
Answer:
[tex]y=1.383x-1.526[/tex]
Step-by-step explanation:
The given data table is
x : 4 7 10 12 13
y : 5 7 12 14 18
We need to find the equation of the best fit line.
The general form of a best fit line is
[tex]y=mx+b[/tex] .... (1)
where, m is slope and b is y-intercept.
[tex]m=\frac{\sum_{i=1}^nx_iy_i-n\overline{x}\overline{y}}{\sum_{i=1}^nx_i^2-n\overline{x}^2}[/tex]
[tex]b=\overline{y}-b\overline{x}[/tex]
Using the graphing calculator we get
[tex]m=1.38321\approx 1.383[/tex]
[tex]b=-1.52555\approx -1.526[/tex]
Substitute m=1.383 and b=-1.526 in equation (1).
[tex]y=1.383x-1.526[/tex]
Therefore, the equation of best fit line is [tex]y=1.383x-1.526[/tex].
The scatter plot below shows the relationship between the leaf length (x) and leaf width f(x), in mm, of some leaves of a tree:ordered pairs 11, 0.5 and 12, 1 and 13, 1.5 and 14, 2 and 15, 2.5 and 16, 3 and 17, 3.5 and 18, 4 and 19, 4.5 and 20, 5 and 21, 5.5 and 22, 6Which of the following functions is best represented by the scatter plot?f(x) = −5 + 0.5xf(x) = 5 + 0.5xf(x) = x − 10.5f(x) = −x − 10.5
Answer:
The best function represented by the scatter plot is f(x) = -5 + 0.5 x ⇒ 1st answer
Step-by-step explanation:
* Lets talk about the scatter plot
- Scatter plots are similar to line graphs in that they use horizontal and
vertical axes to plot data points
- Scatter plots show how much one variable is affected by another.
- The relationship between two variables is called their correlation
- There are three types of correlation:
positive: one variable increases so the other increase
negative: as one variable increases, the other decreases
no correlation: there is no clear relationship between the variables
* Lets solve the problem
- The scatter plot shows the relationship between the leaf length (x)
and leaf width f(x)
- Some leaves of a tree are ordered pairs:
# (11 , 0.5) , (12 , 1) , (13 , 1.5) , (14 , 2) , (15 , 2.5) , (16 , 3) , (17 , 3.5) ,
(18 , 4) , (19 , 4.5) , (20 , 5) , (21 , 5.5) , (22 , 6)
∵ The scatter plot is similar to the line graph
- Lets find the equation which represents the relation between
x and f(x)
∵ The form of the linear equation is y = mx + c, where m is the slope
of the line and c is the y-intercept
- The rule of the slope of the line which passes through points (x1 , y1)
and (x2 , y2) is: [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
- Chose any two points to find the slope of the line
∵ (12 , 1) and (14 , 2) are two points on the line
∴ [tex]m=\frac{2-1}{14-12}=\frac{1}{2}=0.5[/tex]
- Substitute the value of m in the equation
∴ y = 0.5 x + c
- To find c use any point from above and substitute x and y by its
coordinates
∵ Point (16 , 3) lies on the line
∴ 3 = 0.5(16) + c ⇒ simplify
∴ 3 = 8 + c ⇒ subtract 8 from both sides
∴ 3 - 8 = c
∴ c = -5
- Substitute the value of c in the equation
∴ y = 0.5 x - 5
* The best function represented by the scatter plot is f(x) = -5 + 0.5 x
Write the equation of the graph shown in factored form.
let's take a peek at the graph.
the graph of the equation touches the x-axis at 1, 2 and 3, at 1 it crosses it, at 2 it crosses it, at 3 is doesn't cross it, it simply bounces off of it.
on the roots/solutions the graph crosses the x-axis, they have ODD multiplicity, on the solutions it bounces off of it, they have EVEN multiplicity, so then.
x = 1 => x - 1 = 0 <------ one factor
x = 2 => x - 2 = 0 <------ another factor
x = 3 => x - 3 = 0 <------ another factor, BUT with even multiplicity
(x-1)¹(x-2)¹(x-3)² = f(x)
(x-1)(x-2)(x-3)² = f(x).
A rectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. The equation (x + 5)x = 104 represents the situation, where x represents the width of the rectangle.
The first step in solving by factoring is to write the equation in standard form, setting one side equal to zero. What is the equation for the situation, written in standard form?
Choose one of the best answers.
A. x² – 99 = 0
B. x² – 99x = 0
C. x² + 5x + 104 = 0
D. x² + 5x – 104 = 0
Please explain your answer?
If your answers is wrong, it's going mark your answer report and it's called "improper answer."
No need to spam answers, if your answer is spam is going to be report.
Don't copied or paste answers with someone else answers from other sites. If you copied and paste answers from other websites and it mark your answer report and it's called "plagiarism."
Thank you!
-Charlie
Answer:
D
Step-by-step explanation:
(x + 5)x = 104
Distribute:
x² + 5x = 104
Subtract 104 from both sides:
x² + 5x − 104 = 0
Taylor fires a toy rocket from ground level. The height of the rocket with respect to time can be represented by quadratic function. If the toy rocket reaches a maximum height of 34 feet, 3 seconds after it was fired, which of the following functions could represent the height, h, of the rocket t seconds after it was fired?
A) h(t)=-16(t-3)²+34
B) h(t)=-16(t+3)²+34
C) h(t)=16(t-3)²+34
D) h(t)=16(t+3)²+34
Answer:
The function in choice
A) [tex]h(t) = -16(t - 3)^{2} + 34[/tex]
could possibly represent this relationship.
Step-by-step explanation:
Consider the vertex form of parabolas with a local extrema at [tex](x_{0}, y_{0})[/tex].
[tex]y = a(x - x_{0})^{2} + y_0[/tex].
Note the minus sign in front of [tex]x_0[/tex] in this expression.
The coefficient [tex]a[/tex] cannot be zero. The value of [tex]a[/tex] depends on the direction and width of the parabola's opening:
[tex]a > 0[/tex] if the parabola opens upwards, and[tex]a < 0[/tex] if the parabola opens downwards.The width of the opening decreases as the value of [tex]a[/tex] increases.For this parabola,
[tex]a < 0[/tex] since the parabola opens downwards: the height of the rocket will eventually decrease as the rocket falls back to the ground;[tex]t_0 = 3[/tex], and[tex]h_0 = 34[/tex].Among the four functions, only the function in A) meets the requirements.
In order to be accepted into a top university, applicants must score within the top 5% on the SAT exam. Given that the test has a mean of 1000 and a standard deviation of 200, what is the lowest possible score a student needs to qualify for acceptance into the university?
Answer:
1329
Step-by-step explanation:
A suitable calculator can tell you the minimum score is 1329.
Using the concept of z-scores and normal distributions, the lowest possible SAT score a student needs to qualify for acceptance into a top university, that requires top 5% of SAT scores, is approximately 1328.
Explanation:The subject of your question falls under Mathematics, particularly statistics. The problem involves understanding SAT scores and how they apply to scholarships. The problem also asks for the understanding of z-scores and how they apply to normal distributions.
In this case, the SAT score requirement is stated to be within the top 5% of all test-takers. In terms of z-scores, this requirement matches with a z-score of approximately 1.64, since z-scores of this value represent the cut-off for the top 5% in a normal distribution.
To calculate the corresponding SAT score, we use the formula for z-score which is Z = (X - μ) / σ, where X is the SAT score, μ is the mean and σ is the standard deviation. We rearrange the formula to find X, where X = Z * σ + μ. Since we know the mean (μ = 1000), standard deviation (σ = 200), and Z (Z = 1.64), we can substitute these values to get X = 1.64 * 200 + 1000 = 1328.
Therefore, the lowest possible score a student needs to qualify for acceptance into the university is approximately 1328.
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Lori purchases a new set of watercolor paints and some canvases to create art for her next exhibit. The watercolor paint set costs $15 and the canvases are $24.50 each. If Lori buys 6 canvases, what is the total amount of money she spends for her next exhibit?
Answer:172
Step-by-step explanation:
24.5 times 6 is 157
Plus 15 for the paint is 172 for the TOTAL for ALL she spent
Answer:
The answer is $162.00Step-by-step explanation
Matthew earned $325 giving haircuts. He charged $25 for each haircut. How many haircuts did he give? PLEASE ANSWER AS SOON AS POSSIBLE (nvm i got it)
Answer: 13
Step-by-step explanation:
Divide 325 by 25
Please answer this multiple choice question for 27 points and brainliest!!
Answer:
A
Step-by-step explanation:
The equation will be in the form
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, 5) and (x₂, y₂ ) = (2.5, 0) ← 2 points on the line
m = [tex]\frac{0-5}{2.5-0}[/tex] = - 2
The line crosses the y- axis at (0, 5) ⇒ c = 5
y = - 2x + 5 or
y = 5 - 2x → A
I need Help!!!! Please Solve and show WORK!!!
3(x+2)=15
Answer: x=3
Step-by-step explanation: First we do distributive property in the parentheses. Next we subtract both sides by 6. Lastly we divide both sides by 3. Algebraic Rules!!!
Work:
3(x+2)=15
3x+6=15
3x+6-6=15-6
3x=9
3x/3=9/3
x=3
Multiply the bracket by 3
3x+6=15
3x+6-6=15-6
3x=9
divide by 3 for 3x and 9
3x/3=9/3
x=3
Check answer by using substitution method
3(x+2)=15
3(3+2)= 15
Multiply the bracket by 3
9+6= 15
15= 15
Answer is x= 3
please give me the Brainliest.
Thanks
UGH SOMEONE PLS HELP IF YOUR GOOD AT GEOMETRY
Answer: First option.
Step-by-step explanation:
Knowing that the transformation T maps triangle XYZ onto triangle X'Y'Z', you can identifyfrom the figure that the triangle XYZ is the preimage, because it is the original shape and the triangle X'Y'Z' is the image, because is the shape obtained after the transformation.
You can observe in the figure that the image of the vertex X is the vertex X', the image of the vertex Y is the vertex Y' and the image of the vertex Z is the vertex Z'.
Therefore, the conclusion is: The image of Y is Y'.
Given the equation 6/x=3/k+2, and the constraints x ≠ 0 and k ≠-2, what is x in terms of k?
A) x=2k+4
B) x=2k+12
C) x=2k-1/4
D) x=1/4+12
Answer:
A) 2k+4
Step-by-step explanation:
To solve for terms of x, we need to. she sure that x is on its own side while every other term is on the other side.
To start, we will cross multiply. If we have a/b=c/d, then ad=bc
We can perform the same calculation here,
6/x=3/(k+2)
6(k+2)=3x
Divide both sides by 3
2(k+2)=x
x=2k+4
Solve x − 7y = 8 for x.
A.x = −7y + 8
B.x= −7y − 8
C.x = 7y − 8
D.x = 7y + 8
Answer:
D
Step-by-step explanation:
you need to get the x alone so to do that, you need to add 7y so you do it on both sides and it gives you x=7y+8
The value of the expression x − 7y = 8 will be x = 7y + 8. The correct option is D.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given expression is x − 7y = 8. The value of x will be calculated as below:-
x − 7y = 8
x = 7y + 8
Therefore, the value of the expression x − 7y = 8 will be x = 7y + 8. The correct option is D.
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I have a model motorcycle that is all metal parts and is 18" long. Since the size all the models online are given in a scale, What scale to an actual motorcycle do I have and where do I look to find a value?
Answer:
See below.
Step-by-step explanation:
The model may have the scale written somewhere. Try looking for it.
If you can't find it, then you can calculate this way.
Search online for the real motorcycle's length.
Then divide the scale model's length, 18 inches, by the real length. Express that as a ratio. That is the scale.
Let's say the length of a real motorcycle of this type is 90 inches.
Divide 18 inches by 90 inches.
18/90 = 1/5
The scale, then, is 1:5.
write a verbal expression to represent
w^2 =32w
BRAINLIEST!
Verbal expression of w^2 = 32w is:
W to the second power equals 32 with a variable of w.
To the second power means exponent of 2.
Variable is an unknown number represented by a letter. In this case, the variable is "w".
Hope this helps!
- Melanie
Answer:
Step-by-step explanation:
The square of variable w is equal to 32 times that variable.
If carol travels 30 miles and her car averages 48 miles per hour, how long will it take carol to complete the distance?
[tex]\bf \begin{array}{ccll} miles&hours\\ \cline{1-2} 48&1\\ 30&x \end{array}\implies \cfrac{48}{30}=\cfrac{1}{x}\implies \cfrac{8}{5}=\cfrac{1}{x}\implies 8x=5 \\\\\\ x=\cfrac{5}{8}\qquad \textit{37 minutes and 30 seconds}[/tex]
Cube shaped box for packing tape Cube shaped container the edge of the length of the storage container is 2 and 1/2 ft of each block is 1/5 of the storage container what is the volume in cubic feet of one of the shape
Answer:
1/8 ft³
Step-by-step explanation:
Apparently cubic blocks that are 1/5 of 2 1/2 ft on a side are used to fill the cube that is 2 1/2 ft on a side. Then each edge of the block is ...
(1/5) × (5/2 ft) = 1/2 ft
The volume of the block is the cube of that:
(1/2 ft)³ = 1/8 ft³
What does the graph of an equation reveal about the solutions to the equation? How do you solve a system of equations approximately using graphs and tables?
Final answer:
The graph of an equation reveals all possible solutions, and a system of equations can be solved graphically by finding the intersection points of their lines. Changing the slope or intercept allows manipulation of these lines, and growth rates show the rate of increase as perce
Explanation:
The graph of an equation illustrates the relationship between two variables and reveals the set of all possible solutions that satisfy the equation. When graphing a line, the slope dictates the direction and steepness of the line, while the intercept indicates where the line crosses the y-axis. To manipulate a line on a graph, you can change the slope or the intercept, altering its position and angle.
To solve a system of equations using graphs, plot each equation on the same set of axes. The point where the lines intersect represents the solution to the system, which is the set of values that satisfies all equations simultaneously. If using tables, input different values for one variable and solve for the other to find ordered pairs. When the pairs from different equations match, you've found an approximate solution. A growth rate can be determined by calculating the percentage change and can be interpreted as the rate at which a quantity increases over time.
Learning how to read and manipulate a graph is critical to interpret and express equations visually. Graphs not only convey solutions but also the behavior of equations, such as trends and growth rates, which are essential in understanding and communicating mathematical concepts effectively.
Solve for x.
5(2x - 1) = 6
x = 1/10
x = 11/10
x = 1/2
Answer:
Distributive Law : x= [tex]\frac{11}{10}[/tex]
Step-by-step explanation:
5(2x - 1) = 6
Using Distributive law on right hand side we get
5*2x - 5 * 1 = 6
10x - 5 = 6
Now we add 5 on both hand sides
10x-5+5=6+5
10x= 11
Now we divide both sides by 10
[tex]\frac{10x}{10} = \frac{11}{10}[/tex]
Hence we get
x= [tex]\frac{11}{10}[/tex]
Where do you find sculptures of great baseball sluggers math worksheet answers?
The sculptures of great baseball sluggers are found in famous places of the city.
Here,
The sculptures of any famous personalities are installed in the places that are frequently visited by the public , so that the it will gain traction.
Thus,
The sculptures of famous baseball players will be available in city malls , museums , parks or baseball stadium.
The players coming to play baseball will be motivated by seeing their idols.
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what is the exact value of cos 90degrees as found on the unit circle?
Answer:
it is 0 because cosine is the x and sine is the y. Sin is 1 and cos is 0
Find the solution of this system of equations -4x-y=-18 , -7x+y=-4
Answer:
(x, y) = (2, 10)
Step-by-step explanation:
Adding the two equations will eliminate the y-variable:
(-4x -y) +(-7x +y) = (-18) +(-4)
-11x = -22 . . . . . simplify
x = 2 . . . . . . . . . divide by -11
__
Put this into the first equation to find y:
-4·2 -y = -18
-8 +18 = y = 10 . . . . . add 18+y
The solution is (x, y) = (2, 10).
Answer:
x = 2 and y = 10
Step-by-step explanation:
It is given that,
-4x - y = -18 ---(1)
-7x + y= -4 ---(2)
To find the solution of equations
Step 1: Add eq(1) + eq(2)
-4x - y = -18 ---(1)
-7x + y= -4 ---(2)
-11x + 0 = -22
11x = 22
x = 22/11 = 2
Step 2: Substitute the value of x in eq (2)
-7x + y= -4 ---(2)
-7*2 + y = -4
-14 + y = -4
y = -4 + 14 = 10
Therefore x = 2 and y = 10
Suppose you have 52 feet of fencing to enclose a rectangular dog pen. The function A = 26x – x2, where x = width, gives you the area of the dog pen in square feet. What width gives you the maximum area? What is the maximum area? Round to the nearest tenth as necessary. width = 26 ft; area = 364 ft2 width = 26 ft; area = 169 ft2 width = 13 ft; area = 507 ft2 width = 13 ft; area = 169 ft2
Answer:
width = 13 ft; area = 169 ft^2
Step-by-step explanation:
The equation for the area can be factored as ...
A = x(26 -x)
This has zeros at x=0 and x=26. The vertex of this downward-opening parabola will be halfway between those, at x=13. Then the area for a width of 13 feet is ...
A = 13(26 -13) = 13^2 = 169 . . . . ft^2
The maximum area is 169 ft^2, when the width is 13 ft.
_____
You will note that these dimensions make the pen be a square. It can be useful to remember that a square is the rectangle with the largest area for a given perimeter length.
The width that gives the maximum area for the given fencing is 13 feet, and the maximum area is 169 square feet (option B).
Explanation:
The formula given is a quadratic function where x is the width and A is the area. In a quadratic function, the maximum or minimum value occurs at the vertex. The x-coordinate of the vertex can be found using the formula -b/2a where a and b are the coefficients of the quadratic function. Here, a is -1 and b is 26, therefore the x-coordinate of the vertex is -26/-2*-1 = 13. This means that a width of 13 ft will give the maximum area. To find the maximum area, we substitute x = 13 into the function: A = 26*13 - 13^2 = 169 ft2. So, the width that will give the maximum area is 13 feet and the maximum area is 169 square feet.
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jackson bought 555 ounces of raisins for \$4$4dollar sign, 4. How much do raisins cost per ounce? \$$dollar sign How many ounces of raisins can be bought for \$1$1dollar sign, 1? ounces
Answer:
$.80 and 1.25
Step-by-step explanation:
hope this helps
I NEED HELP
Analyze the diagram below and complete the instructions that follow.
Find the value of x and the value of y.
answer is B)
x= 85, y = 100
Answer:
D, x=100 and y=85
Step-by-step explanation:
Hello
In every convex polygon, the sum of the measure of the interior angles is given by the expression SUM = 180 ° (n - 2) where n is the number of sides
the polygon has our sides MN, NO,OP and PM, the sum of the interior angles is
[tex]sum=180(4-2)\\sum=360 degrees[/tex]
[tex]360= x +y +80+95\\360-80-95= x+y\\x+y=185[/tex]
looking at the graph it is observed that angle x° is obtuse (more than 90° but less than 180°.) and the angle y is acute (The acute angle is the small angle which is less than 90°)
so
[tex]x>y[/tex]
[tex]x+y=185[/tex]
the response option that meets these two conditions is D, x=100 and y=85
TW is a perpendicular bisector of chord QE. Identify the diameter. The answer with the red arrow is Incorrect!
Answer:
50m.
Step-by-step explanation:
When 2 chords of a circle intersect the following products are equal:
15 * 15 = 5 * (TW - 5)
5TW = 225 + 25 = 250
TW = 250/5 = 50 m
Option c 50m
What is the theorem of the chord from the center?When a line passes through the center of the circle to the chord then the line is perpendicular bisector of the same chord which means it divide the chord in equal parts and makes an angle of 90 degrees with the chord.
What is the Pythagoras theorem?Pythagoras theorem is the theorem used to calculate the hypotenuse in a right-angled triangle from the two legs of the triangle.
hypotenuse² = base²+height².
Solving the problemLet the center (the point in bold be C) and the point of intersection between QE and TW be R, So CQ is the radius, CR = radius-5.
Let the radius be 'r' so In Triangle CQR using the Pythagoras theorem
r² = (r-5)²+15²
r²-(r-5)²=225
(r-(r-5))(r+r-5) = 225
5.(2r-5)=225
(2r-5)=45
2r - 5 =45
2r=50
r = 25 and diameter is equal to 2*r and hence the diamter is 50.
The diameter in the figure is 50m
Learn more about Properties of Circle here
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