Answers
First, notice that the line intersects the y-axis at the point (0,5), and that it also passes through the point (2,4). Then, we can use the equation for the slope given two points:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]in this case, we get the following:
[tex]\begin{gathered} (x_1,y_1)=(2,4)_{} \\ (x_2,y_2)=(0,5) \\ \Rightarrow m=\frac{5-4}{0-2}=-\frac{1}{2} \\ m=-\frac{1}{2} \end{gathered}[/tex]now that we have that the slope is m = -1/2 and that the y-intercept is 5 (since the intersection is the point (0,5)), then, the equation of the line in slope intercept form is:
[tex]y=-\frac{1}{2}x+5[/tex]Related Questions
In the figure, LMN is congruent to QRS.What is the value of x and y?
Answers
If they are congruent, then;
3x + 5 = 2x + 10
collect like term
3x - 2x = 10 - 5
x = 5
Similarly,
y + 6 = 2y - 12
collect like term
2y - y = 6 + 12
y = 18
whats the constant proportionality of the table. x 30 24 9 y 10 8 3
Answers
Let:
y = kx
Where:
k = constant proportionality of the table
If x = 30, y = 10:
10 = k30
Solving for k:
k = 10/30 = 1/3
Verify the answer:
If x = 24, y = 8:
y = kx = 1/3*24 =24/3 = 8
Therefore, the constant proportionality of the table is 1/3
a spinner with 10 equally sized slices has four yellow slices, three red slices, and three blue slices. Martina spun the dial 500 times and got the following results. (refer to pic)answer the following. Round your answers to the nearest thousand.a) from Martinas results, compute the experimental probability of landing on red.b) assuming that the spinner is fair, compute the theoretical probability of landing on red.c) assuming that the spinner is fair, choose the statement below that is true. 1. the larger the number of spins, the greater the likelihood that the experimental probability will be close to the theoretical probability. 2. the smaller the number spins, the greater the likelihood that the experimental probability will be close to the theoretical probability. 3. the experimental probability will never be close to the theoretical probability, no matter the number of spins.
Answers
Given the experimental results of spinning the spinner:
Yellow: 212
Red: 144
Blue: 144
The sum of times = 500
a) from Martina's results, compute the experimental probability of landing on red.
So, the answer will be probability = 144/500 = 0.288
b) assuming that the spinner is fair, compute the theoretical probability of landing on red.
As shown: the spinner has 10 equally sized slices.
The number of red slices = 3
So, the probability of red = 3/10 = 0.3
c) assuming that the spinner is fair, choose the statement below that is true.
The true statement will be:
1. the larger the number of spins, the greater the likelihood that the experimental probability will be close to the theoretical probability.
A building has two sizes of apartments, small and regular. The ratio of small apartments to regular apartments is 6 to 18. What percent of apartments in the building are small?
Answers
Convert 59°F to degrees Celsius.If necessary, round your answer to the nearest tenth of a degree.Here are the formulas.C= (5/9) (F -32).
Answers
15 ° C
Explanation
to convert form Farenheit to Celcius degree we need to use the formula
[tex]C=\frac{5}{9}(F-32)[/tex]then
Let
F=59
now, replace and evaluate
[tex]\begin{gathered} C=\frac{5}{9}(F-32) \\ C=\frac{5}{9}(59-32) \\ C=\frac{5}{9}(27) \\ C=15 \end{gathered}[/tex]therefore, the answer is
15 ° C
I hope this helps you
The system of equations y= -x - 1 is graphed. what is the solution to the system of equations ?
Answers
We solve as follows:
*First: Given one function, we corroborate and find the second one.
*We have that the first function passes by the points (0, -1) & (1, 0); we find its function:
[tex]m=[/tex]Use the graph to respond to the questions. 6a. What is the height of the ball before its thrown? b. Approximately how high in the air did the ball go? C. NWAOOOOO INW Approximately long did it take the ball to reach the max height? d. How long was the ball in the air? 34(0.3) 2 e. (-0.2.0) -2 -1 (3.0) t 3 4 What does the point (3, 0) tell us about this situation? 1 INV
Answers
Given data:
The given graph is shown.
a)
The initial height of the ball is 3 units.
b)
The maximum height of the ball is approx 12.5 units.
c)
The time taken by the ball to reach maximum height is 1.5 units.
d)
The time ball was in air is 3 units.
e)
The point (3,0) denoted the coordinate of time is 3 when height is zero.
Which function is nonlinear?Which equation represents a nonlinear function? (Let me know if you can’t read the possible answers for the equation and I will send them)
Answers
Given:
There are 4 equation representations are given.
To find:
The nonlinear equation.
Explanation:
A)
[tex]\begin{gathered} 3x-2y=7 \\ i.e)3x-2y-7=0 \end{gathered}[/tex]Which is of the linear form,
[tex]ax+by+c=0[/tex]B)
[tex]y=\frac{2}{3}x+8[/tex]Which is of the linear form,
[tex]y=mx+c[/tex]C)
Let us consider the two points.
[tex](5,0),(6,2)[/tex]Using the two-point formula,
[tex]\begin{gathered} \frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1} \\ \frac{y-0}{2-0}=\frac{x-5}{6-5} \\ \frac{y}{2}=\frac{x-5}{1} \\ y=2x-10 \end{gathered}[/tex]Substituting the first point to verify the linear equation,
[tex]\begin{gathered} -4=2(3)-10 \\ -4=-4 \end{gathered}[/tex]Therefore, the linear equation is satisfied for all 4 points.
Thus, options A, B, and C are linear equation.
So, the nonlinear equation must be given options D.
Final answer:
The correct option is D.
Can you please help me with this question D and E
Answers
Solution
Part d
T= -2ºC, V=15 km/hr
We can convert to F and mi/h like this:
T= 1.8*(-2)+ 32= 28.4ºF
Ms= As/0.62= 15 km/hr /0.62= 24.19 mi/hr
Replacing we have:
[tex]WC=35.74+0.6215\cdot(28.4)-35.75(24.19^{0.16})+0.4275(28.4)(24.19^{0.16})[/tex]Solving we got:
[tex]WC=35.74+17.651-59.519+20.213=14.08[/tex]Rounded to one decimal we got:
14.1
Part e
T= 10ºC = 1.8(10)+ 32=50ºF
Ms = 34 km/hr
Ms= As/0.62= 34 km/hr/ 0.62= 54.84 mi/hr
Replacing we got:
[tex]WC=35.74+0.6215\cdot(50)-35.75\cdot(54.84^{0.16})+0.4275(50)(54.84^{0.16})[/tex][tex]WC=35.74+31.075-67.847+40.566=39.53[/tex]Rounded to the nearest tenth we got:
39,5
Althought the reported temperature is 50 ºFahrenheit, because of wind it feels like 39.5 Fahrenheit
Elisa's school is selling tickets to a choral performance. On the first day of ticket sales the school sold 8 senior citizen tickets and 5 child tickets for a total of $94. The school took in $152 on the second day by selling 4 senior citizen tickets and 10 child tickets. What is the price each of one senior citizen ticket and one child ticket?
Answers
Let's define the next variables:
x: price of one senior ticket
y: the price of one child ticket
On the first day of ticket sales, the school sold 8 senior citizen tickets and 5 child tickets for a total of $94. That is:
8x + 5y = 94 (eq. 1)
The school took in $152 on the second day by selling 4 senior citizen tickets and 10 child tickets. That is:
4x + 10y = 152 (eq. 2)
Multiplying equation 2 by 2, we get:
2(4x + 10y) = 2*152
8x + 20y = 304 (eq. 3)
Subtracting equation 1 to equation 3, we get:
8x + 20y = 304
-
8x + 5y = 94
------------------------
15y = 210
y = 210/15
y = 14
Substituting this result into equation 1:
8x + 5(14) = 94
8x + 70 = 94
8x = 94 - 70
8x = 24
x = 24/8
x = 3
Each senior citizen ticket cost $3 and each child ticket cost $14
At an amusement park, the two most popular rollercoasters are the Python and the Vortex. The Python is 212 feet long and the Vortex is 210 feet long. How many times as long is the Python as the Vortex?
Answers
Python is 1.01 times as long as Vortex.
What is division ?
In mathematics, division is the process of dividing a given sum into equal pieces. As an illustration, we could divide a group of 20 people into 4 groups of 5, 5 groups of 4, and so on. The opposite of multiplication is division. When you multiply three groups of four to produce twelve, you get four in each group when you split twelve into three equal groups. The basic objective of splitting is to determine how many equal groups are created or how many people are in each group after a fair distribution.
Here the given ,
length of Python = 212 feet
length of Vortex = 210 feet
Here to find the length we need to divide python length by vortex length
=> [tex]\frac{212}{210}[/tex]
=> 1.01 times.
Therefore Python is 1.01 times as long as Vortex.
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Consider the following graph. Explain why it is possible to find an Euler circuit for this graph. Then, using Fleury's algorithm, identify and draw an Euler circuit starting with point A and choosing the first edge as A to F. Show all work using the required method. Draw the graph properly. (If you choose not to draw on my graph, then draw a LARGE graph on your paper.)
Answers
The Euler circuit for the graph using Fleury's algorithm is attached below.
The following steps are to be used to form the circuit.
Of the three edges coming from vertex "2" should I choose? We avoid choosing the edge "2-3" because it is a bridge and we cannot return to "3".
Any of the two remaining edges is ours to choose. Let's say we choose "2-0." By eliminating this edge, we can travel to vertex "0."
We pick the one edge from vertex "0" that is present, remove it, and then move to vertex "1." The Euler tour changes to "2-0 0-1."
We take the lone edge from vertex "1," delete it, and then move to vertex "2." The Euler tour is now "2-0 0-1 1-2."
Once more, vertex 2 has just one edge, so we pick it, remove it, and continue on to vertex 3.
Hence we get the required circuit.
The term "Eulerian graph" has two different meanings in graph theory. One interpretation applies to a graph with an Eulerian circuit, whereas the other applies to a graph where each vertex has an even degree. These definitions apply to linked graphs.
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18. Light Bulbs: The mean lifespan of a standard 60 watt incandescent light bulb is 875 hours with a standard deviation of 80 hours. The mean lifespan of a standard 14 watt compact fluorescent light bulb (CFL) is 10,000 hours with a standard deviation of 1,500 hours. These two bulbs put out about the same amount of light. Assume the lifespan’s of both types of bulbs are normally distributed to answer the following questions. (a) I select one incandescent light bulb and put it in my barn. It seems to last forever and I estimate that it has lasted more than 2000 hours. What is the probability of selecting a random incandescent light bulb and having it last 2000 hours or more. Did something unusual happen here? (b) I select one CFL bulb and put it in the bathroom. It doesn’t seem to last very long and I estimate that it has lasted less than 5,000 hours. What is the probability of selecting a random CFL and having it last less than 5,000 hours. Did something unusual happen here? (c) Compare the the lifespan of the middle 99% of all incandescent and CFL light bulbs. (d) Is there much of a chance that I happen to buy an incandescent light bulb that lasts longer than a randomly selected CFL?
Answers
Set
[tex]\begin{gathered} \mu_1=875,\sigma_1=80 \\ \text{and} \\ \mu_2=10000,\sigma=1500 \end{gathered}[/tex]a) The Z-score formula is
[tex]Z=\frac{x-\mu}{\sigma}[/tex]Therefore, in our case, if x=2000
[tex]\Rightarrow Z=\frac{2000-875}{80}=\frac{1125}{80}=14.0625[/tex]Using a Z-score table,
[tex]\begin{gathered} P(z\ge2000)=1-P(z<2000)\approx1-1=0 \\ \Rightarrow P(z\ge2000)=0 \end{gathered}[/tex]A value of 2000 hrs is 14 standard deviations away from the mean. The probability is practically zero.
b) Similarly, set x=5000; then,
[tex]Z=\frac{5000-10000}{1500}=-\frac{5000}{1500}=-3.333\ldots[/tex]Thus, using a z-score table
[tex]P(z\le5000)=0.0004[/tex]The probability is 0.0004=0.04%. It is quite improbable but not an impossible event.
c) According to the empirical rule 99.8% of the data lies within 3 standard deviations; thus,
[tex]\begin{gathered} Incandescent \\ \mu_1\pm3\sigma_1=\lbrack875-240,875+240\rbrack=\lbrack635,1115\rbrack \\ \text{CFL} \\ \mu_2\pm3\sigma_2=\lbrack10000-4500,10000+4500\rbrack=\lbrack5500,14500\rbrack \end{gathered}[/tex]The lifespan of 99% of all incandescent bulbs is between 635 and 1115 hrs, whereas that of all CFL bulbs is between 5500 and 14500 hrs.
d) If we randomly select a CFL, the most probably lifespan is the mean of the distribution, in other words, 10000 hrs.
The probability of an incandescent bulb lasting 10000 hrs is
[tex]\begin{gathered} Z=\frac{10000-875}{80}=114.0625 \\ \Rightarrow P(z\ge10000)=1-P(z<10000)=0 \end{gathered}[/tex]The event is practically impossible.
How would you solve this question or similar questions? It is solving for x.
Answers
Given the initial expression
[tex]\sqrt[]{2x+3}=\sqrt[]{2x}+3[/tex]Then,
[tex]\begin{gathered} \sqrt[]{2x+3}=\sqrt[]{2x}+3 \\ \Rightarrow(\sqrt[]{2x+3})^2=(\sqrt[]{2x}+3)^2 \\ \Rightarrow2x+3=2x+6\sqrt[]{2x}+9 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \Rightarrow3=6\sqrt[]{2x}+9 \\ \Rightarrow-6=6\sqrt[]{2x} \\ \Rightarrow\sqrt[]{2x}=-\frac{6}{6}=-1 \\ \Rightarrow\sqrt[]{2x}=-1 \\ \Rightarrow\sqrt[]{2}\sqrt[]{x}=-1 \\ \Rightarrow\sqrt[]{x}=-\frac{1}{\sqrt[]{2}} \end{gathered}[/tex]And sqrt(x)>=0 for any real number.
Therefore, there is no real solution to the equation.
When simplified, |9+ (4-3) – 17| has a value of ______.
Answers
We have the following expression:
[tex]|9+(4-3)-17|[/tex]First, let's solve the operation inside the parenthesis.
[tex]|9+1-17|[/tex]Second, we add and subtract accordingly.
[tex]\lvert-7\rvert[/tex]Third, we apply the absolute value property.
[tex]\lvert-7\rvert=7[/tex]In conclusion, the values is 7
A property owner paid $960 for the tiles to cover a 800 sq. ft yard. Then he decided to tile an additional 260 sq. ft. How much will be paid for the additional tiles?
Answers
Answer:
$312 will be paid for the addditional tile
Explanation:
Given that the property owner paid $960 for tiles to cover a 800 sq. ft yard
Since he decided to tile an additional 260 sq. ft, to know how much will be paid for the additional tiles, we need to know how much he paid for each of the last set of tiles.
The amount is
960/800 = 1.2
He paid $1.2 per tile.
For 260 sq. ft, he will pay:
$1.2 * 260
= $312
2 Quadrilateral A'B'CD is the result of dilating quadrilateral ABCD about point D by a scale factor of 3 1 ita -4 -3 -2 B Determine whether each claim about the properties of ABCD and A'B'C'D' is true or false. AB and A' B' are on distinct parallel lines. True/false v AD and A'D' are on the same line. True/false v
Answers
Solution
AB and A' B' are on distinct parallel lines. TRUE
Since when we apply the scale factor the new A'B' is on a different line but parallel
AD and A'D' are on the same line. FALSE
The new triangle with the scale factor produce an A'D' line different
solve the given system of equations2y=x+93x-6y=-15
Answers
Answer:
No solutions
Explanation:
The given system of equations is
2y = x + 9
3x - 6y = -15
To solve the system, we first need to solve the first equation for x, so
2y = x + 9
2y - 9 = x + 9 - 9
2y - 9 = x
Then, replace x = 2y - 9 on the second equation
3x - 6y = -15
3(2y - 9) - 6y = -15
3(2y) + 3(-9) - 6y = -15
6y - 27 - 6y = -15
-27 = -15
Since -27 is not equal to -15, we get that this system of equation doesn't have solutions.
ans (alpha particles) at Figure 127 Exercises 12.6. complete the following: Find the intercepts and domain and perform the symmetry test (a) 9x^2 - 16y^2 = 144
Answers
We have that the general equation of the hyperbola is the following:
[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]where 'a' and '-a' are the x-intercepts.
In this case, we have the following equation:
[tex]9x^2-16y^2=144[/tex]then, we have to divide both sides by 144 to get on the right side 1, thus, we have the following:
[tex]\begin{gathered} (9x^2-16y^2=144)(\frac{1}{144}) \\ \Rightarrow\frac{9}{144}x^2-\frac{16}{144}y^2=1 \\ \Rightarrow\frac{x^2}{16}-\frac{y^2}{9}=1 \end{gathered}[/tex]now, notice that we have that:
[tex]a^2=16[/tex]then, the x-intercepts are:
[tex]\begin{gathered} a^2=16 \\ \Rightarrow a=\pm\sqrt[]{16}=\pm4 \\ a_1=4 \\ \text{and} \\ a_2=-4 \end{gathered}[/tex]therefore, the x-intercepts are 4 and -4.
Now that we know that the intercepts are on those points, we can see that the hyperbola has the following graph:
we can see that the hyperbola is not defined between -4 and 4, therefore, the domain of the hyperbola is:
[tex](-\infty,-4\rbrack\cup\lbrack4,\infty)[/tex]finally, to perform the symmetry test, we have to check first both axis simmetries by changing x to -x and y to -y:
[tex]\begin{gathered} \frac{x^2}{16}-\frac{(-y)^2}{9}=1 \\ \Rightarrow\frac{x^2}{16}-\frac{y^2}{9}=1 \\ then \\ \frac{(-x)^2}{16}-\frac{y^2}{9}=1 \\ \Rightarrow\frac{x^2}{16}-\frac{y^2}{9}=1 \end{gathered}[/tex]since the hyperbola got symmetry about the x-axis and the y-axis, we have that the hyperbola got symmetry about the origin
Write an equation to represent the sum modeled in the following number line. H H H -4 -3 -2 -1 0 1 2 3 4
Answers
The number line shows numbers graded into three parts each such that each point between numbers represent 0.33 units.
This means the red line moving towards the left is a negative because it falls to the left of point 0, where the division between positive and negative numbers take place.
Hence the red line indicates -3.33
The blue line is movin towards the right which means its a positive value. Note that it begins from -3.33 and ends at -1.33. Hence the blue line is a positive value and it covers two units.
The equation that models this number line can be written out as
[tex]x=-3.33+2[/tex]Find the midpoint and distance on points (5,5) and (-1,3)
Answers
Given:
Two points (5, 5) and (-1, 3).
To find the midpoint and distance:
Using the midpoint formula,
[tex]\begin{gathered} m=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ =(\frac{5-1}{2},\frac{5+3}{2}) \\ =(\frac{4}{2},\frac{8}{2}) \\ =(2,4) \end{gathered}[/tex]Thus, the mid-point formula is (2, 4).
Using the distance formula,
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2_{}} \\ =\sqrt[]{(-1-5)^2+(3-5)^2} \\ =\sqrt[]{(-6)^2+(-2)^2} \\ =\sqrt[]{36+4} \\ =\sqrt[]{40} \\ =2\sqrt[]{10}\text{ units} \end{gathered}[/tex]Thus, the distance between the two points is,
[tex]2\sqrt[]{10}units[/tex]I need help answering this question and the solution set
Answers
Let's first try to rewrite the expression to see if we can write it in a fomr more familiar:
[tex]\begin{gathered} x-\sqrt{10-3x}=0, \\ x=\sqrt{10-3x}, \\ x^2=10-3x, \\ x^2+3x-10=0. \end{gathered}[/tex]This is the same equation, but now we recognize a quadratic expression equal to 0. We can use the quadratic formula to find the solutions of this equation:
[tex]x_{1,2}=\frac{-3\pm\sqrt{3^2-4\cdot1\cdot(-10)}}{2\cdot1}[/tex]And solve:
[tex]\begin{gathered} x_{1,2}=\frac{-3\pm\sqrt{9+40}}{2}=\frac{-3\pm7}{2} \\ x_1=\frac{-3+7}{2}=\frac{4}{2}=2 \\ x_2=\frac{-3-7}{2}=\frac{-10}{2}=-5 \end{gathered}[/tex]Thus, the solution set of the equation is x = -5, x = 2
how many square inches of wrapping paper are needed to wrap a present that is 12 inches wide, 5 inches deep and 12 inches tall
Answers
ok
Area of a rectangular prism: 2(wide x deep) + 2(wide x tall) + 2(tall x deep)
Substitution
Area = 2(12 x 5) + 2(12 x 12) + 2(5 x 12)
Simplification
Area = 2(60) + 2(144) + 2(60)
Area = 120 + 288 + 120
Result
Area = 528 in^2
a. Make a scatter plot of the data in the table below.b. Does it appear that a linear model or an exponential model is the better fit for the data?
Answers
a) Option C
b) A linear model
Explanation:To determine the correct plot from the options, we trace the x and y values given
Option A:
When x = 5, y = 1
when x = 6.6, y = 2
We see this is exact opposite of the values in the given table
Option B:
when x = 5, y = 5
when x = 6.6, y = 6.6
This is also different from the given values in the table
Option C:
when x = 1, y = 5
when x = 2, y = 6.6
when x = 3, y = 8.4
This is the same as the given values in the table.
Hence, the correct scatter plot is option C
We need to check if the points are linear:
[tex]\begin{gathered} u\sin g\text{ any two points on the table,} \\ \text{rate = }\frac{6.6\text{ - 5}}{2-1}\text{ = 1.6/1 = 1.6} \\ \text{rate = }\frac{8.4\text{ - 6.6}}{3-2}\text{ = 1.8/1 = 1.8} \\ \text{rate = }\frac{10.2\text{ - 8.4}}{3\text{ - 2}}\text{ = 1.8/1 = 1.8} \\ \text{rate = }\frac{12-10.2}{4-3}\text{ = 1.2/1 = 1.2} \end{gathered}[/tex]A linear model fit the data
The local seven-digit telephone numbers in city A have 1,8,0, as the first three digits. How many different telephone numbers are possible in city A?
Answers
ANSWER
10,000
EXPLANATION
Given:
The first-three digits to be 1, 8, 0 out of seven-digit telephone numbers.
Desired outcome:
Total number of possible different telephone numbers
Determine the possibilities of the 4th, 5th, 6th and the 7th digits
The 4th digit has 10 possibilities (i.e: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
The 5th also has 10 possibilities,
likewise the 6th and the 7th digits.
Now, we have:
10 x 10 x 10 x 10 = 10^4 = 10,000
Hence, the number of possible different telephone numbers is 10,000.
In triangle EFG, m∠E = 91.6° and m∠F = 30.7°. Determine the measure of the exterior angle to ∠G.
57.7°
60.9°
119.1°
122.3°
Answers
Answer:
122.3
Step-by-step explanation:
91.6 + 30.7 = 122.3
180 - 122.3 = 57.7 (angles in a triangle = 180)
180 - 57.7 = 122.3 (angles on a straight line = 180)
Answer: 122.3
Step-by-step explanation: did the practice test
x/6 -7 = -4 what value of x makes this equation true
Answers
Answer:
x=18
Explanation:
Given the equation:
[tex]\frac{x}{6}-7=-4[/tex]To solve for x, follow the steps below.
Step 1: Add 7 to both sides of the equation.
[tex]\begin{gathered} \frac{x}{6}-7+7=-4+7 \\ \implies\frac{x}{6}=3 \end{gathered}[/tex]Step 2: Multiply both sides of the equation by 6.
[tex]\begin{gathered} \frac{x}{6}\times6=3\times6 \\ x=18 \end{gathered}[/tex]The value of x that makes the equation true is 18.
In right triangle XYZ, the hypotenuse measures 14 inches and one leg measures 10 inches. Find the length of the other leg. Show your work and write your answer in simplest radical form.
Answers
As per given by the question,
There are given that a triangle XYZ, and the hypotenuse of the triangle is 14 in., and one leg is 10 in.
Now,
First draw the triangle XYZ.
Now,
From the triangle XYZ, XZ is hypotenuse of the triangle, XY is the first leg of the triangle, and YZ is second leg of the triangle.
So,
First leg z is 10, then find the value of second leg x.
Then,
To find the value of second leg, here use pythagoras theorem.
So,
From the pythagoras theorem;
[tex]XY^2+YZ^{2^{}^{}}=XZ^2[/tex]Now,
[tex]\begin{gathered} XY^2+YZ^2=XZ^2 \\ 10^2+x^2=14^2 \\ 100+x^2=196 \\ x^2=196-100 \\ x^2=96 \end{gathered}[/tex]Then,
[tex]\begin{gathered} x^2=96 \\ x=\sqrt{96}^{} \\ x=9.79 \end{gathered}[/tex]Hence, the length of the other leg is 9.79.
Section 1- Question 10Use the quadratic formula to solve the following equation:4m2-7m +2=57+√97A87+√17B87 + √1C87+√-63D8
Answers
The Solution:
Given:
[tex]4m^2-7m+2=5[/tex]We are required to use the Quadratic Formula to solve the equation above.
[tex]\begin{gathered} 4m^2-7m+2-5=0 \\ 4m^2-7m-3=0 \end{gathered}[/tex]The Quadratic Formula is:
[tex]m=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]In this case:
[tex]\begin{gathered} a=4 \\ b=-7 \\ c=-3 \end{gathered}[/tex]Substitute:
[tex]m=\frac{-(-7)\pm\sqrt{(-7)^2-4(4)(-3)}}{2(4)}[/tex][tex]m=\frac{7\pm\sqrt{49+48}}{8}=\frac{7\pm\sqrt{97}}{8}[/tex]Therefore, the correct answer is [option A]
Zach wanted to prove that the arcs on a railroad crossing symbol did not each equal90°. He drew an inscribed angle A with arc BC as the intercepted arc. Angle Ameasured 35°. Fill in the blank with the measure of the intercepted arc.BmBC =RXR35°A
Answers
The given problem can be exemplified in the following diagram:
In this case the value of angle "x" is 35 degrees, therefore, the measure of arc BC is double this angle, that is:
[tex]\begin{gathered} \text{mBC}=35\times2 \\ mBC=70 \end{gathered}[/tex]