Answers
The short line on the sides of the triangle tells us that those sides are equal.
We can see that LN = NJ and
LO = KO
This means that triangle LNO is similar to triangle triangle LJK
LO/NO = (LO + OK)/JK
Given that NO = 16 and JK = 6x + 8, it means that
LO/16 = (LO + OK)/(6x + 8)
Since LO = OK, it means that
LO + OK = LO + LO = 2LO
Therefore
LO/16 = 2LO/(6x + 8)By cross multiplying, it becomes
LO(6x + 8) = 2LO * 16
LO(6x + 8) = 32LO
Dividing both sides of the equation by LO, it becomes
6x + 8 = 32
6x = 32 - 8
6x = 24
x = 24/6
x = 4
Related Questions
There are 9 boys and 12 girls in the drama club. Which is the ratio of boys to girls?
Answers
boys: 9
Girls: 12
Ratio boys to girls :
9:12 = 3/4
A triangle has base 2 3/8 feet and height 2 1/4 feet. Find the area of the triangle as a mixed number.
Answers
Area of a triangle is given by the formula;
[tex]A=\frac{1}{2}\times b\times h[/tex]where A is the area of triangle
b is the base and h is the height.
From the question given:
b= 2 3/8 = 19/8
h= 2 1/4 =9/4
Substitute the values into the formula and evaluate.
[tex]A=\frac{1}{2}\times\frac{19}{8}\times\frac{9}{4}[/tex][tex]=\frac{171}{64}[/tex][tex]=2\frac{43}{64}\text{ square f}eet\text{ }[/tex]8. For which of the following sets of ordered pairs will the slope between the two points be -3 ? A. (2,4) and (3.8) B. (4,1) and (4.6) C. (1.3) and (-5, -5) D. (1,0) and (0,3)
Answers
D. (1,0) and (0,3)
Would we use ">" or "<" to replace the in 5.1489 ? 5.2019. Write only the symbol that is true.
Answers
5.1489 is less than 5.2019
Therefore, the symbol between the two decimals would be less than symbol.
That is,
[tex]5.1489<5.2019[/tex]The symbol that would replace ? is <
Upon replacing the symbols, the equation would look like:
5.1489 < 5.2019
Hence, “<“ is the symbol that would take the place of the question mark.
Carla had an eight-sided die numbered 1 to 8. Find each probability for the number she
rolled.
17. P(3)
19. P(9)
18. P(odd number)
20. P(number greater than 2)
plo and 3 orange popsicle sticks in a container. Without looking
Answers
The most appropriate choice for probability will be given by -
P(3) = [tex]\frac{1}{8}[/tex]
P(9) = 0
P(odd number) = [tex]\frac{1}{2}[/tex]
P(number greater than 2) = [tex]\frac{3}{4}[/tex]
What is probability?
Probability gives us the information about how likely an event is going to occur
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probability of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
For P(3)
Number of favourable outcomes = 1
Total number of outcomes = 8
P(3) = [tex]\frac{1}{8}[/tex]
For P(9)
Number of favourable outcomes = 0
P(9) = 0
For P(odd number)
Favourable outcomes = {1, 3, 5, 7}
Number of favourable outcomes = 4
P(odd number) = [tex]\frac{4}{8}[/tex] = [tex]\frac{1}{2}[/tex]
For P(Number greater than 2)
Favourable outcomes = {3, 4, 5, 6, 7, 8}
Number of favourable outcomes = 6
P(number greater than 2) = [tex]\frac{6}{8}[/tex] = [tex]\frac{3}{4}[/tex]
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find the cost of each.Gwen Chester has $41.70 in her piggybank. She has one more than threetimes as many dimes as she has nick-els, and she has five times as manyquarters as nickels. How many ofeach coin does she have?
Answers
Given that
10 dimes = 1 dollar, this is also known as 10 cents.
4 quarters = 1 dollar, this is also known as 25 cents
20 nickels = 1 dollar, this is also known as 5 cents
Let d represent dime
Let q represent quarter
Let n represent nickel
From the first statement,
[tex]d=3n+1[/tex]From the second statement,
[tex]q=5n[/tex]The total of the coins will be,
[tex]d+q+n=\text{ \$41.70}[/tex]Also,
[tex]0.1d+0.25q+0.05n=41.70[/tex]From the first two equations above,
[tex]\begin{gathered} 0.1(3n+1)+0.25(5n)+0.05n=41.70 \\ 0.3n+0.1+1.25n+0.05n=41.70 \\ 0.3n+1.25n+0.05n=41.70-0.1 \\ 1.6n=41.60 \\ \frac{1.6n}{1.6}=\frac{41.60}{1.6} \\ n=26 \\ \therefore n=\text{26} \end{gathered}[/tex]Let us now get the quantities of the remaining coins
[tex]\begin{gathered} d=(3n+1)=(3(26)+1)=(78+1)=79 \\ \therefore d=79 \end{gathered}[/tex][tex]\begin{gathered} q=5n=5(26)=130 \\ \therefore q=130 \end{gathered}[/tex]Hence, the numbers of each coins are
[tex]\begin{gathered} d=79=0.1(79)=\text{ \$7.9} \\ q=130=0.25(130)=\text{ \$32.5}0 \\ n=26=0.05(26)=\text{ \$1.30} \end{gathered}[/tex]Which function is nonlinear? х y -7 -2 -6 2 4 -3 O {(1, 1). (4.2). (9. 3). (16,4)} у 5 0 4 1 3 3 1 O {(-2.-10). (0.4). (2.2), (4.8)}
Answers
In order to find the nonlinear function we are going to graph each one:
Find the equation (in terms of xx ) of the line through the points (-4,1) and (3,-2)
Answers
First, find the slope of the line that passes through the given points using the slope formula:
[tex]m=\frac{\Delta y}{\Delta x}[/tex]Next, substitute the value of the slope and the coordinates of one of the given points into the slope-intercept form of the equation of a line to find the y-intercept b:
[tex]y=mx+b[/tex]Compute the value of the slope:
[tex]\begin{gathered} m=\frac{(-2)-(1)}{(3)-(-4)} \\ =\frac{-2-1}{3+4} \\ =\frac{-3}{7} \\ =-\frac{3}{7} \end{gathered}[/tex]Replace m=-3/7, x=-4 and y=1 into the slope-intercept form of the equation of a line:
[tex]\begin{gathered} \Rightarrow1=-\frac{3}{7}(-4)+b \\ \Rightarrow1=\frac{12}{7}+b \\ \Rightarrow1-\frac{12}{7}=b \\ \Rightarrow-\frac{5}{7}=b \\ \therefore b=-\frac{5}{7} \end{gathered}[/tex]Replace m=-3/7 and b=-5/7 to get the equation of the line through the points (-4,1) and (3,-2):
[tex]y=-\frac{3}{7}x-\frac{5}{7}[/tex]Therefore, the answer is:
[tex]y=-\frac{3}{7}x-\frac{5}{7}[/tex]
Which inequality is true?А. Зп > 9B. 7 + 8< 11C. 27 -1 < 5D. 2 > 2SUBMIT< PREVIOUS
Answers
For the given options, we will find which inequality is true:
A)
[tex]\begin{gathered} 3\pi>9 \\ 3\pi=3\cdot3.14=9.42>9 \end{gathered}[/tex]so, the inequality is true
B) 7 + 8 < 11
7 + 8 = 15 > 11
So, the inequality is wrong
C) 27 - 1 < 5
27 - 1 = 26 > 5
So, the inequality is Wrong
D) 2 > 2
2 = 2
so, the inequality is wrong
So, the answer will be the true inequality option A) 3п > 9
[tex]undefined[/tex]what is circle in mathematics
Answers
Sintaye, this is the answer to your question:
Circle is a shape made by drawing a curve that is always the same distance from a center.
Write an equation in slope-intercept form of the line that contains the points in the table.
Answers
Step 1. We are given a table of (x, y) values and we need to select the option that represents the slope calculation.
First, we remember the formula to calculate the slope:
[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x1, y1) and (x2, y2) are two points or sets of values given for the line.
Step 2. In the numerator of the slope formula, we have a subtraction between y-values.
In the table, the y-values are:
Therefore, in the numerator of the calculation, we must have a subtraction between two of these numbers. This discards options A, and B.
Step 3. In options C and D we have this:
[tex]C.\frac{9-(-3)}{1-(-2)}[/tex][tex]D.\frac{-3-11}{-2-4}[/tex]In option C, there is a correct subtraction of 9 and -3, but in option D, the correct subtraction would be -3-(-11). Therefore option D is also discarded and the correct answer is C.
Answer: C
xyz with vertices x(1,5) and z(1,1) has an area of 10 units2. what are the coordinates of the third vertex
Answers
Answer:
Explanation:
Given the following vertices:
x(1, 5) and y(1, 1)
Suppose the area for thes is 10 units, with the third vertice (a, b) unknown, we have the area of a triangles as:
[tex]undefined[/tex]How many solutions does this equation have?
–10k + 6 = –2k + 6 + 18k
Answers
Answer: 0
Step-by-step explanation:
-10k + 6 =-2k +6+18k
Combine like terms
-10k + 6 = 16k + 6
Rearrange the terms
=10k - 16k=6-6
Simplify
-10k - 16k = 0
Combine like terms
-26k = 0
Divide both sides
k= 0
6.) An artist was carving a sculpture for a
client. It took 12.5 hours to complete the
task. A second artist will take 2.9 times
longer to complete the task. How much
time would the second artist take?
0
Answers
Answer:
12.5 X 2.9
Decimal place is
1dp
answer = 362.5
13/10÷2/10 please help me solve this i need explanation.
Answers
When we are doing divisions with fractions, the best thing to do is also write the division as a fraction like this:
[tex]\begin{gathered} \frac{13}{10}\frac{\cdot}{\cdot}\frac{2}{10} \\ \Rightarrow\frac{\frac{13}{10}}{\frac{2}{10}} \end{gathered}[/tex]Now, we multiply 13x2 and put it in the numerator, and 10x2 in the denominator:
[tex]\frac{\frac{13}{10}}{\frac{2}{10}}=\frac{13\cdot10}{2\cdot10}[/tex]Then we solve and simplify if needed:
[tex]\frac{13\cdot10}{2\cdot10}=\frac{130}{20}=\frac{13}{2}[/tex]therefore, the answer is 13/2
whitch object has the mass of about one gram
Answers
2y + 2x = 14 solve for y
Answers
Answer:
y = -x + 7
Step-by-step explanation:
Answer:
y = 7 - x
Step-by-step explanation:
move all the terms to the right side of the equation then solve for the variable y
hope this helped
have a good day ^^
During an experiment, the current in a circuit was measured 8 times and recorded as shown below. Calculate the standard deviation of the current to two decimal places.
Answers
Standard Deviation for given set of data is 0.25634797778466.
What is standard deviation?
Standard deviation is a measurement of how evenly distributed a set of numbers is. Since the variance is the squared average of the squared deviations from the mean, it represents the square root of the variance.For instance: To determine the standard deviation, sum all of the numbers inside this data set, divide by the total number of numbers, and the result is the standard deviation.Given that,
Sample size :12.3,11.9,12.5,12.1,12.6,11.9,12.2,12.1
Count, N: 8
Sum, submission x: 97.6
Mean, x: 12.2
Variance, s2: 0.065714285714286
s^2 = Σ(xi - x)^2/N - 1
= (12.3 - 12.2)2 + ... + (12.1 - 12.2)^2/8 - 1
= 0.46/7
= 0.065714285714286
s = √0.065714285714286
= 0.25634797778466
Standard Deviation for given set of data is 0.25634797778466.
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The ratio of measurement of 1 : 2 : 3 is 4 : 9 : 5. Of the three angles, find the measurements of the largest.
Answers
Given:
The ratio of the three angles is 4:9:5.
To find the largest angle:
Let the first, second, and third angles be,
[tex]\begin{gathered} \angle1=4x \\ \angle2=9x \\ \angle3=5x \end{gathered}[/tex]Using the angle sum property of a triangle we get,
[tex]\begin{gathered} \angle1+\angle2+\angle3=180 \\ 4x+9x+5x=180 \\ 18x=180 \\ x=10 \end{gathered}[/tex]So, the largest angle is,
[tex]\begin{gathered} 9x=9\times10 \\ =90 \end{gathered}[/tex]Hence, the measurement of the largest angle is 90 degrees.
Select the correct answer.
The tables show the subscription costs for two magazines. What is the ratio of the cost of Magazine A to the cost of Magazine B?
Magazine A
Duration of Subscription
12 months 36
24 months 72
36 months 108
Magazine B
Duration of Subscription Subscription Cost
(dollars)
12 months 32
24 months 64
36 months 96
A.9:4
B.9:7
C.9:8
D.9:5
Answers
We can conclude that the ratio of the cost of magazine A to the cost of magazine B is (C) 9:8.
What is the ratio?A ratio depicts the quantity of one thing in relation to another. Ordinarily, ratios are expressed in the format a:b. If you're making orange squash, the ratio of orange to water will be one part orange to four parts water (1:4). It matters in what order a ratio is stated.So, the ratio of the cost of magazine A: the cost of magazine B:
Magazine A
3672108Magazine B
326496Then, magazine A:Magazine B -
36:32 = 36/32 = 9/8 = 9:872:64 = 72/64 = 9/8 = 9:8108:96 = 108/96 = 9/8 = 9:8Therefore, we can conclude that the ratio of the cost of magazine A to the cost of magazine B is (C) 9:8.
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8. Marcy is a real estate agent. She sold a house for $356,700. Her commission from that sale was $12,484.50. What is her commission rate?
Answers
Marcy is a real estate agent. She sold a house for $356,700. Her commission from that sale was $12,484.50. What is her commission rate?
we have that
$356,700 represent 100%
so
applying proportion
Find out how much percentage represent $12,484.50
100/356,700=x/12,484.50
solve for x
x=(100/356,700)*12,484.50
x=3.5%
therefore
the answer is 3.5%what is 6 feet 4 inches in decimal form
Answers
Answer:
6.333
Step-by-step explanation:
put this equation into slope intercept form
3x-2y=4
Answers
Answer:
I got you!
The slope graph and answer are set below!
Step-by-step explanation:
(-1,0), (1,6) Find slope intercept form if the y-intercept is (0,3)
Answers
We have two points that will help us to find the slope (m)
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where
(-1,0)=(x1,y1)
(1,6)=(x2,y2)
then we substitute the values
[tex]m=\frac{6-0}{1+1}=\frac{6}{2}=3[/tex]If the y intercept is (0,3)
the slope-intercept form is
[tex]y=mx+b[/tex]where
m=slope=3
b=y-intercept= 3
[tex]y=3x+3[/tex]
help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeeee
thank you
Answers
Based on the graph of the function shown, we can logically deduce the following information:
A. The domain can be best described using interval notation. The domain is (-∞, ∞).
B. The range can be best described using the roster method. The range is {y | y = -∞, -3}.
How to identify the domain and range of this graph?The horizontal extent of a graph represents all domain values and they are also read and written from smaller to larger numerical values, and from the left of the graph to the right.
Similarly, the vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph of the continuous function shown above, we can reasonably infer and logically deduce the following information:
The domain is equal to (-∞, ∞).The range is equal to {y | y = -∞, -3}.Read more on range here: brainly.com/question/17003159
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Solve the inequality for X
2x ≥ 2(4x + 7) + 4
Show each step of the solution.
Answers
2x greater than equal to 8x + 14 + 4
2x greater than equal to 8x + 18
2x - 8x greater than equal to 18
-6x greater than equal to 18
x less than equal to -18/6
x less than equal to -3
What do ALL these quadrilaterals have in common?
Answers
Answer:
Explanation:
prepedicualr sides look
Mrs. Martinez has $33.00 to spend on name tags. The material for each name tag
costs $0.44. Mrs. Martinez can buy
name tags with $33.00
A 0.013
B 1457
C
75
D 750
Answers
⚠ If you are in a rush, only read the bold.
To find how many items someone can buy with a set amount of money, divide the set amount of money that they have (in this case 33) by the cost of each item (in this case 0.44).
If you liked this answer, please rate it 4-5 stars and thank me! If you didn't like it, please rate it 1-3 stars and write what I did wrong in the comments. Thanks!
Question 7 10 pt The figure on the left is reflected over the vertical line to form the image on the right. What happens to the angle and side measurements after a reflection? 2 2.2 143° 3.2 1089 639 Edit I
Answers
The reflection on the left (known as the pre-image) has dimensions clearly given, while the shape on the right (known as the image) has no dimensions given but, a careful observation shows that the scale factor is the same, that is, 1 : 1.
This means the sides and angles do not change value(s). The image simply lies in a different location, that is, a different quadrant. The shape, the size and the orientation has not changed which means the dimensions in the image is the same as the pre-image.
A scientist has discovered a new strain of bacteria. The bacteria grows exponentially at a rate of 68% each hour as shown in the table below. Identify the equation used to calculate the growth, and estimate the population of the bacteria when the time has reached 10 hours
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
A scientist has discovered a new strain of bacteria.
The bacteria grows exponentially at a rate of 68% each hour as shown in the table below.
Identify the equation used to calculate the growth, and estimate the population of the bacteria when the time has reached 10 hours.
Step 2:
The details of the solution are as follows:
Since the bacteria grows exponentially at a rate of 68% each hour, and the initial population is 1. 2 billiion.
This means that:
[tex]f(x)\text{ = 1. 2 \lparen 1 + }\frac{68}{100})\text{ }^x[/tex][tex]\begin{gathered} f(x)\text{ = 1. 2 \lparen1 + 0. 68 \rparen}^x \\ This\text{ gives us:} \\ f(x)\text{ = 1. 2 \lparen1. 68 \rparen}^x \end{gathered}[/tex][tex]\begin{gathered} \text{when x = 10 hours, we have that:} \\ f(x)\text{ = 1. 2 \lparen1.68\rparen}^{10\text{ }}=\text{ 214.9186299 }\approx\text{ 214. 92 billion} \\ \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]f(x)\text{ = 1. 2 \lparen1.68 \rparen}^{x\text{ }};\text{ 214. 92 billion \lparen OPTION D \rparen}[/tex]
