Answers
Step-by-step explanation:
use Pythagoras theorem,
\( {a}^{2} + {b}^{2} = {c}^{2} \)
\({6}^{2} + {8}^{2} = {c}^{2} \\ 36 + 64 = {c}^{2} \\ c = \sqrt{100 } \\ c = 10\)
Answer:
The length of missing side of triangle is 10 m.
Step-by-step explanation:
Solution :Here, we have given that the two sides of triangle are 6 m and 8 m.
Finding the third side of triangle by pythagorean theorem formula :
\({\longrightarrow{\pmb{\sf{{(c)}^{2} = {(a)}^{2} + {(b)}^{2}}}}}\)
\(\pink\star\) a = 6 m\(\pink\star\) b = 8 m\(\pink\star\) c = ?Substituting all the given values in the formula to find the third side of triangle :
\(\begin{gathered} \qquad{\longrightarrow{\sf{{(c)}^{2} = {(a)}^{2} + {(b)}^{2}}}}\\\\\qquad{\longrightarrow{\sf{{(c)}^{2} = {(6)}^{2} + {(8)}^{2}}}}\\\\\qquad{\longrightarrow{\sf{{(c)}^{2} = (6 \times 6)+ (8 \times 8)}}}\\\\\qquad{\longrightarrow{\sf{{(c)}^{2} = (36)+ (64)}}}\\\\\qquad{\longrightarrow{\sf{{(c)}^{2} = 36 + 64}}}\\\\\qquad{\longrightarrow{\sf{{(c)}^{2} =100}}}\\\\\qquad{\longrightarrow{\sf{c = \sqrt{100}}}}\\\\\qquad{\longrightarrow{\sf{c = 10 \: m}}}\\\\\qquad\star{\underline{\boxed{\sf{\red{c = 10 \: m}}}}}\end{gathered}\)
Hence, the length of missing side of triangle is 10 m.
\(\rule{300}{2.5}\)
Related Questions
the x y coordinate plane is given. the curve begins at (0, 5) goes down and right becoming less steep, changes direction at (1, 2) goes up and right becoming more steep, goes through the approximate point (2, 3.1), goes up and right becoming less steep, changes directions at (3, 4), goes down and right becoming more steep, sharply changes direction at (4, 1), goes up and right becoming less steep passing through the approximate point (5, 4.2) and ends at (6, 6).
Answers
a)Function is increasing in intervals (1,3) and (4,6).
b)Function is decreasing in intervals (0,1) and (3,4).
c)Graph is concave upward in the interval (0,2) and (3,5).
d)Graph is concave downward in the interval (3,4).
e)Points of inflection are x=3 and x=5.
Now, According to the question:
Let us make the graph of the given function. In the graph, We have connected points linearly, please consider it as a curve.
What is the point of inflection?
The point of inflection or inflection point is a point in which the concavity of the function changes.
Therefore, From the attached graph, we can see that:
a)Function is increasing in intervals (1,3) and (4,6).
b)Function is decreasing in intervals (0,1) and (3,4).
c)Graph is concave upward in the interval (0,2) and (3,5).
d)Graph is concave downward in the interval (3,4).
e)Points of inflection are x=3 and x=5.
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The complete question is this:
The x y coordinate plane is given. The curve begins at (0, 5) goes down and right becoming less steep, changes direction at (1, 2) goes up and right becoming more steep, goes through the approximate point (2, 3.1), goes up and right becoming less steep, changes directions at (3, 4), goes down and right becoming more steep, sharply changes direction at (4, 1), goes up and right becoming less steep passing through the approximate point (5, 4.2) and ends at (6, 6).
(a) Find the interval(s) on which f is increasing. (Enter your answer using interval notation.)
(b) Find the interval(s) on which f is decreasing. (Enter your answer using interval notation.)
(c) Find the open interval(s) on which f is concave upward. (Enter your answer using interval notation.)
(d) Find the interval(s) on which f is concave downward. (Enter your answer using interval notation.)
(e) Find the coordinates of the point(s) of inflection.
(x, y) = ( )
Given the two functions, which statement is true? f(x) = 3x, g(x) = 3x + 5 Question 12 options: g(x) is translated up 5 units compared to f(x) g(x) is translated left 5 units compared to f(x) g(x) is translated down 5 units compared to f(x) g(x) is translated right 5 units compared to f(x)
Answers
The correct statement is: g(x) is translated up 5 units compared to f(x).
The correct answer is A.
To determine the translation between the two functions, we can observe that the only difference between them is the constant term.In f(x) = 3x, there is no constant term, so the graph of f(x) passes through the origin (0, 0).In g(x) = 3x + 5, there is a constant term of 5 added to the function. This means that the graph of g(x) is shifted vertically upward by 5 units compared to the graph of f(x).Therefore, g(x) is translated up 5 units compared to f(x).The correct answer is A.
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Make a frequency table using five classes.
class 31-38 39-46 47-54 55-62 63-70
f
11
24
15
7
3
Then estimate the mean and sample standard deviation using the frequency table. (Round s to two decimal places.)
Answers
Answer: C
Step-by-step explanation:
Explain how to use the unit-factor method to convert 120 pounds to kilograms.
Answers
Answer:
Step-by-step explanation:
lets remember that 1kg=2.2 lb
if
2.2 lbs................................1 kg
120lbs...................................? kg
120/2.2=54.54 kg
name the quadrilateral with 2 pairs of consecutive congruent sides with diagonals that meet at a right angle
Answers
The quadrilateral you're describing is a Kite. A kite is a quadrilateral with two pairs of consecutive congruent sides, and its diagonals meet at a right angle.
2 more than n is the quotient of n and 6
Answers
Answer:
6n+2
Step-by-step explanation:
6. Solve for x. Round to the nearest hundredth if necessary.
34.28
10.53
21.72
39.19
Answers
The value of x was found to be 34.28.
What is Trigonometric Functions?
Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.
Given the base of the triangle is x
The perpendicular = 19
So we can write tan(29°) = 19 / x
x = 19 / tan(29°)
x = 19/0.55
x=34.28
Hence the value of x was found to be 34.28.
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Answer:
34.28
Step-by-step explanation:
The value of x was found to be 34.28.
What is Trigonometric Functions?
Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.
Given the base of the triangle is x
The perpendicular = 19
So we can write tan(29°) = 19 / x
x = 19 / tan(29°)
x = 19/0.55
x=34.28
Hence the value of x was found to be 34.28.
Torah says he made to the development of Judaism.
Jewish Leader Action as Leader Contribution to Judaism
Abraham Start typing here..
Moses
David
Solomon
Answers
The development made to the Judaism is mentioned below;
Action as Leader;
Abraham;
Abraham's care for others is one of his leadership strengths. Abraham expressed his sorrow for Sodom and Gomorrah when the Lord informed him that they would be destroyed. He "stick his neck out for his people," as one who cares for others. He pleaded with God on their behalf.
Moses;
Early on, Moses realized he didn't have to handle everything by himself. He eventually succeeded as a leader by using delegation.
David;
As a man of God, David had learned to wait on the Lord, but he also had to learn how to be patient with those around him.
Solomon;
His name in Hebrew means peace and he used his wisdom to bring about peace in the world through deeds rather than conquest.
Contribution to Judaism
Abraham;
Before Abraham, people believed in multiple gods; Abraham was the first to preach that there is only one God. Ironically, Terach, Abraham's father, had made a fortune by selling idols of several deities.
Moses;
The Jews were delivered from slavery in Egypt by Moses, who also guided them to the Holy Land that God had promised.
David;
Many of the Old Testament Psalms are attributed to him; they were probably penned on his renowned lyre, upon which he was reputed to be a master.
Solomon;
As the Israelite monarch who constructed the first Temple in Jerusalem, Solomon is well-known. He was also the second and final king of a united Israel, which was at the height of its power during his rule (after his father, David).
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Find the unit rate (constant of proportionality) of the distance traveled.
Number of hours
0.25 1.5 2.5 3
Distance traveled (km) 3 18 30 36
Answers
Answer:
12.
Step-by-step explanation:
if to re-write the given condition, then
\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)
it is clear, the required constant is 12 (12 per hour).
What is this shape called
Answers
Answer:
curved ramp
or quadrant circle map
Step-by-step explanation:
Answer:
polygon
Step-by-step explanation:
The shape has 4 sides. It could be something like a hemisphere.
4x(x + 1) − (3x − 8)(x + 4)
Answers
The simplified form of the expression 4x(x + 1) − (3x − 8)(x + 4) is -3x^2 - 4x - 32.
To simplify the expression 4x(x + 1) − (3x − 8)(x + 4), we can expand the parentheses and combine like terms.
Expanding the first term, we get 4x^2 + 4x.
Expanding the second term, we have -(3x)(x) - (3x)(4) - (-8)(x) - (-8)(4), which simplifies to -3x^2 - 12x - (-8x) - (-32), further simplifying to -3x^2 - 12x + 8x - 32.
Combining like terms, we obtain -3x^2 - 4x - 32.
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IS 2x+3y=1 and y = 2x+3 parallel or perpendicular
Answers
======================================================
Explanation:
Solve the first equation for y
2x+3y = 1
3y = -2x+1
y = (-2x+1)/3
y = (-2/3)x + 1/3
The last equation shown above is in y = mx+b form
m = -2/3 = slope
b = 1/3 = y intercept
We see that the slope of y = 2x+3 is m = 2.
Since the two slopes (-2/3 and 2) are different, this means the lines aren't parallel. They aren't perpendicular either because the slopes don't multiply to -1.
Find the measure of the indicated angle.
99⁰
96⁰
98⁰
92°
L
120°
K
N
M
64
Answers
Answer:
? = 92°
Step-by-step explanation:
the chord- chord angle ? is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, that is
? = \(\frac{1}{2}\) (LM + AK) = \(\frac{1}{2}\) (120 + 64)° = \(\frac{1}{2}\) × 184° = 92°
A farmer wants to increase the area of his rectangular pen but keep the pen a rectangular shape He decides to add 1.3 meters of
fencing to the width of the pen but the length will remain 10.4 meters. The new area will be 81.12 square meters
Which equation can be used to determine the original width, w of the pen?
Answers
Answer:
81.12 square meters
Step-by-step explanation:
Using the equation for the area of a rectangle, the original width w of the pen is determined by 10.4(w + 1.3) = 81.12
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
Given that farmer wants to increase the area of his rectangular pen but keep the pen a rectangular shape then he decides to add 1.3 meters of
fencing to the width of the pen but the length will remain 10.4 meters.
Length = 10.4 meters.
Width w = (w + 1.3)
The new area of rectangle = 81.12 square meters
Then: Using the equation for the area of a rectangle, the original width w of the pen is determined by 10.4(w + 1.3) = 81.12
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Four years ago, you invested $1000 in an account that returns 5.1% annually. The table shows the value of your investment
at the end of each year.
Time (in years)
1
2
Value (in dollars)
$1051.00
$1104.60
$1160.94
$1220.14
3
4
Does the data represent a linear function? Why or why not?
a. Yes, it appears on a straight line.
C. Yes, the average rate of change is constant.
b. No, it does not appear on a straight line.
d. There is not enough information to determine
whether this is a linear function,
Please coloct the boot
Answers
Answer:
It B
Step-by-step explanation:
The data provided in the table does not represent a linear pattern option (b) No, it does not appear on a straight line correct.
What is the rate of change?It is defined as the change in values of a dependent variable with respect to the independent variables.
It is given that:
Four years ago, you invested $1000 in an account that returns 5.1% annually.
The table represents the value of your investment at the end of each year.
Time (in years) Value (in dollars)
1 $1051.00
2 $1104.60
3 $1160.94
4 $1220.14
Plot the point (x, y) on the coordinate plane:
From the graph, as we can see (1, $1051.00) does not lie on the line.
Thus, the data provided in the table does not represent a linear pattern option (b) No, it does not appear on a straight line correct.
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Which expression is equivalent to ? Assume
Answers
[(2x³y⁴)² × 2x]½
(2x³y⁴)½ ×(2x)½
2x³y⁴(2x)½
Solve for b
10, b, 150degrees, 12degrees
Answers
Hello!
We have all angles of the triangle:
We will use the law of cosines. This relation is valid for all sides of any t
We have:
angle A = 12°
côté a = 10
angle B = 150°
This is therefore the first case of application of the sine law.
So:
\(\sf \dfrac{b}{sin~B} = \dfrac{a}{sin~A}\)
\(\sf b =\dfrac{sin~B~*~a}{sin~A} = \dfrac{sin~150~*~10cm}{sin~12} = \dfrac{arcsin~0.5~*~10cm}{arcsin~0.2079116908} = \dfrac{30~*~10cm}{12} = \dfrac{300cm}{12} = \boxed{\sf25cm}\)
b = 25cm
How can I solve this math problem within 5 minutes
Answers
The equation a² + b² = c² represents the Pythagorean theorem.
What is the Pythagorean theorem?This is a theorem that states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
The Pythagorean theorem is used to find the length of one of the sides of a right-angled triangle when the lengths of the other two sides are known.
To solve the problem, you need to have at least two side lengths given. Then, you can use the equation to find the length of the third side. For example:
If you know the lengths of sides a and b and need to find the length of the hypotenuse (c):
Plug in the known values for a and b into the equation and solve for c.
Example: If a = 3 and b = 4, then 3² + 4² = c², which gives 9 + 16 = c², so c² = 25, and c = sqrt(25) = 5.
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You can use these steps to work out the amount of income tax you pay each month.
Work out
monthly salary - 987.5
Work out
answer to Step 1 +5
Step 1
Step 2
Cho has a salary of £24 000 per year.
Helen has a salary of £1720 per month.
How much more income tax does Cho pay than Helen each month?
Answers
The amount more in income tax that Cho pays than Helen each month would be £56.
How to find the income tax ?First, find Helen's yearly salary :
= 1, 720 x 12
= £ 20, 640
Both Cho's and Helen's annual salaries fall within the Basic rate tax bracket.
Cho 's monthly tax would be:
= (( 24, 000 - 12, 570 ) x 20 % ) / 12
= £ 190. 50
Helen's monthly tax :
= (( 20, 640 - 12, 570 ) x 20 % ) / 12
= £ 134.50
The difference is therefore :
= 190. 50 - 134.50
= £56
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Dividing by 5 is the same thing as multiplying by
Answers
Answer: 1/5
Step-by-step explanation:
Multiplying by a number is the same thing as dividing by its multiplicative inverse (1/x), and same goes both ways
Answer:
Assuming you meant to write "divided by 1/5" rather than just "divided by," then yes. Explanation: Multiplying by a number is the same
the moon is about 1.2x 10^9 killometers from earth.what is the distance in standerd form
Answers
Answer:
1 200 000 000
Step-by-step explanation:
this is the answer
A small deck of twenty cards consists of eight red cards and twelve green cards. Draw five cards at random, without replacement. How many five-card selections are possible?
Answers
At random selection, there are 4, five-card selections possible.
What is Random selection?Random selection describes how the sample is drawn from the entire population, whereas random assignment describes how the participants are then assigned to either the experimental or control groups. In an experiment, both random selection and random assignment are possible.Since there are only 20 cards in the deck so there are 4 sections of 5 cards each is possible as 4 × 5 = 20.
Therefore, there are 4, five-card selections possible.
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A football stadium holds 5000 people.
On a match day z of the stadium is full.
40% of the children are girls.
The ratio of adults to children is 2:3
How many of the children attending are boys?
Can someone plz help me with this
Answers
Answer:
1000 children
Step-by-step explanation:
Find the total units of adults and children = 2 + 3 = 5
5 units = 5000
1 unit = 5000 ÷ 5 = 1000
100% ÷ 5 units = 20% each unit
3 units = 20% x 3 = 60%
Since we all know that 60% of the people are children and 40% of the children are girls...
60 - 40 = 20%
20% = 1000
Archaeology: Tree Rings. At Burnt Mesa Pueblo, the method of tree-ring dating gave the following years A.D. for an archaeological excavation site: 1189, 1271, 1267, 1272, 1268, 1316, 1275, 1317, 1275. Find a 90% confidence interval for the mean of all tree ring dates from this archeological site.
Answers
After answering the presented question, standard deviation t Lower bound = X - \((t * (s/\sqrt(n))) = 1271.89 - (1.860 * (34.753/\sqrt(9))) = 1238.94\)
What is standard deviation?A statistic that expresses the variability or variation of a bunch of values is the standard deviation. A high standard deviation indicates that the values are more distributed, whereas a low standard deviation indicates that the numbers are closer to the set mean. The standard deviation is a measure of how far the data are from the mean (or ). When the standard deviation is small, the data tends to cluster around the mean; when it is great, the data is more spread. The standard deviation represents the average variability of the data collection. It displays the average deviation from the mean of each score.
Next, we need to find the t-value for a 90% confidence interval with 8 degrees of freedom (n-1):
t = t(0.05, 8) = 1.860
Now we can calculate the lower and upper bounds of the confidence interval:
Lower bound = X - \((t * (s/\sqrt(n))) = 1271.89 - (1.860 * (34.753/\sqrt(9))) = 1238.94\)
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Solve the following equation in two different ways. Explain what you did differently.
5(x + 2) = 45
5(x + 2) = 45
Answers
The following equations can be solved in two different ways
On solving the equation we get the value as \(x=7\)
What is an equation?
An equation is a formula that represents the equality between two expressions.
Method 1) : We are given an equation
\(5(x+2)=45\)
Divide both sides by 5, we get
\(x+2=9\)
Subtracting 2 from both sides we get,
\(x=7\)
Method 2)
We are given an equation
\(5(x+2)=45\)
On simplifying the equation we get
\(5x+10=45\)
Subtracting 10 from both sides
\(5x=35\)
Dividing both sides by 5 we get
\(x=7\)
In the first method we first perform division then subtraction and in the second method we simplify the right side of the equation then subtract 10 and finally divide by 5.
Hence We solve the equation by 2 ways And in both cases we get the answer as 7
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Solve for x round to the nearest tenth of a degree if necessary. HURRYYYY TY
Answers
The value of x is 58.51 degree.
We have,
Perpendicular= 8
Base = 4.9
Using trigonometry
tan x = Perpendicular/ Base
tan x = 8/4.9
tan x= 1.63265306122449
x = 58.51253064
Thus, the value of x is 58.51 degree.
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1+1/6 in simplest form
Answers
Answer:
1 1/6
Step-by-step explanation:
1 is nothing but 6/6
So then you would have 6/6+1/6
then you would do 6+1=7
And keep denominator same
So you have 7/6
Which is the same 1 1/6
Because 6 goes one time into 7/6
But you still have 1/6 left
Company A offers him 16% commission on all sales. Company B pays a basic salary
of R6 000,00 and a further 10% commission on all sales. He is paid at the end of the
month.
2.
In order for Sdumo to be able to make a decision of which offer to take, he uses a
table to determine his possible income per month.
Use the information above to answer the questions that follow.
Name the dependent and the independent variables.
Write down the formula for the total income from company A, hence use the
formula to complete TABLE 1.
TABLE 1: COMPANY A
25 000
Total
sales (R)
Total
income(R)
0
0
4 000
55 000 65 000
8 800
A
75 000
12 000
B
16 000
125 000
20 000
(3)
(7)
Answers
a) In this scenario, the dependent variable is the total income from Company A while the independent variable is the total sales.
b) The completion of Table 1 for Company A showing the total sales and total income is as follows:
TABLE 1: COMPANY A
Total Total
Sales (R) Income(R)
$25,000 $4,000
$55,000 $8,800
$65,000 $10,400
$75,000 $12,000
$125,000 $20,000.
What are dependent and independent variables?A dependent variable is a value obtained through the manipulation of the independent variable.
On the other hand, an independent variable is a changeable or controllable variable that influences the dependent variable, causing it to change after manipulation.
TABLE 1: COMPANY A
Total Total
Sales (R) Income(R)
$25,000 $4,000 ($25,000 x 16%)
$55,000 $8,800 ($55,000 x 16%)
$65,000 $10,400 ($65,000 x 16%)
$75,000 $12,000 ($75,000 x 16%)
$125,000 $20,000 ($125,000 x 16%)
TABLE 1: COMPANY B
Total Total
Sales (R) Income(R)
$25,000 $8,500 ($6,000 + $25,000 x 10%)
$55,000 $11,500 ($6,000 + $55,000 x 10%)
$65,000 $12,500 ($6,000 + $65,000 x 10%)
$75,000 $13,500 ($6,000 + $75,000 x 10%)
$125,000 $18,500 ($6,000 + $125,000 x 10%)
Company A:
Commission on all sales = 16%
Company B:
Basic salary = R6,000.00
Commission on all sales = 10%
Thus, when higher sales are recorded (for example, above $120,000), it pays better with Company A's offer than Company B's.
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HELP!!!!
Which statements about opposites are true? Select each correct answer. Responses The opposite of a negative number is always a positive number. The opposite of a negative number is always a positive number. The opposite of zero is zero. The opposite of zero is zero. A number and its opposite are located the same distance from zero on a number line. A number and its opposite are located the same distance from zero on a number line. The product of a number and its opposite is always 1.
Answers
The statements about opposites that are true include will be;
The opposite of a negative number is always a positive number.
A number and its opposite are situated at the same distance from zero on a number line.
The opposite of zero is; zero.
What is a number line?Integers are arranged at equal intervals along horizontal straight lines called number lines. A number line can be used to represent every number in a series. The endpoints of this line go on forever. Some will have a defined beginning and end. It refers to those as closed number lines.
Since the "opposite" of a number is that number with its sign changed.
Remember that the opposite of a negative number is always a positive number. This is referred to as an additive inverse.
For example 2 - (-2) = +4.
The statements about opposites that are true include will be;
The opposite of a negative number is always a positive number.
A number and its opposite are situated at the same distance from zero on a number line.
The opposite of zero is; zero.
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The line AB is shown on the grid.
0%
6-
a) Find the gradient of a line
perpendicular to AB.
5-
3-
b) Find the equation of the line
perpendicular to AB and passing
through the midpoint of AB.
B В
+
Х
-B
LE
0
ab
А
2-
Answers
Answer:
1) The gradient of a line perpendicular to AB.→ [-2}
2) The equation of the line perpendicular to AB and passing
through the midpoint of AB. →[y=-2x+6]
\(---------\)
hope it helps....
have a great day!!
Answer:
-2
Step-by-step explanation:
yep