Answer:
4
Step-by-step explanation:
Since this is a right triangle, and one of the angles measures 60 degrees, we can conclude that the last side measures 30 degrees.
We can see that this is a 30-60-90 degree triangle.
The rules of 30-60-90 degree triangles are that the side opposite the 90 degree angle, or the hypotenuse can be measured with the variable [tex]2a[/tex]. The side opposite the 30 degree angle can be measured with [tex]a[/tex], and the side opposite the 60 degree angle will be measured with [tex]a\sqrt{3}[/tex].
We can see that 8 represents [tex]2a[/tex] because it is the hypotenuse. Since the side marked [tex]x[/tex] is separated by the hypotenuse by an angle of 60 degrees, we note that side marked [tex]x[/tex] is opposite the angle measuring 30 degrees. We note that the side opposite 30 degrees is marked [tex]a[/tex], and since we already know that 8 is equal to [tex]2a[/tex], we realize that the side marked x is equal to [tex]a[/tex], or 4.
The value of x in the triangle is 4.
What is the Pythagorean theorem ?
The square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.
It is given this is a right triangle, and one of the angles measures 60 degrees, we can conclude that the last side measures 30 degrees. By the sum of all the three interior angles of a triangle is 180 degrees
The side opposite the 90 degree angle, or the hypotenuse can be measured with the variable '2a' . The side opposite the 30 degree angle can be measured with 'a' , and the side opposite the 60 degree angle will be measured with 'a√3'.
8 represents '2a' because it is the hypotenuse. Since the side marked x is separated by the hypotenuse by an angle of 60 degrees, we note that side marked x is opposite the angle measuring 30 degrees. We note that the side opposite 30 degrees is marked 'a', and since we already know that 8 is equal to '2a', we realize that the side marked x is equal to
'a' , or 4.
2a=8
a=4
x=a=4
so, the the value of x in the triangle is 4.
Learn more about the Pythagorean theorem here:
https://brainly.com/question/24154260
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A 17 feet ladder is placed against a building. The bottom of the ladder is 15 feet away from the building. How many feet high is the top of the ladder?
7 feet
12 feet
8 feet
15 feet
Answer:
[tex]8 \ feet[/tex]
Step-by-step explanation:
In this situation, one is given the following information. A ladder is leaning against a wall and has a measure of (17) feet. The bottom of the ladder is (15) feet away from the wall. One can infer that the wall forms a right angle with the ground. Thus, the triangle formed between the ground, ladder, and wall is a right triangle. Therefore, one can use the Pythagorean theorem. The Pythagorean theorem states the following,
[tex]a^2+b^2=c^2[/tex]
Where (a) and (b) are the legs or the sides adjacent to the right angle of the right triangle. The parameter (c) represents the hypotenuse or the side opposite the right angle. In this case, the legs are the ground and wall, and the hypotenuse is the ladder. Substitute this into the formula a solve for the height of the wall.
[tex]a^2+b^2=c^2[/tex]
Substitute,
[tex](ground)^2+(wall)^2=(ladder)^2\\\\(15)^2+(wall)^2=(17)^2\\[/tex]
Simplify,
[tex](15)^2+(wall)^2=(17)^2\\\\225+(wall)^2=289[/tex]
Inverse operations,
[tex]225+(wall)^2=289\\\\(wall)^2=64\\\\wall=8[/tex]
class 7th chapter: Simple Equation
The solution of the equation p-1 =20 is -------- *
a) 19
b) 20
c) 21
Answer:
C
Step-by-step explanation:
p=20+1
PLEASE HELP!!!! Choose the best graph that represents the linear equation: 4x + y = 0 Graph A On a coordinate plane, a line goes through (0, 0) and (1, 4). Graph B On a coordinate plane, a line goes through (0, 0) and (1, negative 4). Graph C On a coordinate plane, a line goes through (0, 0) and (4, negative 1). Graph D On a coordinate plane, a line goes through (0, 0) and (4, 1). a. Graph A c. Graph C b. Graph B d. Graph D Please select the best answer from the choices provided A B C D
Answer:
see graph...
B On a coordinate plane, a line goes through (0, 0) and (1, negative 4).
Step-by-step explanation:
Answer:
Step-by-step explanation:
To determine the graph that represents the linear equation 4x + y = 0, we need to rearrange the equation in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
Starting with the given equation:
4x + y = 0
Subtracting 4x from both sides:
y = -4x
Now we have the equation in the form y = mx + b, where m = -4 (the coefficient of x) and b = 0.
Looking at the given graphs:
Graph A: The line goes through (0, 0) and (1, 4). This graph does not represent the equation y = -4x, as the slope is 4, not -4.
Graph B: The line goes through (0, 0) and (1, -4). This graph does represent the equation y = -4x, as it has a slope of -4 and passes through the origin.
Graph C: The line goes through (0, 0) and (4, -1). This graph does not represent the equation y = -4x, as it does not have the correct slope.
Graph D: The line goes through (0, 0) and (4, 1). This graph does not represent the equation y = -4x, as it does not have the correct slope.
Therefore, the best graph that represents the linear equation 4x + y = 0 is:
b. Graph B
Camille bought a set of kitchen chairs discounted 25% off of the original price of $170. What was the dollar amount of discount of the set of chairs?
Answer:
$42.50
Step-by-step explanation:
All you have to do is simply multiply
170 x 0.25=$42.50
write seven million six hundred twenty thousand six hundred fifty in standard form?
Answer:
7,620,650
Step-by-step explanation:
___________
Answer:
7,620,650
Step-by-step explanation:
To write in standard form, you just write the entire number out.
determine lcm and HCF of 24 and 26 using prime factors
Answer:
WHAT IS THE FACTOR?
Step-by-step explanation:
Please help. Solve the triangle. Round ans to the nearest tenth.
9514 1404 393
Answer:
C = 21°a = 13.3c = 5.4Step-by-step explanation:
The third angle can be found from the sum of angles in a triangle.
A + B + C = 180°
C = 180° -62° -97°
C = 21°
__
The remaining side lengths can be found using the Law of Sines.
a/sin(A) = b/sin(B)
a = sin(62°)(15/sin(97°)) ≈ 13.34
Similarly, ...
c/sin(C) = b/sin(B)
c = sin(21°)(15/sin(97°)) ≈ 5.42
The remaining side lengths are approximately ...
a ≈ 13.3
c ≈ 5.4
The number of measles cases increased 26.3% to 321 cases this year. What was the number of cases prior to the increase? Express your answer rounded correctly to the nearest whole number.
Answer:
The right answer is "[tex]x\simeq 254[/tex]".
Step-by-step explanation:
Let the number of earlier case will be "x".
Now,
⇒ [tex]x+x\times \frac{26.3}{100}=321[/tex]
or,
⇒ [tex]x+x\times 0.263=321[/tex]
By taking "x" common, we get
⇒ [tex]x(1+0.263)=321[/tex]
⇒ [tex]x=\frac{321}{1.263}[/tex]
⇒ [tex]=254.15[/tex]
or,
⇒ [tex]x\simeq 254[/tex]
help? haha
solve the equation below:)
3x - 5 = 10 + 2x
Step-by-step explanation:
3x-2x=5+10 [taking variables on one side and constant on other]
x=15
soln:
3x-5= 2x+10
3x -5+5=2x+10+5 [ adding 5 on both side]
3x=2x+15
3x-2x=2x+15-2x [subtracting 2x on both side]
x=15
Ans=15
Answer:
[tex]x = 15[/tex]
Step-by-step explanation:
[tex]3x - 5 = 10 + 2x[/tex]
[tex]3x - 2x = 10 + 5[/tex]
[tex]1x = 15[/tex]
[tex]x = 15[/tex]
Hope it is helpful.....How many students rank themselves as introverts? Demonstrate your work!!
Answer:
36 (maybe...)
Step-by-step explanation:
Technically there is no way to answer this question, it says that 120 ADULTS were surveyed and then asks how many STUDENTS rank themselves as introverts. But if we a supposed to assume that all adults are students:
The ratio of 3:7 means that for every 3 introverts, there are 7 extroverts.
In other words for every 10 people (total introvert+extrovert) there are 3 introverts.
So to find the number of introverts in the group of 120, just multiply by 3/10 or 0.3
The answer would be 36
How many different simple random samples of size 4 from a population size 46
This is one single number. The number is slightly larger than 163 thousand.
====================================================
Explanation:
Consider four slots labeled A,B,C,D
We have....
46 choices for slot A45 choices for slot B44 choices for slot C43 choices for slot DThere's a countdown going on (46,45,44,43) when filling up the slots. This countdown is because we cannot reselect any specific person for multiple slots at the same time.
If order mattered, then we'd have 46*45*44*43 = 3,916,440 permutations possible.
However, order doesn't matter. For any group of 4 people, there are 4! = 4*3*2*1 = 24 ways to arrange them. So we must divide the previous result over 24 to get (3,916,440)/24 = 163,185
This means there are 163,185 different combinations and this is the number of possible samples of size 4 from a population of 46 people. The order of any sample doesn't matter.
Geometry Oddsseseyware
The quadratic function y = -10x2 + 160x - 430 models a store's daily profit (y), in dollars, for selling T-shirts priced at x dollars.
Answer:
shall I have to answer for x pls tell
Answer:
D, B, C, A
Step-by-step explanation:
Nuts Galore sells a trail mix containing dried banana chips, roasted almonds, and chocolate chips that sells for $6.52 per pound. The dried banana chips costs $4 per pound, the roasted almonds cost $8 per pound, and the chocolate chips cost $6 per pound. The amount of roasted almonds used is three times the amount of chocolate chips used. If they plan to make 100 pounds of this trail mix, how many pounds of each ingredient should be used
Answer:
[tex]x = 28[/tex] ----- Banana
[tex]y = 54[/tex] ----- Almonds
[tex]z = 18[/tex] ---- Chocolate
Step-by-step explanation:
Let
[tex]x \to[/tex] banana
[tex]y \to[/tex] almonds
[tex]z \to[/tex] chocolate
So, we have:
[tex]x + y + z = 100[/tex] --- total used
[tex]4x + 8y + 6z = 652[/tex] -- i.e. 6.52 * 100 --- total sales from 100 pounds
[tex]y = 3z[/tex]
Required
The number of pounds of each (i.e. x, y and z)
Substitute [tex]y = 3z[/tex] in [tex]x + y + z = 100[/tex]
[tex]x + 3z + z = 100[/tex]
[tex]x + 4z = 100[/tex]
Make x the subject
[tex]x = 100 - 4z[/tex]
Substitute [tex]y = 3z[/tex] in [tex]4x + 8y + 6z = 652[/tex]
[tex]4x + 8 * 3z + 6z = 652[/tex]
[tex]4x + 24z + 6z = 652[/tex]
[tex]4x + 30z = 652[/tex]
Substitute [tex]x = 100 - 4z[/tex]
[tex]4(100 - 4z) + 30z = 652[/tex]
[tex]400 - 16z + 30z = 652[/tex]
Collect like terms
[tex]- 16z + 30z = 652-400[/tex]
[tex]14z = 252[/tex]
Divide by 14
[tex]z = 18[/tex]
Substitute [tex]z = 18[/tex] in [tex]x = 100 - 4z[/tex]
[tex]x = 100 - 4 * 18[/tex]
[tex]x = 100 - 72[/tex]
[tex]x = 28[/tex]
To calculate y, we have:
[tex]y = 3z[/tex]
[tex]y = 3 * 18[/tex]
[tex]y = 54[/tex]
Write the ratio 4 3/5 to 1 1/5 as a fraction in lowest terms
Answer:
23/6
Step-by-step explanation:
Given fractions
4 3/5 to 1 1/5
Write 4 3/5 as improper fraction= 23/5
Write 1 1/5 as improper fraction= 6/5
Then find the ratio
23/5 : 6/5
Ratio is finding division of two terms
(23/5) / (6/5)
= 23/5 × 5/6
5 at the denominator cancel out 5 at numerator then we have
= 23/6
Hence, fraction in lowest terms here is
23/6
A riverboat travels 52 km downstream in 2 hours. It travels 66 km upstream in 3 hours. Find the speed of the boat and the speed of the stream
The speed of the boat is
and the speed of the stream is
Answer:
The speed of the boat is 24 kilometers per hour, and the speed of the stream is 2 kilometers per hour.
Step-by-step explanation:
Given that a riverboat travels 52 km downstream in 2 hours, and it travels 66 km upstream in 3 hours, the following calculations must be performed to find the speed of the boat and the speed of the stream:
Downstream = 52/2 = 26
Upstream = 66/3 = 22
Stream = 4/2 = 2
Therefore, the speed of the boat is 24 kilometers per hour, and the speed of the stream is 2 kilometers per hour.
The number 55 is attached to a two-digit number to its left and the formed 4-digit number is divisible by 24. What could be the 2-digit number? List all options
the answer will be 44 I think I hoped I helped if not sorry.
Suppose y varies inversely with x, and y = 18 when x = 12. What is the value of x when y = 24? NO LINKS OR ANSWERING YOU DON'T KNOW?
a. 24
b. 9
c. 12
d. 18
Answer:
B. 9
Step-by-step explanation:
We are given that y varies inversely with x. Recall that inverse variation has the form:
[tex]\displaystyle y=\frac{k}{x}[/tex]
Where k is the constant of variation.
We are given that y = 18 when x = 12. Hence:
[tex]\displaystyle (18)=\frac{k}{(12)}[/tex]
Solve for k. Multiply both sides by 12:
[tex]k=12(18)=216[/tex]
Thus, our equation is:
[tex]\displaystyle y=\frac{216}{x}[/tex]
We want to find x when y = 24. Substitute:
[tex]\displaystyle \frac{24}{1}=\frac{216}{x}[/tex]
Cross-multiply:
[tex]24x=216[/tex]
Divide both sides by 24. Hence:
[tex]x=9[/tex]
Our answer is B.
Answer:
B
Step-by-step explanation:
Given that y varies inversely with x then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
To find k use the condition y = 18 when x = 12 , then
18 = [tex]\frac{k}{12}[/tex] ( multiply both sides by 12 )
216 = k
y = [tex]\frac{216}{x}[/tex] ← equation of variation
When y = 24 , then
24 = [tex]\frac{216}{x}[/tex] ( multiply both sides by x )
24x = 216 ( divide both sides by 24 )
x = 9
What is the graph of x=1
Answer:
Slope: Undefined
Step-by-step explanation:
Since x=1
is a vertical line, there is no y-intercept and the slope is undefined.
y-intercept: No y-intercept
Not sure how to do this.
Answer:
-4 ≤ x ≤ -2, 4 ≤ x ≤ 7
Step-by-step explanation:
A function shows the relationship between two or more variables. A function is said to be constant over an interval if its output value is same for every input value within that interval.
As seen in the question, the x variable is the input while the y variable is the output. The function is constant from x = -4 to x = -2. Also, the function is constant within the interval from x = 4 to x = 7. Hence, the interval is:
-4 ≤ x ≤ -2, 4 ≤ x ≤ 7
PLEASE HELP THX<3
Solve for w.
Answer:
- [tex]\frac{26}{15}[/tex]
Step-by-step explanation:
[tex]\frac{1}{5}[/tex] = - [tex]\frac{1}{2}[/tex]w - [tex]\frac{2}{3}[/tex]
multiply equation by a common denominator. Let's use 30.
you get :
6 = -15w - 20
26 = -15w
w = - [tex]\frac{26}{15}[/tex]
Find the mean of 2,2,2,2 and 2
Answer:
2
Step-by-step explanation:
mean = sum of data / no of data
=2+2+2+2+2/5
=10/5
=2
The following is a scatterplot of the percent of children under age 18 who are not in school or in the labor force vs. the number of juvenile violent crime arrests for each of the 50 states. The least-squares regression line has been drawn in on the plot. We would like to predict what the number of juvenile violent crime arrests would be in a state if 25% of children are not in school or in the labor force. This is called
Answer:
Extrapolation
Step-by-step explanation:
From the linear regression plot created in the picture given, se could see that Tha percentage of student covered by the the plot is just above 16%. Therefore, to predict the percentage of the number of juvenile violent crime arrests would be in a state if 25% of children are not in school or in the labor force will require us to assume that the current trend continues into the future. Hence, we use the information and indications we have at present to make prediction into the future based on the assumption that we the current trend will remain relevant and applicable. This assumption into the future based on current trend is called EXTRAPOLATION.
Can someone help me with this question an my other work?
Mathematics puzzle from my calculus text book.
Answer:
[tex]{ \tt{g(x) = a {x}^{2} + bx + c = 0 }} \\ { \tt{f(x) = {a'x}^{2} + b 'x + c' = 0}} \\ { \boxed{ \bf{f(g(x)) = g(f(x))}}} : \\ { \tt{ =( \frac{a}{a'})x {}^{2} + ( \frac{b}{b'}) x} + \frac{c}{c'} } = 0[/tex]
What is the product?
(ay3)2 + 3y - 5)
54% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability
that the number of U.S. adults who have very little confidence in newspapers is (a) exactly five, (b) at least six, and (c)
less than four.
(a) P(5) =
(Round to three decimal places as needed.)
(b) P(x26) =
(Round to three decimal places as needed.)
(c) P(x<4) =
(Round to three decimal places as needed.)
Part B is not clear and the clear one is;
P(X ≥ 6)
Answer:
A) 0.238
B) 0.478
C) 0.114
Step-by-step explanation:
To solve this, we will make use of binomial probability formula;
P(X = x) = nCx × p^(x)•(1 - p) ^(n - x)
A) 54% of U.S. adults have very little confidence in newspapers. Thus;
p = 0.54
10 random adults are selected. Thus;
P(X = 5) = 10C5 × 0.54^(5) × (1 - 0.54)^(10 - 5)
P(X = 5) = 0.238
B) P(X ≥ 6) = P(6) + P(7) + P(8) + P(9) + P(10)
From online binomial probability calculator, we have;
P(X ≥ 6) = 0.2331 + 0.1564 + 0.0688 + 0.01796 + 0.0021 = 0.47836 ≈ 0.478
C) P(x<4) = P(3) + P(2) + P(1) + P(0)
Again with online binomial probability calculations, we have;
P(x<4) = 0.1141 ≈ 0.114
Find the Greatest common factor of 120? Show your work!
Answer:
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60
Step-by-step explanation:
1x120, 2x60, 3x40, 4x30, 5x24, 6x20, 8x15, 10x12, 12x10,15x8, 20x6, 24x5, 30x4, 40x3, 60x2
What is center of a circle whose equation is x2
Answer:
I think it is 160 x2 so you would probably divide 160 by x2 which would 144
Step-by-step explanation:
Two lamps marked 100 W - 110 V and 100 W - 220 V are connected i
series across a 220 V line. What power is consumed in each lamp?
The power consumed in the lamp marked 100W - 110V is 15.68W
The power consumed in the lamp marked 100W - 220V is 62.73W
Step-by-step explanation:
Given:
First lamp rating
Power (P) = 100W
Voltage (V) = 110V
Second lamp rating
Power (P) = 100W
Voltage (V) = 220V
Source
Voltage = 220V
i. Get the resistance of each lamp.
Remember that power (P) of each of the lamps is given by the quotient of the square of their voltage ratings (V) and their resistances (R). i.e
P = [tex]\frac{V^2}{R}[/tex]
Make R subject of the formula
⇒ R = [tex]\frac{V^2}{P}[/tex] ------------------(i)
For first lamp, let the resistance be R₁. Now substitute R = R₁, V = 110V and P = 100W into equation (i)
R₁ = [tex]\frac{110^2}{100}[/tex]
R₁ = 121Ω
For second lamp, let the resistance be R₂. Now substitute R = R₂, V = 220V and P = 100W into equation (i)
R₂ = [tex]\frac{220^2}{100}[/tex]
R₂ = 484Ω
ii. Get the equivalent resistance of the resistances of the lamps.
Since the lamps are connected in series, their equivalent resistance (R) is the sum of their individual resistances. i.e
R = R₁ + R₂
R = 121 + 484
R = 605Ω
iii. Get the current flowing through each of the lamps.
Since the lamps are connected in series, then the same current flows through them. This current (I) is produced by the source voltage (V = 220V) of the line and their equivalent resistance (R = 605Ω). i.e
V = IR [From Ohm's law]
I = [tex]\frac{V}{R}[/tex]
I = [tex]\frac{220}{605}[/tex]
I = 0.36A
iv. Get the power consumed by each lamp.
From Ohm's law, the power consumed is given by;
P = I²R
Where;
I = current flowing through the lamp
R = resistance of the lamp.
For the first lamp, power consumed is given by;
P = I²R [Where I = 0.36 and R = 121Ω]
P = (0.36)² x 121
P = 15.68W
For the second lamp, power consumed is given by;
P = I²R [Where I = 0.36 and R = 484Ω]
P = (0.36)² x 484
P = 62.73W
Therefore;
The power consumed in the lamp marked 100W - 110V is 15.68W
The power consumed in the lamp marked 100W - 220V is 62.73W
