Answer:
27/35
Step-by-step explanation:
(f/g)(5) means f(5)/g(5).
So we will need to find both f(5) and g(5).
f(5) means replace x with 5 in f. This gives us 7+4×5.
Let's simplify 7+4×5:
7+4×5
7+20
27.
g(5) means replace x with 5 in g. This gives us 7×5.
Simplifying 7×5 gives us 35.
(f/g)(5)=f(5)/g(5)=27/35.
The problem refers to triangle ABC. Find the area of the triangle. Round to three significant digits. B = 9° 20', C = 80° 40', b = 2.92 ft
Answer:
Area of the triangle is 25.9 feet²
Step-by-step explanation:
* Lets explain how to solve the problem
- In Δ ABC
∵ m∠ B = 9° 20' = 9 + 20/60 = (28/3)°
∵ b = 2.92 feet
- b is the side opposite to angle B
∵ m∠ C = 80° 40' = 80 + 40/60 = (242/3)°
- Lets find c the side opposite to angle C by sing the sine rule
∵ [tex]\frac{b}{sinB}=\frac{c}{sinC}[/tex]
∴ [tex]\frac{2.92}{sin(28/3)}=\frac{c}{sin(242/3)}[/tex]
- By using cross multiplication
∴ [tex]c=\frac{2.92(sin(242/3)}{sin(28/3)}=17.77[/tex]
- The area of the triangle = 1/2 (b)(c)sin∠A
∵ The sum of the interior angles of a triangle is 180°
∴ m∠ A + m∠ B + m∠ C = 180°
∵ m∠ B = (28/3)°
∵ m∠ C = (242/3)°
∴ m∠ A + 28/3 + 242/3 = 180
∴ m∠ A + 90° = 180° ⇒ subtract 90 from both sides
∴ m∠ A = 90°
∴ Area of the triangle = 1/2 (2.92)(17.77) sin(90)
∵ sin(90) = 1
∴ Area of the triangle = 1/2 (2.92)(17.77) = 25.9 feet²
* Area of the triangle is 25.9 feet²
Rhombus EFHS is shown. What is the measure of HGJ? Help me ASAP
Answer:
Id say 35
Sorry of im wrong :{
Write as an equation: Patrick age increased by 8 years is 18 years
Let P = Patrick's age
P + 8 = 18
The equation is P + 8 = 18
Let P = Patrick's age
What's an equation example?An equation is a mathematical statement this is made up of expressions related with the aid of the same signal. for instance, 3x – five = 16 is an equation. Solving this equation, we get the price of the variable x as x = 7.
A one-step equation is an algebraic equation you may resolve in the most effective one step. You've got solved the equation when you get the variable through itself, and not using numbers in the front of it, on one side of the same signal.
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Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles.
This is a triangle. side a has a length of 9mm. side b has a length of 6 mm. side c has a length of 12 mm. The altitude to side c has a length of X mm.
The height of the triangle is approximately [tex]4.35\text{ mm}[/tex]
Step-by-step explanation:
The area of a triangle can be calculated by using the Heron's formula.
Heron's formula:
Suppose a triangle has sides [tex]a'[/tex], [tex]b'[/tex] and [tex]c'[/tex], then the semi-perimeter [tex]S[/tex] of the triangle is represented by the expression,
[tex]S=\frac{a'+b'+c'}{2}[/tex]
The area [tex]A[/tex] of the traingle is formulated below.
[tex]\fbox {\begin\\A=\sqrt{s(s-a')(s-b')(s-c')}\end{minispace}}[/tex]
To calculate the area of the triangle with sides [tex]9 \text{ mm}[/tex] , [tex]6 \text{ mm}[/tex] and [tex]12 \text{ mm}[/tex], first find the semi-perimeter.
[tex]S=\frac{9+6+12}{2}\\S=\frac{27}{2}\\S=13.5 \text{ mm}[/tex]
Now, the area of the triangle is calculated below.
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}\\A=\sqrt{13.5(13.5-9)(13.5-6)(13.5-12)}\\A=\sqrt{13.5 \times 4.5 \times 7.5 \times 1.5}\\A=\sqrt{\frac{135}{10}\times\frac{45}{10}\times\frac{75}{10}\times\frac{15}{10}} \\A=\sqrt{\frac{(15\times3\times3) \times (15\times3) \times (15\times5) \times15}{100\times100}}\\A=\frac{15\times15\times3\sqrt{15 } }{100} \\A=2.25\times3\times3.87\\A=26.122[/tex]
Area A of a triangle with a altitude P and one side as base B on which the altitude P is drawn, can be calculated as,
[tex]\fbox{\begin\\A= \left[\frac{1}{2}(B)(P)\right]\\\end{minispace}}[/tex]
Now, the area of the same triangle can also be calculated as,
[tex]A=\frac{1}{2}(12)(x)\\A=6x[/tex]
In the above calculations, area of the triangle is calculated in two ways.
Therefore, both the areas can be equated to obtain the altitude [tex]x[/tex].
[tex]6x=26.122\\x=\frac{26.122}{6}\\x=4.35[/tex]
Thus, the height of the triangle is evaluated as [tex]\fbox{4.35 \text{ mm}}[/tex].
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Answer Details
Grade: Junior High School
Subject: Mathematics
Chapter: Area of triangle
Keywords: area of triangle, heron's formula, base multiplied by height, base multiplied by perpendicular, base multiplied by altitude, right triangle, altitude corresponding to base, area of right triangle
Answer:
4.3 mm
Step-by-step explanation:
I got it correct on founders edtell
Enter the correct answer in the box.
Cheryl is taking an online test that gives her instant results. After answering 16 questions, the test revealed that 10 were answered correctly. She
then answered I consecutive questions correctly and achieved her goal of 80% accuracy, Write an equation that can be used to determine how
many questions she answered correctly to reach her goal.
sin cos tan sin costant
na Big
λ μ ρ φ
1-
CSC seccot log log. In
L
.
0.80 =
Reset
Next
Answer:
(L + 10)/(L + 16) = 0.8
Step-by-step explanation:
She needs to answer L more questions to get a grade of 80%.
When she answers L more questions correctly, she will have answered L + 10 questions correctly.
The total number of questions will be L + 16.
L + 10 must be 80% of L + 16
(L + 10)/(L + 16) = 0.8
Cheryl must use the equation 0.80 = (10 + I) / (16 + I) to determine how many consecutive questions she needs to answer correctly to reach her goal of 80% accuracy on her test.
Cheryl has answered 16 questions on her online test with 10 correct responses. To achieve her goal of 80% accuracy, she must determine how many additional questions she must answer correctly in a row.
To find the necessary total number of correct answers (T) for 80% accuracy, we use the equation:
0.80 = (10 + I) / (16 + I)
where I represents the number of consecutive questions Cheryl answered correctly after the initial 16 questions.
Sound travels along a telephone cable at 1.91 * 10^8 ms^-1 .How long does it take Tetsuo's voice to travel from his office phone in Tokyo to his wife's phone 3740m away?
Answer:
1.958 * 10^-5 seconds or 0.00001958 seconds.
Step-by-step explanation:
3740 = 3.74 * 10^3 in scientific notation.
Time = distance / speed.
= 3. 74 * 10^3 / 1.91 * 10^8
= 1.958 * 10^-5 seconds.
It takes Tetsuo's voice approximately 1.96*10^-5 seconds to travel from his office phone in Tokyo to his wife's phone 3740m away using the speed of sound in telephone cables.
Explanation:SolutionTo find the time it takes for sound to travel a certain distance, we can use the formula time = distance / speed. In this case, the speed of sound along the telephone cable is 1.91 * 10^8 ms⁻¹ and the distance is 3740m.
So the time = 3740 / 1.91 * 10^8 = 1.96 * 10^-5 seconds.
Therefore, it takes Tetsuo's voice approximately 1.96*10^-5 seconds to travel from his office phone in Tokyo to his wife's phone 3740m away.
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Express each ratio as a fraction in lowest terms.
1) 3 goals in 6 attempts:
2) 5 quarters out of 15 coins:
Express each rate as a unit rate.
If the answer is in dollars and cents, it must begin with a dollar sign ($).
3) $197 for 4 theater tickets:
(Price per ticket in dollars and cents)
mph (Answer rounded to nearest tenth of a
4) 111.7 miles in 8.4 hours:
mile per hour.)
20 POINTS!!! Please Help
At a space exploration center, astronauts are training on a human centrifuge that has a diameter of 70 feet.
a. The centrifuge makes 72 complete revolutions in 2 minutes. What is the angular velocity of the centrifuge in radians per second? What distance does an astronaut travel around the center each second?
b. Acceleration is the rate of change of velocity with time. An object
moving at a constant velocity v in circular motion with a radius of r 2
has an acceleration a of a = _v_. What is the astronaut’s acceleration? r
(Note that the acceleration will have units of feet per second squared.)
c. One“g”istheaccelerationcausedonEarth’ssurfacebygravity.This acceleration is what gives you your weight. Some roller coasters can produce an acceleration in a tight loop of 5 or even 6 g’s. Earth’s gravity produces an acceleration of 32 ft/s2. How many g’s is the astronaut experiencing in the centrifuge?
The astronaut is experiencing approximately 6.21 g's in the centrifuge.
a. To find the angular velocity of the centrifuge in radians per second, we first need to convert the number of revolutions per minute to revolutions per second. Since there are 60 seconds in a minute, the angular velocity (ω) can be calculated as follows:
Angular velocity (ω) = (Number of revolutions per minute) / 60
Given that the centrifuge makes 72 complete revolutions in 2 minutes:
ω = 72 / 2 / 60 = 1.2 revolutions per second
Next, to find the distance an astronaut travels around the center each second, we can use the formula for the circumference of a circle:
Circumference = π × diameter
Circumference = π × 70 feet
Circumference ≈ 220 feet
Distance traveled each second = Circumference × ω
Distance traveled each second = 220 feet × 1.2 revolutions per second ≈ 264 feet
So, the angular velocity of the centrifuge is approximately 1.2 radians per second, and an astronaut travels around the center approximately 264 feet each second.
b. The acceleration (a) of an object moving in circular motion with a constant velocity (v) and a radius (r) is given by the formula:
[tex]a = v^2 / r[/tex]
Since the astronaut is moving at a constant velocity around the center of the centrifuge, we can use the same formula to find their acceleration. The velocity of the astronaut is the distance traveled each second (264 feet) and the radius of the centrifuge is half of its diameter (70 feet / 2 = 35 feet):
Acceleration (a) = (264 feet per second)^2 / 35 feet ≈ 198.86 feet per second squared
So, the astronaut's acceleration is approximately 198.86 feet per second squared.
c. To find how many g's the astronaut is experiencing in the centrifuge, we need to compare their acceleration with the acceleration due to gravity on Earth (32 feet per second squared). One g is equivalent to the acceleration due to gravity.
Number of g's = Acceleration (astronaut) / Acceleration due to gravity on Earth
Number of g's = 198.86 feet per second squared / 32 feet per second squared ≈ 6.21 g's
So, the astronaut is experiencing approximately 6.21 g's in the centrifuge.
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A cleaner recommends mixing 1 1/2 cup of cleaner for every 12 cups of water. What is the ratio of cleaner to water.
Answer: [tex]\frac{1}{8}[/tex] or [tex]1:8[/tex]
Step-by-step explanation:
First, you can convert the mixed number [tex]1\ \frac{1}{2}[/tex] into a decimal number. To do this, you need to divide the numerator (which is 1) by the denominator (which is 2) of the fraction:
[tex]\frac{1}{2}=0.5[/tex]
Now you must add 0.5 to the whole number part. Then:
[tex]1+0.5=1.5[/tex]
In order to find the ratio of cleaner to water, you must divide 1.5 cups of cleaner by 12 cups of water.
Therefore, the ratio is:
[tex]ratio=\frac{1.5}{12}=\frac{1}{8}[/tex] or [tex]1:8[/tex]
What is the y-intercept of the line perpendicular to the line y = -x + 1 that includes the point (4, 1)?
Answer:
-3
Step-by-step explanation:
If a line is perpendicular to another the product of their slope should equal -1. The slope of the first equation is -1 and -1*1=-1 so the slope of the second equation is 1. That means that the equation looks like y=x+b. We know that when x is 4 y is 1. So plugging in those values you get 1=4+b, subtracting 4 you get -3=b. So the y-intercept is -3
How to do solve this?
4x^2(5x^4 / 2x^2)
Answer:
4x^2(5x^4 / 2x^2)= 10 x^4
Step-by-step explanation:
We want factorize the expression 4x^2(5x^4 / 2x^2)
And to do this, we need to remember key properties of exponents.
Those are:
[tex]x^{m} / x^{n} = x^{m-n}[/tex]
[tex]x^{m} * x^{n} = x^{m+n}[/tex]
So
4x^2(5x^4 / 2x^2)= 4x^2(5/2 x^2)=10 x^4
Lola tossed a coin twice. She made a tree diagram to show the possible outcomes. Which tree diagram shows the sample
Answer:
Its C. XD sorry i just answered this.
Step-by-step explanation:
Hope this helped again! :3
Answer:
Each path in the diagram is a possible outcome with a probability of 1/4. The sum of all paths should equal 1.
The answer is C.
The sum of one third a number and 4 is at the most the sum of twice that number and 12
Answer:
1/3x+4 ≤ 2x+12
Step-by-step explanation:
x ≤ -24/5
Answer:
4 + [tex]\frac{1x}{3}[/tex] ≤ 2x + 12.
Step-by-step explanation:
Given : The sum of one third a number and 4 is at the most the sum of twice that number and 12.
To find : Write expression .
Solution : We have given statement
According to question :
Let the number = x
One third of a number = [tex]\frac{1x}{3}[/tex].
Sum of one third of number and 4 = 4 + [tex]\frac{1x}{3}[/tex].
Twice a number = 2x
Sum of twice that number and 12 = 2x + 12
So, sum of one third a number and 4 is at the most the sum of twice that number and 12.
4 + [tex]\frac{1x}{3}[/tex] ≤ 2x + 12.
greater than equal to sign for at most.
Therefore, 4 + [tex]\frac{1x}{3}[/tex] ≤ 2x + 12.
The domain of a function is
A. The set of all points on the function
B. The set of all first elements of the function
C. The set of all second elements of the function
Answer:
B.the set of all first elements of the function
Step-by-step explanation:
the domain is all the x variables in a function
Answer:
B. The set of all first elements of the function.
Step-by-step explanation:
We have been given a incomplete sentence. We are asked to complete our given sentence.
We know that the domain of a function is all real values of independent variable for which a function is defined and gives exactly one output.
We know that independent variable is x, which is first element of a point, therefore, the domain of a function is the set of all first elements of the function.
Line CD passes through points (0, 2) and (4.6). Which equation represents line CD?
O y=2x-2
O y=28=2
O y=x+2
O y=x-2
Answer:
y = x + 2Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept → (0, b)
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
============================================
We have the points (0, 2) → b = 2 and (4, 6).
Calculate the slope:
[tex]m=\dfrac{6-2}{4-0}=\dfrac{4}{4}=1[/tex]
Substitute the values of the slope and the y-intercept to the equation of a line:
[tex]y=1x+2[/tex]
Answer:
y=x+2
Step-by-step explanation:
The price of a concert ticket was $85.00 two decades ago. A report says that a concert ticket is now 250% of what it was 20 years ago, how much would it cost today? Express answer rounded to the nearest cent.
Answer: $212.5
Step-by-step explanation:
250% = 2.5
So we multiply 85.00 by 2.5
85*2.5=212.5
So it is $212.5
Answer:
your answer is $212.5
Step-by-step explanation:
6. what percent the comes clonefro modelories e
A serving of ice cream contains 5000 calories. 200 calories come from
fat. What percent of the total calories come from fat?
Step-by-step explanation:
200 calories come from fat, out of 5000 calories total. We can find the percentage with a proportion:
200 / 5000 = x / 100
x = 4
4% of the total calories come from fat.
how many triangles are there that satisfy the conditions a=13, b=6, a= 6°
Answer:
1 triangle is possible
Step-by-step explanation:
If there are two sides and a non included angle is given then there could be 0,1 or 2 triangles depend on the measure of the given angle and the lengths of the given sides.
We will discuss some conditions which will clarify that how many triangles are there in the given condition.
CASE 1: If A is obtuse and a>b then there is 1 triangle.
CASE 2: If A is obtuse and a<b then there is 0 triangle.
CASE 3: If A is acute and a>b then there is 1 triangle.
CASE 4: If A is acute and h<a<b then there are 2 triangles possible.
CASE 5: If A is acute and a=h then there is 1 right angle triangle.
CASE 6: If A is acute and a<h then there are 0 triangles possible.
Therefore according to the given condition A= 6° which is acute and a>b, So this condition matches the CASE 3:
According to this there is 1 triangle possible....
Two boats depart from a port located at (–8, 1) in a coordinate system measured in kilometers and travel in a positive x-direction. The first boat follows a path that can be modeled by a quadratic function with a vertex at (1, 10), whereas the second boat follows a path that can be modeled by a quadratic function with a vertex at (0, –7). Which system of equations can be used to determine whether the paths of the boats cross?
Answer:
[tex]\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.[/tex]
Step-by-step explanation:
1st boat:
Parabola equation:
[tex]y=ax^2 +bx+c[/tex]
The x-coordinate of the vertex:
[tex]x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=1\\ \\b=-2a[/tex]
Equation:
[tex]y=ax^2 -2ax+c[/tex]
The y-coordinate of the vertex:
[tex]y_v=a\cdot 1^2-2a\cdot 1+c\Rightarrow a-2a+c=10\\ \\c-a=10[/tex]
Parabola passes through the point (-8,1), so
[tex]1=a\cdot (-8)^2-2a\cdot (-8)+c\\ \\80a+c=1[/tex]
Solve:
[tex]c=10+a\\ \\80a+10+a=1\\ \\81a=-9\\ \\a=-\dfrac{1}{9}\\ \\b=-2a=\dfrac{2}{9}\\ \\c=10-\dfrac{1}{9}=\dfrac{89}{9}[/tex]
Parabola equation:
[tex]y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}[/tex]
2nd boat:
Parabola equation:
[tex]y=ax^2 +bx+c[/tex]
The x-coordinate of the vertex:
[tex]x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=0\\ \\b=0[/tex]
Equation:
[tex]y=ax^2+c[/tex]
The y-coordinate of the vertex:
[tex]y_v=a\cdot 0^2+c\Rightarrow c=-7[/tex]
Parabola passes through the point (-8,1), so
[tex]1=a\cdot (-8)^2-7\\ \\64a-7=1[/tex]
Solve:
[tex]a=-\dfrac{1}{8}\\ \\b=0\\ \\c=-7[/tex]
Parabola equation:
[tex]y=\dfrac{1}{8}x^2 -7[/tex]
System of two equations:
[tex]\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.[/tex]
Use the substitution method to solve the system of equations. Choose the
correct ordered pair.
y = 7x + 8
y = x+ 20
Answer:
(2, 22 )
Step-by-step explanation:
Given the 2 equations
y = 7x + 8 → (1)
y = x + 20 → (2)
Substitute y = 7x + 8 into (2)
7x + 8 = x + 20 ( subtract x from both sides )
6x + 8 = 20 ( subtract 8 from both sides )
6x = 12 ( divide both sides by 6 )
x = 2
Substitute x = 2 in (2) for corresponding value of y
y = x + 20 = 2 + 20 = 22
Solution is (2, 22 )
Answer:
(2,22)
Step-by-step explanation:
A-P-E-X :)
what can you conclude about the survey
I WILL MARK YOU BRAINLIEST
full questions and answer options above
Answer: G.
Step-by-step explanation: When reading the choices F & J will make you say : "Well F is not true because look at the amount of men compared to women. And J, the choice is unbiased doesn't refers to any kind of opinion based reponse so I'll cross 'em off immediatly". The leave you with G & H H is true but it's also opinion based reponse, and G told you that more men are surveyed than women an it's true because look at the sport section! High off top! But still more than women even if the minivans section is little of men but women also so fair and square!
- I'm sorry this is so long. Just comment if you have questions :)
Which expression is equivalent to (x^6y^8)^3\x^2y^2
Answer:
[tex]\large\boxed{\dfrac{(x^6y^8)^3}{x^2y^2}=x^{16}y^{22}}[/tex]
Step-by-step explanation:
[tex]\dfrac{(x^6y^8)^3}{x^2y^2}\qquad\text{use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^{nm}\\\\=\dfrac{(x^6)^3(y^8)^3}{x^2y^2}=\dfrac{x^{(6)(3)}y^{(8)(3)}}{x^2y^2}=\dfrac{x^{18}y^{24}}{x^2y^2}\qquad\text{use}\ \dfrac{a^m}{a^n}=a^{m-n}\\\\=x^{18-2}y^{24-2}=x^{16}y^{22}[/tex]
Answer: [tex]x^{16}\ y^{22}[/tex]
Step-by-step explanation:
The given expression : [tex]\dfrac{(x^6y^8)^3}{x^2y^2}[/tex]
Using identity , [tex](a^m)^n=a^{mn}[/tex] , we have
[tex]{(x^6y^8)^3=x^{6\times3}\ y^{8\times3}\\\\=x^{18}\ y^{24}[/tex]
Now, [tex]\dfrac{(x^6y^8)^3}{x^2y^2}=\dfrac{x^{18}\ y^{24}}{x^2\ y^2}[/tex]
( its also an equivalent expression to given expression.)
Using identity , [tex]\dfrac{a^n}{a^m}=a^{n-m}[/tex] , we have
[tex]\dfrac{x^{18}\ y^{24}}{x^2\ y^2}=x^{18-2}\ y^{24-2}\\\\=x^{16}\ y^{22}[/tex]
Hence, the expression is equivalent to given expression :
[tex]x^{16}\ y^{22}[/tex]
what are all the possible rectangles with whole-number side
lengths that have a perimeter of 10 units.
Answer:
So (L,W) possibilities are:
(1,4),(4,1),(2,3),(3,2)
That makes 4 possibilities.
Step-by-step explanation:
The perimeter of a rectangle is P=2L+2W where L is the length and W is the width.
We have that P=10, so 10=2L+2W.
10=2L+2W
10=2(L+W) By factoring using the distributive property.
2(5)=2(L+W) I factored 10 as 2(5).
If 2(5)=2(L+W), then 5=L+W.
Whole numbers are {0,1,2,3,4,5,6,7,8,9,10,...}. They are your counting numbers and 0.
I think they want natural numbers {1,2,3,4,...}. This is also just called the counting numbers. The reason I think they want this because if one of the dimensions is 0, we won't actually have a rectangle.
So now looking for numbers from this set that satisfy: L+W=5.
L+W=5
1+4=5
4+1=5
2+3=5
3+2=5
So (L,W) possibilities are:
(1,4),(4,1),(2,3),(3,2)
That makes 4 possibilities.
If you have a system of two equations with two unknowns, and the graphs of
the two equations are the same, the system must have.
A. 1 solution
B. No Solution
C.At Least 1 Solution
D. More Than 1 Solution
Answer:
D. More Than 1 Solution
Step-by-step explanation:
Let the system of equations be:
[tex]a_1x+b_1y=c_1...(1)[/tex]
[tex]a_2x+b_2y=c_2...(2)[/tex]
If the graph of equation (1) and (2) are the same, then the two graphs coincide with each other.
What that means is that; the two graphs intersects at infinitely many points.
Therefore the system must have infinitely many solutions.
In other words the system has more than one solution.
NB: At least one solution means exactly one solution and/or more than one solution. But lines that coincide cannot have exactly one solution.
Find the value of 1.85+38*4.1
Answer:
157.65
Step-by-step explanation:
38*4.1=155.8
155.8+1.85=157.65
For this case we must find the value of the following expression:
[tex]1.85 + 38 * 4.1 =[/tex]
According to the PEMDAS algebraic resolution method, multiplications must be made before the addition. So, we have:
[tex]1.85 + 155.8 =[/tex]
Adding we have:
157.65
Answer:
157.65
A wooden pole is 20 m high. A steel wire is tied to the top of the pole and fixed to the ground. If the angle made by the
wire with the ground is 60°, find the length of the steel wire.
Answer:
23.09 meters.
Step-by-step explanation:
Sin(60) = opposite / hypotenuse = pole / steel wire
pole = 20 m
angle = 60 degrees.
sin(60) = 20/ hypotenuse multiply both sides by the hypotenuse
hypotenuse * sin(60) = 20 divide by sin(60)
hypotenuse = 20 / 0.866 do the division
hypotenuse = 23.09
The steel wire = 23.09 meters.
Choose the correct translation for the following statement.
It is at most ten.
x < 10
x ≤ 10
x > 10
x ≥ 10
Answer:
[tex]x\leq10[/tex]
Step-by-step explanation:
we know that
The algebraic expression of the phrase "It is at most ten" is equal to
[tex]x\leq10[/tex]
All real numbers less than or equal to 10 (the number 10 is included)
The solution of this inequality is the interval -----> (-∞,10]
Answer:
B
Step-by-step explanation:
A sink is shaped like a half sphere,as shown in the diagram. Find it’s approximate volume,ignoring the space occupied by the drain
Answer:
Option C. 2508 cubic inches is the correct answer
Step-by-step explanation:
From the figure we can see that, a sink
Points to remember
Volume of hemisphere = (2/3)πr³
Where 'r' is the radius
To find the volume of large hemisphere
Here radius = 13 in
Volume V₁ = (2/3)πr³
= (2/3) * 3.14 * 13³
= 4599.33 cubic inches
To find the volume of small hemisphere
Here radius = 13 - 3 = 10 in
Volume V₂ = (2/3)πr³
= (2/3) * 3.14 * 10³
=2093.33 cubic inches
To find the volume of sink
Volume = V₂ - V₁
= 4599.05 - 2093.33
=2505.72 ≈ 2508 cubic inches
Option C. 2508 cubic inches is the correct answer
Find the measure of the numbered angle.
Select one:
A. 115
B. 125
C. 120
D. 130
Answer:
Option B 125°
Step-by-step explanation:
In this problem we need to calculate the measure of angle ∠6
we know that
The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.
see the attached figure to better understand the problem
∠6=(1/2)[arc AB+arc CD]
(arc AB+arc CD)=360°-(60°+50°)=250°
substitute
∠6=(1/2)[250°]=125°
Solve the system of equations below by graphing both equations with a
pencil and paper. What is the solution?
y=x+5
y=-2x-1