With the value tanθ = 4/3 on the interval (π, 3π/2), using trigonometric identities sin 2θ = 24/25 , cos 2θ = -7/25 , tan 2θ = -8/7.
First, we'll find sin 2θ:
sin 2θ = 2sinθcosθ
We can use the identity tanθ = sinθ/cosθ to find sinθ and cosθ:
sinθ = 4/5 and cosθ = 3/5
So,
sin 2θ = 2(4/5)(3/5) = 24/25
Next, we'll find cos 2θ:
cos 2θ = cos^2θ - sin^2θ = 1 - 2sin^2θ
Using the values of sinθ and cosθ that we found earlier:
cos 2θ = 1 - 2(4/5)^2 = 1 - 32/25 = -7/25
Finally, we'll find tan 2θ:
tan 2θ = (2tanθ)/(1 - tan^2θ)
Using the value of tanθ that we were given:
tan 2θ = (2(4/3))/(1 - (4/3)^2) = (8/3)/(-7/9) = -8/7
So, the values of sin 2θ, cos 2θ, and tan 2θ are:
sin 2θ = 24/25
cos 2θ = -7/25
tan 2θ = -8/7
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a= (6,7) and b= (1,2) if a-b =(x,y) work out values of x and y
The values of x and y are x = 5 and y = 5.
How to calculate vector sums?The subtraction of vectors a and b can be represented as the vector sum of a and the negative of b:
a - b = a + (-b)
To find the negative of b, simply multiply each component by -1:
-b = (-1) × (1, 2) = (-1, -2)
So,
a - b = a + (-b) = (6, 7) + (-1, -2) = (5, 5)
Therefore, the values of x and y are 5 and 5 respectively.
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1. What number am I?
I have four digits.
My tens and tenths are the same value.
My hundredths is the difference of 5 and 1.
My tens is double my hundredths.
My ones is the other factor of 4 besides 1 and itself.
If the volume of the cylinder is represented by 5x² +
15x + 2 and the height is 5x, which expression
represents the area of the base?
Answer:
its A. x² + 3x + 2/5x because it's the right answer
Cindy is making a paste. For every 1 1/8 cups of water she uses 2 5/8 of flour. How much flour does Cindy need for each cup of flour?
Answer:
0.43 cup of water
Step-by-step explanation:
We know
For every 1 1/8 cups of water, she uses 2 5/8 of flour.
1 1/8 = 9/8 = 1.125
2 5/8 = 21/8 = 2.625
How much water does Cindy need for each cup of flour?
1.125 divided by 2.625 = 0.43 cup of water
So, Cindy needs 0.43 cup of eater for each cup of flour
D(-5, -6), E(5,2), F(4, -4), G(-6, -12) (Distance & Slope Formulas)
The distance between D(-5, -6) and E(5,2) is 12.8, and the slope is 0.8. The distance between E(5,2) and F(4, -4) is 6.08, and the slope is 6. The distance between F(4, -4) and G(-6, -12) is 12.8, and the slope is 0.8.
Distance Formula:
The distance between two points A(x1, y1) and B(x2, y2) is calculated using the following formula:
d = √((x2-x1)² + (y2-y1)²)
Slope Formula:
The slope of the line between two points A(x1, y1) and B(x2, y2) is calculated using the following formula:
m = (y2-y1)/(x2-x1)
Distance between D(-5, -6) and E(5,2):
d = √((5-(-5))² + (2-(-6))²)
d = √((10)² + (8)²)
d = √(100 + 64)
d = √164
d = 12.8
Slope between D(-5, -6) and E(5,2):
m = (2-(-6))/(5-(-5))
m = (8)/(10)
m = 0.8
Distance between E(5,2) and F(4, -4):
d = √((4-5)² + (-4-2)²)
d = √((-1)² + (-6)²)
d = √(1 + 36)
d = √37
d = 6.08
Slope between E(5,2) and F(4, -4):
m = (-4-2)/(4-5)
m = (-6)/(-1)
m = 6
Distance between F(4, -4) and G(-6, -12):
d = √((-6-4)² + (-12-(-4))²)
d = √((-10)² + (-8)²)
d = √(100 + 64) …
d = √164
d = 12.8
Slope between F(4, -4) and G(-6, -12):
m = (-12-(-4))/(-6-4)
m = (-8)/(-10)
m = 0.8
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The slope is 0.8 and the distance between D(-5, -6) and E(5,2) is 12.8.
The slope is 6 and the distance between E(5,2) and F(4, -4) is 6.08.
The slope is 0.8 and the distance between F(4, -4) and G(6, -12) is 12.8.
The formula for Distance:
The following formula is used to determine the distance that separates points A (x1, y1) and B (x2, y2) from one another:
d = √((x2-x1)² + (y2-y1)²)
Slope Method:
The following formula can be used to determine the slope of the line that connects the two points A (x1, y1) and B (x2, y2):
m = (y2-y1)/(x2-x1)
The distance that separates D(-5, -6) from E(5,2):
d = √((5-(-5))² + (2-(-6))²)
d = √((10)² + (8)²)
d = √(100 + 64)
d = √164
d = 12.8
Slope from D(-5, -6) to E(5,2):
m = (2-(-6))/(5-(-5))
m = (8)/(10)
m = 0.8
Between E(5, 2) and F(4, -4):
d = √((4-5)² + (-4-2)²)
d = √((-1)² + (-6)²)
d = √(1 + 36)
d = √37
d = 6.08
Slope between E(5,2) and F(4, -4):
m = (-4-2)/(4-5)
m = (-6)/(-1)
m = 6
Distance between F(4, -4) and G(-6, -12):
d = √((-6-4)² + (-12-(-4))²)
d = √((-10)² + (-8)²)
d = √(100 + 64) …
d = √164
d = 12.8
Slope between F(4, -4) and G(-6, -12):
m = (-12-(-4))/(-6-4)
m = (-8)/(-10)
m = 0.8
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A paperweight, the shape of a hemisphere, fits snugly inside a cylinder-shaped box with a radius of 9 cm. A cone fits snugly inside the paperweight hemisphere.
What is the volume of the cylinder in terms of
? Show all work.
What is the volume of the cone in terms of
? Show all work.
Estimate the volume of the hemisphere in terms of
by calculating the average of the volumes of the cylinder and cone. Show all work.
The volume of the cylinder is 162πx, the volume of the cone (1/3)πx^3 and the volume of the hemisphere is (162πx + (1/3)πx^3)/2
Volume of the cylinder:
The volume of a cylinder can be calculated using the formula V = πr^2h, where r is the radius and h is the height of the cylinder.
In this case, the height of the cylinder is equal to the diameter of the paperweight hemisphere, which is twice the radius of the cone.
Let's call the radius of the cone "x". The diameter of the paperweight hemisphere is equal to 2x, so the height of the cylinder is equal to 2x. The radius of the cylinder is 9 cm, so we can calculate the volume of the cylinder as follows:
V = πr^2h = π * 9^2 * 2x = 162πx
Volume of the cone:
The volume of a cone can be calculated using the formula V = (1/3)πr^2h, where r is the radius and h is the height of the cone. In this case, the height of the cone is equal to the radius of the cone, so we can calculate the volume of the cone as follows:
V = (1/3)πr^2h = (1/3)π * x^2 * x = (1/3)πx^3
Volume of the hemisphere:
The volume of a hemisphere can be calculated using the formula V = (2/3)πr^3, where r is the radius of the hemisphere. To estimate the volume of the hemisphere, we can calculate the average of the volumes of the cylinder and cone.
V_hemisphere = (V_cylinder + V_cone)/2 = (162πx + (1/3)πx^3)/2
This expression represents the estimated volume of the hemisphere in terms of x, the radius of the cone.
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giving 50 points and brainliest to the best correct answer. thanks.
correlation is to as experimentation is to . a. single variables; multiple variables b. unobtrusiveness; correlation c. measurement of variables; manipulation of variables d. manipulation of variables; measurement of variables
Correlation is to "measurement of variables", as experimentation is to "manipulation of variables".
Correlation refers to the statistical relationship between two or more variables, where changes in one variable are related to changes in the other variable(s). It measures the strength and direction of the relationship, but it does not establish cause and effect.
Experimentation, on the other hand, involves the manipulation of variables to determine the cause-and-effect relationship between variables. The experimenter changes the independent variable and measures the effect it has on the dependent variable.
This method allows the experimenter to establish cause and effect and to control extraneous variables that might interfere with the relationship between the independent and dependent variables.
Therefore, the correct answer is D.
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--The given question is incomplete; the complete question is
"Correlation is to___as experimentation is to___.
A. manipulation of variables; measurement of variables
B. unobtrusiveness: correlation
C. single variables; multiple variables
D. measurement of variables; manipulation of variables"--
cuanto es 5^3 - 3 √(375 ÷ 3) + (7 + 2)^2 - 9^11 ÷ 9^9
Consecuencia de 5^3 - 3 √(375 ÷ 3) + (7 + 2)^2 - 9^11 ÷ 9^9 es 91.46.
Sobre el número exponencialPotencias es una operación matemática para la multiplicación repetida de un número tanto como el rango. El rango de un número es un número que se escribe más pequeño y se ubica ligeramente hacia arriba. Basado en la semántica de escribir letras se llama superíndice, por ejemplo: 2², 3², 4³ y otros. En inglés, el exponencial se llama "potencia" o "exponente".
5³=125
3√(375:3) =3√125=3√5³= 3.5^3/2
(7+2) ²=9²=81
9¹¹÷9^9=9²=81
5³ - 3 √(375 ÷ 3) + (7 + 2)² - 9¹¹ ÷ 9^9= 5³-3.5^3/2+81-81 =125-3√125=125-(3(11.18) = 125- 33.54=91.46
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Help me urgentt 16 pointsssss
Answer:
Step-by-step explanation:
Sorry did you already finish?
1. B. 2/3 = 8/12 b/c 2x4 = 8 and 3x4 = 12
2. D. 5/6 = 10/12 b/c 5x2 = 10 and 6x2 = 12
3. 2
4. A. simplified is 2/3 C. self-explanatory D. simplified is 3/4
Please hurry
Choose the best method for solving
and solve. Show your work.
y=x-7
y=x+7
The system of equations has no solution
How to determine the solutionFrom the question, we have the following parameters that can be used in our computation:
y = x - 7
y = x + 7
By substituting the first equation in the second equation
So, we have the following representation
x + 7 = x - 7
Evaluate the like terms
7 = -7
The above equation is false
Hence, the system has no solution
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Fill in the answers on the right
Long's Coffee Shop sells a refill mug for $8. 95. Each refill costs $1. 50. Last month, Jalissa spent $26. 95 on a mug and refills. How many refills did she buy?
constant:
Rate:
Equation:
Solve:
Constant: Mug price = $8.95, Refill price = $1.50, Rate: Refill rate = $1.50, Equation: 8.95 + 1.50x = 26.95, Solve: x = 15 refills. Jalissa purchased 15 refills last month, paying $26.95 for the mug and refills combined.
To calculate the number of refills Jalissa purchased last month, we must first define the constants of the equation. The cost of the mug is $8.95 and the cost of the refill is $1.50. After establishing these constants, we can create an equation using the rate of refills ($1.50) and the total amount that Jalissa spent ($26.95). The equation is 8.95 + 1.50x = 26.95. This equation can then be solved to find the value of x, which is the number of refills Jalissa purchased. To solve the equation, subtract 8.95 from both sides to get 1.50x = 18. This equation can then be divided by 1.50 to find the value of x, which is 15. This means that Jalissa purchased 15 refills last month, paying $26.95 for the mug and refills combined.
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please help!! for 20 points
The solution is given below.
What is transformation?
A transformation is a dramatic change in form or appearance. An important event like getting your driver's license, going to college, or getting married can cause a transformation in your life. A transformation is an extreme, radical change.
here, we have,
the reflection is with respect to y=x line,
so, the transformation will be,
(x,y)⇒(y,x)
so, we get,
X = (-3,8 ) ⇒ X' = (8,-3)
Y(2,5)⇒Y(5,2)
Z(-4,-1)⇒Z'(-1,-4)
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The show johnny want to binge is 61 episodes long, it takes him 5 hours to complete 12 episodes, and 10 hours to complete 24 episodes. If johnny were to watch 12 episodes a day, how many days would it take johnny to finish the show?
Answer:
6 days
Step-by-step explanation:
This is an easy problem if you think about it. Let’s start by identifying unnecessary information. I’ll go ahead and point this out: we don’t need to know how long it takes Johnny to watch the episodes. The question already says he’s only watching 12 episodes per day, so the time information is useless. If you rewrite the problem with only message information, you get something like this:
“The show Johnny wants to binge watch is 61 episodes long. If Johnny were to watch 12 episodes a day, how many days would it take him to finish the show?”
That makes it seem so much easier! Let’s start by dividing the show into sets of 12 episodes. 61 divided by 12 is 5 R1. Since he needs another day to finish the show, even if he only watches one episode, the answer is 6 days.
Here is a pentagon work out the value y.
Answer:
y = 125°
Step-by-step explanation:
the sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 5 , then
sum = 180° × (5 - 2) = 180° × 3 = 540°
sum the interior angles and equate to 540°
y + 86° + 142° + 72° + 115° = 540°
y + 415° = 540° ( subtract 415° from both sides )
y = 125°
Answer:
125°
Step-by-step explanation:
First you find the value of total interior angles
Since it's a Pentagon
[tex](5- 2) \times 180[/tex]
Then you arrive at 540°
When you sum all the angles in the Pentagon together they should be equal to 540
[tex]540 = 86 + 142 + 72 + 115 + y[/tex]
[tex]540 = 415 + y[/tex]
[tex]540 - 415 = y[/tex]
[tex]y = 125[/tex]
Which of these numbers is equivalent to 5.1 ÷ (–2)?
A. -25.5
B. -2.55
C. 2.55
D. 25.5
Answer:
B
Step-by-step explanation:
[tex]1. \: 5.1 \div - 2 \\ 2. \: - 2.55[/tex]
PLEASE ME WITH MY MATH THE QUESTION IS IN THE PICTURE
The discriminant is the expression b2 - 4ac for the quadratic equation ax2 + bx + c = 0. The discriminant's value reveals how many roots f(x) has: - The quadratic function has two unique real roots if b2 - 4ac > 0, otherwise it does not. The quadratic function has one repeating real root if b2 - 4ac = 0.
What are the quadratic equation's roots' sum and product?A quadratic equation's roots are equal to the second term's coefficient negated, divided by the leading coefficient. The constant term (the third term), divided by the leading coefficient, is equivalent to the product of the roots of a quadratic equation.
What is the Product Rule Simplified?According to the Product Rule, the derivative of a product of two functions is equal to the product of the first function times the second function's derivative plus the second function times the first function's derivative.
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The sum of three consecutive natural numbers is 1197, find the numbers.
The three numbers in increasing order are
Answer: 398 + 399 + 400 equals 1197
Step-by-step explanation: The sum of three consecutive natural numbers is 1197, find the numbers X) + (X + 1) + (X + 2) = 1197 To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:X + X + 1 + X + 2 = 11973X + 3 = 11973X + 3 - 3 = 1197 - 33X = 11943X/3 = 1194/3X = 398Which means that the first number is 398, the second number is 398 + 1 and the third number is 398 + 2. Therefore, three consecutive integers that add up to 1197 are 398, 399, and 400.
9. Triangle LMN with vertices L(-7, 4), M(-3, 0),
and N(-8, 1):
(a) Translation: (x,y) → (x + 5, y-6)
(b) Reflection: in the line y=-x
L’
М'
N'
10
The transformation of the vertices of the triangle is a. L' = (-7 + 5, 4 - 6) = (-2, -2), M' = (-3 + 5, 0 - 6) = (2, -6), N' = (-8 + 5, 1 - 6) = (-3, -5). b. L' = (-7, 4) = (-4, 7), M' = (-3, 0) = (0, 3), and N' = (-8, 1) = (-1, 8).
What are transformations?The transformation, or f: X X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation.
The vertices of the triangle are L (-7, 4), M(-3, 0) and N(-8, 1).
a. Translation: (x,y) → (x + 5, y-6) is as follows:
L' = (-7 + 5, 4 - 6) = (-2, -2)
M' = (-3 + 5, 0 - 6) = (2, -6)
N' = (-8 + 5, 1 - 6) = (-3, -5)
b. Reflection in line y = -x is as follows:
Here, the value of y coordinate is negative x coordinate and x coordinate is negative y coordinate.
L' = (-7, 4) = (-4, 7)
M' = (-3, 0) = (0, 3)
N' = (-8, 1) = (-1, 8)
Hence, the transformation of the vertices of the triangle is a. L' = (-7 + 5, 4 - 6) = (-2, -2), M' = (-3 + 5, 0 - 6) = (2, -6), N' = (-8 + 5, 1 - 6) = (-3, -5). b. L' = (-7, 4) = (-4, 7), M' = (-3, 0) = (0, 3), and N' = (-8, 1) = (-1, 8).
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what are the beat numbers
The musical frequency of notes is decreasing between beat number 6 and 7.
What is beat frequency?
Beats refer to the periodic variations in the loudness of a sound resulting from the interference between two waves of slightly different frequencies. When two waves of different frequencies overlap, they create an interference pattern that results in a waveform that varies in amplitude (loudness) over time. The resulting pattern of loud and soft sounds is known as beats.
The musical note frequency is in the given question is measured in Hz and it started decreasing from a frequency of 444 Hz to frequency of 392 Hz.
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A badge is made from a triangle and three-quarters of a circle as shown.
Answer:
3404.9(1dp)
Step-by-step explanation:
2. Use the linear combination method to solve the system of equations. Explain each step of your solution.
2x – 3y = 13
3x + y = -8
To use the linear combination method to solve the system of equations:
2x – 3y = 13
3x + y = -8
We can multiply the second equation by 3 to get:
9x + 3y = -24
Now we can add this equation to the first equation to eliminate the y term:
2x – 3y + 9x + 3y = 13 - 24
Simplifying the left-hand side and the right-hand side of the equation:
11x = -11
Finally, we can solve for x:
x = -1
Substitute x = -1 in either of the original equations:
2x – 3y = 13
2(-1) - 3y = 13
-2 - 3y = 13
-3y = 15
y = -5
Therefore, the solution to the system of equations is x = -1 and y = -5.
Explanation: We used the linear combination method to eliminate one of the variables by adding the two equations together. Then, we solved for the remaining variable and substituted the value back into one of the original equations to solve for the other variable.
Which expressions are equivalent to t(-7.4s+3.8-4.5)-t? Select all that apply.
-7.4st-1.7t
t(-3.6s-4.5)-t
t(3.8s-7.4-4.5)+10.2t
t(-7.4s-0.7)-t
t(7.4s+3.8)-5.5t
The equivalent expressions to t(-7.4s+3.8-4.5)-t are:
-7.4st-1.7tt(-3.6s-4.5)-tt(7.4s+3.8)-5.5tWhat are the equivalent expression?This expression can be simplified as follows:
t(-7.4s + 3.8 - 4.5) - t
= t(-7.4s - 0.7) - t
= -7.4st - 1.7t.
t(-7.4s+3.8-4.5)-t
= t(-3.6s-4.5)-t
-7.4s + 3.8 - 4.5t - t
= t(7.4s+3.8)-5.5t
Therefore the correct options are A, B, E.
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The value in the table below represents Function B, which is a linear function
Function L is represented by the equation y = 6x + 4.
Part A
Answer
X
-3
-1
1
3
By comparing Function B and Function L, which has the greater rate of chan
Show your work.
Part B
Determine which function has the greater y-intercept.
Show your work.
Answer
y
-7
-1
5
11
Part C
Explain why both of your answers above are correct.
Part A: By comparing B and L, L has greater rate of change.
Part B: By comparing B and L, B has greater y-intercept.
This can be solved using the concept of equation of function.
What is functions?Function is a mathematical phrase, rule, or law that establishes the connection between an independent variable and a dependent variable (the dependent variable). A function is described as a relationship between a group of inputs and one output each. In simple terms, a function is a connection between inputs, with each input corresponding to exactly one output. Every function has its own domain and codomain, as well as a range. f(x), where x is the input, is a common way to refer to a function.
Part B:
Let, the equation of function B is,
Y = mx+c
Where m is slope and C is intercept
At (-3,-7)
-7 = -3m+c
C = 3m-7
At (-1,-1)
-1 = -m+3m-7
-1 = 2m -7
2m = 6
m = 3
C = 3m-7
C = 3×3 - 7
C =2
So, equation of line B is
Y = mx+c
Y = 3x+2
Where intercept is 2, note y intercept can also be found by putting x = 0, slope = 3
Part A:
Rate of change is slope for B can also be found by -1-(-7)/-1-(-3)=6/2=3
For equation L.
Y=6x+4
Slope=6, intercept =4
For L: when x=0, y=4,x=1,y=10
Rate of change=slope=(10 - 4)/ (1 - 0)=6
Line Equation Rate of change(slope(m) Y intercept (c)
B y = 3x+2 3 2
L y = 6x- 4 6 - 4
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Anna compra helado y naranjas en la tienda.
• Ella paga un total de $59.53.
• Ella paga un total de $6.49 por el helado.
• Ella compra 8 bolsas de naranjas que cuestan la misma cantidad cada una.
Escribe y resuelve una ecuación que se pueda usar para determinar X, cuánto cuesta
cada bolsa de naranjas.
Ecuación:
Respuesta: X=
Answer:
Ecuación: 59.53 - 6.49 = 53.04
53.04 / 8 = X
X = 6.63
Respuesta: X=6.63
A balloon archway has been ordered for decorating high school gym for a 1950 style prom. The archway will contain 275 balloons each holding 1. 2 liters of helium. Each balloon has a mass of 27 milligrams when empty and all the string and fixings that hold the balloons together total 45 grams. If helium has a density of 0. 1785 grams per liter , what is the mass of the entire archway
We could calculate the weight of individual balloons from given density and empty mass. From that calculate the total weight of balloons and added to the weight of fixings. So the weight of archway becomes 111.33g.
Volume of helium each balloon is holding = 1.2L
Density of helium = 0.1785
Density = mass/volume
Mass = density/volume
So mass of helium in each balloon = 1.2×0.1785 = 0.2142 g = 214.2 mg
Mass of empty balloon = 27 mg
So the total mass of a balloon after filled with helium = 214.2 + 27 = 241.2 mg
Mass of 275 such balloons = Mass of 1 balloon × 275
= 241.2 ×275 = 66330 mg = 66.33 g
Mass of all strings and fixings = 45 g
Total mass of archway = mass of 275 balloons + mass of fixings and strings = 66.33 + 45 = 111.33 g
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chen's pedometer says he walked 5,600 meters today. how many kilometers has chen walked today?
Answer:
5.6km
Step-by-step explanation:
1km = 1000 meters
5,600 meters = 5.6km
5600 divided by 1000 = 5.6km
So, Chen walked 5.6km today.
How does g(x)=8x change over the interval from x=3 to x=5?
The function g(x) = 8x is increasing over the interval from x=3 to x=5.
The graph of the function g(x) = 8x is shown below.
We can observe that the graph of g(x) is a staright line passing through origin (0, 0)
This means that the function g(x) is a linear function.
For x = 3, the value of function would be,
g(3) = 8 × (3)
g(3) = 24
And for input value x = 5, the value of function would be,
g(5) = 8 × (5)
g(5) = 40
This means that the value of function g(x) increases from x = 3 to x = 5
Also, from the graph the function g(x) is increasing over the interval [3, 5]
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In a cookie jar, 1/5 of the cookies are chocolate chip and 1/2 of the rest are peanut butter. what fraction of all the cookies are peanut butter?
Answer: 3/10
Step-by-step explanation: Convert given fractions into like terms. In this case 1/5 becomes 2/10 and 1/2 becomes 5/10. Add them up and you get 7/10. Subtract from the total of 10/10 and the result is 3/10. Since the final fraction can't be simplified, this is the final answer.
Can you guy solve it please
The area of the triangle in the diagram is one square foot.
How to find the area of the triangle?We know that the area of a triangle of base B and height H is given by the formula:
Area = B*H/2
On the diagram we can se that the measure of the base is 3 ft, and the height is 2/3 ft, then the area of that triangle will be:
Area = (3 ft)*(2/3 ft)/2 = 1 ft²
The area of the triangle is one square foot.
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