Answer: A
Step-by-step explanation:
Solve the following equation for x, where 0≤x<2π. cos^2 x+4cosx=0
Select the correct answer below:
x=0
x=π/2
x=0 and π
x=π/2,3π/2,5π/2
x=π/2 and 3π/2
The correct answer for equation is x = π/2 and x = 3π/2.
Which values of x satisfy the equation\(cos^2(x) + 4cos(x) = 0?\)To solve the equation \(cos^2(x) + 4cos(x) = 0\), we can factor out cos(x):
cos(x)(cos(x) + 4) = 0
Now we set each factor equal to zero and solve for x:
Setting each factor equal to zero, we find:
cos(x) = 0
x = π/2 and x = 3π/2
cos(x) + 4 = 0
cos(x) = -4 (which is not possible since the range of cosine is -1 to 1)
There are no solutions for this equation.
Therefore, the correct answer is x = π/2 and x = 3π/2. These values satisfy the original equation and fall within the given interval of 0 ≤ x < 2π.
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a rectangle's length is 5cm more than its width, if it has an area of 336 cm squared find the length
The length of the rectangle is 19 cm.
The formula for the area of a rectangle,
Area = Length x Width
Given that the area is 336 cm squared.
So, we can set up an equation,
⇒ 336 = (w + 5)w
where w represents the width of the rectangle.
Expanding this equation,
⇒ 336 = w² + 5w
Moving all terms to one side:
⇒ w² + 5w - 336 = 0
This is a quadratic equation that we can solve using the quadratic formula,
⇒ w = (-5 ± √(5² - 4(1)(-336))) / (2(1))
⇒ w = (-5 ± 23) / 2
We'll take the positive value,
⇒ w = 14
So, the width of the rectangle is 14 cm.
We also know that the length is 5 cm more than the width,
Therefore,
⇒ l = w + 5
⇒ l = 14 + 5
⇒ l = 19
Therefore, the length of the rectangle is 19 cm.
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I need to know the answer to this and how to solve it .
Answer:
b.125 is the answer because look at the 90 degree and the angle bod it is 35° measure it with protector and add 90° of doe and the sum of 90 and 35 is 125°
If f(x) = x³ + 15x² +68x + 84, which of the following is not a factor of f(x)?
○ (x+6)
○ (x + 2)
○ (x + 7)
(x+8)
Submit Answer
what is the expression answer simplyfy2(3x-5y)=
Answer:
is 2×3=6x & 2×-5= -10y
so answer is 6x-10y
Hana runs 3 kilometers in 25 minutes. At the same rate, how many kilometers would she run in 20 minutes?
Answer:
2.4 km.
Let's see the 3 km as metres:
1 km = 1000 m
3 km = ?
1000 × 3 = 3000 m
How many metres is 1 minute:
25 minutes = 3000 m
1 minute = ?
3000 ÷ 25 = 120 m
How many metres is 20 minutes:
1 minute = 120 m
20 minutes = ?
120 × 20 = 2,400 m
Turn it to km:
1000 m = 1 km
2,400 m = ?
2,400 ÷ 1000 = 2.4 km.
The answer is 2.4 km.
four spheres of radius 6cm fit into a cylinder with a height of 12cm. calculate the volume inside the cylinder that is empty. leave your answer in terms of pi.
Answer:
V = 432pi cm^3
Step-by-step explanation:
Pi x r^2 x h
Pi x 6^2 x 12 cm = 432 pi cm^3
How does the graph of the function f(x) = x³ + 1
compare to the parent function f(x) = x³?
A. shifted up 1 unit
B.
shifted down 1 unit
C. shifted left 1 unit
D. shifted right 1 unit
When function f(x) = x^3 + 1 compared to its parent f(x) = x^3, it shifted left by 1 unit.
According to the question, given that
function f(x) = x³ + 1 , compare to the parent function f(x) = x³
when function f(x) = x³ + 1 comparing to the parent function f(x) = x³
then shifted left 1 unit.
graph of the function given below
In mathematics, some graphs are frequently seen. As a result, these initial, widespread functions—which also comprise graphs of quadratic functions, square roots, absolute values, cubic, and cube roots—are referred to as parent graphs.
quadratic function graphing
The utmost power or square to which an unknown number or variable can be raised is known as a quadratic function. The parent graph of all other quadratic functions is the function y=x2 or f(x) = x2, which is a quadratic function.
A parabola is the name for any quadratic function's graph. The fundamental shape of a parabola is uniform.
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I don’t understand this very much pls help
Answer:
Side RP
Step-by-step explanation:
so you see the dashes on the sides that means theyre equal so...
Side LM has one dash and Side RP has one dash so they are corresponding
A movie theater in town posted these prices for tickets and snacks.
A 2-column table with 7 rows. Column 1 is labeled Item with entries adult ticket, child ticket, drink, popcorn, veggie cup, soft pretzel, apple slices. Column 2 is labeled cost (dollars) with entries 9, 6, 1.35, 3.50, 1.74, 2.65, 3.85.
Sally and Anne went to the movies. They each purchased a drink. They also bought one popcorn and one veggie cup to share. Which expression can be used to find how much money each woman spent?
One-half (9 + 1.35 + 3.50 + 1.74)
9 + 1.35 + one-half (3.50 + 1.74)
18 + 2.70 + one-half (3.50 + 1.74)
9+1.35+2(3.50+1.7)
Answer:
9 + 1.35 + one-half (3.50 + 1.74)
Step-by-step explanation:
Sally pay
9 - adult ticket
1.35 - drink
1/2 ( 3.50 popcorn + 1.74 veggie cup)
= 9 + 1.35 + 1/2(3.50 +1.74)
HELP PLEASEE!!!
In Asha's science experiment, her bacteria are dying at a constant rate of $600$ an hour. If she drew a graph of the number of bacteria in her culture where $x$ represented the time in minutes since the start of the experiment and $y$ represented the number of bacteria remaining in the colony, her graph would be a line. What would be the slope of this line?
Answer:
-10
Step-by-step explanation:
The rate of change is also known as the slope of the function thus the slope will be -600.
What is the slope?A slope is a tangent or angle at a point and a slope is the intensity of inclination of any geometrical lines.
Slope = Tanx where x will be the angle from the positive x-axis at that point.
The slope is also calculated by differentiation for example slope of y = sinx will be y' = cosx.
As per the given,
Bacteria are dying at a constant rate of $600$ an hour.
The rate of change = -600/hour
Slope = y/x = number of bacteria change/time taken
If the graph is a straight line then it will remain constant.
Slope = -600
Hence "The rate of change is also known as the slope of the function thus the slope will be -600".
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Multiply:4x^3sqrt4x^2(2^3sqrt32x^2-x^3sqrt2x)
8x^5\left(32\sqrt{2}x^2-\sqrt{2}x^4\right)
Please help!!!
If data set A has a larger standard deviation than data set B, data set B is
more spread out thar data set A.
O A. True
O B. False
Answer:
the answer is B.FALSE
Step-by-step explanation:
hope it helps
How do I solve sinhx= -2 and sinhx= \(\frac{7}{2}\)
and get the answer in logs?
Answer:
Step-by-step explanation:
1)
\(sinh(x)=-2\\\\\dfrac{e^x-e^{-x}}{2} =-2\\\\e^{2x}-1=-4e^x\\\\(e^x)^2+4e^x-1=0\\\\\Delta=16+4=20\\\\e^x=\dfrac{-4-\sqrt{5} }{2} \ (exclude) \ or\ e^x=-2+\sqrt{5} \approx{0,236067977...}\\\\x=ln(-2+\sqrt{5} ) \approx{-1,443635475178...}\\\\\)
2)
\(sinh(x)=\dfrac{7}{2} \\\\\dfrac{e^x-e^{-x}}{2} =\dfrac{7}{2} \\\\e^{2x}-1=7e^x\\\\(e^x)^2-7e^x-1=0\\\\\Delta=49+4=53\\\\e^x=\dfrac{7-\sqrt{53} }{2} \ (exclude) \ or\ e^x=\dfrac{7+\sqrt{53}}{2} \approx{7,1400549...}\\\\x=ln(7+\sqrt{53} ) \approx{1,96572...}\\\\\)
Sam and jeremy have ages that are consecutive odd interferes. The product of their ages is 783. Which equation could be used to find Jeremy’s age, j, if he is the younger man?
So, the equation we could use to find Jeremy's age, j, if he is the younger man, is: j = x + 2, where x satisfies the equation x(x + 2) = 783.
What is equation?An equation is a mathematical statement that asserts the equality of two expressions. In an equation, an expression is written on the left side of an equals sign (=), and another expression is written on the right side of the equals sign. The equals sign indicates that the two expressions have the same value.
Here,
Let's use algebra to solve this problem. We can start by representing Sam's age as x and Jeremy's age as x + 2, since they are consecutive odd integers. We know that the product of their ages is 783, so we can set up the following equation:
x(x + 2) = 783
We can simplify this equation by multiplying out the left side:
x² + 2x = 783
Now we have a quadratic equation in standard form. We can solve for x by using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
In this case, a = 1, b = 2, and c = -783, so we can substitute these values into the formula:
x = (-2 ± √(2² - 4(1)(-783))) / 2(1)
Simplifying the expression under the square root, we get:
x = (-2 ± √(3136)) / 2
x = (-2 ± 56) / 2
So, we have two possible values for x:
x = 27 or x = -29
We can reject the negative value, since it does not make sense in the context of the problem. Therefore, we have:
x = 27
Now we can use this value to find Jeremy's age, which is x + 2:
j = x + 2
= 27 + 2
= 29
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what are the intercepts of the line y=−2x−21
Answer:
-21
Step-by-step explanation:
the formula is y=mx+b
m is the slope and b is the y-intercept
here, for the y value, there's -21 so the y-intercept is -21
hope this helps
The last time Caralina visited the post office, she spent $4.49 to mail letters and packages. Each letter cost $0.37 to mail, while each package cost $0.88 to mail. if she sent two more letters than packages, how many letters did she mail?
Answer:
5 letters
Step-by-step explanation:
let x = # of packages
x+2 = # of letters
$0.37(x+2) + $0.88x = $4.49
.37x + .74 + .88x = 4.493
1.25x + .74 = 4.49
1.25x = 3.75
x = 3.75/1.25 = 3 = # of packages
# of letters = x+2 = 3+2 = 5
the circumference of a circle is 36cm what is the radius of the circle? set up the equation and then solve round to the tenths place
The radius of the circle is equal to 5.7 cm to nearest tenth.
How to calculate for the radius of the circleTo calculate the circumference of a circle, you can use the formula:
Circumference = 2 × π × radius
where π (pi) is a constant equal to 22/7 or approximately 3.14, and the radius is the distance from the center of the circle to any point on its edge.
36 cm = 2πr
36 cm = 2 × 22/7 × radius
radius = (36cm × 7)/44 {cross multiplication}
radius = 252cm/44
radius = 5.7273 cm
Therefore, the radius of the circle is equal to 5.7 cm to nearest tenth.
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10. Error Analysis The base of a rectangle
is 3 feet. The area of this rectangle is
40 square feet. Michaela claims the
height of the rectangle is 133 feet.
a. What is the correct height?
b. What is Michaela's error?
A. To solve 33 = h = 40, Michaela
used subtraction instead of
addition.
.
B. To solve 40 h = 33, Michaela
used division instead of
multiplication.
C. To solve 3+ h
=
40, Michaela
used addition instead of
subtraction.
D. To solve 3 h = 40, Michaela
used multiplication instead of
division.
.
E. To solve 3 h = 40, Michaela
used division instead of
multiplication.
The correct height is 13.3 feet.
To solve 33 = h + 3, Michaela used subtraction instead of addition.
a.
The correct height of the rectangle can be found by dividing the area by the length of the base:
height = area/base
= 40 / 3
= 13.33 feet
b.
Michaela's error is that she claimed the height to be 133 feet, which is way too large and unrealistic.
It seems like she made a mistake in her calculation and likely used addition instead of division.
Therefore,
The correct height is 13.3 feet.
To solve 33 = h + 3, Michaela used subtraction instead of addition.
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Convert to scientific notation:
520,000,000
1. 52 x 10^7
2. 5.2 x 10^7
3. 0.52 x 10^9
4. 5.2 x 10^8
Answer:
number 4 is right
find an equation of the tangent plane to the given surface at the specified point. z = ln(x − 7y), (8, 1, 0)
To find the equation of the tangent plane to the surface z = ln(x - 7y) at the point (8, 1, 0), we need to determine the partial derivatives of z with respect to x and y at that point.
First, let's find the partial derivative ∂z/∂x:
∂z/∂x = 1/(x - 7y)
Next, let's find the partial derivative ∂z/∂y:
∂z/∂y = -7/(x - 7y)
Now, let's evaluate these partial derivatives at the point (8, 1, 0):
∂z/∂x = 1/(8 - 7(1)) = 1/(8 - 7) = 1
∂z/∂y = -7/(8 - 7(1)) = -7/(8 - 7) = -7
At the point (8, 1, 0), the partial derivatives are ∂z/∂x = 1 and ∂z/∂y = -7.
The equation of a plane can be expressed as:
z - z0 = (∂z/∂x)(x - x0) + (∂z/∂y)(y - y0)
Using the values we calculated:
z - 0 = 1(x - 8) + (-7)(y - 1)
Simplifying, we get:
z = x - 8 - 7y + 7
Rearranging terms, the equation of the tangent plane to the surface at the point (8, 1, 0) is:
z = x - 7y - 1
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A landscaper is designing a display of flowers for an area in a public park. The flower seeds will be planted at points that lie on a circle that has a diameter of 8 feet. the point where any seed is planted must be 2 feet away from the seeds on either side of it. what is the maximum number of flower seeds that can be planted using the design?
after planting the flower seeds the landscaper has 20 seeds left over. the landscaper wants to plant all of the remaining seeds in another circle so that the seeds are 2 feet apart. what is the diameter of the smallest circle that the landscaper can use to plant all of the remaining seeds?
The z-score for P(? ≤ z ≤ ?) = 0.60 is approximately 0.25.
The z-score for P(z ≥ ?) = 0.30 is approximately -0.52.
How to find the Z score
P(Z ≤ z) = 0.60
We can use a standard normal distribution table or a calculator to find that the z-score corresponding to a cumulative probability of 0.60 is approximately 0.25.
Therefore, the z-score for P(? ≤ z ≤ ?) = 0.60 is approximately 0.25.
For the second question:
We want to find the z-score such that the area under the standard normal distribution curve to the right of z is 0.30. In other words:
P(Z ≥ z) = 0.30
Using a standard normal distribution table or calculator, we can find that the z-score corresponding to a cumulative probability of 0.30 is approximately -0.52 (since we want the area to the right of z, we take the negative of the z-score).
Therefore, the z-score for P(z ≥ ?) = 0.30 is approximately -0.52.
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Is 1.52 a irrational number
Answer:
yes
Step-by-step explanation:
Answer:
It is rational
Step-by-step explanation:
1.52 = 1 + 52/100 = 152/100 which is rational, because it can be expressed as a fraction
in the right triangle abc, the median to the hypotenuse has a length of 15 units and the altitude to the hypotenuse has a length of 12 units. what is the length of the shorter leg of the triangle abc?
The length of the shorter leg of the triangle ABC is approximately 24.49 units. Let's denote the right triangle ABC, where C is the right angle.
Let D be the midpoint of AB, and E be the foot of the altitude from C to AB. Then we have:
CD = 1/2 AB (definition of median)
CE = 12 (given altitude to the hypotenuse)
Let x be the length of the shorter leg of the triangle ABC. Then we have:
AE = x (definition of altitude)
EB = AB - x (definition of complementary leg)
By the Pythagorean theorem, we have:
AC^2 = AB^2 + BC^2
(2CD)^2 = AB^2 + x^2
AB^2 = 4CD^2 - x^2
By the similarity of triangles AEC and ABC, we have:
CE/AC = AE/AB
12 / (AB + BC) = x / AB
AB = x / (12/x + 1)
Substituting AB into the previous equation, we get:
4CD^2 - x^2 = x^2 / (12/x + 1)^2
Simplifying and solving for x, we get:
x^4 - 576x^2 - 14400 = 0
This is a quadratic equation in x^2, so we can solve for it using the quadratic formula:
x^2 = [576 ± sqrt(576^2 + 4*14400)] / 2
x^2 = [576 ± 624] / 2
Since x is a length, we take the positive square root:
x^2 = 600
x ≈ 24.49
Therefore, the length of the shorter leg of the triangle ABC is approximately 24.49 units.
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pleas help a lot of points
Answer:
54 ft
Step-by-step explanation:
Add all the side lengths ; 18+18+18 = 54.
You pend 2/3 hour reading a book daily. How many hour did you pend reading after a week?
The total number of hours spent on reading in a week is 14/3 hours.
Define the term fraction of a number?A fraction is a number that is a component of a whole. By breaking a whole into a number of parts, it is evaluated.The components of a whole or group of items are described by fractions. The numerator is the figure only at top of the line. It details the number of equal portions which have been taken from the total or collection. The denominator is the figure that appears below the line.For the given question-
Number of hours spent of reading = 2/3 hours.
Total number of days in a week = 7.
Total number of hours spent on reading = 2/3 x 7
Total number of hours spent on reading = 14/3
Thus, the total number of hours spent on reading in a week is 14/3 hours.
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NEED HELP NOW! 5 questions, 76 points!
1.
Given points B(−12,2), T(−8,10), A(−7,12), F(−6,10), and G(−2,2), which of the following proves that △BAG~△TAF?
2.
Given points A(2,1), B(1,4), C(−1,10), D(8,13), and E(4,5), which of the following proves that △ABE~△ACD?
Answers:
By the Distance Formula,AB=310‾‾‾√,AC=10‾‾‾√, AE=65‾√, and AD=25‾√. Since, ABAC=AEAD=13, and ∠A≅∠A by the Reflexive Property, △ABE∼△ACD by SAS ∼.
By the Distance Formula,AB=310‾‾‾√,AC=10‾‾‾√, AE=65‾√, and AD=25‾√. Since, ABAC=AEAD=13, and ∠A≅∠A by the Reflexive Property, △ABE∼△ACD by SSS ∼.
By the Distance Formula,AB=10‾‾‾√,AC=310‾‾‾√, AE=25‾√, and AD=65‾√. Since, ABAC=AEAD=13, and ∠A≅∠A by the Reflexive Property, △ABE∼△ACD by SSS ∼.
By the Distance Formula,AB=10‾‾‾√,AC=310‾‾‾√, AE=25‾√, and AD=65‾√. Since, ABAC=AEAD=13, and ∠A≅∠A by the Reflexive Property, △ABE∼△ACD by SAS ∼.
3.
Given points M(1,2), N(4,4), P(5,−1), J(−7,−1), K(−1,3), and L(1,−7), which of the following proves that △MNP≈△JKL?
Answers:
By the Distance Formula,MN=13‾‾‾√,NP=26‾‾‾√, and PM=5.Also, JK=213‾‾‾√,KL=226‾‾‾√, and LJ=10.Therefore, MNJK=NPKL=PMLJ=12, andtherefore, △MNP∼△JKL by SAS ∼.
By the Distance Formula,MN=13‾‾‾√,NP=26‾‾‾√, and PM=5.Also, JK=213‾‾‾√,KL=226‾‾‾√, and LJ=10.Therefore, MNJK=NPKL=PMLJ=12, andtherefore, △MNP∼△JKL by SSS ∼.
By the Distance Formula,MN=13,NP=26, and PM=25.Also, JK=52,KL=104, and LJ=100.Therefore, MNJK=NPKL=PMLJ=14, andtherefore, △MNP∼△JKL by SSS ∼.
By the Distance Formula,MN=13,NP=26, and PM=25.Also, JK=52,KL=104, and LJ=100.Therefore, MNJK=NPKL=PMLJ=14, andtherefore, △MNP∼△JKL by SAS ∼.
4.
Given points M(−5,5), R(−2,6), I(−2,4), B(2,−2), A(8,0), and G(8,−4), which of the following proves that △MRI~△BAG?
Answers:
By the Distance Formula,MR=10‾‾‾√,RI=2, and IM=10‾‾‾√.Also, BA=210‾‾‾√,AG=4, and GB=210‾‾‾√.Therefore, MRBA=RIAG=IMGB=10√210√=12,and therefore, △MRI~△BAG by SSS ~.
By the Distance Formula,MR=10,RI=2, and IM=10.Also, BA=40,AG=8, and GB=40.Therefore, MRBA=RIAG=IMGB=1040=14,and therefore, △MRI∼△BAG by SSS ∼.
By the Distance Formula,MR=2,RI=10, and IM=10.Also, BA=8,AG=40, and GB=40.Therefore, MRBA=RIAG=IMGB=1040=14,and therefore, △MRI∼△BAG by SAS ∼.
By the Distance Formula,MR=10‾‾‾√,RI=2, and IM=10‾‾‾√.Also, BA=210‾‾‾√,AG=4, and GB=210‾‾‾√.Therefore, MRBA=RIAG=IMGB=10√210√=12,and therefore, △MRI∼△BAG by SAS ∼.
5.
Given points L(−2,−2), A(−6,−3), U(−14,−5), X(4,−5), and P(0,−3), which of the following proves that △XUL~△PAL?
By the Distance Formula,LX=317‾‾‾√,PL=17‾‾‾√, LA=5‾√, and LU=35‾√. Since, LXPL=LULA=31=3, and ∠L≅∠L by the Reflexive Property, △XUL∼△PAL by SSS ∼.
By the Distance Formula,LX=35‾√,PL=5‾√, LA=17‾‾‾√, and LU=317‾‾‾√. Since, LXPL=LULA=31=3, and ∠L≅∠L by the Reflexive Property, △XUL∼△PAL by SAS ∼.
By the Distance Formula,LX=35‾√,PL=5‾√, LA=17‾‾‾√, and LU=317‾‾‾√. Since, LXPL=LULA=31=3, and ∠L≅∠L by the Reflexive Property, △XUL∼△PAL by SSS ∼.
By the Distance Formula,LX=317‾‾‾√,PL=17‾‾‾√, LA=5‾√, and LU=35‾√. Since, LXPL=LULA=31=3, and ∠L≅∠L by the Reflexive Property, △XUL∼△PAL by SAS ∼.
Answer:
Q1: 5, 5 SAS
Step-by-step explanation:
Q2: 10 sas
Q3:13 sss
Q4: 10 sss
Q5: 35 sas
9 ^ (- 1/2) + 25 ^ (- 1/2) + 32 ^ (3/5)
Evaluate
Answer:
8.533333
Step-by-step explanation:
9^(− 1/ 2 )+25− 1 2 +32^ (3/ 5) = 9 (−1 /2) +25(− 1 /2) +32 ^(3 /5)
=0.333333+25^(− 1/ 2) +32 ^(3 /5)
=0.333333+25 ^(−1 /2) +32 ^(3/ 5)
=0.333333+0.2+32^ (3/ 5)
=0.533333+32 ^(3 /5)
=0.533333+8
=8.533333
The mass of a piece of aluminum is 250 grams. The density of aluminum is 2.7 g/mL. What is the volume of the piece of aluminum? A. 92.59 mL, B. 247.3 mL, C. 95 mL, D. 0.01
Answer:
LETTER A
Step-by-step explanation:
BECAUSE IF YOU DIVIDE THE 250 GRAMS TO 2.7 G/ML THE ANSWER IS 92.59ml
Answer:
A. 92.59 mL
Step-by-step explanation:
Triangle PQR ~Triangle TUV. In Triangle PQR, ∡P = 33 degrees and ∡Q = 42 degrees. Find the measure of ∡V.
Answer:
angle v is 105
Step-by-step explanation:
the triangles are similar, so the angles will be the same so both triangles, the sum of the angles for a triangle must add up to 180 degrees