The perimeter of the triangle STU is 20.6 units
What is the perimeter of the triangle?To find the perimeter of triangle STU, we need to use the formula of distance between two points and then take the sum of all the sides.
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\\[/tex]
For line ST;
(-4, -2) and (-4, 5)
[tex]d = \sqrt{(-4 - (-4))^2 + (5 - (-2))^2} \\d = 7[/tex]
For line TU;
(-4, 5) and (-9, -2)
[tex]d = \sqrt{(-9 - (-4))^2 - (-2 - 5)^2} \\d = \sqrt{74} \\d = 8.6[/tex]
For line US;
(-9, -2) and (-4, -2)
[tex]d = \sqrt{(-9 - (-4))^2 + (-2 - (-2))^2}\\d = 5[/tex]
The distance between the sides are 7, 8.6 and 5 units.
The perimeter of the triangle = 7 + 8.6 + 5 = 20.6 units
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3
f(x)=3(2¹)-1
g(x)=3(2-)-1
Which statement is TRUE?
A. The y-values of both functions decrease by a
factor of 2 for each unit increase in x.
C. The functions both have the same x-intercept.
B. The y-values of both functions increase by a factor
of 2 for each unit increase in x.
D. The functions both have the same y-intercept.
The correct statement regarding the exponential functions in this problem is given as follows:
D. The functions both have the same y-intercept.
How to define an exponential function?An exponential function has the definition presented according to the equation as follows:
[tex]y = ab^x[/tex]
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The functions in this problem are given as follows:
[tex]f(x) = 3(2^x) - 1[/tex][tex]g(x) = 3(2^{-x}) - 1[/tex]Hence the y-intercept for each function is given as follows:
[tex]f(0) = 3(2^0) - 1 = 3 - 1 = 2[/tex][tex]g(x) = 3(2^{0}) - 1 = 3 - 1 = 2[/tex]More can be learned about exponential functions at brainly.com/question/2456547
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secx csc x = 2 csc x
Answer:
Step-by-step explanation:
[tex]\frac{1}{cosx} . \frac{1}{sinx} =\frac{2}{sinx}\\ \frac{1}{cosx} . \frac{1}{sinx} - \frac{2}{sinx} = 0\\\frac{1}{sinx}(\frac{1}{cosx} - 2) = 0\\\frac{1}{cosx} = 2\\cosx = \frac{1}{2} \\x = 60[/tex]
1,300 aliens from Area 51 escaped at 2:00am on Wednesday, and the armed forces are able to capture half of them every four hours. How many aliens will remain free at 8:00pm on Wednesday?
Answer:
Let's start by figuring out how many aliens are captured every four hours. If half of the aliens are captured every four hours, that means the number of remaining aliens is also halved every four hours. So we can use exponential decay to model the number of aliens remaining after t four-hour periods:
N(t) = N₀ (1/2)^t
where N₀ is the initial number of aliens and t is the number of four-hour periods that have passed.
The initial number of aliens is 1,300, and we want to know how many remain after 14 four-hour periods (from 2:00am to 8:00pm, a total of 16 hours with 4-hour intervals):
N(14) = 1,300 (1/2)^14
N(14) ≈ 20.16
So there will be approximately 20 aliens remaining free at 8:00pm on Wednesday. Note that the actual number may be slightly different due to rounding, and also because we assumed that the capture rate remains constant throughout the 16-hour period.
Step-by-step explanation:
Let's start by figuring out how many aliens are captured every four hours. If half of the aliens are captured every four hours, that means the number of remaining aliens is also halved every four hours. So we can use exponential decay to model the number of aliens remaining after t four-hour periods:
N(t) = N₀ (1/2)^t
where N₀ is the initial number of aliens and t is the number of four-hour periods that have passed.
The initial number of aliens is 1,300, and we want to know how many remain after 14 four-hour periods (from 2:00am to 8:00pm, a total of 16 hours with 4-hour intervals):
N(14) = 1,300 (1/2)^14
N(14) ≈ 20.16
So there will be approximately 20 aliens remaining free at 8:00pm on Wednesday. Note that the actual number may be slightly different due to rounding, and also because we assumed that the capture rate remains constant throughout the 16-hour period. please give brainliest! :D
100 Points! State the amplitude, period, and phase shift for each function. Then graph the function. Photo attached. Thank you!
hello
the answer to the question is:
y = a tan(bx – c) + d
a = 1, b = 1, c = π/2
the midline is y = d, so y = 0 and there's no vertical shift
the vertical stretch is 1, so label the y-axis so the inflection point of the curve is 1 above the midline, 1, and the other inflection point is 1 below the midline, −1
the period is:
T = π/b ----> T = π
the phase shift is:
PS = c/b ----> PS = π/2
and also, there's no amplitude for tangent and cotangent, there is only the vertical stretch that takes the place of an amplitude
The hexagonal prism below has a base area of 36 units
2
2
and a height of 5.9 units. Find its volume.
The volume of the hexagonal prism is 212.4 unit square
What is Prism?Prism is three-dimensional solid which has identical faces at both ends. It is a polyhedron, which means all faces are flat.
How to determine this
When an hexagonal prism has a base area = 36 units
Height = 5.9 units
Volume of Prism = Base area * Height
Volume of prism = 36 units * 5.9 units
Volume = 212.4 units square
Therefore, the volume of the hexagonal prism is 212.4 units square
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Solve for x. Round to the nearest tenth of a
degree, if necessary.
S
to
3.9
8.5
R
Q
Answer:
Set your calculator to degree mode.
[tex]x = {cos}^{ - 1} \frac{3.9}{8.5} = 62.7 \: degrees[/tex]
Angle x measures about 62.7°.
△BCD is a right triangle. The length of the hypotenuse is 19 centimeters. The length of one of the legs is 13 centimeters.
What is the length of the other leg?
The length of the other leg of the right triangle is 13.9 cm.
How to find the side of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The side of the right triangle can be named according to it angle position as hypotenuse side, adjacent side and opposite side.
Therefore, let's find the other leg of a right triangle with hypotenuse as 19 cm and one leg as 13 cm using Pythagoras's theorem as follows:
c² = a² + b²
where
c = hypotenusea and b are the other legsTherefore,
b = √19² - 13²
b = √361 - 169
b = √192
b = 13.8564064606
Therefore,
length of the other leg = 13.9 cm
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Next
7
Post Test: Ratios and Proportional Relationships
Select the correct answer.
Area Buckeye Butterflies Monarch Butterflies
A
B
C
D
E
Rachel traveled to five different areas (A, B, C, D, and E) to study the number of buckeye butterflies and the number of monarch butterflies living
there. The table shows her findings.
OA
OB.
n. All rights reserved
15
27
12
24
44
areas A and B
areas C and E
Submit Test
16
36
25
32
33
The relationship between the number of buckeye butterflies and the number of monarch butterflies is not proportional across all areas. Which two
areas have buckeyes and monarchs in the same proportion?
Reader Tools
The two areas where buckeyes and monarchs have the same proportion are areas A and B.
How to determine the two areas have buckeyes and monarchs in the same proportionBased on the information given, we can determine the two areas where the number of buckeye butterflies and the number of monarch butterflies are in the same proportion.
Comparing the data in the table, we can see that the ratio of buckeye butterflies to monarch butterflies is consistent in areas A and B.
In area A, there are 15 buckeye butterflies and 27 monarch butterflies, which simplifies to a ratio of 5:9.
In area B, there are 27 buckeye butterflies and 48 monarch butterflies, which also simplifies to a ratio of 5:9.
Therefore, the two areas where buckeyes and monarchs have the same proportion are areas A and B.
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15. The volumes of two similar solids are 857.5 mm^3 and 540 mm^3. The surface area of the smaller solid is 108 mm^2. What is the surface area of the larger solid?
The surface area of the larger solid is approximately 172 mm sq. approx
Given
The volume of the smaller solid = 540 mm cube
The volume of the larger solid = 857.5 mm cube
The surface area of the smaller solid = 108 mm sq.
Required to find the surface area of the larger solid =?
Let the surface area of the larger solid be x.
(surface area of smaller solid) / (volume of smaller solid) = (surface area of larger solid) / (volume of larger solid)
Putting the values in the above formula we get the value of x.
108 mm^2 / 540 mm^3 = x / 857.5 mm^3
x = 171.5 mm sq
Thus, the surface area of the larger solid is approximately 172 mm sq
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Can someone help me on 3-6?
Directions: Find the volume of each figure. Round the nearest hundredth.
Using the formula of volume of a sphere and hemisphere, the volume of the figures are given as;
1. 2144.57 m³
2. 696.6 m³
3. 20569.1m³
4. 2637ft³
5. 56.5km³
6. 6381.79 in³
What is volume of sphere?The volume of a sphere is given as 4/3πr³
Where π is a constant whose value is equal to 3.14 approximately. “r” is the radius of the hemisphere.
1. The volume of the sphere is;
v = 4/3 * 3.14 * 8³ = 2144.57m³
2. The volume of the sphere is;
v = 4/3 * 3.14 * (11/2)³ = 696.6m³
3. The volume of the sphere is;
v = 4/3 * 3.14 * 17³ = 20569.1m³
4. The volume of the hemisphere is;
v = 2/3 * 3.14 * 10.8³ = 2637ft³
5. The volume of the hemisphere is;
v = 2/3 * 3.14 * 3³ = 56.5km³
6. The volume of the hemisphere is;
v = 2/3 * 3.14 * (29/2)³ = 6381.79in³
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What is the mode of the data set below? 0, 4 , 3, 4, 0, 9, 1
The mode of the data is 0
What are the measures of central tendency?Central tendency is defined as the statistical measure identifying a single value as representative of an entire distribution.
It provides an accurate description of the entire data.
The three major measures of central tendency are given as;
ModeMeanMedianThe mode is defined as the measure of central tendency representing the most occurring number in a given data set
From the information given, we have;
0, 4 , 3, 4, 0, 9, 1
Then, the mode is 0
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Ada realized she had 2 more quarters than she had originally thought in her pocket, if all of the change in his quarters and it totals to $8.75. how many quarters did he originally think we're in his pockets?
The number of quarters he originally think we're in his pocket is 33.
We are given that;
More quarters she had= 2
Total= $8.75
Now,
Let’s name that number x.
We can translate the table into an equation by equating the total value of the quarters to $8.75:
0.25(x + 2) = 8.75
To solve this equation by simplifying and isolating x:
0.25x + 0.5 = 8.75 0.25x = 8.25 x = 33
The answer by plugging it back into the equation:
0.25(33 + 2) = 8.75 0.25(35) = 8.75 8.75 = 8.75
This makes sense, so we have the correct answer. 7.
Therefore, by algebra the answer will be 33.
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A rock is thrown from the top of a building. The height s (in feet) as a function of time (in seconds) can be modeled by the function
s(t) = -16t² + 3000
Approximately when will the rock be 1,976 feet above the ground.
O a
Ob
C
8 sec
135 sec
85 sec
15 sec
Answer: the rock will be at a height of 1,976 feet above the ground after approximately 8 seconds
Step-by-step explanation:
We can start by setting the height function equal to 1,976 and solving for t:
-16t² + 3000 = 1976
Subtracting 1976 from both sides, we get:
-16t² + 1024 = 0
Dividing both sides by -16, we get:
t² - 64 = 0
Factoring, we get:
(t + 8)(t - 8) = 0
So t = 8 or t = -8. We can ignore the negative solution since time cannot be negative.
Therefore, the rock will be at a height of 1,976 feet above the ground after approximately 8 seconds.
Answer: (A) 8 sec
If sing, which of the following are possible for the same value of a?
A. sec9 =
B. cose =
C. cose =
√5
3
D. sece=
√5
3
and tang =
and tang
8=-2 and 1
-7/5
3
and tang =
tang =
-7/5
25
Like
SUBMIT
The correct answer is:
B. cosθ = √5/3 and tanθ = 2/√5
C. cosθ = -√5/3 and tanθ = 2/√5
To solve this question, we can use the given information that sinθ = 2/3 and determine the values of the other trigonometric functions based on that.
Recall the trigonometric identity: sin^2θ + cos^2θ = 1
Since sinθ = 2/3, we can substitute this value into the identity and solve for cosθ:
(2/3)^2 + cos^2θ = 1
4/9 + cos^2θ = 1
cos^2θ = 1 - 4/9
cos^2θ = 5/9
Taking the square root of both sides, we get:
cosθ = ±√(5/9) = ±(√5/3)
Now, let's analyze the given options:
A. secθ = 3/√5 and tanθ = 2/√5
B. cosθ = √5/3 and tanθ = 2/√5
C. cosθ = -√5/3 and tanθ = 2/√5
D. secθ = -3/2 and tanθ = 2/√5
From our calculations, we found that cosθ can be either √5/3 or -√5/3. So, option B and C are valid.
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What postulate or theorem allows you to state that angle DEF is congruent to angle GHJ
Then you can state that angle DEF is congruent to angle GHJ.
The postulate or theorem that allows you to state that angle DEF is congruent to angle GHJ is the Angle-Angle (AA) Postulate.
This postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles must also be congruent.
In this case, if you have two triangles, one with angles DEF and the other with angles GHJ, and
you know that angle D is congruent to angle G and angle E is congruent to angle H, then by the AA Postulate, you can conclude that angle F is congruent to angle J.
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Luna has 8 pints of juice. Michael has 2% times as many
pints of juice as Luna.a) How many pints of juice does Michael have?b) How many more pints of juice does Michael have than
Luna?Give your answers as whole numbers or as fractions in their simplest form.
Answer: 0.16
Step-by-step explanation:
Find the measure of the red arc or chord in ⊙C.
The calculated measure of the red arc in ⊙C is 11
How to find the measure of the red arc or chord in ⊙C.From the question, we have the following parameters that can be used in our computation:
The congruent circles
From the circles, we have
Centers = C and P
Also, we have
Corresponding segments are equal segments
Using the above as a guide, we have the following:
QR = LM
Where
LM = 11
This gives
QR = 11
Hence, the value of QR is 11
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Can I get help, please
Answer:
see attached
Step-by-step explanation:
You want the areas of the four triangles in the figure.
Triangle areaThe area of a triangle is given by the formula ...
A = 1/2bh
where b is the base of the triangle, and h is its height perpendicular to the base.
Triangles A, B, C are right triangles, so their areas are easy to figure. Triangle D will be the difference between the area of the square and the areas of the other triangles.
The calculations are shown in the first attachment. Confirmation is provided by a geometry program in the second attachment.
__
Additional comment
If all you have are the coordinates of the vertices of triangle D, this method of finding its area is as good as any. There are other methods that can also be used, but they can be more trouble.
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what type of data would best be displayed in a box plot
Answer:(2x+7)+(2x+7)
Step-by-step explanation:
what you do is put 2x on the top and on the side and then seven on the top and on the side and then you got your answer
Identify as a monomial, binomial, trinomial, or polynomial.
x^3 + y^2 - 3
7y^2
x^3 + 2x^2 - x + 10
x + 7
18 points!
The given expressions can be identified as:
1. Trinomial
2. Monomial
3. Polynomial
4. Binomial
Answer to the questionThe given expressions can be identified as:
1. x^3 + y^2 - 3: This is a trinomial since it consists of three terms.
2. 7y^2: This is a monomial since it consists of only one term.
3. x^3 + 2x^2 - x + 10: This is a polynomial since it consists of four terms.
4. x + 7: This is a binomial since it consists of two terms.
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6:1 scale with dimensions of 24 inches by 36 inches. what are the real dimensions?
The real dimensions of the object are 144 inches by 216 inches.
Given that, 6:1 scale with dimensions of 24 inches by 36 inches.
The basic formula to find the scale factor of a figure is expressed as,
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
In a 6:1 scale, the real dimensions of an object would be 6 times the scaled dimensions. Therefore, the real dimensions of the object given in the question would be 24 inches x 6 = 144 inches by 36 inches x 6 = 216 inches. So, the real dimensions of the object are 144 inches by 216 inches.
Therefore, the real dimensions of the object are 144 inches by 216 inches.
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A 4th of July sale at your local truck dealership is advertising big discounts on pickup trucks. The truck you've had your eye on is now listed at $23,000 which is 23% off the original price. What was the original price of the truck?
If the value of the truck is at $23,000 which is 23% off the original price. Then the original price of the truck will be $ 29,870.13.
What is the percentage?
The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.
A 4th of July sale at your local truck dealership is advertising big discounts on pickup trucks.
The truck you've had your eye on is now listed at $23,000 which is 23% off the original price.
Then the original price of the truck will be given as
Let the original price of the truck will be x. Then we have
0.77 × x = $ 23,000
x = $ 29,87
Use the 68-95-99.7 rule to find the following quantities. Do not round any answers.
What portion of scores are between 59 and 91?
What portion of exam scores are less than 67?
What portion of exam scores are between 67 and 91?
The portion of scores that are between 59 and 91 is 98%.
The portion of exam scores that are less than 67 is 16%.
The portion of exam scores that are between 67 and 91 is 82%.
What is a normal distribution curve?A normal distribution curve is a type of probability distribution that is commonly used in statistics to represent a large set of data. It is also known as a bell curve. The curve is bell-shaped, symmetrical, and smooth.
Comparing the exam score diagram in the question, to a standard normal distribution curve, we will have the following;
The portion of scores that are between 59 and 91 is;
= 100% - (59 to 43 portion)
= 100% - 2%
= 98%
The portion of exam scores that are less than 67 is;
= (67 to 59) + (59 to 43)
= 14% + 2%
= 16%
The portion of exam scores that are between 67 and 91 is ;
= (67 to 75) + (75 to 83) + (83 to 91)
= 34% + 34% + 14%
= 82%
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{-1} x even times of times
The number which is the result of the exponential expression [tex](-1)^x[/tex], in which x is an even number, is given as follows:
1.
How to obtain the rule for the powers of -1?The exponential expression representing the power x of the base -1 is given as follows:
[tex](-1)^x[/tex].
There are two possible results, given as follows, depending if x is even or odd:
If x is an even number, the result of the expression is of 1.If x is an odd number, the result of the expression is of -1.For this problem, we have that the exponent x is an even number, hence the result is of 1.
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Solve the system of equations using elimination. 6x + 6y = 36 5x + y = 10 (1, 5) (2, 0) (3, 3) (4, 2)
Answer:
begin equation begin cases x = 1y = 5 end cases end equation. Rearrange like terms to the same side of the equation
Step-by-step explanation:
begin equation begin cases x = 1y = 5 end cases end equation. Rearrange like terms to the same side of the equation
The table shows the mass of four packages. What is the total mass of the packages?
The total mass of the packages is 37.04 kg
What is the total mass of the packages?In math, mass means the amount an object weighs. To find the mass we use a balance or weights. The units used to denote mass are gram (g) and kilogram (kg).
Given that:
Masses (KG) are 3.94, 14.18, 11.27 and 7.65 (KG) for Package 1 to 4 respectively.
The total mass of the packages is:
= 3.94 + 14.18 + 11.27 + 7.65
= 37.04 kg
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100 Points! Algebra question. Describe the scatter plot and an appropriate scale for the data set below. Photo attached. Please show as much work as possible. Thank you!
Strength: TThe strength of the scatterplot refers to how closely the data points cluster around a line or curve. Direction: The direction of the scatterplot refers to the general trend or pattern exhibited by the data points.
Answers to the aforementioned questionsTo describe the scatterplot and determine an appropriate scale, we can analyze the given data set:
x: 0, 2, -5, 3, 1, -4, 8, -6, -1
y: -3, -1, -13, 3, -1, -11, 12, -15, -5
Strength: TThe strength of the scatterplot refers to how closely the data points cluster around a line or curve.
Direction: The direction of the scatterplot refers to the general trend or pattern exhibited by the data points.
Scale: The appropriate scale for the scatterplot depends on the range of values for the x and y variables. To determine the scale, we need to consider the minimum and maximum values for each variable.
For x: The minimum value is -6 and the maximum value is 8.
For y: The minimum value is -15 and the maximum value is 12.
Based on these ranges, an appropriate scale for both x and y could be chosen with intervals of 2 or 5 units, depending on the desired level of detail.
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Find the coordinates of B if p(1, 2) partition segment AB in the ratio 1:2 and A (2, 4).
The calculated coordinates of point B on line AB is (-1, 0)
Calculating the coordinates of point BFrom the question, we have the following parameters that can be used in our computation:
P = (1,2)
A = (2,4)
Also, we have
m : n = 1 : 2
The coordinates of point P are calculated using
P = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)
Substitute the known values in the above equation, so, we have the following representation
(1, 2) = 1/(1 + 2) * (1 * x + 2 * 2, 1 * y + 2 * 4)
Evaluate
(3, 6) = (x + 4, y + 6)
So, we have
x = -1 and y = 0
Hence, the coordinates of point B on line AB is (-1, 0)
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A rocket is launched in the air. Its height in feet is given by h= -16t^2 + 56t where t represents the time in seconds after launch. What is the appropriate domain for this Solution?
The domain of the function (t) in h = - 16t² + 56t should be greater than
or equal to 43.5 seconds as the height of the rocket can not be negative.
Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given that;
A rocket is launched into the air. Its height in feet is given by
h = - 16t² + 72t.
Where t represents time in seconds and h represents the height in feet.
We know that height can not be negative.
h ≥ 0.
So, - 16t² + 56t ≥ 0.
- 16t² ≥ -56t.
16t² ≥ 56t.
16t ≥ 56.
t ≥ 56/16.
t ≥ 3.5 seconds.
Therefore, the domain of the function (t) in h = - 16t² + 56t should be greater than or equal to 3.5 seconds.
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solve for C using law of cosine tuned to the nearest tenth
The value of angle C is calculated by applying cosine rule as 50.67 ⁰.
What is the value of C?The value of angle C is calculated by applying cosine rule as shown below;
c² = a² + b² - 2ab cosC
The given parameters in the diagram;
length a = 22
length b = 18
c = 20
The value of angle C is calculated as;
20² = 22² + 18² - (2 x 22 x 18) cos C
792 cos C = 502
cos C = 502/792
cos C = 0.6334
C = arc cos (0.6334)
C = 50.67 ⁰
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