For this case we have to, by definition:
[tex]cos (F) = \frac {h} {26.4}[/tex]
This means that, the cosine of the angle F, will be equal to the leg adjacent to the angle on the hypotenuse of the triangle.
So, by clearing h we have:
[tex]h = 26.4 * cos (35)\\h = 26.4 * 0.81915204\\h = 21.6256[/tex]
Rounding out the value of h we have:
[tex]h = 21.6[/tex]
Answer:
Option B
Answer:
The correct answer is option b. 21.6
Step-by-step explanation:
Points to remember:-
Trigonometric ratio
Cos θ = adjacent side/Hypotenuse
From the figure we can see a right triangle triangle FGH.
To find the value of h
It is given that, g=26.4 and F= 35°
Cos F = adjacent side/Hypotenuse
Cos 35 = adjacent side/Hypotenuse
= FG/FH = h/g
h = g * Cos F = 26.4 * Cos 54 = 26.4 * 0.8191 = 21.62 ≈ 21.6
Therefore the correct answer is option b. 21.6
A rectangular prism is 4 meters long, 5 meters wide, and has a height of 7 meters. What is its surface area?
a.140 m2
b.166 m2
c.84 m2
d.70 m2
Answer:
5 by 4 face = 20 * 2 = 40
5 by 7 face = 35 * 2 = 70
4 by 7 face = 28 * 2 = 56
Total surface area = 166 square meters
Answer is "b"
Step-by-step explanation:
Answer:
your answer will be A
There are 1,000 meters in 1 kilometer. Convert 5,000 meters to kilometers. A) 0.5 km B) 5 km C) 50 km D) 500 km
Answer:
5,000 meters * 1 kilometer / 1,000 meters = 5 kilometers answer is B
Step-by-step explanation:
Answer:
the answer is 5k
Step-by-step explanation:
What is the answer to the following problem:
1+1
Answer: 2
Step-by-step explanation:
add the 1 to the other 1 and it equals 2
Answer:
2
Step-by-step explanation:
1 and 1 is 2
Kevin ate 2 slices of cake. Ben ate 1 slice. If Kevin ate 2/6 of the cake and all the slices are the same size, what fraction of the cake was eaten in total
1/2 of the cake was eaten
1+2=3. 3/6=1/2
All the slices are the same size
The box plots below show student grades on the most recent exam compared to overall grades in the class:
Which of the following best describes the information about the medians?
a. The exam outlier at 60 makes the IQR narrower and the median higher.
b. The class data is more evenly spread, which pulls its median down.
c. The class median is lower than the exam median.
d. The class Q3 is higher than the exam Q3.
i dunno man, B looks about right.
Answer: c. The class median is lower than the exam median.
Step-by-step explanation:
the median is at a lower point on the number line, its to the left of the exam, so that means its lower
If the arc on a particular circle has an arc length of 14 inches, and the circumference of the circle is 84 inches, what is the angle measure of the arc?
A.
60°
B.
90°
C.
120°
D.
180°
Answer:
A
Step-by-step explanation:
The arc length formula is:
Arc Length = [tex]\frac{\theta}{360}*2\pi r[/tex]
Where
[tex]\theta[/tex] is the angle measure of the arc, and
2πr is the circumference
Putting 84 in place of circumference and 14 in place of arc length, we can solve for [tex]\theta[/tex]:
Arc Length = [tex]\frac{\theta}{360}*2\pi r[/tex]
14 = [tex]\frac{\theta}{360}*(84)[/tex]
14 = [tex]\frac{84\theta}{360}[/tex]
[tex]14*360=84\theta\\5040=84\theta\\\theta=\frac{5040}{84}=60[/tex]
answer choice A is right.
Given the similarity statement ΔDEF ∼ ΔXYZ, which side corresponds with ED?
A. EF
B. ZY
C. XZ
D. YX
YX is corresponding with ED
Hope it helps.
Please mark me brainliest
Which sequences are geometric? Check all that apply. 10, 7.5, 5.625, 4.21875, … 160, 40, 10, 2.5, … 20, 70, 245, 857.5, … 13, 16.5, 20, 23.5, … 5, 5.5, 6.05, 6.655, … 16, 17.1, 18.2, 19.3, …
The sequence that shows geometric progression are options A), B), C), and E) and this can be determined by finding the geometric ratio.
Check all the options in order to determine which sequence is the geometric sequence.
A) 10, 7.5, 5.625, 4.21875,...
Check from the geometric ratio whether the above sequence is a geometric sequence or not.
Ratio between first and second term:
[tex]\rm r =\dfrac{7.5}{10}[/tex]
r = 0.75
Ratio between second and third term:
[tex]\rm r =\dfrac{5.625}{7.5}[/tex]
r = 0.75
So, yes this sequence is in geometric progression.
B) 160, 40, 10, 2.5, …
Check from the geometric ratio whether the above sequence is a geometric sequence or not.
Ratio between first and second term:
[tex]\rm r =\dfrac{40}{160}[/tex]
r = 0.25
Ratio between second and third term:
[tex]\rm r =\dfrac{10}{40}[/tex]
r = 0.25
So, yes this sequence is in geometric progression.
C) 20, 70, 245, 857.5, …
Check from the geometric ratio whether the above sequence is a geometric sequence or not.
Ratio between first and second term:
[tex]\rm r =\dfrac{70}{20}[/tex]
r = 3.5
Ratio between third and fourth term:
[tex]\rm r =\dfrac{857.5}{245}[/tex]
r = 3.5
So, yes this sequence is in geometric progression.
D) 13, 16.5, 20, 23.5, …
Check from the geometric ratio whether the above sequence is a geometric sequence or not.
Ratio between first and second term:
[tex]\rm r =\dfrac{16.5}{13}[/tex]
r = 1.27
Ratio between third and fourth term:
[tex]\rm r =\dfrac{23.5}{20}[/tex]
r = 1.175
So, no this sequence is not in geometric progression.
E) 5, 5.5, 6.05, 6.655, …
Check from the geometric ratio whether the above sequence is a geometric sequence or not.
Ratio between first and second term:
[tex]\rm r =\dfrac{5.5}{5}[/tex]
r = 1.1
Ratio between third and fourth term:
[tex]\rm r =\dfrac{6.655}{6.05}[/tex]
r = 1.1
So, yes this sequence is in geometric progression.
F) 16, 17.1, 18.2, 19.3, …
Check from the geometric ratio whether the above sequence is a geometric sequence or not.
Ratio between first and second term:
[tex]\rm r =\dfrac{17.1}{16}[/tex]
r = 1.07
Ratio between third and fourth term:
[tex]\rm r =\dfrac{19.3}{18.2}[/tex]
r = 1.06
So, no this sequence is not in geometric progression.
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Answer:
1, 2, 3, 5
Step-by-step explanation:
Which of the following equations is the formula of f(x) = x^1/3 but shifted 4 units to the left and 4 units up?
A. [tex]f(x) = (x-4)^{1/3} +4[/tex]
B. [tex]f(x) = 4x^{1/3} -4[/tex]
C. [tex]f(x)=(x+4)^{1/3} +4[/tex]
D. [tex]f(x) = 4x^{1/3} +4[/tex]
Answer:
Hence correct chcie is C.
[tex]f\left(x\right)=(x+4)^{\frac{1}{3}}+4[/tex]
Step-by-step explanation:
Given function is [tex]f\left(x\right)=x^{\frac{1}{3}}[/tex]
Now it says that function is shifted 4 units to the left and 4 units up.
We need to find about which of the given choice is correct for the given transformation.
When f(x) is shifted "h" units left then we write f(x+h)
So [tex]f\left(x\right)=x^{\frac{1}{3}}[/tex] will change to
[tex]f\left(x\right)=(x+4)^{\frac{1}{3}}[/tex]
When f(x) is shifted "h" units up then we write f(x)+h
So [tex]f\left(x\right)=(x+4)^{\frac{1}{3}}[/tex] will change to
[tex]f\left(x\right)=(x+4)^{\frac{1}{3}}+4[/tex]
Answer:
C
Step-by-step explanation:
For a function f(x) = [tex]x^{\frac{1}{3}}[/tex], we have:
f(x) = [tex](x-b)^{\frac{1}{3}}[/tex] is original translated b units rightf(x) = [tex](x+b)^{\frac{1}{3}}[/tex] is original translated b units leftf(x) = [tex]x^{\frac{1}{3}}+c[/tex] is original translated c units upf(x) = [tex]x^{\frac{1}{3}}-c[/tex] is original translated c units downKeeping these translation rules in mind, we can clearly say that 4 units shifted left and 4 units up has the equation [tex]f(x)=(x+4)^{\frac{1}{3}}+4[/tex]
correct answer is C
How much carpet do I need for the Master Bedroom?
Answer:
The carpet needed is [tex]288\ units^{2}[/tex]
Step-by-step explanation:
we know that
The area of the master bedroom is the area of a rectangle
so
The area is equal to
[tex]A=bh[/tex]
we have
[tex]b=16\ units[/tex]
[tex]h=18\ units[/tex]
substitute
[tex]A=(16)(18)=288\ units^{2}[/tex]
therefore
The carpet needed is [tex]288\ units^{2}[/tex]
How many liters of pure water should be mixed with 18 liters of a 12% saline solution to make a saline solution that is 3% salt?
Four litres of pure water should be mixed with 18 litres of a 12% saline solution to make a saline solution that is 3% salt.
To find the litres of pure water mixed:
Given:
Pure water is mixed with 18 litres of a 12% saline solution to make a saline solution that is 3% salt.
Amount of pure water mixed =?
Now,
As given in the question, we have
18 litres of 12% saline solution
= 18 × (12/100)
= 2.16 litres
To make a saline solution containing 3% salt
Hence, four litres should be mixed to obtain a saline solution having 3% salt.
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y varies inversely as x. y = 12 when x = 7. Find y when x = 6.
hope it helps you!!!!!!!!!!!!!
Answer: Y=2 !! ;) XD ;P
Find the area of the composite figure. Round to the nearest hundredth.
**Cracks knuckles** let's do this.
Area of triangle = 31.25 yd^2
10 x 6.25 = 62.5
62.5 / 2 = 31.25
Area of rectangle A = 50 yd^2
10 (length) x 5 (7.5 - 2.5) (width) = 50
Area of rectangle B = 48.75 yd^2
7.5 x 6.5 = 48.75
Total area of composite = 130 yd^2
31.25 + 50 + 48.75 = 130
(08.06 MC) The distances (y), in miles, of two cars from their starting points at certain times (x), in hours, are shown by the equations below: Car A y = 55x + 32 Car B y = 42x + 58 After how many hours will the two cars be at the same distance from their starting point and what will that distance be? (5 points) 2 hours, 142 miles 2 hours, 145 miles 3 hours, 142 miles 3 hours, 145 miles
Answer:
2 hours, 142 miles
Step-by-step explanation:
Write a distance formula for both cars and then equate these formulas:
Car A: y = 55x + 32 = y = 42x + 58: Car B
Then 55x + 32 = y = 42x + 58 → 13x = 26, and so x = 2
That distance will be 55(2) + 32, or 142 miles.
The cars will reach the same point after 2 hours (first possible answer)
An equation is formed when two equal expressions. The correct option is A, 2hours, and 142 miles.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given the equation for the distance covered by car A in x hours is y = 55x + 32, similarly, the equation for the distance covered by Car B in x hours is y=42x+58.
Now, to know at what time and at what distance the two cars will meet we need to solve the two equations. Since the car will cover the same distance we can write,
y = y
55x + 32 = 42x + 58
55x - 42x = 58 - 32
13x = 26
x = 2
Substitute the value of x in any one of the equations,
y = 55x + 32
y = 55(2) + 32
y = 110 + 32
y = 142
Thus, the car will meet after 2 hours, and the distance will be 142 miles.
Hence, the correct option is A, 2hours, and 142 miles.
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which element is located at a32?
a=[6, 9, -1]
[0, 2, 4]
[7, 8, 2]
What kind of geometric transformation is shown in the music?
Will give BRAINLIEST.
Is this glide? I can't really see it. Thank you!
The geometric transformation shown in the figure is reflection.
What is Reflection?Reflection is a type of geometric transformation where the figure is flipped. In other words, a figure when undergoes reflection becomes it's mirror image.
here, we have,
Given is a set of lines in the music note.
Three line are drawn separating from a line.
In the first part, when we find the mirror image of the first part, we will get the second part.
Mirror images are found in the transformation of reflection.
So, here, we can say that reflection is the transformation here.
Hence the kind of geometric transformation shown in the line of music is reflection.
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The half-life of a certain substance is 20 years. How much of a 100 gram sample will be left after 20 years?
[tex]\bf \textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &100\\ t=\textit{elapsed time}\dotfill &20\\ h=\textit{half-life}\dotfill &20 \end{cases} \\\\\\ A=100\left( \frac{1}{2} \right)^{\frac{20}{20}}\implies A=100\left( \frac{1}{2} \right)^1\implies A=50[/tex]
50 grams of that sample will be left after 20 years since it’s only gone through one half-life exactly.
Can I get an explanation please.
Answer:
The correct option is letter D.
Step-by-step explanation:
We have the following expression:
sqrt(y^3) + sqrt(9y^3) - 3y*sqrt(y)
We now that sqrt(a*b) = sqrt(a)sqrt(b)
Applying this rule, we have:
sqrt(y^3) + sqrt(9y^3) - 3y*sqrt(y)
sqrt(y^3) + 3sqrt(y^3) - 3y*sqrt(y)
Also we know that a*sqrt(b) = sqrt(b*a^2)
Applying this we have:
sqrt(y^3) + 3sqrt(y^3) - 3y*sqrt(y) = sqrt(y^3) + 3sqrt(y^3) - 3sqrt(y^3)
Then the result is:
sqrt(y^3) + 3sqrt(y^3) - 3sqrt(y^3) = sqrt(y^3) = y*sqrt(y)
The correct option is letter D.
What is the surface area of the cube below?
A. 150 units^2
B. 75 units^2
C. 300 units^2
D. 50 units^2
ANSWER
A. 150 units^2
EXPLANATION
The surface area of a cube is calculated using the formula:
[tex]SA=6 {l}^{2} [/tex]
where
[tex]l = 5[/tex]
We substitute the length to obtain:
[tex]SA=6 {l}^{2} [/tex]
[tex]SA=6 \times {5}^{2} [/tex]
[tex]SA=150 \: {units}^{2} [/tex]
To the nearest hundredth, what is the value of x?
Answer:
1. We already have the measure of the hypotenuse and one out of two acute angle, therefore:
sin53° = x/45 => x = sin53° · 45 ≈35.94
2. We already have one out of two legs of the triangle and one acute angle so we know that:
tan27° = 48/x => x = 48/tan27° ≈ 94.21
The value of x in the first right angle triangle is 27.08.
The value of x in the second right angle triangle is 24.46.
What is the value of x?In order to determine the value of x in the first triangle, cos would be used.
Cos 53 = opposite / hypotenuse
Cos 53 = x / 45
0.7071 = x /45
x = 45 x 0.6018
x = 27.08
In order to determine the value of x in the second triangle, tan would be used.
Tan 27 = opposite / adjacent
Tan 27 = x / 48
x = 0.5095 x 48
x = 24.46
What is the area of the rhombus? The figure is not drawn to scale.
Answer:
126 cm²
Step-by-step explanation:
The area (A) of a rhombus is calculated as
A = [tex]\frac{1}{2}[/tex] × d₁ × d₂ ← diagonals
The diagonals of a rhombus are perpendicular bisectors of each other, thus
d₁ = 7 + 7 = 14 and d₂ = 9 + 9 = 18, hence
A = 0.5 × 14 × 18 = 126 cm²
The area of the rhombus is equal to 126 cm². The correct option is B.
What is an area of the rhombus?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rhombus in a two-dimensional plane is called the area of the rhombus.
The area (A) of a rhombus is calculated as
A = × d₁ × d₂ ← diagonals
The diagonals of a rhombus are perpendicular bisectors of each other,
d₁ = 7 + 7 = 14
d₂ = 9 + 9 = 18, hence
The area of the rhombus will be calculated as,
A = 0.5 × d₁ × d₂
A = 0.5 × 14 × 18
A = 126 cm²
Therefore, the area of the rhombus is equal to 126 cm². The correct option is B.
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Justin packed two suitcases for his trip and compared the weights of the items he packed in each of the suitcases. Which statement is true about the box plots? The data for suitcase 1 have an outlier. The data for suitcase 2 have an outlier. Suitcase 1 contains the lightest and heaviest item. Suitcase 2 contains the lightest and heaviest item.
Answer:
A
Step-by-step explanation:
Find the length of the hypotenuse.
18
9√2
√18
18√2
Answer:
18
Step-by-step explanation:
The hypotenuse is BC.
According to the Pythagorean Theorem;
[tex]BC^2=AC^2+AB^2[/tex]
Since the base angles are equal:
[tex]AC=BC=9\sqrt{2}[/tex]
We substitute the given values into the formula to obtain:
[tex]BC^2=AC^2+AB^2[/tex]
[tex]BC^2=(9\sqrt{2})^2+(9\sqrt{2})^2[/tex]
[tex]BC^2=81(2)+81(2)[/tex]
[tex]BC^2=162+162[/tex]
[tex]BC^2=324[/tex]
Take positive square root.
[tex]BC=\sqrt{324}[/tex]
[tex]BC=18[/tex]
Hence the hypotenuse is 18 units
what is the explicit formula for the geometric sequence with this recursive formula? a1=-7
an=an-1*(1/3)
A. an=- 1/3*7^(n-1)
B. an=1/3*(-7)*^(n-1)
C. an=7*(- 1/3)^(n-1)
D. an=-7*(1/3)^(n-1)
ANSWER
D. [tex]a_n= - 7( \frac{1}{3} )^{n - 1}[/tex]
EXPLANATION
The given explicit formula is
[tex]a_1= - 7[/tex]
and
[tex]a_n=\frac{1}{3} a_{n-1}[/tex]
This implies that,
[tex]r = \frac{1}{3} [/tex]
The explicit formula is given by:
[tex]a_n=a_{1}( \frac{1}{3} )^{n - 1} [/tex]
We substitute the known values to get;
[tex]a_n= - 7( \frac{1}{3} )^{n - 1}[/tex]
Answer:
D
Step-by-step explanation: A P E X
What is the surface area of the rectangular prism below?
A. 700 units^2
B. 1260 units^2
C. 823 units^2
D. 740 units^2
Answer:
The surface area of the rectangular prism is 700 units² ⇒ answer A
Step-by-step explanation:
* Lets revise how to find the surface are of the rectangular prism
- The rectangular prism has 6 rectangular faces
- Each two opposite faces are equal
- It has 4 side faces and 2 bases
* We can find the surface area of it by adding the area of
the 6 faces
- In the problem
# The dimensions of the bases are 12 units and 14 units
# The dimensions of the side faces are 12 units and 7 units,
14 units and 7 units
* Now lets find the area of each 2 equal faces
- In the bases
∵ Area of the rectangle = length × width
∴ The area of one base = 12 × 14 = 168 units²
∴ The area of the two bases = 2 × 168 = 336 units² ⇒ (1)
- In the two opposite faces with dimensions 12 units and 7 units
∵ The area of one face = 12 × 7 = 84 units²
∴ The area of the two faces = 2 × 84 = 168 unit² ⇒ (2)
- In the two opposite faces with dimensions 14 units and 7 units
∵ The area of one face = 14 × 7 = 98 units²
∴ The area of the two faces = 2 × 98 = 196 unit² ⇒ (3)
* To find the surface area of the prism add (1) , (2) , (3)
∴ The surface area of the prism = 336 + 168 + 196 = 700 units²
* The surface area of the rectangular prism is 700 units²
In a village of 3500 people, 12% are left handed, and 15% of the left hand are blonde hair. How many people in the village are blonde and left-handed?
In the village of 3500 people, 63 individuals are both left-handed and have blonde hair.
Explanation:To find out how many people in the village are both left-handed and have blonde hair, we first need to calculate the number of left-handed people, and then find 15% of that number to determine those who are also blonde.
Calculate the number of left-handed people: 12% of 3500 = 0.12 × 3500 = 420.Calculate the number of left-handed people who are blonde: 15% of 420 = 0.15 × 420 = 63.Therefore, 63 people in the village are both left-handed and blonde-haired.
Evaluate the expression −11−(−7−9) by rewriting the subtraction as addition
Answer:
5
Step-by-step explanation:
Let's rewrite this a bit.
[tex]-11-(-7-9)=-11+7+9[/tex]
This is because there is a -1 before the expression inside the parentheses, so every sign is reversed.
Now we can add.
[tex]-11+7+9=5[/tex]
Devon's mom ordered 3 pizzas for the girls slumber party to eat. The girls ate 5/2 of the pizza. How is this amount of pizza written as a mixed number?
A. 2 1/2
b. 2 1/5
C. 3
Answer:
2 1/2
Step-by-step explanation:
you have 2 whole pizzas and 1 half (1/2)
Claire purchases a new dress for the prom. The dress is priced $160, but it is on sale for 30% off. Claire's aunt works at the store and can give her an additional 10% off. If the sales tax is 7.5%, how much does Claire pay for the dress? a. $93.24 b. $103.20 c. $108.36 d. $120.40
The dress is originally 160$, but we take 30% off which is that same as .3 .
To find 30% or .3 of 160 we multiply 160 by .3 which gets us 48.
48 is 30% of 160 so to find the new price of the dress we need to subtract
160 - 48 = 112. The new price of the dress is 112$.
Since Claire's aunt works at the store Claire will get an additional 10% off from the "new" price which is 112$. 10% is also .1, so we will multiply 112 by .1 which equals 11.20.
As 10% of 112 is 11.20 so we will subtract 11 dollars and 20 cents from the price. 112 - 11.20 = 100.80$.
For sales tax we will do the same thing, multiply 100.80 by .075 which equals 7.56. This time since we are ADDING sales tax, we will add 100.80 and 7.56 rather than subtract. 100.80 + 7.56 = 108.36.
Claire will be paying 108.36$ for the prom dress.
Answer:
c
Step-by-step explanation:
Which algebraic expression represents the phrase "two times the quantity of a number minus 12"? A. 2y - 12 B. 2(y -12) C. 2(y + 12) D. 2y + 12
Answer:
B
Step-by-step explanation:
Two times the quantity of a number minus 12.
Represent the number with the variable y.
The quantity of a number minus 12 is then: (y-12).
Two times this quantity is 2(y-12).
So the answer is 2(y-12), which is B.