Answers
z / 4 = (16 + 4)/z
z^2 / 4 = 20
z^2 = 80
z = 4√5
Therefore the answer to this question is z = 4√5.
[tex]\Delta ABD\ and\ \Delta BCD\ are\ similar,\ therefore:\\\\\dfrac{y}{4}=\dfrac{16}{y}\ \ \ \ |cross\ multiply\\\\y\cdot y=4\cdot16\\\\y^2=64\to y=\sqrt{64}\to y=8[/tex]
Use Pythagorean theory:
[tex]z^2=4^2+8^2\\\\z^2=16+64\\\\z^2=80\to z=\sqrt{80}\\\\z=\sqrt{16\cdot5}\\\\z=\sqrt{16}\cdot\sqrt5\\\\\boxed{z=4\sqrt5}[/tex]
Related Questions
It costs $5.75 to enter an arcade and $0.50 to play an arcade game. You have $7.25. Write an equation that represents the number g of games you can play.
Answers
Hope that helps
About 11 games
What is the equivalent decimal? Drag the answer into the box to match the fraction. 5/45
Answers
what you do is divide 5 into 45 to make it a decimal
An earthquake strikes and an isolated area is without food or water. three crews arrive. one can dispense needed supplies in 4545 hours, a second in 9090 hours, and a third in 6060 hours. how long will it take all three crews working together to dispense food and water?
Answers
1 person takes 20h, the second would hake 30h, third 60h.
1/20+1/30+1/60=1/10
Calculate the length of AC to one decimal?
Answers
As one side of the rectangle is given length of 4cm, the parallel other must also be equal to 4cm. Hence, Length of A to E is equal to 11cm-4cm=7cm.
Now, we use this length of 7 cm as this is opposite to our desired angle(a colored green) and by making 16cm our hypotenuse we find angle a to be 25.9°. [tex]sin x^{-1}(7/16)=25.9^{o} [/tex]
Next we find angle b by adding angle a with 90. hence getting 115.9°.
Finally we consider our triangle ABC to find the length of AC. We know one angle and length of two sides and can easily use cosine rule to find the remaining length AC. The equation and working is shown in diagram.
Answer= 18.1
The average age of the children at a campout is shown in the box plot below. Which statement is true about the box plot? The youngest age is 7. It is skewed right. More of the children were close to 12 years old than 6 years old. Half of the children were between 6 and 9 years old.
Answers
The statement that is true about the box plot is that: C. more of the children were close to 12 years old than 6 years old.
What is a Box Plot?A box plot shows how a data is distributed, as it displays the five-number summary.
here, we have,
The five-number summary of the box plot representing the average age of children is:
Min = 6 (youngest age)
Lower quartile (Q1) = 9 (25% of the children are below 9)
Median = 10
Upper quartile = 11 (50%, which is half of the children are between 9 years and 11 years old)
Max = 12 (oldest)
Therefore, the statement that is true about the box plot is that: C. more of the children were close to 12 years old than 6 years old.
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The members of a chorus agree to buy at least 250 tickets for and outside concert. They buy 20 fewer ow tickets that balcony tickets. What is the lowest number of balcony tickets bought
Answers
This is because you can set balcony equal to x and ow equal to x - 20. Then you can add them together and set equal to 250. Simplify and solve for x.
What are the similarities and differences between these data sets in terms of their centers and their variability?
Data Set A: 14, 21, 24, 28, 28, 35
Data Set B: 18, 19, 21, 25, 29, 32
Select from the drop-down menus to correctly complete the statements.
Comparing the centers of the data sets, the median for Data Set A is (less than, greater than, equal to) the median for Data Set B. The mean for Data Set A is (less than, greater than, equal to) the mean for Data Set B.
Answers
the mean for data A is greater.
Answer:
a
Step-by-step explanation:
y varies directly as x and y = 18 when x= 1/2. write an equation that relates y and x
Answers
Please help!!! Mark is learning to snowboard. The club charges $10 per hour for snowboard lessons and $40 for the lift ticket and a snowboard rental. Which value represents the rate of change for this scenario?
Answers
10h + 40
(40 represents, well $40)
Sina played basketball on a rectangular court that was 74 feet by 42 feet. after the game, she walked across the court diagonally from one corner to the opposite corner. approximately what distance did sina walk in feet?
Answers
Distance walked = 85.088 feet
The distance Sina walked would be equal to the length of the diagonal of rectangle.
As every angle in a rectangle is 90 degree. So, we can apply Pythagoras theorem in right triangle formed by sides,
Base- 74 feet, Altitude- 42 feet and Hypotenuse- Diagonal
Base^2 + Altitude ^ 2 = Hypotenuse ^2
74^2 + 42 ^ 2 = Diagonal ^2
On solving,
Diagonal = 85.088 feet
To calculate the distance Sina walked diagonally across the basketball court, we utilize the Pythagorean theorem using the court's length and width. The calculation gives us a diagonal distance of approximately 85 feet.
To calculate the distance Sina walked across the rectangular basketball court diagonally, we can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Since the court is 74 feet long and 42 feet wide, these dimensions can be considered the two shorter sides of a right triangle, with the diagonal Sina walked being the hypotenuse.
The Pythagorean theorem formula is:
[tex]c^2 = a^2 + b^2[/tex]
Where c is the length of the hypotenuse, and a and b are the lengths of the other two sides. Substituting the known values:
[tex]c^2 = 742 + 422\\c^2 = 5476 + 1764\\c^2 = 7240[/tex]
To find c, we take the square root of 7240:
c ≈ 85.09 feet
Therefore, Sina walked approximately 85 feet diagonally across the basketball court.
For an angle Θ with the point (12, −5) on its terminating side, what is the value of cosine?
−5
12
negative 5 over 13
12 over 13
Answers
opposite=-5
adjacent=12
thus using using Pythagorean theorem, the hypotenuse will be:
c^2=a^2+b^2
plugging the values we obtain:
c^2=(12)^2+(-5)^2
c^2=144+15
c^2=169
thus
c=13
but
cos θ=adjacent/ hypotenuse
therefore:
cos θ=12/13
Answer is option . D
There is a ratio of 5 girls to 3 boys in the class in the chorus.there are 24 boys in the chorus how many girls are in the chorus
Answers
Please help with geometry
Answers
[tex]\pi . {12}^{2} . \dfrac{300}{360} + {12}^{2} \dfrac{ \sqrt{3} }{4} \\ {12}^{2} ( \dfrac{5.\pi}{6} + \dfrac{ \sqrt{3} }{4} ) \\( 120\pi + 36 \sqrt{3} ) {cm}^{2} [/tex]
[tex]\dfrac{60^o}{360^o}=\dfrac{1}{6}[/tex]
The sector is 1/6 of the circle, therefore the area of the sector is 1/6 of area of the circle.
The formula of an area of the circle: [tex]A_O=\pi r^2[/tex]
The area of the sector:
[tex]A_s=\dfrac{1}{6}\cdot\pi\cdot12^2=\dfrac{1}{6}\pi\cdot144=24\pi\ m^2[/tex]
The formula of an area of the equilateral triangle: [tex]A_\Delta=\dfrac{a^2\sqrt3}{4}[/tex]
[tex]A_\Delta=\dfrac{12^2\sqrt3}{4}=\dfrac{144\sqrt3}{4}=36\sqrt3\ m^2[/tex]
The area of the segment: [tex]A_{sg}=A_s-A_\Delta\to A_{sg}=(24\pi-36\sqrt3)m^2[/tex]
The area of the shaded region:
[tex]A=A_O-A_{sg}\to A=144\pi-(24\pi-36\sqrt3)=144\pi-24\pi+36\sqrt3\\\\=\boxed{A=(120\pi+36\sqrt3)m^2}[/tex]
what is the complete factorization of the polynomial below
x^3-4x^2+x-4?
A. (x-4)(x+i)(x-1)
B. (x+4)(x+i)(x-i)
C. (x+4)(x-i)(x-i)
D. (x-4)(x-i)(x-i)
Answers
Answer:
B. (x+4)(x+i)(x-i)
Step-by-step explanation:
Let [tex]P(x)=x^3-4x^2+x-4[/tex]
We can factor this polynomial by grouping:
[tex]P(x)=x^2(x-4)+1(x-4)[/tex]
We factor further to obtain:
[tex]P(x)=(x^2+1)(x-4)[/tex]
[tex]P(x)=(x^2-\sqrt{-1}^2)(x-4)[/tex]
We apply difference of two squares to get:
[tex]P(x)=(x-i)(x+i)(x-4)[/tex]
Answer:
(x+1)(x-1)(x+4)
Step-by-step explanation:
A wood board is one of a 6 different parts in a shelf kit. the width, depth, and height dimensions of the board are 42 inches x 8 inches x .75 inches, respectively. the board is made from southern yellow pine, which has an air dry weight density of .021 lbs/in.3. (watch the units of measure)
Answers
A wood board is one of a 6 different parts in a shelf kit. the width, depth, and height dimensions of the board are 42 inches x 8 inches x .75 inches, respectively. the board is made from southern yellow pine, which has an air dry weight density of .021 lbs/in.3. (watch the units of measure)
1) What is the volume of the wood board? Precision = 0.00
2) What is the surface area of the wood board? Precision = 0.00
3)What is the weight of the wood board? Precision = 0.00
4) If one gallon of paint will cover 35,000 square inches, how many gallons would be needed to give two coats of paint to 15,000 boards? Round your answer to the nearest gallon
Part 1) What is the volume of the wood board? Precision = 0.00
we know that
volume=L*W*H-----> 42*8*0.75----> 252 in³
the answer Part 1) is 252 in³
Part 2) What is the surface area of the wood board? Precision = 0.00
surface area=2*area of the base+perimeter of the base*height
area of the base=42*8----> 336 in²
perimeter of the base=2*[42+8]----> 100 in
height=0.75 in
surface area=2*336+100*0.75----> 672+75----> 747 in²
the answer Part 2) is 747 in²
Part 3)What is the weight of the wood board? Precision = 0.00
we know that
density=mass/volume-----> mass=density*volume
density=0.021 lbs/in³
volume=252 in³
mass=0.021*252----> 5.292 lbs
the answer Part 3) is 5.29 lbs
Part 4) If one gallon of paint will cover 35,000 square inches, how many gallons would be needed to give two coats of paint to 15,000 boards? Round your answer to the nearest gallon
if 1 gallons cover------------> 35000 in²
x -----------------------> 747 in² (one board)
x=747/35000-----> x=0.021 gallons per 1 board
so
15000*0.021------> 320.14 gallons
but remember ------> two coats of paint
so
320.14*2-----> 640.28 gallons------> 640 gallons
the answer Part 4) is 640 gallons
The mass of a grain of sand is about 10^-3 gram. About how many grains of sand are in a 10kg bag of sand?
Answers
Divide the mass of the bag by the mass of sand. First you need to convert kg to g
About how many grains of sand are in the bag of sand
Answer
10 kg* (1000 g/ 1 kg)* (1 grain of sand/ 10^(-3) g)= 10^7 grains of sand.
(Note that the units cancel out so you get the answer)
The final answer is 10^7 grains of sand.
Hope this helps~
Find the number if the square root of another number that is 6 greater than this number is equal to the number itself.
Answers
Answer:
The number is 3 and the another number is 9
Step-by-step explanation:
Let
x-------> the number
y-----> another number
we know that
[tex]y=x+6[/tex] ----> equation A
[tex]\sqrt{y}=x[/tex] ----> equation B
Substitute equation A in equation B
[tex]\sqrt{x+6}=x[/tex]
squared both sides
[tex]x+6=x^{2} \\x^{2}-x-6=0[/tex]
Using a graphing tool
solve the quadratic equation
see the attached figure
The solution is x=3
Find the value of y
[tex]y=x+6[/tex] -------> [tex]y=3+6=9[/tex]
Jamal is 167 cm tall. Which expression finds Jamal’s height in dekameters? Use the metric table to help answer the question.
Answers
1 cm is equal to -----------> 0.001 dekameters
so
167 cm------------------> X
x=167*0.001------> x=0.167 dekameters
Expression to finds Jamal’s height in dekameters
[Jamal’s height in cm]*0.001 or [Jamal’s height in cm]/1000
Answer:
It is D
Step-by-step explanation:
Can somone help me with this 1 problem? QRST is a parallelogram. Determine the measure of ∠Q
Q (4x+10) bottom left
R (9x+1) top left
S (5x-3) top right
T bottom left
Answers
In a rhombus, opposite angles are congruent based on the alternate interior angle theorem. In other words, R and T along with Q and S are both alternate interior angle pairs.
(You can actually test this by printing out a rhombus, cutting out the angles, and matching up the opposite ones.)
We know that Q is equal to 4x + 10, but we need to solve for x. Since Q and S are congruent, we can set them equal to each other:
1) 4x + 10 = 5x - 3
2) 4x + 13 = 5x
3) 5x = 4x + 13
4) x = 13
Now let's plug 13 in for Q:
5) 4(13) + 10 = 52+10 = 62
I got m<Q = 62 degrees. Hope this helps!
In the parallelogram QRST then measure of ∠Q is 62 degrees.
What is Quadrilateral?A quadrilateral is a four-sided polygon, having four edges and four corners.
Given that QRST is a parallelogram.
We have to find the measure of ∠Q.
Both pairs of opposite sides are parallel, quadrilateral QRST is a parallelogram.
∠Q= ∠S
4x+10=5x-3
We have to find the value of to find ∠Q measure.
10+3=5x-4x
13=x
Now let us plug in the value of x in ∠Q measure.
∠Q = 4x+10
Now plug in x value in ∠Q
∠Q = 4(13)+10
=52+10
=62 degrees
Hence, in the parallelogram QRST then measure of ∠Q is 62 degrees.
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How many solutions does 15x+11=8x
Answers
How many solutions does 15x + 11 = 8x
Answer: 1 solution
-------------------------------------------------------------------------------------------------------
Explanation:
To solve this, we must isolate the x.
15x + 11 = 8x
We will subtract 15x from each side to isolate the x.
15x + 11 = 8x
- 15x -15x
11 = -7x
Finally, we must simplify this by dividing each side by -7
11 = -7x
--- ----
-7 -7
Our answer is: -11/7 = x
Ths means that this equation only has one solution.
I hope I helped!
Let me know if you need anything else!
~ Zoe
To get the number of solutions that the equation is giving, we are going to need to solve the equation. Here’s how to find the solution...
15x+11= 8x
If we collect it sorta like terms we are going to get:
11=8x-15x
11=-7x dividing both of the sides by -7 we get:
x=-7/11
The number of solutions you have is 1. So your answer would be one.
In ΔPQR, what is sin Q written as a decimal?
Answers
sin Q = 9/15
sin Q = 0.6
The sine of an angle is opposite over hypotenuse. Looking at angle Q, we know the opposite side is 9 and the hypotenuse is 15. These numbers give us this equation: sin Q = 9/15. Upon solving this equation, the result is approximately 56.5.
Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
PLEASE HELP 20 POINTS
Answers
A sample of Bromine-82 begins at 80 mL. We are given that this value will decrease by half of its current amount every 35 hours. First, we'll determine the number of times that 35 goes into 140. This will reveal the number of times we should divide the sample by 2:
140 ÷ 35 = 4
We have now proven that there are 4 periods of 35 hours in 140 hours. This means that we will divide the sample in half a total of 4 times, as follows:
1. 80 ÷ 2 = 40
2. 40 ÷ 2 = 20
3. 20 ÷ 2 = 10
4. 10 ÷ 2 = 5
We have now proven that an 80 mL sample of Bromine-82 will be reduced to only 5 mL after 140 hours. Therefore, the correct answer is 5 mL.
I hope this helps!
[tex]A = P( \frac{1}{2} )^{\frac{t}{h} } [/tex]
This is what it looks like with the values from this scenario plugged in:
[tex]A = 80( \frac{1}{2} )^{\frac{140}{35} } \\ A = 5[/tex]
There are 5 mL of the 80 mL Bromine sample left after 140 hours.
What's the probability a number is odd given that it's an integer between 0 and 11?
Answers
sample space=s={1,2,3....,10}=total 10 numbers
So,
m=total no. of odd numbers{1,3,5,7,9} in our sample space=5 numbers
probability that number is odd=p=m/s
p=5/10=0.5
Ellen needs to buy 180 inches of ribbon to wrap a present. The store sells ribbon only in whole yards. How many yards does Ellen need to buy to have enough ribbion
Answers
Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
r = 5 + 4 cos θ
Answers
Explaining how to determine the symmetry of a polar graph based on the given equation r = 5 + 4 cos θ.
To determine the symmetry of the graph r = 5 + 4 cos θ, we can substitute (-θ) for θ in the equation and check if the resulting polar equation remains the same, indicating symmetry about the origin.
If replacing (-θ) gives us the same equation, the graph is symmetric about the y-axis. If replacing (π - θ) gives the same equation, then the graph is symmetric about the x-axis.
In this case, replacing (-θ) in r = 5 + 4 cos θ gives r = 5 + 4 cos(-θ), which simplifies to r = 5 + 4 cos θ, indicating symmetry about the y-axis.
40 points!!!!!!!!!!!!!! *If one of the legs of a right triangle is 4 in and the hypotenuse is 8 in, find the length of the other leg (use a calculator if necessary). Can you guess the measures of the acute angles?
Answers
the ratio of the sides of the triangle = 8 : 4 :4 sqrt3 = 2:1:sqrt3 so this is a
30-60-90 degree triangle
A distribution of numbers has the following five-number summary:
20.2, 22.4, 30.0, 37.6, 39.8
True or False? These numbers can be used to calculate the standard deviation of the distribution.
Please Answer quickly! I need this done ASAP! Please.
Answers
The correct answer is:
False.
Explanation:
Using the five number summary, we can estimate the standard deviation.
The quartiles are about 0.67 standard deviations from the mean; this could be used to estimate the standard deviation.
However, we cannot accurately calculate the standard deviation using only the fie number summary.
A boy flies a kite with a 100-foot-long string. The angle of elevation of the string is 48°. Find the vertical distance between the kite and the point at which the boy is holding the string.
Answers
sinθ=opposite/hypotenuse
where:
θ=48°
opposite=h
hypotenuse=100 ft
thus
sin 48=h/100
hence
h=100 sin48
h=74.315 ft
Answer: 74.315 ft
Using the sine function of trigonometry, the vertical distance between the kite and the point where the boy is holding the string is calculated to be approximately 74.31 feet when the string's angle of elevation is 48 degrees.
To find the vertical distance between the kite and the point at which the boy is holding the string, we can use trigonometric functions, specifically the sine function which is defined as the ratio of the opposite side to the hypotenuse in a right triangle. Since we know the length of the string, which acts as the hypotenuse of the triangle, and the angle of elevation, we can set up our equation as follows:s
sin(48°) = opposite/hypotenuse
sin(48°) = vertical distance/100 feet
W then multiply both sides by the hypotenuse (100 feet) to solve for the vertical distance:
vertical distance = 100 feet \sin(48°)
To get the numerical value, we use a calculator to find:
vertical distance ≈ 100 feet * 0.7431
vertical distance ≈ 74.31 feet
Therefore, the vertical distance between the kite and the point where the boy is holding the string is approximately 74.31 feet.
If the surface area of a sphere is 256π cm2, what is the radius?
4 cm
8 cm
12 cm
16 cm
Answers
If you rearrange the equation for surface area to solve for r then you can plug the 256pi into the equation and get 8.
The formula for surface area of the sphere is -
Surface area of sphere = 4πr²
Now, the surface area of sphere is given to us as = 256π cm²
Thus,
4πr² = 256π cm²
While equating the equations, we will get
4r² = 256 cm²
r² = 64 cm²
64 is the square of 8, thus the radius of sphere will be = 8 cm.
The correct answer will be = 8 cm radius
In a factory, a parabolic mirror to be used in a searchlight was placed on the floor. It measured 40 cm tall and 90 cm wide. Find an equation of the parabola with its vertex at the origin.
Answers
point on the parabola:(45,40)
equation:
45^2=4p(40)
4p=45^2/40=40.625
thus
x^2=(50.625)y
Answer: x^2=(50.625)y