Answers
The equations representing the proportional relationships between two variables:
k = 5 · hk = (5 / 4) · hk = (1 / 5) · hWhat are the equations of proportional relationship for each table of values?
In this problem we find three cases of tables showing proportional relationships between two variables. Proportional relationships are represented by equations of the form:
y = k · x
Where:
x - Independent variable.y - Dependent variable.k - Proportionality factor.Each table represents a proportional relationship if and only if each pair of variables has one and same proportionality factor. After a quick inspection, we find the following features:
The first table has a proportionality factor of 5. The equation is k = 5 · h.The second table has a proportionality factor of 5 / 4. The equation of k = (5 / 4) · h.The third table has a proportionality factor of 1 / 5. The equation of k = (1 / 5) · h.To learn more on proportional relationships: https://brainly.com/question/12917806
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Related Questions
(g) (4 5)(2 -1)
(h) (2 6)(-3 -4)
(i) (1 2)(4 6 5 7)
(j) (0 5)(3 6 4 1)
Answers
22-7
8:8
2/3
Thats the prababek answer but not Herę
At noon, ship A is 10 nautical miles due west of ship B. Ship A is sailing west at 16 knots and ship B is sailing north at 21 knots. How fast (in knots) is the distance between the ships changing at 4 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)
Answers
At [tex]$5 \mathrm{pm}$[/tex] the distance between the ships is changing at the speed of [tex]$\mathbf{3 0 . 2 1}$[/tex] knots
Firstly we need to an equation to represent both ships and the distance between each. A is moving [tex]$25 \mathrm{knots}$[/tex] west and [tex]$B$[/tex] is moving [tex]$17 \mathrm{knot}$[/tex] north. [tex]$D$[/tex]will be the distance between the two. Drawing it, you'll notice that it creates a right triangle.
So we use the Pythagorean Theorem:
[tex]$$D^{\wedge} 2=A^{\wedge} 2+B^{\wedge} 2$$[/tex]
Differentiate in relation to time:
[tex]$$2 \mathrm{D}(\mathrm{dD} / \mathrm{dt})=2 \mathrm{~A}(\mathrm{dA} / \mathrm{dt})+2 \mathrm{~B}(\mathrm{~dB} / \mathrm{dt})$$[/tex]
Now we must find all of our variables.
[tex]& A=\text { time(speed })+\text { original distance }=5(25)+10=135 \\[/tex]
[tex]& B=5(17)+0=85 \\[/tex]
[tex]& D=V\left(A^{\wedge} 2+B^{\wedge} 2\right)=159.53 \\[/tex]
[tex]& d A / d t=25 \\[/tex]
[tex]& d B / d t=17[/tex]
Plug in all your variables and solve for
[tex]$(\mathrm{dD} / \mathrm{dt})$ :[/tex]
[tex]& 2 \mathrm{D}(\mathrm{dD} / \mathrm{dt})=2 \mathrm{~A}(\mathrm{dA} / \mathrm{dt})+2 \mathrm{~B}(\mathrm{~dB} / \mathrm{dt}) \\[/tex]
[tex]& 2(159.53)(\mathrm{dD} / \mathrm{dt})=2(135)(25)+2(85)(17) \\[/tex]
[tex]& 319.061(\mathrm{dD} / \mathrm{dt})=9640 \\[/tex]
[tex]& \mathrm{dD} / \mathrm{dt}=9640 / 319.061 \\[/tex]
[tex]& \mathrm{dD} / \mathrm{dt}=30.21 \text { knots }\end{aligned}[/tex]
At [tex]$5 \mathrm{pm}$[/tex] the distance between the ships is changing at the speed of [tex]$\mathbf{3 0 . 2 1}$[/tex] knots
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An arch has the shape of a semi-ellipse (the top half of an ellipse). The arch has a height of 6 feet and a span of 22 feet. Find an equation for the ellipse. (Assume a center at (0, 0)). Use the equation to find the height of the arch at a distance of 3 feet from the center. (Round your answer to two decimal places.)
Answers
The equation of ellipse is [tex]\frac{x^2}{11^2} + \frac{y^2}{6^2} = 1[/tex] and height of arch is 5.77 feet
Assume that the center of the ellipse is at the origin.
So, The general equation for an ellipse is:
[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1[/tex]
Where:
x is Horizontal distance, in feet.
y is Vertical distance, in feet.
a is Horizontal semiaxis length (half-width), in feet.
and b is Vertical semiaxis length (height), in feet.
According to the question,
x = 3 , a = 11 and b = 6
Putting all the values ,
So , the equation of ellipse will be
[tex]\frac{x^2}{11^2} + \frac{y^2}{6^2} = 1[/tex]
Putting x = 3,
[tex]\frac{3^2}{11^2} + \frac{y^2}{6^2} = 1[/tex]
Solving for y,
[tex]\frac{y^2}{36} = 1 - \frac{9}{121}[/tex]
=> [tex]y^2 = \frac{(121 - 9)36}{121}[/tex]
=> y² = 4032 / 121
=> y = √33.32
=> y = 5.77 feet
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Graph the compound inequality on the number line
x ≤-6 or x≥6
Answers
Answer:
I think like this but I not sure what format you learn
A large container holds 4.7 gallon of water. Use the following information to convert this amount of water to liters.1 gallon =4 quarts 1L =1.057 quarts
Answers
Answer:
Step-by-step explanation:
To convert the amount of water in gallons to liters, we need to first convert the number of gallons to quarts and then convert the number of quarts to liters.We know that 1 gallon is equal to 4 quarts, so 4.7 gallons is equal to 4.7 gallons * 4 quarts/gallon = 4.7*4=18.8 quarts.We also know that 1 liter is equal to 1.057 quarts, so to convert the number of quarts to liters, we can divide the number of quarts by 1.057 quarts/liter: 18.8 quarts / 1.057 quarts/liter = 18.8/1.057=17.8 liters.Therefore, 4.7 gallons is equal to 17.8 liters.
Compare the monthly payments and total loan costs for the following pairs of loan options. Assume that both loans are fixed rate and have the same closing costs.
You need a $160,000 loan.
Option 1: a 30-year loan at an APR of 10%
Option 2: a 15-year loan at an APR of 9.5%
Find the monthly payment for each option.
The monthly payment for option 1 is $___
The monthly payment for option 2 is $___
Answers
Monthly payment option 1 = $300,000 / 166.79161 = $1,798.65 and the monthly payment option 2 = $300,000 / 130.7201 = $2,294.98.
How to calculate the monthly payment?The numbers are missing, so I looked for similar questions to fill in the blanks:
You need a $300,000 loan. Option 1: a 30-year loan at an APR of 6%. Option 2: a 15-year loan at an APR of 4.5%.
We can use the present value of an annuity formula to calculate monthly payments.
Present value = monthly payment x PV annuity factor
Monthly payment = present value / PV annuity factor
Present value = $300,000
Option 1: PV annuity factor, 0.5%, 360 periods = 166.79161
Option 2: PV annuity factor, 0.375%, 180 periods = 130.7201
Monthly payment option 1 = $300,000 / 166.79161 = $1,798.65
Monthly payment option 2 = $300,000 / 130.7201 = $2,294.98
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Income taxes that are withheld from employees' pay and not remitted as of the balance sheet date will constituted a ____________ to be verified by the auditors.
Answers
Income taxes that are withheld from employees' pay and not remitted as of the balance sheet date will constituted a liability to be verified by the auditors.
A tax placed on people or organizations in relation to their income or profits is known as an income tax. Tax rates multiplied by taxable income are typically used to calculate income taxes.
Tax rates might change depending on the taxpayer's attributes and source of income. As taxable income rises, the tax rate can also. Corporate tax, which is often assessed at a fixed rate, is the name given to the tax charged on businesses. Individual income is frequently subject to progressive taxation.
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if sinθ 1÷2 and θ is in quadrant , evaluate each expression. a) sin 2θ b) cos 2θ c) tan 2θ
Answers
The values of sin 2θ, cos 2θ, and tan 2θ are:
a) sin 2θ = √(3)/2
b) cos 2θ = 1/2
c) tan 2θ = √(3)
What is a quadrant?Generally, If sin θ = 1/2 and θ is in quadrant I, then θ is equal to 30 degrees.
To evaluate each expression, we can use the trigonometric identities:
a) sin 2θ = 2 * sin θ * cos θ
= 2 * (1/2) * (√(3)/2)
= √(3)/2
b) cos 2θ = cos^2 θ - sin^2 θ
= (√(3)/2)^2 - (1/2)^2
= (3-1)/4 = 1/2
c) tan 2θ = (2 * tan θ) / (1 - tan^2 θ)
= (2 * (√(3)/3)) / (1 - (√(3)/3)^2)
= 2 * √(3) / (4 - 3)
= √(3)
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Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels 18 miles per hour slower than the westbound train. If the two trains are 320 miles apart after 2 hours, what is the rate of the eastbound train?
Answers
Answer:
71 mph
Step-by-step explanation:
Lets call the speed of the eastbound train E and the speed of the westbound train W.
E = W - 18
distance travelled = speed * time
thus
Wt + Et = 320
Wt + (W - 18)t = 320
factor out t
t * (2W - 18) = 320
t = 2 hours
2 * (2W - 18) = 320
2W - 18 = 160
2W = 178
W = 89
Then, E = (89) - 18 = 71 mph
The average person burns approximately 221 calories per half-hour while bicycling. If a person
does 2 hours of bicycling per day then how many calories will they burn in a week if they work
out 5 days a week?
Answers
Write an equation for a line passing through points (-2,3) and (3,5)
Answers
Answer:
[tex]y=\frac{2}{5}x+\frac{31}{5}[/tex]
Step-by-step explanation:
The slope of the line is [tex]\frac{3-5}{-2-3}=-\frac{2}{5}[/tex].
So, the equation is:
[tex]y-5=-\frac{2}{5}(x-3) \\ \\ y-5=-\frac{2}{5}x+\frac{6}{5} \\ \\ y=\frac{2}{5}x+\frac{31}{5}[/tex]
Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
h(p) =
p − 4 /
p^2 + 5
Answers
The critical points of the given function are p = 2 ± √13.
What are functions?A relation between a collection of inputs and outputs is known as a function.
A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
Each function has a range, codomain, and domain.
Critical function:
The key points are locations inside the function's domain where the function's nature changes.
The function stops increasing or decreasing at these places.
The function is: [tex]h(p)=\frac{p-2}{p^2+9}[/tex]
The derivative test will be applied here:
[tex]\begin{aligned}& \therefore h^{\prime}(p)=0 \\& \Rightarrow \frac{d}{d p}\left(\frac{p-2}{p^2+9}\right)=0 \\& \Rightarrow \frac{\frac{d}{d p}(p-2)\left(p^2+9\right)-\frac{d}{d p}\left(p^2+9\right)(p-2)}{\left(p^2+9\right)^2}=0 \\& \Rightarrow \frac{1 \cdot\left(p^2+9\right)-2 p(p-2)}{\left(p^2+9\right)^2}=0 \\& \Rightarrow \frac{-p^2+4 p+9}{\left(p^2+9\right)^2}=0 \\& \Rightarrow-p^2+4 p+9=0\end{aligned}[/tex]
Then,
[tex]\begin{aligned}& \Rightarrow p_{1,2}=\frac{-4 \pm \sqrt{4^2-4(-1) 9}}{2(-1)} \\& \Rightarrow p_{1,2}=\frac{-4 \pm \sqrt{52}}{-2} \\& \Rightarrow p_{1,2}=-\frac{-4 \pm \sqrt{52}}{2} \\& \Rightarrow p_{1,2}=-\frac{-4 \pm 2 \sqrt{13}}{2} \\& \Rightarrow p_{1,2}=2 \pm \sqrt{13}\end{aligned}[/tex]
Therefore, the critical points of the given function are p = 2 ± √13.
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Solve
3 x+10=14 y
8 x-7 y=34
Answers
Answer:
x = 6, y = 2
Step-by-step explanation:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Which expression is equivalent to √80
4√2·√5
√2⁴.√5
√2.√2.√5
√2².√2².√5²
Answers
As we can solve the square root 80 or [tex]\sqrt{80\\}[/tex] = [tex]\sqrt{2^4}.\sqrt{5}[/tex]
so [tex]\sqrt{2^4}.\sqrt{5}[/tex] is the correct answer for square root 80
What is Square root?
The component of a number that, when multiplied by itself, yields the original number is known as the square root of the number. Special exponents include squares and square roots. Think about the number 9. When the number 3 is multiplied by itself, the result is 9. This can be expressed as either 32 or 3 3. We refer to this as a square since there is a 2 exponent. When the exponent is now 1/2, the square root of the integer is being discussed. For instance, when n is a positive integer, n = n1/2
The value of a number's power 1/2 is the number's square root. It is the number whose product by itself yields the original number, to put it another way. It is symbolised by the character "." The number behind the square root sign is referred to as the radicand, whereas the square root symbol itself is known as a radical.
1)
[tex]\sqrt[4]{2} .\sqrt{5}[/tex] =[tex]2^{\frac{1}{4} } .\sqrt{5}[/tex]
which is not equal to [tex]\sqrt{80\\}[/tex]
2)
[tex]\sqrt{2^4}.\sqrt{5}[/tex] = [tex]2^{4.\frac{1}{2} } .\sqrt{5}[/tex]
=[tex]4\sqrt{5}[/tex] or[tex]\sqrt{16 * 5} =\sqrt{80}[/tex]
3)
[tex]\sqrt{2}. \sqrt{2}. \sqrt{5} =2\sqrt{5}[/tex]
which is not equal to [tex]\sqrt{80\\}[/tex]
4)
[tex]\sqrt{2^{2} } .\sqrt{2^{2} } .\sqrt{5^{2} } = 2.2.5 \\\\\4.5 = 20[/tex]
which is not equal to [tex]\sqrt{80\\}[/tex]
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A small box measures 6in by 11in by 13 in high. Find the volume of the box.
Answers
The volume of the box is 858 cube inches.
What is a cuboid?A cuboid is a three-dimensional solid shape that has 6 faces, 8 vertices, and 12 edges. It is one of the most commonly seen shapes around us which has three dimensions: length, width, and height
length of box = 13 inches
Width of box = 11 inches
height of box = 6 inches
Volume of cuboid = length x width x height
volume of cuboid = 13 x 11 x 6 which is 858 cube inches
In conclusion the volume of the box is 858 cube inches
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Write an equation of the line that passes through the given points.
(−7,0),(−7,5)
Answers
The given points form an equation for a line that has a value of 14.
How do you determine the equation of a line that goes through two points?Utilize the slope formula to determine the slope. To determine the y-intercept, use the slope and one of the points (b). Once you are aware of the values for m and b, you can enter these values into the slope-intercept form of a line (y = mx + b) to obtain the equation for the line.The equation that depicts the line that crosses the coordinates (-7 , 0) and (-7, 5).A line's equation is y=mx+c. Since you have two points, you may use the formula m=y2y1x2x1 to determine the slope.Explanation:
m =( -5 - -7)(0 - -7)
= 2*7
= 14.
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. If F F G H text is a rhombus, find each missing value
J G=
F J=
m ∠ E F H=
m ∠H G E=
2. If J K Z If is a square, find each missing value
J L=
M A=
m ∠ R N L=
R∠ M E U=
Answers
The value of JG = 24,
FJ = 7,
∠EFH = 74°,
∠HGE = 16°
What are the properties of a diagonal of rhombus?
In a rhombus, diagonals bisect each other at right angles. Diagonals bisect the angles of a rhombus. The sum of two adjacent angles is equal to 180 degrees. You will get a rectangle when you join the midpoint of the sides.
Solution:
Given :
EJ = 24
∴ GJ = 24
∠FHG = 74°
∴ ∠EFH = 74° by alternate angle properties
Now, we know
FG² =FJ² + GJ² - 2FJ × GJ × cos(90) ------ diagonals of the rhombus are perpendicular to each other
Substitute FG = 25, GJ = 24, we get
25² = FJ² + 24² - 2FJ × GJ × cos(90)
FJ² = 49
∴FJ = 7
180 =∠GHJ +∠HGJ + ∠GJH ------ sum of all angles of a triangle is 180°
∴ ∠HGE = ∠HGJ = 180 - 90 - 74
∴ ∠HGE = 16°
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2. The value of JL = 14
ML = 7√2
∠KNL = 90°
∠MKJ = 45°
What are the properties of diagonals of a square?
The diagonals of the square bisect each other at 90°.The two diagonals of the square are equal to each other. The diagonal of the square divide it into two similar isosceles triangles.
Solution:
Given; NM = 7
We know that diagonals of the square are equal
∴ NM = NL = NK = NJ = 7
∵ JL = JN + NL
∴ JL = 7 + 7
∴JL = 14
∠KNL = 90° ----- as we know that diagonals bisect each other at 90°
For ∠MKJ
we know that KM = KN + NM = 14
KJ = JM = 7√2------- property of isosceles triangle
∠KJM = 90° ----- all angles of square are 90°
We know that diagonals of a square dissects the square into two equal isosceles triangle.
∴ ∠MKJ = JMK = ∠KJM/2
∴ ∠MKJ = 90/2
∴ ∠MKJ = 45°
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The value of JG = 24 , FJ = 7, ∠EFH = 74°, ∠HGE = 16°
What are the properties of a diagonal of rhombus?
In a rhombus, diagonals bisect each other at right angles. Diagonals bisect the angles of a rhombus. The sum of two adjacent angles is equal to 180 degrees. You will get a rectangle when you join the midpoint of the sides.
Given :
EJ = 24
∴ GJ = 24
∠FHG = 74°
∴ ∠EFH = 74° by alternate angle properties
Now, we know
FG² =FJ² + GJ² - 2FJ × GJ × cos(90) ------ diagonals of the rhombus are perpendicular to each other
Substitute FG = 25, GJ = 24, we get
25² = FJ² + 24² - 2FJ × GJ × cos(90)
FJ² = 49
∴FJ = 7
180 =∠GHJ +∠HGJ + ∠GJH ------ sum of all angles of a triangle is 180°
∴ ∠HGE = ∠HGJ = 180 - 90 - 74
∴ ∠HGE = 16°
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2. The value of JL = 14
ML = 7√2
∠KNL = 90°
∠MKJ = 45°
What are the properties of diagonals of a square?The diagonals of the square bisect each other at 90°.The two diagonals of the square are equal to each other. The diagonal of the square divide it into two similar isosceles triangles.
Given; NM = 7
We know that diagonals of the square are equal
∴ NM = NL = NK = NJ = 7
∵ JL = JN + NL
∴ JL = 7 + 7
∴JL = 14
∠KNL = 90° ----- as we know that diagonals bisect each other at 90°
For ∠MKJ
we know that KM = KN + NM = 14
KJ = JM = 7√2------- property of isosceles triangle
∠KJM = 90° ----- all angles of square are 90°
We know that diagonals of a square dissects the square into two equal isosceles triangle.
∴ ∠MKJ = JMK = ∠KJM/2
∴ ∠MKJ = 90/2
∴ ∠MKJ = 45°
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Solve the equation -128 = 4x for x
-124
132
-32
32
Answers
x= -32.
Step-by-step explanation:1. Write the expresion.[tex]-128 = 4x[/tex]
2. Divide both sides by 4.[tex]\frac{-128}{4} = \frac{4x}{4} \\\\-32=x\\ \\x=-32[/tex]
A school hockey team was given a budget at the start of
the year. The team used 60% of the money for uniforms,
10% for equipment, and 30% for travel. Which circle
graph shows this information?
Answers
The circle which shows the distribution of the money has been attached.
What is a circle?A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.
In our daily life, we always see circular objects for example our bike wheel.
As per the given,
The team used 60% of the money for uniforms,10% for equipment, and 30% for travel.
60% of the area of the circle is used for uniforms.
10% of the area of the circle is used for equipment.
30% of the area of the circle is used for travel.
Hence "The attached circle depicts how the funds were distributed.".
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A train travels for 3.75 hours at 80 miles an hour. Use the formula d = r. t, where
d = distance, r = rate, and t = time, to find the distance the train traveled.
The distance traveled is
miles.
The solution is
Answers
Distance travelled is 300 miles
What is distance ?The total movement of an object, independent of direction, is its distance. The amount of space that an object has traveled, regardless of where it started or ended, is referred to as distance.
According to the given information
You know the equation: D = r × t.
where D represents the distance traveled, r is the train's speed, and t denotes the amount of time (in hours) required.
Train travels for 3.75 hours at 80 miles per hour
By putting the values in the above equation
D = 80 miles in 3.75 hours per hour
= 80 × 3.75
= 300 miles
Distance travelled is 300 miles
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Need help please:
show that the two quadrilaterals are congruent
Answers
The two quadrilaterals JKLQ and LMNP are congruent.
What is congruent quadrilaterals?
You will always have two opposite pairs of parallel sides if the two pairs of opposite sides in a quadrilateral are congruent. They must measure similarly to be considered congruent. Consider this: two congruent sides must always maintain the same separation between the opposing lines to maintain the other pair of opposite sides.
To prove that all corresponding pairs of sides and angles are congruent, you must put the interior angles and sides of one quadrilateral in correspondence with those of another.
For the given quadrilaterals JKLQ and LMNP it is given that,
JK ≅ MN, JQ ≅ NP, QL ≅ PL and KL ≅ ML
Also,
∠J ≅ ∠N, ∠Q ≅ ∠P, ∠K ≅ ∠M, and ∠L is the common for both quadrilaterals.
Here the corresponding sides and angles of the quadrilaterals are congruent.
Hence, the two quadrilaterals JKLQ and LMNP are congruent.
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Emma needs to order liquid fertilizer for her landscaping company. She plans to keep the fertilizer in a large cylindrical storage tank, but isn’t sure how much it will hold. The tank is 10 feet tall and the circular base has a radius of 5 feet. What is the volume of her storage tank?
Answers
It is to be noted that the volume of Emma's storage tank is: 785.3cubic feet.
What is the rationale for the above calculation?
Start by calculating the area of the base of the storage tank. The area of a circle is calculated by: A = π*r², where r is the radius of the circle.
Where:
π = 22/7
r = radius of the circular base
Recall that for Emma’s cylindrical storage tank, the radius of the base is 5 feet.
So we replace this value in the formula and calculate the area of the base, which is equal to:
A = π*5²
A = 22/7 * 5²
= 78.5714285714
[tex]\approx[/tex] 78.54 square feet.
Now we need to compute the volume of the cylindrical storage tank. The volume of a cylinder is calculated by:
V = π*r²*h,
where r is the radius of the circle and h is the height of the cylinder.
Recall that for Emma’s tank, the height is 10 feet. Hence,
We substitute these values in the formula and calculate the volume, which is equal to:
V = π*5²*10 = 785.4 cubic feet.
Therefore, Emma’s cylindrical storage tank has a capacity of 785.4 cubic feet.
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The approximate length of side XY is
units
The approximate length of side YZ
units.
The approximate length of side ZX is
v units.
The approximate perimeter of triangle XYZ is
units
Answers
please mark me brainlieset and click the stars i spent so long on this :>
Answer:
ZX = 3√2, XY =√10, YZ = 4, Perimeter of ΔXYZ = 14√5 units
Step-by-step explanation:
1. We can see that if we were to draw an altitude from vertex X to side ZY of this triangle, the length of this altitude would be: 3 units
2. The length of ZX can be determined through Pythagorean Theorem. If this altitude were to be called XW, it would be one of the legs of a mini triangle ZXW, along with leg ZW. ZW clearly = 3, thus ZX^2 = 3^2 + 3^2 = 18, and ZX = √18 units = 3√2.
3. The same thing can be applied to another "mini" triangle YXW. This triangle would have legs XW (altitude of the triangle ZXY) and YW. Knowing XW to have a length of 3 units, and YW to have length of 1 unit ⇒ XY^2 = XW^2 + YW^2 = 3^2 + 1^2, and XY = √10.
4. YZ is visualized to have a length of 4 units.
5. Knowing that ZX = 3√2, XY =√10, and YZ = 4 ⇒ Perimeter of ΔXYZ = ZX + XY + YZ = 3√2 + √10 + 4 = 14√5 units. To simplify this, it would be that the Perimeter of ΔXYZ = 14√5 units
ZX = 3√2, XY =√10, YZ = 4, Perimeter of ΔXYZ = 14√5 units
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
1. We can see that if we were to draw an altitude from vertex X to side ZY of this triangle,
the length of this altitude would be: 3 units
2. The length of ZX can be determined through Pythagorean Theorem.
If this altitude were to be called XW, it would be one of the legs of a mini triangle ZXW, along with leg ZW.
ZW clearly = 3,
thus
[tex]ZX^2 = 3^2 + 3^2 = 18[/tex],
and ZX = √18 units = 3√2.
3. The same thing can be applied to another "mini" triangle YXW. This triangle would have legs XW (altitude of the triangle ZXY) and YW.
Knowing XW to have a length of 3 units, and YW to have a length of 1 unit [tex]= > XY^2 = XW^2 + YW^2 \\= > 3^2 + 1^2[/tex],
and XY = √10.
4. YZ is visualized to have a length of 4 units.
5. Knowing that
ZX = 3√2, XY =√10, and YZ = 4
⇒ Perimeter of ΔXYZ = ZX + XY + YZ
⇒ Perimeter of ΔXYZ = 3√2 + √10 + 4
⇒ Perimeter of ΔXYZ = 14√5 units.
To simplify this, it would be that the Perimeter of ΔXYZ = 14√5 units
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Martin will receive a pay raise of 6%. He currently makes $30 per hour. What will be his new hourly rate?
Answers
Answer:
New hourly rate is $31.8-------------------
GivenCurrent rate is $30,Pay raise is 6%,SolutionNew rate is:
$30 + 6% = $30 + $30*6/100 =$30 + $1.8 = $31.8A high - powered model rocket is traveling at 150 mph What is the rockets speed in feet per second ?
Answers
Speed of rocket travelling at 150 m/h into feet per second is 0.1367 feet per second
How to covert meter to feet ?3.28084 feet is about equal to one meter. Multiply 3.28084 feet to the given meter value to convert
According to the given information
Speed of rocket in meter per hour is 150 m/h
To know the speed of rocket in feet per second
1 meter = 3.280 feet
15o meter = 150 × 3.280
= 492 feet
1 hour = 60 × 60
= 3600 second
So,
speed of rocket in feet per second = [tex]\frac{492}{3600}[/tex]
= 0.1367 feet per second
Speed of rocket travelling at 150 m/h into feet per second is 0.1367 feet per second
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Select the postulate that confirms each statement.
a. Angles GFH and are supplementary angles.
Linear Pair Postulate
Segment Addition Postulate
Vertical Angle Postulate
Angle Addition Postulate
Answers
The correct postulate is the Linear Pair postulate. It can be find out by the concept of supplementary angles.
What is supplementary angles?
Two angles are said to be supplementary if their sums total 180 degrees.
Linear Pair postulate: When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°.
Segment Addition Postulate: According to the segment addition postulate, if two points on a line segment, A and C, are given, a third point, B, will only be found on line segment AC if and only if the distances between the points satisfy the conditions of the equation AB + BC = AC. This option is not correct.
Vertical Angles: When two lines intersect each other then the angles made on the opposite sides of the intersection point is known as vertical angles and they give equal measurment. This option is not correct.
Addition Postulate states: The measure of an angle formed by two angles side by side is the sum of the measures of the two angles. This option is not correct.
Hence, the correction postulate is the Linear Pair postulate. It can be find out by the concept of supplementary angles.
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4. Classify the system as independent, dependent, or inconsistent.
-3x + y = 4
x-1/3y = 1
Answers
The system of equation is dependent because both equation has same slope.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
An equation is an expression that shows the relationship between two or more numbers and variables.
We are given a system of equation as;
-3x + y = 4
x-1/3y = 1
Therefore, we need to write as straight line equation.
-3x + y = 4
y = 3x + 4
Thus, the slope is 3 and the y intercept is 4
Now x-1/3y = 1
x= 1 + 1/3y
y = 3x - 3
Thus, the slope is 3 and the y intercept is -3
The system of equation is dependent.
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How do you write 5 as a fraction??
Ples answer quick its grading day
Answers
Answer:
5/1
Step-by-step explanation:
I think?
PLS HURRY A recipe calls for 6 ounces of raisins. How many milligrams of raisins is this? (1 ounce = 28.35 grams and 1 gram = 1,000 milligrams)
170.1 milligrams
1,701 milligrams
17,010 milligrams
170,100 milligrams
Answers
Answer:
170,100 milligrams
Step-by-step explanation:
1 ounce = 28.35 grams
6 ounces = ?
6*28.35 = 171.10 grams
1 gram - 1000 milligrams
171.10 grams = ?
171.10*1000 =
171,100 milligrams
Answer:
A recipe calls for 170,100 milligrams of raisins.
Step-by-step explanation:
I took the exam and got it right
pls solve before friday
Answers
The result of the given mathematical expression is 8459.46
What is Mathematical expression and decimal
Mathematical expression consist of combination of numbers along with addition, subtraction, multiplication and division.
Decimal numbers are those numbers which have an integer part and a fractional part.
Decimal can be terminating as well as non terminating.
Terminating decimals are those numbers which have finite number of digits after decimal point.
Non terminating decimals are those numbers which have infinite number of digits after decimal point.
Mathematical expression to be solved
[tex]31520 \times 0.029 \times \frac{(1+0.029)^4}{(1+0.029)^4-1}[/tex]
Decimal number is present in the above expression.
The given expression is to be simplified to get a solution
Now,
[tex]31520 \times 0.029 \times \frac{(1+0.029)^4}{(1+0.029)^4-1}\\\\31520 \times 0.029 \times \frac{(1.029)^4}{(1.029)^4-1}\\\\31520 \times 0.029 \times \frac{1.1211442633}{0.1211442633}[/tex]
8459.46
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