Answer: The length of each side of the triangle is;
Equal sides, x = 21.02 = PQ = PR
QR = 28.03
Step-by-step explanation: The trusses made by the manufacturer have the shape of an isoscellestriangle and as such two congruent sides PQ ≅ PR) are equal and QR is the third side whose length is 4/3 of the congruent sides.
The perimeter of each truss is 70ft.
Let the length of each congruent side be x ft.
Therefore,
Perimeter = x + x + (4/3)x
Perimeter, p = 70 = 3.33x
x = 70/3.33
x = 21.02
Therefore, Length of QR is; QR = (4/3) x
QR = (4/3) × 21.02
QR = 28.03
6 divided by 791 (long division with remainders) Grade 4 division worksheet
Therefore , the solution of the given problem of long division is Quotient is 131 and the Remainder is 5
How does long synthetic division take place?Synthetic division is another way to divide a polynomial but by binary x - c, while c is a constant. The divisor frequently assumes the form of (x a). In synthetic division, you are just interested in the coefficients of the polynomials, unlike long division.
Here,
The given Divisor = 6 and Dividend = 791
Step 1: Take the first digit of the dividend from the left. ...
Step 2: Then divide it by the divisor and write the answer on top as the quotient.
Step 3: Subtract the result from the digit and write the difference below.
long division is a method for dividing large numbers into steps or parts, breaking the division problem into a sequence of easier steps. It is the most common method used to solve problems based on division.
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Find the area of triangle XYZ
Answer:
[tex] \displaystyle A _{XYZ - \text{triangle}} = 24 {cm}^{2} [/tex]
Step-by-step explanation:
we have two right angle triangles
we want to figure out the area of XYZ triangle
we are given the base not the altitude (height) so we need to figure the height of XYZ to figure out the area of XYZ
in that case we can use Pythagoras theorem given by
[tex] \displaystyle {a}^{2} + {b}^{2} = {c}^{2} [/tex]
given that, c=5 and b=3 thus
substitute:
[tex] \displaystyle {3}^{2} + {a}^{2} = {5}^{2} [/tex]
simplify squares:
[tex] \displaystyle 9 + {a}^{2} = 25[/tex]
cancel 9 from both sides:
[tex] \displaystyle {a}^{2} = 16[/tex]
square root both sides:
[tex] \displaystyle {a}^{} = 4[/tex]
we have figured out the height of XYZ triangle
remember that,
[tex] \displaystyle A _{ \text{triangle}} = \frac{1}{2} bh[/tex]
we have h=4 and b=9+3=12
substitute:
[tex] \displaystyle A _{ \text{triangle}} = \frac{1}{2} \times 12\times 4[/tex]
reduce fraction:
[tex] \displaystyle A _{ \text{triangle}} = 12\times 2[/tex]
simplify multiplication:
[tex] \displaystyle A _{ \text{triangle}} = 24[/tex]
hence,
the area of triangle XYZ is 24 cm²
1/5t + 2 - 2 = 17 - 2
Answer:
[tex]t=75[/tex]
Step-by-step explanation:
Given
[tex]\frac{1}{5} t+2-2=17-2[/tex]
Lets solve for [tex]t[/tex].
Subtract 2 from 2.
[tex]\frac{1}{5} t=17-2[/tex]
Subtract 2 from 17.
[tex]\frac{1}{5} t=15[/tex]
Combine [tex]\frac{1}{5}[/tex] and [tex]t[/tex].
[tex]\frac{t}{5} =15[/tex]
Multiply both sides of the equation by 5.
[tex]\frac{t}{5}*5 =15*5[/tex]
[tex]t=75[/tex]
The line has a slope 5 / 4 and passes through ( − 3, 4 ). What is the equation of the line ? Select one: a. 4x + 5y + 31 = 0 b. 5x − 4y + 31 = 0 c. 4x − 5y + 31 = 0 d. 5x − 4y − 31 = 0
Answer:
b: 5x-4y+31=0
Step-by-step explanation:
Let's look for an equation of the form y=mx+b, where m is the slope and b the y-intercept (the value of y when x=0).
We are given the slope, m, as (5/4), so we can write: y = (5/4)x+b.
To find b, just enter the given point, (-3,4), into the above equation and solve for b:
y=(5/4)x + b
4=(5/4)(-3) + b for (-3,4)
4 = -(15/4)+b
4 + (15/4) = b
4 + (3 3/4) = b
b = 7 3/4
The equation becomes y = (5/4)x + 7 3/4
Also written as: y = (5/4)x + (31/4)
To match this with one of the options, let's multiply by 4 to remove the two fractions:
y = (5/4)x + (31/4)
4y = (5)x + (31)
Rearrange so that the expression is = 0:
4y-5x-31 = 0
Now multiply by -1: -4y+5x+31=0
Rearrange and this will match option b: 5x-4y+31=0
What is median?
the sum of values in a set of data multiplied by the number of values in the set
the sum of values in a set of data divided by the number of values in the set
the middle value in a data set when the values are put in order
the value that occurs most often in a data set
the middle value in a data set when the values are put in order
For example, the set {3,1,2} sorts to {1,2,3} where the median is 2.
Another example: The set {1,2,3,4} has 2 and 3 tied for the middle most position. The midpoint is (2+3)/2 = 5/2 = 2.5 which is the median.
Which segment(s) are perpendicular to overline AB ? B A. Segment CE only B. Segment CD and segment CE C. Segments CD , CE , and CF
Answer:
A letter A
Step-by-step explanation:
Segment CE only
mypoints!
The perpendicular line AB is segment CE only. The correct option is A.
What is trigonometry?
The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle termed trigonometry.
Two geometric objects are perpendicular in simple geometry if they intersect at a right angle. If two lines cross at a right angle, they are said to be perpendicular to one another.
The line CE is making an angle of 90 degrees with the line AB, then the line CE will be perpendicular to the line AB.
Therefore, the perpendicular line AB is segment CE only. The correct option is A.
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help me pleaseeeeeeeee!!
Answer:
2nd
Step-by-step explanation:
Answer: They are not proportional.
Step-by-step explanation: The numerator is multiplied my 0.5 but the denominator is not.
15 points !!!!! Given: x - y = 11.
If x = -17, what is y?
Please put your answer in the format “y=____”
Answer:
y=-28
Step-by-step explanation:
-17-y=11
-y=11+17
-y=28
y=-28
The triangular symbol for "play" on many electronic devices has
the shape of an isosceles triangle. Find the other two angles
if angle P measures 30°.
A triangle that is equilateral has three equal sides and three equal angles.
Find the other two angles if angle P measures 30°?The angles are all 60 degrees each. Two 90-degree angles are formed when the height of an equilateral triangle is drawn to the base of the triangle, and the top angle is divided into two 30-degree angles. A triangle with sides of 30-60-90 always has sides that are 1:3:2.
The 30-60-90 triangle formula for sides y is also known as y3: 2y. The angles of the triangle are always 30, 60, and 90 degrees. Given that one of the angles is 90 degrees, this triangle is always a right triangle. These angles come together to form a right-angled triangle. Furthermore, the right angle is equivalent to the sum of two sharp angles, which will have the ratios of 1: 2 or 2: 1.
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The game has 12 three-minute rounds. If the players stop after two minutes of the twelfth round, for how many minutes did they play?
A karaoke machine regularly costs $146 and is on sale for 35% off. What is the discount?
Answer:51.1
Step-by-step explanation:
Which is the equation of OB?
A. (x - 2)2 + y2 = 16
B. (x + 2)2 + y2 = 16
C. (x - 2)2 - y2 = 16
D. (x + 2)2 - y2 = 16
find value of m
[tex] {m}^{2} + 35 = 240 \div (12 \div 3)[/tex]
Answer:
5 ( or ) - 5
Step-by-step explanation:
12/3 = 4
240/4 = 60
m² + 35 = 60
m² = 60 - 35
m² = 25
m = - 5 ( or ) 5
Because,
( - 5 )² = - 5 * - 5 = 25
5² = 5 * 5 = 25
In describing the cost equation, Y = a + bX, "a" is:
- A) The dependent variable cost.
- B) The independent variable the level of activity.
- C) The total fixed cost.
- D) The variable cost per unit of activity.
Answer:
C) The total fixed cost.
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Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a radius of 9 feet and a height of 10 feet. Container B has a radius of 5 feet and a height of 20 feet. Container A is full of water and the water is pumped into Container B until Containter B is completely full.
To the nearest tenth, what is the percent of Container A that is empty after the pumping is complete?
Answer:
61.74%
Step-by-step explanation
Find the vol of container one: Volume = Pi(r^2)(height) = 3.14159*81*10 = 2544.69 cu.ft.
Find the vol of container two: Pi(r^2)(height) = 1570.79 cu.ft.
Now the % of container A that is empty is
(1 - ((Volume A - Volume B)/Volume A))*100% = 61.73%
If AT = 12 and KN = 18, find OB.
Answer:
15
Step-by-step explanation:
There is a formula for this it is,
B1+B2/2
B1= Base one or TA in this case
B2= Base two or NK in this case
You replace the values with the variable:
B1=12
B2=18
12+18/2 = 30/2= 15
OB=15
The midsegment of the trapezium OB is 15
Mid segment of a trapezium:The midsegment of a trapezoid is parallel to each base, and its length is one-half the sum of the lengths of the bases.
OB = mid segment
Therefore, mathematically,
OB = 1 / 2 (AT + KN)
where
AT = 12
KN = 18
Therefore,
OB = 1 / 2(12 + 18)
OB = 30 / 2
OB = 15
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PLEASE HELP. Simplify the expression
-4x - 2 + 3x - 4
Answer:
-x-6
Step-by-step explanation:
-4x - 2 + 3x - 4
Combine -4x and 3x -x - 2 - 4
Combine -2 and -4 -x - 6
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\text{-4x - 2 + 3x - 4}[/tex]
[tex]\underline{\underline{\huge\text{COMBINE the LIKE TERMS }}}[/tex]
[tex]\huge\text{= (-4x + 3x) + (-2 - 4)}[/tex]
[tex]\huge\text{-4x + 3x = \bf -1x}[/tex]
[tex]\huge\text{-2 - 4 = \bf -6}[/tex]
[tex]\huge\text{= \underline{\bf -1x - 6 }\huge\text{\textsf{\underline{\underline{\underline{or}}}}\underline{ \bf -x - 6 }}}[/tex]
[tex]\boxed{\boxed{\huge\text{Answer: \boxed{\bf -1x - 6} (also known as \boxed{\bf -x - 6})}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]{\huge\text{\frak{Amphitrite1040:)}}}[/tex]
if 12 men complete a piece of work in 10 days in how many days would 15 men complete the same work
Step-by-step explanation:
number of men =12
time taken = 10 days
time taken to complete the work by 15 men = 12÷10=1.2
= 1.2 ×15 = 18
therefore, 18 days is taken to complete the work by 15 men
Solve for the indicated values.
For both
Answer:
CH = 22°
Step-by-step explanation:
We know that Arc AC and Arc CH both equal to 180°, therefore we can say;
AC + CH = 180°
158 + CH = 180°
CH = 180 - 158
CH = 22°
Hope this helps!
Victoria has a total of 65 dimes and quarters worth $10.70. How many of each type of coin does she have?
Victoria has 37 dimes and 28 quarters in total.
What is equation modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.
Given is that Victoria has a total of 65 dimes and quarters worth $10.70.
We can write the system of equations as -
x + y = 65
(1/10)x + (1/4)y = 10.70
Refer to the graph attached. On solving the equation graphically, we get-
x = 37, y = 28
Therefore, Victoria has 37 dimes and 28 quarters in total.
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A car is traveling at a rate of 48 miles per hour. What is the car's rate in miles per minute? How many miles will the car travel in 20 minutes? Do not round your answers.
Will give brainliest. Please Help
Answer:
Speed of car in miles per minute = 0.8 miles per minute
Distance cover by car in 20 minutes = 16 miles
Step-by-step explanation:
Given:
Speed of car = 48 miles per hour
Time taken by car = 20 minutes
Find:
Speed of car in miles per minute
Distance cover by car in 20 minutes
Computation:
Speed of car = 48 miles per hour
1 hour = 60 minutes
So,
Speed of car = 48/60 miles per minute
Speed of car in miles per minute = 0.8 miles per minute
Distance cover by car in 20 minutes = 20 x Speed of car in miles per minute
Distance cover by car in 20 minutes = 20 x 0.8
Distance cover by car in 20 minutes = 16 miles
I need help please please pleade
Answer:
B
Step-by-step explanation:
Answer:
the answer is B most likely
Please help I’ll mark brainliest
Please Help!! Offering 8 points to each answerer and a Brainliest! Please answer the following parts of this question.
(02.05 HC)
The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x):
Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points)
Part B: Solve for k in each type of transformation. (4 points)
Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)
Answer:
Part A: Two types of transformations: translation and reflection.
Part B: g(x)=f(x)+k
-1= -1+ k
k= -1+1=0
g(x)=f(x)+k
-1= 5+k
k= -1-5=-6
g(x)=f(x)+k
14= 14+k
k= 0
k= -6,0,-6,0
Part C: For horizontal translation, g(x)=f(x+2)
In case of vertical translation, g(x)=f(x)+10
Therefore, the equation of transformation can be written as g(x)=f(x+2)+10.
Step-by-step explanation:
I thought. :') Ever since yesterday, and today. Hope this helps!
What is Y + 4 = 3x + (-5) as a y = mx + b equation??
What is the relationship between xzw and wzv on a vertical angle?
The relationship between xzw and wzv on the vertical angle is as follows:
∠ xzw + ∠ wzv = 180
How to find the relationship between angles?Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines. Vertically opposite angles share the same vertex and they are congruent to each other.
Therefore,
∠vzy ≅ ∠wzx(vertical angles)
Hence, the relationships between angles xzw and wzv is as follows:
∠ xzw + ∠ wzv = 180 (sum of angles on a straight line)
3x + 17 + x - 9 = 180
4x + 8 = 180
4x = 180 - 8
4x = 172
x = 172 / 4
x = 43
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Eating at the all-you-can-eat buffet at your favorite restaurant currently costs $18.50, and increases in cost by 6% each year.
1. Write a function that correctly depicts this scenario.
2. How much will this buffet cost 10 years from now? Round your answer to the nearest cent.
3. How much did this buffet cost 15 years ago? Round your answer to the nearest cent.
The function of the scenario is f(x) = 18.5(1.06)^x
The cost 10 years from now is $33.13The cost 15 years ago is $7.72How to determine the function of the scenarioFrom the question, we have the following parameters that can be used in our computation:
Initial value = $18.50
Rate = 6%
The function of the scenario is then represented as
f(x) = Initial value * (1 + rate)^x
Substitute the known values in the above equation, so, we have the following representation
f(x) = 18.5(1 + 6%)^x
Evaluate
f(x) = 18.5(1.06)^x
How much will this buffet cost 10 years from nowThis means that
x = 10
So, we have
f(10) = 18.5(1.06)^10
Evaluate
f(10) = 33.13
How much did this buffet cost 15 years ago?This means that
x = -15
So, we have
f(-15) = 18.5(1.06)^(-15)
Evaluate
f(-15) = 7.72
Hence, the price is $7.72
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HELP DUE IN 15 MINS!
Find the length of the diagonal of the square and the variables. You can round to the nearest tenth.
diagonal =??
x =?? degrees
° y =?? degrees
Answer:
Diagonal ⇒ d = 6√2 = 8.5 iny = 90° (diagonals are perpendicular)x = 45° (isosceles right triangle)Mason invested $65,000 in an account paying an interest rate of 4. 6% compounded annually. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $142,200?
It would take about 17.4 years, to the nearest year, for the value of the account to reach $142,200 if the interest rate is 4.6% and no deposits or withdrawals are made.
Therefore the answer is 17.4 years.
To find out how long it would take for the value of the account to reach $142,200, we need to use the formula for compound interest:
A = P(1 + r)^(t)
Where:
A = the future value of the account
P = the present value of the account ($65,000)
r = the annual interest rate (4.6%)
t = the number of years
We know the future value of the account (A) and the present value of the account (P), so we can substitute these values into the formula and solve for t:
142,200 = 65,000(1 + 0.046)^t
To solve for t, we can take the natural logarithm of both sides:
ln(142,200) = ln(65,000(1 + 0.046)^t)
ln(142,200) = ln(65,000) + t(ln(1 + 0.046))
Then we can divide both sides by ln(1+0.046) and take the power of e:
t = (ln(142,200) - ln(65,000)) / ln(1+0.046)
To the nearest year, this gives us t = 17.4 years.
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CPM 6-18
AP statistics
Consider a random variable X with μx = 40 and σx = 5. Let Z = X + X + X + X.
a. Find μz and σz.
d. Find μ1/4z and σ1/4z.
Consequently, the solution of the given question of probability comes out to be P(x<5.67 = 0.63
What is probability?Probability fundamentals. A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
Here,
we use the z-score algorithm to answer this query.
Score Z = x - 40/5
x = the raw score
population mean= μ
Population standard deviation is σ
Hence,
x = 40 μ = 5.67, σ =5
Z = 5.67 - 40/5
z=0.37
Probability based on the Z-Table:
P(x<5.67 = 0.63
Consequently, the solution of the given question of probability comes out to be P(x<5.67 = 0.63 .
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