144.) The value of X if the two angles of the triangle are congruent would be = 4. That is option D.
145.) The equation that should be used to find the value of X would be = 13x -15 = 22x + 9. That is option H.
How to determine the value of X when two triangles are congruent?
For question 144.)
Two triangles are congruent means that the angles are equal to each other. That is;
2.3x +25 = 5.8x + 11
Bring like terms together;
5.8x-2.3x = 25-11
3.5x = 14
X = 14/3.5
= 4.
For question 145.)
When two parallel lines are being cut across by a diagonal line a relationship exists between the angles that are formed.
The two given angles are congruent;
That is;
13x -15 = 22x + 9
Therefore the expression that can be used to calculate X would be = 13x -15 = 22x + 9
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What is the median of the following set of numbers? 35, 33, 36, 34, 33, 33, 32, 38, 35
A.35
B. 34
C.33
D.36
Median of the set is 34, as it is the middle value of the ordered set (32, 33, 33, 33, 34, 35, 35, 36, 38).
To find the middle of a bunch of numbers, the initial step is to organize the numbers all together from least to most prominent. For this situation, the arranged set is: 32, 33, 33, 33, 34, 35, 35, 36, 38.
The middle is the center number in the arranged set. On the off chance that there is an odd number of values, the middle is the center worth. On the off chance that there is a considerably number of values, the middle is the normal of the two center qualities.
For this situation, there are nine qualities in the set, which is an odd number. The center worth is the fifth worth, which is 34. Thusly, the middle of the set is B. 34.
To confirm, we can count four qualities before 34 and four qualities after 34 in the arranged set. Since there are an equivalent number of values when the middle, we can infer that 34 is for sure the middle.
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2) Factor by CTS: x² +12
please show work
The factored form of x² + 12 using the difference of squares formula is
(x + 2√3)(x - 2√3).
We have,
To factor x² + 12 using the difference of squares formula, we need to express it as the difference between two squares:
x² + 12 = x² + (2√3)²
Now we can use the difference of squares formula, which states that:
a² - b² = (a + b)(a - b)
In this case, we have a = x and b = 2√3. So we can write:
= x² + 12
= x² + (2√3)²
= (x + 2√3)(x - 2√3)
Therefore,
The factored form of x² + 12 using the difference of squares formula is
(x + 2√3)(x - 2√3).
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Ole has a window that has the dimensions and shape like the trapezoid shown below. He also has a large rectangular piece of poster board that measures 25 inches by 60 inches. If Ole cuts out a piece of poster board that is exactly the same size as the window, which equation can be used to calculate the amount of poster board that will be left over?
The amount of poster board left over will be 1275 square inches, the equation used is A = (b₁ + b₂)h/2.
To calculate the amount of poster board that will be left over after Ole cuts out a piece of poster board that is the same size as the window,
we need to find the area of the trapezoid window and subtract it from the area of the poster board.
The formula to find the area of a trapezoid is A = (b₁ + b₂)h/2, where b₁ and b₂ are the lengths of the parallel sides and h is the height.
Let's assume that the length of the top parallel side of the trapezoid is 20 inches, the length of the bottom parallel side is 10 inches, and the height is 15 inches.
Using the formula, we get A = (20 + 10) x 15 / 2 = 225 square inches. This is the area of the window.
To find the area of the poster board, we multiply the length and width, which gives 25 x 60 = 1500 square inches.
Finally, we subtract the area of the window from the area of the poster board using the equation:
1500 - 225 = 1275 square inches.
Therefore, the amount of poster board left over will be 1275 square inches.
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The complete question is
Ole has a window that has the dimensions and shape like the trapezoid shown below. He also has a large rectangular piece of poster board that measures 25 inches by 60 inches. If Ole cuts out a piece of poster board that is exactly the same size as the window, which equation can be used to calculate the amount of poster board that will be left over?
i need the answer for this asap Please!
[tex]y \geq -3x + 2\\\\y \leq x + 3[/tex]
is the equation of the given system.
Equation of the line using the coordinates (-3, 0) and (0, 3), we get:
slope = (3 - 0) / (0 - (-3)) = 1
Now we have the slope of the line. Next, we can use the point-slope form of the equation of a line, which is:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line.
Using the point (-3, 0) and the slope we just found (which is also the slope of the line passing through the point (0, 3)), we get:
y - 0 = 1(x - (-3))
Simplifying, we get:
y = x + 3
Therefore, the equation of the line passing through (-3, 0) and (0, 3) is y=x+3.
Similarly, the equation of the line passing through (1, -1) and (0, -4) is y = -3x + 2.
Thus, from the graph the equation of the system is,
[tex]y \geq -3x + 2\\\\y \leq x + 3[/tex]
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If someone walks along the outside of the garden from point A to point B, what percent of the garden's border would they have walked around? Round your answer to the nearest whole percent. Type the correct answer in the box. Use numerals instead of words. They would have walked around approximately % of the outside border of the garden.
The outside border of the garden would have walked around approximately 58%.
Without more information about the shape and dimensions of the garden, it's impossible to give an exact answer. However, if we assume that the garden is a rectangle, we can use the formula for the perimeter of a rectangle to estimate the percentage of the garden's border that would be walked around.
Let's say that the length of the garden is L and the width of the garden is W. The perimeter of the rectangle is then:
P = 2L + 2W
If the person walks from point A to point B along the outside of the garden, they are essentially walking along two sides of the rectangle. Let's call these sides S1 and S2. Depending on the location of A and B, S1 and S2 may be two adjacent sides, two opposite sides, or one side and one diagonal.
To estimate the percentage of the garden's border that the person would walk around, we can calculate the length of S1 and S2 and divide by the total perimeter of the rectangle:
Percentage walked = (S1 + S2) / P * 100%
Again, without more information about the shape and dimensions of the garden, we can't give an exact answer. However, if we assume that the person walks along two adjacent sides of the rectangle, the percentage of the garden's border that they would walk around would be:
Percentage walked = (2L + W) / (2L + 2W) * 100%
Simplifying this expression, we get:
Percentage walked = (2L + W) / (2(L + W)) * 100%
Assuming that L and W are measured in the same units (e.g. meters), we can simplify further:
Percentage walked = (2 + W/L) / (2 + 2W/L) * 100%
For example, if the length of the garden is 10 meters and the width of the garden is 5 meters, then the percentage of the garden's border that the person would walk around if they walked along two adjacent sides would be:
Percentage walked = (2 + 5/10) / (2 + 2*5/10) * 100%
= 7/12 * 100%
= 58.3%
So the outside border of the garden would have walked around approximately 58%.
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A study of religious practices among college students interviewed a sample of 125
students; 105
of the students said that they prayed at least once in a while. What is the sample proportion who said they pray?
0.84
1.19
105
84
The sample proportion who said they pray is approximately 0.84, or 84%.
How to solve for the sample proportionThe sample proportion of college students who said they pray can be calculated by dividing the number of students who said they pray (105) by the total number of students in the sample (125).
Sample proportion = Number of students who said they pray / Total number of students in the sample
Sample proportion = 105 / 125
Sample proportion = 0.84
Therefore, the sample proportion who said they pray is approximately 0.84, or 84%.
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What is the total cost of 20 books at R25 each?
Answer:
R500
Step-by-step explanation:
20 books x R25 each = R500.
Math
Language arts
Seventh grade> Y.7 Circles: word problems P56
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millimeters
Y
The button on Jasmine's pants has a radius of 5 millimeters. What is the button's
diameter?
9
Answer:
10 millimeters
Step-by-step explanation:
The diameter of the button is twice the radius. Therefore, the diameter of Jasmine's pants button is 10 millimeters.
Roughly how much more does auto insurance cost for a 16 year old compared to a middle aged (40-50 year old) driver
A 16-year-old on their own policy pays on average $4,000 more per year than a 50-year-old would have to pay
The cost of insuranceAuto insurance costs vary significantly depending on factors such as location, vehicle type, and driving history. However, on average, a 16-year-old driver can expect to pay significantly more for auto insurance compared to a middle-aged driver (40-50 years old).
The exact amount varies, but it's not uncommon for a 16-year-old driver to pay two to three times more for auto insurance than a middle-aged driver. This is mainly because younger drivers are considered riskier due to their inexperience and higher likelihood of being involved in accidents.
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Find g(x), where g(x) is the translation 2 units left and 4 units down of f(x)=x^2.
Write your answer in the form a(x–h)^2+k, where a, h, and k are integers.
g(x) =
The function g(x) in the form a(x-h)^2 + k is: [tex]g(x) = (x + 2)^2 - 4[/tex]
Starting with[tex]f(x) = x^2[/tex], the translation 2 units left and 4 units down would result in the following transformation:
g(x) = f(x + 2) - 4
Substituting[tex]f(x) = x^2:[/tex]
[tex]g(x) = (x + 2)^2 - 4[/tex]
Expanding the square:
[tex]g(x) = x^2 + 4x + 4 - 4[/tex]
Simplifying:
[tex]g(x) = x^2 + 4x[/tex]
Now we need to rewrite this expression in the form [tex]a(x-h)^2 + k.[/tex] To do this, we will complete the square:
[tex]g(x) = x^2 + 4x\\g(x) = (x^2 + 4x + 4) - 4\\g(x) = (x + 2)^2 - 4[/tex]
Therefore, the function g(x) in the form a(x-h)^2 + k is:
[tex]g(x) = (x + 2)^2 - 4[/tex]
Where a = 1, h = -2, and k = -4.
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There are 3 feet in a yard. How many centimeters are in a yard?
-49 = 7i, what number is the i.
Answer:
-7
Step-by-step explanation:
divide by 7 on both sides and you get i = -7
ABCD is a rectangle. If AC is 20 inches, what is DE?
B
Al
E
C
D
The measurement of DE is 10 inches.
If we know that E is the point where the diagonals of the rectangle intersect, then we know that DE is equal to half the length of the diagonal BD.
Using the Pythagorean theorem, we can relate the length of the diagonal BD to the sides of the rectangle.
Let's assume that the length of the rectangle is L and the width of the rectangle is W. Then, the length of the diagonal BD is given by:
BD = √(L^2 + W^2)
Since we know that the diagonals of a rectangle are equal, we have:
AC = BD
BD = 20
Therefore, DE = 1/2 BD = 1/2 (20) = 10 inches.
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Carlos is a door to door vacuum salesman. His weekly salary, S, is $400 plus $35 for each vacuum he sells.
This can be written as S = 400+35v , where v is the number of vacuums sold.
If Carlos earns $1590 for a week's work, how many vacuums did he sell?
Answer:
34
Step-by-step explanation:
1. Plug in the week's salary into the formula
S=400+35v
1590=400+35v
2. Solve for v.
1590=400+35v
Subract 400 from both sides. Since the opposite of addition is subraction, soing this cancels out the 400.
1190=35v
Divide each side by 35. Since the opposite of multiplication (35v = 35 times v) is division, this will cancel out the 35.
34=v
1
4
(
8
−
6
x
+
12
)
?
1
4
(
8
−
6
x
+
12
)
?
A.
7
2
x
7
2
x
B.
−
13
2
x
−
13
2
x
C.
−
6
x
+
14
−
6
x
+
14
D.
−
3
2
x
+
5
The equivalent expression is 5 - 3x/2. Option D
What are algebraic expressions?Algebraic expressions are described as expressions that are made up of variables, their coefficients, factors and constants.
these algebraic expressions are also composed of mathematical operations. These operations includes;
BracketParenthesesSubtractionMultiplicationDivisionAdditionFrom the information given, we have that;
1/ 4(8 - 6x + 12)
expand the bracket, we have;
Add the like terms
1/4(20 - 6x)
now, multiply the values, we have;
20 - 6x/4
Divide by the denominator
5 - 3x/2
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The complete question:
Simply the expression:
1/ 4(8 - 6x + 12)
How many turning points are in the graph of the polynomial function?
4 turning points
5 turning points
6 turning points
7 turning points
Which point would be a solution to the system of linear inequalities shown below?
The coordinates in the solution to the systems of inequalities is (12, 1)
Solving the systems of inequalitiesFrom the question, we have the following parameters that can be used in our computation:
y > -4x + 6
y > 1/3x - 7
Next, we plot the graph of the system of the inequalities
See attachment for the graph
From the graph, we have solution to the system to be the shaded region
The coordinates in the solution to the systems of inequalities graphically is (12, 1)
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The dosage the pharmacy carries in stock (on hand), is different than the prescribers order. Use ratio and proportion to calculate the total quantity of tablets to dispense for each of the prescriptions below: Order: Zocor 40 mg po qd for 60 days On hand: 20 mg tabs How many 20 mg tabs should be given? Give:
Using ratios and proportions, the number of 20 mg tabs that should be given in place of 40 mg po qd for 60 days is 120 tabs.
How the number is determined:Using ratios and proportions, the number of tabs of 20 mg that should be given in place of 40 mg qd for 60 days is determined as follows:
Order: Zocor 40 mg po qd for 60 days
= 60 tabs since it is once per day (qd)
Total mg = 2,400 mg (40 mg x 60 tabs)
On hand: 20 mg tabs
Proportionately, 20 mg = 120 tabs (2 x 60) since 40 mg is for 60 tabs
Total mg = 2,400 mg (20 mg x 120 tabs)
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Select the matrix that represents the parallelogram
The correct matrix representation is; [tex]\left[\begin{array}{ccc}1&5\\3&2\end{array}\right][/tex]
Based on the coordinates of a vector, We can represent a vector pointing at a point by its x coordinate, and y coordinate,
Consider that there are two points represented by their x-, y coordinates as P₁(x₁,y₁) P₂(x₂,y₂)
Given here the points are P₁(1, 3) and P₂(5, 2)
Thus, by the coordinates of the two vectors, we can represent the matrix ;
[tex]\left[\begin{array}{ccc}1&5\\3&2\end{array}\right][/tex]
Hence, Option A) is the correct answer.
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Is this negative and odd or even and positive or negative and even and positive and odd?
Answer:
Hold on, our servers are swamped. Wait for your answer to fully loadHold on, our servers are swamped. Wait for your answer to fully loadHold on, our servers are swamped. Wait for your answer to fully loadHold on, our servers are swamped. Wait for your answer to fully load
Step-by-step explanation:
Hold on, our servers are swamped. Wait for your answer to fully loadHold on, our servers are swamped. Wait for your answer to fully load
I do not understand why the answer is a) for this equation: y'=2y+x. I assumed that the answer is c) or a), because numbers in the equation are positive, but I'm not sure this is the correct method here
The slope field for the differential equation would be D . Graph D .
What are slope fields ?A slope field provides a pictorial representation of differential equations that displays the magnitude and direction of the derivative or slope for solution curves at various points in the plane .
The length of line segments represents the magnitude, while the direction indicates the sign of the slope.
The equation given is y = 2 y + x which means that the slope is positive. This is why we can tell that Graph D has the correct slope field as it goes up for positive.
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Find the missing probability.
P(B)=1/4P(AandB)=3/25P(A|B)=?
The missing probability is P(A|B) is 12/25 if P(B) is 1/4P and (A and B) is 3/25P.
P(B) = 1/4
P(A and B) = 3/25
The conditional probability is used to find the P(A|B):
P(A|B) = P(A and B) / P(B)
Conditional probability is defined as the number of possible outcomes from a given event based on the previous outcomes of the events.
By substituting the given values in the given probability, we get:
P(A|B) = (3/25) / (1/4)
Divide the fraction and multiply it with its reciprocal:
P(A|B) = (3/25) * (4/1)
P(A|B) = 12/25
Therefore, we can conclude that the missing probability is P(A|B) is 12/25.
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The complete question is:
Find the missing probability.
P(B)=1/4P
(AandB)=3/25P
P(A|B)=?
Find the area of the following figure. Round to the nearest hundred if necessary.
14 m
9.5 m
17 m
The area of the given figure is 133 m²
Given is quadrilateral with sides 17m and 9.5m with height of 14m we need to find its area,
The given quadrilateral is a parallelogram, we know that area of the parallelogram is = base x height
Therefore,
The area of the given figure = 9.5 x 14 = 133
Hence, the area of the given figure is 133 m²
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A small toy rocket is launched from a 48-foot pad. The height (h, in feet) of the rocket t seconds after
taking off is given by the formula h = - 3t2 +0t + 48. How long will it take the rocket to hit the
ground?
t =
Okay, here are the steps to solve this problem:
1) The height (h) of the rocket t seconds after launch is given as: h = - 3t2 + 0t + 48
2) We want to find the time (t) when the rocket hits the ground (h = 0)
3) Set the formula equal to 0: - 3t2 + 0t + 48 = 0
4) Factor the left side: - 3(t2 - 0t) + 48 = 0
5) Solve for t2 - 0t: t2 - 0t = 16
6) Add 0t to both sides: t2 = 16 + 0t
7) Take the square root of both sides: t = 4
Therefore, the time for the rocket to hit the ground is 4 seconds.
So in this case, t = 4
Let me know if you have any other questions!
Answer:
4 seconds.
Step-by-step explanation:
When the rocket hits the ground, its height will be 0. Therefore, since we are given an expression for the height of the rocket dependent on the time, we can simply set it equal to 0 and solve for the time and find how long the rocket will take to hit the ground. I'm assuming the equation is[tex]h = -3t^{2} + 48[/tex]
Now set this equal to 0
[tex]0 = -3t^2+48[/tex]. Solve for t by isolating it.
[tex]-48 = -3t^2[/tex]
[tex]16 = t^2[/tex]
From here, by taking the square root, we see that t is either equal to 4 or -4 in seconds. Since we can't have negative time, we can clearly see that the answer is 4 seconds.
Hope this helps
4 3/8 + 5 1/2= in fractions
Answer:
9 7/8
Step-by-step explanation:
1. 4 3/8 can be converted into the improper fraction 35/8, and 5 1/2 can be converted into 11/2.
2. Now that we have 35/8 + 11/2, we have to find a common denominator. Since 2 goes into 8 four times, we can turn 11/2 into 44/8 by multiplying the numerator and denominator (the top and the bottom numbers) by 4.
3. Now we have 35/8 + 44/8. At this point, the all we have to do is add the numerators (the top numbers). 35+44=79, so our answer is 79/8, which we can simplify to 9 7/8.
What is the volume of this
rectangular pyramid?
6 ft
8.4 ft
8.6 ft
The volume of the rectangular pyramid is 144.48 cubic feet.
What is a rectangular pyramid?A pyramid with a rectangular base is known as a rectangle pyramid. When viewed from the bottom, this pyramid seems to be a rectangle. As a result, the base has two equal parallel sides.
The apex, which is located at the summit of the pyramid's base, serves as its crown. Right or oblique pyramids can be seen in rectangular shapes. If it is a right rectangular pyramid, the peak will be directly over the base's center; if it is an oblique rectangular pyramid, the apex will be angled away from the base's center.
The volume of a rectangular pyramid is given as:
[tex]\sf V = \dfrac{(l)(b)(h) }{3}[/tex]
[tex]\sf V = \dfrac{(8.4)(8.6)(6) }{3}[/tex]
[tex]\sf V = \dfrac{433.44 }{3}[/tex]
[tex]\sf V = 144.48 \ cubic \ feet[/tex].
Hence, the volume of the rectangular pyramid is 144.48 cubic feet.
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Write the coordinates of the vertices after a dilation with a scale factor of 1 2 , centered at the origin.
The coordinates of the vertices after a dilation of the scale factor would be:
W' = (2.5, 5)V' = (0, -5)U' = (2.5, -5)How to dilate the vertices ?To perform a dilation with a scale factor of 1/2 centered at the origin, we multiply the coordinates of each vertex by the scale factor.
Given the vertices:
W = (5, 10)
V = (0, -10)
U = (5, -10)
After applying the dilation with a scale factor of 1/2, the new coordinates of the vertices would be:
W' = (5 * 1/2, 10 x 1/2) = (2.5, 5)
V' = (0 * 1/2, -10 x 1/2) = (0, -5)
U' = (5 * 1/2, -10 x 1/2) = (2.5, -5)
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the coldest temperature ever recorded on earth was -89.2
The statement that "the coldest temperature ever recorded on earth was - 89. 2 ° " is True.
What was the coldest temperature recorded ?The Soviet Union's Vostok Station in Antarctica recorded the coldest temperature ever observed on Earth, measuring at -89.2°C on July 21, 1983 via satellite and weather station data.
This natural occurrence saw a temperature that presents significant risks to animal and human life due to poor insulation available against such extreme colds. Without suitable warming tools, survival is near impossible.
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Given that A={1,2,3,4,5} list the elements of the following sets. i.{x2:x€A} ii.{ :x€A} iii.{2x :x€A} iv.{4x+1:x€A}
Answer:no idea
Step-by-step explanation:
jasmine bikes the same distance every day. in 8 days, she biked a total of 32 miles. How far will she bike in 5 days?
Answer:
20
Step-by-step explanation:
She biked an equal amount each day for 8 days to a total of 32 miles. We can write that as 8x = 32. 32/8 = 4 so x = 4. To find how much shell bike in 5 days, we multiply it by x(4). 5*4 = 20.