Answers
Part 1
E. There is a pair of congruent angles and a pair of congruent right triangles, so the triangles are similar by the AA [tex]\sim[/tex] postulate.
Part 2
Note that 4 ft 6 in = 4.5 ft. Using the fact that corresponding sides of similar triangles have proportional side lengths,
[tex]\frac{x}{14}=\frac{4.5}{4} \implies \boxed{x=15.75 \text{ ft}}[/tex]
Related Questions
Julio’s car can travel 300 miles on one 12-gallon tank of gas. Viet’s car uses gas as described by the equation m=13g
, where m is the miles traveled and g is the gallons of gas used. Which statement is true?
Answers
The true statement is "viet's car can uses 13 gallons of gas for every miles it travels.
The correct answer choice is option B.
Which statement is true?Julio's car:
m = k × g
Where,
m = miles traveled
g = gallons of gas used
m = k × g
300 = k × 12
300 = 12k
divide both sides by 12
k = 300/12
k = 12
So,
m = 12g
Viet's car:
m=13g
Therefore, the correct statement is viet's car uses 13 gallons of gas for every mile.
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Step-by-step explanation:
please make me brainalist and keep smiling
Billy needs to paint a logo made using two right triangles. The dimensions of the logo are shown below. What is the total area of the two triangles that need to be painted? Two right triangles are attached along their longest side. The smaller triangle has height 6 cm and base 2 cm. The height of the larger triangle is 9 cm, and its base is 3 cm.
A. 7.5 cm 2
B. 15.0 cm2
C. 19.5 cm2
D. 39.0 cm2
Answers
A student starts a walk at (-7, -9). If the student walks 3 miles north, south, east, or west, which of the following could be their location at the end of the walk?
O(-10,-9). (-4,-9), (-7,-6). (-7, -12)
O(-9,-7), (-12, -7), (-4,-6), (-10,-6)
O(-7,3), (-7, -12), (-4,-9). (3,-9)
O (3,-9), (6,-9), (-7,-4), (-7, -12)
Answers
If the student walks 3 miles north, south, east, or west, the location at the end of the walk are respectively, (-10,-9). (-4,-9), (-7,-6). (-7, -12).
So Option A is correct
What is subtraction and addition ?In mathematics, subtraction is an operation which means taking away a few portions of the group or few things from a whole part.
For example, if we take 4 pencils out of 10 then remaining pencils are 6
so this process is called subtraction.
And opposite operation of subtraction is known as addition, which means in addition, few portion provided to the whole part.
Given that,
A student starts a walk at (-7, -9)
If the student walks 3 miles north, south, east, or west,
The location at the end of the walk = ?
Plotting dotted diagram,
East
|
North --------- |-------------- South
|
West
Suppose, he goes to north direction
Then, 3 will be subtracted from x coordinate,
It can be written as,
(-7-3, -9)
(-10, -9)
Similarly, for South, (-4, -9)
East, (-7, -6)
West, (-7, -12)
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Anastasia is grocery shopping with her father and wonders how much shopping is left to do. "We already have 60\%60%60, percent of the items on our list," her father says. Anastasia sees 121212 items in the cart.
Answers
The number of items on their grocery shopping list given the percentage already bought is 20 items.
How many grocery items are on the list?Percentage of items bought already= 60%
Number of items bought already= 12
Total number of items on the list= x
Number of items bought already = Percentage of items bought already × Total number of items on the list
12 = 60% × x
12 = 0.6 × x
12 = 0.6x
divide both sides by 0.6
x = 12/0.6
x = 20 items
Hence, there are a total of 20 items on their grocery list.
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system of linear equations includes the line that is created by the equation y = x+ 3, graphed below, and the line through the points (3, 1) and (4, 3). On a coordinate plane, a line goes through (0, 3) and (2, 5). What is the solution to the system of equations? (–1, 2) (1, 3) (8, 11) (9, 12) Mark this and return
Answers
The solution of the system of equations is (8, 11).
What is the solution of the system of equations?We know that one of the equations of the system is:
y = x + 3
And the other line passes through the points (3, 1) and (4, 3), then the slope of that line is:
a = (3 - 1)/(4 - 3) = 2
So the line is something like:
y = 2*x + b
To find the value of b, the y-intercept, we can replace the values of one of the points.
I will use (3, 1)
1 = 2*3 + b
1 = 6 + b
1 - 6 = b
-5 = b
So the other line is y = 2x - 5
Then the system of equations is:
y = x + 3
y = 2x - 5
Now we can solve the system:
x + 3 =2x - 5
3 + 5 = 2x -x
8 =x
The x-value of the solution is 8, then the only option that can be correct is.
(8, 11)
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If $600 is put in the bank and each year the account earns 7 % simple interest, then how much interest
will be earned in two years?
$42
$63
$84
$420
Answers
Answer: $84
Step-by-step explanation:
The interest earned in 2 years would be $600 * 7% * 2 = $84.
The point where the graphs of two equations intersect has y-coordinate 2. One equation is y=-3x+5. Complete the other equation in the
form y = mx + b if its graph has a slope of 1.
Answers
The other equation in the form y = mx + b is y = x + 3
How to complete the equation of the other lineFrom the question, we have the following parameters that can be used in our computation:
y = -3x + 5
y = mx + b has a slope of 1
So, we have
y = x + b
The point where the graphs of two equations intersect has y-coordinate 2.
So, we have
3x + 5 = 2
x + b = 2
Eliminate x
So, we have
3b - 5 = 6 - 2
Evaluate
3b = 9
So, we have
b = 3
hence, the equation is y = x + 3
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g (7) g (x) = - 10x - 7
Answers
g(7) is the output of the function g when the input is 7. To find g(7), we plug in 7 for x in the equation g(x) = -10x - 7, which gives us:
g(7) = -10 * 7 - 7 = -77
So the value of g(7) is -77.
>
The perimeter of the figure is 15 feet.
Find the missing side length.
4 ft
?
3 ft
3 ft
Answers
Add a phrase to the shape's perimeter to get the side length that is missing.The total length of all of a shape's sides makes up the shape's perimeter.
How do you find the missing side length of a perimeter ?Add a phrase to the shape's perimeter to get the side length that is missing.The total length of all of a shape's sides makes up the shape's perimeter.The sides' known lengths are added.The side length that makes the addition sentence true can be found.The lengths of a rectangle's four sides should be added to determine its perimeter.You can locate all four sides quite quickly if you only know the width and height (two sides are each equal to the height and the other two sides are equal to the width). Add the outcomes after multiplying the height and breadth by two.
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The missing side length of perimeter of the figure is 15 feet is 5.
How do you calculate a perimeter's missing side length?To get the length of the missing side, subtract the perimeter from the total of the known sides. Advice: Consider it. The whole and one component are both known. You deduct the known portion from the total to determine the missing component.
Since there are two of each side length, it is easy to do this by simply adding the length and breadth and multiplying the result by two. The perimeter formula is defined as
perimeter=(length + width)2.
or
add all sides
4 + 3+ 3+ x = 15
10 +x = 15
x = 15 -10 = 5
x = 5
The missing side length of perimeter of the figure is 15 feet is
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Mathmatics for Calculus
Answers
The value of function for f'(2) is 0.22.
What is the differentiation?The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.
Given that, f(x)= √(x+3) at the specific point x=2.
f'(2)= [tex]\lim_{h \to \ 0}[/tex]((f(2+h)-f(2))/h)
Find the derivative using the chain and power rules.
[tex]f(x)=(x+3)^{\frac{1}{2} }[/tex]
f'(x) = [tex]\frac{1}{2(x+3)^{\frac{1}{2} }}[/tex]
f'(2)= [tex]\frac{1}{2(2+3)^{\frac{1}{2} }}[/tex]
f'(2)= [tex]\frac{1}{2(2+3)^{\frac{1}{2} }}[/tex]
f'(2)= 1/2√5
f'(2)= 1/4.47
f'(2)= 0.22
Therefore, the value of function for f'(2) is 0.22.
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erastdyfugihojlhgfdszerWestdyfughilj;hgufydtyrstzerxytcfyguhlij;lk
Answers
Answer:
36/27
Step-by-step explanation:
SOHCAHTOA, so tan is opposite over adjacent.
opposite = 36
adjacent = 27
So, tan C is 36/27
Indicate the method you would use to prove the two 's . If no method applies, enter "none". SSS SAS ASA AAS None 45 degrees
Answers
Answer:
hi
Step-by-step explanation:
This table represents function f. If function g is a quadratic function that contains the points (-3, 5) and (0, 14), which statement is true over the interval [-3, 0] A. The average rate of change of f is more than the average rate of change of g. B. The average rate of change of f is less than the average rate of change of g. C. The average rate of change of f is the same as the average rate of change of g. D. The average rates of change of f and g cannot be determined from the given information.
Answers
Answer:
D. The average rates of change of f and g cannot be determined from the given information.
Step-by-step explanation:
To determine the average rate of change of a function, we need the equation of the function. Since the equation of g is not given, we cannot determine the average rate of change of g and compare it with the average rate of change of f. Hence, option D is the correct answer.
Pls help asap Solve for x. x =
Answers
The ratio will remain constant. Then the value of the variable 'x' will be 2.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
The ratio will remain constant. Then the equation is given as,
9/4 = 13.5 / (x + 4)
9(x + 4) = 13.5 (4)
9x + 36 = 54
9x = 18
x = 2
The ratio will remain constant. Then the value of the variable 'x' will be 2.
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2/x x 3/2x-5 rational expressions
Answers
Answer: To find the product of two rational expressions, we multiply the numerators together to get the new numerator and multiply the denominators together to get the new denominator.
So, (2/x) * (3/2x-5) = (2 * 3) / (x * (2x-5)) = 6 / (2x^2 - 5x)
Step-by-step explanation:
100 parking spaces on the lot. how many spaces were full if 70% of the lot was being used
Answers
Answer:
70 parking spaces were full.
Step-by-step explanation:
To calculate this, multiply the total number of parking spaces (100) by the percentage of the lot being used (70%):
100 * 0.70 = 70
16. AQRS is an equilateral triangle. If QR is seventeen more than twice x, RS is 19 less than six times x,
and QS is one less than four times x, find x and the measure of each side.
Topic 4: Congruent Triangles
18. Write three valid congruency statements given the triangles below.
P
17. In AJKL, if JK = JL, m/J = 23x - 4, m/K = 4x - 1, and m/L = 9x - 31, find x and the
measure of each angle.
¥
Q
R
S
|||
T
U
19. If AKPLAACM, complete each part.
a) KL =
d)
e) ZK =
c) PL=
f) ZM =
a)
b)
c)
W
15 m
Topic 5: Triangle Congruence & Proofs
21. What are the methods to prove triangles are congruent?
20. If AWXY AHJI, complete each part.
a) JI =
b) JH =
c) m/W=
d) m/J=
e) m/I=
114°
X
16 m
J
Y
37°
X:
H
QR=
RS =
QS =
22. Determine if the triangles below are congruent. If yes, state which method.
a)
b)
c)
=
X =
m/J=
m/K=
m/L=
d)
40
Answers
The value of x is 9 and the measure of each side is 35 units.
What is an Equilateral Triangle?A triangle is said to be equilateral if each of its three sides is the same length.
In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.
Given, Triangle QRS is an equilateral triangle.
QR is seventeen more than twice x ---> QR = 17 + 2x
RS is 19 less than six times x, ---> RS= 6x - 19
And QS is one less four times x, ---> QS = 4x -1
We have to find x and measure of each side.
Now, we know that, the sides of an equilateral triangle are equal,
If we solve for RS and QS, we find they are both equals to 35.
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A square piece of cloth with an area of 324 square inches is folded in half twice to form the napkin shown. What is
the area of the folded napkin?
Answers
The area of the napkin will be 162.5 inches².
What is the area of a square?The area of a square is -
{A} = Side x Side
Given is that a square piece of cloth with an area of 324 inches² is folded in half twice to form the napkin.
The area of the cloth is -
{A} = 324
Let the side of the square cloth be {a}. So, we can write -
a² = 324
a = √324
{a} = 18 ... Eq { 1 }
The diagonal of the square will be the base length of the napkin (in the form of triangle). So, we can write -
d² = a² + a²
d² = 2a²
d² = 648
d = √648
{d} = 25.5 inches ... Eq { 2 }
The height would be -
h = d/2
h = 25.5/2
{h} = 12.75
The area of the napkin would be -
1/2 x d x h
1/2 x 25.5 x 12.75
162.5 inches²
Therefore, the area of the napkin will be 162.5 inches².
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6
x
+
8
=
3
x
+
6
Give your answer as a fraction
Answers
Answer: x = -2/3
Step-by-step explanation:
6x+8=3x+6
First, subtract 8 from each side. we now have 6x = 3x - 2. now we subtract 3x from each side and we get 3x = -2. we have to divide both by 3 now. The 3’s cancel each other out so now we have x = -2/3
f(x)=1/x to g(x)=1/5x transformation
Answers
The transformation from the function f(x)=1/x to g(x)=1/5x can be achieved by multiplying the input value x by 5.
f(x)=1/x becomes g(x)=1/(5x) after the transformation
What is mathematical transformation?A mathematical transformation is a function that maps one set of values (input) to another set of values (output) based on a set of rules or operations. Transformations can be used to manipulate geometric figures, to change coordinate systems, to map one image to another, and more. Common examples of mathematical transformations include translation, rotation, scaling, and reflection.
It could then be concluded that the transformation is achieved by multiplying the input value x by 5.
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The complete question goes thus:
Describe the f(x)=1/x to g(x)=1/5x transformation
In a recent survey, a group of people were asked if they were happy or unhappy with the state of the country. The data are shown in the contingency table below, organized by political party. What is the odds ratio for people unhappy with the state of the country to be republicans against people happy with the state of the country to be republicans? Round your answer to two decimal places
Answers
The data are shown in the contingency table below, organized by political party therefore the odds ratio for people unhappy with the state of the country to be republicans against people happy with the state of the country to be republicans is 0.64.
What is Data?This is referred to as information that has been translated into a form that is efficient for movement or processing.
Number of people unhappy with the state of the country to be republicans = 98
Number of people happy with the state of the country to be republicans = 152
Therefore the ratio is 98/152 = 0.64
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Answer:
Step-by-step explanation:
0.46
Review the graph.
On a coordinate plane, a vector has origin (0, 0) and terminal point (3, 2).
What is the magnitude of the vector shown?
5
13
StartRoot 5 EndRoot
StartRoot 13 EndRoot
Answers
On a coordinate plane, a vector has origin (0, 0) and terminal point (3, 2). The magnitude of the vector is 5
How did we get the value?The magnitude of a vector can be calculated using the distance formula, which is the square root of the sum of the squares of the differences of the x and y components. In this case, the x component is 3 and the y component is 2, so the magnitude can be calculated as follows:
√(3^2 + 2^2) = √(9 + 4) = √(13) = 5
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Answer:
its D
Step-by-step explanation:
on edge
eBook
Quick ratio
Adieu Company reported the following current assets and current liabilities for two recent years:
Dec. 31, 20Y4 Dec. 31, 2013
Show Me How
Cash
Temporary investments
Accounts receivable
$750
1,100
850
Inventory
2,300
Accounts payable
1,800
a. Compute the quick ratio on December 31 for each year. Round to one decimal place.
2014
20Y3
$1,180
1,400
920
2,500
2,500
b. Is the quick ratio improving or declining?
Improving
V
Answers
On December 31 of each year, the quick ratio is 1.6. According to the above computation, the quick ratio is improving.
Which quick ratio is ideal?A good fast ratio is often anything greater than 1 or 1:1. If the ratio is 1:1, the company's liquid assets and current liabilities are equal in amount. A greater ratio means the business could more than cover its current liabilities.
The quick ratio calculation is displayed below:
For the present year
Current liabilities minus Quick Assets is the Quick Ratio.
= ($1,000 + $1,200 + $800) ÷ $1,875
= $3,000 ÷ $1,875
= 1.6
For Previous yearCurrent liabilities minus Quick Assets is the Quick Ratio.
=($1,140 + $1,400 + $910) ÷ $2,300
= $3,450 ÷ $2,300
= 1.5
b. according to the above computation, the quick ratio is improving.
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PLEASE ANSWER UNDER 5 MIN!!!! ily!!!!
what is the period of the sinusoidal function? enter your answer in the box.
Answers
Answer:
Step-by-step explanation:
10
Ws
select the expression that is equivalent to (x+5)^2-(x-3)(x+5)
Answers
The equivalent expression is 8x + 40.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
(x + 5)² - (x - 3)(x + 5)
x² + 10x + 25 - (x² + 5x - 3x - 15)
x² + 10x + 25 - x² - 2x + 15
8x + 40
Thus,
8x + 40 is the equivalent expression.
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water and food are products of?
Answers
Mr Kai had some packets of salt. He sold 5/6 of the packets of salt and had 15 packets left. How many packets of salt did Mr Kai have at first?
Answers
Answer:
90
Step-by-step explanation:
[tex]\frac{1}{6}+\frac{5}{6}[/tex]
in here [tex]\frac{1}{6}= 15\\ \\so\\\\\frac{5}{6} =75\\\\\frac{1}{6} +\frac{5}{6}=\frac{6}{6} \\[/tex]
in this case it is 15+75=90
Nico, Aditi, Erick, Raj, and Sandra are solving the equation. Two-fifths (5 + x) = 8 Each student begins to solve the problem as shown. Nico Aditi Erick Two-fifths (5 + x) = 8. (Five-halves) two-fifths (5 + x) = 8 (five-halves) Two-fifths (5 + x) = 8. Five-halves (5) + five-halves x = (five-halves) 8 Two-fifths (5 + x) = 8. Two-fifths (5 + x) minus 5 = 8 minus 5 Raj Sandra Two-fifths (5 + x) = 8. (one-half) two-fifths (5 + x) = 8 (one-half) Two-fifths (5 + x) = 8. two-fifths (5) + two-fifths x = 8 Which students are correct in their approach to solving the problem? Select three options. Nico Aditi Erick Raj Sandra
Answers
The solution for the given equation is 15. Therefore, Nico, Raj and Sandra are correct.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is 2/5 (5+x)=8
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Method 1:
Now, 2(5+x)=40
5+x=20
x=15
Method 2:
Multiply 5/2 on both the sides of an equation, we get
2/5 (5+x)×5/2 =8×5/2
5+x=20
x=15
Therefore, Nico, Raj and Sandra are correct.
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"Your question is incomplete, probably the complete question/missing part is:"
Nico, Aditi, Erick, Raj, and Sandra are solving the equation.
Two-fifths (5 + x) = 8
Each student begins to solve the problem as shown.
Nico
Aditi
Erick
Two-fifths (5 + x) = 8. (Five-halves) two-fifths (5 + x) = 8 (five-halves)
Two-fifths (5 + x) = 8. Five-halves (5) + five-halves x = (five-halves) 8
Two-fifths (5 + x) = 8. Two-fifths (5 + x) minus 5 = 8 minus 5
Raj
Sandra
Two-fifths (5 + x) = 8. (one-half) two-fifths (5 + x) = 8 (one-half)
Two-fifths (5 + x) = 8. two-fifths (5) + two-fifths x = 8
Which students are correct in their approach to solving the problem? Select three options.
Nico
Aditi
Erick
Raj
Sandra
Does the relationship in this table represent a proportional relationship?
X 0.2 0.4 0.75 0.875
Y 0.4 0.8 1.5 1.75
Select from the drop down menu to correctly complete the statement.
The relationship ______ represent a proportional relationship
PLEASE HELPPP!!
Answers
Answer: I don't know what's in the drop down menu, but the relationship you displayed is indeed a proportonial relationship
Step-by-step explanation: For each change of x, an equal change of y occurs. If you double x, y doubles as well. That means that the relationship between x and y is dirctly proportional.
Answer:
Step-by-step explanation:
does not I think
Consider the complex number -i√5.
What is the imaginary part?
Answers
The Imaginary part is [tex]& \frac{-5 \sqrt{3}-2}{4}[/tex]
What is complex number?A complex number can be represented in the form a + bi, where a and b are real numbers. A complex number is a part of a number system that extends the real numbers by adding an element designated by the symbol.Mathematical Complex Numbers. Complex numbers are those expressed as a+ib, where a, b are real numbers and I is a fictitious number called a "iota." I is equal to (-1). A complex number is, for instance, 2+3i, where 2 is a real number (Re) and 3i is an imaginary number (Im).Real and imaginary components are combined to form complex numbers, which have two elements. The foundation of more complex mathematics, like algebra, are complex numbers. They are applicable to a wide range of real-world situations, particularly in the fields of electronics and electromagnetism.[tex]& \frac{5+2 i}{-1+\sqrt{3} i} \times \frac{-1-\sqrt{3} i}{-1-\sqrt{3} i} \\[/tex]
[tex]& =\frac{-5-5 \sqrt{3} i-2 i+2 \sqrt{3}}{4} \\[/tex]
[tex]& =\frac{-5+2 \sqrt{3}}{4}+i\left(\frac{-5 \sqrt{3}-2}{4}\right) \\[/tex]
Imaginary part
[tex]& \frac{-5 \sqrt{3}-2}{4}[/tex]
The complete question is,
Find the imaginary part of 5+2i/-1+√3i
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The complex number -i5 has -i5 as its imaginary component.
What is the imaginary part in given terms?The given complex number is -i√5, which can be written as:-i√5 = 0 - i√5The imaginary part of the complex number is -i√5.Here's a step-by-step explanation:A complex number having the real part and the imaginary part.The real part is the coefficient of the real unit (i.e., 1), while the imaginary part is the coefficient of the imaginary unit (i.e., i).In this case, the given complex number is -i√5.We can write this as 0 - i√5, where 0 is the real part and -i√5 is the imaginary part.Therefore, the imaginary part of the complex number -i√5 is -i√5.
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