Answer:
2 hours
Step-by-step explanation:
Because if the total round trip took 6 hours then it mustve taken him 2 hours to drive there at 70mph and 4 hours to drive back at 50mph.
For the following exercises, graph the given functions by hand.
48. f(x) = | 2x − 4 | − 3
A horizontal translation of the function by 4 units and a vertical translation down by 3 units
Graph of modulus functionThe parent function of the given function is g(x) = |x|. The resulting function (x) = | 2x − 4 | − 3 shows the following translations
A vertical stretch of the graph by 2 units
A horizontal translation of the function by 4 units and a vertical translation down by 3 units
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In a sequence, each number is 2 less than double the previous number. morgan finds the number directly before 48 in the sequence. his answer has two digits. he adds these two digits to get a new number. what is the new number
The new number in the sequence is found to be 7.
What is the term of the sequence?In mathematics, a sequence is a list of components, usually numbers, where the components' order is important. Here, everything fits into a predetermined pattern.
A sequence can be arranged in either ascending or descending order.
There are certain unique sequences, including the triangular number series, square number sequence, cube number sequence, geometric sequence, Fibonacci sequence, and harmonic sequence.
According to the question, the sequence follows the pattern:
Next number=2(Previous number)-2
On substituting the values,
48=2(Previous number)-2
50=2(Previous number)
Previous number=[tex]\frac{50}{2}[/tex]=25
New number=sum of digits of the previous number in the sequence
=2+5
=7
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Glven: AABC with DE || AC
AD CE
EB
Prove: DB
B
1. DE
2.
Statement
E
Reason
C
given
If two parallel lines are
cut by a transversal, the
corresponding angles are
congruent.
What is the missing step in this proof?
OAZCAB
OB. ZADE
OC.
OD. ZCABLEDB, ZACB DEB
LACB, LEDB ZDEB
ZDBE, ZCED= LEBD
ZCAD ZACE, ZADEZCED
The missing statement in the proof is; AB/BD = CB/EB
What are similar triangles?Similar triangles have the same corresponding angle measures and proportional side lengths.
The given proof is the triangle proportionality theorem which states that the segments formed by side DE are proportional.
The two column proof is presented as follows;
Statement Reason
1. DE || AC 1. Given
2. ∠CAB ≅ ∠EDB 2. Corresponding angles formed between ║ lines
3. ΔABC ~ ΔDBE 3. AA criterion for similarity
4. AB/BD = CB/EB 4. Corr. sides of similar Δs are prop.
5. AB = AD + DB 5. Segment addition CB = CE + EB
6. (AD + DB)/(DB) = (CE + EB)/(EB) 6. Substitution Property of Equality
7. (AD)/(DB) + 1 = (CE)/(EB) + 1 7. Division
8. (AD)/(DB) = (CE)/(EB) 8. Subtraction Property of Equality
Hence, the missing statement in the proof is; AB/BD = CB/EB
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CAN SOMEONE HELP ME PLEASE???
Answer:
16
Step-by-step explanation:
Referring to the diagram, we can use Pythagoras' Theorem to find ZY. (which is the distance from Point Y to WX)
By Pythagoras' Theorem,
[tex]c^{2} =a^{2} +b^{2} \\WY^{2} =WZ^{2} +ZY^{2} \\(16\sqrt{2}) ^{2} =16^{2} +ZY^{2} \\ZY^{2} = (16\sqrt{2}) ^{2} -16^{2} \\ZY^{2} =512-256\\ZY^{2} =256\\ZY=\sqrt{256} \\ZY=16[/tex]
Please help if you want, would really appreciate it
Answer: 140°
Step-by-step explanation:
- all straight lines are 180°
- since ACD and DCB help to create the straight line they must equal 180° when combined
- so 180 - 40 = 140
- therefore, ACD is 40° and DCB is 140°
hope this helps :)
Which of the following expressions are equivalent to -3 x -6/10
A. 3/6 x 1/10
B. -3/10 x -6
C. None of the above
what are the domain and range of the function represented by the set of ordered pairs {(-6,5),(-3,2),(-1,0),(5,-4)}
Answer:
Greetings !domain ={-6,-3,-1,5}to find domain just take the first values of each ordered pairs
range ={5,2,0,-4}to find the range just take the second values of each ordered pairs.
Triangle QRS is to be dilated using the rule D Subscript P, three-fourths.
Point P is the center of dilation. Triangle Q R S is shown. The length of P S is 8.
What will be the distance from the center of dilation, P, to the image S'?
2 units
4 units
6 units
8 units
The distance from the center of dilation, P, to.the image vertice S' is; 6 units.
What is the distance from the center of dilation, P, to the image S'?It follows from the task content that the center of dilation of the triangle QRS is point P and the length of segment PS in the pre-image is; 8 units.
Ultimately, since the dilation factor is; three-fourths, it therefore follows that the distance of point P to S' in the image is; (3/4) × 8 = 6 units.
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Answer: OPTION C
Step-by-step explanation:
Solve for h.
144 = h²
Answer:
h = 12 OR h = -12Step-by-step explanation:
h² means h * h
We can start with a number like "10". 10*10 = 100, so we have to guess a bit higher.
12*12 = 144.
However, it can also be -12 * -12 since the two negative signs will cancel each other out.
So, h can be 12 or -12
Answer: +12 or -12
Step-by-step explanation:
h^2=144
taking sqrt root on both sides
h=±12
so answer is +12 or-12
Which equation represents the transformed function below?
parent function; y=√x
= transformed function
If we know the concepts of transformations and horizontal translation and that f(x) = √x and k = - 2, then the transformed function is g(x) = √(x + 2).
How to determine the transformed function in terms of its parent function
The transformation of functions are operations which modify the relationship between input and outputs in a function. The parent function represents a canonical square root function and the transformed function is the consequence of applying a horizontal translation.
This kind of transformation is defined by the following expression:
g(x) = f(x - k) (1)
Where k represents a rightward translation for k > 0.
If we know that f(x) = √x and k = - 2, then the transformed function is g(x) = √(x + 2).
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Simplify and state any restrictions on the variable. Remember the order of operations. Show all your work for full
marks!
Step-by-step explanation:
6+8-90+90008-70000000
HELP ASAP
Given: ABCD is a parallelogram and ABC is a right angle.
Prove: BD is congruent to AC.
ABC is a right angle
ABCD is a parallelogram
Opposite sides of a parallelogram are equal
So
BC=ADAB=DCOpposite angles are equal
<B=<D
Hence
∆ABC and ∆CDB are congruent by SAS
BD=ACWriting an Informative Essay about an Event in History? HURRY
When writing an informative essay about an event in history, you should:
Pick an engaging topic with several sources of information. Clearly state your thesis in your introduction. Use every paragraph to expand on a separate point. Avoid using long sentences. Reference sources accurately. How can you write an informative essay on historical events?To avoid finding it difficult to find information on your topics, pick a topic that has been well researched and has several sources of information on it. European history is well researched.
In the introduction, talk about why you think this topic is significant and include a thesis statement that would be the main logic you are producing details about.
Then divide this thesis into several points and talk about each point in a different paragraph. Use sentences that are not too long so that people don't lose interest.
Use primary and secondary information sources but make sure you reference these sources in the required format.
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Determine an equivalent expression by rationalizing the denominator: (5√3)/(4-√6)
Step-by-step explanation:
so when you want to rationalize the denominator when it's in the form [tex](a-\sqrt{b})[/tex] you multiply by the conjugate which is [tex](a+\sqrt{b})[/tex] which is where the sign is the opposite. This is because it's using the difference of squares to get rid of the square root. Because [tex](a-b)(a+b) = a^2-b^2[/tex] this will remove the square root since it's going to become square and the ab - ab will cancel so there will be no square root
Multiply by conjugate
[tex]\frac{5\sqrt3}{4-\sqrt6} * \frac{4+\sqrt6}{4+\sqrt6}\\[/tex]
Simplify:
[tex]\frac{20\sqrt{3} + 5\sqrt{6 * 3}}{16-6}[/tex]
Simplify radical
[tex]\frac{20\sqrt{3} + 15\sqrt{2}}{10}\\[/tex]
You could go further and do
[tex]2\sqrt{3} + 1.5\sqrt{2}[/tex]
The data below represent the number of days absent per year in a population of three employees of a small company:
1 4 7
Assuming that you sample without replacement, select all possible samples of n = 2 and construct the sampling distribution of the mean. Compare the mean of all the samples means and also compute the population mean. Are they equal? What is the property called?
Repeat (a) for all the sampling distribution of the mean in (a) for n= 3. Which sampling distribution has less variability? Why?
Assuming that you sample with replacement, repeat (a) through (c) and compare the results. Which sampling distribution have the least variability – those in (a) or (b) ? Why?
The sampling distribution is illustrated below.
How to illustrate the sampling?Based on the information given, the population is illustrated as 1, 4, 7. The sample without replacement will be:
Sample Mean
1 and 4. 2.5
1 and 7. 4
4 and 7. 5.5
The population mean will be:
= (1 + 4 + 7)/3
= 4
The sample mean is an unbiased estimator of the population mean.
The sampling with replacement illustrates that the mean will be:
= 36/9 = 4
Also, when n = 3, the number of samples will be:
= 3³ = 27
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A triangle has integer length sides. If two sides of the triangle are 16 and 21, how many possible lengths are there for the third side
There are 31 possible lengths for the third side.
Unknown Side + 16 > 21
Unknown Side > 5
16 + 21 > Unknown Side
37 > Unknown Side
Unknown Side < 37
So, the possible integer lengths range from
6 - 36
= 36 - 6 + 1
= 31 possible lengths
The length of the third side of a triangle has to continually be among (but not equal to) the sum and the distinction among the alternative facets. As an instance, take the example of two, 6, and seven. and consequently, the 0.33 facet length has to be extra than four and less than eight.
The regulation of Cosines to calculate the unknown aspect, then use the Law of Sines to find the smaller of the opposite angles and then use the 3 angles add to 180° to find the final attitude.
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How would you write x + y = 2, x + 2y = 3 as a word problem?
Answer: x+y=
Step-by-step explanation:
you would just write it out step by step explaining wht u need to do to solve the question
Which expression is equivalent to the difference shown?
5x+1/5x - 4x+1/4x
Answer:
1 9/20x or 29/20x
Step-by-step explanation:
Reorder so it can be seen better
5x-4x+1/5x+1/4x
Combine like terms
x+1/5x+1/4x
Common multiple
x+4/20x+5/20x
Combine like terms
9/20x+x
Finalize
29/20x
Simplified
1 9/20x
Answer: -1/20x
Step-by-step explanation:
got all 5 correct this one was one of my five
The cost to rent a moving van for a day is an initial cost of $39 plus $0.35 per mile driven. What is the total cost if you drive 325 miles
The cost to drive 325 miles is $152.75.
Given: Initial cost = $39
Per mile cost= $0.35
To find: To find the total cost for 325 miles
Concept: Multiplication is the method of finding the product of two or more numbers. It is a primary arithmetic operation that is used quite often in real life.
The cost to drive 325 miles without adding the initial cost = $0.35*325 = $ 113.75
The cost to drive 325 miles while adding the initial cost = $ 113.75 +39 = $ 152.75
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When p2 – 4p is subtracted from p2 + p – 6, the result is
[tex]\Large\maltese\underline{\textsf{Our problem:}}[/tex]
When [tex]\bf{p^2-4p}[/tex] is subtracted from[tex]\bf{p^2+p-6}[/tex], the result is...?
[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]
[tex]\bf{Subtract:}[/tex]
[tex]\bf{p^2+p-6-p^2-4p}[/tex]. | combine like terms
[tex]\bf{p^2-p^2+p-4p-6}[/tex] | simplify
[tex]\bf{0p^2-3p-6}[/tex] | simplify
[tex]\bf{-3p-6}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{-3p-6}[/tex]
[tex]\boxed{\bf{aesthetic \not101}}[/tex]
Answer:
5p - 6
Step-by-step explanation:
p² + p - 6 - (p² - 4p) ← distribute parenthesis by - 1
= p² + p - 6 - p² + 4p ← collect like terms
= 5p - 6
In the diagram, ABCDE is a regular pentagon. The sides AB and DC are produced to meet at F. Find the angles x, y and z.
Answer:
x = 108°
y = 72°
z = 36°
Step-by-step explanation:
Finding unknown angles:If all sides are equal in a pentagon, then it is a regular pentagon.
n = the number of sides = 5
Sum of all angles in a pentagon = (n -2) * 180
= (5 - 2)* 180
= 3 *180
= 540°
Sum of each angle of regular pentagon = 540 ÷ 5
= 108°
[tex]\sf \boxed{\bf x= 108^\circ}[/tex]
Linear pair: If the non common arm of adjacent angles form a straight line, then the adjacent angles are called linear pair and they add up to 180°
∠DCB + y = 180 ° {Linear pair}
108 + y = 180
y = 180 - 108
[tex]\sf \boxed{\bf y = 72^\circ}[/tex]
Exterior angle property of triangle: The exterior angle equals the sum of opposite interior angles.
In Δ BCF ,
x = y + z
Now, substitute the values of x and y , and we can find the value of z.
108° = 72 + z
108 - 72 = z
[tex]\sf \boxed{\bf z = 36^\circ}[/tex]
Solve to find x and y in the diagram.
The figure shows two parallel lines and a transversal. The intersection of the first line and the transversal forms four angles, the top right angle is labeled as a right angle, the bottom right angle measures 6 times x plus 5 times y degrees. The intersection of the second line and the transversal forms four angles, the bottom right angle measures 10 times y degrees.
The values of x and y by the descriptions in the task content are; 7.5 and 9 respectively.
What are the values of x and y?It follows from the task content that the description in the task content registers the bottom right angle measure of the second intersection as equal to 10y.
Hence, it follows that; 10y = 90 and; y = 9.
From the first intersection; 6x + 5y = 90;
6x + 5(9) = 90
6x + 45 = 90
6x = 45
x = 45/6 = 7.5
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i need help with this one
Answer:
horizontal asymptote of y = -7
Step-by-step explanation:
The parent function is shown on the coordinate plane. The graph of the parent function has a horizontal asymptote (an imaginary line that the graph approaches, but never touches or intersects) of y = 0.
Since the function of g(x) = e^x - 7 is the graph of the parent function translated 7 units down, the function would have a horizontal asymptote of y = -7.
What is the value of g( − 3) when g(x) = 2x-2
Hello,
[tex]g(x) = 2x - 2[/tex]
[tex]g(-3) = 2 \times (- 3) - 2 = -6 - 2 = -8[/tex]
Answer: g(-3) = -8
Given that:
g(x) = 2x - 2To find g(-3), insert (x = -3):
⇒ g(-3) = 2(-3) - 2
⇒ g(-3) = -6 - 2
⇒ g(-3) = -8
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Which is equivalent to (negative 2 m 5 n) squared, and what type of special product is it?
The difference of squares is 4m^2 - 20mn + 25n^2
Its a perfect square trinomial.
What is perfect square trinomial?A perfect square trinomial is the square of a binomial. It follows a pattern when it is factored, so that the first and last terms are perfect squares of monomials and the middle term is twice their product. If the pattern does not fit for a particular trinomial, it is not a perfect square trinomial.
How to solve this equation?(-2m + 5n)^2
(-2m + 5n)(-2m + 5n)
4m^2-10mn-10mn+25n^2
4m^2 - 20mn + 25n^2
Thus, the difference of squares is 4m^2 - 20mn + 25n^2
Its a perfect square trinomial.
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What is the area of a rectangle with vertices at (−3, −1), (1, 3), (3, 1), and (−1, −3)?
Do not round any side lengths
Using the distance formula, the area of the rectangle is: 16 units².
What is the Area of a Rectangle?Area of a rectangle = (length)(width).
Given the vertices:
A(−3, −1)B(1, 3)C(3, 1)D(−1, −3)Area = (AB)(BC)
Apply the distance formula, [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex], to find AB and BC:
AB = √[(1−(−3))² + (3−(−1))²]
AB = √[(4)² + (4)²]
AB = √32
BC = √[(1−3)² + (3−1)²]
BC = √[(−2)² + (2)²]
BC = √8
Area = (√32)(√8) = √256
Area = 16 units²
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PLS HELP THIS IS URGENT!
GIVING BRAINLIEST
Answer: 36
Step-by-step explanation:
[tex]\overline{AB} \cong \overline{BC}[/tex] (Triangle ABC is isosceles)
[tex]m\angle CAB=m\angle CBA=30^{\circ}[/tex] (base angles of an isosceles triangle are congruent)
[tex]\angle MCB=90^{\circ}[/tex] (In triangle CMB, angles in a triangle add to 180 degrees)
[tex]\angle ACM=30^{\circ}[/tex] (triangle sum theorem)
[tex]MB=24[/tex] (30-60-90 triangle CMB)
[tex]AB=12[/tex] (sides opposite congruent angles in a triangle are congruent)
[tex]AB=36[/tex] (segment addition postulate)
The value of AB = 36
What is an isosceles triangle?An isosceles triangle is a triangle with base angles equal with any two sides equal.
Analysis:
∠ACB = 120
ABC is isosceles, so ∠CAB = ∠CBA = x
x + x + 120 = 180 ( sum of angles in Δ ABC)
2x = 60
x = 30
∠AMC = 180 - ∠BMC( angles on a straight line)
= 180 - 60 = 120
∠ACM = 180 - (30 + 120) = 180 - 150 = 30°
∠MCB = 90°
using sine rule,
12/sin 30 = AM/ sin 30
AM = 12
MB/sin 90 = 12/sin30
MB sin 30 = 12 sin 90
MB = 12/sin 30 = 12/0.5 = 24
AB = MB + AM = 24 + 12 = 36
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A deck has side lengths 16 feet, 18 feet, 16 feet, 8 feet, and 12 feet.
The dimensions of a proposed deck are written on the floor plan. What is the area of the proposed deck? Round to the nearest square foot.
317 square feet
413 square feet
437 square feet
513 square feet
The area of the deck is 413 square feet
How to determine the area of the proposed deck?Start by calculating the area of the outer rectangle using:
Area = Length * Width
This gives
Area1 = (18 + 12) * (16 + 8)
Area1 = 720
Next, calculate the area of the inner rectangle using:
Area = Length * Width
This gives
Area2 = 16 * (18 + 8)
Area2 = 416
Subtract these areas
A1 = Area1 - Area2
A1 = 720 - 416
A1 = 304
Next, calculate the area of the outer semicircle using:
Area = 0.5πR²
This gives
Area1 = 0.5 * 3 * (12-1)²
Area1 = 181.5
Next, calculate the area of the inner semicircle using:
Area = 0.5πr²
This gives
Area2 = 0.5 * 3 * (7)²
Area2 = 73.5
Subtract these areas
A2 = Area1 - Area2
A2 = 181.5 - 73.5
A2 = 108
Add A1 and A2
A = 304 + 108
Evaluate the sum
A = 412
Hence, the area of the deck is 413 square feet
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PLS HELP I NEED THIS QUICK THANK YOU IN ADVANCE
Use the substitution method to solve the system of equations. Choose the
correct ordered pair.
y = 5x-17
y = x + 3
OA. (5,8)
OB. (4,7)
O C. (1,-12)
OD. (5,-17)
Answer:
A(5 ; 8)
Step-by-step explanation:
y = 5x - 17
y = x + 3
5x - 17 = x + 3
⇔ 5x - x = 3 + 17
⇔ 4x = 20
⇔ x = 20/4
⇔ x = 5
y = 5 + 3 = 8
So (5 ; 8)
Answer:
We can use the substitution method to solve the system of equations.
Since y = x + 3, we can substitute this expression for y in the first equation:
y = 5x - 17
x + 3 = 5x - 17
Subtracting x from both sides, we get:
3 = 4x - 17
Adding 17 to both sides, we get:
20 = 4x
Dividing both sides by 4, we get:
x = 5
Substituting this value of x into either equation, we get:
y = x + 3 = 5 + 3 = 8
Therefore, the correct ordered pair is (5, 8), which corresponds to the point where the two lines intersect.
The correct answer is (A) (5,8).
7. Try It #7
Look at the graph in Figure 22 and identify the following for the function j(t) :
d. Is j(t) parallel or perpendicular to h(t) (or neither)?
Answer:
The given lines are un-related.
Step-by-step explanation:
In the question two functions are given as h(t)=3t-4 and j(t)=5-t.
It is required to find whether these lines are perpendicular, parallel or neither.
Step 1 of 1
Find the slope of two lines by comparing these to the standard form.
y=mx+b
Then, [tex]$m_{1}[/tex]=3
And [tex]$m_{2}[/tex]=-1
Since, both slopes are neither equal nor reciprocal of each other.
Therefore, the lines are un-related.