Answer:
The speed of slower car is 55 miles per hour.
Step-by-step explanation:
Given as :
The speed of slower car = [tex]s_2[/tex] = s mph
The speed of faster car = [tex]s_1[/tex] = ( s + 20 ) mph
The distance cover by slower car = [tex]d_2[/tex] = 165 miles
The distance cover by faster car = [tex]d_1[/tex] = 225 miles
The time taken by both cars for travelling = t hours
The speed of the cars remains constant
Now, According to question
∵ Time = [tex]\dfrac{\textrm Distance}{\textrm Speed}[/tex]
So, For slower car
t = [tex]\dfrac{d_2}{s_2}[/tex]
Or, t = [tex]\dfrac{165}{s}[/tex] ............1
So, For faster car
t = [tex]\dfrac{d_1}{s_1}[/tex]
Or, t = [tex]\dfrac{225}{s+20}[/tex] ............2
Now, equating both the equations
I.e [tex]\dfrac{225}{s+20}[/tex] = [tex]\dfrac{165}{s}[/tex]
By cross multiplying
Or, 225 × s = 165 × (s + 20)
Or, 225 s = 165 s + 3300
Or, 225 s - 165 s = 3300
Or, 60 s = 3300
∴ s = [tex]\dfrac{3300}{60}[/tex]
I.e s = 55 miles per hour
So , The speed of slower car = [tex]s_2[/tex] = s = 55 miles per hour
Hence , The speed of slower car is 55 miles per hour. Answer
The points (0, -5) and (x, y) have a slope of 0. What could be the coordinates of the point (x, y)?The points (0, -5) and (x, y) have a slope of 0. What could be the coordinates of the point (x, y)?
Answer:
(∞,-5)
Step-by-step explanation:
For a line to have a slope of 0, it has to be horizontal.
Any point that has a y value of -5 could form a horizontal line along with (0,-5).
What do the expressions (3up3)and (3up4) have in common
Answer:
They both have 3 up ig
Step-by-step explanation:
evaluate the indicated function for f(x)=x^2-7 and g(x) =x-2
Answer:
f(g(x))=(x-2)^2 - 7
(x-2)(x-2) - 7
x^2-2x-2x+4-7
x^2-4x-3
g(f(x))=x^2-2-7
x^2-9
(x+3)(x-3)
Step-by-step explanation:
to solve for f(x), replace x with the g(x).since we don't multiply a bracket with the negative or the positive signs to the exponent, you have to factor into two binomials.use the FOIL method to eliminate the brackets.add like-termsto find g(x), replace x with the f(x).add like-termssince there's difference of square, factor them into two binomialsTo evaluate functions, you substitute x with the given value in the function and perform the calculation. For example, evaluating f(3) for the function f(x)=x^2-7 gives f(3)=2, while evaluating g(3) for the function g(x)=x-2 gives g(3)=1.
Explanation:The functions given are f(x)=x^2-7 and g(x)=x-2. To evaluate these functions, we substitute a value for x into the function and perform the calculation. For example, if we want to evaluate f(3), we replace x in the function f(x) with 3.
So for f(3)=3^2-7, we do the following: f(3)=9-7=2.
For g(3), we substitute x in the function g(x) with 3: g(3)=3-2=1
It's important to note that the value you're evaluating might change depending on the question, but this is the basic process for evaluating a function at a given value or values.
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Theo wants to use a cokkie recipe that makes 36 cookies but he wants to reduce the number of cookies to 24.if the recipe specifes using 2 cups of sugar, how many sugar should he use ?
Answer:
Theo Should use 1.3 cups of Sugar to make 24 cookies.
Step-by-step explanation:
Given;
Number of cookies required by recipe = 36 cookies
Number of cookies Theo wants to use = 24 cookies
Number of cups sugar recipe requires = 2 cups
We need to find Number of cups sugar Theo should use to make cookie according to recipe.
Now,
For 36 cookies = 2 cups of sugar
So For 24 cookies = Number of cups of sugar required for 24 cookies.
By Using Cross Multiplication we get;
Number of cups of sugar required for 24 cookies = [tex]\frac{24\times2}{36}= 1.33\ cups[/tex]
Hence Theo Should use 1.3 cups of Sugar to make 24 cookies.
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Which of the following shows that polynomials are closed under subtraction when two polynomials, (5x2 + 2x − 6) − (3x2 − 6x + 2), are subtracted?
2x2 − 4x − 4; will be a polynomial
2x2 − 4x − 4; may or may not be a polynomial
2x2 + 8x − 8; will be a polynomial
2x2 + 8x − 8; may or may not be a polynomial
Answer:
For [tex](2x^2 + 8x - 8)[/tex], the group is CLOSED as it a polynomial.
Step-by-step explanation:
Here, the given polynomials are:
[tex]P(x)=(5x^2+2x-6)\\Q(x)=(3x^2-6x+2)[/tex]
Now, a group G is said to be CLOSED UNDER SUBTRACTION if,
a and b are he elements of G ⇒ (a-b) is ALSO AN ELEMENT of G
Now, here:
[tex]R(x) = P(x) - Q(x) = (5x^2+2x-6) - (3x^2-6x+2) = (2x^2 + 8x - 8)[/tex]
or, [tex]R(x) = (2x^2 + 8x - 8)[/tex]
Also, R(x) is a POLYNOMIAL.
So, R(x) is an Element of group G.
So, the set G of polynomials.
Hence, for the polynomial [tex](2x^2 + 8x - 8)[/tex], it will be a polynomial the group is CLOSED.
Answer:
The answer would be C
Step-by-step explanation:
Find the coordinates for the midpoint of the segment with endpoints give (3,5) and (-2,0)
Answer:
The coordinates of the mid-point are :
[tex](\frac{1}{2}, \frac{5}{2})[/tex]
Step-by-step explanation:
We know that, the coordinates of the mid-point (x, y) of a line segment joining the points (x₁, y₁) and (x₂, y₂) is given by
[tex](x, y) = (\frac{x_{1} +x_{2} }{2},\frac{y_{1}+y_{2} }{2} )[/tex]
Now, we have the given points as (3, 5) and (-2, 0).
By using the above formula, coordinates of the mid-point (x, y) of the line-segment joining the points (3, 5) and (-2, 0) is given by,
[tex]x = \frac{3+(-2)}{2} = \frac{3-2}{2} = \frac{1}{2}[/tex]
[tex]y = \frac{5+0}{2} = \frac{5}{2}[/tex]
∴ coordinates of the mid-point of the line-segment joining the points (3,5) and (-2,0) is [tex](\frac{1}{2}, \frac{5}{2})[/tex].
Rewrite the equation 2x + 3y = 6 in slope-intercept form. y = -2 x + 6 y = - x + 2 y = 2 x + 6 3 y = -2 x + 6
Answer:
y=-2/3x+2
\\\\\\\\\\\\\\\\\\\\\
In the figure, CD=EF and AB= CE. Complete the statements to prove that AB = DF.
CD + DE= EF+ DE by the (addition,subtraction,substitution, or transitive)
Property of Equality.
CE=CD + DE and DF = EF + DE by (addition,subtraction, segment addition, or transitive)
CE = DF by the (addition,subtraction, segment addition, or transitive) Property of Equality.
Given, AB = CE and CE = DF implies AB = DF by the (addition,subtraction, segment addition, or transitive) Property of Equality.
Answer:
Hence Proved AB = DF
Step-by-step explanation:
In the Figure:
Given;
CD = EF
AB = CE
We need to prove AB = DF
Solution:
CD = EF ⇒ (Given)
Now Adding both side by DE we get;
CD + DE = EF + DE ⇒by the (Addition) Property of Equality.
CE=CD + DE and DF = EF + DE ⇒(Segment Addition)
Now we know that if [tex]a=b \ and \ b =c \ so \ a=c[/tex]
CE = DF ⇒by the (transitive) Property of Equality.
Now Given:
AB = CE
CE = DF
Now we know that if [tex]a=b \ and \ b =c \ so \ a=c[/tex]
AB = DF ⇒by the (Transitive) Property of Equality)
The correct options to fill in the gaps are:
Addition postulateSegment AdditionTransitive Property of EqualityTransitive Property of EqualityFrom the diagram given, we have that;
CD = EFAB = CEWe are to show that the segment AB is congruent to DF
Also from the diagram
CD + DE = EF + DE according to the Addition postulate of Equality CE = CD + DE and DF = DE + EF according to the Segment AdditionSince CD = EF, hence DF = DE + CE, this meansCD = DF by the Transitive Property of EqualitySimilarly, given that:
AB = CE and CE = DF implies AB = DF by the Transitive Property of Equality.
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What is the slope of the line passing through the point 3,5 and -1,7
Answer:
m = -1/2
Step-by-step explanation:
As we move from the point (-1, 7) to the point (3, 5), x increases by 4 (this is the "run") and y decreases by 2 (this is the "rise").
Thus, the slope of the line connecting these two points is
m = rise / run = -2/4, or m = -1/2.
Answer:
1/2
Step-by-step explanation:
A camping leader bought the items listed in the table for his team. What is the average cost of an item in his purchase?
A. $7.75
B.$7.58
C.$6.60
D.$5.44
The right answer is Option D: $5.44
Step-by-step explanation:
Given,
Cost of one sun visor = $6.25
Cost of 11 sun visors = 6.25*11 = $68.75
Cost of one sunglasses = $8.90
Cost of 4 sunglasses = 8.90*4 = $35.60
Cost of one water bottle = $9.50
Cost of 8 water bottles = 9.50*8 = $76
Cost of one whistle = $1.75
Cost of 15 whistles = 1.75*15 = $26.25
Total number of items = 11+4+8+15 = 38
Total cost of items = 68.75+35.60+76+26.25 = $206.60
Average = [tex]\frac{Sum\ of\ prices}{No.\ of\ items}[/tex]
[tex]Average=\frac{206.60}{38}\\Average=\$5.436[/tex]
Rounding off to nearest hundredth
Average = $5.44
The average price of an item is $5.44
The right answer is Option D: $5.44
Keywords: average, sum
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Greg wants to find the amount of concrete needed to cast a pillar he has designed. The pillar will have a base area of square yard and a height of yard. How much concrete does he need to cast the pillar?
Answer:
1/392 cubic yard
Step-by-step explanation:
V = Bh = (1/28 yd²)·(1/14 yd) = 1/(28·14) yd³ = 1/392 yd³
Answer:
1/392
Step-by-step explanation:
i was foing this test and turns out this is right.
alexandra earns 12$ an hour babysitting. she babysat 10 hours last week and 12 hours this week what equation shows how to find how much money (m) she earned in all
$120 +$144 =$264
Alexndra earns $264
Can you plz tell me the answer to:
1. Make w the subject of
y-aw=2w-1
2. Make q the subject of
2(q+p)=1+5q
3. Make r the subject of
t=r/r-3
4. Make r the subject of
P=10(q-3r)/r
Answer: see attached file
Step-by-step explanation: see attached file for explanation. Thanks!
You pick a card at random, put it back, and then pick another card at random. What is the probability of picking a number less than 7 and then picking a 7 when you have 4 card: 4567
Answer:
1/8
Step-by-step explanation:
1 chance of of 4 cards. * because since she draws 4 times you do 4+4 = 8.
Can someone help me with these problems? I'm in k12 and this assignment was in classkick, so if anyone already completed this and can help, please do. I also am going to be asking some more questions, if you can help with those too. Thanks! (Will give brainliest.)
Answer:
See the explanation
Step-by-step explanation:
Given function
[tex]Y=3x+1[/tex]
We need to find [tex]y[/tex] value corresponding to each [tex]x[/tex] value.
So, plug each [tex]x[/tex] value in equation we get,
[tex]plug\ x=4\\y=3(4)+1\\y=12+1\\y=13\\\\plug\ x=6\\y=3(6)+1\\y=18+1\\y=19\\\\plug\ x=10\\y=3(10)+1\\y=30+1\\y=31[/tex]
Now in next part of question it ask us to check each ordered pair.
Let us plug each [tex]x[/tex] value and [tex]y[/tex] value in the function [tex]y=-3x-5[/tex]
[tex]plug\ (1,-8)\\-8=-3(1)-5\\-8=-3-5\\-8=-8\\\\plug(-5,0)\\0=-3(-5)-5\\0=15-5\\0\neq10\\\\plug\ (-2,1)\\1=-3(-2)-5\\1=6-5\\1=1\\\\plug\ (-1,-2)\\-2=-3(-1)-5\\-2=3-5\\-2=-2\\[/tex]
we can see ordered pair [tex](1,8),(-2,1)and(-1,-2)[/tex] true for function [tex]y=-3x-5[/tex]
The triangle will be rotated 180° clockwise around the point (3, 4) to create A A'B'C.Which
characteristics of AA'B'C' will be the same for the corresponding characteristics of AABC? Select ALL that
apply.
The question is incomplete. Here is the complete question:
The triangle will be rotated 180° clockwise around the point (3, 4) to create A A'B'C.Which
characteristics of AA'B'C' will be the same for the corresponding characteristics of AABC? Select ALL that apply.
(A) The coordinates of A'.
(B) The coordinates of B'.
(C) The perimeter of Δ A'B'C'.
(D) The area of Δ A'B'C'.
(E) The measure of ∠B'.
(F) The length of segment A'B'.
Answer:
(C) The perimeter of Δ A'B'C'.
(D) The area of Δ A'B'C'.
(E) The measure of ∠B'.
(F) The length of segment A'B'.
Step-by-step explanation:
Given:
A triangle ABC rotated by 180° clockwise around the vertex C(3,4) to create Δ A'B'C.
Now, a rotation is a rigid motion transformation. In rigid transformation, the size, length, angle measures, perimeter and area of the figure doesn't change and remains the same as the original figure.
Rotation only changes the position of the points on the figure.
Here, as the triangle ABC is rotated about vertex C, the position of vertex A and B will change. But, the angles made by each of the vertices will remain same. Also, the side lengths of the triangle will remain the same. So, the perimeter and area will also not change. As the point of rotation is point C, the vertex C' will be same as vertex C.
So, the correct options are (C), (D), (E), and (F).
A card is drawn at random from a standard 52-card deck. What is the probability that it is an odd number (3,5,7,9) or a spade (or both)?
Answer:
The probability of selecting the given event = [tex]\frac{25}{52}[/tex]
Step-by-step explanation:
A card is drawn at random from a standard 52-card deck.
We have to find the probability of selecting an odd numbered card(3,5,7,9) or spade or both.For this we have to find the number of favourable cases.
Favorable cases = 13 (all the spades) + 12(4 odd numbered cards from each of the remaining 3 )
= 25
Final probability = [tex]\frac{number of favourable cases}{total number of cases}[/tex]
= [tex]\frac{25}{52}[/tex]
Hence the probability = [tex]\frac{25}{52}[/tex]
5( q + 27 ) - -30=95
STEPS:
First distribute the 5 through the parentheses to get 5q + 135. So the problem now reads 5q + 135 - (-30) = 95.
Now, minus a negative can be changed to plus a positive so - (-30) can be changed to +30 so our equation now reads 5q + 135 + 30 = 95.
Before adding or subtracting anything from both sides of the equation, make sure you simplify the left side as much as possible. Notice that we can add 135 and 30 to get 165 so the left side simplifies to 5q + 165 = 95.
Now we can simply subtract 165 from both sides of the equation to get 5q = -70.
Now simply divide both sides of the equation by 5 to get q = -14.
Complete the inequality statement.
14 ft ____ 4 1/2 yd.
<
>
='
PLEASE ANSWER CORRECTLY
DO NOY ANSWER INCORRECTLY JUST FOT POINTS TY
Answer: 14ft > 41/2
Step-by-step explanation:
Your answer is:
14ft > 41/2yd
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The lengths of the diagonals of a rhombus are 2x and 10x. What expression gives the perimeter of the rhombus?
A. 42
B.
196
Answer:
[tex]P=4x\sqrt{26}\ units[/tex]
Step-by-step explanation:
we know that
The sides of a rhombus are all congruent and the diagonals are perpendicular bisectors of each other
so
Applying the Pythagorean Theorem
[tex]c^2=a^2+b^2[/tex]
where
c is the length side of the rhombus
a and b are the semi-diagonals
we have
[tex]a=2x/2=x\ units\\b=10x/2=5x\ units[/tex]
substitute the values
[tex]c^2=x^2+(5x)^2[/tex]
[tex]c^2=26x^2[/tex]
[tex]c=x\sqrt{26}\ units[/tex]
To find out the perimeter of the rhombus multiply the length side by 4
[tex]P=(4)(x\sqrt{26})[/tex]
[tex]P=4x\sqrt{26}\ units[/tex]
What is the value of x when solving the equation 4x+(-4) = -2x+8
Answer:
You have to simplify the equation and find the answer
Step-by-step explanation:
[tex]4x + ( - 4) = - 2x + 8 \\ \\ 4x + 2x = 4 + 8 \\ \\ 6x = 12 \\ \\ x = 2[/tex]
Answer:
Step-by-step explanation:
4x+(-4) = -2x+8
4x - 4 = -2x + 8
Collecting like terms
4x + 2x = 8 + 4
6x = 12
Dividing through by 6
x = 12/6
x = 2
Name two coordinates that are on the line: [tex]y = 12[/tex]
Name two coordinates that are on the line: [tex]x = -5[/tex]
Answer:
(1,12) and (2,12).
(- 5,1) and (- 5, 2).
Step-by-step explanation:
y = 12 is a line that is parallel to the x-axis and at a constant distance of 12 units above the x-axis. Therefore, the points on the line will have any x-coordinate but have a constant y-coordinate i.e. 12.
Therefore, the two points on the line y = 12 can be (1,12) and (2,12).
x = - 5 is a line that is parallel to the y-axis and at a constant distance of 5 units left of the y-axis. Therefore, the points on the line will have any y-coordinate but have a constant x-coordinate i.e. - 5.
Therefore, the two points on the line x = - 5 can be (- 5,1) and (- 5, 2). (Answer)
How many 1/3 are in 1 2/3
Answer:12
Step-by-step explanation:bcs in 1/3 it has the same denominatoor
A candidate for mayor plans to campaign at 5 shopping malls before the election
In how many different ways can the candidate schedule the vists?
Enter your answer as a whole number
I’ll put you as brainliest
Answer:
120 ways
Step-by-step explanation:
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Answer:
56
Step-by-step explanation:
add
Andre is working from home to a festival that is 1 5/8 km away. He takes a quick rest after walking 1/3 km what fraction of the trip has Andre completed
Answer:
The fraction of trip completed by Andre is [tex]\frac{31}{24}[/tex] km
Step-by-step explanation:
Given as :
The Total distance between the home to a festival = 1 [tex]\frac{5}{8}[/tex] km
I.e The total distance between the home to a festival = [tex]\frac{13}{8}[/tex] km
The distance cover by Andre before taking rest = [tex]\frac{1}{3}[/tex] km
Let The fraction of trip completed by Andre = x km
So, According to question
The fraction of trip completed by Andre = The Total distance between the home to a festival - The distance cover by Andre before taking rest
or, x = [tex]\frac{13}{8}[/tex] km - [tex]\frac{1}{3}[/tex] km
or, x = [tex]\frac{39 - 8}{24}[/tex] km
∴ x = [tex]\frac{31}{24}[/tex] km
Or, The fraction of trip completed by Andre = x = [tex]\frac{31}{24}[/tex] km
Hence , The fraction of trip completed by Andre is [tex]\frac{31}{24}[/tex] km Answer
Answer:
[tex]\frac{4}{15}[/tex]
Step-by-step explanation:
We know that the total distance is
[tex]1\frac{5}{8}km[/tex] which is standard fraction would be [tex]\frac{13}{8}km[/tex].
So, Andre walks [tex]\frac{1}{3}km[/tex], that means he needs to walk the following distance to get to the festival
[tex]\frac{13}{8}-\frac{1}{3}=\frac{39-8}{24}=\frac{31}{24}km[/tex]
Now, to find the fraction of the tripe that represents the distance he already completed, we have to divide
[tex]\frac{1}{3} \div \frac{13}{8}=\frac{1}{3} \times \frac{8}{13}=\frac{8}{30}=\frac{4}{15}[/tex]
Therefore, we completed a [tex]\frac{4}{15}[/tex] part of the total distance.
Given the equations, identify which way the parabola opens by matching an equation on the left with a term on the
right
Answer:
1) up
2) correct
3) left
4) down
Step-by-step explanation:
do you not have a graphing calculator, it really helps you with these.
The parabola opens by matching an equation are as follows,
[tex]&x^{2}=3 y \\[/tex] up[tex]&y^{2}=6 x \\[/tex] Right[tex]&y^{2}=-2 x \\[/tex] Left[tex]&x^{2}=-10 y[/tex] DownWhat is Parabola?The standard equation of a regular parabola exists [tex]y^{2} = 4ax.[/tex] Some of the important representations below are helpful to understanding the features and parts of a parabola. Focus: The point (a, 0) is the focus of the parabola.
A positive value denotes the parabola opens up, and a negative value means the parabola opens down. That stands If the quadratic exists given in standard or vertex form.If a exists positive, then the parabola opens up. If a stands negative, then the parabola opens down.A parabola is a plane curve that exists mirror-symmetrical and is approximately U-shaped. It fits several superficially various mathematical descriptions, which can all be established to define the same curves.
The parabola opens by matching an equation are as follows,
[tex]&x^{2}=3 y \\[/tex] up[tex]&y^{2}=6 x \\[/tex] Right[tex]&y^{2}=-2 x \\[/tex] Left[tex]&x^{2}=-10 y[/tex] DownTo learn more about Parabola refer to:
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A toll collector on a highway receives $8 for trucks and $5 for sedans. At the end of a 3-hour period, she collected $208. How many trucks and sedans passed through the toll booth during that period? List all possible solutions.
Answer:
The number of trucks and sedans can be
(0 trucks ,26 sedans)
(8 trucks ,21 sedans)
(24 trucks ,11 sedans)
(25 trucks ,1 sedans)
(32 trucks ,6 sedans)
(16 trucks ,16 sedans)
Step-by-step explanation:
Given:
The cost for trucks =$5
The cost for sedans =$8
The total amount collected = $208
To Find:
Number of trucks and sedans passed through the toll booth =?
Solution:
Let the number of trucks be x and the number of sedans be y
Then
5x + 8y = 208-------------------------------(1)
By Trail and error method
5(0) + 8(26) = 208
5(8) + 8(21) = 208
5(24) +8(11) =208
5(25) + 8(1) = 208
5(32) + 8(6) =208
5(16) + 8(16) = 208
5. What is the amplitude of the sinusoidal function? Please help
Answer: 4
Step-by-step explanation:
The amplitude is the distance from the baseline to the maximum.
What is 272,062 rounded to the nearest hundred?
Answer:
272,100
This is because 62 rounds up
Answer:
272,100
You get this answer by looking at the hundreds place and then looking at the right of it. The hundreds place is the 0 and the the right of it is 6, so 5 and up round up 4 and down round down and in this case, 6 is above 5, so it rounds up to 272,100!
Hope this helped!
How many ways are there to answer a $10$-question true/false test, where at least $3$ of the questions have been answered with a false?
Answer:
968 ways
Step-by-step explanation:
This is a question of permutation and combination.
Each equation can have two different answers.
Thus the total number of cases will be (for 10 questions) :
[tex]2*2*2*2*.....10times=2^{10}[/tex] cases.
Now to find the number of ways to at least answer 3 questions False will be total minus the number of question with at most 2 False answers.
Number of ways in which no answer is False : 1 ( all are true )Number of ways in which ONLY one answer is False : [tex]10_C_1[/tex] where [tex]n_C_r=\frac{n!}{(n-r)!r!}[/tex]Number of ways in which ONLY two answers are False :[tex]10_C_2[/tex]Total ways (at most 2 answers false) = [tex]1+10_C_1+10_C_2[/tex] ;
∴
The number of ways in which at least 3 have False as the answer is :
[tex]2^{10}-(1+10_C_1+10_C_2)\\=968[/tex] WAYS.