Okay, here we have this:
Considering the provided information, we are going to write and solve the correspondinf system of equation, so we obtain the following:
According to the information given, we obtain the following system of equations, where we take x as money spent on fruit and y as money spent on green vegetables, so we have:
[tex]\begin{gathered} x+y=30 \\ x+(x+5)=30 \end{gathered}[/tex]Now let's solve for x in the second equation:
x+x+5=30
2x+5=30
2x=30-5
2x=25
x=25/2
x=12.5
Now from the value of x that we got, then we will plug it into the first equation to get the value of y:
[tex]\begin{gathered} x+y=30 \\ 12.5+y=30 \\ y=30-12.5 \\ y=17.5 \end{gathered}[/tex]Then, finally we obtain that she spend $12.5 on fruits and $17.5 on green vegetables.
By driving 10 miles per hour faster, Goldie was able to
Ishave 2 hours and 30 minutes off her 50-mile trip to visit
her grandmother who lives in the mountains. Select the
equation that could be used to solve this problem. Use x to
represent her faster driving rate.
The faster driving rate of Goldie is 20 miles/hour.
Given that, by driving 10 miles per hour faster, Goldie was able to have 2 hours and 30 minutes off her 50-mile trip.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
Here, Speed = 10 miles/hour, Time = 2 hours and 30 minutes = 2.5 hours and Distance = 50 mile.
Now, Distance = Speed × Time
Let the faster driving rate be x.
50 = x × 2.5
⇒ x = 50/2.5
⇒ x = 20 miles/hour
Therefore, the faster driving rate of Goldie is 20 miles/hour.
To learn more about the speed, distance, and time visit:
brainly.com/question/4978052.
#SPJ1
Answer:
Step-by-step explanation:
I don't agree with the other answer.
You need to you systems of equations
So
d=50 t=t-2.5 x=r+10
d=rt
50=(r+10)(t-2.5) (faster equation)
50=rt (slower equation)
t=[tex]\frac{50}{r}[/tex] (substitute into faster equation)
50 = (r+10)(50/r -2.5) mult both sides by r to get rid of fraction
50r = (r+10)(50-2.5r) FOIL
50r = 50r -2.5r² + 500 -25r Simplify
2.5r²+25r-500=0 divide all by 2.5
r²+10r-200 factor
(r-20)(r+10) eliminate negative answer
r=20
x=r+10 =20+10 =30 mph
You and a friend have each randomly draw a card.
There are 52 cards in a deck.
There are 12 face cards in the deck, that is 3 face cards per suit.
The probability of getting at least from two draws is given to be:
[tex]P=P(X=1)+P(X=2)[/tex]Therefore, the probability is calculated using the formula:
[tex]P=\frac{^{12}C_1\times^{40}C_1}{^{52}C_2}+\frac{^{12}C_2}{^{52}C_2}[/tex]Using the combination formula, we have the solution to be:
[tex]\begin{gathered} \Rightarrow\frac{12\times40}{1326}+\frac{66}{1326}=\frac{480}{1326}+\frac{66}{1326} \\ P=\frac{546}{1326} \\ P=\frac{7}{17} \end{gathered}[/tex]The LAST OPTION is correct.
explain how you got it please
The simplest form of the expression as we have it is; (-4x^4z^2)(2xy^3z^2)
What does it mean to simplify?When we are asked to simplify, what we are asked to do is to write the expression that we have in a form that is simplest. That is, we should put the expression in a form that there would not be any simpler presentation of the expression.
We have;
(-2x^2z)^2(2xy^3z^2)
Then we now have to deal with the exponent outside the bracket;
(-4x^4z^2)(2xy^3z^2)
Thus, we now have the expression in the simplest form that it can take and it can not be further broken down.
Learn more about simplifying expressions:https://brainly.com/question/18077352
#SPJ1
5. Which expression does not have a value of 3?
å
O
O
-16-(-11)
19-16
-13-(-16)
1-(-2)
For which value of x does the graph of the following function F(x) have a
vertical asymptote?
F(x) =
1
X-11
Answer:
x = 1
Step-by-step explanation:
Horizontal asymptotes are the y-values for which a particular function is undefined;
Finding the horizontal asymptote for linear reciprocal function is quite simple;
For this kind of function, where there is no x term in the numerator, the horizontal asymptote is just equivalent to the constant added to the fraction (note: having no added constant is the same as having an added 0);
so:
f(x) = 1/(x - 1) = (1/( - 1 )) + 0
The horizontal asymptote is y = 0 for this function.
If it was F(x) = (1/(x - 1)) + 1, the horizontal asymptote would be y = 1
hope it help!! :)
can you show how to solve this proplem
In the given figure : lines l and m are parallel and a, b are transversal
Since, the lines a and b are parallel and l act as a transversal.
Then,
[tex]\begin{gathered} \angle BAC=\angle ACb\text{ (alternate interior angles)} \\ \text{ Substitute the values} \\ 2x=46 \\ x=\frac{46}{2} \\ x=23 \end{gathered}[/tex]x = 23
Answer : x = 23
name the rule and list the next three terms in the pattern 2,4,8,16,32...
This is Geometric progression G P
[tex]\begin{gathered} \\ 2^1=2 \\ 2^2=4 \\ 2^3=8 \\ 2^4=16 \\ 2^5=32 \\ 2^6=64 \\ 2^7=128 \\ 2^8=256 \end{gathered}[/tex]The next three terms are;
64,128,256
A model of a ship is made to a scale of 3:400
The surface area of the model is 7200 cm²
Calculate, in m², the surface area of the ship.
Answer:
Given:
Model : Ship = 3 : 400
The surface area of the model = 7200 cm²
To Find:
The surface area of the actual ship in m²
Let's start with the map scale given:
Model : Ship = 3 : 400
We start by adding in a unit. Usually, we choose the units associated with the model:
Model : Ship = 3 cm : 400 cm
Now, according to tot the question, we know that the actual ship is in m:
Model : Ship = 3 cm : 400 ÷ 100 m
Model : Ship = 3 cm : 4 m
The question asked for surface area, so the units have to be in squares:
Model : Ship = (3 cm)² : (4 m)
Model : Ship = 9 cm² : 16 m²
Now, that we have the units set correctly according to the question requirement, we will find 1 branch of the model:
Model : Ship = 9 cm² : 16 m²
Model : Ship = 9÷9 cm² : 16÷9 m²
Model : Ship = 1 cm² : 16/9 m²
Finally, we can find the required units by multiplying both sides with the required units:
Model : Ship = 1 cm² : 16/9 m²
Model : Ship = 1 x 7200 cm² : 16/9 x 7200 m²
Model : Ship = 7200 cm² : 12800 m²
Answer: The surface area of the ship is 12800 m²
(by the way, this was copied from the same website)
hope this helps :)
5-52: the first card selected from a standard 52-card deck is a king. a. if it is returned to the deck, what is the probability that a king will be drawn on the second selection? b. if the king is not replaced, what is the probability that a king will be drawn on the second selection? c. in part (b), are we assuming the card selections are independent? justify your answer.
Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability.
The probability of getting a king card is 1/13 or 0.077.
What is meant by probability?A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Given: Total number of probability - 52
Now, the first selected card is king and it is returned to the deck.
So it contains no effect on the second selection card.
Then, we have to estimate probability to obtain a king
probability = favourable outcomes for a king / total possible outcomess
= 4 king cards / 52 cards in total
= 4 / 52 = 1 / 13
The probability of getting a king card is 1 / 13 or 0.077
Therefore, the correct answer is option B. 1/13, or 0.077.
The complete question is:
The first card selected from a standard 52-card deck was a king. It isreturned to the deck, what is the probability that a king will be drawn on the second selection?
A. 1/4 or 0.25
B. 1/13, or 0.077
C. 12/13, or 0.923
D. 1/3 or 0.33
E. None of the above
To learn more about probability refer to:
https://brainly.com/question/13604758
#SPJ4
Karina is baking bread. she buys a small bag of flour that contains 2 2/3 cups of flour. the recipe calls for 2 5/7 cups of flour. does she have enough flour to bake the bread? explain how she can compare the fractions to know for sure.
Using approximation, the two are the same and she contains enough flour.
What is meant by the unitary method?The unitary technique entails finding the value by multiplying the single value and then solving the problem using the initial value of a single unit. If an event may take place in m different ways and a second event can take place in n different ways after it, then the two events that follow can take place in m n different ways.
Given that Karina buys a small bag of flour that has 2 2/3 cups of flour. The recipe calls for 2 5/7 cups of flour.
1) 2 2/3 cups of flour.
= ((2 × 3)+2)/3
= 2.666
Therefore, she get 2.666
2) 2 5/7 cups of flour.
= ((2 × 7) + 5)/7
= 2.714
Therefore, she get 2.714
Using approximation, the two are the same and she has enough flour.
To learn more about the unitary method, refer to;
brainly.com/question/23423168
#SPJ13
The cost (in dollars) of a basic music streaming service for m months
is represented by B(m) = 5m. The cost of the premium service is represented by
P(m) 10m. Describe the transformation from the graph of B to the graph of P.
The transformation from the graph of B to the graph of P is a vertical stretch by a scale factor of 2
How to determine the transformation?From the question, the function definitions are given as
B(m) = 5m
P(m) = 10m
Rewrite the function P(m) as follows
P(m) = 2 x 5m
Substitute B(m) = 5m in the equation P(m) = 2 x 5m
P(m) = 2 x B(m)
When a function is represented as
f(x) = kg(x), then the transformation is a vertical stretch by k
Hence. the transformation a vertical stretch by 2
Read more about transformation at
https://brainly.com/question/27224272
#SPJ1
A hyperbola has vertices (±5, 0) and one focus (6, 0). What is the standard-form equation of the hyperbola?show steps
The standard form of a hyperbola with center (h,k) is
We know the vertices are at (5,0) and (-5,0)
The vertices are at (h+a,k) and ( h-a,k)
The center must be at (0,0) and the a value is 5
The coordinates of the foci are at ( h+c,k) and ( h-c, k) and we know one of the foci is at (6,0)
c is equal to 6
We know that c^2 = a^2+b^2
6^2 = 5^2 + b^2
36 = 25+b^2
11 = b^2
We can write the equation
The following question has two parts. First, answer part A. Then, answer part B.
Use the model to answer the questions.
A rectangle is divided into two sections by a vertical line. The left section is labeled inside with 260. The right section is labeled inside with B. The left edge of the rectangle is labeled 13. Across the top outside of the rectangle, the sections are labeled A tens, a plus sign above the vertical line, and C.
Part A
Carter wants to use the model above to solve 273÷13. Explain how he would find parts A, B, and C of the model.
Part B
The final quotient for 273÷13 is
The knowledge of place value helped in solving 273÷13 with a rectangular model developed by Carter
The part labelled A is 26 tens
The part labelled B is 13 units
The part labelled C is 13 ones
How to determine parts A, B, and C using rectangular model developed by Carterinformation given in the question
A rectangle is divided into two sections by a vertical line
The left section is labeled inside with 260
The left edge of the rectangle is labeled 13
other information is in the attached diagram
How to used the model
Carter's model is a rectangle of length 273 and breadth 13.
273 / 13 = 21
This means that dividing the length into 13 places each unit is 13
273 - 13 = 260
hence the 260 represents 20 units, since one unit is subtracted
The knowledge of place value help to get the numbers to be arranged in tens and ones
putting the numbers in tens is done by dividing by 10
= 260 / 10
= 26
hence, A in tens is equivalent to 26
putting the numbers in ones is dine by dividing by 1
C = 13 / 1
C = 13 ones
a unit is 13, B = 13
B covers same space as C so they are equal
Learn more about using rectangular models :
https://brainly.com/question/27271326
#SPJ1
Need help making sure I have everything correct if wrong please advise Thank you
To question 16, we see that for every change of plus 2 drinks, they pay an additional value of $2.50. It means that each drink does cost half of this value.
This way, the equation that will give the value of the total cost will be:
[tex]Y=1.25\times X[/tex]Where X stands for the number of drinks, and 1.25 is the value of a single drink.
From the solution presented above, we are able to conclude that the rate of change represents the value of a unitary drink, in the present situation.
separate 84 into two parts such that one part will be 12 less than twice the other
Answer:
32, 52
Step-by-step explanation:
84=x+y
x=2y-12
Solving the system of equations
Plug second equation into first
84=(2y-12)+y
84=3y-12
y=32
Plug y into first equation
84=x+32
x=52
Hemework -13 .
Express the ratio 20cm to 15m in the form 1:n
Answer:
1: 75
Step-by-step explanation:
20cm : 15m
Convert meters to cm
1 meter = 100 cm
15m = 15 x 100 = 1500 cm
20cm:1500cm
Divide both sides of the ratio by 20
=> 1 : 1500/20 = 1: 75
The ratio of 20cm to 15m in the form 1:n is 1:75.
What is a ratio?A ratio is a mathematical comparison of two or more quantities expressed in terms of the number of times one quantity contains another quantity.
It is used to express the relationship between two or more numbers or variables and is usually written as a fraction or with a colon between the two numbers.
We have,
First, we need to convert both measurements to the same unit.
Let's convert 20cm to meters:
20 cm = 20/100 m = 0.2 m
Now we can express the ratio of 20cm to 15m as:
0.2m : 15m
To simplify this ratio, we can divide both sides by the greatest common factor of the two numbers, which is 0.1m:
0.2m/0.1m : 15m/0.1m
2 : 150
Finally, we can simplify the ratio by dividing both sides by 2:
1 : 75
Therefore,
The ratio of 20cm to 15m in the form 1:n is 1:75.
Learn more about ratios here:
https://brainly.com/question/2462048
#SPJ2
Can someone help me with this
Answer:
1st one- 4
2nd one- 1
3rd one- 5
4th one-6
5th one-3
6th one-2
Katerina runs 15 miles in 21/2 hours. What is the average number of minutes it takes her to run 1 mile?
A. 6
B. 10
C. 12 1/2
D. 16 2/3
E. 17 1/2
If Katerina completes a 15-mile run in 2 1/2 hours. She will complete a mile in an average of five minutes. Option B is correct.
What is average?It is described as a single number that indicates either the closed value for each entry in the set of data or the mean value for the entire set of data.
It is given that, In 2 1/2 hours, Katerina completes a 15-mile run.
We have to find the average number of minutes it takes her to run 1 mile.
15 miles = 2 1/2 hours
15 miles=5/2 hours
The unitary approach allows us to calculate the value of a single unit and then use that value to calculate the value of the required number of units.
1 miles= 5 /30 hours
1 miles = 1/6 hours
As we know that 1 hour consists of 60 minutes.
1 hours = 60 minute
1 mile = 60 / 6 minutes
1 miles = 10 minute
Thus, the average number of minutes it takes her to run 1 mile will be 10 minutes. Option B is correct.
Learn more about the average here:
brainly.com/question/24057012
#SPJ2
Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. The sample of 2100 bacteria selected from this population reach the size of 2249 bacteria in two and a half hours. Find the hourly growth rate parameter.This is a continuous exponential growth model.Write your answer as a percentage. Do not round any intermediate computations, and round your percentage to the nearest hundredth.
In this problem, we have a continuous exponential growth model
so
the equation is of the form
[tex]y=a(e)^{kt}[/tex]where
a is the initial value ------> a=2,100
y is the number of bacteria
x ----> number of hours
so
[tex]y=2,100(e)^{kt}[/tex]For x=2.5 hours, y=2,249 bacteria
substitute
[tex]2,249=2,100(e)^{(2.5k)}[/tex]solve for k
apply ln both sides
[tex]\ln (\frac{2,249}{2,100})=2.5k\cdot\ln (e)[/tex]k=0.0274
convert to percentage
k=2.74%PLEASE HELP!!!
The function f(x) is shown on the graph.
The graph shows a downward opening parabola with a vertex at negative 3 comma 16, a point at negative 7 comma 0, a point at 1 comma 0, a point at negative 6 comma 7, and a point at 0 comma 7.
What is the standard form of the equation of f(x)?
f(x) = −x2 − 6x + 7
f(x) = −x2 + 6x + 7
f(x) = x2 − 6x + 7
f(x) = x2 + 6x + 7
The standard form of the equation of f(x) is option a -x² - 6x + 7
Given,
The graph shows a downward open parabola.
The vertex points are:
(-3, 16), (-7, 0), (1, 0), (-6, 7), (0, 7)
Now,
We have to find the standard form of the function f(x):
As from the graph:
Parabola opens downward, so the function will be negative.
We have the options with:
a = -1, b = -6 and c = 7
Now,
Use x = -b/2a
x = 6/2 × -1 = 6/-2 = -3
Now,
f(x) = -x² - 6x + 7
f(-3) = -(-3)² - 6(-3) + 7
f(-3) = -9 + 18 + 7
f(-3) = 9 + 7
f(-3) = 16
That is, the points for the vertex in this equation is (-3, 16)
Then, the standard form of the equation of f(x) is option a -x² - 6x + 7
Learn more about functions here:
https://brainly.com/question/27940244
#SPJ1
Rational equations from algebra 2. Please provide steps. You don't have to solve all of the equations, any one of them will help. Thank you!
The rational equation is simplified to x² - 17x = 0
What is an algebraic expression?An algebraic expression can simply be defined as an expression composed of factors, variables, terms, coefficients and constants.
These expression are also described as expressions consisting of arithmetic operations such as;
ParenthesesBracketMultiplicationAdditionSubtractionDivision, etcGiven the expression;
1/2 - 7/2x = 5/x
find the lowest common multiple
x - 7 /2x = 5/ x
cross multiply
x(x - 7) = 5(2x)
multiply through
x² - 7x = 10x
collect like terms
x² = 10x + 7x
x² - 17x = 0
Hence, the equation is x² - 17x = 0
Learn more about algebraic expressions here:
https://brainly.com/question/4344214
#SPJ1
The boxplot displays the arm spans for 44 students.
Which of the following is not a true statement?
There are no outliers in this distribution.
The shape of the boxplot is fairly symmetric.
The range of the distribution is around 60 cm.
The center of the distribution is around 180 cm.
The statements The range of the distribution is around 60 cm and
the center of the distribution is around 180 cm are true.
What is statistics?Statistics is the study and manipulation of data, including ways to gather, review, analyze, and draw conclusions from data.
In the given statements
There are no outliers in this distribution.
The shape of the boxplot is fairly symmetric.
The range of the distribution is around 60 cm.
The center of the distribution is around 180 cm.
The statement "The range of the distribution is around 60 cm" is true.
The range is the spread of your data from the lowest to the highest value in the distribution.
In the given graph
Range=200-140
=60
So it is true.
The center of the distribution is around 180 cm is also true.
Hence the statements The range of the distribution is around 60 cm and
the center of the distribution is around 180 cm are true.
To learn more on Statistics click:
https://brainly.com/question/23091366
#SPJ1
Which of the following solution sets show all the values of x that can make the inequality -2x + 3 < 9 true?
A. x > 3
B. x < -3
C. x > -3
D. x ≥ -3
Answer:
B
Step-by-step explanation:
9 - 3 = 6
6 ÷ -2
= -3
I think it's b
4(8g+5)+6
I thought the answer was 32g+26 but its not on there
Answer:
32g + 6(you got it right, not quite sure why it isn't there though!)
Step-by-step explanation:
remember PEMDAS
parentheses first
(8g+5) but we can't add them up since they not like terms
now we go from left to right (since we have Multiplication first and then Addition)
distribute the 4 to the (8g+5)
which makes it 32g +20
now we go back to the equation,
32g +20 + 6
are there any like terms we can combine?
yes, the 20 and the 6
20+6=26
leaving us with
32g + 26Question 10 of 183Consider the line y = -x +6.(a) Find the equation of the line that is parallel to this line and passes through the point (2, 6).(b) Find the equation of the line that is perpendicular to this line and passes through the point (2, 6).Note that a graphing calculator may be helpful in checking your answer.
Answer:
Part A:
[tex]y=-x+8[/tex]Part B:
[tex]y=x+4[/tex]Step-by-step explanation:
Part A:
Remember that two parallel lines have the same slope. This way, we can conclude that the slope of this particular line is:
[tex]m_a=-1[/tex]Since we already know that this line passes through point (2,6), we can use this point, the slope we've found and the slope-point form to get an equation for the line:
[tex]\begin{gathered} y-6=-1(x-2) \\ \rightarrow y-6=-x+2 \\ \\ \Rightarrow y=-x+8 \end{gathered}[/tex]Therefore, we can conclude that the equation of this line is:
[tex]y=-x+8[/tex]Part B:
Remember that the product between the slopes of two perpendicular lines is -1. This way, we'll have that:
[tex]\begin{gathered} -1\times m_2=-1 \\ \\ \Rightarrow m_2=1 \end{gathered}[/tex]Since we already know that this line passes through point (2,6), we can use this point, the slope we've found and the slope-point form to get an equation for the line:
[tex]\begin{gathered} y-6=(x-2) \\ \rightarrow y=x+4 \end{gathered}[/tex]Therefore, we can conclude that the equation of this line is:
[tex]y=x+4[/tex]A bouncy ball is dropped such that the height of its first bounce is 3.75 feet and each successive bounce is 79% of the previous bounce's height. What would be the height of the 7th bounce of the ball? Round to the nearest tenth (if necessary).
If a bouncy ball is dropped such that the height of its first bounce is 3.75 feet and each successive bounce is 79% of the previous bounce's height. The height of the 7th bounce of the ball is 0.7.
Determining the height of the ballGiven data:
First bounce = 3.75 feet
Successive bounce = 79% or 0.79%
Bounce = 7
Now let determine the height of thee 7th bounce of the ball using this formula
Height = First bounce × (Successive bounce) ^ Number of bounce
Let plug in the formula
Height = 3.75 × (0.79 ) ^7
Height = 0.7
Therefore the height is 0.7.
Learn more about height here: https://brainly.com/question/26837257
#SPJ1
Simplify. 14(3x−7)+34x Responses 34x−1 3 over 4 end fraction x minus 1 334x−134 3 and 3 over 4 end fraction x minus 1 and 3 over 4 34x+212 3 over 4 end fraction x plus 2 and 1 half 112x−134
Answer: 1 1/2x−1 3/4
Step-by-step explanation: i took the test on k12
The simplified form of the given expression is option c 1 1/2x - 1 3/4
Given,
The expression; 1/4 (3x - 7) + 3/4x
We have to simplify this expression;
Simplification of expressions;
To simplify a phrase, create an equivalent expression without any terms that are identical. The expression will then be rewritten using the fewest terms feasible.
Then,
1/4 (3x - 7) + 3/4x
= 1/4 × 3x - 1/4 × 7 + 3/4x
= 3/4x - 7/4x + 3/4x
= 6x/4 - 7/4
= 3x/2 - 7/4
= 1 1/2x - 1 3/4
Therefore,
The simplified form of the given expression is option c 1 1/2x - 1 3/4
Learn more about simplification of expressions here;
brainly.com/question/1522393
#SPJ1
please answer fast!!!!! find x
Step-by-step explanation:
the triangles are congruent out at least similar, so both have the same angles.
therefore,
2x = 80
x = 40
a) Write an equation of a line in point slope form given the slope -2/3 and the point (-3,2). b) Write an equation in slope intercept form through the points (3,-3) and (2,0) c) write an equation based on this model. Gas cost $4.00 per gallon. If someone paid a startup fee of 5.00, write an equation in slope intercept form based on this model in y = mx+b
Answer:
[tex]y-2\text{ = -}\frac{2}{3}(x+3)[/tex]Explanation:
Here, we want to write the equation of a line in point-slope form
Mathematically, we have that as:
[tex]y-y_1=m(x-x_1)[/tex]where m, which is the slope is -2/3 and (x1,y1) which is the point is (-3,2)
Substituting the values, we have it that:
[tex]y-2\text{ = -}\frac{2}{3}(x+3)[/tex]A hen was given $10, a spider was given $40, a bee was given $30. How much would be given to a dog?
Answer:
Umm 20 dollars?
Step-by-step explanation:
