I copy the complete questions again to make them clearer:
Priya and Han are biking in the same direction on the same path.
a. Han is riding at a constant speed of 16 miles per hour. Write an expression that shows how many miles Han has gone after [tex]t[/tex] hours.
b. Priya started riding a half hour before Han. If Han has been riding for [tex]t[/tex] hours, how long has Priya been riding?
c. Priya is riding at a constant speed of 12 miles per hour. Write an expression that shows how many miles Priya has gone after Han has been riding for [tex]t[/tex] hours.
d. Use your expressions to find when Han and Priya meet.
Answer:
a) [tex]H=16t[/tex]b) [tex]t+0.5[/tex]c) [tex]P=12(t+0.5)[/tex]d) Han and Priya meet 1.5 hours after Han started riding.Explanation:
a. Since Han is riding at a constant speed of 16 miles per hour, the number of miles that he has gone is proportional to the number of hours, t, that he has been riding, the constant of variation is 16, and the expression for the number of miles he has gone is:
[tex]H=16\times t=16t[/tex]Where, H is the number of miles Han has gone, and t is the number of hours.
b. Since Priya started riding a half hour before Han, you have to add 1/2 or 0.5 to the time of Han, which is t, to express how long Priya has been riding:
[tex]t+0.5[/tex]c. Since, Priya is riding at a constant speed of 12 miles per hour, the number of miles that she has gone is proportional to the number of hours, t + 0.5, that she has been riding, the constant of variation is 12, and the expression for the number of miles she has gone is:
[tex]P=12\times (t+0.5)=12(t+0.5)[/tex]Where P is the number of miles Priya has gone, and t is the number of hours since Han is riding.
d. To find when Han and Priya meet, you just need to solve the sytem of equations, making H = P, which means that the number of miles that both Han and Priya rides is equal:
[tex]H=P\\ \\ 16t=12(t+0.5)\\ \\ 16t=12t+6\\ \\ 4t=6\\ \\ t=6/4=3/2=1.5[/tex]
Which means that they meet when it has passed 1.5 hours since Han started riding.
11. The sum of two numbers
is 29 and the difference of the
same two numbers is 15.
What are the two numbers?
Answer:
(22, 7)
Step-by-step explanation:
Let x and y be the unknown two numbers.
x+y=29
x-y=15
----------
2x=44
x=44/2
x=22
----------
22+y=29
y=29-22=7
x=22, y=7.
si camilo tiene 6 años mas que juan, juan tiene 7 años menos que andrés y andrés tiene 35 años
¿cuantos años tiene camilo y tiene juan? plantea la ecuación
¿cual es la diferencia entre la edad de camilo y juan?
si la abuela de andres tiene 65 años ¿la suma de las edades de camilo y juan coinciden con la edad de la abuela de andres?
Answer:
Part a) Camilo is 34 years old and Juan is 28 years old
Part b) The difference between Camilo's age and Juan's age is 6 years
Part c) The sum of the ages of Camilo and Juan not coincide with the age of Andres' grandmother
Step-by-step explanation:
The question in English is
If Camilo is 6 years older than Juan, Juan is 7 years younger than Andrés and Andrés is 35 years old .
Part a) How old is Camilo and how old is Juan? raises the equation.
Part b) What's the difference between Camilo's age and Juan's age?
Part c) If Andres's grandmother is 65 years old, does the sum of the ages of Camilo and Juan coincide with the age of Andres' grandmother?
Part a) How old is Camilo and how old is Juan? raises the equation.
Let
x -----> Camilo's age
y -----> Juan's age
z -----> Andres's age
we know that
[tex]x=y+6[/tex] -----> equation A
[tex]y=z-7[/tex] -----> equation B
[tex]z=35[/tex] -----> equation C
Find the value of y
substitute the value of z in the equation B
[tex]y=35-7=28[/tex]
Find the value of x
substitute the value of y in the equation A
[tex]x=28+6=34[/tex]
therefore
Camilo is 34 years old and Juan is 28 years old
Part b) What's the difference between Camilo's age and Juan's age?
Subtract Juan's age from Camilo's age
so
[tex]x-y=34-28=6\ years[/tex]
Part c) If Andres's grandmother is 65 years old, does the sum of the ages of Camilo and Juan coincide with the age of Andres' grandmother?
Adds Camilo's age and Juan's age
[tex]x+y=34+28=62\ years[/tex]
[tex]62\ years\neq 65\ years[/tex]
therefore
The sum of the ages of Camilo and Juan not coincide with the age of Andres' grandmother
Keith has $500 in a savings account at the beginning of the summer. He wants to have at least $200 at the end of the summer. He withdraws $25 per week for food. How many weeks can Keith withdraw money from his account?
Keith can withdraw money from his account for 12 weeks.
Step-by-step explanation:
Total savings = $500
Amount to be left in his account = $200
Withdrawal per week = $25
Let,
x be the number of weeks.
According to given statement;
Total savings - Withdrawal per week * no. of weeks = Amount to be left
[tex]500-25x=200\\-25x=200-500\\-25x=-300\\[/tex]
Dividing both sides by -25
[tex]\frac{-25x}{-25}=\frac{-300}{-25}\\x=12[/tex]
Keith can withdraw money from his account for 12 weeks.
Keywords: savings, linear expression
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Final answer:
Keith can withdraw money from his account for food for 12 weeks before reaching his minimum account balance requirement of $200.
Explanation:
To determine how many weeks Keith can withdraw money from his account while maintaining a balance of at least $200, we need to perform a simple subtraction and division operation. First, we calculate the amount he needs to leave in the account:
$500 initial balance - $200 desired end balance = $300 available to spend.
Keith withdraws $25 per week for food. To find out how many weeks his money will last, we divide the total amount he can spend by the weekly withdrawal amount:
$300 \/ $25 per week = 12 weeks.
Therefore, Keith can withdraw money for food for 12 weeks before his account balance reaches his minimum requirement of $200.
What is the answer to, (4-1) . n = n . _
Answer:
(4-1)•n=n•(4-1)
Step-by-step explanation:
It should equal each other so no matter what n equals it will equal each other :3
Step-by-step explanation:
Commutative property: a · b = b · a
(4 - 1) · n = n · (4 - 1)
y = x - 4
-2x + y = 18
Use elimination pls
Answer:
x = -22 , y = -26
Step-by-step explanation:
Solve the following system:
{y = x - 4 | (equation 1)
y - 2 x = 18 | (equation 2)
Express the system in standard form:
{-x + y = -4 | (equation 1)
-(2 x) + y = 18 | (equation 2)
Swap equation 1 with equation 2:
{-(2 x) + y = 18 | (equation 1)
-x + y = -4 | (equation 2)
Subtract 1/2 × (equation 1) from equation 2:
{-(2 x) + y = 18 | (equation 1)
0 x+y/2 = -13 | (equation 2)
Multiply equation 2 by 2:
{-(2 x) + y = 18 | (equation 1)
0 x+y = -26 | (equation 2)
Subtract equation 2 from equation 1:
{-(2 x)+0 y = 44 | (equation 1)
0 x+y = -26 | (equation 2)
Divide equation 1 by -2:
{x+0 y = -22 | (equation 1)
0 x+y = -26 | (equation 2)
Collect results:
Answer: {x = -22 , y = -26
Answer:
x = -22, y = -26Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}y=x-4&\text{subtract}\ x\ \text{from both sides}\\-2x+y=18\end{array}\right\\\\\left\{\begin{array}{ccc}-x+y=-4\\-2x+y=18&\text{change the signs}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-x+y=-4\\2x-y=-18\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad x=-22\\\\\text{Put the value of}\ x\ \text{to the first equation:}\\\\y=-22-4\\y=-26[/tex]
An electrolyte solution has an average current density of 111 ampere per square decimeter \left( \dfrac{\text{A}}{\text{dm}^2}\right)(
dm
2
A
)left parenthesis, start fraction, start text, A, end text, divided by, start text, d, m, end text, squared, end fraction, right parenthesis.
What is the current density of the solution in \dfrac{\text{A}}{\text{m}^2}
m
2
A
start fraction, start text, A, end text, divided by, start text, m, end text, squared, end fraction?
Answer:
The current density of the solution in [tex]m^2[/tex] is [tex]11100A/m^2[/tex]
Step-by-step explanation:
One square decimeter is equal to 0.01 square meter, Thus the current density in square meters is
[tex]\frac{111A}{dm^2} =\frac{111A}{0.01m^2} =\frac{111}{0.01}*\frac{A}{m^2}=\boxed{11100A/m^2}[/tex]
11100 Amperes per square meter.
Answer:
The numbers are messed up, don't copy and paste from khan.
The answer is 100
Step-by-step explanation:
I took the test
If f(x) = 1x1 + 9 and g(x) = -6, which describes the value of (f + g)(x)?
(f + g)(x) > 3 for all values of x
(f + g)(x) < 3 for all values of x
(f + g)(x) < 6 for all values of x
(f + g)(x) 6 for all values of x
Save and Exit
Ne
Mark this and return
Answer:
The answers are "(f+g)(x)> 3 for all values of x" and "(f+g)(x)<6 for all values of x".
Step-by-step explanation:
If f(x) = 1x1 + 9 =10, then f(x) is a constant for every value of x, which means that y=f(x) will take the value of 10 no matter which value takes x.If g(x)= -6, then g(x) is a constant for every value of x, which means that it will take the value of -6 no matter the value of x.(f+g)(x)=10 + (-6) = 10 - 6= 4. Then, no matter the value of x, the function (f+g)(x) will equal 4 (a constant). According to the available options, both "(f+g)(x)>3" and "(f+g)(x)<6" are true, because (f+g)(x)=4>3 and (f+g)(x)=4 <6.Please answer this correctly
Answer:
9:59
Step-by-step explanation:
all you have to do is add the hours to the hours and the minutes to the minutes but if you get a number over 60 in the minutes section then you need to subtract 60 from that side until get a number under 60 then you add however many times you did that to the hours
Answer:
Step-by-step explanation:
9 minutes past 4 = 04:09
Then in 5hours:50minutes, add it to 04:09, then we obtain 09:59
Name two pairs of congruent angles in the figure. Justify the answer.
Answer:
A and D
Step-by-step explanation:
Statement (A) and statement (D) are the two pairs of congruent angles in the figure.
What is the congruent figures?Congruent figures are those that are exactly the same size and shape. Congruent is represented by the symbol ≅ When the three sides and three angles of one triangle match the dimensions of the three sides and three angles of another triangle, they are said to be congruent.
It is given that:
The angles are shown in the picture.
It is required to name the two pairs of congruent angles in the figure.
From the figures:
According to the right angles congruent theorem, angle DIB and angle CIA
The right angles congruent theorem states that angle BIA and angle CIB are congruent.
Angle DIB and angle CIA according to the right angles congruent theorem
Angle BIA and angle CIB according to the right angles congruent theorem
Thus, statement (A) and statement (D) are the two pairs of congruent angles in the figure.
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3x minus 7 divided by 2 equals negative 5
Answer: x=0.5
Step-by-step explanation: In order to solve this problem, you need to simplify the rest of the problem first. You can do this by dividing -7 by 2, which will result in -3.5, making the equation 3x-3.5=-5. If you add 3.5 to both sides, the equation becomes 3x = 1.5. If you divide 1.5 by 3, you are left with 0.5, so x=0.5.
Final answer:
The solution to the linear equation '3x minus 7 divided by 2 equals negative 5' is found by performing algebraic operations to isolate the variable, resulting in x = -1.
Explanation:
The question involves solving a linear equation which is a fundamental concept in mathematics. To solve the equation 3x minus 7 divided by 2 equals negative 5, you will perform algebraic operations to isolate the variable x. Here is a step-by-step process:
Multiply both sides of the equation by 2 to get rid of the denominator: 2 * (3x - 7)/2 = -5 * 2.Simplify both sides: 3x - 7 = -10.Add 7 to both sides to isolate the 3x term: 3x = -10 + 7.Simplify the right side: 3x = -3.Divide both sides by 3 to solve for x: x = -3/3.Finally, x simplifies to -1 as the solution.Applying this process, you can see that the original equation is satisfied when x = -1, which completes our solution.
From the list below, select the most likely correlation coefficient for the graphed data.
A. −0.1
B. −0.8
C. 0.8
D. 0.1
Answer:
C
Step-by-step explanation:
First of all,
if the line goes Upward (from left to right), it is sloping upward and the correlation coefficient would be POSITIVE.If the line goes Downward (from left to right), it is sloping downward and the correlation coefficient would be NEGATIVE.Since, from the graph we can see that the line is sloping upward, we know the correlation coefficient would be POSITIVE, so we can immediately eliminate choices A & B.
Now, the closer the correlation coefficient value is to 0, the less steep the line is. The closer it is to 1, the more steeper it is.
Looking at the graph, it isn't that flat, it is quite steep. So the correlation coefficient would be 0.8, NOT 0.1
So, answer choice C is right.
45pts help! what is the vertex of the function
f(x)=- -|x + 7| - 4
Answer: (-7, -4)
========================================
Explanation:
The general equation y = a| x-h | + k has the vertex (h,k)
Rewrite the original function in this form to get f(x) = -1|x - (-7)| + (-4) and we see that h = -7 and k = -4
So that's why the vertex is (h,k) = (-7, -4)
The V shape graph opens downward meaning that the vertex (-7, -4) is at the highest point. The graph is shown below. I used GeoGebra to make the graph.
Answer:
-7,-4
Step-by-step explanation:
Look at 4x + 5y - 12 - x + 3y . Have all of the like terms been combined? Explain in 1-2 sentences.
Answer:
no 4x and -x can be combined to form 3x, and 5y and 3y can be combned to form 8y. the correct equation should be 3x+8y-12
Step-by-step explanation:
The function relating the height of an object off the ground to the time spent falling is a quadratic relationship. Travis drops a
tennis ball from the top of an office building 90 meters tall. Three seconds later, the ball lands on the ground. After 2
seconds, how far is the ball off the ground?
Answer:
the ball is on the ground after 3 seconds right so it would still be on the ground
Step-by-step explanation:
Answer:50 meters
Step-by-step explanation:
Evaluate the expression. ab if a = 6 and b = 7
Answer:
42
Step-by-step explanation:
ab is a x b
[tex]a \times b[/tex]
[tex]6 \times 7 = 42[/tex]
Answer:279,936
Step-by-step explanation:
i hope its helps
AP:2,x,26.
Find the value of x
2,x, 26 are in A. P.
a2-a1 = a3-a2
x-2 = 26-x
2x = 26+2
2x = 28
So x = 14.
Find the slope of the line that goes through the given points.
(3, 5) and (3, -5)
For this case we have that by definition, the slope of a line
is given by:
[tex]m = \frac {y_ {2} -y_{1}} {x_ {2} -x_ {1}}[/tex]
Where:
[tex](x_ {1}, y_ {1})\ and\ (x_ {2}, y_ {2})[/tex] are two points through which the line passes.
According to the statement we have:
[tex](x_ {1}, y_ {1}): (3,5)\\(x_ {2}, y_ {2}): (3, -5)[/tex]
Substituting we have:
[tex]m = \frac {-5-5} {3-3}[/tex]
It is noted that the slope is undefined.
Answer:
The slope is undefined
Are the expressions 4b-7-
2b + 11 and b + 3+ b + 1
equivalent?
Answer:
2b+4 so yes there are equivalent
Step-by-step explanation:
4b-7-2b+11
4b-2b-7+11
2b+4
b+3+b+1
2b+4
we need to solve for Y
xy=5
Answer:
y=5/x
Step-by-step explanation:
Just divide by x on both sides to isolate y
Answer:
=2.5
Step-by-step explanation:
Anton has 1 7/8 cups of ice cream to make ice cream sundaes.He uses 2/3 cups of ice cream for each sundae.What is the maximum amount of sundaes that Anton can make with ice cream
Answer:
45/16 or 2 13/16, the maximum amount of sundaes that Anton can make with ice cream is 2.
Step-by-step explanation:
1 7/8=15/8
2/3x<=15/8
x<=(15/8)/(2/3)
x<=(15/8)(3/2)=45/16
Three friends bought 4, 6, and 8 books. The table shows the cost of the books.
Number of Books 4 6 8
Cost ($) 30 45 60
What is the constant of proportionality?
(A) 2
(B) 7.5
(C) 15
(D) 30
Answer: B 7.5
Step-by-step explanation:
Y = Kx
4 = k30
k = 30/4
k = 7.5
or
Y = KX
X Y
1.25×4+3×2 divided By (1/2) third power
Answer:
(1.25×4+3×2 )/((1/2)^3) = 88
Step-by-step explanation:
The solution to the equation 1.25×4+3×2 divided By (1/2) third power is 53 applying the order of operation PEMDAS.
Explanation:To solve 1.25×4+3×2 divided By (1/2) third power, we first have to follow the order of operation, that is Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right), also known as PEMDAS.
Step 1: Solve the expressions in parentheses and the exponent. As there's none, we move to the next step.
Step 2: Solve the multiplication and division.
1.25×4 equals 5, then 3×2 equals 6, and then 1/2, to the third power, equals 0.125.
So our equation now reads 5+6 divided by 0.125.
Step 3: Execute the division operation. 6 divided by 0.125 equals 48.
Our equation now reads 5 + 48.
Step 4: The last step is addition. 5 + 48 equals 53. So, the answer to the equation 1.25×4+3×2 divided By (1/2) third power is 53.
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1. The half-life of the radioactive element krypton-91 is 10 seconds. If 32
grams of krypton - 91 are initially present, how many grams are present
after 30 seconds? Show the decay function. Use A = A0ekt
Answer:
4 g after 30 seconds.
Step-by-step explanation:
After 10 seconds 32 * 1/2 = 16 g are present.
After 20 seconds 32 * (1/2)^2 = 8 g are present
After 30 seconds 32 * (1/2)^3 = 4 g are present.
Is 12/30 and 18/45 proportional, or not proportional?
12/30 = 18/45, so first you're going to cross multiply and you'll get (30)(18) = (12)(45). Then you can see that 540 = 540 same number so they're proportional...
BTW THIS WAY IS A LOT EASIER.
12/30 = 2/5
18/45 = 2/5
So yes, in summary, they're proportional to each other. Hope this helps, have a BLESSED and wonderful day! :-)
Answer:
proportional
Step-by-step explanation:
12/30 multiplied by a factor of 1.5 is 18/45 so it is proportional
what ordered pairs are a solution to the equations
3x-5y=4
-5x+4y=2
(-7,0)
(6,8)
(3,1)
(-2,-2)
Answer:
x=-2, y=-2. (-2, -2)
Step-by-step explanation:
3x-5y=4
-5x+4y=2
-------------
5(3x-5y)=5(4)
3(-5x+4y)=3(2)
---------------------
15x-25y=20
-15x+12y=6
-------------------
-13y=26
y=26/-13
y=-2
3x-5(-2)=4
3x+10=4
3x=4-10
3x=-6
x=-6/3
x=-2
x=-2, y=-2.
Is (2,-5) a solution to the equation f(x)= -x - 3
Replace x in the equation with the x value of the given solution:
f(x) = -2 -3 = -5
Since replacing x with 2 , the equation equals -5, then (2,-5) is a solution.
Answer:
yes
Step-by-step explanation:
find the value of x in this figure
x equals 47 degrees
Explanation:Remember you must provide full questions in order to get excellent and precise answers. However, I have attached a figure in order to set the problem in context. Here we have a triangle. The most basic definition for a triangle is a polygon with three edges and three vertices, but there is something that is very important for all triangles:
The internal angles of every triangle add up to 180 degrees.By knowing this, we can write:
[tex]x^{\circ}+95^{\circ}+38^{\circ}=180^{\circ} \\ \\ Isolating \ x: \\ \\ x^{\circ}=180^{\circ}-95^{\circ}-38^{\circ} \\ \\ x^{\circ}=47^{\circ} \\ \\ \\ Where: \\ \\ \boxed{x=47}[/tex]
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how many pumpkin plants would be in 2 rows
Answer:
If a vine tear is occurs after the fruit, cover it with soil and it should produce secondary roots. Number of Fruit on a Vine: A single pumpkin plant normally produces two to five pumpkins. Miniature varieties will produce up to a dozen or so.
Step-by-step explanation:
what value of n solves the equation 2n =1/8
A. -3
B. -4
C. 3
D. 4
Answer:
n = - 3
Step-by-step explanation:
We have to solve the equation [tex]2^{n} = \frac{1}{8}[/tex] for n.
Now, as the variable is in power, we will take a log on both sides.
So, [tex]2^{n} = \frac{1}{8}[/tex]
⇒ [tex]\log 2^{n} = \log \frac{1}{8}[/tex]
⇒ n log 2 = log 1 - log 8 {Since we know the property of logarithm [tex]\log a^{b} = b \log a[/tex] and [tex]\log \frac{a}{b} = \log a - \log b[/tex]}
⇒ n log 2 = - log 2³ { Since, log 1 = 0}
⇒ n log 2 = - 3 log 2
⇒ n = - 3 (Answer)
Find m∠UVT m∠WVU = 169° m∠WVT = (2x + 20)° m∠UVT = (3x + 19)° A) 91° B) 94° C) 97° D) 100°\
Answer:
m ∠ UVT = 97° is the required answer.
Step-by-step explanation:
Given:
m∠WVU = 169°
m∠WVT = (2x + 20)°
m∠UVT = (3x + 19)°
To Find:
m∠UVT = ?
Solution:
Angle Addition Postulate is that if you place two angles side by side, then the measure of the resulting angle will be equal to the sum of the two original angle measures.
So By applying this property in the diagram below we get,
m∠ WVT + m∠UVT = m∠WVU ............{Angle Addition Postulate}
[tex](2x+20) + (3x+19) = 169\\5x + 39 = 169\\5x=169-39\\5x=130\\\therefore x=\frac{130}{5} \\\therefore x=26\\[/tex]
Now,
m∠UVT = (3x + 19)°
Substituting x = 26 we get
m∠UVT = 3 ×26 + 19
= 78 +19
∴ m∠UVT = 97°